{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<a id='multiplicative-functionals'></a>\n",
    "<div id=\"qe-notebook-header\" style=\"text-align:right;\">\n",
    "        <a href=\"https://quantecon.org/\" title=\"quantecon.org\">\n",
    "                <img style=\"width:250px;display:inline;\" src=\"https://assets.quantecon.org/img/qe-menubar-logo.svg\" alt=\"QuantEcon\">\n",
    "        </a>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiplicative Functionals\n",
    "\n",
    "\n",
    "<a id='index-0'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contents\n",
    "\n",
    "- [Multiplicative Functionals](#Multiplicative-Functionals)  \n",
    "  - [Overview](#Overview)  \n",
    "  - [A Log-Likelihood Process](#A-Log-Likelihood-Process)  \n",
    "  - [Benefits from Reduced Aggregate Fluctuations](#Benefits-from-Reduced-Aggregate-Fluctuations)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Co-authored with Chase Coleman and Balint Szoke"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "This lecture is a sequel to the [lecture on additive functionals](additive_functionals.html).\n",
    "\n",
    "That lecture\n",
    "\n",
    "1. defined a special class of **additive functionals** driven by a first-order vector VAR  \n",
    "1. by taking the exponential of that additive functional, created an associated **multiplicative functional**  \n",
    "\n",
    "\n",
    "This lecture uses this special class to create and analyze two examples\n",
    "\n",
    "- A  **log likelihood process**, an object at the foundation of both frequentist and Bayesian approaches to statistical inference.  \n",
    "- A version of Robert E. Lucas’s [[Luc03]](../zreferences.html#lucas2003) and Thomas Tallarini’s [[Tal00]](../zreferences.html#tall2000) approaches to measuring the benefits of moderating aggregate fluctuations.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Log-Likelihood Process\n",
    "\n",
    "Consider a vector of additive functionals $ \\{y_t\\}_{t=0}^\\infty $ described by\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "    x_{t+1} & = A x_t + B z_{t+1}\n",
    "    \\\\\n",
    "    y_{t+1} - y_t & = D x_{t} + F z_{t+1},\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where $ A $ is a stable matrix, $ \\{z_{t+1}\\}_{t=0}^\\infty $ is\n",
    "an i.i.d. sequence of $ {\\cal N}(0,I) $ random vectors, $ F $ is\n",
    "nonsingular, and $ x_0 $ and $ y_0 $ are vectors of known\n",
    "numbers.\n",
    "\n",
    "Evidently,\n",
    "\n",
    "$$\n",
    "x_{t+1} = \\left(A - B F^{-1}D \\right)x_t\n",
    "    + B F^{-1} \\left(y_{t+1} - y_t \\right),\n",
    "$$\n",
    "\n",
    "so that $ x_{t+1} $ can be constructed from observations on\n",
    "$ \\{y_{s}\\}_{s=0}^{t+1} $ and $ x_0 $.\n",
    "\n",
    "The distribution of $ y_{t+1} - y_t $ conditional on $ x_t $ is normal with mean $ Dx_t $ and nonsingular covariance matrix $ FF' $.\n",
    "\n",
    "Let $ \\theta $ denote the vector of free parameters of the model.\n",
    "\n",
    "These parameters pin down the elements of $ A, B, D, F $.\n",
    "\n",
    "The **log likelihood function** of $ \\{y_s\\}_{s=1}^t $ is\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "    \\log L_{t}(\\theta)  =\n",
    "    & - {\\frac 1 2} \\sum_{j=1}^{t} (y_{j} - y_{j-1} -\n",
    "         D x_{j-1})'(FF')^{-1}(y_{j} - y_{j-1} - D x_{j-1})\n",
    "    \\\\\n",
    "    & - {\\frac t 2} \\log \\det (FF') - {\\frac {k t} 2} \\log( 2 \\pi)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Let’s consider the case of a scalar process in which $ A, B, D, F $ are scalars and $ z_{t+1} $ is a scalar stochastic process.\n",
    "\n",
    "We let $ \\theta_o $ denote the “true” values of $ \\theta $, meaning the values that generate the data.\n",
    "\n",
    "For the purposes of this exercise,  set $ \\theta_o = (A, B, D, F) = (0.8, 1, 0.5, 0.2) $.\n",
    "\n",
    "Set $ x_0 = y_0 = 0 $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulating sample paths\n",
    "\n",
