{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Foundations of Computational Economics #41\n", "\n", "by Fedor Iskhakov, ANU\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "## Endogenous gridpoint method (EGM)\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "\n", "[https://youtu.be/MZ0MmprYMQo](https://youtu.be/MZ0MmprYMQo)\n", "\n", "Description: Fastest and most accurate solution methods for consumption-savings model. Class of models solvable by EGM. Generalizations of EGM method." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Endogenous gridpoint method (EGM)\n", "\n", "- *fastest and most accurate* solution methods for *particular* problems with continuous choice \n", "- finite and infinite horizon, discrete time \n", "- best way to solve stochastic consumption-savings problem \n", "- applicable to many other important problems \n", "- has multiple generalizations which are applicable to a larger class of problems \n", "\n", "\n", "1. Theory in this video \n", "1. Implementation in the next video " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### EGM is like magic\n", "\n", "Most accurate solution method for consumption-savings problem we have so far?\n", "\n", "- time iterations = repeatedly solving F.O.C. in the Bellman maximization problem *in every point in the state space* \n", "- VFI with continuous choices = repeatedly solving optimization problem *in every point in the state space* \n", "\n", "\n", "EGM on the other hand: **no root-finding operations!**\n", "\n", "- but .. only applies to a certain class of problems \n", "- hard to grasp right away, best studied by example " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "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" } }, "source": [ "#### Euler equation for Deaton model\n", "\n", "FOC: $ \\quad u'(c^\\star) - \\beta R \\mathbb{E}_{y} V'\\big(R(M-c^\\star)+\\tilde{y}\\big) = 0 $\n", "\n", "Envelope theorem: $ \\quad V'(M) = \\beta R \\mathbb{E}_{y} V'\\big(R(M-c^\\star)+\\tilde{y}\\big) $\n", "\n", "**Euler equation**:\n", "\n", "$$\n", "u'\\big(c^\\star(M)\\big) = \\beta R \\mathbb{E}_{y} u'\\big(c^\\star\\big(\\underset{=M'}{\\underbrace{R[M-c^\\star(M)]+\\tilde{y}}}\\big)\\big)\n", "$$\n", "\n", "(see video 39)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### New variable needed for EGM\n", "\n", "Let $ A $ denote **end-of-period** wealth = wealth after consumption (savings)\n", "\n", "Timing of the model:\n", "\n", "$$\n", "M \\rightarrow c(M) \\rightarrow A = M-c(M) \\rightarrow M' = R(M-c(M)) + \\tilde{y} = RA + \\tilde{y}\n", "$$\n", "\n", "$$\n", "0 \\le c \\le M \\; \\Rightarrow \\; 0 \\le A = M-c \\le M\n", "$$\n", "\n", "- $ A $ contains all the information needed for the calculation of the expected value function in the next period, “sufficient statistic” for the current period state and choice \n", "- $ A $ is often referred to as *post-decision state* " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Euler equation with post-decision state\n", "\n", "$$\n", "u'\\big(c(M)\\big) = \\beta R \\mathbb{E}_{y} u'\\big(c(RA+\\tilde{y})\\big)\n", "$$\n", "\n", "- if policy function $ c(M) $ is optimal, then it satisfies the above equation with $ A = M-c(M) $ \n", "- given any policy function $ c(M) $, an updated policy function $ c'(M') $ is given as a *parameterized curve* \n", "\n", "\n", "$$\n", "\\begin{cases}\n", "c' = (u')^{-1} \\Big( \\beta R \\mathbb{E}_{y} u'(c\\big(RA+\\tilde{y})\\big) \\Big) \\\\\n", "M' = A + c'\n", "\\end{cases}\n", "$$\n", "\n", "- where parameter $ A $ ranges over the interval $ (0,M) $ " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Coleman-Reffett operator\n", "\n", "Recall *Coleman-Reffett operator* $ K(c)(M) : \\mathcal{P} \\rightarrow \\mathcal{P} $\n", "\n", "- takes as input policy function $ c(M) \\in \\mathcal{P} $ \n", "- returns the updated policy function $ c'(M) \\in \\mathcal{P} $ that for every $ M $ satisfies \n", "\n", "\n", "$$\n", "u'\\big(c'(M)\\big) = \\beta R \\mathbb{E}_{y} u'\\big(c[R(M-c'(M))+\\tilde{y}]\\big)\n", "$$\n", "\n", "Standard implementation:\n", "\n", "1. Fix grid over $ M $ \n", "1. With given $ c(M) $ solve the equation for $ c $ in each point $ M $ on the grid " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### EGM implementation of Coleman-Reffett operator\n", "\n", "1. Fix grid over $ A $ \n", "1. With given $ c(M) $ for each point on the grid compute \n", "\n", "\n", "$$\n", "\\begin{cases}\n", "c' = (u')^{-1} \\Big( \\beta R \\mathbb{E}_{y} u'(c\\big(RA+\\tilde{y})\\big) \\Big) \\\\\n", "M' = A + c'\n", "\\end{cases}\n", "$$\n", "\n", "1. Build the returned policy function $ c'(M) $ as interpolation over computed points $ (M',c') $ \n", "\n", "\n", "*EGM is time iterations solver with a much more efficient implementation of Coleman-Reffett operator*" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### EGM