30_cake_ongrid.ipynb

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    "# Foundations of Computational Economics #30\n",
    "\n",
    "by Fedor Iskhakov, ANU\n",
    "\n",
    "<img src=\"_static/img/dag3logo.png\" style=\"width:256px;\">"
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    "## Cake eating in discrete world\n",
    "\n",
    "<img src=\"_static/img/lecture.png\" style=\"width:64px;\">"
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    "<img src=\"_static/img/youtube.png\" style=\"width:65px;\">\n",
    "\n",
    "[https://youtu.be/IwKxNceuar4](https://youtu.be/IwKxNceuar4)\n",
    "\n",
    "Description: Cake eating problem setup. Solution “on the grid”."
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    "### Cake eating problem\n",
    "\n",
    "<img src=\"_static/img/cake.png\" style=\"width:128px;\">\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 $  "
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    "### Model specification and parametrization\n",
    "\n",
    "- **Choices of the decision maker**\n",
    "  - How much cake to eat  \n",
    "- **State space of the problem**\n",
    "  - A full list of variables that are relevant to the choices in question  \n",
    "- **Preferences of the decision maker**\n",
    "  - Utility flow from cake consumption\n",
    "  - Discount factor  \n",
    "- **Beliefs of the decision agents about how the state will evolve**\n",
    "  - Transition density/probabilities of the states\n",
    "  - May be conditional on the choices  "
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    "### Preferences in the cake eating\n",
    "\n",
    "Let the flow utility be given by\n",
    "\n",
    "$$\n",
    "u(c_{t})=\\log(c_t)\n",
    "$$\n",
    "\n",
    "Overall goal is to maximize the discounted expected utility\n",
    "\n",
    "$$\n",
    "\\max_{\\{c_{t}\\}_{0}^{\\infty}}\\sum_{t=0}^{\\infty}\\beta^{t}u(c_{t})\n",
    "\\longrightarrow \\max\n",
    "$$"
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    "### Value function\n",
    "\n",
    "**Value function** $ V(W_t) $ = the maximum attainable\n",
    "value given the size of cake $ W_t $ (in period $ t $)\n",
    "\n",
    "- State space is given by single variable $ W_t $  \n",
    "- Transition of the variable (**rather, beliefs**) depends on the choice  \n",
    "\n",
    "\n",
    "$$\n",
    "W_{t+1}=W_t-c_t\n",
    "$$"
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    "### Bellman equation (recursive problem)\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray*}\n",
    "  V(W_{0}) & = & \\max_{\\{c_{t}\\}_{0}^{\\infty}}\\sum_{t=0}^{\\infty}\\beta^{t}u(c_{t}) \\\\\n",
    "  & = & \\max_{0 \\le c_{0}\\le W_0}\\{u(c_{0})+\\beta\\max_{\\{c_{t}\\}_{1}^{\\infty}}\\sum_{t=1}^{\\infty}\\beta^{t-1}u(c_{t})\\} \\\\\n",
    "  & = & \\max_{0 \\le c_{0}\\le W_0}\\{u(c_{0})+\\beta V(W_{1})\\}\n",
    "\\end{eqnarray*}\n",
    "$$\n",
    "\n",
    "$$\n",
    "V(W_{t})=\\max_{0 \\le c_{t} \\le W_t}\\big\\{u(c_{t})+\\beta V(\\underset{=W_{t}-c_{t}}{\\underbrace{W_{t+1}}})\\big\\}\n",
    "$$"
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    "### 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) $, 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) $  "
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    "### Maybe we can find analytic solution?\n",
    "\n",
    "- Start with a (good) guess of $ V(W)=A+B\\log W $  \n",
    "  $$\n",
    "  \\begin{eqnarray*}\n",
    "  V(W) & = & \\max_{c}\\big\\{u(c)+\\beta V(W-c)\\big\\} \\\\\n",
    "  A+B\\log W & = & \\max_{c} \\big\\{\\log c+\\beta(A+B\\log (W-c)) \\big\\}\n",
    "  \\end{eqnarray*}\n",
    "  $$\n",
    "- Determine $ A $ and $ B $ and find the optimal rule for cake\n",
    "  consumption.  \n",
    "- This is only possible in **few** models!  "
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    "F.O.C. for $ c $\n",
    "\n",
    "$$\n",
    "\\frac{1}{c} - \\frac{\\beta B}{W - c} = 0, \\quad c = \\frac {W} {1 + \\beta B}, W - c = \\frac {\\beta B W} {1 + \\beta B}\n",
    "$$\n",
    "\n",
    "Then we have\n",
    "\n",
    "$$\n",
    "A + B\\log W = \\log W + \\log\\frac{1}{1+\\beta B} +\n",
    "\\beta A + \\beta B \\log W + \\beta B \\log\\frac{\\beta B}{1+\\beta B}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray*}\n",
    "A &=& \\beta A + \\log\\frac{1}{1+\\beta B} + \\beta B \\log\\frac{\\beta B}{1+\\beta B} \\\\\n",
    "B &=& 1 + \\beta B\n",
    "\\end{eqnarray*}\n",
    "$$"
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    "After some algebra\n",
    "\n",
    "$$\n",
    "c^{\\star}(W) =  \\frac {W} {1 + \\beta B} = \\frac {W} {1 + \\frac{\\beta}{1-\\beta}} = (1-\\beta)W\n",
    "$$\n",
    "\n",
    "$$\n",
    "V(W) = \\frac{\\log(W)}{1-\\beta} + \\frac{\\log(1-\\beta)}{1-\\beta} + \\frac{\\beta \\log(\\beta)}{(1-\\beta)^2}\n",
    "$$"
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    "### Bellman operator\n",
    "\n",
    "The Bellman equation becomes operator in functional space\n",
    "\n",
    "$$\n",
    "T(V)(W) \\equiv \\max_{0 \\le c \\le W} \\big[u(c)+\\beta V(W-c)\\big]\n",
    "$$\n",
    "\n",
    "The Bellman equations is then $ V(W) = T({V})(W) $, with the\n",
    "solution given by the fixed point (solution to $ T({V}) = V $)"
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    "### Value function iterations (VFI)\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  "
