# Risk Uncertainty Value
`Expansion Suite` is an open source Python toolbox for macro-finance research. It solves the nonlinear DSGE model with recursive utility formulation motivated by robustness or risk concerns based on the small-noise expansion method.
`Expansion Suite` is built on the Linear Quadratic framework proposed by [Borovička and Hansen (2014)](https://larspeterhansen.org/wp-content/uploads/2016/10/Examining-Macroeconomic-Models-through-the-Lens-of-Asset-Pricing.pdf). It follows the algorithm in [Exploring Recursive Utility](https://larspeterhansen.org/class-notes/) to approximate the model solution under uncertainty.
## Jupyter Notebook Illustrations
[uncertainexpansion.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/uncertainexpansion.ipynb)
- A guide to solve the DSGE model with `Expansion Suite`.
- An example of the Adjustment Cost Model is provided in the notebook.
[shockelasticity.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/shockelasticity.ipynb)
- A guide to compute shock elasticities with `Expansion Suite`
- An example of the Bansal Yaron Long-run Risk Model is provided in the notebook.
[quickguide.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/quickguide.ipynb)
- Provides a five-minute guide to solve the DSGE model using the expansion suite, as well as how to
- compute shock elasticities and IRF
- approximate and simulate variables based on model solutions.
- Provides some examples for `LinQuadVar` computations
## Source Files
[lin_quad.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/lin_quad.py)
- Defines the linear-quadratic variable structure to facilitate operations in expansion solvers and elasticity calculation with `LinQuadVar` class.
[lin_quad_util.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/lin_quad_util.py)
- Integrated operation tools on `LinQuadVar`.
[utilities.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/utilities.py)
- Matrix and linear algebra operation functions facilitate the computation.
[derivatives.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/derivatives.py)
- Functions to compute numerical derivatives used in the expansion solver.
[uncertain_expansion.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/uncertain_expansion.py)
- Functions to implement first and second order expansion, approximate the continuation values, change of probability measure, and iteration schemes.
[elasticity.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/elasticity.py)
- Functions to compute shock elasticities.
[BY_example_sol.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/BY_example_sol.py)
- Produce the solutions for the Bansal Yaron Long-run Risk Model used in the [shockelasticity.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/shockelasticity.ipynb).
## Recent Updates, by Jan. 27, 00:12, CT
1. [uncertainexpansion.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/uncertainexpansion.ipynb)
- remove `gb_tp1` as a state variable
- parameters updating for the adjustment cost model example, which are consistent with the homework.
- Note the $\gamma=1$ cannot be solved by the `Expansion Suite`, the reason is that $1-\gamma$ will show in denominators of the recursive utility adjustment terms, we can try to use values close to $1$, `γ=1+1e-5`, for example.
```python
γ = 10.
ρ = 4./3
β = np.exp(-0.0025)
a = 0.0288
ϕ_2 = 88.
ϕ_1 = 1/ϕ_2
α_k = 0.0088
σ_k = np.array([[0.477],[0]]) * 0.01
A = np.exp(-0.014)
B = np.array([[0.011,0.025]]) * 0.01
```
2. [uncertain_expansion.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/uncertain_expansion.py), [lin_quad_util.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/lin_quad_util.py), [BY_example_sol.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/BY_example_sol.py)
- New functions and methods added
3. [quickguide.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/quickguide.ipynb)
- New notebook added
- Section 1 is a five-minute guide for the `Expansion Suite` as a DSGE solver.
- Section 2 are examples for the computations in `LinQuadVar`.
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"description": "# Risk Uncertainty Value\n\n`Expansion Suite` is an open source Python toolbox for macro-finance research. It solves the nonlinear DSGE model with recursive utility formulation motivated by robustness or risk concerns based on the small-noise expansion method.\n\n\n\n`Expansion Suite` is built on the Linear Quadratic framework proposed by [Borovi\u010dka and Hansen (2014)](https://larspeterhansen.org/wp-content/uploads/2016/10/Examining-Macroeconomic-Models-through-the-Lens-of-Asset-Pricing.pdf). It follows the algorithm in [Exploring Recursive Utility](https://larspeterhansen.org/class-notes/) to approximate the model solution under uncertainty. \n\n\n\n## Jupyter Notebook Illustrations\n\n[uncertainexpansion.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/uncertainexpansion.ipynb)\n\n- A guide to solve the DSGE model with `Expansion Suite`. \n\n- An example of the Adjustment Cost Model is provided in the notebook.\n\n[shockelasticity.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/shockelasticity.ipynb)\n\n- A guide to compute shock elasticities with `Expansion Suite` \n\n- An example of the Bansal Yaron Long-run Risk Model is provided in the notebook.\n\n[quickguide.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/quickguide.ipynb)\n\n- Provides a five-minute guide to solve the DSGE model using the expansion suite, as well as how to \n - compute shock elasticities and IRF\n - approximate and simulate variables based on model solutions. \n- Provides some examples for `LinQuadVar` computations\n\n## Source Files\n\n[lin_quad.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/lin_quad.py)\n- Defines the linear-quadratic variable structure to facilitate operations in expansion solvers and elasticity calculation with `LinQuadVar` class.\n\n[lin_quad_util.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/lin_quad_util.py)\n- Integrated operation tools on `LinQuadVar`.\n\n[utilities.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/utilities.py)\n- Matrix and linear algebra operation functions facilitate the computation.\n\n[derivatives.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/derivatives.py)\n- Functions to compute numerical derivatives used in the expansion solver.\n\n[uncertain_expansion.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/uncertain_expansion.py)\n\n- Functions to implement first and second order expansion, approximate the continuation values, change of probability measure, and iteration schemes.\n\n[elasticity.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/elasticity.py)\n- Functions to compute shock elasticities.\n\n[BY_example_sol.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/BY_example_sol.py)\n\n- Produce the solutions for the Bansal Yaron Long-run Risk Model used in the [shockelasticity.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/shockelasticity.ipynb).\n\n\n\n## Recent Updates, by Jan. 27, 00:12, CT\n\n1. [uncertainexpansion.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/uncertainexpansion.ipynb)\n - remove `gb_tp1` as a state variable\n\n - parameters updating for the adjustment cost model example, which are consistent with the homework.\n\n - Note the $\\gamma=1$ cannot be solved by the `Expansion Suite`, the reason is that $1-\\gamma$ will show in denominators of the recursive utility adjustment terms, we can try to use values close to $1$, `\u03b3=1+1e-5`, for example.\n\n ```python\n \u03b3 = 10.\n \u03c1 = 4./3\n \u03b2 = np.exp(-0.0025)\n a = 0.0288\n \u03d5_2 = 88.\n \u03d5_1 = 1/\u03d5_2\n \u03b1_k = 0.0088\n \u03c3_k = np.array([[0.477],[0]]) * 0.01\n A = np.exp(-0.014)\n B = np.array([[0.011,0.025]]) * 0.01\n ```\n\n2. [uncertain_expansion.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/uncertain_expansion.py), [lin_quad_util.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/lin_quad_util.py), [BY_example_sol.py](https://github.com/lphansen/RiskUncertaintyValue/blob/main/src/BY_example_sol.py)\n - New functions and methods added\n\n3. [quickguide.ipynb](https://github.com/lphansen/RiskUncertaintyValue/blob/main/quickguide.ipynb)\n - New notebook added\n - Section 1 is a five-minute guide for the `Expansion Suite` as a DSGE solver. \n - Section 2 are examples for the computations in `LinQuadVar`.\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n",
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