{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Timber Harvesting Model - Cubic Spline Approximation\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demdp01.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2022-Oct-22\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## About\n", "\n", "Profit maximizing owner of a commercial tree stand must decide when to clearcut the stand." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.gridspec as gridspec\n", "from compecon import DPmodel, BasisSpline, NLP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model Parameters\n", "Assuming that the unit price of biomass is $p=1$, the cost to clearcut-replant is $\\kappa=0.2$, the stand carrying capacity $s_{\\max}=0.5$, biomass growth factor is $\\gamma=10\\%$ per period, and the annual discount factor $\\delta=0.9$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "price = 1.0\n", "κ = 0.2\n", "smax = 0.5\n", "ɣ = 0.1\n", "δ = 0.9" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### State Space\n", "The state variable is the stand biomass, $s\\in [0,s_{\\max}]$. \n", "\n", "Here, we represent it with a cubic spline basis, with $n=200$ nodes.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "n = 200\n", "basis = BasisSpline(n, 0, smax, labels=['biomass'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Action Space\n", "The action variable is $j\\in\\{0:\\text{'keep'},\\quad 1:\\text{'clear cut'}\\}$.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "options = ['keep', 'clear-cut']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reward function\n", "If the farmer clears the stand, the profit is the value of selling the biomass $ps$ minus the cost of clearing and replanting $\\kappa$, otherwise the profit is zero." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def reward(s, x, i , j):\n", " return (price * s - κ) * j" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### State Transition Function\n", "If the farmer clears the stand, it begins next period with $\\gamma s_{\\max}$ units. If he keeps the stand, then it grows to $s + \\gamma (s_{\\max} - s)$.\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def transition(s, x, i, j, in_, e):\n", " if j:\n", " return np.full_like(s, ɣ * smax)\n", " else:\n", " return s + ɣ * (smax - s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model Structure\n", "The value of the stand, given that it contains $s$ units of biomass at the beginning of the period, satisfies the Bellman equation\n", "\n", "\\begin{equation}\n", "V(s) = \\max\\left\\{(ps-\\kappa) + \\delta V(\\gamma s_{\\max}),\\quad \\delta V[s+\\gamma(s_{\\max}-s)] \\right\\} \n", "\\end{equation}\n", "\n", "To solve and simulate this model, use the CompEcon class ```DPmodel```." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving infinite-horizon model collocation equation by Newton's method\n", "iter change time \n", "------------------------------\n", " 0 3.1e-01 0.0209\n", " 1 1.1e-01 0.0299\n", " 2 1.1e-02 0.0389\n", " 3 4.6e-03 0.0469\n", " 4 1.6e-16 0.0559\n", "Elapsed Time = 0.06 Seconds\n" ] } ], "source": [ "model = DPmodel(basis, reward, transition,\n", " discount=δ,\n", " j=options)\n", "\n", "S = model.solve()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ```solve``` method retuns a pandas ```DataFrame```, which can easily be used to make plots. To see the first 10 entries of `S`, we use the `head` method" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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biomassvalueresidj*value[keep]value[clear-cut]
biomass
0.0000000.0000000.067287-1.387779e-17keep0.067287-0.132713
0.0002500.0002500.067320-7.491474e-09keep0.067320-0.132462
0.0005000.0005000.067353-5.953236e-09keep0.067353-0.132212
0.0007500.0007500.067387-1.332984e-09keep0.067387-0.131962
0.0010010.0010010.0674207.309628e-10keep0.067420-0.131712
\n", "