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    "### 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  "
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    "### Can interpolation be avoided?\n",
    "\n",
    "- Note that conditional on $ W_t $, the choice of $ c $ defines\n",
    "  $ W_{t+1} $  \n",
    "- Can replace $ c $ with $ W_{t+1} $ in Bellman equation so\n",
    "  that **next period cake size is the decision variable**  \n",
    "- Solving “on the grid”  "
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    "### Adjustment to the Bellman equation\n",
    "\n",
    "$$\n",
    "V_{i}(\\vec{W})=\\max_{0 \\le \\vec{W}' \\le \\vec{W}}\\{u(\\vec{W}-\\vec{W}')+\\beta V_{i-1}(\\vec{W}')\\}\n",
    "$$\n",
    "\n",
    "- Compute value and policy function sequentially point-by-point  \n",
    "- Note that grid $ \\vec{W}\\in\\{0,\\dots\\overline{W}\\} $ is used\n",
    "  twice: for state space and for decision space  \n",
    "\n",
    "\n",
    "*Can you spot the potential problem?*"
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    "import numpy as np\n",
    "\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"
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      " 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163\n",
      " 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163\n",
      " 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163\n",
      " 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163\n",
      " 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163\n",
      " 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163\n",
      " 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163 0.20408163\n",
      " 0.40816327 0.40816327]\n"
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    "model = cake_ongrid(beta=0.92,Wbar=10,ngrid=50)\n",
    "V,c = model.solve()\n",
    "print(c)"
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.rcParams['axes.autolimit_mode'] = 'round_numbers'\n",
    "plt.rcParams['axes.xmargin'] = 0\n",
    "plt.rcParams['axes.ymargin'] = 0\n",
    "plt.rcParams['patch.force_edgecolor'] = True\n",
    "from cycler import cycler\n",
    "plt.rcParams['axes.prop_cycle'] = cycler(color='bgrcmyk')\n",
    "\n",
    "fig1, ax1 = plt.subplots(figsize=(12,8))\n",
    "plt.grid(b=True, which='both', color='0.65', linestyle='-')\n",
    "ax1.set_title('Value function convergence with VFI')\n",
    "ax1.set_xlabel('Cake size, W')\n",
    "ax1.set_ylabel('Value function')\n",
    "\n",
    "def callback(iter,grid,v,c):\n",
    "    '''Callback function for DP solver'''\n",
    "    if iter<5 or iter%10==0:\n",
    "        ax1.plot(grid[1:],v[1:],label='iter={:3d}'.format(iter),linewidth=1.5)\n",
    "\n",
    "V,c = model.solve(callback=callback)\n",
    "\n",
    "plt.legend(loc=4)\n",
    "# plt.savefig('cake1value.eps', format='eps', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### How to measure numerical errors?\n",
    "\n",
    "- In our case there is an analytic solution  \n",
    "\n",
    "\n",
    "$$\n",
    "c^{\\star}(W) = (1-\\beta)W\n",
    "$$\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": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### When there is no analytic solution\n",
    "\n",
    "We can find some **derived theoretical property** of the model\n",
    "and check if it holds in the computed numerical solution\n",
    "\n",
    "- Typically very dense (slow) grid is used in place of true solution  \n",
    "- We’ll look at this in more detail later  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Comparison of value function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hide-output": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8bb8ec28d0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fun = 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",
    "grid = model.grid\n",
    "plt.plot(grid[1:],V[1:],linewidth=1.5)\n",
    "plt.plot(grid[1:],fun(grid[1:]),linewidth=1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Comparison of policy function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hide-output": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8bb8f8fc90>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "apol = lambda w: (1 - model.beta) * w\n",
    "grid = model.grid\n",
    "plt.plot(grid[1:],c[1:],linewidth=1.5)\n",
    "plt.plot(grid[1:],apol(grid[1:]),linewidth=1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hide-output": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8b90298510>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = cake_ongrid(beta=0.92,Wbar=10,ngrid=250)\n",
    "V,c = m.solve()\n",
    "plt.plot(m.grid[1:],c[1:],linewidth=1.5)\n",
    "plt.plot(m.grid[1:],apol(m.grid[1:]),linewidth=1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Conclusion\n",
    "\n",
    "Solving “on the grid” allows to avoid interpolation of the value function,\n",
    "but leads to huge inaccuracies for low levels of wealth!"
   ]
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    "#### Further learning resources\n",
    "\n",
    "- 📖 Adda and Russell Cooper “Dynamic Economics. Quantitative Methods and Applications.” *Chapters: 2, 3.3*  \n",
    "- QuantEcon DP section\n",
    "  [https://lectures.quantecon.org/py/index_dynamic_programming.html](https://lectures.quantecon.org/py/index_dynamic_programming.html)  "
   ]
  }
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