algorithm\n", "\n", "1. Set a grid on (discretize) post-decision state $ A $ instead of state $ M $ \n", "1. Set the initial policy $ c_0(M) = M $ defined over two points $ M \\in \\{0,\\bar{M}\\} $ \n", "1. Increment iteration counter $ i $ (initialized to 0) \n", "1. For each point $ A_j $ on the grid over $ A $ perform the **EGM step** and return the corresponding value of\n", " consumption $ c_j $ and the endogenous point of wealth $ M_j = A_j+c_j $ \n", "1. Combine all computed endogenous points in the state space $ M_j $, and their corresponding consumption levels $ c_j $ to build the\n", " updated policy function $ c_i(M) $ \n", "1. Return to step 3, unless convergence achieved (policy functions $ c_i(M) $ and $ c_{i-1}(M) $ are within given tolerance) " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### EGM algorithm (EGM step)\n", "\n", "Given point $ A_j $ on the grid over $ A $:\n", "1. Compute the next period wealth $ M'_j = RA_j + \\tilde{y} $, replacing $ \\tilde{y} $ with quadrature points\n", "2. Compute the optimal consumption in the next period in all quadrature points, using the previous iteration policy function $ c_{i-1}(\\cdot) $\n", "3. Compute the marginal utility for each value of consumption, and complete the calculation of the expectation in RHS of Euler equation\n", "4. Using inverse marginal utility function, compute optimal consumption $ c_j $ in current period, corresponding to the point $ A_j $\n", "5. complete the EGM step by computing endogenous state point $ M_j = A_j + c_j $" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Properties of EGM algorithm\n", "\n", "- successive approximations in the policy function space \n", "- same structure as time iterations, with new implementation of Coleman-Reffett operator \n", "- the updating of policy function is done with the EGM step \n", "- **no root-finding operations**, direct computation instead $ \\rightarrow $ **fast** \n", "- Euler equation holds in the generated endogenous state points $ \\rightarrow $ **accurate** " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### EGM principle\n", "\n", "- Instead of finding the optimal decision in each point of a fixed grid over the state space .. \n", "- find the point in the state space where a “guessed” decision would be optimal. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Example using deterministic consumption-savings model\n", "\n", "$$\n", "V(M)=\\max_{0 \\le c \\le M}\\big\\{log(c)+\\beta V\\big(R(M-c)+y\\big)\\big\\}\n", "$$\n", "\n", "$$\n", "u'\\big(c^\\star(M)\\big) = \\beta R u'\\big(c^\\star\\big(R[M-c^\\star(M)]+y\\big)\\big)\n", "$$\n", "\n", "$$\n", "\\begin{cases}\n", "c' = (u')^{-1} \\Big( \\beta R u'(c\\big(RA+y)\\big) \\Big) \\\\\n", "M' = A + c\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[H\u001b[2J" ] } ], "source": [ "%clear # clear notebook memory\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import interpolate\n", "%matplotlib inline\n", "\n", "beta,R,y = 0.95,1.,0. # fundamentals (cake eating)\n", "Mbar,ngrid = 10,5 # technical parameters\n", "u = lambda c: np.log(c) # utility function\n", "mu = lambda c: 1/c # marginal utility function\n", "imu = lambda u: 1/u # inverse marginal utility function\n", "\n", "A = np.linspace(0,Mbar,ngrid) # What are the bounds of A?\n", "c0 = np.array([0,Mbar])\n", "M0 = np.array([0,Mbar])" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set up plotting\n", "fig, ax = plt.subplots(1,3,figsize=(14,6))\n", "for axi in ax:\n", " axi.grid(b=True, which='both', color='0.65', linestyle='-')\n", "ax[0].set_title('consumption c(A)')\n", "ax[1].set_title('wealth M(A)')\n", "ax[2].set_title('consumption c(M)')\n", "ax[0].set_xlabel('Savings (post decision state) A')\n", "ax[1].set_xlabel('Savings (post decision state) A')\n", "ax[2].set_xlabel('Wealth M')\n", "# make colors generator\n", "# https://stackoverflow.com/questions/37890412/increment-matplotlib-color-cycle\n", "from itertools import cycle\n", "prop_cycle = plt.rcParams['axes.prop_cycle']\n", "colors = cycle(prop_cycle.by_key()['color'])\n", "def plot_iter(a,m,c):\n", " color = next(colors)\n", " ax[0].plot(a,c,linewidth=0.5,c=color)\n", " ax[1].plot(a,m,linewidth=0.5,c=color)\n", " ax[2].plot(m,c,linewidth=0.5,c=color)\n", " ax[0].scatter(a,c,s=11,c=color)\n", " ax[1].scatter(a,m,s=11,c=color)\n", " ax[2].scatter(m,c,s=11,c=color)\n", " return fig" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Iteration 0\n", "plot_iter(np.full(2,np.nan),M0,c0)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Iteration 1\n", "policy = interpolate.interp1d(M0,c0,kind='slinear',fill_value=\"extrapolate\") # interpolation function for policy\n", "M1 = np.full(ngrid,np.nan)\n", "c1 = np.full(ngrid,np.nan)\n", "for j,aj in enumerate(A):\n", " Mpr = max(R*aj+y,1e-10) # next period wealth\n", " cpr = policy(Mpr) # next period consumption\n", " c1[j] = imu( beta*R*mu(cpr) ) # inverse