{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lucas Asset Pricing with advanced Approximation Methods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### João Brogueira and Fabian Schütze" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This note describes why and how we modified the computer code of the original lucastree.py module. We briefly reformulate Lucas' asset pricing problem as found in the lecture notes . Denote by $y$ the fruit of the tree. The fruitâ€™s growth rate follows the process $G(y,z') = y^\\alpha z'$ with $z' \\sim \\log N(0,\\sigma^2)$. The investor has CRRA preferences with curvature parameter $\\gamma$ and discount factor $\\beta$. Following Lucas (1978) , the pricing function, $p(y)$, solves the functional equation:\n", "\n", "$$f(y) = h(y) + \\beta \\int_Z f(G(y,z')) Q(dz').$$\n", "with\n", "\\begin{align*}\n", " f(y) &= p(y)y^{-\\gamma}, \\\\ \n", " h(y) &= \\beta \\int_Z \\left( G(y,z') \\right)^{1-\\gamma} Q(dz') = \\beta y^{ (1-\\gamma)\\alpha } \\exp \\left( (1-\\gamma)^2 \\sigma^2/2 \\right).\n", "\\end{align*}\n", "\n", "We want the numeric solution $f$ to comply with theoretical predictions about its functional form. In the following, it is first documented under which circumstances $h$ transmits montoncity and concavity onto $f$. In particular, we prove that if $G$ is strictly increasing and concave 1, $h$ transmits the sign of its first and second derivatives onto $f$. Additionally, we show that if both $G$ and $h$ are strictly decreasing and convex, $f$ is strictly decreasing and convex as well. The solution to the functional equation is numerically obtained by iterating the contraction mapping $Tf(y) = h(y) + \\beta \\int_Z f(G(y,z')) Q(dz')$ until the distance between two successive iterations is smaller than a tolerance criteria. To compute the integral numerically, $f(G(y,z'))$ needs to be evaluated at arguments $y$ that are not on the grid. This is a chance to impose the properties of $h$ onto $f$ through an appropriate approximation routine. This note discusses how to implement such a routine at the end.\n", "\n", "1. For the sake of brevity, when writing strictly increasing and concave we really mean strictly increasing and strictly concave. Also, strictly decreasing and convex refers to strictly decreasing and strictly convex, etc. \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Theoretical Predictions about the Functional Form of the Solution to Lucas' Asset Pricing Equation " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This section documents under which circumstances $f$ inherits the sign of the first and second derivatives of $h$. In the following, suppose all necessary assumptions to guarantee a unique solution to Lucas' asset pricing problem are satisfied. One assumption is that the function $h$ is bounded in the supremum norm. Numercially, the assumption is satisfied because the lower end of the interval $Y$ is striclty positive and because $Y$ is bounded. Theoretically, one can prove that the $h$ needs only be bounded in a weighted supremum norm when the parameter $\\alpha > 0$. Based on exercise 9.7 of the book by Stokey and Lucas with Prescott (1989), we prove the following proposition: \n", "\n", "**Proposition** \n", "\n", "1. Suppose $G$ is strictly increasing and concave in $y$. If $h$ is sctrictly increasing and convave, $f$ is strictly increasing and concave. If $h$ is sctrictly decreasing and convex, $f$ is strictly decreasing and convex.\n", "2. Suppose $G$ is strictly decreasing and convex in $y$. If $h$ is strictly decreasing and convex, $f$ is strictly decreasing and convex.\n", "\n", "**Proof**\n", "\n", "**1** Following the notation of the lecture notes, denote by $cb\\mathbf{R}_+$ the set of continuous and bounded functions $f:\\mathbf{R}_{+} \\rightarrow \\mathbf{R}_{+}$ . The set $cb'\\mathbf{R}_{+} \\subset cb\\mathbf{R}_{+}$ is the set of continuous, bounded, nondecreasing and concave functions, and $cb''\\mathbf{R}_{+} \\subset cb'\\mathbf{R}_{+}$ imposes additionally strict monotonicity and concavity. We want to show that the contraction operator $T$ maps any function $\\tilde{f} \\in cb'\\mathbf{R}_{+}$ into the subset $cb''\\mathbf{R}_{+}$. As the solution to the functional equation is characterized by $Tf = f$ and $cb'\\mathbf{R}_{+}$ is a closed set, if the operator $T$ transforms any nondecreasing and concave function into a strictly increasing and concave function, then $f$ is strictly increasing and concave (Corollary 1 of the Contraction Mapping Theorem in Stokey and Lucas with Prescott (1989), p. 52).