diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
index 99126fdd..dbf570f4 100644
--- a/.github/workflows/main.yml
+++ b/.github/workflows/main.yml
@@ -23,51 +23,27 @@ jobs:
           - macos-latest
           - windows-latest
         python-version:
-          - '3.12'
+          - '3.13'
     steps:
-      - uses: actions/checkout@v4
-      - uses: prefix-dev/setup-pixi@v0.8.0
+      - uses: actions/checkout@v5
+      - uses: prefix-dev/setup-pixi@v0.9.1
         with:
-          pixi-version: v0.29.0
+          pixi-version: v0.56.0
           cache: true
           cache-write: ${{ github.event_name == 'push' && github.ref_name == 'main' }}
           environments: test-cpu
           activate-environment: true
+          frozen: true
       - name: Run pytest
+        if: runner.os != 'Linux' || matrix.python-version != '3.13'
+        shell: bash -l {0}
+        run: pixi run -e test-cpu tests
+      - name: Run pytest with coverage
+        if: runner.os == 'Linux' && matrix.python-version == '3.13'
         shell: bash -l {0}
         run: pixi run -e test-cpu tests-with-cov
       - name: Upload coverage report
-        if: runner.os == 'Linux' && matrix.python-version == '3.12'
-        uses: codecov/codecov-action@v4
+        if: runner.os == 'Linux' && matrix.python-version == '3.13'
+        uses: codecov/codecov-action@v5
         env:
           CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }}
-  # run-mypy:
-  #   name: Run mypy on Python 3.12
-  #   runs-on: ubuntu-latest
-  #   strategy:
-  #     fail-fast: false
-  #   steps:
-  #     - uses: actions/checkout@v4
-  #     - uses: prefix-dev/setup-pixi@v0.8.0
-  #       with:
-  #         pixi-version: v0.28.2
-  #         cache: true
-  #         cache-write: ${{ github.event_name == 'push' && github.ref_name == 'main' }}
-  #         environments: mypy
-  #     - name: Run mypy
-  #       shell: bash -l {0}
-  #       run: pixi run mypy
-  # run-explanation-notebooks:
-  #   name: Run explanation notebooks on Python 3.12
-  #   runs-on: ubuntu-latest
-  #   steps:
-  #     - uses: actions/checkout@v4
-  #     - uses: prefix-dev/setup-pixi@v0.8.0
-  #       with:
-  #         pixi-version: v0.28.2
-  #         cache: true
-  #         cache-write: ${{ github.event_name == 'push' && github.ref_name == 'main' }}
-  #         environments: test
-  #     - name: Run explanation notebooks
-  #       shell: bash -l {0}
-  #       run: pixi run -e test explanation-notebooks
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index d3f0c8b8..6364f1b2 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -6,11 +6,11 @@ repos:
       - id: check-useless-excludes
       # - id: identity  # Prints all files passed to pre-commits. Debugging.
   - repo: https://github.com/lyz-code/yamlfix
-    rev: 1.17.0
+    rev: 1.18.0
     hooks:
       - id: yamlfix
   - repo: https://github.com/pre-commit/pre-commit-hooks
-    rev: v4.6.0
+    rev: v6.0.0
     hooks:
       - id: check-added-large-files
         args:
@@ -37,11 +37,11 @@ repos:
       - id: check-ast
       - id: check-docstring-first
   - repo: https://github.com/adrienverge/yamllint.git
-    rev: v1.35.1
+    rev: v1.37.1
     hooks:
       - id: yamllint
   - repo: https://github.com/astral-sh/ruff-pre-commit
-    rev: v0.6.4
+    rev: v0.13.3
     hooks:
       # Run the linter.
       - id: ruff
@@ -59,14 +59,14 @@ repos:
           - pyi
           - jupyter
   - repo: https://github.com/kynan/nbstripout
-    rev: 0.7.1
+    rev: 0.8.1
     hooks:
       - id: nbstripout
         args:
           - --extra-keys
           - metadata.kernelspec metadata.language_info.version metadata.vscode
   - repo: https://github.com/executablebooks/mdformat
-    rev: 0.7.17
+    rev: 0.7.22
     hooks:
       - id: mdformat
         additional_dependencies:
diff --git a/docs/source/getting_started/tutorial.ipynb b/docs/source/getting_started/tutorial.ipynb
index 60cd0351..7d46c546 100644
--- a/docs/source/getting_started/tutorial.ipynb
+++ b/docs/source/getting_started/tutorial.ipynb
@@ -23,6 +23,13 @@
     "from skillmodels.maximization_inputs import get_maximization_inputs"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
diff --git a/docs/source/how_to_guides/model_specs.rst b/docs/source/how_to_guides/model_specs.rst
index d043760d..ecd7ff05 100644
--- a/docs/source/how_to_guides/model_specs.rst
+++ b/docs/source/how_to_guides/model_specs.rst
@@ -96,14 +96,8 @@ Any python string is possible as factor name. The values are dictionaries with t
 entries:
 
 - measurements: A nested list that is as long as the number of periods of the model.
-  Each sublist contains the names of the measurements in that period. If A factor has
-  no measurements in a period, it has to be an empty list. If a factor only has
-  measurements up to a certain period you can leave out the empty lists at the end. In
-  the example this is done for factor 3. Note that even in that case, the measurements
-  have to be specified as nested list. If a factor only starts having measurements in
-  some period, you still have to specify the empty lists for all periods before that
-  period.
-
+  Each sublist contains the names of the measurements in that period. If a factor has
+  no measurements in a period, it has to be an empty list.
 
 - normalizations: This entry is optional. It is a dictionary that can have the keys
   ``"loadings"`` and ``"intercepts"``. The values are lists of dictionaries. The list
@@ -114,7 +108,7 @@ entries:
 - transition_equation: A string with the name of a pre-implemented transition equation
   or a custom transition equation. Pre-implemented transition equations are
   linear, log_ces (in the known location and scale version), constant and translog.
-  The example model dictionary only uses pre-implement transition functions.
+  The example model dictionary only uses pre-implemented transition functions.
 
   To see how to use custom transition functions, assume that the yaml file shown above
   has been loaded into a python dictionary called ``model`` and look at the following
diff --git a/environment.yml b/environment.yml
deleted file mode 100644
index 81a0ab22..00000000
--- a/environment.yml
+++ /dev/null
@@ -1,31 +0,0 @@
----
-name: skillmodels
-channels:
-  - conda-forge
-  - opensourceeconomics
-dependencies:
-  - python=3.9
-  - jax>=0.1.7
-  - jaxlib>=0.1.51
-  - pip
-  - conda-build
-  - doc8
-  - jupyter
-  - numpy
-  - pandas
-  - pytest
-  - pytest-xdist
-  - restructuredtext_lint
-  - tox-conda
-  - scipy
-  - sphinxcontrib-bibtex
-  - pydata-sphinx-theme>=0.3
-  - anaconda-client
-  - nbsphinx
-  - pdbpp
-  - filterpy
-  - dags
-  - plotly
-  - pip:
-      - pre-commit
-      - black
diff --git a/pixi.lock b/pixi.lock
index 3efe3f8a..f5f6303a 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -1,4 +1,4 @@
-version: 5
+version: 6
 environments:
   cuda:
     channels:
@@ -9,276 +9,268 @@ environments:
       linux-64:
       - conda: https://conda.anaconda.org/conda-forge/linux-64/_libgcc_mutex-0.1-conda_forge.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/linux-64/_openmp_mutex-4.5-2_gnu.tar.bz2
-      - conda: https://conda.anaconda.org/conda-forge/noarch/_sysroot_linux-64_curr_repodata_hack-3-h69a702a_16.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/annotated-types-0.7.0-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/anyio-4.4.0-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/argon2-cffi-23.1.0-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/argon2-cffi-bindings-21.2.0-py312h66e93f0_5.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/arrow-1.3.0-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/asttokens-2.4.1-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/async-lru-2.0.4-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/attrs-24.2.0-pyh71513ae_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/babel-2.14.0-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/beautifulsoup4-4.12.3-pyha770c72_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/binutils_impl_linux-64-2.40-ha1999f0_7.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/binutils_linux-64-2.40-hb3c18ed_2.conda
-      - conda: https://conda.anaconda.org/conda-forge/noarch/bleach-6.1.0-pyhd8ed1ab_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/brotli-1.1.0-hb9d3cd8_2.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/brotli-bin-1.1.0-hb9d3cd8_2.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/brotli-python-1.1.0-py312h2ec8cdc_2.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/bzip2-1.0.8-h4bc722e_7.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/c-ares-1.33.1-heb4867d_0.conda
-      - conda: https://conda.anaconda.org/conda-forge/linux-64/ca-certificates-2024.8.30-hbcca054_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/_python_abi3_support-1.0-hd8ed1ab_2.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/anyio-4.11.0-pyhcf101f3_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/argon2-cffi-25.1.0-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/argon2-cffi-bindings-25.1.0-py314h5bd0f2a_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/arrow-1.3.0-pyhd8ed1ab_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/asttokens-3.0.0-pyhd8ed1ab_1.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/async-lru-2.0.5-pyh29332c3_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/attrs-25.4.0-pyh71513ae_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/babel-2.17.0-pyhd8ed1ab_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/beautifulsoup4-4.14.2-pyha770c72_0.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/binutils_impl_linux-64-2.44-hdf8817f_2.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/binutils_linux-64-2.44-h4852527_2.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/bleach-6.2.0-pyh29332c3_4.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/bleach-with-css-6.2.0-h82add2a_4.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/brotli-1.1.0-hb03c661_4.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/brotli-bin-1.1.0-hb03c661_4.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/brotli-python-1.1.0-py314ha160325_4.conda
+      - conda: https://conda.anaconda.org/conda-forge/linux-64/bzip2-1.0.8-hda65f42_8.conda
+      - conda: https://conda.anaconda.org/conda-forge/noarch/ca-certificates-2025.10.5-hbd8a1cb_0.conda
       - conda: https://conda.anaconda.org/conda-forge/noarch/cached-property-1.5.2-hd8ed1ab_1.tar.bz2
       - conda: https://conda.anaconda.org/conda-forge/noarch/cached_property-1.5.2-pyha770c72_1.tar.bz2
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+      - conda: https://conda.anaconda.org/conda-forge/noarch/decorator-5.2.1-pyhd8ed1ab_0.conda
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+  - vc >=14.3,<15
+  - vc14_runtime >=14.44.35208
+  - ucrt >=10.0.20348.0
+  license: MIT
+  license_family: MIT
   purls: []
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-  name: zeromq
-  version: 4.3.5
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   license: MPL-2.0
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   license: MPL-2.0
   license_family: MOZILLA
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+- conda: https://conda.anaconda.org/conda-forge/linux-64/zstandard-0.25.0-py313h54dd161_0.conda
+  sha256: 9d79d176afe50361cc3fd4366bedff20852dbea1e5b03f358b55f12aca22d60d
+  md5: 1fe43bd1fc86e22ad3eb0edec637f8a2
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-  license: Zlib
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-  name: zstandard
-  version: 0.23.0
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-  md5: a4cde595509a7ad9c13b1a3809bcfe51
-  depends:
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+  - python
   - cffi >=1.11
-  - python >=3.12,<3.13.0a0
-  - python >=3.12,<3.13.0a0 *_cpython
-  - python_abi 3.12.* *_cp312
-  - zstd >=1.5.6,<1.5.7.0a0
-  - zstd >=1.5.6,<1.6.0a0
+  - zstd >=1.5.7,<1.5.8.0a0
+  - libgcc >=14
+  - __glibc >=2.17,<3.0.a0
+  - zstd >=1.5.7,<1.6.0a0
+  - python_abi 3.13.* *_cp313
   license: BSD-3-Clause
   license_family: BSD
   purls:
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-  size: 330788
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-  name: zstandard
-  version: 0.23.0
-  build: py312h7122b0e_1
-  build_number: 1
-  subdir: osx-64
-  url: https://conda.anaconda.org/conda-forge/osx-64/zstandard-0.23.0-py312h7122b0e_1.conda
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-  depends:
-  - __osx >=10.13
+  size: 471152
+  timestamp: 1757930114245
+- conda: https://conda.anaconda.org/conda-forge/linux-64/zstandard-0.25.0-py314h31f8a6b_0.conda
+  sha256: ec4e66b4e042ea9554b9db92b509358f75390f7dcbafb8eead940a2880486a63
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+  - python
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-  - python_abi 3.12.* *_cp312
-  - zstd >=1.5.6,<1.5.7.0a0
-  - zstd >=1.5.6,<1.6.0a0
+  - zstd >=1.5.7,<1.5.8.0a0
+  - libgcc >=14
+  - __glibc >=2.17,<3.0.a0
+  - zstd >=1.5.7,<1.6.0a0
+  - python_abi 3.14.* *_cp314
   license: BSD-3-Clause
   license_family: BSD
   purls:
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-  size: 410873
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-- kind: conda
-  name: zstandard
-  version: 0.23.0
-  build: py312h7606c53_1
-  build_number: 1
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-  url: https://conda.anaconda.org/conda-forge/win-64/zstandard-0.23.0-py312h7606c53_1.conda
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+  size: 127864
+  timestamp: 1757930108791
+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/zstandard-0.25.0-py314h163e31d_0.conda
+  sha256: 5b707d7b80d9b410fce776a439273213745ffc3fa4553ec31f264bbaf63a6ec6
+  md5: c824d8cd887ce1d7af8963ca4087a764
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+  - python
   - cffi >=1.11
-  - python >=3.12,<3.13.0a0
-  - python_abi 3.12.* *_cp312
-  - ucrt >=10.0.20348.0
-  - vc >=14.2,<15
-  - vc14_runtime >=14.29.30139
-  - zstd >=1.5.6,<1.5.7.0a0
-  - zstd >=1.5.6,<1.6.0a0
+  - zstd >=1.5.7,<1.5.8.0a0
+  - __osx >=11.0
+  - python 3.14.* *_cp314
+  - zstd >=1.5.7,<1.6.0a0
+  - python_abi 3.14.* *_cp314
   license: BSD-3-Clause
   license_family: BSD
   purls:
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-  size: 320624
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-- kind: conda
-  name: zstandard
-  version: 0.23.0
-  build: py312hef9b889_1
-  build_number: 1
-  subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/zstandard-0.23.0-py312hef9b889_1.conda
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+- conda: https://conda.anaconda.org/conda-forge/win-64/zstandard-0.25.0-py314h4667ab5_0.conda
+  sha256: 285890e987cb14b2ac27f74a4ae844eb80e73654ab3321f085e13538c6ac7d23
+  md5: 765406da1e9f31231a56ea4d2e191d7c
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+  - python
   - cffi >=1.11
-  - libgcc >=13
-  - python >=3.12,<3.13.0a0
-  - python_abi 3.12.* *_cp312
-  - zstd >=1.5.6,<1.5.7.0a0
-  - zstd >=1.5.6,<1.6.0a0
+  - zstd >=1.5.7,<1.5.8.0a0
+  - vc >=14.3,<15
+  - vc14_runtime >=14.44.35208
+  - ucrt >=10.0.20348.0
+  - vc >=14.3,<15
+  - vc14_runtime >=14.44.35208
+  - ucrt >=10.0.20348.0
+  - zstd >=1.5.7,<1.6.0a0
+  - python_abi 3.14.* *_cp314
   license: BSD-3-Clause
   license_family: BSD
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-  size: 419552
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-- kind: conda
-  name: zstd
-  version: 1.5.6
-  build: h0ea2cb4_0
-  subdir: win-64
-  url: https://conda.anaconda.org/conda-forge/win-64/zstd-1.5.6-h0ea2cb4_0.conda
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-  license: BSD-3-Clause
-  license_family: BSD
-  purls: []
-  size: 349143
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-- kind: conda
-  name: zstd
-  version: 1.5.6
-  build: h915ae27_0
-  subdir: osx-64
-  url: https://conda.anaconda.org/conda-forge/osx-64/zstd-1.5.6-h915ae27_0.conda
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-  md5: 4cb2cd56f039b129bb0e491c1164167e
+  size: 285971
+  timestamp: 1757930137171
+- conda: https://conda.anaconda.org/conda-forge/linux-64/zstd-1.5.7-hb8e6e7a_2.conda
+  sha256: a4166e3d8ff4e35932510aaff7aa90772f84b4d07e9f6f83c614cba7ceefe0eb
+  md5: 6432cb5d4ac0046c3ac0a8a0f95842f9
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-  - __osx >=10.9
-  - libzlib >=1.2.13,<2.0.0a0
+  - __glibc >=2.17,<3.0.a0
+  - libgcc >=13
+  - libstdcxx >=13
+  - libzlib >=1.3.1,<2.0a0
   license: BSD-3-Clause
   license_family: BSD
   purls: []
-  size: 498900
-  timestamp: 1714723303098
-- kind: conda
-  name: zstd
-  version: 1.5.6
-  build: ha6fb4c9_0
-  subdir: linux-64
-  url: https://conda.anaconda.org/conda-forge/linux-64/zstd-1.5.6-ha6fb4c9_0.conda
-  sha256: c558b9cc01d9c1444031bd1ce4b9cff86f9085765f17627a6cd85fc623c8a02b
-  md5: 4d056880988120e29d75bfff282e0f45
+  size: 567578
+  timestamp: 1742433379869
+- conda: https://conda.anaconda.org/conda-forge/osx-arm64/zstd-1.5.7-h6491c7d_2.conda
+  sha256: 0d02046f57f7a1a3feae3e9d1aa2113788311f3cf37a3244c71e61a93177ba67
+  md5: e6f69c7bcccdefa417f056fa593b40f0
   depends:
-  - libgcc-ng >=12
-  - libstdcxx-ng >=12
-  - libzlib >=1.2.13,<2.0.0a0
+  - __osx >=11.0
+  - libzlib >=1.3.1,<2.0a0
   license: BSD-3-Clause
   license_family: BSD
   purls: []
-  size: 554846
-  timestamp: 1714722996770
-- kind: conda
-  name: zstd
-  version: 1.5.6
-  build: hb46c0d2_0
-  subdir: osx-arm64
-  url: https://conda.anaconda.org/conda-forge/osx-arm64/zstd-1.5.6-hb46c0d2_0.conda
-  sha256: 2d4fd1ff7ee79cd954ca8e81abf11d9d49954dd1fef80f27289e2402ae9c2e09
-  md5: d96942c06c3e84bfcc5efb038724a7fd
+  size: 399979
+  timestamp: 1742433432699
+- conda: https://conda.anaconda.org/conda-forge/win-64/zstd-1.5.7-hbeecb71_2.conda
+  sha256: bc64864377d809b904e877a98d0584f43836c9f2ef27d3d2a1421fa6eae7ca04
+  md5: 21f56217d6125fb30c3c3f10c786d751
   depends:
-  - __osx >=11.0
-  - libzlib >=1.2.13,<2.0.0a0
+  - libzlib >=1.3.1,<2.0a0
+  - ucrt >=10.0.20348.0
+  - vc >=14.2,<15
+  - vc14_runtime >=14.29.30139
   license: BSD-3-Clause
   license_family: BSD
   purls: []
-  size: 405089
-  timestamp: 1714723101397
+  size: 354697
+  timestamp: 1742433568506
diff --git a/pyproject.toml b/pyproject.toml
index b5051725..27362f7a 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -12,9 +12,10 @@ maintainers = [
     { name = "Hans-Martin von Gaudecker", email = "hmgaudecker@uni-bonn.de" },
 ]
 description = "Estimators for skill formation models"
-requires-python = ">=3.12"
+requires-python = ">=3.13"
 dependencies = [
     "dags",
+    "jax>=0.7",
     "numpy",
     "pandas",
 ]
@@ -84,42 +85,29 @@ allow-direct-references = true
 
 [tool.pixi.project]
 channels = ["conda-forge"]
-platforms = ["linux-64", "osx-64", "osx-arm64", "win-64"]
+platforms = ["linux-64", "osx-arm64", "win-64"]
 
 # Development Dependencies (conda)
 # --------------------------------------------------------------------------------------
 
 [tool.pixi.dependencies]
 filterpy = "*"
+ipykernel = "*"
 jupyterlab = "*"
-nbformat = ">=5.10.4,<6"
-optimagic = "*"
-pixi-kernel = ">=0.4.0,<0.5"
-plotly = ">=5.2,<6"
+nbformat = "*"
+networkx = "*"
+# optimagic = "*"
+plotly = ">=6.2"
 pre-commit = "*"
 pybaum = "*"
-python = ">=3.12.5"
-python-kaleido = "*"
-scipy = "<=1.13"
-
-
-# Development Dependencies (pypi)
-# --------------------------------------------------------------------------------------
-
-[tool.pixi.target.unix.dependencies]
-jax = ">=0.4.20"
-jaxlib = ">=0.4.20"
-
-# Development Dependencies (pypi)
-# --------------------------------------------------------------------------------------
+python = "~=3.13"
+python-kaleido = ">=1.0"
+scipy = "*"
 
 [tool.pixi.pypi-dependencies]
-pdbp = "*"
 skillmodels = {path = ".", editable = true}
-
-[tool.pixi.target.win-64.pypi-dependencies]
-jax = { version = ">=0.4.20", extras = ["cpu"] }
-jaxlib = ">=0.4.20"
+optimagic = { git = "https://github.com/optimagic-dev/optimagic.git", branch = "main"}
+pdbp = "*"
 
 # Features and Tasks
 # --------------------------------------------------------------------------------------
@@ -128,10 +116,11 @@ jaxlib = ">=0.4.20"
 platforms = ["linux-64"]
 system-requirements = {cuda = "12"}
 
-[tool.pixi.feature.cuda.target.linux-64.dependencies]
+[tool.pixi.feature.cuda.dependencies]
 cuda-nvcc = ">=12"
-jax = ">=0.4.20"
-jaxlib = { version = ">=0.4.20", build = "cuda12*" }
+
+[tool.pixi.feature.cuda.pypi-dependencies]
+jax = {version = ">=0.7", extras = ["cuda12"]}
 
 [tool.pixi.feature.test.dependencies]
 pytest = "*"
@@ -174,7 +163,7 @@ test-gpu = {features = ["test", "cuda"], solve-group = "cuda"}
 # ======================================================================================
 
 [tool.ruff]
-target-version = "py312"
+target-version = "py313"
 fix = true
 line-length = 88
 
@@ -218,6 +207,9 @@ extend-ignore = [
     # exception must not use an f-string literal
     "EM102",
 
+    # Boolean-typed positional arguments.
+    "FBT001",
+
     # Boolean default positional argument in function definition
     "FBT002",
 
@@ -236,9 +228,6 @@ extend-ignore = [
     # pd.merge is fine
     "PD015",
 
-    # df is just fine
-    "PD901",
-
     # Many suggestions to use list comprehension are not helpful
     "PERF401",
 
@@ -276,9 +265,19 @@ extend-ignore = [
 "src/skillmodels/simulate_data.py" = ["D417"]
 "src/skillmodels/visualize_*.py" = ["BLE001", "D417"]
 "src/skillmodels/*_heatmap*.py" = ["D417"]
-"tests/*" = ["ARG001", "FBT003", "INP001", "PD002", "NPY002", "PTH123", "S506"]
 "**/*.ipynb" = ["B018", "T201", "E402", "PLR2004", "INP001", "PTH100"]
 "docs/**/*" = ["A001", "ERA001", "INP001", "PTH100", "PTH123", "S506"]
+"tests/*" = [
+    "ARG001",
+    "E712",
+    "FBT003",
+    "INP001",
+    "PD002",
+    "PT011",
+    "NPY002",
+    "PTH123",
+    "S506"
+]
 
 [tool.ruff.lint.pydocstyle]
 convention = "google"
diff --git a/src/skillmodels/__init__.py b/src/skillmodels/__init__.py
index fbda2074..e55229ad 100644
--- a/src/skillmodels/__init__.py
+++ b/src/skillmodels/__init__.py
@@ -9,4 +9,4 @@
 from skillmodels.maximization_inputs import get_maximization_inputs
 from skillmodels.simulate_data import simulate_dataset
 
-__all__ = ["get_maximization_inputs", "simulate_dataset", "get_filtered_states"]
+__all__ = ["get_filtered_states", "get_maximization_inputs", "simulate_dataset"]
diff --git a/src/skillmodels/check_model.py b/src/skillmodels/check_model.py
index 4da82573..41dc1e4c 100644
--- a/src/skillmodels/check_model.py
+++ b/src/skillmodels/check_model.py
@@ -1,7 +1,7 @@
 import numpy as np
 
 
-def check_model(model_dict, labels, dimensions, anchoring):
+def check_model(model_dict, labels, dimensions, anchoring, has_endogenous_factors):
     """Check consistency and validity of the model specification.
 
     labels, dimensions and anchoring information are done before the model checking
@@ -15,44 +15,56 @@ def check_model(model_dict, labels, dimensions, anchoring):
         model_dict (dict): The model specification. See: :ref:`model_specs`
         dimensions (dict): Dimensional information like n_states, n_periods, n_controls,
             n_mixtures. See :ref:`dimensions`.
-
         labels (dict): Dict of lists with labels for the model quantities like
             factors, periods, controls, stagemap and stages. See :ref:`labels`
-
         anchoring (dict): Dictionary with information about anchoring.
             See :ref:`anchoring`
+        has_endogenous_factors (bool): Whether the model has any endogenous factors
 
     Raises:
         ValueError
 
     """
-    report = _check_stagemap(
-        labels["stagemap"],
-        labels["stages"],
-        dimensions["n_periods"],
+    report = check_stagemap(
+        stagemap=labels["aug_stagemap"],
+        stages=labels["aug_stages"],
+        n_periods=dimensions["n_aug_periods"],
+        is_augmented=has_endogenous_factors,
     )
     report += _check_anchoring(anchoring)
-    report += _check_measurements(model_dict, labels["latent_factors"])
+    invalid_measurements = _check_measurements(model_dict, labels["latent_factors"])
+    if invalid_measurements:
+        report += invalid_measurements
+    elif has_endogenous_factors:
+        # Make this conditional because the check only works for valid meas.
+        report += _check_no_overlap_in_measurements_of_states_and_inv(
+            model_dict, labels
+        )
     report += _check_normalizations(model_dict, labels["latent_factors"])
 
     report = "\n".join(report)
     if report != "":
-        raise ValueError(f"Invalid model specification:\n{report}")
+        raise ValueError(f"Invalid model specification: {report}")
 
 
-def _check_stagemap(stagemap, stages, n_periods):
+def check_stagemap(stagemap, stages, n_periods, is_augmented):
     report = []
-    if len(stagemap) != n_periods - 1:
+    step_size = 2 if is_augmented else 1
+    if len(stagemap) != n_periods - step_size:
         report.append(
-            "The stagemap needs to be of length n_periods - 1. n_periods is "
-            f"{n_periods}, the stagemap has length {len(stagemap)}.",
+            f"The stagemap needs to be of length n_periods - {step_size}. "
+            f" n_periods is {n_periods}, the stagemap has length {len(stagemap)}.",
         )
-
     if stages != list(range(len(stages))):
         report.append("Stages need to be integers, start at zero and increase by 1.")
 
