{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Exact Value Function for Recursive Utility"
      ],
      "id": "77dee6fa-cf2d-4083-b355-6241cc3018a7"
    },
    {
      "cell_type": "raw",
      "metadata": {
        "raw_mimetype": "tex"
      },
      "source": [
        "\\renewcommand{\\perp}{\\mathrel\\bot}\n",
        "\\newcommand{\\ev}{\\operatorname{E}}\n",
        "\\newcommand{\\var}{\\operatorname{V}}\n",
        "\\newcommand{\\cov}{\\operatorname{Cov}}\n",
        "\\newcommand{\\Normal}{\\mathcal{N}}\n",
        "\\newcommand{\\qedf}{\\qed{\\parfillskip=0pt \\par}}\n",
        "\\renewcommand{\\vec}[1]{\\mathbf{#1}}\n",
        "\\newcommand{\\gvec}[1]{\\pmb{#1}}\n",
        "\\newcommand{\\inner}[1]{\\langle{#1}\\rangle}\n",
        "\\newcommand{\\norm}[1]{\\lVert{#1}\\rVert}\n",
        "\\newcommand{\\prob}{\\operatorname{P}}\n",
        "\\newcommand{\\1}[1]{1\\kern-0.25em\\text{l}_{\\{#1\\}}}"
      ],
      "id": "4b2b25b5-2eda-4182-a7ac-605abe157e53"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Introduction\n",
        "\n",
        "The [Affine Recursive Utility in Continuous\n",
        "Time](recursive-utility-affine-model.qmd) notebook derived the exact\n",
        "nonlinear ODE for the log continuation-value function\n",
        "$$  q(x) = \\ln h(x),$$\n",
        "in the one-factor Gaussian endowment economy\n",
        "$$  d\\ln c_t = (\\mu_0 + \\mu_1 x_t)\\,dt + \\sigma_c\\,dB_t,\n",
        "  \\qquad\n",
        "  dx_t = \\xi(\\bar{x} - x_t)\\,dt + \\sigma_x\\,dB_t.$$\n",
        "That notebook then switched to a local affine approximation because it\n",
        "delivers closed-form intuition. This notebook goes the other way: it\n",
        "solves the exact boundary-value problem numerically and uses it to\n",
        "assess the affine approximation.\n",
        "\n",
        "For one benchmark calibration, how much does the exact nonlinear\n",
        "solution differ from the affine approximation? Everything below is\n",
        "organized around that question. First we solve the boundary-value\n",
        "problem, then we recover the implied equilibrium objects, and finally we\n",
        "compare them with the affine benchmark.\n",
        "\n",
        "With the homothetic value function\n",
        "$$  V(W,x) = \\frac{W^{1-\\gamma}}{1-\\gamma} h(x),$$\n",
        "the exact nonlinear ODE is\n",
        "$$  0\n",
        "  =\n",
        "  \\theta\\!\\left(\\delta^\\psi e^{-(\\psi/\\theta) q(x)}-\\delta\\right)\n",
        "  + (1-\\gamma)(\\mu_0+\\mu_1x)\n",
        "  + \\psi\\xi(\\bar{x}-x)q'(x)$$\n",
        "<span id=\"eq-exact-bvp\">\n",
        "$$  \\qquad\n",
        "  + \\frac{1}{2}\\psi\\sigma_x^2 q''(x)\n",
        "  + \\psi(1-\\gamma)\\sigma_c\\sigma_x q'(x)\n",
        "  + \\frac{1}{2}\\psi^2\\sigma_x^2 q'(x)^2\n",
        "  + \\frac{1}{2}(1-\\gamma)^2\\sigma_c^2,\n",
        " \\qquad(1)$$</span> where\n",
        "$$  \\theta = \\frac{1-\\gamma}{1-1/\\psi}.$$\n",
        "The boundary conditions are\n",
        "$$  q'(x_{\\min}) = 0,\n",
        "  \\qquad\n",
        "  q'(x_{\\max}) = 0,$$\n",
        "which approximate the tail conditions $q'(x)\\to 0$ as $x\\to \\pm \\infty$\n",
        "on a finite interval.\n",
        "\n",
        "Once $q(x)$ is known, the main equilibrium objects follow immediately:\n",
        "$$  m(x) = \\delta^\\psi e^{-(\\psi/\\theta)q(x)},$$\n",
        "\n",
        "$$  \\sigma_W(x) = \\sigma_c + \\frac{\\psi}{\\theta} q'(x)\\sigma_x,$$\n",
        "and\n",
        "$$  \\mu_W(x)\n",
        "  =\n",
        "  \\mu_0+\\mu_1x+\\frac{\\psi}{\\theta}q'(x)\\xi(\\bar{x}-x)\n",
        "  + \\frac{1}{2}\\frac{\\psi}{\\theta}q''(x)\\sigma_x^2\n",
        "  + \\frac{1}{2}\\sigma_W(x)^2.$$\n",
        "\n",
        "## Calibration\n",
        "\n",
        "The numerical solution needs a concrete parameterization. The values\n",
        "below are chosen to make the recursive-utility channel visible while\n",
        "keeping the boundary-value problem well behaved on a compact grid. The\n",
        "goal is not a broad sensitivity analysis, but a single clean benchmark\n",
        "against which to judge the affine approximation."