\n", " \n", "To show the desired result, suppose first that $h$ is strictly increasing and concave and pick any $\\tilde{f} \\in cb'\\mathbf{R}_{+}$. To begin, study whether $T\\tilde{f}$ is strictly increasing. For any pair $\\hat{y},y \\in Y$ with $\\hat{y} > y$, the function $T\\tilde{f}$ satisfies: \n", "\n", "\\begin{align*}\n", "T\\tilde{f}(\\hat{y}) &= h(\\hat{y}) + \\beta \\int_Z \\tilde{f}( G(\\hat{y},z')) Q(dz')\\\\\n", "\t\t\t \t \t&> h(y) + \\beta \\int_Z \\tilde{f}( G(y,z')) Q(dz')\\\\\n", "\t\t \t \t&= T\\tilde{f}(y).\n", "\\end{align*}\n", " \n", "The inequality holds because $G$ and $h$ are strictly increasing and $\\tilde{f}$ is nondecreasing. Hence, $T\\tilde{f}$ is strictly increasing. \n", "\n", "To analyze concavity, define $y_{\\omega} = \\omega y + (1-\\omega) y'$, for any $y,y' \\in Y$, $y \\neq y'$, and $0 < \\omega < 1$. The strict concavity form of $h$ and $G$, together with $\\tilde{f}$ being concave, ensure that:\n", "\n", "\\begin{align*}\n", "T\\tilde{f}(y_\\omega) &= h(y_\\omega) + \\beta \\int_Z \\tilde{f}( G(y_\\omega,z')) Q(dz') \\\\\n", "\t \t\t &> \\omega \\left[ h(y) + \\beta \\int_Z \\tilde{f}( G(y,z')) Q(dz') \\right] + (1 - \\omega) \\left[ h(y') + \\beta \\int_Z \\tilde{f}( G(y',z')) Q(dz') \\right] \\\\\n", "\t\t \t \t\t &= \\omega T\\tilde{f}(y) + (1-\\omega) T \\tilde{f}(y').\n", "\\end{align*}\n", "\n", "The function $T\\tilde{f}$ is stricly concave. Taken together, we know that for any $\\tilde{f} \\in cb'\\mathbf{R}_{+}$, $T\\tilde{f} \\in cb''\\mathbf{R}_{+}$. Hence, $f$ must be an element of the set $cb''\\mathbf{R}_+$, guaranteeing that $f$ has the same functional form as $h$.

\n", "Now, suppose $h$ is convex and decreasing. We could again define the operator $T$ as $Tf(y) = h(y) + \\beta \\int_Z f(G(y,z')) Q(dz')$ and study into which subset a candidate solution is mapped into. To facilitate analysis though, take a different route. Look at the modified operator \n", "$$Tf_{-} = h_{-} + \\beta \\int_Z f_{-} (G(y,z')) Q(z'),$$\n", "with $h_{-}\t = -h$ and $f_{-} = -f$. Under the same assumptions guaranteeing a unique solution to the original contraction mapping, there exists a unique solution to the modified contraction mapping. As $h_{-}$ is strictly increasing and concave, the proof above applies to the modified contraction mapping. As $f_{-}$ is strictly increasing and concave, $f$ is strictly decreasing and convex and inherits the properties of $h$. \n", "\n", "**2** As both $G$ and $h$ are strictly decreasing and convex, one can proceed in a similar fashion as in case (1.) to show that $h$ transmits its functional form to $f$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The different cases of the proposition can be rephrased in terms of the values of the parameters $\\gamma,\\alpha$. The functional form of $h$ is jointly determined by $\\gamma,\\alpha$ as $h(y) = y^{(1-\\gamma)\\alpha} \\exp \\left( (1-\\gamma)^2 \\sigma^2/2 \\right)$. If $0 < \\alpha < 1$, $G$ is strictly increasing and concave and case (1.) of the proposition applies. If $0 < \\gamma < 1$, $f$ is strictly increasing and concave. If $\\gamma > 1$, $f$ is strictly decreasing and convex. In contrast, suppose $-1 < \\alpha < 0$. If $0 < \\gamma < 1$ case (2.) of the proposition applies and $f$ is strictly decreasing and convex. If $\\gamma > 1$, theory does not offer any help in determining the functional form of $f$. In this situation $G$ is decreasing and convex, while $h$ is increasing. Our proposition is deliberately more restrictive than the one in exercise 9.7 of Stokey and Lucas with Prescott (1989). Because we can calculate the functions $f$ analytically for the special cases of $\\alpha \\in \\left\\lbrace 0,1\\right\\rbrace$, numercial techniques are not