-    if not np.isin(np.array(stagemap[1:]) - np.array(stagemap[:-1]), (0, 1)).all():
-        report.append("Consecutive entries in stagemap must be equal or increase by 1.")
+    # Hijacking the stagemap for endogenous factors leads to interleaved elements.
+    to_consider = [stagemap] if not is_augmented else [stagemap[0::2], stagemap[1::2]]
+    for sm in to_consider:
+        if not np.isin(np.array(sm[1:]) - np.array(sm[:-1]), (0, step_size)).all():
+            report.append(
+                "Consecutive entries in stagemap must be equal or increase by 1."
+            )
     return report
 
 
@@ -83,7 +95,7 @@ def _check_measurements(model_dict, factors):
         candidate = model_dict["factors"][factor]["measurements"]
         if not _is_list_of(candidate, list):
             report.append(
-                f"measurements must lists of lists. Check measurements of {factor}.",
+                f"measurements must be lists of lists. Check measurements of {factor}.",
             )
         else:
             for period, meas_list in enumerate(candidate):
@@ -96,6 +108,24 @@ def _check_measurements(model_dict, factors):
     return report
 
 
+def _check_no_overlap_in_measurements_of_states_and_inv(model_dict, labels):
+    report = []
+    for period in labels["periods"]:
+        meas = {}
+        for factor in labels["latent_factors"]:
+            props = model_dict["factors"][factor]
+            if props.get("is_endogenous", False):
+                meas["endogenous_factors"] = set(props["measurements"][period])
+            else:
+                meas["states"] = set(props["measurements"][period])
+        if overlap := meas["states"].intersection(meas["endogenous_factors"]):
+            report.append(
+                "Measurements for exogenous and endogenous latent factors must not "
+                f"overlap.\n\nCheck measurements {overlap} in period {period}.",
+            )
+    return report
+
+
 def _check_normalizations(model_dict, factors):
     report = []
     for factor in factors:
diff --git a/src/skillmodels/constraints.py b/src/skillmodels/constraints.py
index fa71942a..1decb850 100644
--- a/src/skillmodels/constraints.py
+++ b/src/skillmodels/constraints.py
@@ -1,13 +1,25 @@
 """List of constraints for a model, which can be converted to optimagic constraints."""
 
+import functools
 import warnings
+from dataclasses import dataclass
+from typing import Any
 
 import numpy as np
+import optimagic as om
+import pandas as pd
 
-import skillmodels.transition_functions as tf
+import skillmodels.transition_functions as t_f_module
 
 
-def get_constraints(dimensions, labels, anchoring_info, update_info, normalizations):
+def get_constraints_dicts(
+    dimensions,
+    labels,
+    anchoring_info,
+    update_info,
+    normalizations,
+    endogenous_factors_info,
+) -> list[dict]:
     """Generate constraints implied by the model specification.
 
     The result can easily be converted to optimagic-style constraints.
@@ -25,45 +37,65 @@ def get_constraints(dimensions, labels, anchoring_info, update_info, normalizati
             loadings and intercepts for each factor. See :ref:`normalizations`.
 
     Returns:
-        list[dict]: List of constraints.
+        A list of constraints dictionaries with entries:
+        - "type": str, one of "fixed", "equality", "probability", "increasing",
+            "pairwise_equality". Must map to an optimagic constraint, see
+            :func:`constraints_dicts_to_om`.
+        - "loc": The location of the affected row(s) in the params DataFrame
+        - "value": float, only present if type is "fixed"
+        - "description": str, optional description of the constraint
 
     """
-    constr = []
-
-    constr += _get_normalization_constraints(normalizations, labels["latent_factors"])
-    constr += _get_mixture_weights_constraints(dimensions["n_mixtures"])
-    constr += _get_stage_constraints(labels["stagemap"], labels["stages"])
-    constr += _get_constant_factors_constraints(labels)
-    constr += _get_initial_states_constraints(
-        dimensions["n_mixtures"],
-        labels["latent_factors"],
+    constraints_dicts = []
+
+    constraints_dicts += _get_normalization_constraints(
+        normalizations, labels["latent_factors"]
+    )
+    constraints_dicts += _get_mixture_weights_constraints(dimensions["n_mixtures"])
+    constraints_dicts += _get_stage_constraints(
+        stagemap=labels["aug_stagemap"],
+        stages=labels["aug_stages"],
+    )
+    constraints_dicts += _get_constant_factors_constraints(labels=labels)
+    constraints_dicts += _get_initial_states_constraints(
+        n_mixtures=dimensions["n_mixtures"],
+        factors=labels["latent_factors"],
     )
-    constr += _get_transition_constraints(labels)
-    constr += _get_anchoring_constraints(
-        update_info,
-        labels["controls"],
-        anchoring_info,
-        labels["periods"],
+    constraints_dicts += _get_transition_constraints(labels=labels)
+    constraints_dicts += _get_anchoring_constraints(
+        update_info=update_info,
+        controls=labels["controls"],
+        anchoring_info=anchoring_info,
+        periods=labels["aug_periods"],
     )
+    if endogenous_factors_info["has_endogenous_factors"]:
+        constraints_dicts += _get_constraints_for_augmented_periods(
+            labels=labels,
+            endogenous_factors_info=endogenous_factors_info,
+        )
 
-    for i, c in enumerate(constr):
+    for i, c in enumerate(constraints_dicts):
         c["id"] = i
 
-    return constr
+    return constraints_dicts
+
 
+def add_bounds(params: pd.DataFrame, bounds_distance: float) -> pd.DataFrame:
+    """Add bounds for standard deviations to params.
 
-def add_bounds(params_df, bounds_distance=0.0):
-    """Add the bounds to params_df that are not implied by other constraints.
+    Lower and upper bounds are set to (minus) infinity; lower bounds for standard
+    deviation-like parameters are set to *bounds_distance*. Note that the latter will be
+    overridden for parameters where fixed constraints are imposed.
 
     Args:
-        params_df (DataFrame): see :ref:`params_df`.
-        bounds_distance (float): sets bounds stricter by this amount. Default 0.0.
+        params: see :ref:`params`.
+        bounds_distance: set standard deviation-like to this amount.
 
     Returns:
-        df (DataFrame): modified copy of params_df
+        Modified copy of params
 
     """
-    df = params_df.copy()
+    df = params.copy()
     with warnings.catch_warnings():
         warnings.filterwarnings(
             "ignore",
@@ -71,6 +103,9 @@ def add_bounds(params_df, bounds_distance=0.0):
         )
         if "lower_bound" not in df.columns:
             df["lower_bound"] = -np.inf
+        if "upper_bound" not in df.columns:
+            df["upper_bound"] = np.inf
+
         df.loc["meas_sds", "lower_bound"] = bounds_distance
         df.loc["shock_sds", "lower_bound"] = bounds_distance
 
@@ -95,7 +130,7 @@ def _is_diagonal_entry(ind_tup):
     return is_diag
 
 
-def _get_normalization_constraints(normalizations, factors):
+def _get_normalization_constraints(normalizations, factors) -> list[dict]:
     """List of constraints to enforce normalizations.
 
     Args:
@@ -103,49 +138,44 @@ def _get_normalization_constraints(normalizations, factors):
         loadings and intercepts for each factor. See :ref:`normalizations`.
 
     Returns:
-        constraints (list)
+        constraints_dicts
 
     """
     msg = "This constraint was generated because of an explicit normalization."
     periods = range(len(normalizations[factors[0]]["loadings"]))
 
-    index_tuples = []
-    fixed_values = []
-
+    constraints_dicts = []
     for factor in factors:
         if "variances" in normalizations[factor]:
             raise ValueError("normalization for variances cannot be provided")
         for period in periods:
-            loading_norminfo = normalizations[factor]["loadings"][period]
-            for meas, normval in loading_norminfo.items():
-                index_tuples.append(("loadings", period, meas, factor))
-                fixed_values.append(normval)
-
-            intercept_norminfo = normalizations[factor]["intercepts"][period]
-            for meas, normval in intercept_norminfo.items():
-                index_tuples.append(("controls", period, meas, "constant"))
-                fixed_values.append(normval)
-
-    if index_tuples:
-        constraints = [
-            {
-                "loc": index_tuples,
-                "type": "fixed",
-                "value": fixed_values,
-                "description": msg,
-            },
-        ]
-    else:
-        constraints = []
+            for meas, normval in normalizations[factor]["loadings"][period].items():
+                constraints_dicts.append(
+                    {
+                        "loc": ("loadings", period, meas, factor),
+                        "type": "fixed",
+                        "value": normval,
+                        "description": msg,
+                    }
+                )
+            for meas, normval in normalizations[factor]["intercepts"][period].items():
+                constraints_dicts.append(
+                    {
+                        "loc": ("controls", period, meas, "constant"),
+                        "type": "fixed",
+                        "value": normval,
+                        "description": msg,
+                    }
+                )
 
-    return constraints
+    return constraints_dicts
 
 
-def _get_mixture_weights_constraints(n_mixtures):
+def _get_mixture_weights_constraints(n_mixtures) -> list[dict]:
     """Constrain mixture weights to be between 0 and 1 and sum to 1."""
     if n_mixtures == 1:
         msg = "Set the mixture weight to 1 if there is only one mixture element."
-        return [
+        constraints_dicts = [
             {
                 "loc": "mixture_weights",
                 "type": "fixed",
@@ -153,79 +183,83 @@ def _get_mixture_weights_constraints(n_mixtures):
                 "description": msg,
             },
         ]
-    msg = "Ensure that weights are between 0 and 1 and sum to 1."
-    return [{"loc": "mixture_weights", "type": "probability", "description": msg}]
+    else:
+        msg = "Ensure that weights are between 0 and 1 and sum to 1."
+        constraints_dicts = [
+            {"loc": "mixture_weights", "type": "probability", "description": msg}
+        ]
+    return constraints_dicts
 
 
-def _get_stage_constraints(stagemap, stages):
+def _get_stage_constraints(stagemap, stages) -> list[dict]:
     """Equality constraints for transition and shock parameters within stages.
 
     Args:
-        stagemap (list): map periods to stages
-        stages (list): stages
+        stagemap (list): map aug_periods to aug_stages
+        stages (list): aug_stages
     Returns:
-        constrainst (list)
+        constraints_dicts
 
     """
     msg = (
         "This constraint was generated because all involved periods belong to stage {}."
     )
-    constraints = []
+    constraints_dicts = []
 
     stages_to_periods = {stage: [] for stage in stages}
-    for period, stage in enumerate(stagemap):
-        stages_to_periods[stage].append(period)
+    for aug_period, stage in enumerate(stagemap):
+        stages_to_periods[stage].append(aug_period)
 
     for stage, stage_periods in stages_to_periods.items():
         if len(stage_periods) > 1:
-            locs_trans = [("transition", p) for p in stage_periods]
-            locs_q = [("shock_sds", p) for p in stage_periods]
-            constraints.append(
+            loc_trans = [("transition", p) for p in stage_periods]
+            loc_q = [("shock_sds", p) for p in stage_periods]
+            constraints_dicts.append(
                 {
-                    "locs": locs_trans,
+                    "loc": loc_trans,
                     "type": "pairwise_equality",
                     "description": msg.format(stage),
                 },
             )
-            constraints.append(
+            constraints_dicts.append(
                 {
-                    "locs": locs_q,
+                    "loc": loc_q,
                     "type": "pairwise_equality",
                     "description": msg.format(stage),
                 },
             )
 
-    return constraints
+    return constraints_dicts
 
 
-def _get_constant_factors_constraints(labels):
-    """Fix shock variances of constant factors to 0.
+def _get_constant_factors_constraints(labels) -> list[dict]:
+    """Fix shock variances of constant factors to `bounds_distance`.
 
     Args:
         labels (dict): Dict of lists with labels for the model quantities like
             factors, periods, controls, stagemap and stages. See :ref:`labels`
 
     Returns:
-        constraints (list)
+        constraints_dicts
 
     """
-    constraints = []
+    constraints_dicts = []
     for f, factor in enumerate(labels["latent_factors"]):
         if labels["transition_names"][f] == "constant":
             msg = f"This constraint was generated because {factor} is constant."
-            for period in labels["periods"][:-1]:
-                constraints.append(
+            for aug_period in labels["aug_periods"][:-1]:
+                constraints_dicts.append(
                     {
-                        "loc": ("shock_sds", period, factor, "-"),
+                        "loc": ("shock_sds", aug_period, factor, "-"),
                         "type": "fixed",
                         "value": 0.0,
                         "description": msg,
                     },
                 )
-    return constraints
+    return constraints_dicts
 
 
-def _get_initial_states_constraints(n_mixtures, factors):
+def _get_initial_states_constraints(n_mixtures, factors) -> list[dict]:
     """Enforce that the x values of the first factor are increasing.
 
     Otherwise the model would only be identified up to the order of the start factors.
@@ -235,7 +269,7 @@ def _get_initial_states_constraints(n_mixtures, factors):
         factors (list): the latent factors of the model
 
     Returns:
-        constraints (list)
+        constraints_dicts
 
     """
     msg = (
@@ -245,18 +279,18 @@ def _get_initial_states_constraints(n_mixtures, factors):
     )
 
     if n_mixtures > 1:
-        ind_tups = [
+        locs = [
             ("initial_states", 0, f"mixture_{emf}", factors[0])
             for emf in range(n_mixtures)
         ]
-        constr = [{"loc": ind_tups, "type": "increasing", "description": msg}]
+        constraints_dicts = [{"loc": locs, "type": "increasing", "description": msg}]
     else:
-        constr = []
+        constraints_dicts = []
 
-    return constr
+    return constraints_dicts
 
 
-def _get_transition_constraints(labels):
+def _get_transition_constraints(labels) -> list[dict]:
     """Collect possible constraints on transition parameters.
 
     Args:
@@ -264,25 +298,28 @@ def _get_transition_constraints(labels):
             factors, periods, controls, stagemap and stages. See :ref:`labels`
 
     Returns:
-        constraints (list)
+        constraints_dicts
 
     """
-    constraints = []
+    constraints_dicts = []
     for f, factor in enumerate(labels["latent_factors"]):
         tname = labels["transition_names"][f]
         msg = f"This constraint is inherent to the {tname} production function."
-        for period in labels["periods"][:-1]:
+        for aug_period in labels["aug_periods"][:-1]:
             funcname = f"constraints_{tname}"
-            if hasattr(tf, funcname):
-                func = getattr(tf, funcname)
-                constr = func(factor, labels["all_factors"], period)
-                if "description" not in constr:
-                    constr["description"] = msg
-                constraints.append(constr)
-    return constraints
+            if func := getattr(t_f_module, funcname, False):
+                c = func(
+                    factor=factor, factors=labels["all_factors"], aug_period=aug_period
+                )
+                if "description" not in c:
+                    c["description"] = msg
+                constraints_dicts.append(c)
+    return constraints_dicts
 
 
-def _get_anchoring_constraints(update_info, controls, anchoring_info, periods):
+def _get_anchoring_constraints(
+    update_info, controls, anchoring_info, periods
+) -> list[dict]:
     """Constraints on anchoring parameters.
 
     Args:
@@ -293,12 +330,12 @@ def _get_anchoring_constraints(update_info, controls, anchoring_info, periods):
         periods (list): Period of the model
 
     Returns:
-        constraints (list)
+        constraints_dicts
 
     """
     anchoring_updates = update_info[update_info["purpose"] == "anchoring"].index
 
-    constraints = []
+    constraints_dicts = []
     if not anchoring_info["free_constant"]:
         msg = (
             "This constraint was generated because free_constant in the anchoring "
@@ -307,7 +344,7 @@ def _get_anchoring_constraints(update_info, controls, anchoring_info, periods):
         locs = []
         for period, meas in anchoring_updates:
             locs.append(("controls", period, meas, "constant"))
-        constraints.append(
+        constraints_dicts.append(
             {"loc": locs, "type": "fixed", "value": 0, "description": msg},
         )
 
@@ -320,7 +357,7 @@ def _get_anchoring_constraints(update_info, controls, anchoring_info, periods):
         for period, meas in anchoring_updates:
             for cont in [c for c in controls if c != "constant"]:
                 ind_tups.append(("controls", period, meas, cont))
-        constraints.append(
+        constraints_dicts.append(
             {"loc": ind_tups, "type": "fixed", "value": 0, "description": msg},
         )
 
@@ -336,10 +373,203 @@ def _get_anchoring_constraints(update_info, controls, anchoring_info, periods):
                 meas = f"{outcome}_{factor}"
                 ind_tups.append(("loadings", period, meas, factor))
 
-        constraints.append(
+        constraints_dicts.append(
             {"loc": ind_tups, "type": "fixed", "value": 1, "description": msg},
         )
 
-    constraints = [c for c in constraints if c["loc"] != []]
+    constraints_dicts = [c for c in constraints_dicts if c["loc"] != []]
+
+    return constraints_dicts
+
+
+def _get_constraints_for_augmented_periods(
+    labels, endogenous_factors_info
+) -> list[dict]:
+    """Constraints for augmented periods.
+
+    - Carry forward states from uneven periods to even periods
+    - Carry forward endogenous factors even periods to uneven periods
+    - Set shock_sds to 0 when carrying anything forward
+
+    Both depend on the transition function.
+
+    Args:
+        labels (dict): Dict of lists with labels for the model quantities like
+            factors, periods, controls, stagemap and stages. See :ref:`labels`
+
+    Returns:
+        constraints_dicts
+
+    """
+    constraints_dicts = []
+    for f, factor in enumerate(labels["latent_factors"]):
+        tname = labels["transition_names"][f]
+        if tname == "constant":
+            continue
+        # We are restricting transitions and shocks, not measurements. So this might
+        # look counterintuitive...
+        aug_period_meas_type_to_constrain = (
+            "states"
+            if endogenous_factors_info[factor]["is_state"]
+            else "endogenous_factors"
+        )
+        aug_periods_to_constrain = [
+            k
+            for k, v in endogenous_factors_info[
+                "aug_periods_to_aug_period_meas_types"
+            ].items()
+            if v == aug_period_meas_type_to_constrain
+        ]
+        for aug_period in aug_periods_to_constrain:
+            if func := getattr(t_f_module, f"identity_constraints_{tname}", False):
+                constraints_dicts += func(
+                    factor=factor,
+                    aug_period=aug_period,
+                    all_factors=labels["all_factors"],
+                )
+        for aug_period in aug_periods_to_constrain[:-1]:
+            constraints_dicts.append(
+                {
+                    "loc": ("shock_sds", aug_period, factor, "-"),
+                    "type": "fixed",
+                    "value": endogenous_factors_info["bounds_distance"],
+                    "description": "Identity constraint.",
+                }
+            )
+
+    return constraints_dicts
+
+
+def _sel(params, loc):
+    return params.loc[loc]
+
+
+@dataclass(frozen=True)
+class SkillmodelsPairwiseEqualityConstraint(om.PairwiseEqualityConstraint):
+    """Thin wrapper around om.PairwiseEqualityConstraint.
+
+    Adds fields to preserve information from the internal constraints dictionary.
+    """
+
+    loc: pd.MultiIndex | tuple | str | None = None
+    description: str | None = None
+    type: str = "Just to be able to use **constraints_dict"
+    id: int | None = None
+
+
+@dataclass(frozen=True)
+class SkillmodelsFixedConstraint(om.FixedConstraint):
+    """Thin wrapper around om.FixedConstraint.
+
+    Adds fields to preserve information from the internal constraints dictionary.
+    """
+
+    loc: pd.MultiIndex | tuple | str | None = None
+    description: str | None = None
+    type: str = "Just to be able to use **constraints_dict"
+    id: int | None = None
+    value: float | None = None
+
+
+@dataclass(frozen=True)
+class SkillmodelsEqualityConstraint(om.EqualityConstraint):
+    """Thin wrapper around om.EqualityConstraint.
+
+    Adds fields to preserve information from the internal constraints dictionary.
+    """
+
+    loc: pd.MultiIndex | tuple | str | None = None
+    description: str | None = None
+    type: str = "Just to be able to use **constraints_dict"
+    id: int | None = None
+
+
+@dataclass(frozen=True)
+class SkillmodelsProbabilityConstraint(om.ProbabilityConstraint):
+    """Thin wrapper around om.ProbabilityConstraint.
+
+    Adds fields to preserve information from the internal constraints dictionary.
+    """
+
+    loc: pd.MultiIndex | tuple | str | None = None
+    description: str | None = None
+    type: str = "Just to be able to use **constraints_dict"
+    id: int | None = None
+
+
+@dataclass(frozen=True)
+class SkillmodelsIncreasingConstraint(om.IncreasingConstraint):
+    """Thin wrapper around om.IncreasingConstraint.
+
+    Adds fields to preserve information from the internal constraints dictionary.
+    """
+
+    loc: pd.MultiIndex | tuple | str | None = None
+    description: str | None = None
+    type: str = "Just to be able to use **constraints_dict"
+    id: int | None = None
+
+
+def constraints_dicts_to_om(
+    constraints_dicts: list[dict],
+) -> list[om.constraints.Constraint]:
+    """Convert constraints provided in dictionary form to optimagic constraints.
+
+    Args:
+        constraints_dicts (list): see :ref:`get_constraints_dicts`.
+
+    Returns:
+        List of optimagic constraints.
+    """
+    om_style = []
+    for c_d in constraints_dicts:
+        if c_d["type"] == "pairwise_equality":
+            om_style.append(
+                SkillmodelsPairwiseEqualityConstraint(
+                    selectors=[functools.partial(_sel, loc=loc) for loc in c_d["loc"]],
+                    **c_d,
+                )
+            )
+        else:
+            sel = functools.partial(_sel, loc=c_d["loc"])
+            if c_d["type"] == "fixed":
+                om_style.append(SkillmodelsFixedConstraint(selector=sel, **c_d))
+            elif c_d["type"] == "equality":
+                om_style.append(SkillmodelsEqualityConstraint(selector=sel, **c_d))
+            elif c_d["type"] == "probability":
+                om_style.append(SkillmodelsProbabilityConstraint(selector=sel, **c_d))
+            elif c_d["type"] == "increasing":
+                om_style.append(SkillmodelsIncreasingConstraint(selector=sel, **c_d))
+            else:
+                raise TypeError(c_d["type"])
+    return om_style
+
+
+def enforce_fixed_constraints(
+    params_template: pd.DataFrame,
+    constraints_dicts: list[dict[str, Any]],
+) -> pd.DataFrame:
+    """Enforce fixed constraints on params_template.
+
+    For fixed constraints, we also set the lower and upper bounds to the fixed value.
+    This means that any robust bounds will be overridden for fixed parameters.
+
+    Args:
+        params_template (pd.DataFrame): see :ref:`params_df`.
+        constraints_dicts (list): see :ref:`get_constraints_dicts`.
+
+    Returns:
+        pd.DataFrame: modified copy of params_template
+    """
+    params = params_template.copy()
+    with warnings.catch_warnings():
+        warnings.filterwarnings(
+            "ignore",
+            message="indexing past lexsort depth may impact performance.",
+        )
+        for constraint in constraints_dicts:
+            if constraint["type"] == "fixed":
+                params.loc[constraint["loc"], "value"] = constraint["value"]
 
-    return constraints
+    # Setting via loc may expand the index, so reduce to the original index
+    return params.loc[params_template.index].astype(float)
diff --git a/src/skillmodels/correlation_heatmap.py b/src/skillmodels/correlation_heatmap.py
index e3f9d5e3..67e45933 100644
--- a/src/skillmodels/correlation_heatmap.py
+++ b/src/skillmodels/correlation_heatmap.py
@@ -134,9 +134,10 @@ def get_measurements_corr(data, model_dict, factors, periods):
             and extract measurements for each period.
         factors (list, str or NoneType): List of factors, to retrieve measurements for.
             If None, then calculate correlations of measurements of all factors.
-        periods (int,float, list or NoneType): If int, the period within which to
+        periods (int, float, list or NoneType): If int, the period within which to
             calculate measurement correlations. If a list, calculate correlations over
-            periods. If None, calculate correlations across all periods.
+            periods. If None, calculate correlations across all periods. Note: Periods
+            refer to originl periods, not the augmented periods.
 