      ],
      "id": "06d78018-266f-4b7e-8612-04182ce82773"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from scipy.integrate import solve_bvp\n",
        "from scipy.optimize import root_scalar"
      ],
      "id": "a7af3edf"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "params = {\n",
        "    \"delta\": 0.02,\n",
        "    \"gamma\": 8.0,\n",
        "    \"psi\": 1.5,\n",
        "    \"mu0\": 0.015,\n",
        "    \"mu1\": 0.02,\n",
        "    \"xi\": 0.35,\n",
        "    \"xbar\": 0.0,\n",
        "    \"sigma_c\": 0.02,\n",
        "    \"sigma_x\": 0.06,\n",
        "}\n",
        "\n",
        "delta = params[\"delta\"]\n",
        "gamma = params[\"gamma\"]\n",
        "psi = params[\"psi\"]\n",
        "theta = (1 - gamma) / (1 - 1 / psi)\n",
        "alpha = psi / theta\n",
        "\n",
        "param_table = pd.Series(\n",
        "    {\n",
        "        \"δ\": delta,\n",
        "        \"γ\": gamma,\n",
        "        \"ψ\": psi,\n",
        "        \"θ\": theta,\n",
        "        \"μ₀\": params[\"mu0\"],\n",
        "        \"μ₁\": params[\"mu1\"],\n",
        "        \"ξ\": params[\"xi\"],\n",
        "        \"x̄\": params[\"xbar\"],\n",
        "        \"σ_c\": params[\"sigma_c\"],\n",
        "        \"σ_x\": params[\"sigma_x\"],\n",
        "    }\n",
        ")\n",
        "\n",
        "param_table.to_frame(\"Value\")"
      ],
      "id": "40b28d44"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Solving the Boundary-Value Problem\n",
        "\n",
        "Write $y_1(x)=q(x)$ and $y_2(x)=q'(x)$. Then\n",
        "(<a href=\"#eq-exact-bvp\" class=\"quarto-xref\">1</a>) becomes a\n",
        "first-order system:\n",
        "$$  y_1'(x) = y_2(x),$$\n",
        "\n",
        "$$  y_2'(x)\n",
        "  =\n",
        "  -\\frac{2}{\\psi \\sigma_x^2}\n",
        "  \\Bigg[\n",
        "    \\theta\\!\\left(\\delta^\\psi e^{-\\alpha y_1(x)}-\\delta\\right)\n",
        "    + (1-\\gamma)(\\mu_0+\\mu_1x)\n",
        "    + \\psi\\xi(\\bar{x}-x)y_2(x)$$\n",
        "\n",
        "$$    \\qquad\n",
        "    + \\psi(1-\\gamma)\\sigma_c\\sigma_x y_2(x)\n",
        "    + \\frac{1}{2}\\psi^2\\sigma_x^2 y_2(x)^2\n",
        "    + \\frac{1}{2}(1-\\gamma)^2\\sigma_c^2\n",
        "  \\Bigg].$$\n",
        "\n",
        "We solve this system on the truncated interval\n",
        "$[x_{\\min}, x_{\\max}] = [-0.12, 0.12]$ using\n",
        "`scipy.integrate.solve_bvp`. As an initial guess, we use the\n",
        "deterministic steady state obtained by setting $x=\\bar{x}$ and imposing\n",
        "$q'(\\bar{x})=q''(\\bar{x})=0$."