    "Let’s write a program to simulate sample paths of $ \\{ x_t, y_{t} \\}_{t=0}^{\\infty} $.\n",
    "\n",
    "We’ll do this by formulating the additive functional as a linear state space model and putting the [LSS](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/lss.jl) struct to work."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "hide-output": true
   },
   "outputs": [],
   "source": [
    "using InstantiateFromURL\n",
    "# optionally add arguments to force installation: instantiate = true, precompile = true\n",
    "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.8.0\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hide-output": false
   },
   "outputs": [],
   "source": [
    "using LinearAlgebra, Statistics\n",
    "using Distributions, Parameters, Plots, QuantEcon\n",
    "import Distributions: loglikelihood\n",
    "gr(fmt = :png);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "loglikelihood (generic function with 4 methods)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AMF_LSS_VAR = @with_kw (A, B, D, F = 0.0, ν = 0.0, lss = construct_ss(A, B, D, F, ν))\n",
    "\n",
    "function construct_ss(A, B, D, F, ν)\n",
    "    H, g = additive_decomp(A, B, D, F)\n",
    "\n",
    "    # Build A matrix for LSS\n",
    "    # Order of states is: [1, t, xt, yt, mt]\n",
    "    A1 = [1 0 0 0 0]       # Transition for 1\n",
    "    A2 = [1 1 0 0 0]       # Transition for t\n",
    "    A3 = [0 0 A 0 0]       # Transition for x_{t+1}\n",
    "    A4 = [ν 0 D 1 0]       # Transition for y_{t+1}\n",
    "    A5 = [0 0 0 0 1]       # Transition for m_{t+1}\n",
    "    Abar = vcat(A1, A2, A3, A4, A5)\n",
    "\n",
    "    # Build B matrix for LSS\n",
    "    Bbar = [0, 0, B, F, H]\n",
    "\n",
    "    # Build G matrix for LSS\n",
    "    # Order of observation is: [xt, yt, mt, st, tt]\n",
    "    G1 = [0 0 1 0 0]               # Selector for x_{t}\n",
    "    G2 = [0 0 0 1 0]               # Selector for y_{t}\n",
    "    G3 = [0 0 0 0 1]               # Selector for martingale\n",
    "    G4 = [0 0 -g 0 0]              # Selector for stationary\n",
    "    G5 = [0 ν 0 0 0]               # Selector for trend\n",
    "    Gbar = vcat(G1, G2, G3, G4, G5)\n",
    "\n",
    "    # Build LSS struct\n",
    "    x0 = [0, 0, 0, 0, 0]\n",
    "    S0 = zeros(5, 5)\n",
    "    return LSS(Abar, Bbar, Gbar, mu_0 = x0, Sigma_0 = S0)\n",
    "end\n",
    "\n",
    "function additive_decomp(A, B, D, F)\n",
    "    A_res = 1 / (1 - A)\n",
    "    g = D * A_res\n",
    "    H = F + D * A_res * B\n",
    "\n",
    "    return H, g\n",
    "end\n",
    "\n",
    "function multiplicative_decomp(A, B, D, F, ν)\n",
    "    H, g = additive_decomp(A, B, D, F)\n",
    "    ν_tilde = ν + 0.5 * H^2\n",
    "\n",
    "    return ν_tilde, H, g\n",
    "end\n",
    "\n",
    "function loglikelihood_path(amf, x, y)\n",
    "    @unpack A, B, D, F = amf\n",
    "    T = length(y)\n",
    "    FF = F^2\n",
    "    FFinv = inv(FF)\n",
    "    temp = y[2:end] - y[1:end-1] - D*x[1:end-1]\n",
    "    obs =  temp .* FFinv .* temp\n",
    "    obssum = cumsum(obs)\n",
    "    scalar = (log(FF) + log(2pi)) * (1:T-1)\n",
    "    return -0.5 * (obssum + scalar)\n",
    "end\n",
    "\n",
    "function loglikelihood(amf, x, y)\n",
    "    llh = loglikelihood_path(amf, x, y)\n",
    "    return llh[end]\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The heavy lifting is done inside the AMF_LSS_VAR struct.\n",
    "\n",
    "The following code adds some simple functions that make it straightforward to generate sample paths from an instance of AMF_LSS_VAR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "population_means (generic function with 2 methods)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function simulate_xy(amf, T)\n",
    "    foo, bar = simulate(amf.lss, T)\n",
    "    x = bar[1, :]\n",
    "    y = bar[2, :]\n",
    "    return x, y\n",
    "end\n",
    "\n",
    "function simulate_paths(amf, T = 150, I = 5000)\n",
    "    # Allocate space\n",