     Returns:
         corr (DataFrame): DataFrame with measurement correlations.
@@ -145,15 +146,15 @@ def get_measurements_corr(data, model_dict, factors, periods):
     data = data.copy(deep=True)
     model = process_model(model_dict)
     periods = _process_periods(periods, model)
-    data = pre_process_data(data, periods)
+    processed_data = pre_process_data(data, periods)
     latent_factors, observed_factors = _process_factors(model, factors)
-    update_info = model["update_info"]
+    update_info_by_period = _get_update_info_for_periods(model)
     df = _get_measurement_data(
-        data,
-        update_info,
-        periods,
-        latent_factors,
-        observed_factors,
+        data=processed_data,
+        update_info_by_period=update_info_by_period,
+        periods=periods,
+        latent_factors=latent_factors,
+        observed_factors=observed_factors,
     )
     corr = df.corr()
     return corr
@@ -186,15 +187,15 @@ def get_quasi_scores_corr(data, model_dict, factors, periods):
     data = data.copy(deep=True)
     model = process_model(model_dict)
     periods = _process_periods(periods, model)
-    data = pre_process_data(data, periods)
+    processed_data = pre_process_data(data, periods)
     latent_factors, observed_factors = _process_factors(model, factors)
-    update_info = model["update_info"]
+    update_info = _get_update_info_for_periods(model)
     df = _get_quasi_factor_scores_data(
-        data,
-        update_info,
-        periods,
-        latent_factors,
-        observed_factors,
+        data=processed_data,
+        update_info_by_period=update_info,
+        periods=periods,
+        latent_factors=latent_factors,
+        observed_factors=observed_factors,
     )
     corr = df.corr()
     return corr
@@ -226,17 +227,16 @@ def get_scores_corr(data, params, model_dict, factors, periods):
     data = data.copy(deep=True)
     model = process_model(model_dict)
     periods = _process_periods(periods, model)
-    data = pre_process_data(data, periods)
+    processed_data = pre_process_data(data, periods)
     latent_factors, observed_factors = _process_factors(model, factors)
-    update_info = model["update_info"]
     params = params.loc[["controls", "loadings"]]
     df = _get_factor_scores_data(
-        data,
-        params,
-        update_info,
-        periods,
-        latent_factors,
-        observed_factors,
+        data=processed_data,
+        params=params,
+        model=model,
+        periods=periods,
+        latent_factors=latent_factors,
+        observed_factors=observed_factors,
     )
     corr = df.corr()
     return corr
@@ -273,7 +273,28 @@ def _get_mask(corr, show_upper_triangle, show_diagonal):
     return mask
 
 
-def _get_measurement_data(data, update_info, periods, latent_factors, observed_factors):
+def _get_update_info_for_periods(model):
+    """Return update_info with user-provided periods instead of augmented periods."""
+    update_info = model["update_info"].copy()
+
+    # Replace period level with user-provided period using set_codes
+    period_values = update_info.index.get_level_values("aug_period").map(
+        model["labels"]["aug_periods_to_periods"]
+    )
+    update_info.index = update_info.index.set_codes(period_values, level="aug_period")
+    update_info.index = update_info.index.set_names(["period", "variable"])
+
+    # Group by period and variable, apply OR logic for boolean columns
+    cols = [col for col in update_info.columns if col != "purpose"]
+    agg_dict = dict.fromkeys(cols, "any")
+    agg_dict["purpose"] = "first"
+
+    return update_info.groupby(["period", "variable"]).agg(agg_dict)
+
+
+def _get_measurement_data(
+    data, update_info_by_period, periods, latent_factors, observed_factors
+):
     """Get data frame with factor measurements in each period, in wide format.
 
     For each factor, retrieve the data on measurements in each period and stack
@@ -297,26 +318,26 @@ def _get_measurement_data(data, update_info, periods, latent_factors, observed_f
     if len(periods) == 1:
         period = periods[0]
         df = _get_measurement_data_for_single_period(
-            data,
-            update_info,
-            period,
-            latent_factors,
-            observed_factors,
+            data=data,
+            update_info_by_period=update_info_by_period,
+            period=period,
+            latent_factors=latent_factors,
+            observed_factors=observed_factors,
         )
     else:
         df = _get_measurement_data_for_multiple_periods(
-            data,
-            update_info,
-            periods,
-            latent_factors,
-            observed_factors,
+            data=data,
+            update_info_by_period=update_info_by_period,
+            periods=periods,
+            latent_factors=latent_factors,
+            observed_factors=observed_factors,
         )
     return df
 
 
 def _get_measurement_data_for_single_period(
     data,
-    update_info,
+    update_info_by_period,
     period,
     latent_factors,
     observed_factors,
@@ -337,7 +358,7 @@ def _get_measurement_data_for_single_period(
         df (pd.DataFrame): DataFrame with measurements of factors for period 'period'.
 
     """
-    period_info = update_info.loc[period].reset_index()
+    period_info = update_info_by_period.loc[period].reset_index()
     measurements = []
 
     for fac in latent_factors:
@@ -346,13 +367,13 @@ def _get_measurement_data_for_single_period(
         )["variable"].to_list()
     for fac in observed_factors:
         measurements.append(fac)
-    df = data.query(f"{update_info.index.names[0]}=={period}")[measurements]
+    df = data.query(f"{update_info_by_period.index.names[0]}=={period}")[measurements]
     return df
 
 
 def _get_measurement_data_for_multiple_periods(
     data,
-    update_info,
+    update_info_by_period,
     periods,
     latent_factors,
     observed_factors,
@@ -361,8 +382,8 @@ def _get_measurement_data_for_multiple_periods(
 
     Args:
         data (pd.DataFrame): Data with observable variables.
-        update_info (pd.DataFrame): DataFrame with information on measurements
-            for each factor in each model period.
+        update_info_by_period (pd.DataFrame): DataFrame with information on measurements
+            for each factor in each user-provided period.
         periods (list): The periods to extract measurements for.
         latent_factors (list): List of latent factors the measurements of which
             correlations are calculated for.
@@ -378,11 +399,11 @@ def _get_measurement_data_for_multiple_periods(
     for period in periods:
         to_concat.append(
             _get_measurement_data_for_single_period(
-                data,
-                update_info,
-                period,
-                latent_factors,
-                observed_factors,
+                data=data,
+                update_info_by_period=update_info_by_period,
+                period=period,
+                latent_factors=latent_factors,
+                observed_factors=observed_factors,
             )
             .add_suffix(f", {period}")
             .reset_index(drop=True),
@@ -393,7 +414,7 @@ def _get_measurement_data_for_multiple_periods(
 
 def _get_quasi_factor_scores_data(
     data,
-    update_info,
+    update_info_by_period,
     periods,
     latent_factors,
     observed_factors,
@@ -424,7 +445,7 @@ def _get_quasi_factor_scores_data(
         period = periods[0]
         df = _get_quasi_factor_scores_data_for_single_period(
             data,
-            update_info,
+            update_info_by_period,
             period,
             latent_factors,
             observed_factors,
@@ -432,7 +453,7 @@ def _get_quasi_factor_scores_data(
     else:
         df = _get_quasi_factor_scores_data_for_multiple_periods(
             data,
-            update_info,
+            update_info_by_period,
             periods,
             latent_factors,
             observed_factors,
@@ -443,7 +464,7 @@ def _get_quasi_factor_scores_data(
 
 def _get_quasi_factor_scores_data_for_single_period(
     data,
-    update_info,
+    update_info_by_period,
     period,
     latent_factors,
     observed_factors,
@@ -452,8 +473,8 @@ def _get_quasi_factor_scores_data_for_single_period(
 
     Args:
         data (pd.DataFrame): Data with observable variables.
-        update_info (pd.DataFrame): DataFrame with information on measurements
-            for each factor in each model period.
+        update_info_by_period (pd.DataFrame): DataFrame with information on measurements
+            for each factor in each user-provided period.
         periods (list): The list of periods that correlations are
             calculated for.
         latent_factors (list): List of latent factors the scores of which
@@ -465,13 +486,13 @@ def _get_quasi_factor_scores_data_for_single_period(
         df (pd.DataFrame): Processed DataFrame to calculate correlations over.
 
     """
-    period_info = update_info.loc[period].reset_index()
+    period_info = update_info_by_period.loc[period].reset_index()
     to_concat = []
     for factor in latent_factors:
         period_factor_measurements = period_info.query(
             f"{factor} == True and purpose == 'measurement'",
         )["variable"].to_list()
-        df = data.query(f"{update_info.index.names[0]}=={period}")[
+        df = data.query(f"{update_info_by_period.index.names[0]}=={period}")[
             period_factor_measurements
         ]
         df = (df - df.mean()) / df.std()
@@ -479,7 +500,7 @@ def _get_quasi_factor_scores_data_for_single_period(
         sr.name = f"{factor}"
         to_concat.append(sr)
     for factor in observed_factors:
-        df = data.query(f"{update_info.index.names[0]}=={period}")[factor]
+        df = data.query(f"{update_info_by_period.index.names[0]}=={period}")[factor]
         to_concat.append(df)
     df = pd.concat(to_concat, axis=1)
     return df
@@ -487,7 +508,7 @@ def _get_quasi_factor_scores_data_for_single_period(
 
 def _get_quasi_factor_scores_data_for_multiple_periods(
     data,
-    update_info,
+    update_info_by_period,
     periods,
     latent_factors,
     observed_factors,
@@ -496,8 +517,8 @@ def _get_quasi_factor_scores_data_for_multiple_periods(
 
     Args:
         data (pd.DataFrame): Data with observable variables.
-        update_info (pd.DataFrame): DataFrame with information on measurements
-            for each factor in each model period.
+        update_info_by_period (pd.DataFrame): DataFrame with information on measurements
+            for each factor in each user-provided period.
         periods (list): The list of periods that correlations are
             calculated for.
         latent_factors (list): List of latent factors the scores of which
@@ -514,7 +535,7 @@ def _get_quasi_factor_scores_data_for_multiple_periods(
         to_concat.append(
             _get_quasi_factor_scores_data_for_single_period(
                 data,
-                update_info,
+                update_info_by_period,
                 period,
                 latent_factors,
                 observed_factors,
@@ -529,7 +550,7 @@ def _get_quasi_factor_scores_data_for_multiple_periods(
 def _get_factor_scores_data(
     data,
     params,
-    update_info,
+    model,
     periods,
     latent_factors,
     observed_factors,
@@ -544,8 +565,7 @@ def _get_factor_scores_data(
         data (pd.DataFrame): Data with observable variables.
         params (pd.DataFrame): Data frame with estimated measurement relevant
             model parameters.
-        update_info (pd.DataFrame): DataFrame with information on measurements
-            for each factor in each model period.
+        model (dict): Processed model dict.
         periods (list): The list of periods that correlations are
             calculated for.
         latent_factors (list): List of latent factors the scores of which
@@ -562,7 +582,7 @@ def _get_factor_scores_data(
         df = _get_factor_scores_data_for_single_period(
             data,
             params,
-            update_info,
+            model,
             period,
             latent_factors,
             observed_factors,
@@ -571,7 +591,7 @@ def _get_factor_scores_data(
         df = _get_factor_scores_data_for_multiple_periods(
             data,
             params,
-            update_info,
+            model,
             periods,
             latent_factors,
             observed_factors,
@@ -583,21 +603,76 @@ def _get_factor_scores_data(
 def _get_factor_scores_data_for_single_period(
     data,
     params,
-    update_info,
+    model,
     period,
     latent_factors,
     observed_factors,
 ):
     """Get frame with factor scores in a given period.
 
+    Careful: When we have endogenous factors, *period* refers to the raw period, but the
+    *params* are for the augmented periods. This function is the layer to abstract from
+    augmented periods.
+
     Args:
         data (pd.DataFrame): Data with observable variables.
         params (pd.DataFrame): Data frame with estimated measurement relevant
             model parameters.
+        model (dict): Processed model dict.
+        period (int): The period that correlations are calculated for.
+        latent_factors (list): List of latent factors the scores of which
+            correlations are calculated for.
+        observed_factors (list): List of observed factors the scores of which
+            correlations are calculated for.
+
+    Returns:
+        df (pd.DataFrame): Processed DataFrame to calculate correlations over.
+
+    """
+    aug_periods = model["endogenous_factors_info"]["aug_periods_from_period"](period)
+    df = pd.concat(
+        [
+            _get_factor_scores_data_for_single_model_period(
+                data=data,
+                params=params,
+                update_info=model["update_info"],
+                aug_period=ap,
+                period=period,
+                latent_factors=latent_factors,
+                observed_factors=observed_factors,
+            )
+            for ap in aug_periods
+        ],
+        axis=0,
+    )
+    df = df.groupby("id").max()
+    return df.set_index(
+        pd.MultiIndex.from_tuples(
+            [(idx, period) for idx in df.index], names=["id", "period"]
+        )
+    )
+
+
+def _get_factor_scores_data_for_single_model_period(
+    data,
+    params,
+    update_info,
+    aug_period,
+    period,
+    latent_factors,
+    observed_factors,
+):
+    """Get frame with factor scores in a given model period.
+
+    In this function, all calculations are at the augmented period level.
+
+    Args:
+        data (pd.DataFrame): Data with observable variables.
+        params (pd.DataFrame): Data frame with estimated measurement relevant
         update_info (pd.DataFrame): DataFrame with information on measurements
             for each factor in each model period.
-        periods (list): The list of periods that correlations are
-            calculated for.
+        aug_period (int): The (augmented) period that correlations are calculated for.
+        period (int): The (raw) period that correlations are calculated for.
         latent_factors (list): List of latent factors the scores of which
             correlations are calculated for.
         observed_factors (list): List of observed factors the scores of which
@@ -605,10 +680,11 @@ def _get_factor_scores_data_for_single_period(
 
     Returns:
         df (pd.DataFrame): Processed DataFrame to calculate correlations over.
-
     """
-    period_info = update_info.loc[period].reset_index()
-    params = params.query(f"period=={period}").droplevel("period")
+    if aug_period not in update_info.index:
+        return pd.DataFrame()
+    period_info = update_info.loc[aug_period].reset_index()
+    params = params.query(f"aug_period=={aug_period}").droplevel("aug_period")
     loadings = params.loc["loadings"]["value"]
     intercepts = (
         params.loc["controls"].query("name2 == 'constant'").droplevel("name2")["value"]
@@ -623,25 +699,22 @@ def _get_factor_scores_data_for_single_period(
         period_factor_measurements = [
             m for m in period_factor_measurements if m not in leave_out_meas
         ]
-        df = data.query(f"{update_info.index.names[0]}=={period}")[
-            period_factor_measurements
-        ]
+        df = data.query(f"period == {period}")[period_factor_measurements]
         for m in period_factor_measurements:
             df[m] = (df[m] - intercepts.loc[m]) / loadings.loc[(m, factor)]
         sr = df.mean(axis=1)
         sr.name = f"{factor}"
         to_concat.append(sr)
     for factor in observed_factors:
-        df = data.query(f"{update_info.index.names[0]}=={period}")[factor]
+        df = data.query(f"period == {period}")[factor]
         to_concat.append(df)
-    df = pd.concat(to_concat, axis=1)
-    return df
+    return pd.concat(to_concat, axis=1)
 
 
 def _get_factor_scores_data_for_multiple_periods(
     data,
     params,
-    update_info,
+    model,
     periods,
     latent_factors,
     observed_factors,
@@ -651,8 +724,7 @@ def _get_factor_scores_data_for_multiple_periods(
     Args:
         data (pd.DataFrame): Data with observable variables.
         params (pd.DataFrame): Data frame with estimated model parameters.
-        update_info (pd.DataFrame): DataFrame with information on measurements
-            for each factor in each model period.
+        model (dict): Processed model dict.
         periods (list): The list of periods that correlations are
             calculated for.
         latent_factors (list): List of latent factors the scores of which
@@ -670,7 +742,7 @@ def _get_factor_scores_data_for_multiple_periods(
             _get_factor_scores_data_for_single_period(
                 data,
                 params,
-                update_info,
+                model,
                 period,
                 latent_factors,
                 observed_factors,
diff --git a/src/skillmodels/filtered_states.py b/src/skillmodels/filtered_states.py
index 5dd2fd75..2efb4c6f 100644
--- a/src/skillmodels/filtered_states.py
+++ b/src/skillmodels/filtered_states.py
@@ -21,6 +21,7 @@ def get_filtered_states(model_dict, data, params):
         states_df=unanchored_states_df,
         model_dict=model_dict,
         params=params,
+        use_aug_period=True,
     )
 
     anchored_ranges = create_state_ranges(
@@ -42,7 +43,7 @@ def get_filtered_states(model_dict, data, params):
     return out
 
 
-def anchor_states_df(states_df, model_dict, params):
+def anchor_states_df(states_df, model_dict, params, use_aug_period):
     """Anchor states in a DataFrame.
 
     The DataFrame is expected to have a column called "period" as well as one column
@@ -57,19 +58,23 @@ def anchor_states_df(states_df, model_dict, params):
     model = process_model(model_dict)
 
     p_index = get_params_index(
-        model["update_info"],
-        model["labels"],
-        model["dimensions"],
-        model["transition_info"],
+        update_info=model["update_info"],
+        labels=model["labels"],
+        dimensions=model["dimensions"],
+        transition_info=model["transition_info"],
+        endogenous_factors_info=model["endogenous_factors_info"],
     )
 
     params = params.loc[p_index]
 
     parsing_info = create_parsing_info(
-        p_index,
-        model["update_info"],
-        model["labels"],
-        model["anchoring"],
+        params_index=p_index,
+        update_info=model["update_info"],
+        labels=model["labels"],
+        anchoring=model["anchoring"],
+        has_endogenous_factors=model["endogenous_factors_info"][
+            "has_endogenous_factors"
+        ],
     )
 
     *_, pardict = parse_params(
@@ -82,10 +87,21 @@ def anchor_states_df(states_df, model_dict, params):
 
     n_latent = model["dimensions"]["n_latent_factors"]
 
-    scaling_factors = np.array(pardict["anchoring_scaling_factors"][:, :n_latent])
-    constants = np.array(pardict["anchoring_constants"][:, :n_latent])
+    _scaling_factors = np.array(pardict["anchoring_scaling_factors"][:, :n_latent])
+    _constants = np.array(pardict["anchoring_constants"][:, :n_latent])
+    if use_aug_period:
+        period_arr = states_df["aug_period"].to_numpy()
+        ap_to_p = model["labels"]["aug_periods_to_periods"]
+        scaling_factors = np.empty(shape=(len(ap_to_p), n_latent))
+        constants = np.empty(shape=(len(ap_to_p), n_latent))
+        for ap, p in ap_to_p.items():
+            scaling_factors[ap] = _scaling_factors[p]
+            constants[ap] = _constants[p]
+    else:
+        period_arr = states_df["period"].to_numpy()
+        scaling_factors = _scaling_factors
+        constants = _constants
 
-    period_arr = states_df["period"].to_numpy()
     scaling_arr = scaling_factors[period_arr]
     constants_arr = constants[period_arr]
 
diff --git a/src/skillmodels/kalman_filters.py b/src/skillmodels/kalman_filters.py
index 37d22ef5..f9cfae97 100644
--- a/src/skillmodels/kalman_filters.py
+++ b/src/skillmodels/kalman_filters.py
@@ -1,17 +1,19 @@
-import functools
-
 import jax
 import jax.numpy as jnp
 
-array_qr_jax = jax.vmap(jax.vmap(jnp.linalg.qr))
+from skillmodels.qr import qr_gpu
 
+array_qr_jax = (
+    jax.vmap(jax.vmap(qr_gpu))
+    if jax.default_backend() == "gpu"
+    else jax.vmap(jax.vmap(jnp.linalg.qr))
+)
 
 # ======================================================================================
 # Update Step
 # ======================================================================================
 
 
-@functools.partial(jax.checkpoint, prevent_cse=False)
 def kalman_update(
     states,
     upper_chols,
@@ -155,7 +157,6 @@ def calculate_sigma_scaling_factor_and_weights(n_states, kappa=2):
     return scaling_factor, weights
 
 
-@functools.partial(jax.checkpoint, static_argnums=0, prevent_cse=False)
 def kalman_predict(
     transition_func,
     states,
@@ -227,7 +228,6 @@ def kalman_predict(
     return predicted_states, predicted_covs
 
 
-@functools.partial(jax.checkpoint, prevent_cse=False)
 def _calculate_sigma_points(states, upper_chols, scaling_factor, observed_factors):
     """Calculate the array of sigma_points for the unscented transform.
 
diff --git a/src/skillmodels/likelihood_function.py b/src/skillmodels/likelihood_function.py
index 61ffee6e..4e7eec21 100644
--- a/src/skillmodels/likelihood_function.py
+++ b/src/skillmodels/likelihood_function.py
@@ -132,8 +132,8 @@ def log_likelihood_obs(
         transition_func=transition_func,
         observed_factors=observed_factors,
     )
-
-    static_out = jax.lax.scan(_body, carry, loop_args)[1]
+    _body = jax.checkpoint(_body, prevent_cse=False)
+    static_out = jax.lax.scan(_body, carry, loop_args, unroll=False)[1]
 
     # clip contributions before aggregation to preserve as much information as
     # possible.
diff --git a/src/skillmodels/maximization_inputs.py b/src/skillmodels/maximization_inputs.py
index b84c96ed..a392e173 100644
--- a/src/skillmodels/maximization_inputs.py
+++ b/src/skillmodels/maximization_inputs.py
@@ -7,7 +7,12 @@
 
 import skillmodels.likelihood_function as lf
 import skillmodels.likelihood_function_debug as lfd
-from skillmodels.constraints import add_bounds, get_constraints
+from skillmodels.constraints import (
+    add_bounds,
+    constraints_dicts_to_om,
+    enforce_fixed_constraints,
+    get_constraints_dicts,
+)
 from skillmodels.kalman_filters import calculate_sigma_scaling_factor_and_weights
 from skillmodels.params_index import get_params_index
 from skillmodels.parse_params import create_parsing_info
@@ -18,12 +23,14 @@
 jax.config.update("jax_enable_x64", True)  # noqa: FBT003
 
 
-def get_maximization_inputs(model_dict, data):
+def get_maximization_inputs(model_dict, data, split_dataset=1):
     """Create inputs for optimagic's maximize function.
 