      ],
      "id": "33dc72c2-5054-418e-ba45-c6a3f78dd67c"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The algorithm converged to the desired accuracy.\n",
            "Solver status: 0\n",
            "Mesh points used: 401"
          ]
        }
      ],
      "source": [
        "x_min, x_max = -0.12, 0.12\n",
        "x_grid = np.linspace(x_min, x_max, 401)\n",
        "\n",
        "steady_term = (\n",
        "    (1 - gamma) * (params[\"mu0\"] + params[\"mu1\"] * params[\"xbar\"])\n",
        "    + 0.5 * (1 - gamma) ** 2 * params[\"sigma_c\"] ** 2\n",
        ")\n",
        "m_steady = delta - steady_term / theta\n",
        "q_steady = -(1 / alpha) * np.log(m_steady / delta**psi)\n",
        "\n",
        "\n",
        "def recursive_utility_ode(x, y):\n",
        "    q = y[0]\n",
        "    q_prime = y[1]\n",
        "\n",
        "    forcing = (\n",
        "        theta * (delta**psi * np.exp(-alpha * q) - delta)\n",
        "        + (1 - gamma) * (params[\"mu0\"] + params[\"mu1\"] * x)\n",
        "        + psi * params[\"xi\"] * (params[\"xbar\"] - x) * q_prime\n",
        "        + psi * (1 - gamma) * params[\"sigma_c\"] * params[\"sigma_x\"] * q_prime\n",
        "        + 0.5 * psi**2 * params[\"sigma_x\"] ** 2 * q_prime**2\n",
        "        + 0.5 * (1 - gamma) ** 2 * params[\"sigma_c\"] ** 2\n",
        "    )\n",
        "\n",
        "    q_second = -2 * forcing / (psi * params[\"sigma_x\"] ** 2)\n",
        "    return np.vstack((q_prime, q_second))\n",
        "\n",
        "\n",
        "def boundary_conditions(left, right):\n",
        "    return np.array([left[1], right[1]])\n",
        "\n",
        "\n",
        "initial_q = q_steady + 0.15 * (x_grid - params[\"xbar\"])\n",
        "initial_q_prime = np.full_like(x_grid, 0.15)\n",
        "initial_guess = np.vstack((initial_q, initial_q_prime))\n",
        "\n",
        "solution = solve_bvp(\n",
        "    recursive_utility_ode,\n",
        "    boundary_conditions,\n",
        "    x_grid,\n",
        "    initial_guess,\n",
        "    tol=1e-6,\n",
        "    max_nodes=20_000,\n",
        ")\n",
        "\n",
        "print(solution.message)\n",
        "print(f\"Solver status: {solution.status}\")\n",
        "print(f\"Mesh points used: {solution.x.size}\")"
      ],
      "id": "8e07af1b"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "To analyze the solution, evaluate it on a fine grid and recover $q''(x)$\n",
        "from the ODE rather than from numerical differentiation."
      ],
      "id": "66552928-b420-43ed-9a3b-80bc23cb5bf6"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [],
      "source": [
        "x_plot = np.linspace(x_min, x_max, 801)\n",
        "q_exact, q_prime_exact = solution.sol(x_plot)\n",
        "\n",
        "forcing_exact = (\n",
        "    theta * (delta**psi * np.exp(-alpha * q_exact) - delta)\n",
        "    + (1 - gamma) * (params[\"mu0\"] + params[\"mu1\"] * x_plot)\n",
        "    + psi * params[\"xi\"] * (params[\"xbar\"] - x_plot) * q_prime_exact\n",
        "    + psi * (1 - gamma) * params[\"sigma_c\"] * params[\"sigma_x\"] * q_prime_exact\n",
        "    + 0.5 * psi**2 * params[\"sigma_x\"] ** 2 * q_prime_exact**2\n",
        "    + 0.5 * (1 - gamma) ** 2 * params[\"sigma_c\"] ** 2\n",
        ")\n",
        "q_second_exact = -2 * forcing_exact / (psi * params[\"sigma_x\"] ** 2)\n",
        "\n",
        "m_exact = delta**psi * np.exp(-alpha * q_exact)\n",
        "sigma_w_exact = params[\"sigma_c\"] + alpha * q_prime_exact * params[\"sigma_x\"]\n",
        "mu_w_exact = (\n",
        "    params[\"mu0\"]\n",
        "    + params[\"mu1\"] * x_plot\n",
        "    + alpha * q_prime_exact * params[\"xi\"] * (params[\"xbar\"] - x_plot)\n",
        "    + 0.5 * alpha * q_second_exact * params[\"sigma_x\"] ** 2\n",
        "    + 0.5 * sigma_w_exact**2\n",
        ")"
      ],
      "id": "f9ca8be6"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The next table summarizes the range of the exact solution over the state\n",
        "grid."