    "    storeX = zeros(I, T)\n",
    "    storeY = zeros(I, T)\n",
    "\n",
    "    for i in 1:I\n",
    "        # Do specific simulation\n",
    "        x, y = simulate_xy(amf, T)\n",
    "\n",
    "        # Fill in our storage matrices\n",
    "        storeX[i, :] = x\n",
    "        storeY[i, :] = y\n",
    "    end\n",
    "\n",
    "    return storeX, storeY\n",
    "end\n",
    "\n",
    "function population_means(amf, T = 150)\n",
    "    # Allocate Space\n",
    "    xmean = zeros(T)\n",
    "    ymean = zeros(T)\n",
    "\n",
    "    # Pull out moment generator\n",
    "    moment_generator = moment_sequence(amf.lss)\n",
    "    for (tt, x) = enumerate(moment_generator)\n",
    "        ymeans = x[2]\n",
    "        xmean[tt] = ymeans[1]\n",
    "        ymean[tt] = ymeans[2]\n",
    "        if tt == T\n",
    "            break\n",
    "        end\n",
    "    end\n",
    "    return xmean, ymean\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have these functions in our took kit, let’s apply them to run some\n",
    "simulations.\n",
    "\n",
    "In particular, let’s use our program to generate $ I = 5000 $ sample paths of length $ T = 150 $, labeled $ \\{ x_{t}^i, y_{t}^i \\}_{t=0}^\\infty $ for $ i = 1, ..., I $.\n",
    "\n",
    "Then we compute averages of $ \\frac{1}{I} \\sum_i x_t^i $ and $ \\frac{1}{I} \\sum_i y_t^i $ across the sample paths and compare them with the population means of $ x_t $ and $ y_t $.\n",
    "\n",
    "Here goes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
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"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F = 0.2\n",
    "amf = AMF_LSS_VAR(A = 0.8, B = 1.0, D = 0.5, F = F)\n",
    "\n",
    "T = 150\n",
    "I = 5000\n",
    "\n",
    "# Simulate and compute sample means\n",
    "Xit, Yit = simulate_paths(amf, T, I)\n",
    "Xmean_t = mean(Xit, dims = 1)\n",
    "Ymean_t = mean(Yit, dims = 1)\n",
    "\n",
    "# Compute population means\n",
    "Xmean_pop, Ymean_pop = population_means(amf, T)\n",
    "\n",
    "# Plot sample means vs population means\n",
    "plt_1 = plot(Xmean_t', color = :blue, label = \"1/I sum_i x_t^i\")\n",
    "plot!(plt_1, Xmean_pop, color = :black, label = \"E x_t\")\n",
    "plot!(plt_1, title = \"x_t\", xlim = (0, T), legend = :bottomleft)\n",
    "\n",
    "plt_2 = plot(Ymean_t', color = :blue, label = \"1/I sum_i x_t^i\")\n",
    "plot!(plt_2, Ymean_pop, color = :black, label = \"E y_t\")\n",
    "plot!(plt_2, title = \"y_t\", xlim = (0, T), legend = :bottomleft)\n",
    "\n",
    "plot(plt_1, plt_2, layout = (2, 1), size = (800,500))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulating log-likelihoods\n",
    "\n",
    "Our next aim is to write a program to simulate $ \\{\\log L_t \\mid \\theta_o\\}_{t=1}^T $.\n",
    "\n",
    "We want as inputs to this program the *same* sample paths $ \\{x_t^i, y_t^i\\}_{t=0}^T $ that we  have already computed.\n",
    "\n",
    "We now want to simulate $ I = 5000 $ paths of $ \\{\\log L_t^i  \\mid \\theta_o\\}_{t=1}^T $.\n",
    "\n",
    "- For each path, we compute $ \\log L_T^i / T $.  \n",
    "- We also compute $ \\frac{1}{I} \\sum_{i=1}^I \\log L_T^i / T $.  \n",
    "\n",
    "\n",
    "Then we to compare these objects.\n",
    "\n",
    "Below we plot the histogram of $ \\log L_T^i / T $ for realizations $ i = 1, \\ldots, 5000 $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function simulate_likelihood(amf, Xit, Yit)\n",
    "    # Get size\n",
    "    I, T = size(Xit)\n",
    "\n",
    "    # Allocate space\n",
    "    LLit = zeros(I, T-1)\n",
    "\n",
    "    for i in 1:I\n",
    "        LLit[i, :] = loglikelihood_path(amf, Xit[i, :], Yit[i, :])\n",
    "    end\n",
    "\n",
    "    return LLit\n",
    "end\n",
    "\n",
    "# Get likelihood from each path x^{i}, Y^{i}\n",
    "LLit = simulate_likelihood(amf, Xit, Yit)\n",
    "\n",
    "LLT = 1 / T * LLit[:, end]\n",
    "LLmean_t = mean(LLT)\n",
    "\n",
    "plot(seriestype = :histogram, LLT, label = \"\")\n",