     Args:
         model_dict (dict): The model specification. See: :ref:`model_specs`
         data (DataFrame): dataset in long format.
+        split_dataset(Int): Controls into how many sclices to split the dataset
+            during the gradient computation.
 
     Returns a dictionary with keys:
         loglike (function): A jax jitted function that takes an optimagic-style
@@ -41,28 +48,41 @@ def get_maximization_inputs(model_dict, data):
         constraints (list): List of optimagic constraints that are implied by the
             model specification.
         params_template (pd.DataFrame): Parameter DataFrame with correct index and
-            bounds but with empty value column.
+            bounds. The value column is empty except for the fixed constraints, which
+            are set including the bounds.
+        data_aug (pd.DataFrame): DataFrame with augmented data. If model contains
+            endogenous factors, we double up the number of periods in order to add
+
+
 
     """
     model = process_model(model_dict)
     p_index = get_params_index(
-        model["update_info"],
-        model["labels"],
-        model["dimensions"],
-        model["transition_info"],
+        update_info=model["update_info"],
+        labels=model["labels"],
+        dimensions=model["dimensions"],
+        transition_info=model["transition_info"],
+        endogenous_factors_info=model["endogenous_factors_info"],
     )
 
     parsing_info = create_parsing_info(
-        p_index,
-        model["update_info"],
-        model["labels"],
-        model["anchoring"],
+        params_index=p_index,
+        update_info=model["update_info"],
+        labels=model["labels"],
+        anchoring=model["anchoring"],
+        has_endogenous_factors=model["endogenous_factors_info"][
+            "has_endogenous_factors"
+        ],
     )
-    measurements, controls, observed_factors = process_data(
-        data,
-        model["labels"],
-        model["update_info"],
-        model["anchoring"],
+    processed_data = process_data(
+        df=data,
+        has_endogenous_factors=model["endogenous_factors_info"][
+            "has_endogenous_factors"
+        ],
+        labels=model["labels"],
+        update_info=model["update_info"],
+        anchoring_info=model["anchoring"],
+        purpose="estimation",
     )
 
     sigma_scaling_factor, sigma_weights = calculate_sigma_scaling_factor_and_weights(
@@ -84,9 +104,9 @@ def get_maximization_inputs(model_dict, data):
         partialed_loglikes[n] = _partial_some_log_likelihood(
             fun=fun,
             parsing_info=parsing_info,
-            measurements=measurements,
-            controls=controls,
-            observed_factors=observed_factors,
+            measurements=processed_data["measurements"],
+            controls=processed_data["controls"],
+            observed_factors=processed_data["observed_factors"],
             model=model,
             sigma_weights=sigma_weights,
             sigma_scaling_factor=sigma_scaling_factor,
@@ -107,7 +127,27 @@ def loglikeobs(params):
     def loglike_and_gradient(params):
         params_vec = partialed_get_jnp_params_vec(params)
         crit = float(_jitted_loglike(params_vec))
-        grad = _to_numpy(_gradient(params_vec))
+        n_obs = processed_data["measurements"].shape[1]
+        _grad = jnp.zeros_like(params_vec)
+        start = 0
+        stop = int(n_obs / split_dataset)
+        step = int(n_obs / split_dataset)
+        for i in range(split_dataset):
+            stop = n_obs if i == split_dataset - 1 else stop
+            measurements_slice = processed_data["measurements"][:, start:stop]
+            controls_slice = processed_data["controls"][:, start:stop, :]
+            observed_factors_slice = processed_data["observed_factors"][
+                :, start:stop, :
+            ]
+            _grad += _gradient(
+                params_vec,
+                measurements=measurements_slice,
+                controls=controls_slice,
+                observed_factors=observed_factors_slice,
+            )
+            start += step
+            stop += step
+        grad = _to_numpy(_grad)
         return crit, grad
 
     def debug_loglike(params):
@@ -117,26 +157,35 @@ def debug_loglike(params):
         tmp["value"] = float(tmp["value"])
         return process_debug_data(debug_data=tmp, model=model)
 
-    constr = get_constraints(
+    _constraints_dicts = get_constraints_dicts(
         dimensions=model["dimensions"],
         labels=model["labels"],
         anchoring_info=model["anchoring"],
         update_info=model["update_info"],
         normalizations=model["normalizations"],
+        endogenous_factors_info=model["endogenous_factors_info"],
     )
 
+    constraints = constraints_dicts_to_om(_constraints_dicts)
+
     params_template = pd.DataFrame(columns=["value"], index=p_index)
     params_template = add_bounds(
-        params_template,
-        model["estimation_options"]["bounds_distance"],
+        params=params_template,
+        bounds_distance=model["estimation_options"]["bounds_distance"],
+    )
+    params_template = enforce_fixed_constraints(
+        params_template=params_template,
+        constraints_dicts=_constraints_dicts,
+    )
+    assert params_template.index.equals(p_index), (
+        "params_template index is not equal to p_index"
     )
-
     out = {
         "loglike": loglike,
         "loglikeobs": loglikeobs,
         "debug_loglike": debug_loglike,
         "loglike_and_gradient": loglike_and_gradient,
-        "constraints": constr,
+        "constraints": constraints,
         "params_template": params_template,
     }
 
@@ -155,14 +204,23 @@ def _partial_some_log_likelihood(
 ):
     update_info = model["update_info"]
     is_measurement_iteration = (update_info["purpose"] == "measurement").to_numpy()
-    _periods = pd.Series(update_info.index.get_level_values("period").to_numpy())
-    is_predict_iteration = ((_periods - _periods.shift(-1)) == -1).to_numpy()
-    last_period = model["labels"]["periods"][-1]
+    _aug_periods = pd.Series(
+        update_info.index.get_level_values("aug_period").to_numpy()
+    )
+    is_predict_iteration = ((_aug_periods - _aug_periods.shift(-1)) == -1).to_numpy()
     # iteration_to_period is used as an indexer to loop over arrays of different lengths
-    # in a jax.lax.scan. It needs to work for arrays of length n_periods and not raise
-    # IndexErrors on tracer arrays of length n_periods - 1 (i.e. n_transitions).
-    # To achieve that, we replace the last period by -1.
-    iteration_to_period = _periods.replace(last_period, -1).to_numpy()
+    # in a jax.lax.scan. It needs to work for arrays of length n_aug_periods and not raise
+    # IndexErrors on tracer arrays of length n_aug_periods - 1 (i.e. n_transitions).
+    # To achieve that, we replace the last aug_period by -1. If there are endogenous factors,
+    # the last aug_period is found at index -2 (there should not be measurements for
+    # endogenous factors in the "second half" of the last period).
+    last_aug_period = (
+        model["labels"]["aug_periods"][-2]
+        if parsing_info["has_endogenous_factors"]
+        else model["labels"]["aug_periods"][-1]
+    )
+    iteration_to_period = _aug_periods.replace(last_aug_period, -1).to_numpy()
+    assert max(iteration_to_period) == last_aug_period - 1
 
     return functools.partial(
         fun,
diff --git a/src/skillmodels/params_index.py b/src/skillmodels/params_index.py
index 4e33cbb0..9251d82d 100644
--- a/src/skillmodels/params_index.py
+++ b/src/skillmodels/params_index.py
@@ -1,7 +1,9 @@
 import pandas as pd
 
 
-def get_params_index(update_info, labels, dimensions, transition_info):
+def get_params_index(
+    update_info, labels, dimensions, transition_info, endogenous_factors_info
+):
     """Generate index for the params_df for optimagic.
 
     The index has four levels. The first is the parameter category. The second is the
@@ -16,29 +18,43 @@ def get_params_index(update_info, labels, dimensions, transition_info):
             factors, periods, controls, stagemap and stages. See :ref:`labels`
         options (dict): Tuning parameters for the estimation.
             See :ref:`estimation_options`.
+        transition_info (dict): Information about the transition equations.
+        endogenous_factors_info (dict): Information about the endogenous factors, if any.
 
     Returns:
         params_index (pd.MultiIndex)
 
     """
-    ind_tups = get_control_params_index_tuples(labels["controls"], update_info)
-    ind_tups += get_loadings_index_tuples(labels["latent_factors"], update_info)
-    ind_tups += get_meas_sds_index_tuples(update_info)
-    ind_tups += get_shock_sds_index_tuples(labels["periods"], labels["latent_factors"])
+    ind_tups = get_control_params_index_tuples(
+        controls=labels["controls"], update_info=update_info
+    )
+    ind_tups += get_loadings_index_tuples(
+        factors=labels["latent_factors"], update_info=update_info
+    )
+    ind_tups += get_meas_sds_index_tuples(update_info=update_info)
+    ind_tups += get_shock_sds_index_tuples(
+        aug_periods=labels["aug_periods"],
+        factors=labels["latent_factors"],
+        has_endogenous_factors=endogenous_factors_info["has_endogenous_factors"],
+    )
     ind_tups += initial_mean_index_tuples(
-        dimensions["n_mixtures"],
-        labels["latent_factors"],
+        n_mixtures=dimensions["n_mixtures"],
+        factors=labels["latent_factors"],
     )
-    ind_tups += get_mixture_weights_index_tuples(dimensions["n_mixtures"])
+    ind_tups += get_mixture_weights_index_tuples(n_mixtures=dimensions["n_mixtures"])
     ind_tups += get_initial_cholcovs_index_tuples(
-        dimensions["n_mixtures"],
-        labels["latent_factors"],
+        n_mixtures=dimensions["n_mixtures"],
+        factors=labels["latent_factors"],
+    )
+    ind_tups += get_transition_index_tuples(
+        transition_info=transition_info,
+        aug_periods=labels["aug_periods"],
+        has_endogenous_factors=endogenous_factors_info["has_endogenous_factors"],
     )
-    ind_tups += get_transition_index_tuples(transition_info, labels["periods"])
 
     index = pd.MultiIndex.from_tuples(
         ind_tups,
-        names=["category", "period", "name1", "name2"],
+        names=["category", "aug_period", "name1", "name2"],
     )
     return index
 
@@ -54,9 +70,9 @@ def get_control_params_index_tuples(controls, update_info):
 
     """
     ind_tups = []
-    for period, meas in update_info.index:
+    for aug_period, meas in update_info.index:
         for cont in controls:
-            ind_tups.append(("controls", period, meas, cont))
+            ind_tups.append(("controls", aug_period, meas, cont))
     return ind_tups
 
 
@@ -74,10 +90,10 @@ def get_loadings_index_tuples(factors, update_info):
     """
     mask = update_info[factors].to_numpy()
     ind_tups = []
-    for i, (period, meas) in enumerate(update_info.index):
+    for i, (aug_period, meas) in enumerate(update_info.index):
         for f, factor in enumerate(factors):
             if mask[i, f]:
-                ind_tups.append(("loadings", period, meas, factor))
+                ind_tups.append(("loadings", aug_period, meas, factor))
     return ind_tups
 
 
@@ -93,26 +109,27 @@ def get_meas_sds_index_tuples(update_info):
 
     """
     ind_tups = []
-    for period, meas in update_info.index:
-        ind_tups.append(("meas_sds", period, meas, "-"))
+    for aug_period, meas in update_info.index:
+        ind_tups.append(("meas_sds", aug_period, meas, "-"))
     return ind_tups
 
 
-def get_shock_sds_index_tuples(periods, factors):
+def get_shock_sds_index_tuples(aug_periods, factors, has_endogenous_factors):
     """Index tuples for shock_sd.
 
     Args:
-        periods (list): The periods of the model.
+        aug_periods (list): The augmented periods of the model.
         factors (list): The latent factors of the model.
 
     Returns:
         ind_tups (list)
 
     """
+    end = -2 if has_endogenous_factors else -1
     ind_tups = []
-    for period in periods[:-1]:
+    for aug_period in aug_periods[:end]:
         for factor in factors:
-            ind_tups.append(("shock_sds", period, factor, "-"))
+            ind_tups.append(("shock_sds", aug_period, factor, "-"))
     return ind_tups
 
 
@@ -177,22 +194,24 @@ def get_initial_cholcovs_index_tuples(n_mixtures, factors):
     return ind_tups
 
 
-def get_transition_index_tuples(transition_info, periods):
+def get_transition_index_tuples(transition_info, aug_periods, has_endogenous_factors):
     """Index tuples for transition equation coefficients.
 
     Args:
         latent_factors (list): The latent factors of the model
         all_factors (list): The latent and observed factors of the model.
-        periods (list): The periods of the model
+        aug_periods (list): The augmented periods of the model
         transition_names (list): name of the transition equation of each factor
+        has_endogenous_factors (bool): Whether the model has endogenous factors.
 
     Returns:
         ind_tups (list)
 
     """
+    end = -2 if has_endogenous_factors else -1
     ind_tups = []
     for factor, names in transition_info["param_names"].items():
-        for period in periods[:-1]:
+        for aug_period in aug_periods[:end]:
             for name in names:
-                ind_tups.append(("transition", period, factor, name))
+                ind_tups.append(("transition", aug_period, factor, name))
     return ind_tups
diff --git a/src/skillmodels/parse_params.py b/src/skillmodels/parse_params.py
index b7dc4509..427406c7 100644
--- a/src/skillmodels/parse_params.py
+++ b/src/skillmodels/parse_params.py
@@ -5,16 +5,20 @@
 import pandas as pd
 
 
-def create_parsing_info(params_index, update_info, labels, anchoring):
+def create_parsing_info(
+    params_index, update_info, labels, anchoring, has_endogenous_factors
+):
     """Create a dictionary with information how the parameter vector has to be parsed.
 
     Args:
-        params_index (pandas.MultiIndex): It has the levels ["category", "period",
+        params_index (pandas.MultiIndex): It has the levels ["category", "aug_period",
             "name1", "name2"]
         update_info (pandas.DataFrame): DataFrame with one row per Kalman update needed
             in the likelihood function. See :ref:`update_info`.
         labels (dict): Dict of lists with labels for the model quantities like
             factors, periods, controls, stagemap and stages. See :ref:`labels`
+        anchoring (dict): Dictionary with anchoring settings.
+        has_endogenous_factors (bool): Whether the model includes endogenous factors.
 
     Returns:
         dict: dictionary that maps model quantities to positions or slices of the
@@ -73,6 +77,9 @@ def create_parsing_info(params_index, update_info, labels, anchoring):
         "ignore_constant_when_anchoring"
     ]
 
+    # Add has_endogenous_factors to parsing_info
+    parsing_info["has_endogenous_factors"] = has_endogenous_factors
+
     return parsing_info
 
 
@@ -206,10 +213,14 @@ def _get_transition_params(params, info, labels):
     """Create a list of arrays with transition equation parameters."""
     trans_params = {}
     t_info = info["transition"]
-    n_periods = len(labels["periods"])
+    n_aug_periods = len(labels["aug_periods"])
+
+    # Use has_endogenous_factors from parsing_info instead of undefined global
+    len_reduction = 2 if info["has_endogenous_factors"] else 1
+
     for factor in labels["latent_factors"]:
         ilocs = t_info[factor]
-        trans_params[factor] = params[ilocs].reshape(n_periods - 1, -1)
+        trans_params[factor] = params[ilocs].reshape(n_aug_periods - len_reduction, -1)
     return trans_params
 
 
diff --git a/src/skillmodels/process_data.py b/src/skillmodels/process_data.py
index 6d9dba21..3b6407af 100644
--- a/src/skillmodels/process_data.py
+++ b/src/skillmodels/process_data.py
@@ -1,18 +1,25 @@
 import warnings
+from typing import Any
 
 import jax.numpy as jnp
 import numpy as np
 import pandas as pd
 
-from skillmodels.process_model import get_period_measurements
 
-
-def process_data(df, labels, update_info, anchoring_info, purpose="estimation"):
+def process_data(
+    df,
+    has_endogenous_factors,
+    labels,
+    update_info,
+    anchoring_info,
+    purpose="estimation",
+):
     """Process the data for estimation.
 
     Args:
         df (DataFrame): panel dataset in long format. It has a MultiIndex
             where the first level indicates the period and the second the individual.
+        has_endogenous_factors (bool):
         labels (dict): Dict of lists with labels for the model quantities like
             factors, periods, controls, stagemap and stages. See :ref:`labels`
         update_info (pandas.DataFrame): DataFrame with one row per Kalman update needed
@@ -21,30 +28,35 @@ def process_data(df, labels, update_info, anchoring_info, purpose="estimation"):
         purpose (Literal["estimation", "anything"]): Whether the data is used for
             estimation (default, includes measurement data) or not.
 
-    Returns:
-        meas_data (jax.numpy.array): Array of shape (n_updates, n_obs) with data on
-            observed measurements. NaN if the measurement was not observed.
-        control_data (jax.numpy.array): Array of shape (n_periods, n_obs, n_controls)
-            with observed control variables for the measurement equations.
-        observed_factors (jax.numpy.array): Array of shape (n_periods, n_obs,
-            n_observed_factors) with data on the observed factors.
+    Returns a dictionary with keys:
+        measurements (jax.numpy.array): Array of shape (n_updates, n_obs) with data on
+            observed measurements. NaN if the measurement was not observed. Only
+            returned if estimation==True
+        controls (jax.numpy.array): Array of shape (n_periods, n_obs, n_controls) with
+            observed control variables for the measurement equations.
+        observed_factors (jax.numpy.array): Array of shape
+            (n_periods, n_obs, n_observed_factors) with data on the observed factors.
+            Only returned if estimation==True
 
     """
     df = pre_process_data(df, labels["periods"])
     df["constant"] = 1
-    df = _add_copies_of_anchoring_outcome(df, anchoring_info)
+    out = {}
+
+    if has_endogenous_factors:
+        df = _augment_data_for_endogenous_factors(df, labels, update_info)
+    else:
+        df = _add_copies_of_anchoring_outcome(df, anchoring_info)
+        df.index = df.index.set_names(["id", "aug_period"])
+
     _check_data(df, update_info, labels, purpose=purpose)
-    n_obs = int(len(df) / len(labels["periods"]))
+    n_obs = int(len(df) / len(labels["aug_periods"]))
     df = _handle_controls_with_missings(df, labels["controls"], update_info)
-    if purpose == "estimation":
-        meas_data = _generate_measurements_array(df, update_info, n_obs)
-    control_data = _generate_controls_array(df, labels, n_obs)
-    observed_data = _generate_observed_factor_array(df, labels, n_obs)
+    out["controls"] = _generate_controls_array(df, labels, n_obs)
+    out["observed_factors"] = _generate_observed_factor_array(df, labels, n_obs)
 
     if purpose == "estimation":
-        out = (meas_data, control_data, observed_data)
-    else:
-        out = (control_data, observed_data)
+        out["measurements"] = _generate_measurements_array(df, update_info, n_obs)
     return out
 
 
@@ -80,6 +92,66 @@ def pre_process_data(df, periods):
     return df
 
 
+def _get_period_data_for_endogenous_factors(
+    aug_period: int,
+    period: int,
+    df: pd.DataFrame,
+    labels: dict[str, Any],
+    update_info: pd.DataFrame,
+) -> pd.DataFrame:
+    meas = _get_period_measurements(update_info, aug_period)
+    controls = labels["controls"]
+    observed = labels["observed_factors"]
+
+    out = df.query(f"period == {period}")[
+        [
+            "id",
+            *meas,
+            *controls,
+            *observed,
+            "period",
+            "__old_id__",
+            "__old_period__",
+        ]
+    ]
+    out["aug_period"] = aug_period
+    return out
+
+
+def _augment_data_for_endogenous_factors(
+    df: pd.DataFrame,
+    labels: dict[str, Any],
+    update_info: pd.DataFrame,
+):
+    """Make room for endogenous factors by doubling up the periods.
+
+    Endogeneity means that current states influence the factor. Typically, this comes
+    as an investment equation. We make that look like a transition for skillmodels'
+    internal machinery.
+
+    """
+    df = df.reset_index()
+    # Make sure datset is balanced
+    n_ids = df["id"].nunique()
+    n_periods = df["period"].nunique()
+    assert n_ids * n_periods == df.shape[0]
+    assert set(df["period"]) == set(labels["aug_periods_to_periods"].values())
+
+    out = pd.concat(
+        [
+            _get_period_data_for_endogenous_factors(
+                aug_period=aug_period,
+                period=period,
+                df=df,
+                update_info=update_info,
+                labels=labels,
+            )
+            for aug_period, period in labels["aug_periods_to_periods"].items()
+        ]
+    )
+    return out.set_index(["id", "aug_period"]).sort_index()
+
+
 def _add_copies_of_anchoring_outcome(df, anchoring_info):
     df = df.copy()
     for factor in anchoring_info["factors"]:
@@ -90,26 +162,30 @@ def _add_copies_of_anchoring_outcome(df, anchoring_info):
 
 def _check_data(df, update_info, labels, purpose):  # noqa: C901
     var_report = pd.DataFrame(index=update_info.index[:0], columns=["problem"])
-    for period in labels["periods"]:
-        period_data = df.query(f"period == {period}")
+    for aug_period in labels["aug_periods"]:
+        period_data = df.query(f"aug_period == {aug_period}")
         for cont in labels["controls"]:
             if cont not in period_data.columns or period_data[cont].isna().all():
-                var_report.loc[(period, cont), "problem"] = "Variable is missing"
+                var_report.loc[(aug_period, cont), "problem"] = "Variable is missing"
 
         if purpose == "estimation":
-            for meas in get_period_measurements(update_info, period):
+            for meas in _get_period_measurements(update_info, aug_period):
                 if meas not in period_data.columns:
-                    var_report.loc[(period, meas), "problem"] = "Variable is missing"
+                    var_report.loc[(aug_period, meas), "problem"] = (
+                        "Variable is missing"
+                    )
                 elif len(period_data[meas].dropna().unique()) == 1:
-                    var_report.loc[(period, meas), "problem"] = (
+                    var_report.loc[(aug_period, meas), "problem"] = (
                         "Variable has no variance"
                     )
 
         for factor in labels["observed_factors"]:
             if factor not in period_data.columns:
-                var_report.loc[(period, factor), "problem"] = "Variable is missing"
+                var_report.loc[(aug_period, factor), "problem"] = "Variable is missing"
             elif period_data[factor].isna().any():
-                var_report.loc[(period, factor), "problem"] = "Variable has missings"
+                var_report.loc[(aug_period, factor), "problem"] = (
+                    "Variable has missings"
+                )
 
     var_report = var_report.to_string() if len(var_report) > 0 else ""
 
@@ -118,12 +194,12 @@ def _check_data(df, update_info, labels, purpose):  # noqa: C901
 
 
 def _handle_controls_with_missings(df, controls, update_info):
-    periods = update_info.index.get_level_values(0).unique().tolist()
+    aug_periods = update_info.index.get_level_values(0).unique().tolist()
     problematic_index = df.index[:0]
-    for period in periods:
-        period_data = df.query(f"period == {period}")
+    for aug_period in aug_periods:
+        period_data = df.query(f"aug_period == {aug_period}")
         control_data = period_data[controls]
-        meas_data = period_data[get_period_measurements(update_info, period)]
+        meas_data = period_data[_get_period_measurements(update_info, aug_period)]
         problem = control_data.isna().any(axis=1) & meas_data.notna().any(axis=1)
         problematic_index = problematic_index.union(period_data[problem].index)
 