      ],
      "id": "d91728cd-0d4a-4a40-84f5-38f860c50d79"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "summary = pd.DataFrame(\n",
        "    {\n",
        "        \"Minimum\": [\n",
        "            q_exact.min(),\n",
        "            q_prime_exact.min(),\n",
        "            q_second_exact.min(),\n",
        "            m_exact.min(),\n",
        "            sigma_w_exact.min(),\n",
        "            mu_w_exact.min(),\n",
        "        ],\n",
        "        \"Maximum\": [\n",
        "            q_exact.max(),\n",
        "            q_prime_exact.max(),\n",
        "            q_second_exact.max(),\n",
        "            m_exact.max(),\n",
        "            sigma_w_exact.max(),\n",
        "            mu_w_exact.max(),\n",
        "        ],\n",
        "    },\n",
        "    index=[\n",
        "        \"q(x)\",\n",
        "        \"q′(x)\",\n",
        "        \"q″(x)\",\n",
        "        \"m(x)\",\n",
        "        \"σ_W(x)\",\n",
        "        \"μ_W(x)\",\n",
        "    ],\n",
        ")\n",
        "\n",
        "summary.round(6)"
      ],
      "id": "19312b21"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Comparing Exact and Affine Solutions\n",
        "\n",
        "The affine approximation from the earlier notebook provides the\n",
        "benchmark. The point here is not to re-derive that approximation, but to\n",
        "measure what it misses relative to the exact nonlinear solution.\n",
        "\n",
        "Under that approximation,\n",
        "$$  q_{\\text{aff}}(x) = a + bx.$$\n",
        "Its coefficients solve\n",
        "$$  \\psi b(\\xi + \\bar{m}) = (1-\\gamma)\\mu_1$$\n",
        "and\n",
        "$$  \\delta\\theta\n",
        "  =\n",
        "  \\theta\\bar{m}\n",
        "  + (1-\\gamma)(\\mu_0+\\mu_1\\bar{x})\n",
        "  + \\frac{1}{2}(1-\\gamma)^2\\sigma_w^2\n",
        "  + \\frac{1}{2}b^2\\sigma_x^2\n",
        "  + (1-\\gamma)b\\sigma_w\\sigma_x,$$\n",
        "where\n",
        "$$  \\sigma_w = \\sigma_c + \\frac{\\psi}{\\theta} b \\sigma_x.$$\n",
        "This leaves a single nonlinear equation in $\\bar{m}$, which we solve\n",
        "numerically and then use to recover $a$ and $b$."
      ],
      "id": "7827ac64-d92d-40ea-a5fd-3956a030bcd0"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "def affine_residual(m_bar):\n",
        "    b = (1 - gamma) * params[\"mu1\"] / (psi * (params[\"xi\"] + m_bar))\n",
        "    sigma_w = params[\"sigma_c\"] + alpha * b * params[\"sigma_x\"]\n",
        "\n",
        "    return (\n",
        "        theta * m_bar\n",
        "        + (1 - gamma) * (params[\"mu0\"] + params[\"mu1\"] * params[\"xbar\"])\n",
        "        + 0.5 * (1 - gamma) ** 2 * sigma_w**2\n",
        "        + 0.5 * b**2 * params[\"sigma_x\"] ** 2\n",
        "        + (1 - gamma) * b * sigma_w * params[\"sigma_x\"]\n",
        "        - delta * theta\n",
        "    )\n",
        "\n",
        "\n",
        "m_bar = root_scalar(affine_residual, bracket=[1e-4, 0.05]).root\n",
        "b = (1 - gamma) * params[\"mu1\"] / (psi * (params[\"xi\"] + m_bar))\n",
        "a = theta * np.log(delta) - (theta / psi) * np.log(m_bar) - b * params[\"xbar\"]\n",
        "\n",
        "q_affine = a + b * x_plot\n",
        "m_affine = delta**psi * np.exp(-alpha * q_affine)\n",
        "sigma_w_affine = params[\"sigma_c\"] + alpha * b * params[\"sigma_x\"]\n",
        "\n",
        "q_error = q_exact - q_affine\n",
        "m_error = m_exact - m_affine\n",
        "sigma_w_error = sigma_w_exact - sigma_w_affine\n",
        "\n",
        "comparison = pd.Series(\n",
        "    {\n",
        "        \"m̄\": m_bar,\n",
        "        \"a\": a,\n",
        "        \"b\": b,\n",
        "        \"σ_w\": sigma_w_affine,\n",
        "        \"max_x |q(x) - q_aff(x)|\": np.max(np.abs(q_exact - q_affine)),\n",
        "        \"max_x |m(x) - m_aff(x)|\": np.max(np.abs(m_exact - m_affine)),\n",
        "    }\n",
        ")\n",
        "\n",
        "comparison.to_frame(\"Value\")"
      ],
      "id": "478643b3"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The affine approximation is not exact, but the discrepancy is easy to\n",
        "quantify directly rather than judge only from the plots."