    "plot!(title = \"Distribution of (I/T)log(L_T)|theta_0\")\n",
    "vline!([LLmean_t], linestyle = :dash, color = :black, lw = 2, alpha = 0.6, label = \"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the log likelihood is almost always nonnegative, implying that $ L_t $ is typically bigger than 1.\n",
    "\n",
    "Recall that the likelihood function is a pdf (probability density function) and **not** a probability measure, so it can take values larger than 1.\n",
    "\n",
    "In the current case, the conditional variance of $ \\Delta y_{t+1} $, which equals  $ FF^T=0.04 $, is so small that the maximum value of the pdf is 2 (see the figure below).\n",
    "\n",
    "This implies that approximately $ 75\\% $ of the time (a bit more than one sigma deviation),  we should expect the **increment** of the log likelihood to be nonnegative.\n",
    "\n",
    "Let’s see this in a simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The pdf at +/- 1.175 sigma takes the value: 1.0001868966924388\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of dL being larger than 1 is approx: 0.7600052842019751\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fraction of dlogL being nonnegative in the sample is: 0.7597743243243243"
     ]
    }
   ],
   "source": [
    "normdist = Normal(0, F)\n",
    "mult = 1.175\n",
    "println(\"The pdf at +/- $mult sigma takes the value: $(pdf(normdist,mult*F))\")\n",
    "println(\"Probability of dL being larger than 1 is approx: \"*\n",
    "        \"$(cdf(normdist,mult*F)-cdf(normdist,-mult*F))\")\n",
    "\n",
    "# Compare this to the sample analogue:\n",
    "L_increment = LLit[:,2:end] - LLit[:,1:end-1]\n",
    "r,c = size(L_increment)\n",
    "frac_nonegative = sum(L_increment.>=0)/(c*r)\n",
    "print(\"Fraction of dlogL being nonnegative in the sample is: $(frac_nonegative)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let’s also plot the conditional pdf of $ \\Delta y_{t+1} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The pdf at +/- one sigma takes the value: 1.2098536225957168 \n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xgrid = range(-1,  1, length = 100)\n",
    "println(\"The pdf at +/- one sigma takes the value: $(pdf(normdist, F)) \")\n",
    "plot(xgrid, pdf.(normdist, xgrid), label = \"\")\n",
    "plot!(title = \"Conditional pdf f(Delta y_(t+1) | x_t)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An alternative parameter vector\n",
    "\n",
    "Now consider alternative parameter vector $ \\theta_1 = [A, B, D, F] = [0.9, 1.0, 0.55, 0.25] $.\n",
    "\n",
    "We want to compute $ \\{\\log L_t \\mid \\theta_1\\}_{t=1}^T $.\n",
    "\n",
    "The $ x_t, y_t $ inputs to this program should be exactly the **same** sample paths $ \\{x_t^i, y_t^i\\}_{t=0}^T $ that we we computed above.\n",
    "\n",
    "This is because we want to generate data under the $ \\theta_o $ probability model but evaluate the likelihood under the $ \\theta_1 $ model.\n",
    "\n",
    "So our task is to use our program to simulate $ I = 5000 $ paths of $ \\{\\log L_t^i  \\mid \\theta_1\\}_{t=1}^T $.\n",
    "\n",
    "- For each path, compute $ \\frac{1}{T} \\log L_T^i $.  \n",
    "- Then compute $ \\frac{1}{I}\\sum_{i=1}^I \\frac{1}{T} \\log L_T^i $.  \n",
    "\n",
    "\n",
    "We want to compare these objects with each other and with the analogous objects that we computed above.\n",
    "\n",
    "Then we want to interpret outcomes.\n",
    "\n",
    "A function that we constructed can  handle these tasks.\n",
    "\n",
    "The only innovation is that we must create an alternative model to feed in.\n",
    "\n",
    "We will creatively call the new model `amf2`.\n",
    "\n",
    "We make three graphs\n",
    "\n",
    "- the first sets the stage by repeating an earlier graph  \n",
    "- the second contains two histograms of values of  log likelihoods of the two models  over the period $ T $  \n",
    "- the third compares likelihoods under the true and alternative models  \n",
    "\n",