Euler\n", " M1[j] = aj + c1[j] # endogenous wealth\n", "plot_iter(A,M1,c1) # returns fig object, plotted automatically" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Iteration 2\n", "policy = interpolate.interp1d(M1,c1,kind='slinear',fill_value=\"extrapolate\") # interpolation function for policy\n", "M2 = np.full(ngrid,np.nan)\n", "c2 = np.full(ngrid,np.nan)\n", "for j,aj in enumerate(A):\n", " Mpr = max(R*aj+y,1e-10) # next period wealth\n", " cpr = policy(Mpr) # next period consumption\n", " c2[j] = imu( beta*R*mu(cpr) ) # inverse Euler\n", " M2[j] = aj + c2[j] # endogenous wealth\n", "plot_iter(A,M2,c2) # returns fig object, plotted automatically" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Corner solutions in EGM\n", "\n", "- So far only covered the interior solutions where the Euler equation holds \n", "- What about the restriction $ 0 \\le c \\le M $ which is equivalent to $ 0 \\le A \\le M $? \n", "\n", "\n", "1. By choosing the grid on $ A $ to respect the constraint $ 0 \\le A \\le M $ EGM only implements interior solutions \n", "1. Corner solutions must be added with an additional provisions in the code " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Lower bound on consumption\n", "\n", "- $ c \\ge 0 $ is never binding if utility function satisfies \n", "\n", "\n", "$$\n", "\\lim_{c \\rightarrow 0} u(c) = -\\infty\n", "$$\n", "\n", "- all our usual utility functions like $ \\log(c) $ or CRRA utility $ \\frac{c^\\lambda - 1}{\\lambda} $ satisfy this condition " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "#### Upper bound on consumption\n", "\n", "- If $ c \\le M $ is binding, then $ A=0 $, can be computed directly \n", "\n", "\n", "**Proposition** If utility function $ u(c) $ in the consumption-savings model is monotone and concave, then end-of-period wealth $ A=M-c $ is non-decreasing in M.\n", "\n", "- Let $ M_0 = (u')^{-1} \\Big( \\beta R \\mathbb{E}_{y} u'(c(\\tilde{y})\\big) \\Big) $ denote the point that corresponds to $ A=0 $ \n", "- Due to the proposition, for all $ M" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# set up plotting\n", "fig, ax = plt.subplots(1,3,figsize=(14,6))\n", "for axi in ax:\n", " axi.grid(b=True, which='both', color='0.65', linestyle='-')\n", "ax[0].set_title('consumption c(A)')\n", "ax[1].set_title('wealth M(A)')\n", "ax[2].set_title('consumption c(M)')\n", "ax[0].set_xlabel('Savings (post decision state) A')\n", "ax[1].set_xlabel('Savings (post decision state) A')\n", "ax[2].set_xlabel('Wealth M')\n", "# make colors generator\n", "# https://stackoverflow.com/questions/37890412/increment-matplotlib-color-cycle\n", "from itertools import cycle\n", "prop_cycle = plt.rcParams['axes.prop_cycle']\n", "colors = cycle(prop_cycle.by_key()['color'])\n", "def plot_iter(a,m,c):\n", " color = next(colors)\n", " ax[0].plot(a,c,linewidth=0.5,c=color)\n", " ax[1].plot(a,m,linewidth=0.5,c=color)\n", " ax[2].plot(m,c,linewidth=0.5,c=color)\n", " ax[0].scatter(a,c,s=11,c=color)\n", " ax[1].scatter(a,m,s=11,c=color)\n", " ax[2].scatter(m,c,s=11,c=color)\n", " return fig" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAzIAAAGDCAYAAADwPCXUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nOzdeZxcdZ3v/9cne0hCCAkESEJWUCIqSARlTUQNKoLzG0fBDRkUZRlnuzM//Y3jeJ3f/O7cmbkzo9egRkUUcEVHGWRsvZoEZF9lX5KQjQBhy07I0p/fH3Uai6Y7qU5X96mqfj0fj3p0nVPfOufd1VXfPp9zvnVOZCaSJEmS1EwGlR1AkiRJknrKQkaSJElS07GQkSRJktR0LGQkSZIkNR0LGUmSJElNx0JGkiRJUtOxkFGfiogPRsQvS1jvJyLi33vQ/taIeE1fZpIGqoiYFhEZEUN20yYjYlYfrHt4RDwQEQfV2P6MiPh+vXNIahzNsm1S9Ty3UbphIaO66WpjJTOvzMy393OOYcBngX/uNH9URGyOiGu7eNq/AF/oj3zSQBcRiyPiY714/ueLvuZTneb/WTH/81Wzzweuy8wnu1nGsdXzM/Nq4MiIeN3e5pPUOBp126Qq152d2k2IiO0RsaJqttso3bCQUSs6E3goMx/vNP+9wIvA2yPi4E6PXQ3M62K+pMb0CHBOp3kfKeZX+wRwefWMiAjgw8BzXSwD4HtUCiBJqpfutk1GRcSRVdMfAB7r1MZtlG5YyJQgIqZExE8i4umIeDYivlzMHxQRn42IlRGxLiK+ExFji8c6KvdzImJVRDwTEX9TtcxjI+L2iNgYEU9FxL8W8+dGxJpO618REW8t7n8+In4UEVdExKaIuDciDo+IzxQZVkfE26ueuzgi/kdxmHNDRPwsIvYvHr6u+Lm+OPLx5oj4aET8tur5x0fEbcVzb4uI4zst++8j4oYiyy8jYsJuXsczI+Lu4ndeFhGnFQ+9A1jSxVPOAb4K3AN8sPqBzNwG3AH06x4aqWwRcW5E/GfV9NKI+GHV9OqIOKq4/+qI+FVEPBcRD0fE+6ravSsi7io+j6s7HRWpXt8/ACcBXy76iS9XPfzWiHg0Ip6PiAVFwdGd24B9OoZbFD9HFvM71nUoMBO4pdNzTwIOAf4UOKvYU1ptMfCu3axbajlum5S2bXI5L9+h8hHgO9UN3EbpnoVMP4uIwcA1wEpgGjAJ6BiP/dHiNg+YAYwGvtxpEScCrwJOBT4XEUcU878IfDEz96Xyj/uH1O7dVD5I44C7gDYq741JVA5lfq1T+48Af0xlQ2An8KVi/snFz/0yc3Rm3tTpd98f+HnRfjzwr8DPI2J8VbMPAOcCBwLDgP/WVeCoDAf5DvBXwH7FulcUD78WeLhT+0OBucCVxe0jXSz2QeD1Xa1PamFLgJOKjZWDgaHACQAR0dEP3RMRo4BfAd+l8vk8G7gkfj9uewuVz9V+VIqACyLiPZ1Xlpl/A1wPXFz0ExdXPXw68EYqn8P3AfP3kP1yfv9ZPodO//yp9AXLM3Nnp/nnAP8J/KBqvdUeBKZFxL57WL/UEtw2KWfbpHAFlR0qg4vXbQyv3PkCbqN0yUKm/x1L5UP2V5m5JTO3ZWbHXoEPAv+amcszczPwGSpv7uovyP73zHwhM38H/I7fv6l3ALMiYkJmbs7Mm3uQ6frMbCv+2f8IOAD4x8zcQaUjmxYR+1W1vzwz78vMLcDfAu8rOsE9eRfwaGZenpk7M/N7wENUOqsO38rMRzLzBSod3lHdLOs84NLM/FVmtmfm45n5UPHYfsCmTu0/AtyTmQ9QGTbymog4ulObTcVzpQEjM5dTee8fBZxCZWPh8Yh4dTF9fWa2U9nYX5GZ3yo+v