{
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"source": [
"# Foundations of Computational Economics #38\n",
"\n",
"by Fedor Iskhakov, ANU\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"## Dynamic programming with continuous choice\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
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"source": [
"\n",
"\n",
"[https://youtu.be/pAEm9cZd92Y](https://youtu.be/pAEm9cZd92Y)\n",
"\n",
"Description: Optimization in Python. Consumption-savings model with continuous choice."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
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"source": [
"Goal: take continuous choice seriously and deal with it without discretization\n",
"\n",
"- no discretization of choice variables \n",
"- need to employ numerical optimizer to find optimal continuous choice in Bellman equation \n",
"- optimization problem has to be solved for all points in the state space \n",
"\n",
"\n",
"Implement the continuous version of Bellman operator for the stochastic consumption-savings model"
]
},
{
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"metadata": {
"slideshow": {
"slide_type": "slide"
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},
"source": [
"### Consumption-savings problem (Deaton model)\n",
"\n",
"$$\n",
"V(M)=\\max_{0 \\le c \\le M}\\big\\{u(c)+\\beta \\mathbb{E}_{y} V\\big(\\underset{=M'}{\\underbrace{R(M-c)+\\tilde{y}}}\\big)\\big\\}\n",
"$$\n",
"\n",
"- discrete time, infinite horizon \n",
"- one continuous choice of consumption $ 0 \\le c \\le M $ \n",
"- state space: consumable resources in the beginning of the period $ M $, discretized \n",
"- income $ \\tilde{y} $, follows log-normal distribution with $ \\mu = 0 $ and $ \\sigma $ "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
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"source": [
"$$\n",
"V(M)=\\max_{0 \\le c \\le M}\\big\\{u(c)+\\beta \\mathbb{E}_{y} V\\big(\\underset{=M'}{\\underbrace{R(M-c)+\\tilde{y}}}\\big)\\big\\}\n",
"$$\n",
"\n",
"- preferences are given by time separable utility $ u(c) = \\log(c) $ \n",
"- discount factor $ \\beta $ \n",
"- gross return on savings $ R $, fixed "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Continuous (non-discretized) Bellman equation\n",
"\n",
"Have to compute\n",
"\n",
"$$\n",
"\\max_{0 \\le c \\le M}\\big\\{u(c)+\\beta \\mathbb{E}_{y} V\\big(R(M-c)+\\tilde{y}\\big)\\big\\} = \\max_{0 \\le c \\le M} G(M,c)\n",
"$$\n",
"\n",
"using numerical optimization algorithm\n",
"\n",
"- constrained optimization (bounds on $ c $) \n",
"- have to interpolate value function $ V(\\cdot) $ for every evaluation of objective $ G(c) $ \n",
"- have to solve this optimization problem for **all possible values** $ M $ "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
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},
"source": [
"#### Numerical optimization in Python\n",
"\n",
"Optimization can be approached\n",
"\n",
"1. **directly**, or through the lenses of analytic \n",
"1. **first order conditions**, assuming the objective function is differentiable \n",
"\n",
"\n",
"- FOC approach is equation solving, see video 13, 22, 23 \n",
"- here focus on optimization itself \n",
"\n",
"\n",
"The two approaches are equivalent in terms of computational complexity, end even numerically"
]
},
{
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"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Newton method as optimizer\n",
"\n",
"$$\n",
"\\max_{x \\in \\mathbb{R}} f(x) = -x^4 + 2.5x^2 + x + 2\n",
"$$\n",
"\n",
"Solve the first order condition:\n",
"\n",
"$$\n",
"\\begin{eqnarray}\n",
"f'(x)=-4x^3 + 5x +1 &=& 0 \\\\\n",
"-4x(x^2-1) + x+1 &=& 0 \\\\\n",
"(x+1)(-4x^2+4x+1) &=& 0 \\\\\n",
"\\big(x+1\\big)\\big(x-\\frac{1}{2}-\\frac{1}{\\sqrt{2}}\\big)\\big(x-\\frac{1}{2}+\\frac{1}{\\sqrt{2}}\\big) &=& 0\n",
"\\end{eqnarray}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
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},
"source": [
"### Taylor series expansion of the equation\n",
"\n",
"Let $ x' $ be an approximate solution of the equation $ g(x)=f'(x)=0 $\n",
"\n",
"$$\n",
"g(x') = g(x) + g'(x)(x'-x) + \\dots = 0\n",
"$$\n",
"\n",
"$$\n",
"x' = x - g(x)/g'(x)\n",
"$$\n",
"\n",
"Newton step towards $ x' $ from an approximate solution $ x_i $ at iteration $ i $ is then\n",
"\n",
"$$\n",
"x_{i+1} = x_i - g(x_i)/g'(x_i) = x_i - f'(x_i)/f''(x_i)\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
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},
"source": [
"### Or use repeated quadratic approximations\n",
"\n",
"Given approximate solution $ x_i $ at iteration $ i $, approximate function $ f(x) $ using first three terms of Taylor series\n",
"\n",
"$$\n",
"\\hat{f}(x) = f(x_i) + f'(x_i) (x-x_i) + \\tfrac{1}{2} f''(x_i) (x-x_i)^2\n",
"$$\n",
"\n",
"The maximum/minimum of this quadratic approximation is given by\n",
"\n",
"$$\n",
"{\\hat{f}}'(x) = f'(x_i) + f''(x_i) (x-x_i) = 0\n",
"$$\n",
"\n",
"Leading to the Newton step\n",
"\n",
"$$\n",
"x = x_{i+1} = x_i - f'(x_i)/f''(x_i)\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"hide-output": false,
"slideshow": {
"slide_type": "slide"
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},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"def newton(fun,grad,x0,tol=1e-6,maxiter=100,callback=None):\n",
" '''Newton method for solving equation f(x)=0\n",
" with given tolerance and number of iterations.\n",
" Callback function is invoked at each iteration if given.\n",
" '''\n",
" for i in range(maxiter):\n",
" x1 = x0 - fun(x0)/grad(x0)\n",
" err = abs(x1-x0)\n",
" if callback != None: callback(err=err,x0=x0,x1=x1,iter=i)\n",
" if err"
]
},
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\n",
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