    "\n",
    "Here’s the code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the second (wrong) alternative model\n",
    "amf2 = AMF_LSS_VAR(A = 0.9, B = 1.0, D = 0.55, F = 0.25) # parameters for θ_1 closer to θ_0\n",
    "\n",
    "# Get likelihood from each path x^{i}, y^{i}\n",
    "LLit2 = simulate_likelihood(amf2, Xit, Yit)\n",
    "\n",
    "LLT2 = 1/(T-1) * LLit2[:, end]\n",
    "LLmean_t2 = mean(LLT2)\n",
    "\n",
    "plot(seriestype = :histogram, LLT2, label = \"\")\n",
    "vline!([LLmean_t2], color = :black, lw = 2, linestyle = :dash, alpha = 0.6, label = \"\")\n",
    "plot!(title = \"Distribution of (1/T)log(L_T) | theta_1)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let’s see a histogram of the log-likelihoods under the true and the alternative model (same sample paths)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(seriestype = :histogram, LLT, bin = 50, alpha = 0.5, label = \"True\", normed = true)\n",
    "plot!(seriestype = :histogram, LLT2, bin = 50, alpha = 0.5, label = \"Alternative\",\n",
    "      normed = true)\n",
    "vline!([mean(LLT)], color = :black, lw = 2, linestyle = :dash, label = \"\")\n",
    "vline!([mean(LLT2)], color = :black, lw = 2, linestyle = :dash, label = \"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we’ll plot the histogram of the difference in log likelihood ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LLT_diff = LLT - LLT2\n",
    "\n",
    "plot(seriestype = :histogram, LLT_diff, bin = 50, label = \"\")\n",
    "plot!(title = \"(1/T)[log(L_T^i | theta_0) - log(L_T^i |theta_1)]\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpretation\n",
    "\n",
    "These histograms of  log likelihood ratios illustrate  important features of **likelihood ratio tests** as tools for discriminating between statistical models.\n",
    "\n",
    "- The loglikeklihood is higher on average under the true model – obviously a very useful property.  \n",
    "- Nevertheless, for a positive fraction of realizations, the log likelihood is higher for the incorrect than for the true model  \n",
    "\n",
    "\n",
    "> - in these instances, a likelihood ratio test mistakenly selects the wrong model  \n",
    "\n",
    "\n",
    "\n",
    "- These mechanics underlie the statistical theory of **mistake probabilities** associated with model selection tests based on  likelihood ratio.  \n",
    "\n",
    "\n",
    "(In a subsequent lecture, we’ll use some of the code prepared in this lecture to illustrate mistake probabilities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Benefits from Reduced Aggregate Fluctuations\n",
    "\n",
    "Now let’s turn to a new example of multiplicative functionals.\n",
    "\n",
    "This example illustrates  ideas in the literatures on\n",
    "\n",
    "- **long-run risk** in the consumption based asset pricing literature (e.g., [[BY04]](../zreferences.html#bansalyaron2004), [[HHL08]](../zreferences.html#hhl2008), [[Han07]](../zreferences.html#hansen2007))  \n",
    "- **benefits of eliminating aggregate fluctuations** in representative agent macro models (e.g., [[Tal00]](../zreferences.html#tall2000), [[Luc03]](../zreferences.html#lucas2003))  \n",
    "\n",
    "\n",
    "Let $ c_t $ be consumption at date $ t \\geq 0 $.\n",
    "\n",
    "Suppose that $ \\{\\log c_t \\}_{t=0}^\\infty $ is an additive functional described by\n",
    "\n",
    "$$\n",
    "\\log c_{t+1} - \\log c_t = \\nu + D \\cdot x_t + F \\cdot z_{t+1}\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\n",
    "x_{t+1} = A x_t + B z_{t+1}\n",
    "$$\n",
    "\n",
    "Here $ \\{z_{t+1}\\}_{t=0}^\\infty $ is an i.i.d. sequence of $ {\\cal N}(0,I) $ random vectors.\n",
    "\n",
    "A representative household ranks consumption processes $ \\{c_t\\}_{t=0}^\\infty $ with a utility functional $ \\{V_t\\}_{t=0}^\\infty $ that satisfies\n",
    "\n",
    "\n",
    "<a id='equation-old1mf'></a>\n",
    "$$\n",
    "\\log V_t - \\log c_t = U \\cdot x_t + {\\sf u} \\tag{1}\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\n",