3cCP6YyZJPMXJyZ9xafx3uofM5O6WGcf8zM9Zm5ClhE95//DlcAZ0fEUOCsYrraK/qCiNgH+CPgu0UfdxWvHF7W8Rz7Aw0UbpuUs20CsIZKgfNWut4h08FtlC5YyPS/KcDKLvYQQqUTWVk1vRIYAkysmlf9hdWtVPaMQOXDczjwUHFYtPMext15qur+C8Azmbmrapqq9QCs7pRxKNDtYdYqnX+/judPqpru7vfrbAqwrJvHnqeyR6PaR6gciSEz11LZC91542UMsL6bZUqtbAmVI5YnF/cXUylCTuH3QyGmAsdFxPqOG5UNnIMAIuK4iFhUDEvZAHyS2vqFarV+/gEoCp6lwP9HZUNkdacmXfUFf0Blb23HST+uBN4REQdUtel4jv2BBgq3TV6uv7ZNOnyHylGvs3nlDpkObqN0wUKm/60GDo2uT0O6lsrGQodDqfzDfaqLti+TmY9m5tlUDnv+T+CqYijIFmCfjnbF3okDul5KzaZ0yrgDeAbIPTyv8+/X8fzOX3yrxWoqh6m7cg+VjhOojH0FDgM+ExFPRsSTwHFU9uRW/x2OoLInSRpoOgqZk4r7S3hlIbMaWJKZ+1XdRmfmBcXj36XyhdQpmTmWyvfRuvuOy576ip74DvCXdL0X8x5gRqfP+TlUNkJWFX3Bj6hs8Jxd1eYIKkefNtYxp9TI3DZ5uT7fNunkx1SODC3PzM5FVQe3UbpgIdP/bgWeAP4xKqcDHhERJxSPfQ/484iYHhGjqexl/EE3e0heJiI+FBEHFENAOir2XVTO4DMiKl/EHUrl1H/De/k7fCgiZhdDNL4AXFXsJXkaaKcyhrYr1wKHR8QHImJIRLwfmE1lXG5PfRM4NyJOLcb2TyqGwnSsp3pIyzlUxvbPpnI4+CjgSCqd6Dugcq0J4JiinTTQLKEy/n1kZq6h8h2W06iMF7+raHMNlc/vhyNiaHF7Y9VY+DHAc5m5rRgn/oHdrO8puu8neuoHVL4A+4qx98Xv8iiVYTNExCQqY/hP5/d9weupbGBVH6E9BfivOuWTmoHbJv2/bfKSYjjcW4AuT0vvNkr3LGT6WfGhejcwC1hFZWzk+4uHL6XyxbbrqJx6bxvwJzUu+jTg/ojYTOXLdWcVY1w3ABcC36Cyd2FLsc7euBy4jMqh1hHAp4rfbSvwD8ANxdCTN1U/KTOfpbIB8ZfAs8BfA6dn5jM9DZCZt1L54t2/ARuobIh17FH5T+DVEXFIRIyg8qXh/52ZT1bdHuPlZwo5A1hcDDuTBpTMfATYTKWAoTgSsRy4oWMoR2ZuolIwnEVlD+aTVAqAjo2PC4EvRMQm4HPs/ku9XwTeG5Wzk31pN+1qyf5CZv6fYux6V75G5VTLFD/vzsxfVvcHVL7k+7r4/SlQz+aVXySWWpbbJv27bdLNc2/PzO6GpbmN0o3IrOcRfrW6iFgMXJGZ3yg7y+5ExPnA7Mz8sxrb3wKcl5n39W0ySf2p2JN5F3BqZj5RQ/t3Ax/OzPftqa2kxtCq2yZVz3MbpRsWMuqRZuksJEnSwOC2ycDl0DJJkiRJTccjMpIkSZKajkdkJEmSJDUdCxlJkiRJTaerCx/1iwkTJuS0adPqtrxNmzYxZkx3F0wtj7l6xlw9U+9cd9xxxzOZ2duLkvU7+5NymatnBkqugdKfNOrfs5oZ68OM9dHTjLvtSzKzlNsxxxyT9fSLX/yirsurF3P1jLl6pt65gNuzpD6hNzf7k3KZq2cGSq6B0p806t+zmhnrw4z10dOMu+tLHFomSZIkqelYyEiSJElqOhYykiRJkpqOhYwkSZKkpmMhI0mSJKnpWMhIkiRJajoWMpIkSZKajoWMJEmSpKZjISNJkiSp6VjISJIkSWo6FjKSJEmSmo6FjCRJamoRcWlErIuI+6rm7R8Rv4qIR4uf48rMKKn+LGQkSVKzuww4rdO8TwO/zszDgF8X05JKkplccfNKVj67hStuXklm9nqZFjKSJKmpZeZ1wHOdZp8JfLu4/23gPf0aStLLXHnLKv7fax5g3eYd/MPPH+S7t67q9TKH1CGXJElSo5mYmU8AZOYTEXFgdw0j4nzgfICJEyfS1tZW80o2bNjQo/ZlMGN9mLF3tj67hePHJ+0Z/PG0DWxZdgdt6x/q1TItZCRJ0oCWmQuBhQBz5szJ+fPn1/zctrY2etK+DGasDzP2zhd//QjX3beUI2Zu4tIVY/ns6Ucw/7ipvVqmQ8skSVIreioiDgYofq4rOY80YO3c1c4zm7bzt+8+grEjh/LZ04/gA8ce2uvlWshIkqRWdDVwTnH/HOBnJWaRBrRLb3iMc46fyjlvns7U8aP44HFTiYheL9dCRpIkNbWI+B5wE/CqiFgTEecB/wi8LSIeBd5WTEvqZ3evXs+o4UOYdeCYui/b78hIkqSmlplnd/PQqf0aRNLLbN2+k5/e9Th/9+7ZfbJ8j8hIkiRJqrtLFi3jwrkz6zKMrCsWMpIkSZLq6tcPPsWRk8Zy4L4j+mwdFjKSJEmS6ubpTS9y+8rnOe3Ig/p0PXssZCLi0ohYFxH3dfN4RMSXImJpRNwTEW+of0xJrcD+RJKk1paZXLJ4KRfNm9Xn66rliMxlwGm7efwdwGHF7XzgK72PJalFXYb9iSRJLeuHt6/m9NcdzOjhfX9OsT0WMpl5HfDcbpqcCXwnK24G9uu4AJUkVbM/kSSpdS1/ejPPbtnOMVP375f11aNUmgSsrppeU8x7onPDiDifyl5WJk6cSFtbWx1WX7Fhw4a6Lq9ezNUz5uqZRs3VC/Ynu2GunjFXzzRqLknNYceudi67cQV/e3rfnGq5K/UoZLo6n1p21TAzFwILAebMmZPz58+vw+or2traqOfy6sVcPWOunmnUXL1gf7Ib5uoZc/VMo+aS1By++dvHOOf4aQwd3H/nEqvHmtYAU6qmJwNr67BcSQOP/YkkSU3mjpXPM3bkUGYeMLpf11uPQuZq4CPF2YbeBGzIzFcMA5GkGtifSJLURLa8uJNr7lnLWW+csufGdbbHoWUR8T1gLjAhItYAfwcMBcjMrwLXAu8ElgJbgXP7Kqyk5mZ/IklSa1mwaCkXzJ1JRFejw/vWHguZzDx7D48ncFHdEklqWfYnkiS1jl/e/yRHHzqOA8eMKGX9/fdtHEmSJEktYd2mbdy9ej1vmz2xtAwWMpIkSZJqlplcsmgZF82bVWoOCxlJkiRJNfv+bas546hDGDW8Hldy2XsWMpIkSZJqsuzpzWx4YQdvOHRc2VEsZCRJkiTt2Y5d7Xz7xhWcd+L0sqMAFjKSJEmSavD165dz7gnTGTq4MUqIxkghSZIkqWHdvuI5xo8axvQJo8qO8hILGUmSJEnd2rRtBz+/9wneN2dK2VFexkJGkiRJUrcuWVw51XJElB3lZSxkJEmSJHXpF/c9wZyp45gwenjZUV7BQkaSJEnSKzy1cRv3Pb6RU4+YWHaULlnISJIkSXqZzOQri5dx4byZZUfploWMJEmSpJe58pZVvOfoSewzbEjZUbplISNJkiTpJY8+tYmt23dy1JT9yo6yWxYykiRJkgDYvrOdy29eyR+fML3sKHtkISNJkiQJgK9fv5zzTpzOkMGNXyY0fkJJkiRJfe7Wx57jwDHDmTp+VNlRamIhI0mSJA1wG7ft4Bf3Pcl7j5lcdpSaWchIkiRJA9yCRUu5aN5MIqLsKDWzkJEkSZIGsGvvfYI3zRjP+NHDy47SIxYykiRJ0gD15IZtPPTERua96sCyo/SYhYwkSZI0ALW3J19dsowL5s4qO8pesZCRJEmSBqArb1nJH75hMiOHDS47yl6xkJEkSZIGmIef3MSLO9t57eSxZUfZaxYykiRJ0gDy4s5dfPeWlZx7wvSyo/SKhYwkSZI0gCxcspyPnTSDwYOa51TLXbGQkSRJkgaIm5Y9y6RxI5my/z5lR+k1CxlJkiRpANjwwg5+/eBT/MHRk8qOUhcWMpIkSdIAcMmipVw0bxYRzT2krIOFjCRJktTi/vN3azlh1gTGjRpWdpS6sZCRJEmSWtja9S+wdN1mTj78gLKj1JWFjCRJktSi2tuThdct54K5M8uOUncWMpIkSVKLuvzmlbz3mMmMGDq47Ch1ZyEjSZIktaAHn9jIrvbkyEljy47SJyxkJEmSpBazbccuvn/rKs45flrZUfqMhYwkSZLUYr62ZDkfP3kGgwe1xqmWu2IhI0mSJLWQG5Y+w9Tx+zB53D5lR+lTFjKSJKllRcSfR8T9EXFfRHwvIkaUnUnqSxu27mDxw+s486hDyo7S5yxkJElSS4qIScCngDmZeSQwGDir3FRS38lMFixeykXzZhHRukPKOljISJKkVjYEGBkRQ4B9gLUl55H6zG3rklMOP4D99hlWdpR+YSEjSZJaUmY+DvwLsAp4AtiQmb8sN5XUN9Y8v5V1W+GEWRPKjtJvhpQdQJIkqS9ExDjgTGA6sB74UUR8KDOv6NTufOB8gIkTJ9LW1lbzOjZs2NCj9mUwY300csb2TH7waDtvO2Bzw2bsUM/X0UJGkiS1qrcCj2Xm0wAR8RPgeOBlhUxmLgQWAsyZMyfnz59f8wra2troSfsymLE+Gjnjt254jL/+w/Gsvvemhs3YoZ6vo0PLJElSq1oFvCki9onKN59PBR4sOZNUV/ev3UAAsw/Zt+wo/a6mQiYiTouIhyNiaUR8uovHD42IRRFxV0TcExHvrH9USa3A/kRSf8nMW4CrgDuBe6ls9ywsNZRUR9t27OJHt6/hI2+eVnaUUuyxkImIwcAC4B3AbODsiJjdqdlngR9m5tFUTmt4Sb2DSmp+9ieS+ltm/l1mvjozj8zMD2fmi2Vnkurlq0uWcf7JMxg0qPVPtdyVWo7IHAsszczlmbkd+D6VL85VS6DjeNZYPLWhpK7Zn0iSVAfXP/o0Mw