@@ -136,24 +212,34 @@ def _handle_controls_with_missings(df, controls, update_info):
     return df
 
 
+def _get_period_measurements(update_info, aug_period):
+    if aug_period in update_info.index:
+        measurements = list(update_info.loc[aug_period].index)
+    else:
+        measurements = []
+    return measurements
+
+
 def _generate_measurements_array(df, update_info, n_obs):
     arr = np.zeros((len(update_info), n_obs))
-    for k, (period, var) in enumerate(update_info.index):
-        arr[k] = df.query(f"period == {period}")[var].to_numpy()
+    for k, (aug_period, var) in enumerate(update_info.index):
+        arr[k] = df.query(f"aug_period == {aug_period}")[var].to_numpy()
     return jnp.array(arr, dtype="float32")
 
 
 def _generate_controls_array(df, labels, n_obs):
-    arr = np.zeros((len(labels["periods"]), n_obs, len(labels["controls"])))
-    for period in labels["periods"]:
-        arr[period] = df.query(f"period == {period}")[labels["controls"]].to_numpy()
+    arr = np.zeros((len(labels["aug_periods"]), n_obs, len(labels["controls"])))
+    for aug_period in labels["aug_periods"]:
+        arr[aug_period] = df.query(f"aug_period == {aug_period}")[
+            labels["controls"]
+        ].to_numpy()
     return jnp.array(arr, dtype="float32")
 
 
 def _generate_observed_factor_array(df, labels, n_obs):
-    arr = np.zeros((len(labels["periods"]), n_obs, len(labels["observed_factors"])))
-    for period in labels["periods"]:
-        arr[period] = df.query(f"period == {period}")[
+    arr = np.zeros((len(labels["aug_periods"]), n_obs, len(labels["observed_factors"])))
+    for aug_period in labels["aug_periods"]:
+        arr[aug_period] = df.query(f"aug_period == {aug_period}")[
             labels["observed_factors"]
         ].to_numpy()
     return jnp.array(arr, dtype="float32")
diff --git a/src/skillmodels/process_debug_data.py b/src/skillmodels/process_debug_data.py
index 3ec3062b..1d5e7dde 100644
--- a/src/skillmodels/process_debug_data.py
+++ b/src/skillmodels/process_debug_data.py
@@ -95,9 +95,11 @@ def process_debug_data(debug_data, model):
 
 def _create_post_update_states(filtered_states, factors, update_info):
     to_concat = []
-    for (period, meas), data in zip(update_info.index, filtered_states, strict=False):
+    for (aug_period, meas), data in zip(
+        update_info.index, filtered_states, strict=False
+    ):
         df = _convert_state_array_to_df(data, factors)
-        df["period"] = period
+        df["aug_period"] = aug_period
         df["id"] = np.arange(len(df))
         df["measurement"] = meas
         to_concat.append(df)
@@ -128,9 +130,9 @@ def _create_filtered_states(filtered_states, log_mixture_weights, update_info, f
     agg_states = (filtered_states * weights.reshape(*weights.shape, 1)).sum(axis=-2)
 
     keep = []
-    for i, (period, measurement) in enumerate(update_info.index):
+    for i, (aug_period, measurement) in enumerate(update_info.index):
         last_measurement = update_info.query(
-            f"purpose == 'measurement' & period == {period}",
+            f"purpose == 'measurement' & aug_period == {aug_period}",
         ).index[-1][1]
 
         if measurement == last_measurement:
@@ -139,7 +141,7 @@ def _create_filtered_states(filtered_states, log_mixture_weights, update_info, f
     to_concat = []
     for period, i in enumerate(keep):
         df = pd.DataFrame(data=agg_states[i], columns=factors)
-        df["period"] = period
+        df["aug_period"] = period
         df["id"] = np.arange(len(df))
         to_concat.append(df)
 
@@ -150,8 +152,10 @@ def _create_filtered_states(filtered_states, log_mixture_weights, update_info, f
 
 def create_state_ranges(filtered_states, factors):
     ranges = {}
-    minima = filtered_states.groupby("period").min()
-    maxima = filtered_states.groupby("period").max()
+    # Group by whichever period column is present
+    period_col = "aug_period" if "aug_period" in filtered_states.columns else "period"
+    minima = filtered_states.groupby(period_col).min()
+    maxima = filtered_states.groupby(period_col).max()
     for factor in factors:
         df = pd.concat([minima[factor], maxima[factor]], axis=1)
         df.columns = ["minimum", "maximum"]
@@ -162,10 +166,10 @@ def create_state_ranges(filtered_states, factors):
 def _process_residuals(residuals, update_info):
     to_concat = []
     n_obs, n_mixtures = residuals[0].shape
-    for (period, meas), data in zip(update_info.index, residuals, strict=False):
+    for (aug_period, meas), data in zip(update_info.index, residuals, strict=False):
         df = pd.DataFrame(data.reshape(-1, 1), columns=["residual"])
         df["mixture"] = np.full((n_obs, n_mixtures), np.arange(n_mixtures)).flatten()
-        df["period"] = period
+        df["aug_period"] = aug_period
         df["id"] = np.arange(len(df))
         df["measurement"] = meas
         to_concat.append(df)
@@ -183,7 +187,7 @@ def _process_all_contributions(all_contributions, update_info):
     ):
         df = pd.DataFrame(data=contribs.reshape(-1, 1), columns=["contribution"])
         df["measurement"] = meas
-        df["period"] = period
+        df["aug_period"] = period
         df["id"] = np.arange(len(df))
         to_concat.append(df)
     return pd.concat(to_concat)
diff --git a/src/skillmodels/process_model.py b/src/skillmodels/process_model.py
index f3ae09e3..7824b783 100644
--- a/src/skillmodels/process_model.py
+++ b/src/skillmodels/process_model.py
@@ -1,4 +1,6 @@
+from copy import deepcopy
 from functools import partial
+from typing import Any, Literal
 
 import numpy as np
 import pandas as pd
@@ -7,8 +9,8 @@
 from jax import vmap
 from pandas import DataFrame
 
-import skillmodels.transition_functions as tf
-from skillmodels.check_model import check_model
+import skillmodels.transition_functions as t_f_module
+from skillmodels.check_model import check_model, check_stagemap
 from skillmodels.decorators import extract_params, jax_array_output
 
 pd.set_option("future.no_silent_downcasting", True)  # noqa:  FBT003
@@ -27,41 +29,98 @@ def process_model(model_dict):
     Returns:
         dict: nested dictionary of model specs. It has the following entries:
         - dimensions (dict): Dimensional information like n_states, n_periods,
-        n_controls, n_mixtures. See :ref:`dimensions`.
+          n_controls, n_mixtures. See :ref:`dimensions`.
         - labels (dict): Dict of lists with labels for the model quantities like
-        factors, periods, controls, stagemap and stages. See :ref:`labels`
+          factors, periods, controls, stagemap and stages. See :ref:`labels`
         - anchoring (dict): Information about anchoring. See :ref:`anchoring`
         - transition_info (dict): Everything related to transition functions.
         - update_info (pandas.DataFrame): DataFrame with one row per Kalman update
-        needed in the likelihood function. See :ref:`update_info`.
+          needed in the likelihood function. See :ref:`update_info`.
         - normalizations (dict): Nested dictionary with information on normalized factor
-        loadings and intercepts for each factor. See :ref:`normalizations`.
+          loadings and intercepts for each factor. See :ref:`normalizations`.
 
     """
-    dims = get_dimensions(model_dict)
-    labels = _get_labels(model_dict, dims)
-    anchoring = _process_anchoring(model_dict)
-    check_model(model_dict, labels, dims, anchoring)
-    transition_info = _get_transition_info(model_dict, labels)
+    has_endogenous_factors = get_has_endogenous_factors(model_dict["factors"])
+    dims = get_dimensions(
+        model_dict=model_dict, has_endogenous_factors=has_endogenous_factors
+    )
+    labels = _get_labels(
+        model_dict=model_dict,
+        has_endogenous_factors=has_endogenous_factors,
+        dimensions=dims,
+    )
+    anchoring = _process_anchoring(model_dict, has_endogenous_factors)
+    if has_endogenous_factors:
+        _model_dict_aug = _augment_periods_for_endogenous_factors(
+            model_dict=model_dict,
+            dimensions=dims,
+            labels=labels,
+        )
+        endogenous_factors_info = _get_endogenous_factors_info(
+            has_endogenous_factors=has_endogenous_factors,
+            model_dict=_model_dict_aug,
+            labels=labels,
+            bounds_distance=model_dict["estimation_options"]["bounds_distance"],
+        )
+    else:
+        _model_dict_aug = model_dict
+        endogenous_factors_info = {"has_endogenous_factors": has_endogenous_factors}
+    check_model(
+        model_dict=_model_dict_aug,
+        labels=labels,
+        dimensions=dims,
+        anchoring=anchoring,
+        has_endogenous_factors=has_endogenous_factors,
+    )
+    transition_info = _get_transition_info(_model_dict_aug, labels)
     labels["transition_names"] = list(transition_info["function_names"].values())
 
     processed = {
         "dimensions": dims,
         "labels": labels,
         "anchoring": anchoring,
-        "estimation_options": _process_estimation_options(model_dict),
+        "estimation_options": _process_estimation_options(_model_dict_aug),
         "transition_info": transition_info,
-        "update_info": _get_update_info(model_dict, dims, labels, anchoring),
-        "normalizations": _process_normalizations(model_dict, dims, labels),
+        "update_info": _get_update_info(_model_dict_aug, dims, labels, anchoring),
+        "normalizations": _process_normalizations(_model_dict_aug, dims, labels),
+        "endogenous_factors_info": endogenous_factors_info,
     }
     return processed
 
 
-def get_dimensions(model_dict):
+def get_has_endogenous_factors(factors: dict[str, Any]) -> bool:
+    """Return True if any endogenous factors are present."""
+    endogenous_factors = pd.DataFrame(
+        [
+            {
+                "factor": f,
+                "is_endogenous": v.get("is_endogenous", False),
+                "is_correction": v.get("is_correction", False),
+            }
+            for f, v in factors.items()
+        ]
+    ).set_index("factor")
+    if (endogenous_factors.dtypes != bool).any():  # noqa: E721
+        raise ValueError(
+            "If specified, 'is_endogenous' and 'is_correction' both need to be of type"
+            f"'bool', got:\n{endogenous_factors}"
+        )
+    if (
+        ~endogenous_factors["is_endogenous"] & endogenous_factors["is_correction"]
+    ).any():
+        raise ValueError(
+            "A factor cannot be a correction and not endogenous, got:\n"
+            f"{endogenous_factors}"
+        )
+    return endogenous_factors["is_endogenous"].any()
+
+
+def get_dimensions(model_dict, has_endogenous_factors):
     """Extract the dimensions of the model.
 
     Args:
         model_dict (dict): The model specification. See: :ref:`model_specs`
+        has_endogenous_factors (bool): Whether endogenous factors are present.
 
     Returns:
         dict: Dimensional information like n_states, n_periods, n_controls,
@@ -69,24 +128,46 @@ def get_dimensions(model_dict):
 
     """
     all_n_periods = [len(d["measurements"]) for d in model_dict["factors"].values()]
+    n_periods = max(all_n_periods)
+    n_aug_periods = 2 * n_periods if has_endogenous_factors else n_periods
 
     dims = {
         "n_latent_factors": len(model_dict["factors"]),
         "n_observed_factors": len(model_dict.get("observed_factors", [])),
-        "n_periods": max(all_n_periods),
-        # plus 1 for the constant
-        "n_controls": len(model_dict.get("controls", [])) + 1,
+        "n_controls": len(model_dict.get("controls", [])) + 1,  # plus 1: constant
         "n_mixtures": model_dict["estimation_options"].get("n_mixtures", 1),
+        "n_aug_periods": n_aug_periods,
+        "n_periods": n_periods,
     }
     dims["n_all_factors"] = dims["n_latent_factors"] + dims["n_observed_factors"]
     return dims
 
 
-def _get_labels(model_dict, dimensions):
+def _get_aug_periods_to_periods(
+    n_aug_periods: int, has_endogenous_factors: bool
+) -> dict[int, int]:
+    """Return mapper of (potentially) augmented periods to user-provided periods."""
+    aug_periods = list(range(n_aug_periods))
+    return (
+        {p: p // 2 for p in aug_periods}
+        if has_endogenous_factors
+        else {p: p for p in aug_periods}
+    )
+
+
+def _aug_periods_from_period(
+    period: int, aug_periods_to_periods: dict[int, int]
+) -> list[int]:
+    """The inverse of the the aug_periods_to_periods mapper."""
+    return [ap for ap, p in aug_periods_to_periods.items() if p == period]
+
+
+def _get_labels(model_dict, has_endogenous_factors, dimensions):
     """Extract labels of the model quantities.
 
     Args:
         model_dict (dict): The model specification. See: :ref:`model_specs`
+        has_endogenous_factors (bool): Whether endogenous factors are present.
         dimensions (dict): Dimensional information like n_states, n_periods, n_controls,
             n_mixtures. See :ref:`dimensions`.
 
@@ -95,15 +176,48 @@ def _get_labels(model_dict, dimensions):
         factors, periods, controls, stagemap and stages. See :ref:`labels`
 
     """
+    aug_periods_to_periods = _get_aug_periods_to_periods(
+        n_aug_periods=dimensions["n_aug_periods"],
+        has_endogenous_factors=has_endogenous_factors,
+    )
+
     stagemap = model_dict.get("stagemap", list(range(dimensions["n_periods"] - 1)))
+    stages = sorted(int(v) for v in np.unique(stagemap))
+
+    report = check_stagemap(
+        stagemap=stagemap,
+        stages=stages,
+        n_periods=dimensions["n_periods"],
+        is_augmented=False,
+    )
+    if report:
+        raise ValueError(f"Invalid stage map: {report}")
+    if has_endogenous_factors:
+        aug_stagemap = []
+        aug_stages_to_stages = {}
+        relevant_aug_periods = sorted(aug_periods_to_periods.keys())[:-2]
+        for aug_p in relevant_aug_periods:
+            p = aug_periods_to_periods[aug_p]
+            s = stagemap[p]
+            aug_s = 2 * s + aug_p % 2
+            aug_stagemap.append(aug_s)
+            aug_stages_to_stages[aug_s] = s
+    else:
+        aug_stagemap = stagemap
+        aug_stages_to_stages = {s: s for s in stages}
 
     labels = {
         "latent_factors": list(model_dict["factors"]),
         "observed_factors": list(model_dict.get("observed_factors", [])),
         "controls": ["constant", *list(model_dict.get("controls", []))],
-        "periods": list(range(dimensions["n_periods"])),
+        "periods": sorted(set(aug_periods_to_periods.values())),
         "stagemap": stagemap,
-        "stages": sorted(np.unique(stagemap)),
+        "stages": stages,
+        "aug_periods": list(aug_periods_to_periods.keys()),
+        "aug_periods_to_periods": aug_periods_to_periods,
+        "aug_stagemap": aug_stagemap,
+        "aug_stages": sorted(int(v) for v in np.unique(aug_stagemap)),
+        "aug_stages_to_stages": aug_stages_to_stages,
     }
 
     labels["all_factors"] = labels["latent_factors"] + labels["observed_factors"]
@@ -125,7 +239,7 @@ def _process_estimation_options(model_dict):
         "sigma_points_scale": 2,
         "robust_bounds": True,
         "bounds_distance": 1e-3,
-        "clipping_lower_bound": -1e250,
+        "clipping_lower_bound": -1e30,
         "clipping_upper_bound": None,
         "clipping_lower_hardness": 1,
         "clipping_upper_hardness": 1,
@@ -138,16 +252,22 @@ def _process_estimation_options(model_dict):
     return default_options
 
 
-def _process_anchoring(model_dict):
+def _process_anchoring(model_dict, has_endogenous_factors):
     """Process the specification that governs how latent factors are anchored.
 
     Args:
         model_dict (dict): The model specification. See: :ref:`model_specs`
+        has_endogenous_factors (bool): Whether the model has any endogenous factors.
 
     Returns:
         dict: Dictionary with information about anchoring. See :ref:`anchoring`
 
     """
+    if "anchoring" in model_dict and has_endogenous_factors:
+        raise ValueError(
+            "anchoring is not supported when endogenous factors are present."
+        )
+
     anchinfo = {
         "anchoring": False,
         "outcomes": {},
@@ -166,6 +286,64 @@ def _process_anchoring(model_dict):
     return anchinfo
 
 
+def _insert_empty_elements_into_list(old, insert_at_modulo, to_insert, aug_p_to_p):
+    return [
+        to_insert if aug_p % 2 == insert_at_modulo else old[p]
+        for aug_p, p in aug_p_to_p.items()
+    ]
+
+
+def _augment_periods_for_endogenous_factors(
+    model_dict: dict[str, Any], dimensions: dict[str, Any], labels: dict[str, Any]
+) -> dict[str, Any]:
+    """Augment periods if endogenous factors are present.
+
+    Args:
+        model_dict: The model specification. See: :ref:`model_specs`
+        dimensions (dict): Dimensional information like n_states, n_periods, n_controls,
+            n_mixtures. See :ref:`dimensions`.
+        labels (dict): Dict of lists with labels for the model quantities like
+            factors, periods, controls, stagemap and stages. See :ref:`labels`
+
+    Returns:
+        Model dictionary with twice the amount of periods
+
+    """
+    aug = deepcopy(model_dict)
+    for fac, v in model_dict["factors"].items():
+        insert_at_modulo = 0 if v.get("is_endogenous", False) else 1
+
+        # Insert empty elements into measurements when we do not have those.
+        if len(v["measurements"]) != dimensions["n_periods"]:
+            raise ValueError(
+                "Measurements must be of length `n_periods`, "
+                f"got {v['measurements']} for {fac}"
+            )
+        aug["factors"][fac]["measurements"] = _insert_empty_elements_into_list(
+            old=v["measurements"],
+            insert_at_modulo=insert_at_modulo,
+            to_insert=[],
+            aug_p_to_p=labels["aug_periods_to_periods"],
+        )
+
+        # Insert empty elements into normalizations when we do not have those.
+        for norm_type, normalizations in v.get("normalizations", {}).items():
+            if not len(normalizations) == dimensions["n_periods"]:
+                raise ValueError(
+                    "Normalizations must be lists of length `n_periods`, "
+                    f"got {normalizations} for {fac}['normalizations']['{norm_type}']"
+                )
+            aug["factors"][fac]["normalizations"][norm_type] = (
+                _insert_empty_elements_into_list(
+                    old=normalizations,
+                    insert_at_modulo=insert_at_modulo,
+                    to_insert={},
+                    aug_p_to_p=labels["aug_periods_to_periods"],
+                )
+            )
+    return aug
+
+
 def _get_transition_info(model_dict, labels):
     """Collect information about transition functions."""
     func_list, param_names = [], []
@@ -175,11 +353,11 @@ def _get_transition_info(model_dict, labels):
     for factor in latent_factors:
         spec = model_dict["factors"][factor]["transition_function"]
         if isinstance(spec, str):
-            func = getattr(tf, spec)
+            func = getattr(t_f_module, spec)
             if spec == "constant":
                 func = rename_arguments(func, mapper={"state": factor})
             func_list.append(extract_params(func, key=factor))
-            param_names.append(getattr(tf, f"params_{spec}")(all_factors))
+            param_names.append(getattr(t_f_module, f"params_{spec}")(all_factors))
         elif callable(spec):
             if not hasattr(spec, "__name__"):
                 raise AttributeError(
@@ -234,6 +412,47 @@ def _extract_factor(states, pos):
     return out
 
 
+def _get_endogenous_factors_info(
+    has_endogenous_factors: bool,
+    model_dict: dict[str, Any],
+    labels: dict[str, Any],
+    bounds_distance: float,
+) -> dict[str, Any]:
+    """Collect information about endogenous factors."""
+    endogenous_factors_info = {
+        "has_endogenous_factors": has_endogenous_factors,
+        "aug_periods_to_aug_period_meas_types": _get_aug_periods_to_aug_period_meas_types(  # noqa: E501
+            aug_periods=labels["aug_periods_to_periods"].keys(),
+            has_endogenous_factors=has_endogenous_factors,
+        ),
+        "bounds_distance": bounds_distance,
+        "aug_periods_from_period": partial(
+            _aug_periods_from_period,
+            aug_periods_to_periods=labels["aug_periods_to_periods"],
+        ),
+    }
+    for fac, v in model_dict["factors"].items():
+        endogenous_factors_info[fac] = {
+            "is_state": (
+                not v.get("is_endogenous", False) and not v.get("is_correction", False)
+            ),
+            "is_endogenous": v.get("is_endogenous", False),
+            "is_correction": v.get("is_correction", False),
+        }
+    return endogenous_factors_info
+
+
+def _get_aug_periods_to_aug_period_meas_types(
+    aug_periods: list[int], has_endogenous_factors: bool
+) -> dict[int, Literal["states", "endogenous_factors"]]:
+    return {
+        aug_p: ("states" if aug_p % 2 == 0 else "endogenous_factors")
+        if has_endogenous_factors
+        else {aug_p: "states"}
+        for aug_p in aug_periods
+    }
+
+
 def _get_update_info(model_dict, dimensions, labels, anchoring_info):
     """Construct a DataFrame with information on each Kalman update.
 
@@ -250,27 +469,30 @@ def _get_update_info(model_dict, dimensions, labels, anchoring_info):
             the likelihood function. See :ref:`update_info`.
 