needed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Imposing the functional form of $h$ onto $f$ through advanced approximation " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This section describes how we impose the functional form of $h$ onto $f$. The solution to the functional equation is numerically obtained by iterating the contraction mapping $Tf(y) = h(y) + \\beta \\int_Z f(G(y,z')) Q(dz')$ until the distance between two successive iterations is smaller than a tolerance criteria. To compute the integral numerically, $f(G(y,z'))$ needs to be evaluated at arguments $x$ that are not on the grid through numerical approximation. This approximation is a chance to impose the properties of $h$ onto $f$. The grid points are a set $Y_{\\text{Grid}} = \\left\\lbrace y_1,y_2,\\ldots, y_{N-1},y_N \\right\\rbrace \\subset Y$, with $y_l < y_m$ if $l < m$, $l,m \\in \\mathbf{N}$. Point $x \\in Y$ is not on the gird. If $y_1 < x < y_N$ we interpolate the functional $f$ at $x$ by: \n", "\n", "\$$\n", "f(x) = f(y_L) + \\dfrac{f(y_H) - f(y_L)}{h(y_H) - h(y_L)} \\left( h(x) - h(y_L) \\right).\n", "\$$\n", "\n", "with $y_L = \\max \\left\\lbrace y_i \\in Y_{\\text{Grid}} : y_i < x \\right\\rbrace$ and $y_H = \\min \\left\\lbrace y_i \\in Y_{\\text{Grid}}: y_i > x \\right\\rbrace$. For any point $x$ lower than $y_1$ or higher than $y_N$, we define the function value as:\n", "\n", "\\begin{align}\n", "f(x) = \n", " \\begin{cases}\n", " f(y_1) + \\dfrac{f(y_1) - f(y_2)}{h(y_1) - h(y_2)} \\left(h(x) - h(y_1) \\right) & \\text{if } x < y_1,\\\\\n", " f(y_N) + \\dfrac{f(y_N) - f(y_{N-1})}{h(y_N) - h(y_{N-1})} \\left( h(x) - h(y_N) \\right) & \\text{if } x > y_N.\n", " \\end{cases}\n", "\\end{align}\n", "\n", "The approximation transmits the slope and shape of the function $h$ onto $f$ as $f'(x) \\propto h'(x)$ and $f''(x) \\propto h''(x)$ because the ratio in front of $h(x)$ is always positive. The function interpolationFunction of the modified lucastree.py module converts this idea into computer code. The entire module is contained in the next cell." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting ./lucastree.py\n" ] } ], "source": [ "%%writefile ./lucastree.py\n", "r\"\"\"\n", "Filename: lucastree.py\n", "\n", "Authors: Joao Brogueira and Fabian Schuetze \n", "\n", "This file is a slight modification of the lucastree.py file \n", "by Thomas Sargent, John Stachurski, Spencer Lyon under the \n", "quant-econ project. We don't claim authorship of the entire file,\n", "but full responsability for it and any existing mistakes.\n", "\n", "Solves the price function for the Lucas tree in a continuous state\n", "setting, using piecewise linear approximation for the sequence of\n", "candidate price functions. The consumption endownment follows the log\n", "linear AR(1) process\n", "\n", ".. math::\n", "\n", " log y' = \\alpha log y + \\sigma \\epsilon\n", "\n", "where y' is a next period y and epsilon is an iid standard normal shock.\n", "Hence\n", "\n", ".. math::\n", "\n", " y' = y^{\\alpha} * \\xi,\n", "\n", "where\n", "\n", ".. math::\n", "\n", " \\xi = e^(\\sigma * \\epsilon)\n", "\n", "The distribution phi of xi is\n", "\n", ".. math::\n", "\n", " \\phi = LN(0, \\sigma^2),\n", " \n", "where LN means lognormal.\n", "\n", "\"\"\"\n", "#from __future__ import division # == Omit for Python 3.x == #\n", "import numpy as np\n", "from scipy.stats import lognorm\n", "from scipy.integrate import fixed_quad\n", "from quantecon.compute_fp import compute_fixed_point\n", "\n", "\n", "class LucasTree(object):\n", "\n", " \"\"\"\n", " Class to solve for the price of a tree in the Lucas\n", " asset pricing model\n", "\n", " Parameters\n", " ----------\n", " gamma : scalar(float)\n", " The coefficient of risk aversion in the investor's CRRA utility\n", " function\n", " beta : scalar(float)\n", " The investor's discount factor\n", " alpha : scalar(float)\n", " The correlation coefficient in the shock process\n", " sigma : scalar(float)\n", " The volatility of the shock process\n", " grid : array_like(float), optional(default=None)\n", " The grid points on which to evaluate the asset prices. Grid\n", " points should be nonnegative. If