4YzSH7jSw7SmlqKWQmAaurptcU86p9HvhQRKwBrgX+pC7pJLUa+xNJknpp/dbtXP/oM5zx+kPKjlKqWs5a1tWxquw0fTZwWWb+r4h4M3B5RByZme0vW1AvTm+4J416Sjxz9Yy5eqZRc+2G/UkvmKtnzNUzjZpL0stlJgsWLeXieYeVHaV0tRQya4ApVdOTeeVQj/OA0wAy86aIGAFMANZVN+rN6Q33pFFPiWeunjFXzzRqrt2wP+kFc/WMuXqmUXNJermf3v048159IGP3GVp2lNLVMrTsNuCwiJgeEcOofPn26k5tVlE5pSERcQQwAni6nkEltQT7E0mS9tLq57ay+rkXOH7mhLKjNIQ9FjKZuRO4GGijcu71H2bm/RHxhYg4o2j2l8DHI+J3wPeAj2Zm5+EikgY4+xNJkvbOrvbk69cv5xOnzCg7SsOoZWgZmXktlS/dVs/7XNX9B4AT6htNUiuyP5Ekqee+dcNjfOC4Qxk+ZHDZURpGTRfElCRJklSO+x7fwLAhg3j1QfvuufEAYiEjSZIkNagXtu/iqjvW8KHjppYdpeFYyEiSJEkN6iuLl/KJU2YwaFBXVzAY2CxkJEmSpAa0+OF1vOqgfTl47MiyozQkCxlJkiSpwTy3ZTs3LX+Wd73u4LKjNCwLGUmSJKmBZCYLFi3lonmzyo7S0CxkJEmSpAby4zsf5+2zJ7LviKFlR2loFjKSJElSg1j17Fae3PACx80YX3aUhmchI0mSJDWAnbva+cZvl3P+yTPLjtIULGQkSZKkBvCtG1bw4TdNZdgQN9Fr4askSZIklex3q9czYthgDps4puwoTcNCRpIkSSrR1u07+Y+7HueDxx5adpSmYiEjSZIklegri5dxwdyZDBoUZUdpKhYykiRJUkl+89BTzD54XybuO6LsKE3HQkaSJEkqwTObX+TWx57nHa89uOwoTclCRpIkSepnmckli5Zx0TxPtby3LGQkSZKkfvajO9bwjtcexJgRQ8uO0rQsZCRJkqR+tOKZLTy96UXeOG3/sqM0NQsZSZIkqZ/s3NXOpTc8xsdPmlF2lKZnISNJkiT1k2/+9jE+8uZpDBviZnhv+QpKkiRJ/eCuVc8zesQQZh04uuwoLcFCRpIkSepjW17cyc/uXssHjj207Cgtw0JGkiRJ6mOXLF7KhXNnEhFlR2kZFjKSJElSH/o/DzzF6ybvx4H7jig7SkuxkJEkSZL6yNObXuTOVc8z/zUHlR2l5VjISJIkSX0gMytDyubNKjtKS7KQkSRJkvrAD25bzemvO4TRw4eUHaUlWchIkiRJdbb86c08v3UHx0wdV3aUlmUhI0mSJNXRjl3tXHbjCj520vSyo7Q0CxlJkiSpjr5x/WN89PhpDB3spnZf8tWVJEmS6uSOlc8zbp+hzDhgdNlRWp6FjCRJklQHm1/cyTX3rOX9b5xSdpQBwUJGkiRJqoNLFi3lwrmziIiyowwIFjKSJElSL7Xd/yRHHzqOA8YMLzvKgGEhI0mSJPXCuo3buGfNet42e2LZUQYUCxlJkiRpL2UmlyxexoVzZ5UdZcCxkJEkSZL20vduXc2ZRx3CqOFDyo4y4FjISJIkSXth6brNbNy2g6MPHVd2lAHJQkaSJEnqoe072/nOTSv42InTy44yYFnISJIkST309euXc+4J0xky2M3psvjKS5IkST1w24rnOGD0cKZPGFV2lAHNQkaSJEmq0aZtO/ive5/kj+ZMLjvKgGchI0mSJNVowaJlXDhvJhFRdpQBz0JGkiS1rIjYLyKuioiHIuLBiHhz2ZnUvH5x3xMcO30cE0YPLzuKsJCRJEmt7YvALzLz1cDrgQdLzqMmtf7F5P61G3nLqyeWHUWFmgqZiDgtIh6OiKUR8elu2rwvIh6IiPsj4rv1jSmpVdifSOovEbEvcDLwTYDM3J6Z68tNpWbU3p78YmU7F8ydWXYUVdnjJUgjYjCwAHgbsAa4LSKuzswHqtocBnwGOCEzn4+IA/sqsKTmZX8iqZ/NAJ4GvhURrwfuAP40M7dUN4qI84HzASZOnEhbW1vNK9iwYUOP2pfBjL235PF2jhy9lesX/brsKLvV6K8j1DfjHgsZ4FhgaWYuB4iI7wNnAg9Utfk4sCAznwfIzHV1SSep1difSOpPQ4A3AH+SmbdExBeBTwN/W90oMxcCCwHmzJmT8+fPr3kFbW1t9KR9GczYO48+tYlVI5/m0BcebdiMHRr5dexQz4y1DC2bBKyuml5TzKt2OHB4RNwQETdHxGl1SSep1difSOpPa4A1mXlLMX0VlcJGqsn2ne1cfvNKzj1hWtlR1IVajsh0dW657GI5hwFzgcnA9RFxZOdxqL05dLsnjXoozVw9Y66eadRcu2F/0gvm6hlz9Uyj5uqNzHwyIlZHxKsy82HgVF5+BFjarYXXLeO8E6czZLDnx2pEtRQya4ApVdOTgbVdtLk5M3cAj0XEw1Q2RG6rbtSbQ7d70qiH0szVM+bqmUbNtRv2J71grp4xV880aq46+BPgyogYBiwHzi05j5rELcuf5aCxI5k6flTZUdSNWsrL24DDImJ60QmcBVzdqc1PgXkAETGBytCQ5fUMKqkl2J9I6leZeXdmzsnM12Xmezq+fyftzsZtO/jlA0/xh2/oPPpZjWSPhUxm7gQuBtqonHv9h5l5f0R8ISLOKJq1Ac9GxAPAIuCvMvPZvgotqTnZn0iSmsGCRUu5aN4sIroaEa1GUcvQMjLzWuDaTvM+V3U/gb8obpLULfsTSVIj+/k9T/DmGePZf9SwsqNoD/zmkiRJkgQ8seEFHn5yI3Nf5SXMmoGFjCRJkga89vbka0uWc8HcWWVHUY0sZCRJkjTgXXHLSt57zGRGDhtcdhTVyEJGkiRJA9rDT25i+852jpw0tuwo6gELGUmSJA1YL+7cxZW3rOTcE6aXHUU9ZCEjSZKkAetrS5bz8ZNmMHiQp1puNhYykiRJGpBuXPYMk8eNZMr++5QdRXvBQkaSJEkDzoYXdvCbB9fxB0dPKjuK9pKFjCRJkgacBYuWctG8WUQ4pKxZWchIkiRpQLn6d2s5cdYExo0aVnYU9YKFjCRJkgaMx9e/wLJ1mzn58APKjqJespCRJEnSgNDenixcsowL5s4sO4rqwEJGkiRJA8K3b1rB+944hRFDB5cdRXVgISNJkqSW98DajWTCaw4ZW3YU1YmFjCRJklrath27+MFtqzjn+GllR1EdWchIkiSppX11yTI+fvIMBg/yVMutxEJGkiRJLeu3jz7D9AmjmDxun7KjqM4sZCRJktSS1m/dzpJH1nHG6w8pO4r6gIWMJEmSWk5msmDRUi6edxgRDilrRRYykiRJajk/u3stc191IGP3GVp2FPURCxlJkiS1lDXPb2Xls1s5YdaEsqOoD1nISJIkqWXsak++ft1yPnHKjLKjqI9ZyEiSJKllfPvGFZx17KGMGDq47CjqYxYykiRJagn3Pb6BQQFHHLxv2VHUDyxkJEmS1PS27djFj25fzUfePK3sKOonFjKSJElqel9ZvIxPnDKTQYM81fJAYSEjSZKkpnbdI08z68DRHLLfyLKjqB9ZyEiSJKlpPb9lOzcsfYZ3v/6QsqOon1nISJIkqSllJgsWLeXCebPKjqISWMhIkiSpKf3HXY9z6hETGTtyaNlRVAILGUmSJDWd1c9t5fHnX+DNM8eXHUUlsZCRJElSU9nVnnz9+uWcf8qMsqOoRBYykiRJairfuuExPnjcVIYPGVx2FJXIQkaSJElN4941Gxg+ZBCvOmhM2VFUMgsZSZIkNYUXtu/ix3eu4YPHTS07ihqAhYwkSZKawlcWL+WTp8xk0KAoO4oagIWMJEmSGt6ih9fx6oP35aCxI8qOogZhISNJkqSG9uzmF7l5+bO887UHlx1FDcRCRpIkSQ0rM1mwaBkXzZtVdhQ1GAsZSZIkNayr7ljDaUcexL4jhpYdRQ3GQkaSJEkNaeWzW3hq4zaOnb5/2VHUgCxkJEmS1HB27mrnm799jPNPnll2FDUoCxlJkiQ1nEtveIwPv2kqw4a4uaqu+c6QJElSQ7l79Xr2GTaEwyaOKTuKGpiFjCRJkhrG1u07+eldj/OBYw8tO4oaXE2FTEScFhEPR8TSiPj0btq9NyIyIubUL6KkVmJ/IknanUsWLeOCuTMZNCjKjqIGt8dCJiIGAwuAdwCzgbMjYnYX7cYAnwJuqXdISa3B/kSStDu/fvApjpy0LxP3HVF2FDWBWo7IHAsszczlmbkd+D5wZhft/h74J2BbHYsedl4AACAASURBVPNJai32J5KkLj2z+UVuW/E8px15cNlR1CRqKWQmAaurptcU814SEUcDUzLzmjpmk9R67E8k9buIGBwRd0WE/UqDykwuWbSMi+Z5qmXVbkgNbboaoJgvPRgxCPg34KN7XFDE+cD5ABMnTqStra22lDXYsGFDXZdXL+bqGXP1TKPm2g37k14wV8+Yq2caNVed/CnwILBv2UHUtRufTM6YexBjRgwtO4qaSC2FzBpgStX0ZGBt1fQY4EhgcUQAHARcHRFnZObt1QvKzIXAQoA5c+bk/PnzexH95dra2qjn8urFXD1jrp5p1Fy7YX/SC+bqGXP1TKPm6q2ImAy8C/gH4C9KjqMuPPbMFjZuhznT9i87ippMLYXMbcBhETEdeBw4C/hAx4OZuQGY0DEdEYuB/9Z5o0OSsD+R1P/+HfhrKjtKutSbI7zNcCSrkTPuak9+uLSd+QdubtiMHRr5deww0DLusZDJzJ0RcTHQBgwGLs3M+yPiC8DtmXl1XZJIann2J5L6U0ScDqzLzDsiYm537XpzhLcZjmQ1csavLlnGZ98/kWV33dCwGTs08uvYYaBlrOWIDJl5LXBtp3mf66bt3N7HktSq7E8k9aMTgDMi4p3ACGDfiLgiMz9Uci4Bd656nn1HDGXWgaNZVnYYNaWaLogpSZLUbDLzM5k5OTOnURnK+huLmMaw5cWdXH33Ws4+dsqeG0vdsJCRJElSv7pk8VIunDeT4sQu0l6paWiZJElSM8vMxcDikmMI+NUDT/H6yftx4JgRZUdRk/OIjCRJkvrFuk3buGvV87z9NQeVHUUtwEJGkiRJfS4z+criZVw0b1bZUdQiLGQkSZLU575/22pOf90hjBruNxtUHxYykiRJ6lPLnt7M+q07OGbquLKjqIVYyEiSJKnP7NjVzrdvXMHHTppedhS1GAsZSZIk9ZlvXP8YHz1+GkMHu9mp+vIdJUmSpD5xx8rn2H/UUGYcMLrsKGpBFjKSJEmqu80v7uSae57gfXOmlB1FLcpCRpIkSXW3YNFSLpw7i4goO4palIWMJEmS6uoX9z3JMYeO44Axw8uOohZmISNJkqS6WbdxG/c+vp63zp5YdhS1OAsZSZIk1UVmcsniZVw0b1bZUTQAWMhIkiSpLr576yrec/Qk9hk2pOwoGgAsZCRJktRrS9dtYvO2nRw1Zb+yo2iAsJCRJElSr2zf2c53blrJeSdOLzuKBhALGUmSJPXK169fzh+fMJ0hg920VP/x3SZJkqS9dutjz3HAmOFMmzCq7CgaYCxkJEmStFc2bdvBL+57kj86ZnLZUTQAWchIkiRpryxYtIyL5s0kIsqOogHIQkaSJEk99l/3PsFx0/dn/OjhZUfRAGUhI0mSpB55csM2HnhiI/NefWDZUTSAWchIkiSpZu3tyVeXLOPCubPKjqIBzkJGkiRJNbvylpX8X2+YxMhhg8uOogHOQkaSJEk1eeSpTWzb0c7rJu9XdhTJQkaSJEl79uLOXVxx80rOPWFa2VEkwEJGkiRJNVi4ZDkfO3EGQwa7+ajG4DtRkiRJu3Xz8mc5eL+RHDp+n7KjSC+xkJEkSVK3Nrywg1898BR/+IZJZUeRXsZCRpIkSd26ZNFSLpo3i4goO4r0MhYykiRJ6tI196zl+FkT2H/UsLKjSK9gISNJkqRXWLv+BR55chOnHH5A2VGkLlnISJIk6WXa25OvLVnGBXNnlR1F6paFjCRJkl7m8ptX8kdzpjBy2OCyo0jdspCRJEnSSx56ciM7drVz5KSxZUeRdstCRpIkSQBs27GL796yinNPmF52FGmPLGQkSZIEwNeWLOfjJ81g8CBPtazGZyEjSZIkblz6DIeOH8mU/fcpO4pUEwsZSZKkAW7D1h385qF1vOeoSWVHkWpmISNJkjTAfXnRo1z8lllEOKRMzcNCRpIkaQD72d2Pc/LhB7DfPsPKjiL1iIWMJEnSAPX4+hdY/vQWTjrsgLKjSD1mISNJkjQA7WpPFi5ZxgVzZ5YdRdorNRUyEXFaRDwcEUsj4tNdPP4XEfFARNwTEb+OiKn1jyqpFdifSFJj+M5NK3j/Gw9lxNDBZUeR9soeC5mIGAwsAN4BzAbOjojZnZrdBczJzNcBVwH/VO+gkpqf/YkkNYYH1m4kE2Yfsm/ZUaS9VssRmWOBpZm5PDO3A98HzqxukJmLMnNrMXkzMLm+MSW1CPsTSSrZth27+MFtqzjn+GllR5F6pZZCZhKwump6TTGvO+cB/9WbUJJalv2JJJXsq0uWcf4pMxk8yFMtq7kNqaFNV+/y7LJhxIeAOcAp3Tx+PnA+wMSJE2lra6sx5p5t2LChrsurF3P1jLl6plFz7Yb9SS+Yq2fM1TONmkv1df2jTzN9wigm7Tey7ChSr9VSyKwBplRNTwbWdm4UEW8F/gY4JTNf7GpBmbkQWAgwZ86cnD9/fo8Dd6etrY16Lq9ezNUz5uqZRs21G/YnvWCunjFXzzRqLtXP+q3bue6Rp/l/3nlE2VGkuqhlaNltwGERMT0ihgFnAVdXN4iIo4GvAWdk5rr6x5TUIuxPJKkEmcmXf7OUi+cdRoRDytQa9ljIZOZO4GKgDXgQ+GFm3h8RX4iIM4pm/wyMBn4UEXdHxNXdLE7SAGZ/Iqk/RcSUiFgUEQ9GxP0R8adlZyrLT+9+nLe8+kDG7jO07ChS3dQytIzMvBa4ttO8z1Xdf2udc0lqUfYnkvrRTuAvM/POiBgD3BERv8rMB8oO1p+eeSF55tkX+IOjPQmkWktNF8SUJElqNpn5RGbeWdzfROVI8O7OlNhydrUnv1rdzidOmVF2FKnuLGQkSVLLi4hpwNHALeUm6V+X3biCkw8ZxIihg8uOItVdTUPLJEmSmlVEjAZ+DPxZZm7s4vG9Pp17I5+2etWmZNmG5A1jNjVsxg6N/Dp2MGN91DOjhYwkSWpZETGUShFzZWb+pKs2vTmde6Oetnrbjl38j2sf5P879zX86le/bMiM1Rr1daxmxvqoZ0aHlkmSpJYUlfMMfxN4MDP/tew8/emSxcv45NyZDBrkqZbVuixkJElSqzoB+DDwluJ07ndHxDvLDtXXljzyNIdPHM3BY0eWHUXqUw4tkyRJLSkzfwsMqEMSz23Zzo1Ln+Ez7zyi7ChSn/OIjCRJUgvITBYsWsqF82aVHUXqFxYykiRJLeAndz7O22ZPZOzIoWVHkfqFhYwkSVKTW/XsVtauf4E3zRhfdhSp31jISJIkNbGdu9r5xm+Xc/4pM8qOIvUrCxlJkqQmdtmNK/jQm6YyfMjgsqNI/cpCRpIkqUnds2Y9w4cM4vCJY8qOIvU7CxlJkqQm9ML2Xfzkzsf54HFTy44ilcJCRpIkqQldsngpnzxlJoMGDahL5UgvsZCRJElqMoseWscRB+/LQWNHlB1FKo2FjCRJUhN5dvOL3PzYs7zztQeXHUUqlYWMJElSk8hMFixaxsXzZpUdRSqdhYwkSVKT+NEdazjtyIMYM2Jo2VGk0lnISJIkNYEVz2zh6U0vcuz0/cuOIjUECxlJkqQGt3NXO5fe8BgfP2lG2VGkhmEhI0mS1OAuveExPvLmqQwb4qab1MFPgyRJUgO7e/V6Rg0fwqwDx5QdRWooFjKSJEkNauv2nfz0rsf5wLGHlh1FajgWMpIkSQ3qkkXLuHDuTCKi7ChSw7GQkSRJakC/fvApjpw0lgP3HVF2FKkhWchIkiQ1mKc3vcjtK5/ntCMPKjuK1LAsZCRJkhpIZnLJ4qVcNG9W2VGkhmYhI0mS1EB+ePtqTn/dwYwePqTsKFJDs5CRJElqEMuf3syzW7ZzzNT9y44iNTwLGUmSpAawY1c7l924go+fNKPsKFJTsJCRJElqAN/87WOcc/w0hg5280yqhZ8USZKkkt2x8nnGjhzKzANGlx1FahoWMpIkSSXa8uJOrrlnLWe9cUrZUaSmYiEjSZJUogWLlnLB3JlERNlRpKZiISNJklSSX97/JEcfOo4Dx4woO4rUdCxkJEmSSrBu0zbuXr2et82eWHYUqSlZyEiSJPWzzOSSRcu4aN6ssqNITctCRpIkqZ9979bVnHHUIYwaPqTsKFLTspCRJEnqR0vXbWbjth284dBxZUeRmpqFjCRJUj/ZvrOdb9+4gvNOnF52FKnpWchIkiT1k69fv5w/PnE6Qwe7CSb1lp8iSZKkfnD7iueYMHoY0yeMKjuK1BIsZCRJkvrYpm07+Pm9T/C+OVPKjiK1DAsZSZKkPragONVyRJQdRWoZNRUyEXFaRDwcEUsj4tNdPD48In5QPH5LREyrd1BJrcH+RNJA84v7nuCN08YxYfTwsqNILWWPhUxEDAYWAO8AZgNnR8TsTs3OA57PzFnAvwH/s95BJTU/+xNJA81TG7dx3+MbOfWIiWVHkVpOLUdkjgWWZubyzNwOfB84s1ObM4FvF/evAk4Nj51KeiX7E0kDRnt78pXFy7hw3syyo0gtqZbLyU4CVldNrwGO665NZu6MiA3AeOCZ6kYRcT5wPsDEiRNpa2vby9ivtGHDhrour17M1TPm6plGzbUb9ie9YK6eMVfPNGquZvbdW1fxnqMnsc+wWja3JPVULZ+srvaE5l60ITMXAgsB5syZk/Pnz69h9bVpa2ujnsurF3P1jLl6plFz7Yb9SS+Yq2fM1TONmqtZPfrUJrZu38lRU/YrO4rUsmoZWrYGqD5X4GRgbXdtImIIMBZ4rh4BJbUU+xNJLW/7zna+c9NK/viE6WVHkVpaLYXMbcBhETE9IoYBZwFXd2pzNXBOcf+9wG8y8xV7UCUNePYnklrewuuW8bGTpjNksFe5kPrSHoeWFWPULwbagMHApZl5f0R8Abg9M68GvglcHhFLqew5PasvQ0tqTvYnklrdLcufZeK+I5g6flTZUaSWV9O3zzLzWuDaTvM+V3V/G/BH9Y0mqRXZn0hqVRu37aDt/qf429OPKDuKNCB4zFOSJKkOFixaykXzZuIZ46X+YSEjSZLUSz+/5wneNGM840cPLzuKNGBYyEiSJPXCkxu28dCTG5n3qgPLjiINKBYykiSpZUXEaRHxcEQsjYhP13v57Zl8dckyLpw7q96LlrQHFjKSJKklRcRgYAHwDmA2cHZEzK7HsjOTK25eyX88so2RwwYzYqibVFJ/81MnSZJa1bHA0sxcnpnbge8DZ9ZjwVfesoq/v+YBtmxv57IbVvDdW1fVY7GSeqCm0y9LkiQ1oUnA6qrpNcBxnRtFxPnA+QATJ06kra1tjwve+uwW5h3QznH77+CocTvYsuwO2tY/VKfY9bVhw4aafqcymbE+BlpGCxlJktSqujoPcr5iRuZCYCHAnDlzcv78+Xtc8BU3r2TJgw8yc/QGLl0xls+efgTzj5va68B9oa2tjVp+pzKZsT4GWkYLGUmS1KrWAFOqpicDa+ux4A8edygRsGXZHXz29CP4wLGH1mOxknrA78hIkqRWdRtwWERMj4hhwFnA1fVYcETwweOmMnX8KD543FQvgimVwCMykiSpJWXmzoi4GGgDBgOXZub9JceSVCcWMpIkqWVl5rXAtWXnkFR/Di2TJEmS1HQsZCRJkiQ1HQsZSZIkSU3HQkaSJElS07GQkSRJktR0LGQkSZIkNR0LGUmSJElNx0JGkiRJUtOxkJEkSZLUdCxkJEmSJDUdCxlJkiRJTScys5wVRzwNrKzjIicAz9RxefVirp4xV8/UO9fUzDygjsvrF/YnpTNXzwyUXAOlP2nUv2c1M9aHGeujpxm77UtKK2TqLSJuz8w5ZefozFw9Y66eadRcza5RX1dz9Yy5eqZRczW6ZnjdzFgfZqyPemZ0aJkkSZKkpmMhI0mSJKnptFIhs7DsAN0wV8+Yq2caNVeza9TX1Vw9Y66eadRcja4ZXjcz1ocZ66NuGVvmOzKSJEmSBo5WOiIjSZIkaYBoukImIk6LiIcjYmlEfLqLx4dHxA+Kx2+JiGkNkusvIuKBiLgnIn4dEVMbIVdVu/dGREZEv5zpopZcEfG+4jW7PyK+2wi5IuLQiFgUEXcVf8t39kOmSyNiXUTc183jERFfKjLfExFv6OtMrcC+pL65qtrZl9SQq4y+pFiv/Umd1PqZKEtETCneYw8W7/0/LTtTdyJicPFZuKbsLN2JiP0i4qqIeKh4Td9cdqbOIuLPi7/1fRHxvYgY0QCZXtHnRMT+EfGriHi0+Dlur1eQmU1zAwYDy4AZwDDgd8DsTm0uBL5a3D8L+EGD5JoH7FPcv6BRchXtxgDXATcDcxohF3AYcBcwrpg+sEFyLQQuKO7PBlb0Q66TgTcA93Xz+DuB/wICeBNwS19navabfUn9cxXt7Etqz9XvfUmxLvuTfvobl30DDgbeUNwfAzzSaBmrsv4F8F3gmrKz7Cbjt4GPFfeHAfuVnalTvknAY8DIYvqHwEcbINcr+hzgn4BPF/c/DfzPvV1+sx2RORZYmpnLM3M78H3gzE5tzqTyZgO4Cjg1IqLsXJm5KDO3FpM3A5P7OFNNuQp/T+VNta0fMtWa6+PAgsx8HiAz1zVIrgT2Le6PBdb2dajMvA54bjdNzgS+kxU3A/tFxMF9navJ2ZfUOVfBvqT2XP3el4D9SR3V+pkoTWY+kZl3Fvc3AQ9S2dhtKBExGXgX8I2ys3QnIvalskH+TYDM3J6Z68tN1aUhwMiIGALsQz/1K7vTTZ9T/f/128B79nb5zVbITAJWV02v4ZUfypfaZOZOYAMwvgFyVTuPyh6vvrbHXBFxNDAlM/vzcG4tr9fhwOERcUNE3BwRpzVIrs8DH4qINcC1wJ/0Q6496en7T/YlPWVfUv9cn6fx+hKwP6lVU71OxdDYo4Fbyk3SpX8H/hpoLzvIbswAnga+VQyB+0ZEjCo7VLXMfBz4F2AV8ASwITN/WW6qbk3MzCegUnADB+7tgpqtkOlqb2jn067V0qbeal5nRHwImAP8c58mKlbXxbyXckXEIODfgL/shyzVanm9hlAZEjIXOBv4RkTs1wC5zgYuy8zJVIZgXF68jmUq4z3f7OxLesa+pP65GrEvAfuTWjXN6xQRo4EfA3+WmRvLzlMtIk4H1mXmHWVn2YMhVIZHfSUzjwa2UBkS1TCK75mcCUwHDgFGFf8nWlojdJo9sQaYUjU9mVceNnupTXFobSy7P4zeX7mIiLcCfwOckZkv9nGmWnKNAY4EFkfECirjoa/uhy/p1vp3/Flm7sjMx4CHqWyMlJ3rPCrjTsnMm4ARwIQ+zrUnNb3/9DL2JfXNZV/S81yN2JeA/UmtmuJ1ioihVIqYKzPzJ2Xn6cIJwBlFv/F94C0RcUW5kbq0BliTmR1HtK6iUtg0krcCj2Xm05m5A/gJcHzJmbrzVMeQ1eLnXg/5bbZC5jbgsIiYHhHDqHwB9+pOba4Gzinuvxf4TRbfJiozVzHs4mtUNjz6Y4z2HnNl5obMnJCZ0zJzGpXx9mdk5u1l5ir8lMqXmomICVSGhyxvgFyrgFOLXEdQ2fh4uo9z7cnVwEeKsw29icrh5CdKztTo7EvqmMu+ZK9yNWJfAvYntarlb1yq4jt93wQezMx/LTtPVzLzM5k5ueg3zqLSzzbcUYTMfBJYHRGvKmadCjxQYqSurALeFBH7FH/7U6l8L6oRVf9/PQf42V4vaW/PElDWjcoh+EeonC3kb4p5X6DyTxMq/wx+BCwFbgVmNEiu/wM8Bdxd3K5uhFyd2i6mH840VOPrFcC/Uuko7gXOapBcs4EbqJyh5m7g7f2Q6XtUxrvuoLJX6Dzgk8Anq16rBUXme/vrb9jsN/uS+ubq1Na+pAH7kmK99id9+DdupBtwIpXhbvdU9RfvLDvXbvLOpbHPWnYUcHvxev6U4kyIjXQD/jvwEHAfcDkwvAEyddXnjAd+DTxa/Nx/b5cfxUokSZIkqWk029AySZIkSbKQkSRJktR8LGQkSZIkNR0LGUmSJElNx0JGkiRJUtOxkOlCRPxNRNwfEfdExN0RcdxeLucbETG73vk6reOqiJhRx+XNjYiaLqAUESuK6zL0dB1nRES3V8SNiDkR8aWeLrcH6/9oRBxSx3b/EhFv2c3jQyLimYj4Hz3NquZnf2J/0sN29icaMCLi3yLiz6qm2yLiG1XT/ysi/mIvl70iIiZExH4RcWHV/LkRcU0Nz78sIrZGxJiqeV+MiNybvkp9w0Kmk4h4M3A68IbMfB2VK6Wu3ptlZebHMrPPLpgUEa8BBmdmPS/uNpc+vhJsZl6dmf+4m8dvz8xP9WGEjwJ73KDoQbv/DXS7IQW8ncrVxN9XXKRKA4T9if3JXrSzP9FAciNFHxERg4AJwGuqHj+eyvWWemM/4MI9turaUuBMeCnfPODxXuZRHVnIvNLBwDOZ+SJAZj6TmWsBIuJzEXFbRNwXEQuLKx8fERG3djw5IqZFxD3F/cURMae4vzki/iEifhcRN0fExGL+zGL6toj4QkRsLuYfHBHXFXtw74uIk7rI+kGqroZarON/RcSdEfHriDigmH9UsY57IuI/ImJcMf9TEfFAMf/7ETGNyoXR/rxY78vWGRHjI+KXEXFXRHyNyoXTOh77UETcWjzvaxExuJh/WpHndxHx62LeRyPiy8X9Pyp+v99FxHXFvJf2lkTE/hHx0yLjzRHxumL+5yPi0uI1Xh4Rr9hQiYjBxR6V+yLi3oj484h4LzAHuLLIOrKbv2tX7Y6JiCURcUex1+jg4j2yEhgfEQd18546G/gixVV3u2mj1mR/Yn9ifyJ17wZ+v7PjNVQu5LgpIsZFxHDgCOAugIj4q+KzdU9E/PeOBRSf6TuicuT7/C7W8Y/AzOKz98/FvNFROQL9UERcGdHtToHvAe8v7s8t8u7sxe+reiv7ip+NdgNGU7n67SPAJcApVY/tX3X/cuDdxf27Ka76DfzfwGeL+4spropM5eq6He3/qarNNcDZxf1PApuL+3/J768GPRgY00XWJcBrq6YT+GBx/3PAl4v793T8HlSuLP3vxf21FFd9BfYrfn4e+G/dvDZfAj5X3H9Xsb4JVDqa/wSGFo9dAnwEOIDK3ufp1a8flT2THdnuBSZ1yjCX4uq+VPZO/l1x/y3A3VU5bwSGFxme7Vh/Vd5jgF9VTXcs/6W/yx7+rtV/v6HF+g4opt8PXFr1vK8Df9jFazayeJ33Ac4HvlT2e9xb/92wP/k89if2J9687eYGrAAOBT5R9Ft/D7wTOAG4rmjzdmAhlR0eg6j0dScXj3X0BSOpFELjq5Y7AZgG3Fe1vrnABmBysaybgBO7yHUZ8F7gZmBc8bk8pWO5Zb9u3io3j8h0kpmbqfzDOh94GvhBRHy0eHheRNwSEfdS+SfYcfjzh8D7ivvvB37QxaK3U/ngAdxB5YMF8GbgR8X971a1vw04NyI+T2XjYlMXyzy4yNihvWrdVwAnRsRYKv9wlxTzvw2cXNy/h8oewg9R2x6Gk4vlkpk/B54v5p9K5TW7LSLuLqZnUNlbeF1mPlY857kulnkDcFlEfJzKBlZnJ1LZGCAzf0NlT+XY4rGfZ+aLmfkMsA6Y2Om5y4EZEfG/I+I0YGM3v1d3f9dqrwKOBH5V/I6fpdIJdlhH18NGTgcWZeZW4MfAH3TsXVbrsz/ZLfsT+xMJfn9U5ngqRcVNVdM3Fm3eXtzuAu4EXg0cVjz2qYj4HZWCY0rV/N25NTPXZGY7lZ1H03bT9ifAWcBxwPU1/1bqFxYyXcjMXZm5ODP/DrgY+MOIGEFlz+B7M/O1VCrzEcVTfkBlvPLhlafn/9/OvYVYVYZhHP8/MtKB3YGsbsRSkixClLqSLvKigq6k8kKjA3kRggRBGERZdhUkUXSAwqQi6QAVREhlB0kSJ8goykIysIFuxByjySEGebt4v82slmvv2XNh43KeHwwze+21vvWtvVjv/k7v/NJQ7EREdvGBE8DQFHXYTX7R/w68Ienuht3GK3VoLKbfOchR0BfJRsM+SX3r1KdMAa9HxPLysyQiNpftfesQEevJL/EFwHeS5jWU3asO/1S2nfSZRsQosIwcCd0AvELNFPe1Xo/9lWtcGhE3V94/m7wfdWuBGyUdIhuc88g1tjZLOJ705XjieGLWzZNZSs6oDJODMtX8GAFPVp6ZxRGxTdJKMvdwRUQsIzs6/eJYV9/nveZtcpbo09LxsdOIOzI1kpZIqvbmlwO/MflgHJHUIacbAYiIX8kHYRPNo6f9DAO3l7/XVOpxOXA4IrYC24BrG479GVhceT2nUq87gK8i4k9gVJPr0+8CvlQmrS2IiF3AQ2QyXAf4CziPZrvJdfRIuoWcagX4HFgt6dLy3kWl/nuBGyQt6m6vFyjpioj4OiIeA46QDZBe51xJ5hv0Ggmtl30xMCci3iPvTfczrF5jz/ta2+8AcIkyeRtJc5XJ0V1XkgG4ev7zyRHgyyJiYUQsJBtAawepv7Wf44njSaUIxxOzZnvI2cajZeDnKBlDVpDPPcAnwLryXCFpfokRFwCjEXFc0lU05431i0NTiogR4BFykMJOM4OMmM02HeB5SReSyyMOAvdFxDFJW8k12IfIpRpV7wBbgEXTPN8DwHZJDwI7yHWbkGs4N0qaAMbINeJ1O8p+n5XXfwPXSNpXyukmqN0DvCTpXHJ5xL3ksovtZVmFgGfKNX4IvCtpFXB/RFSnUZ8A3pL0LbmefgQgIn6S9CiwszRoJoANETFcEu/eL9sPAzfVrmFLaeiJbMB8T65B7doMvKpMeD5ermVQ88ux3Q77w+X3a+XzGCcDZa/7Wt9vNfBc+cyGgGeB/ZLmkg3Ab2rnvw34Ikqid/EB8JSks2rb7czkeOJ4Qo/9HE/M0g9kLsubtW2dstSTiNgp6WpgrzIvfwy4E/gYWF+e6QPkYM5/RMQfkvZI+hH4iIx10xIRL0/3GPt/aHJ1gs2E0hgYj4iQtIZM1F01IkVpHQAAAJxJREFU4LHnALuA6yPihKSxiOicyvraySTdSv573U0zXReb3RxP2s/xxMxscJ6RmXnXAS8ohxiOAesGPTAixiU9To4Ujpyi+tnUhoCnZ7oSZjienAkcT8zMBuQZGTMzMzMzax0n+5uZmZmZWeu4I2NmZmZmZq3jjoyZmZmZmbWOOzJmZmZmZtY67siYmZmZmVnruCNjZmZmZmat8y9lzHc4spMU6QAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Iteration 0\n", "plot_iter(np.full(2,np.nan),M0,c0)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "# Iteration function\n", "Aex = np.full(ngrid+1,np.nan)\n", "Aex[1:] = A\n", "def iter(M0,c0):\n", " policy = interpolate.interp1d(M0,c0,kind='slinear',fill_value=\"extrapolate\") # interpolation function for policy\n", " M1 = np.full(ngrid+1,np.nan)\n", " c1 = np.full(ngrid+1,np.nan)\n", " M1[0] = c1[0] = 0 # add one point at the origin!\n", " for j,aj in enumerate(A):\n", " Mpr = max(R*aj+y,1e-10) # next period wealth\n", " cpr = policy(Mpr) # next period consumption\n", " c = imu( beta*R*mu(cpr) ) # inverse Euler\n", " M = aj + c # endogenous wealth\n", " M1[j+1] = M # save to array\n", " c1[j+1] = c\n", " pt = plot_iter(Aex,M1,c1) # returns fig object, plotted automatically\n", " return M1,c1,pt" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M1,c1,pt = iter(M0,c0)\n", "pt" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M,c,pt = iter(M1,c1)\n", "pt" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hide-output": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "for i in range(10):\n", " M,c,pt = iter(M,c)\n", "pt" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Class of models solvable by EGM\n", "\n", "- finite and infinite horizon dynamic models with continuous choice \n", "- strictly concave monotone and differentiable utility function (with analytic inverse marginal) \n", "- one continuous state variable (wealth) and one continuous choice variable (consumption) \n", "- particular structure of the law of motion for state variables (intertemporal budget constraint) \n", "- occasionally binding borrowing constraints \n", "- can also easily allow additional quasi-exogenous state variables (with motion rules dependent on $ A $ and not $ M $ or $ c $) \n", "\n", "\n", "Rather small class, although many important models in micro and macro economics are included" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Generalizations of EGM\n", "\n", "Multiple dimensions: hard because irregular grids in multiple dimensions\n", "\n", "- 📖 Barillas & Fernandez-Villaverde, JEDC 2007 “A Generalization of the Endogenous Grid Method” \n", "- 📖 Ludwig & Schön, Computational Economics, 2018 “Endogenous Grids in Higher Dimensions: Delaunay Interpolation and Hybrid Methods” \n", "- 📖 Matthew White, JEDC 2015 “The Method of Endogenous Gridpoints in Theory and Practice” \n", "- 📖 Iskhakov, Econ Letters 2015 “Multidimensional endogenous gridpoint method: solving triangular dynamic stochastic optimization problems without root-finding operations” + Corrigendum " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Generalizations of EGM\n", "\n", "Non-convex problems: hard because Euler equation is not a sufficient condition any longer\n", "\n", "- 📖 Giulio Fella, RED 2014 “A Generalized Endogenous Grid Method for Non-Smooth and Non-Concave Problems” \n", "- 📖 Iskhakov, Jørgensen, Rust, Schjerning, QE 2017 “The Endogenous Grid Method for Discrete-Continuous Dynamic Choice Models with (or without) Taste Shocks” \n", "- 📖 Jeppe Druedahl, Thomas Jørgensen, JEDC 2017 “A General Endogenous Grid Method for Multi-Dimensional Models with Non-Convexities and Constraints” " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Further learning resources\n", "\n", "- 📖 Chris Carroll (2006) Original article on EGM\n", " [http://pages.stern.nyu.edu/~dbackus/Computation/Carroll%20endog%20grid%20EL%2006.pdf](http://pages.stern.nyu.edu/~dbackus/Computation/Carroll%20endog%20grid%20EL%2006.pdf) \n", "- Literature cited above \n", "- 📖 >500 citations of Carroll’s paper\n", " [https://scholar.google.com/scholar?cites=20745560105937946&as_sdt=2005&sciodt=0,5&hl=en](https://scholar.google.com/scholar?cites=20745560105937946&as_sdt=2005&sciodt=0,5&hl=en) " ] } ], "metadata": { "celltoolbar": "Slideshow", "date": 1612589586.569124, "download_nb": false, "filename": "41_egm.rst", "filename_with_path": "41_egm", "kernelspec": { "display_name": "Python", "language": "python3", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" }, "title": "Foundations of Computational Economics #41" }, "nbformat": 4, "nbformat_minor": 4 }