" ], "text/plain": [ " biomass value resid j* value[keep] \\\n", "biomass \n", "0.000000 0.000000 0.067287 -1.387779e-17 keep 0.067287 \n", "0.000250 0.000250 0.067320 -7.491474e-09 keep 0.067320 \n", "0.000500 0.000500 0.067353 -5.953236e-09 keep 0.067353 \n", "0.000750 0.000750 0.067387 -1.332984e-09 keep 0.067387 \n", "0.001001 0.001001 0.067420 7.309628e-10 keep 0.067420 \n", "\n", " value[clear-cut] \n", "biomass \n", "0.000000 -0.132713 \n", "0.000250 -0.132462 \n", "0.000500 -0.132212 \n", "0.000750 -0.131962 \n", "0.001001 -0.131712 " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To find the biomass level at which it is indifferent to keep or to clear cut, we interpolate as follows:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "When the biomass is 0.30669 its value is 0.17402 regardless of the action taken by the manager\n" ] } ], "source": [ "scrit = NLP(lambda s: model.Value_j(s).dot([1,-1])).broyden(0.0)\n", "vcrit = model.Value(scrit)\n", "print(f'When the biomass is {scrit:.5f} its value is {vcrit:.5f} regardless of the action taken by the manager')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot the Value Function and Optimal Action" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[1;31mSignature:\u001b[0m\n", "\u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubplots\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m\n", "\u001b[0m \u001b[0mnrows\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n", "\u001b[0m \u001b[0mncols\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n", "\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n", "\u001b[0m \u001b[0msharex\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n", "\u001b[0m \u001b[0msharey\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n", "\u001b[0m \u001b[0msqueeze\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n", "\u001b[0m \u001b[0msubplot_kw\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n", "\u001b[0m \u001b[0mgridspec_kw\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n", "\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mfig_kw\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\n", "\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", "\u001b[1;31mDocstring:\u001b[0m\n", "Create a figure and a set of subplots.\n", "\n", "This utility wrapper makes it convenient to create common layouts of\n", "subplots, including the enclosing figure object, in a single call.\n", "\n", "Parameters\n", "----------\n", "nrows, ncols : int, default: 1\n", " Number of rows/columns of the subplot grid.\n", "\n", "sharex, sharey : bool or {'none', 'all', 'row', 'col'}, default: False\n", " Controls sharing of properties among x (*sharex*) or y (*sharey*)\n", " axes:\n", "\n", " - True or 'all': x- or y-axis will be shared among all subplots.\n", " - False or 'none': each subplot x- or y-axis will be independent.\n", " - 'row': each subplot row will share an x- or y-axis.\n", " - 'col': each subplot column will share an x- or y-axis.\n", "\n", " When subplots have a shared x-axis along a column, only the x tick\n", " labels of the bottom subplot are created. Similarly, when subplots\n", " have a shared y-axis along a row, only the y tick labels of the first\n", " column subplot are created. To later turn other subplots' ticklabels\n", " on, use `~matplotlib.axes.Axes.tick_params`.\n", "\n", " When subplots have a shared axis that has units, calling\n", " `~matplotlib.axis.Axis.set_units` will update each axis with the\n", " new units.\n", "\n", "squeeze : bool, default: True\n", " - If True, extra dimensions are squeezed out from the returned\n", " array of `~matplotlib.axes.Axes`:\n", "\n", " - if only one subplot is constructed (nrows=ncols=1), the\n", " resulting single Axes object is returned as a scalar.\n", " - for Nx1 or 1xM subplots, the returned object is a 1D numpy\n", " object array of Axes objects.\n", " - for NxM, subplots with N>1 and M>1 are returned as a 2D array.\n", "\n", " - If False, no squeezing at all is done: the returned Axes object is\n", " always a 2D array containing Axes instances, even if it ends up\n", " being 1x1.\n", "\n", "subplot_kw : dict, optional\n", " Dict with keywords passed to the\n", " `~matplotlib.figure.Figure.add_subplot` call used to create each\n", " subplot.\n", "\n", "gridspec_kw : dict, optional\n", " Dict with keywords passed to the `~matplotlib.gridspec.GridSpec`\n", " constructor used to create the grid the subplots are placed on.\n", "\n", "**fig_kw\n", " All additional keyword arguments are passed to the\n", " `.pyplot.figure` call.