None is passed, we will create\n", " a reasonable one for you\n", "\n", " Attributes\n", " ----------\n", " gamma, beta, alpha, sigma, grid : see Parameters\n", " grid_min, grid_max, grid_size : scalar(int)\n", " Properties for grid upon which prices are evaluated\n", " init_h : array_like(float)\n", " The functional values h(y) with grid points being arguments \n", " phi : scipy.stats.lognorm\n", " The distribution for the shock process\n", "\n", " Notes\n", " -----\n", " This file is a slight modification of the lucastree.py file \n", " by Thomas Sargent, John Stachurski, Spencer Lyon, [SSL]_ under the \n", " quant-econ project. We don't claim authorship of the entire file,\n", " but full responsability for it and any existing mistakes.\n", "\n", " References\n", " ----------\n", " .. [SSL] Thomas Sargent, John Stachurski and Spencer Lyon, lucastree.py,\n", " GitHub repository, \n", " https://github.com/QuantEcon/QuantEcon.py/blob/master/quantecon/models/lucastree.py\n", "\n", " Examples\n", " --------\n", " >>> tree = LucasTree(gamma=2, beta=0.95, alpha=0.90, sigma=0.1)\n", " >>> grid, price_vals = tree.grid, tree.compute_lt_price()\n", "\n", " \"\"\"\n", "\n", " def __init__(self, gamma, beta, alpha, sigma, grid=None):\n", " self.gamma = gamma\n", " self.beta = beta\n", " self.alpha = alpha\n", " self.sigma = sigma\n", "\n", " # == set up grid == #\n", " if grid is None:\n", " (self.grid, self.grid_min,\n", " self.grid_max, self.grid_size) = self._new_grid()\n", " else:\n", " self.grid = np.asarray(grid)\n", " self.grid_min = min(grid)\n", " self.grid_max = max(grid)\n", " self.grid_size = len(grid)\n", "\n", " # == set up distribution for shocks == #\n", " self.phi = lognorm(sigma)\n", "\n", " # == set up integration bounds. 4 Standard deviations. Make them\n", " # private attributes b/c users don't need to see them, but we\n", " # only want to compute them once. == #\n", " self._int_min = np.exp(-5 * sigma)\n", " self._int_max = np.exp(5 * sigma)\n", "\n", " # == Set up h for the Lucas Operator == #\n", " self.init_h = self.h(self.grid)\n", "\n", " def h(self, x):\n", " \"\"\"\n", " Compute the function values of h in the Lucas operator. \n", "\n", " Parameters\n", " ----------\n", " x : array_like(float)\n", " The arguments over which to computer the function values \n", "\n", " Returns\n", " -------\n", " h : array_like(float)\n", " The functional values \n", "\n", " Notes\n", " -----\n", " Recall the functional form of h \n", "\n", " .. math:: h(x) &= \\beta * \\int_Z u'(G(x,z)) phi(dz)\n", " &= \\beta x**((1-\\gamma)*\\alpha) * \\exp((1-\\gamma)**2 *\\sigma /2) \n", "\n", " \"\"\"\n", " alpha, gamma, beta, sigma = self.alpha, self.gamma, self.beta, self.sigma\n", " h = beta * x**((1 - gamma) * alpha) * \\\n", " np.exp((1 - gamma)**2 * sigma**2 / 2) * np.ones(x.size)\n", "\n", " return h\n", "\n", " def _new_grid(self):\n", " \"\"\"\n", " Construct the default grid for the problem\n", "\n", " This is defined to be np.linspace(0, 10, 100) when alpha >= 1\n", " and 100 evenly spaced points covering 4 standard deviations\n", " when alpha < 1\n", "\n", " \"\"\"\n", " grid_size = 50\n", " if abs(self.alpha) >= 1.0:\n", " grid_min, grid_max = 0.1, 10\n", " else:\n", " # == Set the grid interval to contain most of the mass of the\n", " # stationary distribution of the consumption endowment == #\n", " ssd = self.sigma / np.sqrt(1 - self.alpha**2)\n", " grid_min, grid_max = np.exp(-4 * ssd), np.exp(4 * ssd)\n", "\n", " grid = np.linspace(grid_min, grid_max, grid_size)\n", "\n", " return grid, grid_min, grid_max, grid_size\n", "\n", " def integrate(self, g, int_min=None, int_max=None):\n", " \"\"\"\n", " Integrate the function g(z) * self.phi(z) from int_min to\n", " int_max.\n", "\n", " Parameters\n", " ----------\n", " g : function\n", " The function which to integrate\n", "\n", " int_min, int_max : scalar(float), optional\n", " The bounds of integration. If either of these parameters are\n", " None (the default), they will be set to 4 standard\n", " deviations above and below the mean.