      ],
      "id": "ee59848a-9885-4b4f-aa62-777f43052cbb"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "text/html": [
              "\n",
              "</div>"
            ]
          }
        }
      ],
      "source": [
        "error_summary = pd.DataFrame(\n",
        "    {\n",
        "        \"Max abs. error\": [\n",
        "            np.max(np.abs(q_error)),\n",
        "            np.max(np.abs(m_error)),\n",
        "            np.max(np.abs(sigma_w_error)),\n",
        "        ],\n",
        "        \"RMS error\": [\n",
        "            np.sqrt(np.mean(q_error**2)),\n",
        "            np.sqrt(np.mean(m_error**2)),\n",
        "            np.sqrt(np.mean(sigma_w_error**2)),\n",
        "        ],\n",
        "    },\n",
        "    index=[\n",
        "        \"q(x)\",\n",
        "        \"m(x)\",\n",
        "        \"σ_W(x)\",\n",
        "    ],\n",
        ")\n",
        "\n",
        "error_summary.round(8)"
      ],
      "id": "fb81c51c"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The cleanest way to see what the affine approximation misses is to look\n",
        "directly at the curvature of the exact solution. Because the affine\n",
        "specification imposes $q''(x)=0$, any nonzero curvature is a genuinely\n",
        "nonlinear feature of the Epstein-Zin problem."
      ],
      "id": "7161cef3-17f3-4e46-acc4-f08e1f9cd8fc"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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xJZqnv5sBgyURERG1GkajwJs7z+O/+xIAAE5yGf59Xw9M7hUscWWOgcGSiIiI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\n"
          }
        }
      ],
      "source": [
        "plt.figure(figsize=(7, 4))\n",
        "plt.plot(x_plot, q_second_exact, lw=2)\n",
        "plt.axhline(0.0, color=\"black\", ls=\"--\", lw=1)\n",
        "plt.title(r\"Curvature of the Exact Value Function $q''(x)$\")\n",
        "plt.xlabel(r\"$x$\")\n",
        "plt.ylabel(r\"$q''(x)$\")\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "id": "24bb2b9a"
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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VzZs325W56667ePzxx+nQocM56/Tss88ya9asun8YEWlYFgu07m4eiX8xF2Y/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\nAedtmuo3tC1GAAAAAElFTkSuQmCC\n"
          }
        }
      ],
      "source": [
        "fig, axes = plt.subplots(3, 1, figsize=(7, 12))\n",
        "\n",
        "axes[0].plot(x_plot, q_exact, lw=2, label=\"Exact\")\n",
        "axes[0].plot(x_plot, q_affine, \"--\", lw=2, label=\"Affine\")\n",
        "axes[0].set_title(r\"$q(x) = \\ln h(x)$\")\n",
        "axes[0].set_xlabel(r\"$x$\")\n",
        "axes[0].legend(frameon=False)\n",
        "\n",
        "axes[1].plot(x_plot, m_exact, lw=2, label=\"Exact\")\n",
        "axes[1].plot(x_plot, m_affine, \"--\", lw=2, label=\"Affine\")\n",
        "axes[1].set_title(r\"$m(x) = c/W$\")\n",
        "axes[1].set_xlabel(r\"$x$\")\n",
        "axes[1].legend(frameon=False)\n",
        "\n",
        "axes[2].plot(x_plot, sigma_w_exact, lw=2, label=\"Exact\")\n",
        "axes[2].axhline(sigma_w_affine, ls=\"--\", lw=2, label=\"Affine\")\n",
        "axes[2].set_title(r\"Wealth volatility $\\sigma_W(x)$\")\n",
        "axes[2].set_xlabel(r\"$x$\")\n",
        "axes[2].legend(frameon=False)\n",
        "\n",
        "fig.tight_layout()\n",
        "plt.show()"
      ],
      "id": "88f60e0b"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The next figure makes the same comparison in error form by plotting\n",
        "exact minus affine."