    "U = \\exp(-\\delta) \\left[ I - \\exp(-\\delta) A' \\right]^{-1} D\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "{\\sf u}\n",
    "  = {\\frac {\\exp( -\\delta)}{ 1 - \\exp(-\\delta)}} {\\nu} + \\frac{(1 - \\gamma)}{2} {\\frac {\\exp(-\\delta)}{1 - \\exp(-\\delta)}}\n",
    "\\biggl| D' \\left[ I - \\exp(-\\delta) A \\right]^{-1}B + F \\biggl|^2,\n",
    "$$\n",
    "\n",
    "Here $ \\gamma \\geq 1 $ is a risk-aversion coefficient and $ \\delta > 0 $ is a rate of time preference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Consumption as a multiplicative process\n",
    "\n",
    "We begin by showing that consumption is a **multiplicative functional** with representation\n",
    "\n",
    "\n",
    "<a id='equation-old2mf'></a>\n",
    "$$\n",
    "\\frac{c_t}{c_0}\n",
    "= \\exp(\\tilde{\\nu}t )\n",
    "\\left( \\frac{\\tilde{M}_t}{\\tilde{M}_0} \\right)\n",
    "\\left( \\frac{\\tilde{e}(x_0)}{\\tilde{e}(x_t)} \\right) \\tag{2}\n",
    "$$\n",
    "\n",
    "where $ \\left( \\frac{\\tilde{M}_t}{\\tilde{M}_0} \\right) $ is a likelihood ratio process and $ \\tilde M_0 = 1 $.\n",
    "\n",
    "At this point, as an exercise, we ask the reader please to verify the follow formulas for $ \\tilde{\\nu} $ and $ \\tilde{e}(x_t) $ as functions of $ A, B, D, F $:\n",
    "\n",
    "$$\n",
    "\\tilde \\nu =  \\nu + \\frac{H \\cdot H}{2}\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "\\tilde e(x) = \\exp[g(x)] = \\exp \\bigl[ D' (I - A)^{-1} x \\bigr]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulating a likelihood ratio process again\n",
    "\n",
    "Next, we want a program to simulate the likelihood ratio process $ \\{ \\tilde{M}_t \\}_{t=0}^\\infty $.\n",
    "\n",
    "In particular, we want to simulate 5000 sample paths of length $ T=1000 $ for the case in which $ x $ is a scalar and $ [A, B, D, F] = [0.8, 0.001, 1.0, 0.01] $ and $ \\nu = 0.005 $.\n",
    "\n",
    "After accomplishing this, we want to display a histogram of $ \\tilde{M}_T^i $ for\n",
    "$ T=1000 $.\n",
    "\n",
    "Here is code that accomplishes these tasks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The (min, mean, max) of additive Martingale component in period T is\n",
      "\t (-1.7614516600932575, -0.0005133831693116624, 1.8003019372427829)\n",
      "The (min, mean, max) of multiplicative Martingale component in period T is\n",
      "\t (0.15353309077702101, 0.9984587293023235, 5.408189816030574)\n"
     ]
    }
   ],
   "source": [
    "function simulate_martingale_components(amf, T = 1_000, I = 5_000)\n",
    "    # Get the multiplicative decomposition\n",
    "    @unpack A, B, D, F, ν, lss = amf\n",
    "    ν, H, g = multiplicative_decomp(A, B, D, F, ν)\n",
    "\n",
    "    # Allocate space\n",
    "    add_mart_comp = zeros(I, T)\n",
    "\n",
    "    # Simulate and pull out additive martingale component\n",
    "    for i in 1:I\n",
    "        foo, bar = simulate(lss, T)\n",
    "        # Martingale component is third component\n",
    "        add_mart_comp[i, :] = bar[3, :]\n",
    "    end\n",
    "\n",
    "    mul_mart_comp = exp.(add_mart_comp' .- (0:T-1) * H^2 / 2)'\n",
    "\n",
    "    return add_mart_comp, mul_mart_comp\n",
    "end\n",
    "\n",
    "# Build model\n",
    "amf_2 = AMF_LSS_VAR(A = 0.8, B = 0.001, D = 1.0, F = 0.01, ν = 0.005)\n",
    "\n",
    "amc, mmc = simulate_martingale_components(amf_2, 1_000, 5_000)\n",
    "\n",
    "amcT = amc[:, end]\n",
    "mmcT = mmc[:, end]\n",
    "\n",
    "println(\"The (min, mean, max) of additive Martingale component in period T is\")\n",
    "println(\"\\t ($(minimum(amcT)), $(mean(amcT)), $(maximum(amcT)))\")\n",
    "\n",
    "println(\"The (min, mean, max) of multiplicative Martingale component in period T is\")\n",
    "println(\"\\t ($(minimum(mmcT)), $(mean(mmcT)), $(maximum(mmcT)))\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Comments\n",
    "\n",
    "- The preceding min, mean, and max of the cross-section of the date\n",
