{
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"source": [
"# Foundations of Computational Economics #32\n",
"\n",
"by Fedor Iskhakov, ANU\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"## Cake eating model with discretized choice\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
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"source": [
"\n",
"\n",
"[https://youtu.be/EDcCoXkIU34](https://youtu.be/EDcCoXkIU34)\n",
"\n",
"Description: Using function interpolation to solve cake eating problem with discretized choice."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Cake eating problem\n",
"\n",
"\n",
"\n",
" \n",
"- Cake of initial size $ W_0 $ \n",
"- How much of the cake to eat each period $ t $, $ c_t $? \n",
"- Time is discrete, $ t=1,2,\\dots,\\infty $ \n",
"- What is not eaten in period $ t $ is left for the future $ W_{t+1}=W_t-c_t $ "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Bellman equation\n",
"\n",
"$$\n",
"V(W_{t})=\\max_{0 \\le c_{t} \\le W_t}\\big\\{\\log(c_{t})+\\beta V(\\underset{=W_{t+1}}{\\underbrace{W_{t}-c_{t}}})\\big\\}\n",
"$$\n",
"\n",
"$$\n",
"c^{\\star}(W_t)=\\arg\\max_{0 \\le c_{t} \\le W_t}\\big\\{\\log(c_{t})+\\beta V(\\underset{=W_{t+1}}{\\underbrace{W_{t}-c_{t}}})\\big\\}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Recap: components of the dynamic model\n",
"\n",
"- **State variables** — vector of variables that describe all relevant\n",
" information about the modeled decision process, $ W_t $ \n",
"- **Decision variables** — vector of variables describing the choices,\n",
" $ c_t $ \n",
"- **Instantaneous payoff** — utility function, $ u(c_t)=\\log(c_t) $, with\n",
" time separable discounted utility \n",
"- **Motion rules** — agent’s beliefs of how state variable evolve\n",
" through time, conditional on choices, $ W_{t+1}=W_t-c_t $ \n",
"- **Value function** — maximum attainable utility, $ V(W_t) $ \n",
"- **Policy function** — mapping from state space to action space that\n",
" returns the optimal choice, $ c^{\\star}(W_t) $ "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Value function iterations (VFI) solution\n",
"\n",
"Numerically solve\n",
"\n",
"$$\n",
"V(W) = \\max_{0 \\le c \\le W} \\big[ u(c)+\\beta V(W-c) \\big ]\n",
"$$\n",
"\n",
"Solve the **functional fixed point equation** $ T({V})(W) = V(W) $ for $ V(W) $, where\n",
"\n",
"$$\n",
"T(V)(W) \\equiv \\max_{0 \\le c \\le W} \\big[u(c)+\\beta V(W-c)\\big]\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### VFI algorithm\n",
"\n",
"- Start with an arbitrary guess $ V_0(W) $\n",
" (will see next time that the initial guess is not important) \n",
"- At each iteration $ i $ compute \n",
"\n",
"\n",
"$$\n",
"\\begin{eqnarray*}\n",
"V_i(W) = T(V_{i-1})(W) &=&\n",
"\\max_{0 \\le c \\le W} \\big\\{u(c)+\\beta V_{i-1}(W-c) \\big \\} \\\\\n",
"c_{i-1}(W) &=&\n",
"\\underset{0 \\le c \\le W}{\\arg\\max} \\big\\{u(c)+\\beta V_{i-1}(W-c) \\big \\}\n",
"\\end{eqnarray*}\n",
"$$\n",
"\n",
"- Repeat until convergence "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Numerical implementation of the Bellman operator\n",
"\n",
"- Cake is continuous $ \\rightarrow $ value function is a function\n",
" of continuous variable \n",
"- Solution: **discretize** $ W $\n",
" Construct a *grid* (vector) of cake-sizes\n",
" $ \\vec{W}\\in\\{0,\\dots\\overline{W}\\} $ \n",
"\n",
"\n",
"$$\n",
"V_{i}(\\vec{W})=\\max_{0 \\le c \\le \\vec{W}}\\{u(c)+\\beta V_{i-1}(\\vec{W}-c)\\}\n",
"$$\n",
"\n",
"- Compute value and policy function sequentially point-by-point \n",
"- May need to compute the value function *between grid points*\n",
" $ \\Rightarrow $ Interpolation and function approximation "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Solution “on the grid”\n",
"\n",
"- allows to avoid computation of value function between the grid points \n",
"- but have to rewrite the model with choices in terms of $ W_{t+1} $ \n",
"- consumption is then taken as the difference $ W_{t+1}-W_t $ \n",