     """
-    index = pd.MultiIndex(levels=[[], []], codes=[[], []], names=["period", "variable"])
+    index = pd.MultiIndex(
+        levels=[[], []], codes=[[], []], names=["aug_period", "variable"]
+    )
     uinfo = DataFrame(index=index, columns=labels["latent_factors"] + ["purpose"])
 
     measurements = {}
     for factor in labels["latent_factors"]:
-        measurements[factor] = fill_list(
-            model_dict["factors"][factor]["measurements"],
-            [],
-            dimensions["n_periods"],
-        )
-
-    for period in labels["periods"]:
+        measurements[factor] = model_dict["factors"][factor]["measurements"]
+        if len(measurements[factor]) != dimensions["n_aug_periods"]:
+            raise ValueError(
+                "Measurements must be of length `n_aug_periods`, "
+                f"got {measurements[factor]} for {factor}"
+            )
+
+    for aug_period in labels["aug_periods"]:
         for factor in labels["latent_factors"]:
-            for meas in measurements[factor][period]:
-                uinfo.loc[(period, meas), factor] = True
-                uinfo.loc[(period, meas), "purpose"] = "measurement"
+            for meas in measurements[factor][aug_period]:
+                uinfo.loc[(aug_period, meas), factor] = True
+                uinfo.loc[(aug_period, meas), "purpose"] = "measurement"
         for factor in anchoring_info["factors"]:
             outcome = anchoring_info["outcomes"][factor]
             name = f"{outcome}_{factor}"
-            uinfo.loc[(period, name), factor] = True
-            uinfo.loc[(period, name), "purpose"] = "anchoring"
+            uinfo.loc[(aug_period, name), factor] = True
+            uinfo.loc[(aug_period, name), "purpose"] = "anchoring"
 
     for col in [c for c in uinfo.columns if c != "purpose"]:
         uinfo[col] = uinfo[col].fillna(value=False).astype(bool)
@@ -297,32 +519,14 @@ def _process_normalizations(model_dict, dimensions, labels):
         normalizations[factor] = {}
         norminfo = model_dict["factors"][factor].get("normalizations", {})
         for norm_type in ["loadings", "intercepts"]:
-            candidate = norminfo.get(norm_type, [])
-            candidate = fill_list(candidate, {}, dimensions["n_periods"])
+            candidate = norminfo.get(
+                norm_type, [{} for _ in range(dimensions["n_aug_periods"])]
+            )
+            if not len(candidate) == dimensions["n_aug_periods"]:
+                raise ValueError(
+                    "Normalizations must be of length `n_aug_periods`, "
+                    f"got {norminfo} for {factor}['{norm_type}']"
+                )
             normalizations[factor][norm_type] = candidate
 
     return normalizations
-
-
-def fill_list(short_list, fill_value, length):
-    """Extend a list to specified length by filling it with the fill_value.
-
-    Examples:
-    >>> fill_list(["a"], "b", 3)
-    ['a', 'b', 'b']
-
-    """
-    res = list(short_list)
-    diff = length - len(short_list)
-    assert diff >= 0, "short_list has to be shorter than length."
-    if diff >= 1:
-        res += [fill_value] * diff
-    return res
-
-
-def get_period_measurements(update_info, period):
-    if period in update_info.index:
-        measurements = list(update_info.loc[period].index)
-    else:
-        measurements = []
-    return measurements
diff --git a/src/skillmodels/qr.py b/src/skillmodels/qr.py
new file mode 100644
index 00000000..c690eac7
--- /dev/null
+++ b/src/skillmodels/qr.py
@@ -0,0 +1,70 @@
+import jax
+import jax.numpy as jnp
+
+
+@jax.custom_jvp
+def qr_gpu(a: jax.Array):
+    """Custom implementation of the QR Decomposition."""
+    r, tau = jnp.linalg.qr(a, mode="raw")
+
+    q = _householder(r.mT, tau)
+    return q, jnp.triu(r.mT[: tau.shape[0]])
+
+
+def _householder(r: jax.Array, tau: jax.Array):
+    """Custom implementation of the Householder Product.
+
+    Uses the outputs of jnp.linalg.qr with mode = "raw" to calculate Q. This is needed
+    because the JAX implementation is extremely slow for a batch of small matrices.
+    """
+    m = r.shape[0]
+    n = tau.shape[0]
+    # Calculate Householder Vector which is saved in the lower triangle of R
+    v1 = jnp.expand_dims(r[:, 0], 1)
+    v1 = v1.at[0:0].set(0)
+    v1 = v1.at[0].set(1)
+    h = jnp.eye(m) - tau[0] * (v1 @ jnp.transpose(v1))
+    # Multiply all Householder Vectors Q = H(1)*H(2)...*H(n)
+    for i in range(1, n):
+        vi = jnp.expand_dims(r[:, i], 1)
+        vi = vi.at[0:i].set(0)
+        vi = vi.at[i].set(1)
+        h = h - tau[i] * (h @ vi) @ jnp.transpose(vi)
+    return h[:, :n]
+
+
+def _t(x: jax.Array) -> jax.Array:
+    """Transpose batched Matrix."""
+    return jax.lax.transpose(x, (*range(x.ndim - 2), x.ndim - 1, x.ndim - 2))
+
+
+def _h(x: jax.Array) -> jax.Array:
+    """Hermitian Transpose of a Matrix."""
+    return _t(x).conj()
+
+
+def _tril(m: jax.Array, k: int = 0) -> jax.Array:
+    """Select lower Triangle of a Matrix."""
+    *_, dim_n, dim_m = m.shape
+    mask = jnp.tri(dim_n, dim_m, k, bool)
+    return jax.lax.select(jax.lax.broadcast(mask, m.shape[:-2]), m, jnp.zeros_like(m))
+
+
+@qr_gpu.defjvp
+def qr_jvp_rule(primals, tangents):
+    """Calculates the derivative of the custom QR composition."""
+    # See j-towns.github.io/papers/qr-derivative.pdf for a terse derivation.
+    (x,) = primals
+    (dx,) = tangents
+    q, r = qr_gpu(x)
+    dx_rinv = jax.lax.linalg.triangular_solve(r, dx)  # Right side solve by default
+    qt_dx_rinv = _h(q) @ dx_rinv
+    qt_dx_rinv_lower = _tril(qt_dx_rinv, -1)
+    do = qt_dx_rinv_lower - _h(qt_dx_rinv_lower)  # This is skew-symmetric
+    # The following correction is necessary for complex inputs
+    n = x.shape[-1]
+    i = jax.lax.expand_dims(jnp.eye(n, n), range(qt_dx_rinv.ndim - 2))
+    do = do + i * (qt_dx_rinv - qt_dx_rinv.real.astype(qt_dx_rinv.dtype))
+    dq = q @ (do - qt_dx_rinv) + dx_rinv
+    dr = (qt_dx_rinv - do) @ r
+    return (q, r), (dq, dr)
diff --git a/src/skillmodels/simulate_data.py b/src/skillmodels/simulate_data.py
index 56cfd758..3ae38799 100644
--- a/src/skillmodels/simulate_data.py
+++ b/src/skillmodels/simulate_data.py
@@ -37,7 +37,7 @@ def simulate_dataset(model_dict, params, n_obs=None, data=None, policies=None):
 
     """
     if data is None and n_obs is None:
-        raise ValueError("If data is None, n_obs has to be provided.")
+        raise ValueError("Either `data` or `n_obs` has to be provided.")
 
     model = process_model(model_dict)
 
@@ -50,13 +50,18 @@ def simulate_dataset(model_dict, params, n_obs=None, data=None, policies=None):
         raise ValueError("To simulate a model with controls, data cannot be None.")
 
     if data is not None:
-        control_data, observed_data = process_data(
+        processed_data = process_data(
             df=data,
+            has_endogenous_factors=model["endogenous_factors_info"][
+                "has_endogenous_factors"
+            ],
             labels=model["labels"],
             update_info=model["update_info"],
             anchoring_info=model["anchoring"],
             purpose="simulation",
         )
+        control_data = processed_data["controls"]
+        observed_factors = processed_data["observed_factors"]
         data_n_obs = control_data.shape[1]
 
         if n_obs is not None and data_n_obs != n_obs:
@@ -69,13 +74,14 @@ def simulate_dataset(model_dict, params, n_obs=None, data=None, policies=None):
     else:
         control_data = jnp.ones((n_obs, 1))
         n_periods = model["dimensions"]["n_periods"]
-        observed_data = jnp.zeros((n_periods, n_obs, 0))
+        observed_factors = jnp.zeros((n_periods, n_obs, 0))
 
     params_index = get_params_index(
         update_info=model["update_info"],
         labels=model["labels"],
         dimensions=model["dimensions"],
         transition_info=model["transition_info"],
+        endogenous_factors_info=model["endogenous_factors_info"],
     )
 
     params = params.reindex(params_index)
@@ -85,6 +91,9 @@ def simulate_dataset(model_dict, params, n_obs=None, data=None, policies=None):
         update_info=model["update_info"],
         labels=model["labels"],
         anchoring=model["anchoring"],
+        has_endogenous_factors=model["endogenous_factors_info"][
+            "has_endogenous_factors"
+        ],
     )
 
     states, covs, log_weights, pardict = parse_params(
@@ -95,7 +104,7 @@ def simulate_dataset(model_dict, params, n_obs=None, data=None, policies=None):
         n_obs=n_obs,
     )
 
-    observed_data, latent_data = _simulate_dataset(
+    aug_measurements, aug_latent_data = _simulate_dataset(
         latent_states=states,
         covs=covs,
         log_weights=log_weights,
@@ -103,17 +112,30 @@ def simulate_dataset(model_dict, params, n_obs=None, data=None, policies=None):
         labels=model["labels"],
         dimensions=model["dimensions"],
         n_obs=n_obs,
+        has_endogenous_factors=model["endogenous_factors_info"][
+            "has_endogenous_factors"
+        ],
         update_info=model["update_info"],
         control_data=control_data,
-        observed_factor_data=observed_data,
+        observed_factors=observed_factors,
         policies=policies,
         transition_info=model["transition_info"],
     )
 
+    # Create collapsed versions with user-facing periods
+    latent_data = _collapse_aug_periods_to_periods(
+        df=aug_latent_data,
+        factors=model["labels"]["latent_factors"],
+        aug_periods_to_periods=model["labels"]["aug_periods_to_periods"],
+        endogenous_factors_info=model["endogenous_factors_info"],
+    )
+
+    # Anchor the collapsed version (anchoring only works with period, not aug_period)
     anchored_latent_data = anchor_states_df(
         states_df=latent_data,
         model_dict=model_dict,
         params=params,
+        use_aug_period=False,
     )
 
     out = {
@@ -131,7 +153,14 @@ def simulate_dataset(model_dict, params, n_obs=None, data=None, policies=None):
                 model["labels"]["latent_factors"],
             ),
         },
-        "measurements": observed_data,
+        "aug_unanchored_states": {
+            "states": aug_latent_data,
+            "state_ranges": create_state_ranges(
+                aug_latent_data,
+                model["labels"]["latent_factors"],
+            ),
+        },
+        "aug_measurements": aug_measurements,
     }
 
     return out
@@ -145,9 +174,10 @@ def _simulate_dataset(
     labels,
     dimensions,
     n_obs,
+    has_endogenous_factors,
     update_info,
     control_data,
-    observed_factor_data,
+    observed_factors,
     policies,
     transition_info,
 ):
@@ -163,7 +193,10 @@ def _simulate_dataset(
     policies = policies if policies is not None else []
 
     n_states = dimensions["n_latent_factors"]
-    n_periods = dimensions["n_periods"]
+    if has_endogenous_factors:
+        n_aug_periods = dimensions["n_aug_periods"] - 1
+    else:
+        n_aug_periods = dimensions["n_aug_periods"]
 
     weights = np.exp(log_weights)[0]
     loadings_df = pd.DataFrame(
@@ -193,12 +226,12 @@ def _simulate_dataset(
         }
         dist_args.append(args)
 
-    latent_states = np.zeros((n_periods, n_obs, n_states))
+    latent_states = np.zeros((n_aug_periods, n_obs, n_states))
     latent_states[0] = generate_start_states(n_obs, dimensions, dist_args, weights)
 
-    for t in range(n_periods - 1):
+    for t in range(n_aug_periods - 1):
         # if there is a shock in period t, add it here
-        policies_t = [p for p in policies if p["period"] == t]
+        policies_t = [p for p in policies if p["aug_period"] == t]
         for policy in policies_t:
             position = labels["latent_factors"].index(policy["factor"])
             latent_states[t, :, position] += _get_shock(
@@ -208,7 +241,7 @@ def _simulate_dataset(
             )
 
         # get combined states and observed factors as jax array
-        to_concat = [latent_states[t], observed_factor_data[t]]
+        to_concat = [latent_states[t], observed_factors[t]]
         states = jnp.array(np.concatenate(to_concat, axis=-1))
         # reshaping is just needed for transform sigma points
         states = states.reshape(1, 1, *states.shape)
@@ -245,7 +278,7 @@ def _simulate_dataset(
 
     observed_data_by_period = []
 
-    for t in range(n_periods):
+    for t in range(n_aug_periods):
         meas = pd.DataFrame(
             data=measurements_from_states(
                 latent_states[t],
@@ -256,26 +289,66 @@ def _simulate_dataset(
             ),
             columns=loadings_df.loc[t].index,
         )
-        meas["period"] = t
+        meas["aug_period"] = t
         observed_data_by_period.append(meas)
 
     observed_data = pd.concat(observed_data_by_period, axis=0, sort=True)
     observed_data["id"] = observed_data.index
-    observed_data = observed_data.sort_values(["id", "period"])
+    observed_data = observed_data.sort_values(["id", "aug_period"])
 
     latent_data_by_period = []
-    for t in range(n_periods):
+    for t in range(n_aug_periods):
         lat = pd.DataFrame(data=latent_states[t], columns=labels["latent_factors"])
-        lat["period"] = t
+        lat["aug_period"] = t
         latent_data_by_period.append(lat)
 
     latent_data = pd.concat(latent_data_by_period, axis=0, sort=True)
     latent_data["id"] = latent_data.index
-    latent_data = latent_data.sort_values(["id", "period"])
-
+    latent_data = latent_data.sort_values(["id", "aug_period"])
     return observed_data, latent_data
 
 
+def _collapse_aug_periods_to_periods(
+    df, factors, aug_periods_to_periods, endogenous_factors_info
+):
+    """Collapse dataframe with aug_period index to user-facing period index.
+
+    For each factor, extracts from the appropriate aug_period based on is_endogenous.
+
+    Args:
+        df (pd.DataFrame): DataFrame with columns "aug_period" and "id"
+        latent_factors (list): List of latent factors
+        aug_periods_to_periods (dict): Mapping from aug_period to period
+        endogenous_factors_info (dict): Information about which factors are endogenous
+
+    Returns:
+        pd.DataFrame: DataFrame with "period" column instead of "aug_period"
+    """
+    df = df.copy()
+    if not endogenous_factors_info["has_endogenous_factors"]:
+        return df.rename(columns={"aug_period": "period"})
+
+    df["period"] = df["aug_period"].map(aug_periods_to_periods)
+    df["_aug_period_meas_type"] = df["aug_period"].map(
+        endogenous_factors_info["aug_periods_to_aug_period_meas_types"]
+    )
+
+    endogenous_cols = [
+        fac for fac in factors if endogenous_factors_info[fac]["is_endogenous"]
+    ]
+    state_cols = [fac for fac in factors if fac not in endogenous_cols]
+
+    out = df.query('_aug_period_meas_type == "endogenous_factors"')[
+        ["id", "period", *endogenous_cols]
+    ]
+    return pd.merge(
+        out,
+        df.query('_aug_period_meas_type == "states"')[["id", "period", *state_cols]],
+        on=["id", "period"],
+        how="outer",
+    )
+
+
 def _get_shock(mean, sd, size):
     """Add stochastic effect to a  factor of length n_obs.
 
diff --git a/src/skillmodels/transition_functions.py b/src/skillmodels/transition_functions.py
index cefdb63e..16427076 100644
--- a/src/skillmodels/transition_functions.py
+++ b/src/skillmodels/transition_functions.py
@@ -47,6 +47,22 @@ def params_linear(factors):
     return [*factors, "constant"]
 
 
+def identity_constraints_linear(factor, aug_period, all_factors) -> list[dict]:
+    """Identity constraints for linear transition function."""
+    constraints_dicts = []
+    for regressor in params_linear(all_factors):
+        val = 1.0 if factor == regressor else 0.0
+        constraints_dicts.append(
+            {
+                "loc": ("transition", aug_period, factor, regressor),
+                "type": "fixed",
+                "value": val,
+                "description": "Identity constraint.",
+            }
+        )
+    return constraints_dicts
+
+
 def translog(states, params):
     """Translog transition function.
 
@@ -80,6 +96,22 @@ def params_translog(factors):
     return names
 
 
+def identity_constraints_translog(factor, aug_period, all_factors) -> list[dict]:
+    """Identity constraints for translog transition function."""
+    constraints_dicts = []
+    for regressor in params_translog(all_factors):
+        val = 1.0 if factor == regressor else 0.0
+        constraints_dicts.append(
+            {
+                "loc": ("transition", aug_period, factor, regressor),
+                "type": "fixed",
+                "value": val,
+                "description": "Identity constraint.",
+            }
+        )
+    return constraints_dicts
+
+
 def log_ces(states, params):
     """Log CES production function (KLS version)."""
     phi = params[-1]
@@ -101,12 +133,18 @@ def params_log_ces(factors):
     return [*factors, "phi"]
 
 
-def constraints_log_ces(factor, factors, period):
+def constraints_log_ces(factor, factors, aug_period):
+    """Constraints for log_ces production function."""
     names = params_log_ces(factors)
-    loc = [("transition", period, factor, name) for name in names[:-1]]
+    loc = [("transition", aug_period, factor, name) for name in names[:-1]]
     return {"loc": loc, "type": "probability"}
 
 
+def identity_constraints_log_ces(factors, aug_period, all_factors):
+    """Identity constraints for log_ces."""
+    raise NotImplementedError
+
+
 def constant(state, params):  # noqa: ARG001
     """Constant production function."""
     return state
@@ -137,6 +175,11 @@ def params_robust_translog(factors):
     return params_translog(factors)
 
 
+def identity_constraints_robust_translog(factor, aug_period, all_factors) -> list[dict]:
+    """Identity constraints for robust_translog."""
+    return identity_constraints_translog(factor, aug_period, all_factors)
+
+
 def linear_and_squares(states, params):
     """linear_and_squares transition function."""
     nfac = len(states)
@@ -156,6 +199,24 @@ def params_linear_and_squares(factors):
     return names
 
 
+def identity_constraints_linear_and_squares(
+    factor, aug_period, all_factors
+) -> list[dict]:
+    """Identity constraints for linear_and_squares transition function."""
+    constraints_dicts = []
+    for regressor in params_linear_and_squares(all_factors):
+        val = 1.0 if factor == regressor else 0.0
+        constraints_dicts.append(
+            {
+                "loc": ("transition", aug_period, factor, regressor),
+                "type": "fixed",
+                "value": val,
+                "description": "Identity constraint.",
+            }
+        )
+    return constraints_dicts
+
+
 def log_ces_general(states, params):
     """Generalized log_ces production function without known location and scale."""
     n = states.shape[-1]
@@ -176,3 +237,8 @@ def log_ces_general(states, params):
 def params_log_ces_general(factors):
     """Index tuples for the generalized log_ces production function."""
     return factors + [f"sigma_{fac}" for fac in factors] + ["tfp"]
+
+
+def identity_constraints_log_ces_general(factors, aug_period, all_factors):
+    """Identity constraints for log_ces_general."""
+    raise NotImplementedError
diff --git a/src/skillmodels/utilities.py b/src/skillmodels/utilities.py
index a811f7af..dd4f385b 100644
--- a/src/skillmodels/utilities.py
+++ b/src/skillmodels/utilities.py
@@ -5,7 +5,11 @@
 import pandas as pd
 
 from skillmodels.params_index import get_params_index
-from skillmodels.process_model import get_dimensions, process_model
+from skillmodels.process_model import (
+    get_dimensions,
+    get_has_endogenous_factors,
+    process_model,
+)
 
 
 def extract_factors(factors, model_dict, params=None):
@@ -81,6 +85,9 @@ def remove_factors(factors, model_dict, params=None):
         pandas.DataFrame: The reduced parameter DataFrame (only if params is not None)
 
     """
+    # We need this for the full model when endogenous factors are present.
+    has_endogenous_factors = get_has_endogenous_factors(model_dict["factors"])
+
     out = deepcopy(model_dict)
 
     out["factors"] = _remove_from_dict(out["factors"], factors)
@@ -94,12 +101,14 @@ def remove_factors(factors, model_dict, params=None):
         if out["anchoring"]["outcomes"] == {}:
             out = _remove_from_dict(out, "anchoring")
 
-    # Remove periods if necessary
-    new_n_periods = get_dimensions(out)["n_periods"]
-    out = reduce_n_periods(out, new_n_periods)
+    # Remove periods if necessary, but only if no endogenous factors are present.
+    # (else we would mess up the mapping between raw periods model periods)
+    if not has_endogenous_factors:
+        new_n_periods = get_dimensions(out, has_endogenous_factors)["n_periods"]
+        out = reduce_n_periods(out, new_n_periods)
 
     if params is not None:
-        out_params = _reduce_params(params, out)
+        out_params = _reduce_params(params, out, has_endogenous_factors)
         out = (out, out_params)
 
     return out
@@ -145,7 +154,8 @@ def remove_measurements(measurements, model_dict, params=None):
             )
 
     if params is not None:
-        out_params = _reduce_params(params, out)
+        # This likely won't work if we have endogenous factors.
+        out_params = _reduce_params(params, out, has_endogenous_factors=False)
         out = (out, out_params)
 
     return out
@@ -172,7 +182,8 @@ def remove_controls(controls, model_dict, params=None):
         out = _remove_from_dict(out, "controls")
 
     if params is not None:
-        out_params = _reduce_params(params, out)
+        # This likely won't work if we have endogenous factors.
+        out_params = _reduce_params(params, out, has_endogenous_factors=False)
         out = (out, out_params)
 
     return out
@@ -198,7 +209,8 @@ def switch_translog_to_linear(model_dict, params=None):
             out["factors"][factor]["transition_function"] = "linear"
 
     if params is not None:
-        out_params = _reduce_params(params, out)
+        # This likely won't work if we have endogenous factors.
+        out_params = _reduce_params(params, out, has_endogenous_factors=False)
         out = (out, out_params)
 
     return out
@@ -286,7 +298,7 @@ def _remove_from_dict(dict_, to_remove):
     return {key: val for key, val in dict_.items() if key not in to_remove}
 
 
-def _reduce_params(params, model_dict):
+def _reduce_params(params, model_dict, has_endogenous_factors):
     """Reduce a parameter DataFrame from a larger model to a reduced model.
 
     The reduced model must be nested in the original model for which the params
@@ -295,14 +307,25 @@ def _reduce_params(params, model_dict):
     Args:
         params (pandas.DataFrame or None): The params DataFrame for the full model.
         model_dict (dict): The model specification. See: :ref:`model_specs`.
+        has_endogenous_factors (bool): Whether the model has endogenous factors.
 
     Returns:
         pandas.DataFrame: The reduced parameters DataFrame.
 
     """
     index = _get_params_index_from_model_dict(model_dict)
-    out = params.loc[index]
-    return out
+    # If we have endogenous factors, we need to keep the periods from params.
+    if has_endogenous_factors:
+        df = pd.merge(
+            left=params.reset_index(),
+            right=index.to_frame(index=False)[
+                ["category", "name1", "name2"]
+            ].drop_duplicates(),
+            on=["category", "name1", "name2"],
+            how="right",
+        )
+        index = pd.MultiIndex.from_frame(df[params.index.names])
+    return params.loc[index]
 
 
 def _extend_params(params, model_dict, fill_value):
@@ -325,6 +348,7 @@ def _get_params_index_from_model_dict(model_dict):
         labels=mod["labels"],
         dimensions=mod["dimensions"],
         transition_info=mod["transition_info"],
+        endogenous_factors_info=mod["endogenous_factors_info"],
     )
     return index
 
diff --git a/src/skillmodels/visualize_factor_distributions.py b/src/skillmodels/visualize_factor_distributions.py
index e5cfc3ba..54e6dff8 100644
--- a/src/skillmodels/visualize_factor_distributions.py
+++ b/src/skillmodels/visualize_factor_distributions.py
@@ -217,7 +217,13 @@ def univariate_densities(
         observed_factors=observed_factors,
     )
     observed_states = _get_data_observed_factors(data, factors)
-    df = _process_data(states, period, factors, observed_states)
+    df = _process_data(
+        states=states,
+        period=period,
+        factors=factors,
+        aug_periods_to_periods=model["labels"]["aug_periods_to_periods"],
+        observed_states=observed_states,
+    )
     scenarios = df["scenario"].unique()
     plots_dict = {}
     distplot_kwargs = _process_distplot_kwargs(
@@ -322,7 +328,13 @@ def bivariate_density_contours(
         observed_factors=observed_factors,
     )
     observed_states = _get_data_observed_factors(data=data, factors=factors)
-    df = _process_data(states, period, factors, observed_states)
+    df = _process_data(
+        states=states,
+        period=period,
+        factors=factors,
+        aug_periods_to_periods=model["labels"]["aug_periods_to_periods"],
+        observed_states=observed_states,
+    )
     plots_dict = {}
     contour_kwargs = _process_contour_kwargs(
         contour_kwargs,
@@ -441,7 +453,13 @@ def bivariate_density_surfaces(
         observed_factors=observed_factors,
     )
     observed_states = _get_data_observed_factors(data, factors)
-    df = _process_data(states, period, factors, observed_states)
+    df = _process_data(
+        states=states,
+        period=period,
+        factors=factors,
+        aug_periods_to_periods=model["labels"]["aug_periods_to_periods"],
+        observed_states=observed_states,
+    )
     plots_dict = {}
     layout_kwargs = _process_layout_kwargs_3d(
         layout_kwargs,
@@ -486,12 +504,22 @@ def bivariate_density_surfaces(
     return plots_dict
 
 
-def _process_data(states, period, factors, observed_states=None):
+def _process_data(
+    states, period, factors, aug_periods_to_periods, observed_states=None
+):
+    ap_to_p = pd.Series(aug_periods_to_periods, name="period")
+    ap_to_p.index.name = "aug_period"
     if isinstance(states, pd.DataFrame):
+        one_state_per_period = (
+            states.merge(ap_to_p, left_on="aug_period", right_index=True, how="left")
+            .sort_values(["aug_period", "id"])
+            .groupby(["period", "id"])
+            .last()
+        )
         to_concat = []
         for fac in factors:
-            if fac in states:
-                to_concat.append(states.query(f"period == {period}")[fac])
+            if fac in one_state_per_period:
+                to_concat.append(one_state_per_period.query(f"period == {period}")[fac])
         data = pd.concat(to_concat, axis=1)
         data["scenario"] = "none"
     else:
@@ -499,12 +527,19 @@ def _process_data(states, period, factors, observed_states=None):
             states = dict(enumerate(states))
         to_concat = []
         for name, df in states.items():
-            to_keep = df.query(f"period == {period}")[factors].copy()
+            one_state_per_period = (
+                df.merge(ap_to_p, left_on="aug_period", right_index=True, how="left")
+                .sort_values(["aug_period", "id"])
+                .groupby(["period", "id"])
+                .last()
+            )
+            to_keep = one_state_per_period.query(f"period == {period}")[factors].copy()
             to_keep["scenario"] = name
             to_concat.append(to_keep)
         data = pd.concat(to_concat)
     data = data.reset_index()
     if observed_states is not None:
+        # Not sure whether this will continue to work... But no test case right now.
         data = pd.concat(
             [data, observed_states.query(f"period == {period}").reset_index()],
             axis=1,
diff --git a/src/skillmodels/visualize_transition_equations.py b/src/skillmodels/visualize_transition_equations.py
index c80f58cd..4dc5304b 100644
--- a/src/skillmodels/visualize_transition_equations.py
+++ b/src/skillmodels/visualize_transition_equations.py
@@ -141,6 +141,7 @@ def get_transition_plots(
     n_draws=50,
     colorscale="Magenta_r",
     layout_kwargs=None,
+    include_correction_factors=False,
 ):
     """Get dictionary with individual plots of transition equations for each factor.
 