    "  $ T $ realizations of the multiplicative martingale component of\n",
    "  $ c_t $ indicate that the sample mean is close to its population\n",
    "  mean of 1.  \n",
    "  \n",
    "  - This outcome prevails for all values of the horizon $ T $.  \n",
    "  \n",
    "- The cross-section distribution of the multiplicative martingale\n",
    "  component of $ c $ at date $ T $ approximates a log normal\n",
    "  distribution well.  \n",
    "- The histogram of the additive martingale component of\n",
    "  $ \\log c_t $ at date $ T $ approximates a normal distribution\n",
    "  well.  \n",
    "\n",
    "\n",
    "Here’s a histogram of the additive martingale component"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(seriestype = :histogram, amcT, bin = 25, normed = true, label = \"\")\n",
    "plot!(title = \"Histogram of Additive Martingale Component\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here’s a histogram of the multiplicative martingale component"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(seriestype = :histogram, mmcT, bin = 25, normed = true, label = \"\")\n",
    "plot!(title = \"Histogram of Multiplicative Martingale Component\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Representing the likelihood ratio process\n",
    "\n",
    "The likelihood ratio process $ \\{\\widetilde M_t\\}_{t=0}^\\infty $ can be represented as\n",
    "\n",
    "$$\n",
    "\\widetilde M_t = \\exp \\biggl( \\sum_{j=1}^t \\biggl(H \\cdot z_j -\\frac{ H \\cdot H }{2} \\biggr) \\biggr),  \\quad \\widetilde M_0 =1 ,\n",
    "$$\n",
    "\n",
    "where $ H =  [F + B'(I-A')^{-1} D] $.\n",
    "\n",
    "It follows that $ \\log {\\widetilde M}_t \\sim {\\mathcal N} ( -\\frac{t H \\cdot H}{2}, t H \\cdot H ) $ and that consequently $ {\\widetilde M}_t $ is log normal.\n",
    "\n",
    "Let’s plot the probability density functions for $ \\log {\\widetilde M}_t $ for\n",
    "$ t=100, 500, 1000, 10000, 100000 $.\n",
    "\n",
    "Then let’s use the plots to  investigate how these densities evolve through time.\n",
    "\n",
    "We will plot the densities of $ \\log {\\widetilde M}_t $ for different values of $ t $.\n",
    "\n",
    "Here is some code that tackles these tasks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function Mtilde_t_density(amf, t; xmin = 1e-8, xmax = 5.0, npts = 5000)\n",
    "\n",
    "    # Pull out the multiplicative decomposition\n",
    "    νtilde, H, g =\n",
    "        multiplicative_decomp(amf.A, amf.B, amf.D, amf.F, amf.ν)\n",
    "    H2 = H*H\n",
    "\n",
    "    # The distribution\n",
    "    mdist = LogNormal(-t * H2 / 2, sqrt(t * H2))\n",
    "    x = range(xmin,  xmax, length = npts)\n",
    "    p = pdf.(mdist, x)\n",
    "\n",
    "    return x, p\n",
    "end\n",
    "\n",
    "function logMtilde_t_density(amf, t; xmin = -15.0, xmax = 15.0, npts = 5000)\n",
    "\n",
    "    # Pull out the multiplicative decomposition\n",
    "    @unpack A, B, D, F, ν = amf\n",
    "    νtilde, H, g = multiplicative_decomp(A, B, D, F, ν)\n",
    "    H2 = H * H\n",
    "\n",
    "    # The distribution\n",
    "    lmdist = Normal(-t * H2 / 2, sqrt(t * H2))\n",
    "    x = range(xmin,  xmax, length = npts)\n",
    "    p = pdf.(lmdist, x)\n",
    "\n",
    "    return x, p\n",
    "end\n",
    "\n",
    "times_to_plot = [10, 100, 500, 1000, 2500, 5000]\n",
    "dens_to_plot = [Mtilde_t_density(amf_2, t, xmin=1e-8, xmax=6.0) for t in times_to_plot]\n",
    "ldens_to_plot = [logMtilde_t_density(amf_2, t, xmin=-10.0, xmax=10.0) for t in times_to_plot]\n",
    "\n",
    "# plot_title = \"Densities of M_t^tilda\" is required, however, plot_title is not yet\n",
    "# supported in Plots\n",
    "plots = plot(layout = (3,2), size = (600,800))\n",
    "\n",
    "for (it, dens_t) in enumerate(dens_to_plot)\n",
    "    x, pdf = dens_t\n",
    "    plot!(plots[it], title = \"Density for time (time_to_plot[it])\")\n",
    "    plot!(plots[it], pdf, fillrange = [[0], pdf], label = \"\")\n",
    "end\n",