\n", "\n", " Returns\n", " -------\n", " result : scalar(float)\n", " The result of the integration\n", "\n", " \"\"\"\n", " # == Simplify notation == #\n", " phi = self.phi\n", " if int_min is None:\n", " int_min = self._int_min\n", " if int_max is None:\n", " int_max = self._int_max\n", "\n", " # == set up integrand and integrate == #\n", " integrand = lambda z: g(z) * phi.pdf(z)\n", " result, error = fixed_quad(integrand, int_min, int_max, n=20)\n", " return result, error\n", "\n", " def Approximation(self, x, grid, f):\n", " r\"\"\"\n", " Approximates the function f at given sample points x.\n", "\n", " Parameters\n", " ----------\n", " x: array_like(float)\n", " Sample points over which the function f is evaluated\n", "\n", " grid: array_like(float) \n", " The grid values representing the domain of f \n", "\n", " f: array_like(float)\n", " The function values of f over the grid \n", "\n", " Returns:\n", " --------\n", " fApprox: array_like(float)\n", " The approximated function values at x\n", "\n", " Notes\n", " -----\n", " Interpolation is done by the following function:\n", "\n", " .. math:: f(x) = f(y_L) + \\dfrac{f(y_H) - f(y_L)}{h(y_H) - h(y_L)} (h(x) - h(y_L) ).\n", "\n", " Extrapolation is done as follows:\n", "\n", " .. math:: f(x) = \n", " \\begin{cases}\n", " f(y_1) + \\dfrac{f(y_1) - f(y_2)}{h(y_1) - h(y_2)} \\left(h(x) - h(y_1) \\right) & \\text{if } x < y_1,\\\\\n", " f(y_N) + \\dfrac{f(y_N) - f(y_{N-1})}{h(y_N) - h(y_{N-1})} \\left( h(x) - h(y_N) \\right) & \\text{if } x > y_N.\n", " \\end{cases}\n", "\n", " The approximation routine imposes the functional\n", " form of the function :math:h onto the function math:f, as stated\n", " in chapter 9.2 (in particular theorem 9.6 and 9.7 and exercise 9.7) of the \n", " book by Stokey, Lucas and Prescott (1989).\n", "\n", " \"\"\"\n", " # == Initalize and create empty arrays to be filled in the == #\n", " gamma, sigma, beta = self.gamma, self.sigma, self.beta\n", " hX, hGrid = self.h(x), self.init_h\n", " fL, fH, fApprox = np.empty_like(x), np.empty_like(x), np.empty_like(x)\n", " hL, idxL, idxH, hH = np.empty_like(x), np.empty_like(\n", " x), np.empty_like(x), np.empty_like(x)\n", "\n", " # == Create Boolean array to determine which sample points are used for interpoltion\n", " # and which are used for extrapolation == #\n", " lower, middle, upper = (x < grid[0]), (x > grid[0]) & (\n", " x < grid[-1]), (x > grid[-1])\n", "\n", " # == Calcualte the indices of y_L, idxL[index], and y_H ,idxH[index], that are below and above a sample point, called value.\n", " # In the notation of the interpolation routine, these indices are used to pick the function values\n", " # f(y_L),f(y_H),h(y_L) and h(y_H) == #\n", " for index, value in enumerate(x):\n", " # Calculates the indices of y_L\n", " idxL[index] = (np.append(grid[grid <= value], grid[0])).argmax()\n", " idxH[index] = min(idxL[index] + 1, len(grid) - 1)\n", " fL[index] = f[idxL[index]]\n", " fH[index] = f[idxH[index]]\n", " hL[index] = hGrid[idxL[index]]\n", " hH[index] = hGrid[idxH[index]]\n", "\n", " # == Interpolation == #\n", " if self.alpha != 0:\n", " ratio = (fH[middle] - fL[middle]) / (hH[middle] - hL[middle])\n", " elif self.alpha == 0:\n", " # If self.alpha ==0, ratio is zero, as hH == hL\n", " ratio = (hH[middle] - hL[middle])\n", " fApprox[middle] = fL[middle] + ratio * (hX[middle] - hL[middle])\n", "\n", " # == Extrapolation == #\n", " if self.alpha != 0:\n", " fApprox[lower] = f[\n", " 0] + (f[0] - f[1]) / (hGrid[0] - hGrid[1]) * (hX[lower] - hGrid[0])\n", " fApprox[upper] = f[-1] + \\\n", " (f[-1] - f[-2]) / (hGrid[-1] - hGrid[-2]) * \\\n", " (hX[upper] - hGrid[-1])\n", " elif self.alpha == 0:\n", " fApprox[lower] = f[0]\n", " fApprox[upper] = f[-1]\n", "\n", " return fApprox\n", "\n", " def lucas_operator(self, f, Tf=None):\n", " \"\"\"\n", " The approximate Lucas operator, which computes and returns the\n", " updated function Tf on the grid points.\n", "\n", " Parameters\n", " ----------\n", " f : array_like(float)\n", " A candidate function on R_+ represented as points on a grid\n", " and should be flat NumPy array with len(f) = len(grid)\n", "\n", " Tf : array_like(float)\n", " Optional storage array for Tf\n", "\n", " Returns\n", " -------\n", " Tf : array_like(float)\n", " The updated function Tf\n", "\n", " Notes\n", " -----\n", " The argument Tf is optional, but recommended. If it is passed\n", " into this function, then we do not have to allocate any memory\n", " for the array here. As this function is often called many times\n", " in an iterative algorithm, this can save significant computation\n", " time.