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Merge pull request #1509 from akshayshanker/master
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Makes title of SSJ example more informative
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mnwhite authored Jan 8, 2025
2 parents 7cfd046 + 1e8e45d commit da3442e
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1 change: 1 addition & 0 deletions Documentation/CHANGELOG.md
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- Adds example of integration of HARK with SSJ toolkit. [#1447](https://github.com/econ-ark/HARK/pull/1447)
- Maintains compatibility between EconForge interpolation and numba [#1457](https://github.com/econ-ark/HARK/pull/1457)
- Renanmes 'SSJ_example' to 'HANKFiscal_example' so that it is more informative. [#1509](https://github.com/econ-ark/HARK/pull/1509)

### 0.15.0

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3 changes: 2 additions & 1 deletion Documentation/example_notebooks/Include_list.txt
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examples/ConsNewKeynesianModel/Transition_Matrix_Example.ipynb
examples/ConsNewKeynesianModel/Jacobian_Example.ipynb
examples/ConsNewKeynesianModel/KS-HARK-presentation.ipynb
examples/ConsNewKeynesianModel/SSJ_example.ipynb
examples/ConsNewKeynesianModel/SSJ_explanation.ipynb
examples/ConsNewKeynesianModel/HANKFiscal_example.ipynb
3 changes: 2 additions & 1 deletion Documentation/overview/index.rst
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../../examples/ConsNewKeynesianModel/Transition_Matrix_Example.ipynb
../../examples/ConsNewKeynesianModel/Jacobian_Example.ipynb
../../examples/ConsNewKeynesianModel/KS-HARK-presentation.ipynb
../../examples/ConsNewKeynesianModel/SSJ_example.ipynb
../../examples/ConsNewKeynesianModel/HANKFiscal_example.ipynb
../../examples/ConsNewKeynesianModel/SSJ_explanation.ipynb

.. toctree::
:hidden:
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"id": "9aff8c24",
"metadata": {},
"source": [
"# HARK and the Sequence Space Jacobian (SSJ) Method\n",
"# Fiscal Policy in a HANK model using HARK and SSJ\n",
"\n",
"By William Du ([email protected]) \n",
"\n",
"- This notebook demonstrates how HARK and the SSJ toolkit can be combined to solve HANK models.\n",
"- This notebook demonstrates how HARK and the SSJ toolkit can be combined to the canonical HANK model with fiscal policy \n",
"- Content here builds on the excellent foundation of this [SSJ notebook](https://github.com/shade-econ/nber-workshop-2022/blob/main/Tutorials/Tutorial%201%20Fiscal%20Policy.ipynb) \n",
"\n",
"## HARK Solves for the Microeconomic Steady State\n",
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25 changes: 9 additions & 16 deletions examples/ConsNewKeynesianModel/SSJ_explanation.ipynb
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"id": "10f78487",
"metadata": {},
"source": [
"# Advantages of SSJ\n",
"## Advantages of SSJ\n",
"\n",
"Can solve general equilibrium models with rich microeconomic heterogeneity quickly. (Basic HANK models can take 3 seconds, previous methods take at least 15 minutes)\n",
"\n",
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"id": "4f1bf1b5",
"metadata": {},
"source": [
" ### Households\n",
"### Households\n",
"\n",
"Assume a continuum of atomistic households on the unit interval $[0,1]$ indexed by i. \n",
"\n",
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"\n",
"$y_{it}$ is labor income.\n",
"\n",
"\n",
"#### Labor Income\n",
"\n",
"Labor income is the product of an idiosyncratic transitory shock $\\theta$, the wage rate $w$ (determined in aggregate), and the exogenously fixed individual labor supply $\\ell$. \n",
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"id": "405ddb01",
"metadata": {},
"source": [
"## Firms and Production\n",
"### Firms and Production\n",
"\n",
"Output is produced by firms via a Cobb-Douglas production function over aggregate capital $K_t$ and labor $L_t$, scaled by total factor productivity $Z_t$:\n",
"\n",
"$$Y_{t} = Z_{t}K_{t}^{\\alpha}L_{t}^{1-\\alpha}.$$\n",
"\n",
"### Determination of Wage and Interest Rates\n",
"#### Determination of Wage and Interest Rates\n",
"\n",
"Assume perfectly competitive markets, so that the factor prices are given by their marginal product:\n",
"\n",
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"r_{t} = \\alpha Z_{t} K_{t}^{\\alpha - 1} L_{t}^{1-\\alpha}.\n",
"$$\n",
"\n",
"### Dynamics of Productivity\n",
"#### Dynamics of Productivity\n",
"\n",
"TFP $Z_t$ follows an AR(1) process in logs, with correlation factor $\\rho_Z$ and standard deviation of shocks $\\sigma_Z$.\n",
"\n",
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"id": "ebeea820",
"metadata": {},
"source": [
"## Market Clearing \n",
"### Market Clearing \n",
"\n",
"Aggregate capital and labor are found by aggregating idiosyncratic values over the population. For labor, this is trivial, as each household exogenously supplies $\\ell$ units of labor. To denote the switch to aggregate labor, apply a new label:\n",
"\n",
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"Notice that aggregate capital $K_t$ depends on the entire distribution of idiosyncratic market resources $m_{it}$."
]
},
{
"cell_type": "markdown",
"id": "12cc8957",
"metadata": {},
"source": [
"# The model as a system of difference equations in sequence space"
]
},
{
"cell_type": "markdown",
"id": "01ee68b8",
"metadata": {},
"source": [
"## The model as a system of difference equations in sequence space\n",
"\n",
"The equilibrium of this model can be expressed as a root of a system of difference equations on the sequence of current and future prices and productivity shocks. For notational convenience, the sequence of aggregate outcomes will be represented by $\\textbf{U}$, and the sequence of productivity shocks by $\\textbf{Z}$. For period $t$, the equilibrium conditions are:\n",
"\n",
"$$ H_{t}(\\mathbf{U},\\mathbf{Z}) = \\begin{pmatrix} \n",
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"id": "a545e7ca",
"metadata": {},
"source": [
"# Solve the model by linearizing around the steady state\n",
"## Solve the model by linearizing around the steady state\n",
"\n",
"We are interested in how aggregate outcomes will change in response to exogenous shocks. Denote the endogenous impulse response as $d\\mathbf{U} \\equiv \\left\\{dK_{t} , dr_{t} , dw_{t} \\right\\}_{t=0}^{t=T}$, and the exogenous shock (a change in future productivity shocks) as $d\\mathbf{Z} = \\left\\{ dZ_{t}\\right\\}_{t=0}^{t=T}$.\n",
"\n",
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