      ],
      "id": "9c407494-ffa4-495a-a9e1-a0993f127454"
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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FhYXYunVru7+PnYioL+KhcCIiIiKSBGcsiYiIiEgSDJZEREREJAnex7KdGhoaoNPp4Obm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\nSUREREQOwWBJRERERA7BYElEREREDvH/vZvFHMWB+ucAAAAASUVORK5CYII=\n"
          }
        }
      ],
      "source": [
        "fig, axes = plt.subplots(3, 1, figsize=(7, 10))\n",
        "\n",
        "axes[0].plot(x_plot, q_error, lw=2)\n",
        "axes[0].axhline(0.0, color=\"black\", ls=\"--\", lw=1)\n",
        "axes[0].set_title(r\"Error in $q(x)$: exact minus affine\")\n",
        "axes[0].set_xlabel(r\"$x$\")\n",
        "\n",
        "axes[1].plot(x_plot, m_error, lw=2)\n",
        "axes[1].axhline(0.0, color=\"black\", ls=\"--\", lw=1)\n",
        "axes[1].set_title(r\"Error in $m(x)$: exact minus affine\")\n",
        "axes[1].set_xlabel(r\"$x$\")\n",
        "\n",
        "axes[2].plot(x_plot, sigma_w_error, lw=2)\n",
        "axes[2].axhline(0.0, color=\"black\", ls=\"--\", lw=1)\n",
        "axes[2].set_title(r\"Error in $\\sigma_W(x)$: exact minus affine\")\n",
        "axes[2].set_xlabel(r\"$x$\")\n",
        "\n",
        "fig.tight_layout()\n",
        "plt.show()"
      ],
      "id": "12947a0c"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The exact solution also delivers the endogenous expected return on\n",
        "aggregate wealth."
      ],
      "id": "6bd8bf91-e2c7-4ff9-a72d-be121b7c1295"
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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yJJYuXQozMzPExsbiiSeewL59+wzOAmu1WqSlpSEmJuau9pHorplu3hARNdTtZoUDEFeu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\nPj4+mDNnDmbPng0AqKioQIcOHbB48WJMnTrVoG9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          }
        }
      ],
      "source": [
        "plt.figure(figsize=(7, 4))\n",
        "plt.plot(x_plot, mu_w_exact, lw=2)\n",
        "plt.title(r\"Expected Return on Wealth $\\mu_W(x)$\")\n",
        "plt.xlabel(r\"$x$\")\n",
        "plt.ylabel(r\"$\\mu_W$\")\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "id": "d6bfa4fb"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Interpretation\n",
        "\n",
        "Three features are worth emphasizing.\n",
        "\n",
        "1.  In this benchmark calibration, the exact and affine solutions are\n",
        "    close for $q(x)$, $m(x)$, and $\\sigma_W(x)$, so the affine\n",
        "    approximation captures most of the quantitative variation.\n",
        "2.  The remaining difference is curvature: the exact solution has\n",
        "    $q''(x)\\neq 0$, while the affine approximation rules that out by\n",
        "    construction.\n",
        "3.  That curvature matters most for objects such as $\\mu_W(x)$ that\n",
        "    depend directly on $q''(x)$, so the exact solution is most useful as\n",
        "    a benchmark for what the affine approximation leaves out.\n",
        "\n",
        "This notebook therefore complements the analytical affine solution in a\n",
        "focused way: the affine approximation remains the tractable workhorse,\n",
        "and the exact numerical value function tells us how much nonlinear\n",
        "curvature that workhorse is ignoring in a representative calibration."
      ],
      "id": "2cb8b8e8-51a9-4083-a455-7dd92b3f4797"
    }
  ],
  "nbformat": 4,
  "nbformat_minor": 5,
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "path": "/home/lnaranjo/.pyenv/versions/3.14.3/share/jupyter/kernels/python3"
    },
    "language_info": {
      "name": "python",
      "codemirror_mode": {
        "name": "ipython",
        "version": "3"
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.14.3"
    }
  }
}