\n", "\n", "Returns\n", "-------\n", "fig : `~.figure.Figure`\n", "\n", "ax : `.axes.Axes` or array of Axes\n", " *ax* can be either a single `~matplotlib.axes.Axes` object or an\n", " array of Axes objects if more than one subplot was created. The\n", " dimensions of the resulting array can be controlled with the squeeze\n", " keyword, see above.\n", "\n", " Typical idioms for handling the return value are::\n", "\n", " # using the variable ax for single a Axes\n", " fig, ax = plt.subplots()\n", "\n", " # using the variable axs for multiple Axes\n", " fig, axs = plt.subplots(2, 2)\n", "\n", " # using tuple unpacking for multiple Axes\n", " fig, (ax1, ax2) = plt.subplots(1, 2)\n", " fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2)\n", "\n", " The names ``ax`` and pluralized ``axs`` are preferred over ``axes``\n", " because for the latter it's not clear if it refers to a single\n", " `~.axes.Axes` instance or a collection of these.\n", "\n", "See Also\n", "--------\n", ".pyplot.figure\n", ".pyplot.subplot\n", ".pyplot.axes\n", ".Figure.subplots\n", ".Figure.add_subplot\n", "\n", "Examples\n", "--------\n", "::\n", "\n", " # First create some toy data:\n", " x = np.linspace(0, 2*np.pi, 400)\n", " y = np.sin(x**2)\n", "\n", " # Create just a figure and only one subplot\n", " fig, ax = plt.subplots()\n", " ax.plot(x, y)\n", " ax.set_title('Simple plot')\n", "\n", " # Create two subplots and unpack the output array immediately\n", " f, (ax1, ax2) = plt.subplots(1, 2, sharey=True)\n", " ax1.plot(x, y)\n", " ax1.set_title('Sharing Y axis')\n", " ax2.scatter(x, y)\n", "\n", " # Create four polar axes and access them through the returned array\n", " fig, axs = plt.subplots(2, 2, subplot_kw=dict(projection=\"polar\"))\n", " axs[0, 0].plot(x, y)\n", " axs[1, 1].scatter(x, y)\n", "\n", " # Share a X axis with each column of subplots\n", " plt.subplots(2, 2, sharex='col')\n", "\n", " # Share a Y axis with each row of subplots\n", " plt.subplots(2, 2, sharey='row')\n", "\n", " # Share both X and Y axes with all subplots\n", " plt.subplots(2, 2, sharex='all', sharey='all')\n", "\n", " # Note that this is the same as\n", " plt.subplots(2, 2, sharex=True, sharey=True)\n", "\n", " # Create figure number 10 with a single subplot\n", " # and clears it if it already exists.\n", " fig, ax = plt.subplots(num=10, clear=True)\n", "\u001b[1;31mFile:\u001b[0m c:\\programdata\\anaconda3\\lib\\site-packages\\matplotlib\\pyplot.py\n", "\u001b[1;31mType:\u001b[0m function\n" ] } ], "source": [ "?plt.subplots" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig1, axs = plt.subplots(2,1,figsize=[8,5], gridspec_kw=dict(height_ratios=[3.5, 1]))\n", "\n", "S[['value[keep]', 'value[clear-cut]']].plot(ax=axs[0])\n", "axs[0].set(title='Action-Contingent Value Functions',\n", " xlabel='',\n", " ylabel='Value of Stand',\n", " xticks=[])\n", "\n", "\n", "ymin,ymax = axs[0].get_ylim()\n", "axs[0].vlines(scrit,ymin, vcrit, linestyle=':')\n", "axs[0].annotate('$s^*$', [scrit, ymin])\n", "\n", "S['j*'].cat.codes.plot(ax=axs[1])\n", "axs[1].set(title='Optimal Action',\n", " ylabel='Action',\n", " ylim=[-0.25,1.25],\n", " yticks=[0,1],\n", " yticklabels=options);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot Residuals" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "S['resid2'] = 100*S.resid / S.value\n", "\n", "fig2, ax = plt.subplots()\n", "\n", "ax.plot(S['resid2'])\n", "ax.set(title='Bellman Equation Residual',\n", " xlabel='',\n", " ylabel='Percent Residual')\n", "\n", "ax.hlines(0,0,smax,'k');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation\n", "\n", "The path followed by the biomass is computed by the ```simulate()``` method. Here we simulate 32 periods starting with a biomass level $s_0 = 0$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "H = model.simulate(32, 0.0)\n", "\n", "fig3, ax = plt.subplots()\n", "ax.plot(H['biomass'])\n", "\n", "ax.set(title='Timber harvesting simulation',\n", " xlabel='Period',\n", " ylabel='Biomass');" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.7 ('base')", "language": "python", "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": "3.9.7" }, "vscode": { "interpreter": { "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186" } } }, "nbformat": 4, "nbformat_minor": 1 }