@@ -163,6 +164,8 @@ def get_transition_plots(
         layout_kwargs (dict or NoneType): Dictionary of key word arguments used to
             update layout of plotly image object. If None, the default kwargs
             defined in the function will be used.
+        include_correction_factors (bool): Whether to include correction factors in the
+            plots. Default False.
 
     Returns:
         plots_dict (dict): Dictionary with individual plots of transition equations
@@ -180,25 +183,35 @@ def get_transition_plots(
             "*period* must be the penultimate period of the model or earlier.",
         )
 
-    latent_factors = model["labels"]["latent_factors"]
+    if (
+        include_correction_factors
+        or not model["endogenous_factors_info"]["has_endogenous_factors"]
+    ):
+        latent_factors = model["labels"]["latent_factors"]
+    else:
+        latent_factors = [
+            lf
+            for lf in model["labels"]["latent_factors"]
+            if not model["endogenous_factors_info"][lf]["is_correction"]
+        ]
     all_factors = model["labels"]["all_factors"]
     states = get_filtered_states(model_dict=model_dict, data=data, params=params)[
         "anchored_states"
     ]["states"]
     plots_dict = _get_dictionary_with_plots(
-        model,
-        data,
-        params,
-        states,
-        state_ranges,
-        latent_factors,
-        all_factors,
-        quantiles_of_other_factors,
-        period,
-        n_points,
-        n_draws,
-        colorscale,
-        layout_kwargs,
+        model=model,
+        data=data,
+        params=params,
+        states=states,
+        state_ranges=state_ranges,
+        latent_factors=latent_factors,
+        all_factors=all_factors,
+        quantiles_of_other_factors=quantiles_of_other_factors,
+        period=period,
+        n_points=n_points,
+        n_draws=n_draws,
+        colorscale=colorscale,
+        layout_kwargs=layout_kwargs,
     )
     return plots_dict
 
@@ -237,7 +250,7 @@ def _get_dictionary_with_plots(
 
         latent_factors (list): Latent factors of the model that are outputs of
             transition factors.
-        all_factors (list): All factors of the model that are the inuts of transition
+        all_factors (list): All factors of the model that are the inputs of transition
             functions.
         quantiles_of_other_factors (float, list or None): Quantiles at which the factors
             that are not varied in a given plot are fixed. If None, those factors are
@@ -268,24 +281,38 @@ def _get_dictionary_with_plots(
         title_kwargs=None,
         showlegend=showlegend,
     )
+    has_endogenous_factors = model["endogenous_factors_info"]["has_endogenous_factors"]
+    if has_endogenous_factors:
+        _aug_periods = model["endogenous_factors_info"]["aug_periods_from_period"](
+            period
+        )
+    else:
+        _aug_periods = [period]
     plots_dict = {}
     for output_factor, input_factor in itertools.product(latent_factors, all_factors):
         transition_function = model["transition_info"]["individual_functions"][
             output_factor
         ]
+        if (
+            has_endogenous_factors
+            and model["endogenous_factors_info"][output_factor]["is_endogenous"]
+        ):
+            aug_period = min(_aug_periods)
+        else:
+            aug_period = max(_aug_periods)
         transition_params = {
-            output_factor: pardict["transition"][output_factor][period],
+            output_factor: pardict["transition"][output_factor][aug_period]
         }
 
         if quantiles_of_other_factors is not None:
             plot_data = _prepare_data_for_one_plot_fixed_quantile_2d(
                 states_data=states_data,
                 state_ranges=state_ranges,
-                period=period,
+                aug_period=aug_period,
                 input_factor=input_factor,
                 output_factor=output_factor,
-                quantiles_of_other_factors=quantiles_of_other_factors,
                 n_points=n_points,
+                quantiles_of_other_factors=quantiles_of_other_factors,
                 transition_function=transition_function,
                 transition_params=transition_params,
                 all_factors=all_factors,
@@ -295,7 +322,7 @@ def _get_dictionary_with_plots(
             plot_data = _prepare_data_for_one_plot_average_2d(
                 states_data=states_data,
                 state_ranges=state_ranges,
-                period=period,
+                aug_period=aug_period,
                 input_factor=input_factor,
                 output_factor=output_factor,
                 n_points=n_points,
@@ -341,6 +368,9 @@ def _get_pardict(model, params):
         update_info=model["update_info"],
         labels=model["labels"],
         anchoring=model["anchoring"],
+        has_endogenous_factors=model["endogenous_factors_info"][
+            "has_endogenous_factors"
+        ],
     )
 
     _, _, _, pardict = parse_params(
@@ -360,6 +390,7 @@ def _set_index_params(model, params):
         labels=model["labels"],
         dimensions=model["dimensions"],
         transition_info=model["transition_info"],
+        endogenous_factors_info=model["endogenous_factors_info"],
     )
 
     params = params.reindex(params_index)
@@ -369,30 +400,51 @@ def _set_index_params(model, params):
 def _get_states_data(model, period, data, states, observed_factors):
     if observed_factors and data is None:
         raise ValueError(
-            """The model has observed factors. You must pass the empirical data to
-        'visualize_transition_equations' via the keyword *data*.""",
+            "The model has observed factors. You must pass the empirical data to "
+            "'visualize_transition_equations' via the keyword *data*.",
         )
 
     if observed_factors:
-        _, _, _observed_arr = process_data(
+        _observed_arr = process_data(
             df=data,
+            has_endogenous_factors=model["endogenous_factors_info"][
+                "has_endogenous_factors"
+            ],
             labels=model["labels"],
             update_info=model["update_info"],
             anchoring_info=model["anchoring"],
-        )
+        )["observed_factors"]
         # convert from jax to numpy
         _observed_arr = np.array(_observed_arr)
-        observed_data = pd.DataFrame(
-            data=_observed_arr[period],
-            columns=observed_factors,
-        )
-        observed_data["id"] = observed_data.index
-        observed_data["period"] = period
+        if model["endogenous_factors_info"]["has_endogenous_factors"]:
+            both_aug_periods = [
+                aug_p
+                for aug_p, p in model["labels"]["aug_periods_to_periods"].items()
+                if p == period
+            ]
+            to_concat = []
+            for aug_p in both_aug_periods:
+                df = pd.DataFrame(
+                    data=_observed_arr[aug_p],
+                    columns=observed_factors,
+                )
+                df["id"] = df.index
+                df["aug_period"] = aug_p
+                to_concat.append(df)
+            observed_data = pd.concat(to_concat)
+        else:
+            observed_data = pd.DataFrame(
+                data=_observed_arr[period],
+                columns=observed_factors,
+            )
+            observed_data["id"] = observed_data.index
+            observed_data["aug_period"] = period
+        # Do a left merge because we need all periods for the ranges
         states_data = pd.merge(
             left=states,
             right=observed_data,
-            left_on=["id", "period"],
-            right_on=["id", "period"],
+            left_on=["id", "aug_period"],
+            right_on=["id", "aug_period"],
             how="left",
         )
     else:
@@ -403,18 +455,18 @@ def _get_states_data(model, period, data, states, observed_factors):
 def _prepare_data_for_one_plot_fixed_quantile_2d(
     states_data,
     state_ranges,
-    period,
+    aug_period,
     input_factor,
     output_factor,
-    quantiles_of_other_factors,
     n_points,
+    quantiles_of_other_factors,
     transition_function,
     transition_params,
     all_factors,
 ):
-    period_data = states_data.query(f"period == {period}")[all_factors]
-    input_min = state_ranges[input_factor].loc[period]["minimum"]
-    input_max = state_ranges[input_factor].loc[period]["maximum"]
+    period_data = states_data.query(f"aug_period == {aug_period}")[all_factors]
+    input_min = state_ranges[input_factor].loc[aug_period]["minimum"]
+    input_max = state_ranges[input_factor].loc[aug_period]["maximum"]
     to_concat = []
     for quantile in quantiles_of_other_factors:
         input_data = pd.DataFrame()
@@ -447,7 +499,7 @@ def _process_quantiles_of_other_factors(quantiles_of_other_factors):
 def _prepare_data_for_one_plot_average_2d(
     states_data,
     state_ranges,
-    period,
+    aug_period,
     input_factor,
     output_factor,
     n_points,
@@ -456,12 +508,12 @@ def _prepare_data_for_one_plot_average_2d(
     transition_params,
     all_factors,
 ):
-    period_data = states_data.query(f"period == {period}")[all_factors].reset_index()
+    period_data = states_data.query(f"aug_period == {aug_period}")
 
     sampled_factors = [factor for factor in all_factors if factor != input_factor]
     draws = period_data[sampled_factors].sample(n=n_draws)
-    input_min = state_ranges[input_factor].loc[period]["minimum"]
-    input_max = state_ranges[input_factor].loc[period]["maximum"]
+    input_min = state_ranges[input_factor].loc[aug_period]["minimum"]
+    input_max = state_ranges[input_factor].loc[aug_period]["maximum"]
 
     to_concat = []
     for _, draw in draws.iterrows():
diff --git a/tests/model2.yaml b/tests/model2.yaml
index 5cfd872e..3b80ca3d 100644
--- a/tests/model2.yaml
+++ b/tests/model2.yaml
@@ -45,10 +45,24 @@ factors:
   fac3:
     measurements:
       - [y7, y8, y9]
+      - []
+      - []
+      - []
+      - []
+      - []
+      - []
+      - []
     transition_function: constant
     normalizations:
       loadings:
         - {y7: 1}
+        - {}
+        - {}
+        - {}
+        - {}
+        - {}
+        - {}
+        - {}
 anchoring:
   outcomes: {fac1: Q1}
   free_controls: true
diff --git a/tests/model2_correct_update_info.csv b/tests/model2_correct_update_info.csv
index de382ca8..4f1771ce 100644
--- a/tests/model2_correct_update_info.csv
+++ b/tests/model2_correct_update_info.csv
@@ -1,4 +1,4 @@
-period,variable,fac1,fac2,fac3,purpose
+aug_period,variable,fac1,fac2,fac3,purpose
 0,y1,True,False,False,measurement
 0,y2,True,False,False,measurement
 0,y3,True,False,False,measurement
diff --git a/tests/model2_with_endog_correct_update_info.csv b/tests/model2_with_endog_correct_update_info.csv
new file mode 100644
index 00000000..05ae7973
--- /dev/null
+++ b/tests/model2_with_endog_correct_update_info.csv
@@ -0,0 +1,52 @@
+aug_period,variable,fac1,fac2,fac3,purpose
+0,y1,True,False,False,measurement
+0,y2,True,False,False,measurement
+0,y3,True,False,False,measurement
+0,y4,False,True,False,measurement
+0,y5,False,True,False,measurement
+0,y6,False,True,False,measurement
+1,y7,False,False,True,measurement
+1,y8,False,False,True,measurement
+1,y9,False,False,True,measurement
+2,y1,True,False,False,measurement
+2,y2,True,False,False,measurement
+2,y3,True,False,False,measurement
+2,y4,False,True,False,measurement
+2,y5,False,True,False,measurement
+2,y6,False,True,False,measurement
+4,y1,True,False,False,measurement
+4,y2,True,False,False,measurement
+4,y3,True,False,False,measurement
+4,y4,False,True,False,measurement
+4,y5,False,True,False,measurement
+4,y6,False,True,False,measurement
+6,y1,True,False,False,measurement
+6,y2,True,False,False,measurement
+6,y3,True,False,False,measurement
+6,y4,False,True,False,measurement
+6,y5,False,True,False,measurement
+6,y6,False,True,False,measurement
+8,y1,True,False,False,measurement
+8,y2,True,False,False,measurement
+8,y3,True,False,False,measurement
+8,y4,False,True,False,measurement
+8,y5,False,True,False,measurement
+8,y6,False,True,False,measurement
+10,y1,True,False,False,measurement
+10,y2,True,False,False,measurement
+10,y3,True,False,False,measurement
+10,y4,False,True,False,measurement
+10,y5,False,True,False,measurement
+10,y6,False,True,False,measurement
+12,y1,True,False,False,measurement
+12,y2,True,False,False,measurement
+12,y3,True,False,False,measurement
+12,y4,False,True,False,measurement
+12,y5,False,True,False,measurement
+12,y6,False,True,False,measurement
+14,y1,True,False,False,measurement
+14,y2,True,False,False,measurement
+14,y3,True,False,False,measurement
+14,y4,False,True,False,measurement
+14,y5,False,True,False,measurement
+14,y6,False,True,False,measurement
diff --git a/tests/simplest_augmented_data_expected.csv b/tests/simplest_augmented_data_expected.csv
new file mode 100644
index 00000000..aab98d2f
--- /dev/null
+++ b/tests/simplest_augmented_data_expected.csv
@@ -0,0 +1,13 @@
+id,aug_period,constant,var,inv,of
+0,0,1,0.0,,10.0
+0,1,1,,5.0,10.0
+0,2,1,,,
+0,3,1,,,
+1,0,1,1.0,,11.0
+1,1,1,,6.0,11.0
+1,2,1,2.0,,12.0
+1,3,1,,7.0,12.0
+2,0,1,3.0,,13.0
+2,1,1,,8.0,13.0
+2,2,1,4.0,,14.0
+2,3,1,,9.0,14.0
diff --git a/tests/simplest_augmented_model.yaml b/tests/simplest_augmented_model.yaml
new file mode 100644
index 00000000..04e892b4
--- /dev/null
+++ b/tests/simplest_augmented_model.yaml
@@ -0,0 +1,28 @@
+---
+factors:
+  fac1:
+    is_correction: false
+    is_endogenous: false
+    measurements:
+      -   - var
+      -   - var
+    normalizations:
+      loadings:
+        - {var: 1}
+        - {var: 1}
+    transition_function: linear
+  fac2:
+    is_correction: false
+    is_endogenous: true
+    measurements:
+      -   - inv
+      -   - inv
+    normalizations:
+      loadings:
+        - {inv: 1}
+        - {inv: 1}
+    transition_function: linear
+observed_factors:
+  - of
+estimation_options:
+  bounds_distance: 0.00000001
diff --git a/tests/test_constraints.py b/tests/test_constraints.py
index c31c89ee..ca3bb103 100644
--- a/tests/test_constraints.py
+++ b/tests/test_constraints.py
@@ -1,11 +1,15 @@
+from pathlib import Path
+
 import numpy as np
 import pandas as pd
 import pytest
+import yaml
 from pandas.testing import assert_frame_equal
 
 from skillmodels.constraints import (
     _get_anchoring_constraints,
     _get_constant_factors_constraints,
+    _get_constraints_for_augmented_periods,
     _get_initial_states_constraints,
     _get_mixture_weights_constraints,
     _get_normalization_constraints,
@@ -13,6 +17,10 @@
     _get_transition_constraints,
     add_bounds,
 )
+from skillmodels.process_model import process_model
+
+# importing the TEST_DIR from config does not work for test run in conda build
+TEST_DIR = Path(__file__).parent.resolve()
 
 
 def test_add_bounds():
@@ -28,6 +36,7 @@ def test_add_bounds():
     )
     expected = df.copy(deep=True)
     expected["lower_bound"] = [0.1] * 5 + [0.1, -np.inf, 0.1, -np.inf, 0.1]
+    expected["upper_bound"] = np.inf
 
     calculated = add_bounds(df, 0.1)
     assert_frame_equal(calculated, expected)
@@ -49,15 +58,29 @@ def test_normalization_constraints():
 
     expected = [
         {
-            "loc": [
-                ("loadings", 0, "m1", "fac1"),
-                ("loadings", 0, "m2", "fac1"),
-                ("controls", 0, "m1", "constant"),
-                ("loadings", 1, "m1", "fac1"),
-                ("loadings", 0, "m3", "fac2"),
-            ],
+            "loc": ("loadings", 0, "m1", "fac1"),
+            "type": "fixed",
+            "value": 2,
+        },
+        {
+            "loc": ("loadings", 0, "m2", "fac1"),
+            "type": "fixed",
+            "value": 1.5,
+        },
+        {
+            "loc": ("controls", 0, "m1", "constant"),
+            "type": "fixed",
+            "value": 0.5,
+        },
+        {
+            "loc": ("loadings", 1, "m1", "fac1"),
             "type": "fixed",
-            "value": [2, 1.5, 0.5, 3, 1],
+            "value": 3,
+        },
+        {
+            "loc": ("loadings", 0, "m3", "fac2"),
+            "type": "fixed",
+            "value": 1,
         },
     ]
 
@@ -100,16 +123,44 @@ def test_stage_constraints():
 
     expected = [
         {
-            "locs": [("transition", 0), ("transition", 1), ("transition", 2)],
+            "loc": [("transition", 0), ("transition", 1), ("transition", 2)],
             "type": "pairwise_equality",
         },
         {
-            "locs": [("shock_sds", 0), ("shock_sds", 1), ("shock_sds", 2)],
+            "loc": [("shock_sds", 0), ("shock_sds", 1), ("shock_sds", 2)],
             "type": "pairwise_equality",
         },
     ]
 
-    calculated = _get_stage_constraints(stagemap, stages)
+    calculated = _get_stage_constraints(stagemap=stagemap, stages=stages)
+    for c in calculated:
+        del c["description"]
+    assert_list_equal_except_for_order(calculated, expected)
+
+
+def test_stage_constraints_with_endogenous_factors():
+    stages = [0, 1, 2, 3]
+    stagemap = [0, 1, 0, 1, 2, 3]
+    expected = [
+        {
+            "loc": [("transition", 0), ("transition", 2)],
+            "type": "pairwise_equality",
+        },
+        {
+            "loc": [("transition", 1), ("transition", 3)],
+            "type": "pairwise_equality",
+        },
+        {
+            "loc": [("shock_sds", 0), ("shock_sds", 2)],
+            "type": "pairwise_equality",
+        },
+        {
+            "loc": [("shock_sds", 1), ("shock_sds", 3)],
+            "type": "pairwise_equality",
+        },
+    ]
+
+    calculated = _get_stage_constraints(stagemap=stagemap, stages=stages)
     for c in calculated:
         del c["description"]
     assert_list_equal_except_for_order(calculated, expected)
@@ -123,7 +174,7 @@ def test_stage_constraints():
 def test_constant_factor_constraints():
     labels = {
         "latent_factors": ["fac1", "fac2"],
-        "periods": [0, 1, 2],
+        "aug_periods": [0, 1, 2],
         "transition_names": ["bla", "constant"],
     }
 
@@ -169,7 +220,7 @@ def test_trans_coeff_constraints():
     labels = {
         "latent_factors": ["fac1", "fac2", "fac3"],
         "transition_names": ["log_ces", "bla", "blubb"],
-        "periods": [0, 1, 2],
+        "aug_periods": [0, 1, 2],
     }
     labels["all_factors"] = labels["latent_factors"]
 
@@ -265,8 +316,8 @@ def test_anchoring_constraints_for_controls(anch_uinfo, base_anchoring_info):
         (0, 1),
     )
 
-    for constr in calculated:
-        del constr["description"]
+    for c_t in calculated:
+        del c_t["description"]
 
     expected = [
         {
@@ -305,17 +356,51 @@ def test_anchoring_constraints_for_loadings(anch_uinfo, base_anchoring_info):
         },
     ]
 
-    for constr in calculated:
-        del constr["description"]
+    for c_t in calculated:
+        del c_t["description"]
 
     assert calculated == expected
 
 
-# ======================================================================================
-
-
 def assert_list_equal_except_for_order(list1, list2):
     for item in list1:
         assert item in list2, f"{item} is in list1 but not in list2"
     for item in list2:
         assert item in list1, f"{item} is in list2 but not in list1"
+
+
+@pytest.fixture
+def simplest_augmented_model():
+    with open(TEST_DIR / "simplest_augmented_model.yaml") as y:
+        model_dict = yaml.load(y, Loader=yaml.FullLoader)
+    return process_model(model_dict)
+
+
+def test_get_constraints_for_augmented_periods(simplest_augmented_model):
+    calculated = _get_constraints_for_augmented_periods(
+        labels=simplest_augmented_model["labels"],
+        endogenous_factors_info=simplest_augmented_model["endogenous_factors_info"],
+    )
+    for c in calculated:
+        del c["description"]
+    expected = [
+        {"loc": ("transition", 0, "fac1", "fac1"), "type": "fixed", "value": 1.0},
+        {"loc": ("transition", 0, "fac1", "fac2"), "type": "fixed", "value": 0.0},
+        {"loc": ("transition", 0, "fac1", "of"), "type": "fixed", "value": 0.0},
+        {"loc": ("transition", 0, "fac1", "constant"), "type": "fixed", "value": 0.0},
+        {"loc": ("shock_sds", 0, "fac1", "-"), "type": "fixed", "value": 0.00000001},
+        {"loc": ("transition", 2, "fac1", "fac1"), "type": "fixed", "value": 1.0},
+        {"loc": ("transition", 2, "fac1", "fac2"), "type": "fixed", "value": 0.0},
+        {"loc": ("transition", 2, "fac1", "of"), "type": "fixed", "value": 0.0},
+        {"loc": ("transition", 2, "fac1", "constant"), "type": "fixed", "value": 0.0},
+        {"loc": ("transition", 1, "fac2", "fac1"), "type": "fixed", "value": 0.0},
+        {"loc": ("transition", 1, "fac2", "fac2"), "type": "fixed", "value": 1.0},
+        {"loc": ("transition", 1, "fac2", "of"), "type": "fixed", "value": 0.0},
+        {"loc": ("transition", 1, "fac2", "constant"), "type": "fixed", "value": 0.0},
+        {"loc": ("shock_sds", 1, "fac2", "-"), "type": "fixed", "value": 0.00000001},
+        {"loc": ("transition", 3, "fac2", "fac1"), "type": "fixed", "value": 0.0},
+        {"loc": ("transition", 3, "fac2", "fac2"), "type": "fixed", "value": 1.0},
+        {"loc": ("transition", 3, "fac2", "of"), "type": "fixed", "value": 0.0},
+        {"loc": ("transition", 3, "fac2", "constant"), "type": "fixed", "value": 0.0},
+    ]
+    assert_list_equal_except_for_order(calculated, expected)
diff --git a/tests/test_likelihood_regression.py b/tests/test_likelihood_regression.py
index f973acf4..cd4cbc02 100644
--- a/tests/test_likelihood_regression.py
+++ b/tests/test_likelihood_regression.py
@@ -92,6 +92,19 @@ def test_likelihood_values_have_not_changed(model2, model2_data, model_name, fun
     aaae(new_loglike, old_loglike)
 
 
+def test_splitting_does_not_change_gradient(model2, model2_data):
+    inputs = get_maximization_inputs(model2, model2_data)
+    inputs_split = get_maximization_inputs(model2, model2_data, 13)
+
+    params = inputs["params_template"]
+    params["value"] = 0.1
+
+    _, gradient = inputs["loglike_and_gradient"](params)
+    _, gradient_split = inputs_split["loglike_and_gradient"](params)
+
+    aaae(gradient, gradient_split)
+
+
 @pytest.mark.parametrize(
     ("model_name", "fun_key"), product(MODEL_NAMES, ["loglikeobs"])
 )
diff --git a/tests/test_params_index.py b/tests/test_params_index.py
index e6f0bfee..9e10d61f 100644
--- a/tests/test_params_index.py
+++ b/tests/test_params_index.py
@@ -30,6 +30,7 @@ def model2_inputs():
         "labels": processed["labels"],
         "dimensions": processed["dimensions"],
         "transition_info": processed["transition_info"],
+        "endogenous_factors_info": processed["endogenous_factors_info"],
     }
     return out
 
@@ -119,7 +120,7 @@ def test_shock_sd_index_tuples():
         ("shock_sds", 1, "fac2", "-"),
     ]
 
-    calculated = get_shock_sds_index_tuples(periods, factors)
+    calculated = get_shock_sds_index_tuples(periods, factors, False)
     assert calculated == expected
 
 
@@ -173,7 +174,7 @@ def test_initial_cov_index_tuples():
     assert calculated == expected
 
 
-def test_trans_coeffs_index_tuples():
+def test_trans_coeffs_index_tuples_no_endogenous_factors():
     periods = [0, 1, 2]
 
     param_names = {
@@ -202,6 +203,64 @@ def test_trans_coeffs_index_tuples():
         ("transition", 1, "fac3", "phi"),
     ]
 
-    calculated = get_transition_index_tuples(trans_info, periods)
+    calculated = get_transition_index_tuples(
+        transition_info=trans_info,
+        aug_periods=periods,
+        has_endogenous_factors=False,
+    )
+
+    assert calculated == expected
+
+
+def test_trans_coeffs_index_tuples_has_endogenous_factors():
+    periods = [0, 1, 2, 3, 4, 5]
+
+    param_names = {
+        "fac1": ["fac1", "fac2", "fac3", "constant"],
+        "fac2": [],
+        "fac3": ["fac1", "fac2", "fac3", "phi"],
+    }
+    trans_info = {"param_names": param_names}
+
+    expected = [
+        ("transition", 0, "fac1", "fac1"),
+        ("transition", 0, "fac1", "fac2"),
+        ("transition", 0, "fac1", "fac3"),
+        ("transition", 0, "fac1", "constant"),
+        ("transition", 1, "fac1", "fac1"),
+        ("transition", 1, "fac1", "fac2"),
+        ("transition", 1, "fac1", "fac3"),
+        ("transition", 1, "fac1", "constant"),
+        ("transition", 2, "fac1", "fac1"),
+        ("transition", 2, "fac1", "fac2"),
+        ("transition", 2, "fac1", "fac3"),
+        ("transition", 2, "fac1", "constant"),
+        ("transition", 3, "fac1", "fac1"),
+        ("transition", 3, "fac1", "fac2"),
+        ("transition", 3, "fac1", "fac3"),
+        ("transition", 3, "fac1", "constant"),
+        ("transition", 0, "fac3", "fac1"),
+        ("transition", 0, "fac3", "fac2"),
+        ("transition", 0, "fac3", "fac3"),
+        ("transition", 0, "fac3", "phi"),
+        ("transition", 1, "fac3", "fac1"),
+        ("transition", 1, "fac3", "fac2"),
+        ("transition", 1, "fac3", "fac3"),
+        ("transition", 1, "fac3", "phi"),
+        ("transition", 2, "fac3", "fac1"),
+        ("transition", 2, "fac3", "fac2"),
+        ("transition", 2, "fac3", "fac3"),
+        ("transition", 2, "fac3", "phi"),
+        ("transition", 3, "fac3", "fac1"),
+        ("transition", 3, "fac3", "fac2"),
+        ("transition", 3, "fac3", "fac3"),
+        ("transition", 3, "fac3", "phi"),
+    ]
+
+    calculated = get_transition_index_tuples(
+        transition_info=trans_info,
+        aug_periods=periods,
+        has_endogenous_factors=True,
+    )
 
     assert calculated == expected
diff --git a/tests/test_parse_params.py b/tests/test_parse_params.py
index 5adef84b..33ffbe88 100644
--- a/tests/test_parse_params.py
+++ b/tests/test_parse_params.py
@@ -38,7 +38,13 @@ def parsed_parameters():
     # more meaningful test
     anchoring = {"ignore_constant_when_anchoring": False}
 
-    parsing_info = create_parsing_info(p_index, update_info, labels, anchoring)
+    parsing_info = create_parsing_info(
+        params_index=p_index,
+        update_info=update_info,
+        labels=labels,
+        anchoring=anchoring,
+        has_endogenous_factors=False,
+    )
 
     params_vec = jnp.arange(len(p_index))
     n_obs = 5
diff --git a/tests/test_process_data.py b/tests/test_process_data.py
index 6584aa40..9450f621 100644
--- a/tests/test_process_data.py
+++ b/tests/test_process_data.py
@@ -1,23 +1,30 @@
 import io
 import textwrap
+from pathlib import Path
 
 import jax.numpy as jnp
 import numpy as np
 import pandas as pd
 import pytest
+import yaml
 from numpy.testing import assert_array_equal as aae
 
 from skillmodels.process_data import (
+    _augment_data_for_endogenous_factors,
     _generate_controls_array,
     _generate_measurements_array,
     _generate_observed_factor_array,
     _handle_controls_with_missings,
     pre_process_data,
 )
+from skillmodels.process_model import process_model
+
+# importing the TEST_DIR from config does not work for test run in conda build
+TEST_DIR = Path(__file__).parent.resolve()
 
 
 def test_pre_process_data():
-    df = pd.DataFrame(data=np.arange(10).reshape(10, 1), columns=["var"])
+    df = pd.DataFrame(data=np.arange(20).reshape(2, 10).T, columns=["var", "inv"])
     df["period"] = [1, 2, 3, 2, 3, 4, 2, 4, 3, 1]
     df["id"] = [1, 1, 1, 3, 3, 3, 4, 4, 5, 5]
     df.set_index(["id", "period"], inplace=True)
@@ -26,14 +33,47 @@ def test_pre_process_data():
     period = [0, 1, 2, 3] * 4
     id_ = np.arange(4).repeat(4)
     nan = np.nan
-    data = [0, 1, 2, nan, nan, 3, 4, 5, nan, 6, nan, 7, 9, nan, 8, nan]
-    data = np.column_stack([period, id_, data])
-    exp = pd.DataFrame(data=data, columns=["__period__", "__id__", "var"])
+    data = {
+        "var": [0, 1, 2, nan, nan, 3, 4, 5, nan, 6, nan, 7, 9, nan, 8, nan],
+        "inv": [10, 11, 12, nan, nan, 13, 14, 15, nan, 16, nan, 17, 19, nan, 18, nan],
+    }
+    data = np.column_stack([period, id_, data["var"], data["inv"]])
+    exp = pd.DataFrame(data=data, columns=["__period__", "__id__", "var", "inv"])
     exp.set_index(["__id__", "__period__"], inplace=True)
 
     res = pre_process_data(df, [0, 1, 2, 3])
-
-    assert res["var"].equals(exp["var"])
+    assert res[["var", "inv"]].equals(exp[["var", "inv"]])
+
+
+@pytest.fixture
+def simplest_augmented():
+    out = {}
+    with open(TEST_DIR / "simplest_augmented_model.yaml") as y:
+        out["model_dict"] = yaml.load(y, Loader=yaml.FullLoader)
+    _df = pd.DataFrame(data=np.arange(15).reshape(3, 5).T, columns=["var", "inv", "of"])
+    _df["period"] = [1, 1, 2, 1, 2]
+    _df["id"] = [1, 3, 3, 5, 5]
+    out["data_input"] = _df.set_index(["id", "period"])
+    out["data_exp"] = pd.read_csv(
+        TEST_DIR / "simplest_augmented_data_expected.csv",
+        index_col=["id", "aug_period"],
+    )
+    return out
+
+
+def test_augment_data_for_endogenous_factors(simplest_augmented):
+    model = process_model(simplest_augmented["model_dict"])
+    pre_processed_data = pre_process_data(
+        simplest_augmented["data_input"], model["labels"]["periods"]
+    )
+    pre_processed_data["constant"] = 1
+    res = _augment_data_for_endogenous_factors(
+        df=pre_processed_data,
+        labels=model["labels"],
+        update_info=model["update_info"],
+    )
+    cols = ["var", "inv", "constant", "of"]
+    pd.testing.assert_frame_equal(res[cols], simplest_augmented["data_exp"][cols])
 
 
 def test_handle_controls_with_missings():
@@ -42,11 +82,11 @@ def test_handle_controls_with_missings():
     update_info = pd.DataFrame(index=pd.MultiIndex.from_tuples(uinfo_ind_tups))
     data = [[1, 1, 1], [np.nan, 1, 1], [np.nan, 1, np.nan], [np.nan, np.nan, np.nan]]
     df = pd.DataFrame(data=data, columns=["m1", "m2", "c1"])
-    df["period"] = 0
+    df["aug_period"] = 0
     df["id"] = np.arange(4)
     df["__old_id__"] = df["id"]
-    df["__old_period__"] = df["period"] + 1
-    df.set_index(["id", "period"], inplace=True)
+    df["__old_period__"] = df["aug_period"] + 1
+    df.set_index(["id", "aug_period"], inplace=True)
 
     with pytest.warns(UserWarning):
         calculated = _handle_controls_with_missings(df, controls, update_info)
@@ -58,13 +98,13 @@ def test_generate_measurements_array():
     update_info = pd.DataFrame(index=pd.MultiIndex.from_tuples(uinfo_ind_tups))
 
     csv = """
-    id,period,m1,m2,m3
+    id,aug_period,m1,m2,m3
     0,0,1,2,3
     0,1,4,5,6
     1,0,7,8,9
     1,1,10,11,12
     """
-    data = _read_csv_string(csv, ["id", "period"])
+    data = _read_csv_string(csv, ["id", "aug_period"])
 
     expected = jnp.array([[1, 7], [2, 8], [4, 10], [6, 12.0]])
 
@@ -74,15 +114,15 @@ def test_generate_measurements_array():
 
 def test_generate_controls_array():
     csv = """
-    id,period,c1,c2
+    id,aug_period,c1,c2
     0, 0, 1, 2
     0, 1, 3, 4
     1, 0, 5, 8
     1, 1, 7, 8
     """
-    data = _read_csv_string(csv, ["id", "period"])
+    data = _read_csv_string(csv, ["id", "aug_period"])
 
-    labels = {"controls": ["c1", "c2"], "periods": [0, 1]}
+    labels = {"controls": ["c1", "c2"], "aug_periods": [0, 1]}
 
     calculated = _generate_controls_array(data, labels, 2)
     expected = jnp.array([[[1, 2], [5, 8]], [[3, 4], [7, 8]]])
@@ -91,15 +131,15 @@ def test_generate_controls_array():
 
 def test_generate_observed_factor_array():
     csv = """
-    id,period,v1,v2
+    id,aug_period,v1,v2
     0, 0, 1, 2
     0, 1, 3, 4
     1, 0, 5, 8
     1, 1, 7, 8
     """
-    data = _read_csv_string(csv, ["id", "period"])
+    data = _read_csv_string(csv, ["id", "aug_period"])
 
-    labels = {"observed_factors": ["v1", "v2"], "periods": [0, 1]}
+    labels = {"observed_factors": ["v1", "v2"], "aug_periods": [0, 1]}
 
     calculated = _generate_observed_factor_array(data, labels, 2)
     expected = jnp.array([[[1, 2], [5, 8]], [[3, 4], [7, 8]]])
diff --git a/tests/test_process_model.py b/tests/test_process_model.py
index c8ea18f3..c7dc796b 100644
--- a/tests/test_process_model.py
+++ b/tests/test_process_model.py
@@ -6,7 +6,7 @@
 import yaml
 from pandas.testing import assert_frame_equal
 
-from skillmodels.process_model import process_model
+from skillmodels.process_model import get_has_endogenous_factors, process_model
 
 # ======================================================================================
 # Integration test with model2 from the replication files of CHS2010
@@ -23,6 +23,13 @@ def model2():
     return model_dict
 
 
+def test_has_endogenous_factors(model2):
+    assert (
+        process_model(model2)["endogenous_factors_info"]["has_endogenous_factors"]
+        == False
+    )
+
+
 def test_dimensions(model2):
     res = process_model(model2)["dimensions"]
     assert res["n_latent_factors"] == 3
@@ -74,7 +81,7 @@ def test_update_info(model2):
     test_dir = Path(__file__).parent.resolve()
     expected = pd.read_csv(
         test_dir / "model2_correct_update_info.csv",
-        index_col=["period", "variable"],
+        index_col=["aug_period", "variable"],
     )
     assert_frame_equal(res, expected)
 
@@ -115,3 +122,283 @@ def test_normalizations(model2):
     res = process_model(model2)["normalizations"]
 
     assert res == expected
+
+
+# ======================================================================================
+# Augment model2 with endogenous factors
+# ======================================================================================
+
+
+def test_anchoring_and_endogenous_factors_conflict():
+    with open(TEST_DIR / "model2.yaml") as y:
+        model_dict = yaml.load(y, Loader=yaml.FullLoader)
+    # Set fac3 to be endogenous
+    model_dict["factors"]["fac3"]["is_endogenous"] = True
+    del model_dict["stagemap"]
+    with pytest.raises(
+        ValueError,
+        match=r"anchoring is not supported when endogenous factors are present.",
+    ):
+        process_model(model_dict)
+
+
+def test_stagemap_with_endogenous_factors_wrong_labels():
+    with open(TEST_DIR / "model2.yaml") as y:
+        model_dict = yaml.load(y, Loader=yaml.FullLoader)
+    # Set fac3 to be endogenous
+    model_dict["factors"]["fac3"]["is_endogenous"] = True
+    model_dict["stagemap"] = [0, 0, 1, 1, 2, 2, 4]
+    del model_dict["anchoring"]
+    with pytest.raises(ValueError, match="Invalid stage map:"):
+        process_model(model_dict)
+
+
+def test_stagemap_with_endogenous_factors():
+    with open(TEST_DIR / "model2.yaml") as y:
+        model_dict = yaml.load(y, Loader=yaml.FullLoader)
+    # Set fac3 to be endogenous
+    model_dict["factors"]["fac3"]["is_endogenous"] = True
+    model_dict["stagemap"] = [0, 0, 1, 1, 2, 2, 3]
+    del model_dict["anchoring"]
+    model = process_model(model_dict)
+    assert model["labels"]["stagemap"] == model_dict["stagemap"]
+    assert model["labels"]["stages"] == [0, 1, 2, 3]
+    assert model["labels"]["aug_stagemap"] == [0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7]
+
+
+@pytest.fixture
+def model2_inv():
+    with open(TEST_DIR / "model2.yaml") as y:
+        model_dict = yaml.load(y, Loader=yaml.FullLoader)
+    # Set fac3 to be endogenous
+    model_dict["factors"]["fac3"]["is_endogenous"] = True
+    del model_dict["stagemap"]
+    del model_dict["anchoring"]
+    return model_dict
+
+
+def test_with_endog_has_endogenous_factors(model2_inv):
+    assert (
+        process_model(model2_inv)["endogenous_factors_info"]["has_endogenous_factors"]
+        == True
+    )
+
+
+def test_with_endog_dimensions(model2_inv):
+    res = process_model(model2_inv)["dimensions"]
+    assert res["n_latent_factors"] == 3
+    assert res["n_observed_factors"] == 0
+    assert res["n_all_factors"] == 3
+    assert res["n_aug_periods"] == 16
+    assert res["n_periods"] == 8
+    assert res["n_controls"] == 2
+    assert res["n_mixtures"] == 1
+
+
+def test_with_endog_labels(model2_inv):
+    res = process_model(model2_inv)["labels"]
+    n_aug_periods = 16
+    assert res["latent_factors"] == ["fac1", "fac2", "fac3"]
+    assert res["observed_factors"] == []
+    assert res["all_factors"] == ["fac1", "fac2", "fac3"]
+    assert res["controls"] == ["constant", "x1"]
+    assert res["aug_periods"] == list(range(n_aug_periods))
+    assert res["periods"] == [0, 1, 2, 3, 4, 5, 6, 7]
+    assert res["aug_stagemap"] == list(range(n_aug_periods - 2))
+    assert res["aug_stages"] == list(range(n_aug_periods - 2))
+
+
+def test_with_endog_estimation_options(model2_inv):
+    res = process_model(model2_inv)["estimation_options"]
+    assert res["sigma_points_scale"] == 2
+    assert res["robust_bounds"]
+    assert res["bounds_distance"] == 0.001
+
+
+def test_with_endog_anchoring_is_empty(model2_inv):
+    res = process_model(model2_inv)["anchoring"]
+    assert res["outcomes"] == {}
+    assert res["factors"] == []
+    assert res["free_controls"] is False
+    assert res["free_constant"] is False
+    assert res["free_loadings"] is False
+
+
+def test_with_endog_transition_info(model2_inv):
+    res = process_model(model2_inv)["transition_info"]
+
+    assert isinstance(res, dict)
+    assert callable(res["func"])
+
+    assert list(inspect.signature(res["func"]).parameters) == ["params", "states"]
+
+
+def test_with_endog_update_info(model2_inv):
+    res = process_model(model2_inv)["update_info"]
+    test_dir = Path(__file__).parent.resolve()
+    expected = pd.read_csv(
+        test_dir / "model2_with_endog_correct_update_info.csv",
+        index_col=["aug_period", "variable"],
+    )
+    assert_frame_equal(res, expected)
+
+
+def test_with_endog_normalizations(model2_inv):
+    expected = {
+        "fac1": {
+            "loadings": [
+                {"y1": 1},
+                {},
+                {"y1": 1},
+                {},
+                {"y1": 1},
+                {},
+                {"y1": 1},
+                {},
+                {"y1": 1},
+                {},
+                {"y1": 1},
+                {},
+                {"y1": 1},
+                {},
+                {"y1": 1},
+                {},
+            ],
+            "intercepts": [
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+            ],
+        },
+        "fac2": {
+            "loadings": [
+                {"y4": 1},
+                {},
+                {"y4": 1},
+                {},
+                {"y4": 1},
+                {},
+                {"y4": 1},
+                {},
+                {"y4": 1},
+                {},
+                {"y4": 1},
+                {},
+                {"y4": 1},
+                {},
+                {"y4": 1},
+                {},
+            ],
+            "intercepts": [
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+            ],
+        },
+        "fac3": {
+            "loadings": [
+                {},
+                {"y7": 1},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+            ],
+            "intercepts": [
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+                {},
+            ],
+        },
+    }
+    res = process_model(model2_inv)["normalizations"]
+
+    assert res == expected
+
+
+# ======================================================================================
+# Unit tests
+# ======================================================================================
+
+
+def test_model_has_endogenous_factors_not_specified():
+    factors = {"a": {}}
+    assert get_has_endogenous_factors(factors) == False
+
+
+def test_get_has_endogenous_factors_wrong_type():
+    factors = {"a": {"is_endogenous": 3}}
+    with pytest.raises(ValueError):
+        get_has_endogenous_factors(factors)
+
+
+def test_get_has_endogenous_factors_wrong_constellation():
+    factors = {"a": {"is_endogenous": False, "is_correction": True}}
+    with pytest.raises(ValueError):
+        get_has_endogenous_factors(factors)
+
+
+def test_get_has_endogenous_factors_indeed():
+    factors = {
+        "a": {"is_endogenous": True, "is_correction": False},
+        "b": {"is_endogenous": False, "is_correction": False},
+    }
+    assert get_has_endogenous_factors(factors) == True
+
+
+def test_get_has_endogenous_factors_and_correction():
+    factors = {
+        "a": {"is_endogenous": True, "is_correction": False},
+        "b": {"is_endogenous": False, "is_correction": False},
+        "c": {"is_endogenous": True, "is_correction": True},
+    }
+    assert get_has_endogenous_factors(factors) == True
diff --git a/tests/test_qr.py b/tests/test_qr.py
new file mode 100644
index 00000000..5a35475f
--- /dev/null
+++ b/tests/test_qr.py
@@ -0,0 +1,45 @@
+import jax
+import jax.numpy as jnp
+import numpy as np
+import pytest
+from numpy.testing import assert_array_almost_equal as aaae
+
+from skillmodels.qr import qr_gpu
+
+SEED = 20
+
+
+@pytest.fixture
+def cov_matrix():
+    fixedrng = np.random.default_rng(SEED)
+    factorized = fixedrng.uniform(low=-1, high=3, size=(7, 7))
+    cov = factorized @ factorized.T * 0.5 + np.eye(7)
+    return cov
+
+
+def test_q(cov_matrix):
+    q_gpu, _ = qr_gpu(cov_matrix)
+    q_jax, _ = jnp.linalg.qr(cov_matrix)
+    aaae(q_gpu, q_jax)
+
+
+def test_r(cov_matrix):
+    _, r_gpu = qr_gpu(cov_matrix)
+    _, r_jax = jnp.linalg.qr(cov_matrix)
+    aaae(r_gpu, r_jax)
+
+
+def test_grad_qr(cov_matrix):
+    def f_jax(a):
+        q, r = jnp.linalg.qr(a)
+        return jnp.sum(r) + jnp.sum(q)
+
+    def f_gpu(a):
+        q, r = qr_gpu(a)
+        return jnp.sum(r) + jnp.sum(q)
+
+    grad_qr_jax = jax.grad(f_jax)
+    grad_qr_gpu = jax.grad(f_gpu)
+    grad_gpu = grad_qr_gpu(cov_matrix)
+    grad_jax = grad_qr_jax(cov_matrix)
+    aaae(grad_gpu, grad_jax)
diff --git a/tests/test_utilities.py b/tests/test_utilities.py
index 22b468d2..8041fc98 100644
--- a/tests/test_utilities.py
+++ b/tests/test_utilities.py
@@ -147,11 +147,12 @@ def test_reduce_params_via_extract_factors(model2):
             ("meas_sds", 0, "y7", "-"),
             ("meas_sds", 0, "y8", "-"),
             ("meas_sds", 0, "y9", "-"),
+            ("shock_sds", 0, "fac3", "-"),
             ("initial_states", 0, "mixture_0", "fac3"),
             ("mixture_weights", 0, "mixture_0", "-"),
             ("initial_cholcovs", 0, "mixture_0", "fac3-fac3"),
         ],
-        names=["category", "period", "name1", "name2"],
+        names=["category", "aug_period", "name1", "name2"],
     )
 
     assert_index_equal(reduced_params.index, expected_index)
@@ -175,7 +176,7 @@ def test_extend_params_via_switch_to_translog(model2):
             ("transition", 0, "fac2", "fac2 ** 2"),
             ("transition", 0, "fac2", "fac3 ** 2"),
         ],
-        names=["category", "period", "name1", "name2"],
+        names=["category", "aug_period", "name1", "name2"],
     )
 
     assert_index_equal(added_index, expected_added_index)
diff --git a/tests/test_visualize_factor_distributions.py b/tests/test_visualize_factor_distributions.py
index f0483849..1895301d 100644
--- a/tests/test_visualize_factor_distributions.py
+++ b/tests/test_visualize_factor_distributions.py
@@ -67,7 +67,7 @@ def test_visualize_factor_distributions_runs_with_simulated_states():
     params = params.loc[max_inputs["params_template"].index]
 
     latent_data = simulate_dataset(model_dict, params, data=data, policies=None)[
-        "unanchored_states"
+        "aug_unanchored_states"
     ]["states"]
 
     kde = univariate_densities(