\n", "\n", " \"\"\"\n", " grid, h = self.grid, self.init_h\n", " alpha, beta = self.alpha, self.beta\n", "\n", " # == set up storage if needed == #\n", " if Tf is None:\n", " Tf = np.empty_like(f)\n", "\n", " # == Apply the T operator to f == #\n", " Af = lambda x: self.Approximation(x, grid, f)\n", "\n", " for i, y in enumerate(grid):\n", " Tf[i] = h[i] + beta * self.integrate(lambda z: Af(y**alpha * z))[0]\n", "\n", " return Tf\n", "\n", " def compute_lt_price(self, error_tol=1e-7, max_iter=600, verbose=0):\n", " \"\"\"\n", " Compute the equilibrium price function associated with Lucas\n", " tree lt\n", "\n", " Parameters\n", " ----------\n", " error_tol, max_iter, verbose\n", " Arguments to be passed directly to\n", " quantecon.compute_fixed_point. See that docstring for more\n", " information\n", "\n", "\n", " Returns\n", " -------\n", " price : array_like(float)\n", " The prices at the grid points in the attribute grid of the\n", " object\n", "\n", " \"\"\"\n", " # == simplify notation == #\n", " grid, grid_size = self.grid, self.grid_size\n", " lucas_operator, gamma = self.lucas_operator, self.gamma\n", "\n", " # == Create storage array for compute_fixed_point. Reduces memory\n", " # allocation and speeds code up == #\n", " Tf = np.empty(grid_size)\n", "\n", " # == Initial guess, just a vector of ones == #\n", " f_init = np.ones(grid_size)\n", " f = compute_fixed_point(lucas_operator, f_init, error_tol,\n", " max_iter, verbose, Tf=Tf)\n", "\n", " price = f * grid**gamma\n", "\n", " return price\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following two figures plot the functions $h,f$ and their first and second differences for parameters $(\\gamma,\\alpha) \\in \\left\\lbrace (2,0.75),(0.5,0.75),(0.5,-0.75) \\right\\rbrace$. Note that the x-axis is in indices instead of grid values because the grid values change with different parameters. The graph illustrates that the sign of the slope and shape of $h$ is transmitted to $f$. We used $|\\alpha| = 0.75$ because it generates a relatively strong visual slope of $h$. Our unit testing function also consider autoregressive parameters of $|\\alpha| \\in \\left\\lbrace 0.25, 0.5 \\right\\rbrace$. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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l3eiceyrDsQieea6tzYfQb39beugh6eUv9yH0mmuk8vJc1w4AAABAVD4Fz4sl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\nKSIiIiIiI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RkVLwlCmhtRXuuCOE0F/8AtasCSH09a8Pd8vVdaEiIiIiIpPXpAueZrYCuA6o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\nE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from lucastree import LucasTree\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "# first element gamma, second element alpha\n", "vector = np.array([[2, 0.75], [0.5, 0.75], [0.5, -0.75]])\n", "tree = LucasTree(gamma=2, beta=0.95, alpha=0.5, sigma=0.1)\n", "h, hdiff, hdiff2 = np.empty((len(tree.grid), vector.shape[0])), np.empty(\n", " (len(tree.grid) - 1, vector.shape[0])), np.empty((len(tree.grid) - 2, vector.shape[0]))\n", "for idx, element in enumerate(vector):\n", " tree = LucasTree(gamma=element[0], beta=0.95, alpha=element[1], sigma=0.1)\n", " h[:, idx] = tree.h(tree.grid)\n", " hdiff[:, idx] = np.ediff1d(h[:, idx])\n", " hdiff2[:, idx] = np.ediff1d(hdiff[:, idx])\n", "fig1, (ax1, ax2, ax3) = plt.subplots(3, 1, sharex='col')\n", "annotation = ['(gamma,alpha): ' + str((i)) for i in vector]\n", "ax1.plot(h)\n", "ax2.plot(hdiff)\n", "ax3.plot(hdiff2)\n", "ax1.set_title('Plot of h')\n", "ax2.set_title('Plot of the first difference of h')\n", "ax3.set_title('Plot of the second difference of h')\n", "ax3.legend(annotation, loc='upper center', bbox_to_anchor=(0.5, -0.07),\n", " ncol=2, fancybox=True, shadow=True, fontsize=10)\n", "fig1.suptitle(\n", " 'Plot of the function h and its first