"- very crude representation of consumption choice, thus terribly low accuracy of the solution "
]
},
{
"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",
"class cake_ongrid():\n",
" '''Simple class to implement cake eating problem on the grid'''\n",
"\n",
" def __init__(self,beta=.9, Wbar=10, ngrid=50):\n",
" '''Initializer'''\n",
" self.beta = beta # Discount factor\n",
" self.Wbar = Wbar # Upper bound on cake size\n",
" self.ngrid = ngrid # Number of grid points\n",
" self.epsilon = np.finfo(float).eps # smallest positive float number\n",
" self.grid = np.linspace(self.epsilon,Wbar,ngrid) # grid for both state and decision space\n",
"\n",
" def bellman(self,V0):\n",
" '''Bellman operator, V0 is one-dim vector of values on grid'''\n",
" c = self.grid - self.grid[:,np.newaxis] # current state in columns and choices in rows\n",
" c[c==0] = self.epsilon # add small quantity to avoid log(0)\n",
" mask = c>0 # mask off infeasible choices\n",
" matV1 = np.full((self.ngrid,self.ngrid),-np.inf) # init V with -inf\n",
" matV0 = np.repeat(V0.reshape(self.ngrid,1),self.ngrid,1) #current value function repeated in columns\n",
" matV1[mask] = np.log(c[mask])+self.beta*matV0[mask] # maximand of the Bellman equation\n",
" V1 = np.amax(matV1,axis=0,keepdims=False) # maximum in every column\n",
" c1 = self.grid - self.grid[np.argmax(matV1,axis=0)] # consumption (index of maximum in every column)\n",
" return V1, c1\n",
"\n",
" def solve(self, maxiter=1000, tol=1e-4, callback=None):\n",
" '''Solves the model using VFI (successive approximations)'''\n",
" V0=np.log(self.grid) # on first iteration assume consuming everything\n",
" for iter in range(maxiter):\n",
" V1,c1=self.bellman(V0)\n",
" if callback: callback(iter,self.grid,V1,c1) # callback for making plots\n",
" if np.all(abs(V1-V0) < tol):\n",
" break\n",
" V0=V1\n",
" else: # when i went up to maxiter\n",
" print('No convergence: maximum number of iterations achieved!')\n",
" return V1,c1"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
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},
"source": [
"### Comparison to analytic solution\n",
"\n",
"In video 30 we derived the analytic solution of the cake eating problem\n",
"\n",
"$$\n",
"c^{\\star}(W) = \\frac {W} {1 + \\beta B} = \\frac {W} {1 + \\frac{\\beta}{1-\\beta}} = (1-\\beta)W\n",
"$$\n",
"\n",
"$$\n",
"V(W) = \\frac{\\log(W)}{1-\\beta} + \\frac{\\log(1-\\beta)}{1-\\beta} + \\frac{\\beta \\log(\\beta)}{(1-\\beta)^2}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"hide-output": false,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"def check_analytic(model):\n",
" '''Check the cake eating numerical solution against the analytic solution'''\n",
" # analytic solution\n",
" aV = lambda w: np.log(w)/(1 - model.beta) + np.log(1 - model.beta)/(1 - model.beta) + model.beta* np.log(model.beta)/((1 - model.beta)**2)\n",
" aP = lambda w: (1 - model.beta) * w\n",
" grid = model.grid # grid from the model\n",
" xg = np.linspace(model.epsilon,model.Wbar,1000) # dense grid for analytical solution\n",
" V,policy = model.solve() # solve the model\n",
" # make plots\n",
" fig1, (ax1,ax2) = plt.subplots(1,2,figsize=(14,8))\n",
" ax1.grid(b=True, which='both', color='0.65', linestyle='-')\n",
" ax2.grid(b=True, which='both', color='0.65', linestyle='-')\n",
" ax1.set_title('Value functions')\n",
" ax2.set_title('Policy functions')\n",
" ax1.set_xlabel('Cake size, W')\n",
" ax2.set_xlabel('Cake size, W')\n",
" ax1.set_ylabel('Value function')\n",
" ax2.set_ylabel('Policy function')\n",
" ax1.plot(grid[1:],V[1:],linewidth=1.5,label='Numerical')\n",
" ax1.plot(xg,aV(xg),linewidth=1.5,label='Analytical')\n",
" ax2.plot(grid,policy,linewidth=1.5,label='Numerical')\n",
" ax2.plot(grid,aP(grid),linewidth=1.5,label='Analytical')\n",
" ax1.legend()\n",
" ax2.legend()\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"hide-output": false,
"slideshow": {
"slide_type": "slide"
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\n",
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