    "plot(plots)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These probability density functions illustrate a **peculiar property** of log likelihood ratio processes:\n",
    "\n",
    "- With respect to the true model probabilities, they have mathematical expectations equal to $ 1 $ for all $ t \\geq 0 $.  \n",
    "- They almost surely converge to zero.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Welfare benefits of reduced random aggregate fluctuations\n",
    "\n",
    "Suppose in the tradition of a strand of macroeconomics (for example Tallarini [[Tal00]](../zreferences.html#tall2000), [[Luc03]](../zreferences.html#lucas2003)) we want to estimate the welfare benefits from removing random fluctuations around trend growth.\n",
    "\n",
    "We shall  compute how much initial consumption $ c_0 $ a representative consumer who ranks consumption streams according to [(1)](#equation-old1mf) would be willing to sacrifice to enjoy the consumption stream\n",
    "\n",
    "$$\n",
    "\\frac{c_t}{c_0} = \\exp (\\tilde{\\nu} t)\n",
    "$$\n",
    "\n",
    "rather than the stream described by equation [(2)](#equation-old2mf).\n",
    "\n",
    "We want to compute the implied percentage reduction in $ c_0 $ that the representative consumer would accept.\n",
    "\n",
    "To accomplish this, we write a function that computes the coefficients $ U $\n",
    "and $ u $ for the original values of $ A, B, D, F, \\nu $, but\n",
    "also for the case that  $ A, B, D, F = [0, 0, 0, 0] $ and\n",
    "$ \\nu = \\tilde{\\nu} $.\n",
    "\n",
    "Here’s our code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.54129843114712, 0.24220854072375247, 0, 0.25307727077652764)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function Uu(amf, δ, γ)\n",
    "    @unpack A, B, D, F, ν = amf\n",
    "    ν_tilde, H, g = multiplicative_decomp(A, B, D, F, ν)\n",
    "\n",
    "    resolv = 1 / (1 - exp(-δ) * A)\n",
    "    vect = F + D * resolv * B\n",
    "\n",
    "    U_risky = exp(-δ) * resolv * D\n",
    "    u_risky = exp(-δ) / (1 - exp(-δ)) * (ν + 0.5 * (1 - γ) * (vect^2))\n",
    "\n",
    "    U_det = 0\n",
    "    u_det = exp(-δ) / (1 - exp(-δ))  * ν_tilde\n",
    "\n",
    "    return U_risky, u_risky, U_det, u_det\n",
    "end\n",
    "\n",
    "# Set remaining parameters\n",
    "δ = 0.02\n",
    "γ = 2.0\n",
    "\n",
    "# Get coeffs\n",
    "U_r, u_r, U_d, u_d = Uu(amf_2, δ, γ)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values of the two processes are\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "    \\log V^r_0 &= \\log c^r_0 + U^r x_0 + u^r\n",
    "     \\\\\n",
    "    \\log V^d_0 &= \\log c^d_0 + U^d x_0 + u^d\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "We look for the ratio $ \\frac{c^r_0-c^d_0}{c^r_0} $ that makes\n",
    "$ \\log V^r_0 - \\log V^d_0 = 0 $\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "    \\underbrace{ \\log V^r_0 - \\log V^d_0}_{=0} + \\log c^d_0 - \\log c^r_0\n",
    "      &= (U^r-U^d) x_0 + u^r - u^d\n",
    "    \\\\\n",
    " \\frac{c^d_0}{ c^r_0}\n",
    "     &= \\exp\\left((U^r-U^d) x_0 + u^r - u^d\\right)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Hence, the implied percentage reduction in $ c_0 $ that the\n",
    "representative consumer would accept is given by\n",
    "\n",
    "$$\n",
    "\\frac{c^r_0-c^d_0}{c^r_0} = 1 - \\exp\\left((U^r-U^d) x_0 + u^r - u^d\\right)\n",
    "$$\n",
    "\n",
    "Let’s compute this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hide-output": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0809878812017448"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = 0.0  # initial conditions\n",
    "logVC_r = U_r * x0 + u_r\n",
    "logVC_d = U_d * x0 + u_d\n",
    "\n",
    "perc_reduct = 100 * (1 - exp(logVC_r - logVC_d))\n",
    "perc_reduct"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that the consumer would be willing to take a percentage reduction of initial consumption equal to around 1.081."
   ]
  }
 ],
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