and second difference', fontsize=15)\n", "fig1.set_size_inches(15.5, 10.5)\n", "fig1.show()\n", "\n", "\n", "# first element gamma, second element alpha\n", "vector = np.array([[2, 0.75], [0.5, 0.75], [0.5, -0.75]])\n", "tree = LucasTree(gamma=2, beta=0.95, alpha=0.5, sigma=0.1)\n", "f, fdiff, fdiff2 = np.empty((len(tree.grid), vector.shape[0])), np.empty(\n", " (len(tree.grid) - 1, vector.shape[0])), np.empty((len(tree.grid) - 2, vector.shape[0]))\n", "price = np.empty_like(f)\n", "for idx, element in enumerate(vector):\n", " tree = LucasTree(gamma=element[0], beta=0.95, alpha=element[1], sigma=0.1)\n", " price[:, idx], grid = tree.compute_lt_price(), tree.grid\n", " f[:, idx] = price[:, idx] * grid**(-element[0])\n", " fdiff[:, idx] = np.ediff1d(f[:, idx])\n", " fdiff2[:, idx] = np.ediff1d(fdiff[:, idx])\n", "fig2, (ax1, ax2, ax3) = plt.subplots(3, 1, sharex='col')\n", "annotation = ['(gamma,alpha): ' + str((i)) for i in vector]\n", "ax1.plot(f)\n", "ax2.plot(fdiff)\n", "ax3.plot(fdiff2)\n", "ax1.set_title('Plot of f')\n", "ax2.set_title('Plot of the first difference of f')\n", "ax3.set_title('Plot of the second difference of f')\n", "ax3.legend(annotation, loc='upper center', bbox_to_anchor=(0.5, -0.05),\n", " ncol=2, fancybox=True, shadow=True, fontsize=11)\n", "fig2.suptitle(\n", " 'Plot of the function f and its first and second difference', fontsize=15)\n", "fig2.set_size_inches(15.5, 10.5)\n", "fig2.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The two following figures graphs the solution $f$ if $\\alpha \\in \\left\\lbrace 0,1 \\right\\rbrace$. If dividends follow an i.i.d. process, ($\\alpha = 0$) the function $f$ is constant. We reproduce the numerical results in the top panel of the following figure. The lower subplot graphs the price dividend ratio when dividend growth follows and i.i.d process ($\\alpha =1$). As predicted by theory, the price dividend ratio is a constant. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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NPJVSmp6yh8mJ4QkV09yQUnqgiP+nwMhi+EeAv6SUbkgpvZ1S+i6wtIV4G9yT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\nr263/rbbbmPu3Lls3LiRgw8+mG9961u164444giWLVvGhg0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from lucastree import LucasTree\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "beta, gamma, sigma = 0.95, 2, 0.1\n", "\n", "tree = LucasTree(gamma=gamma, beta=beta, alpha=1, sigma=sigma)\n", "priceLinear, grid = tree.compute_lt_price(), tree.grid\n", "fig1, (ax1, ax2) = plt.subplots(2, 1)\n", "theoreticalPDRatio = np.ones(len(grid)) * beta * np.exp((1 - gamma) **\n", " 2 * sigma**2 / 2) / (1 - beta * np.exp((1 - gamma)**2 * sigma**2 / 2))\n", "ax1.plot(grid, priceLinear / grid, grid, theoreticalPDRatio, 'g^')\n", "annotation = ['Numerical Solution', 'Analytical Solution']\n", "ax1.legend(annotation)\n", "ax1.set_title('price dividend ratio for alpha = 1')\n", "ax1.set_ylim([min(priceLinear / grid) - 1, max(priceLinear / grid) + 1])\n", "tree = LucasTree(gamma=gamma, beta=beta, alpha=0, sigma=sigma)\n", "priceFalling, grid = tree.compute_lt_price(), tree.grid\n", "theoreticalF = np.ones(len(grid)) * beta * \\\n", " np.exp((1 - gamma)**2 * sigma**2 / 2) / (1 - beta)\n", "f = priceFalling * grid**(-2)\n", "ax2.plot(grid, f, grid, theoreticalF, 'g^')\n", "ax2.set_ylim([min(f) - 1, max(f) + 1])\n", "annotation = ['Numerical Solution', 'Analytical Solution']\n", "ax2.legend(annotation)\n", "ax2.set_title('function f for alpha = 0')\n", "fig1.set_size_inches(15.5, 10.5)\n", "fig1.suptitle(\n", " 'Plot of the function f and the price dividend ratio for alpha=0 and alpha=1 respecitvely', fontsize=15)\n", "fig1.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we report the unit testing function accompanying our lucastree.py module. This file tests if the functional form of $f$ adheres to the theoretical predicitons as outlined by the Proposition above. The file can be run from the Shell. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Overwriting ./test_lucastree.py\n" ] } ], "source": [ "%%writefile ./test_lucastree.py\n", "\"\"\"\n", "filename: test_lucastree.py\n", "\n", "Authors: Joao Brogueira and Fabian Schuetze \n", "\n", "This file contains for different test for the \n", "lucastree.py file \n", "\n", "Functions\n", "---------\n", " compute_lt_price() [Status: Tested in test_ConstantPDRatio, test_ConstantF,\n", " test_slope_f, test_shape_f]\n", "\n", "\"\"\"\n", "\n", "import unittest\n", "from lucastree import LucasTree # This relative importing doesn't work!\n", "import numpy as np\n", "\n", "\n", "class Testlucastree(unittest.TestCase):\n", "\n", " \"\"\"\n", " Test Suite for lucastree.py based on the outout of the \n", " LucasTree.compute_lt_price() function.\n", "\n", " \"\"\"\n", " # == Parameter values applicable to all test cases == #\n", " beta = 0.95\n", " sigma = 0.1\n", "\n", " # == Paramter values for different tests == #\n", " ConstantPD = np.array([2, 1])\n", " ConstantF = np.array([2, 0])\n", " FunctionalForm = np.array([[2, 0.75], [2, 0.5], [2, 0.25], [0.5, 0.75], [\n", " 0.5, 0.5], [0.5, 0.25], [0.5, -0.75], [0.5, -0.5], [0.5, -0.25]])\n", "\n", " # == Tolerance Criteria == #\n", " Tol = 1e-2\n", "\n", " def setUp(self):\n", " self.storage = lambda parameter0, parameter1: LucasTree(gamma=parameter0, beta=self.beta, alpha=parameter1,\n", " sigma=self.sigma)\n", "\n", " def test_ConstantPDRatio(self):\n", " \"\"\"\n", " Test whether the numerically computed price dividend ratio is \n", " identical to its theoretical counterpart when dividend \n", " growth follows an idd process\n", "\n", " \"\"\"\n", " gamma, alpha = self.ConstantPD\n", " tree = self.storage(gamma, alpha)\n", " grid = tree.grid\n", " theoreticalPDRatio = np.ones(len(grid)) * self.beta * np.exp(\n", " (1 - gamma)**2 * self.sigma**2 / 2) / (1 - self.beta * np.exp((1 - gamma)**2 * self.sigma**2 / 2))\n", " self.assertTrue(\n", " np.allclose(theoreticalPDRatio, tree.compute_lt_price() / grid, atol=self.Tol))\n", "\n", " def test_ConstantF(self):\n", " \"\"\"\n", " Tests whether the numericlaly obtained solution, math:f \n", " to the functional equation :math:f(y) = h(y) + \\beta \\int_Z f(G(y,z')) Q(z')\n", " is identical to its theoretical counterpart, when divideds follow an \n", " iid process \n", "\n", " \"\"\"\n", " gamma, alpha = self.ConstantF\n", " tree = self.storage(gamma, alpha)\n", " grid = tree.grid\n", " theoreticalF = np.ones(len(\n", " grid)) * self.beta * np.exp((1 - gamma)**2 * self.sigma**2 / 2) / (1 - self.beta)\n", " self.assertTrue(np.allclose(\n", " theoreticalF, tree.compute_lt_price() * grid**(-gamma), atol=self.Tol))\n", "\n", " def test_slope_f(self):\n", " \"\"\"\n", " Tests whether the first difference of the numerically obtained function \n", " :math:f is has the same sign as the first difference of the function \n", " :math:h.\n", "\n", " Notes\n", " -----\n", " This test is motivated by Theorem 9.7 ans exercise 9.7c) of the \n", " book by Stokey, Lucas and Prescott (1989)\n", "\n", " \"\"\"\n", " for parameters in self.FunctionalForm:\n", " gamma, alpha = parameters\n", " tree = self.storage(gamma, alpha)\n", " f = tree.compute_lt_price() * tree.grid ** (-gamma)\n", " h = tree.h(tree.grid)\n", " fdiff, hdiff = np.ediff1d(f), np.ediff1d(h)\n", " if all(hdiff > 0):\n", " self.assertTrue(all(fdiff > 0))\n", " elif all(hdiff < 0):\n", " self.assertTrue(all(fdiff < 0))\n", "\n", " def test_shape_f(self):\n", " \"\"\"\n", " Tests whether the second difference of the numerically obtained function \n", " :math:f is has the same sign as the second difference of the function \n", " :math:h.\n", "\n", " Notes\n", " -----\n", " This test is motivated by Theorem 9.8 ans exercise 9.7d) of the \n", " book by Stokey, Lucas and Prescott (1989)\n", "\n", " \"\"\"\n", " for parameters in self.FunctionalForm:\n", " gamma, alpha = parameters\n", " tree = self.storage(gamma, alpha)\n", " f = tree.compute_lt_price() * tree.grid ** (-gamma)\n", " h = tree.h(tree.grid)\n", " fdiff, hdiff = np.ediff1d(f), np.ediff1d(h)\n", " fdiff2, hdiff2 = np.ediff1d(fdiff), np.ediff1d(hdiff)\n", " if all(hdiff2 > 0):\n", " self.assertTrue(all(fdiff2 > 0))\n", " elif all(hdiff2 < 0):\n", " self.assertTrue(all(fdiff2 < 0))\n", "\n", " def tearDown(self):\n", " pass\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }