{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "653ea87d",
   "metadata": {},
   "source": [
    "## A Demonstration of the Harmenberg (2021) Aggregation Method\n",
    "\n",
    "   - [\"Aggregating heterogeneous-agent models with permanent income shocks\"](https://doi.org/10.1016/j.jedc.2021.104185)\n",
    "\n",
    "## Authors: [Christopher D. Carroll](http://www.econ2.jhu.edu/people/ccarroll/), [Mateo Velásquez-Giraldo](https://mv77.github.io/)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c03a1161",
   "metadata": {},
   "source": [
    "`# Set Up the Computational Environment: (in JupyterLab, click the dots)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2a09f2e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Preliminaries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pyplot as plt\n",
    "from copy import deepcopy\n",
    "\n",
    "from HARK.distributions import calc_expectation\n",
    "from HARK.ConsumptionSaving.ConsIndShockModel import (\n",
    "    IndShockConsumerType,\n",
    "    init_idiosyncratic_shocks,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d940f86a",
   "metadata": {},
   "source": [
    "# Description of the problem\n",
    "\n",
    "$\\newcommand{\\pLvl}{\\mathbf{p}}$\n",
    "$\\newcommand{\\mLvl}{\\mathbf{m}}$\n",
    "$\\newcommand{\\mNrm}{m}$\n",
    "$\\newcommand{\\CLvl}{\\mathbf{C}}$\n",
    "$\\newcommand{\\MLvl}{\\mathbf{M}}$\n",
    "$\\newcommand{\\CLvlest}{\\widehat{\\CLvl}}$\n",
    "$\\newcommand{\\MLvlest}{\\widehat{\\MLvl}}$\n",
    "$\\newcommand{\\mpLvlDstn}{\\mu}$\n",
    "$\\newcommand{\\mWgtDstnMarg}{\\tilde{\\mu}^{m}}$\n",
    "$\\newcommand{\\PermGroFac}{\\pmb{\\Phi}}$\n",
    "$\\newcommand{\\PermShk}{\\pmb{\\Psi}}$\n",
    "$\\newcommand{\\def}{:=}$\n",
    "$\\newcommand{\\kernel}{\\Lambda}$\n",
    "$\\newcommand{\\pShkNeutDstn}{\\tilde{f}_{\\PermShk}}$\n",
    "$\\newcommand{\\Ex}{\\mathbb{E}}$\n",
    "$\\newcommand{\\cFunc}{\\mathrm{c}}$\n",
    "$\\newcommand{\\Rfree}{\\mathsf{R}}$\n",
    "\n",
    "Macroeconomic models with heterogeneous agents sometimes incorporate a microeconomic income process with a permanent component ($\\pLvl_t$) that follows a geometric random walk. To find an aggregate characteristic of these economies such as aggregate consumption $\\CLvl_t$, one must integrate over permanent income (and all the other relevant state variables):\n",
    "\\begin{equation*}\n",
    "\\CLvl_t = \\int_{\\pLvl} \\int_{\\mLvl} \\mathrm{c}(\\mLvl,\\pLvl) \\times f_t(\\mLvl,\\pLvl) \\, d \\mLvl\\, d\\pLvl,\n",
    "\\end{equation*}\n",
    "where $\\mLvl$ denotes any other state variables that consumption might depend on, $\\cFunc(\\cdot,\\cdot)$ is the individual consumption function, and $f_t(\\cdot,\\cdot)$ is the joint density function of permanent income and the other state variables at time $t$.\n",
    "\n",
    "Under the usual assumption of Constant Relative Risk Aversion utility and standard assumptions about the budget constraint, [such models are homothetic](https://econ-ark.github.io/BufferStockTheory/BufferStockTheory3.html#The-Problem-Can-Be-Normalized-By-Permanent-Income). This means that for a state variable $\\mLvl$ one can solve for a normalized policy function $\\cFunc(\\cdot)$ such that\n",
    "\\begin{equation*}\n",
    "    \\mathrm{c}(\\mLvl,\\pLvl) = \\mathrm{c}\\left(\\mLvl/\\pLvl\\right)\\times \\pLvl\n",
    "\\end{equation*}\n",
    "\n",
    "\n",
    "In practice, this implies that one can defined a normalized state vector $\\mNrm = \\mLvl/\\pLvl$ and solve for the normalized policy function. This eliminates one dimension of the optimization problem problem, $\\pLvl$.\n",
    "\n",
    "While convenient for the solution of the agents' optimization problem, homotheticity has not simplified our aggregation calculations as we still have\n",
    "\n",
    "\\begin{equation*}\n",
    "\\begin{split}\n",
    "\\CLvl_t =& \\int \\int \\cFunc(\\mLvl,\\pLvl) \\times f_t(\\mLvl,\\pLvl) \\, d\\mLvl\\, d\\pLvl\\\\\n",
    "=& \\int \\int \\cFunc\\left(\\frac{1}{\\pLvl}\\times \\mLvl\\right)\\times \\pLvl \\times f_t(\\mLvl,\\pLvl) \\, d\\mLvl\\, d\\pLvl,\n",
    "\\end{split}\n",
    "\\end{equation*}\n",
    "\n",
    "which depends on $\\pLvl$.\n",
    "\n",
    "To further complicate matters, we usually do not have analytical expressions for $\\cFunc(\\cdot)$ or $f_t(\\mLvl,\\pLvl)$. What we often do in practice is to simulate a population $I$ of agents for a large number of periods $T$ using the model's policy functions and transition equations. The result is a set of observations $\\{\\mLvl_{i,t},\\pLvl_{i,t}\\}_{i\\in I, 0\\leq t\\leq T}$ which we then use to approximate\n",
    "\\begin{equation*}\n",
    "\\CLvl_t \\approx \\frac{1}{|I|}\\sum_{i \\in I} \\cFunc\\left(\\mLvl_{i,t}/\\pLvl_{i,t}\\right)\\times \\pLvl_{i,t}.\n",
    "\\end{equation*}\n",
    "\n",
    "At least two features of the previous strategy are unpleasant:\n",
    "- We have to simulate the distribution of permanent income, even though the model's solution does not depend on it.\n",
    "- As a geometric random walk, permanent income might have an unbounded distribution. Since $\\pLvl_{i,t}$ appears multiplicatively in our approximation, agents with high permanent incomes will be the most important in determining levels of aggregate variables. Therefore, it is important for our simulated population to achieve a good approximation of the distribution of permanent income among the small number of agents with very high permanent income, which will require us to use many agents (large $I$, requiring considerable computational resources).\n",
    "\n",
    "[Harmenberg (2021)](https://www.sciencedirect.com/science/article/pii/S0165188921001202?via%3Dihub) solves both problems. His solution constructs a distribution $\\tilde{f}(\\cdot)$ of the normalized state vector that he calls **the permanent-income-weighted distribution** and which has the convenient property that\n",
    "\\begin{equation*}\n",
    "\\begin{split}\n",
    "\\CLvl_t =& \\int \\int \\cFunc\\left(\\frac{1}{\\pLvl}\\times \\mLvl\\right)\\times \\pLvl \\times f_t(\\mLvl,\\pLvl) \\, d\\mLvl\\, d\\pLvl\\\\\n",
    "=& \\int \\cFunc\\left(\\mNrm\\right) \\times \\tilde{f}(\\mNrm) \\, d\\mNrm.\n",
    "\\end{split}\n",
    "\\end{equation*}\n",
    "\n",
    "Therefore, his solution allows us to calculate aggregate variables without the need to keep track of the distribution of permanent income. Additionally, the method eliminates the issue of a small number of agents in the tail having an outsized influence in our approximation and this makes it much more precise.\n",
    "\n",
    "This notebook briefly describes Harmenberg's method and demonstrates its implementation in the HARK toolkit."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41ec855e",
   "metadata": {},
   "source": [
    "# Description of the method\n",
    "\n",
    "To illustrate Harmenberg's idea, consider a [buffer stock saving](https://econ-ark.github.io/BufferStockTheory) model in which:\n",
    "- The individual agent's problem has two state variables:\n",
    "    - Market resources $\\mLvl_{i,t}$.\n",
    "    - Permanent income $\\pLvl_{i,t}$.\n",
    "\n",
    "- The agent's problem is homothetic in permanent income, so that we can define $m_t = \\mLvl_t/\\pLvl_t$ and find a normalized policy function $\\cFunc(\\cdot)$ such that\n",
    "\\begin{equation*}\n",
    "\\cFunc(\\mNrm) \\times \\pLvl_t = \\cFunc(\\mLvl_t, \\pLvl_t) \\,\\,\\qquad \\forall(\\mLvl_t, \\pLvl_t)\n",
    "\\end{equation*}\n",
    "where $\\cFunc(\\cdot,\\cdot)$ is the optimal consumption function.\n",
    "\n",
    "- $\\pLvl_t$ evolves according to $$\\pLvl_{t+1} = \\PermGroFac \\PermShk_{t+1} \\pLvl_t,$$ where $\\PermShk_{t+1}$ is a shock with density function $f_{\\PermShk}(\\cdot)$ satisfying $\\Ex_t[\\PermShk_{t+1}] = 1$.\n",
    "\n",
    "To compute aggregate consumption $\\CLvl_t$ in this model, we would follow the approach from above\n",
    "\\begin{equation*}\n",
    "\\CLvl_t = \\int \\int \\cFunc(\\mNrm)\\times\\pLvl \\times \\mpLvlDstn_t(\\mNrm,\\pLvl) \\, d\\mNrm \\, d\\pLvl,\n",
    "\\end{equation*}\n",
    "where $\\mpLvlDstn_t(\\mNrm,\\pLvl)$ is the measure of agents with normalized resources $\\mNrm$ and permanent income $\\pLvl$.\n",
    "\n",
    "## First insight\n",
    "\n",
    "The first of Harmenberg's insights is that the previous integral can be rearranged as\n",
    "\\begin{equation*}\n",
    "\\CLvl_t = \\int_{\\mNrm} \\cFunc(\\mNrm)\\left(\\int \\pLvl \\times \\mpLvlDstn_t(\\mNrm,\\pLvl) \\, d\\pLvl\\right) \\, d\\mNrm.\n",
    "\\end{equation*}\n",
    "The inner integral, $\\int_{\\pLvl} \\pLvl \\times \\mpLvlDstn_t(\\mNrm,\\pLvl) \\, d\\pLvl$, is a function of $\\mNrm$ and it measures *the total amount of permanent income accruing to agents with normalized market resources of* $\\mNrm$. De-trending this object by the deterministic component of growth in permanent income $\\PermGroFac$, Harmenberg defines the *permanent-income-weighted distribution* $\\mWgtDstnMarg(\\cdot)$ as\n",
    "\n",
    "\\begin{equation*}\n",
    "\\mWgtDstnMarg_{t}(\\mNrm) \\def \\PermGroFac^{-t}\\int_{\\pLvl} \\pLvl \\times \\mpLvlDstn_t(\\mNrm,\\pLvl) \\, d\\pLvl.\n",
    "\\end{equation*}\n",
    "\n",
    "\n",
    "The definition allows us to rewrite\n",
    "\\begin{equation}\\label{eq:aggC}\n",
    "\\CLvl_{t} = \\PermGroFac^t \\int_{m} \\cFunc(\\mNrm) \\times \\mWgtDstnMarg_t(\\mNrm) \\, dm.\n",
    "\\end{equation}\n",
    "\n",
    "There are no computational advances yet: We have merely hidden the joint distribution of $(\\mNrm,\\pLvl)$ inside the $\\mWgtDstnMarg$ object we have defined. This helps us notice that $\\mWgtDstnMarg$ is the only object besides the solution that we need in order to compute aggregate consumption. But we still have no practial way of computing or approximating $\\mWgtDstnMarg$.\n",
    "\n",
    "## Second insight\n",
    "\n",
    "Harmenberg's second insight produces a simple way of generating simulated counterparts of $\\mWgtDstnMarg$ without having to simulate permanent incomes.\n",
    "\n",
    "We start with the density function of $\\mNrm_{t+1}$ given $\\mNrm_t$ and $\\PermShk_{t+1}$, $\\kernel(\\mNrm_{t+1}|\\mNrm_t,\\PermShk_{t+1})$. This density will depend on the model's transition equations and draws of random variables like transitory shocks to income in $t+1$ or random returns to savings between $t$ and $t+1$. If we can simulate those things, then we can sample from $\\kernel(\\cdot|\\mNrm_t,\\PermShk_{t+1})$.\n",
    "\n",
    "Harmenberg shows that\n",
    "\\begin{equation*}\\label{eq:transition}\n",
    "\\texttt{transition:    }\\mWgtDstnMarg_{t+1}(\\mNrm_{t+1}) = \\int \\kernel(\\mNrm_{t+1}|\\mNrm_t, \\PermShk_t) \\pShkNeutDstn(\\PermShk_{t+1}) \\mWgtDstnMarg_t(\\mNrm_t)\\, d\\mNrm_t\\, d\\PermShk_{t+1},\n",
    "\\end{equation*}\n",
    "where $\\pShkNeutDstn$ is an altered density function for the permanent income shocks $\\PermShk$, which he calls the *permanent-income-neutral* measure, and which relates to the original density $f_{\\PermShk}$ through $$\\pShkNeutDstn(\\PermShk_{t+1})\\def \\PermShk_{t+1}f_{\\PermShk}(\\PermShk_{t+1})\\,\\,\\, \\forall \\PermShk_{t+1}.$$\n",
    "\n",
    "What's remarkable about this equation is that it gives us a way to obtain a distribution $\\mWgtDstnMarg_{t+1}$ from $\\mWgtDstnMarg_t$:\n",
    "- Start with a population whose $\\mNrm$ is distributed according to $\\mWgtDstnMarg_t$.\n",
    "- Give that population permanent income shocks with distribution $\\pShkNeutDstn$.\n",
    "- Apply the transition equations and other shocks of the model to obtain $\\mNrm_{t+1}$ from $\\mNrm_{t}$ and $\\PermShk_{t+1}$ for every agent.\n",
    "- The distribution of $\\mNrm$ across the resulting population will be $\\mWgtDstnMarg_{t+1}$.\n",
    "\n",
    "Notice that the only change in these steps from what how we would usually simulate the model is that we now draw permanent income shocks from $\\pShkNeutDstn$ instead of $f_{\\PermShk}$. Therefore, with this procedure we can approximate $\\mWgtDstnMarg_t$ and compute aggregates using formulas like the equation `transition`, all without tracking permanent income and with few changes to the code we use to simulate the model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fb35e3a",
   "metadata": {},
   "source": [
    "# Harmenberg's method in HARK\n",
    "\n",
    "Harmenberg's method for simulating under the permanent-income-neutral measure is available in [HARK's `IndShockConsumerType` class](https://github.com/econ-ark/HARK/blob/master/HARK/ConsumptionSaving/ConsIndShockModel.py) and the (many) models that inherit its income process, such as [`PortfolioConsumerType`](https://github.com/econ-ark/HARK/blob/master/HARK/ConsumptionSaving/ConsPortfolioModel.py).\n",
    "\n",
    "As the cell below illustrates, using Harmenberg's method in [HARK](https://github.com/econ-ark/HARK) simply requires setting an agent's property `agent.neutral_measure = True` and then computing the discrete approximation to the income process. After these steps, `agent.simulate` will simulate the model using Harmenberg's permanent-income-neutral measure."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c2b8ea9",
   "metadata": {},
   "source": [
    "`# Implementation in HARK:`"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a4445de-0e32-4cb0-b2ec-5c9b617e8d31",
   "metadata": {},
   "source": [
    "#### Farther down in the notebook, code like this solves the standard model:\n",
    "\n",
    "```python\n",
    "# Create a population with the default parametrization\n",
    "\n",
    "popn = IndShockConsumerType(**params)\n",
    "\n",
    "# Specify which variables to track in the simulation\n",
    "popn.track_vars=[\n",
    "    'mNrm',  # mLvl normalized by permanent income (mLvl = market resources)\n",
    "    'cNrm',  # cLvl normalized by permanent income (cLvl = consumption)\n",
    "    'pLvl']  # pLvl: permanent income\n",
    "\n",
    "popn.cycles = 0  # No life cycles -- an infinite horizon\n",
    "\n",
    "# Solve for the consumption function\n",
    "popn.solve()\n",
    "\n",
    "# Simulate under the base measure\n",
    "popn.initialize_sim()\n",
    "popn.simulate()\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "272bef2d-7f8e-48f2-b6d2-4617e665a721",
   "metadata": {},
   "source": [
    "#### Later, code like this simulates using the permanent-income-neutral measure\n",
    "```python\n",
    "# Harmenberg permanent-income-neutral simulation\n",
    "\n",
    "# Make a clone of the population weighted solution\n",
    "ntrl = deepcopy(popn)\n",
    "\n",
    "# Change the income process to use the neutral measure\n",
    "\n",
    "ntrl.neutral_measure = True\n",
    "ntrl.update_income_process()\n",
    "\n",
    "# Simulate\n",
    "ntrl.initialize_sim()\n",
    "ntrl.simulate()\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4ecbd12",
   "metadata": {},
   "source": [
    "All we had to do differently to simulate using the permanent-income-neutral measure was to set the agent's property `neutral_measure=True`.\n",
    "\n",
    "This is implemented when the function `update_income_process` re-constructs the agent's income process. The specific lines that achieve the change of measure in HARK are in [this link](https://github.com/econ-ark/HARK/blob/760df611a6ec2ff147d00b7d866dbab6fc4e18a1/HARK/ConsumptionSaving/ConsIndShockModel.py#L2734-L2735), or reproduced here:\n",
    "\n",
    "```python\n",
    "if self.neutral_measure == True:\n",
    "    PermShkDstn_t.pmv = PermShkDstn_t.atoms*PermShkDstn_t.pmv\n",
    "```\n",
    "\n",
    "Simple!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a4de660",
   "metadata": {},
   "source": [
    "# The efficiency gain from using Harmenberg's method\n",
    "\n",
    "To demonstrate the gain in efficiency from using Harmenberg's method, we will set up the following experiment.\n",
    "\n",
    "Consider an economy populated by [Buffer-Stock](https://econ-ark.github.io/BufferStockTheory/) savers, whose individual-level state variables are market resources $\\mLvl_t$ and permanent income $\\pLvl_t$. Such agents have a [homothetic consumption function](https://econ-ark.github.io/BufferStockTheory/#The-Problem-Can-Be-Normalized-By-Permanent-Income), so that we can define normalized market resources $\\mNrm_t \\def \\mLvl_t / \\pLvl_t$, solve for a normalized consumption function $\\cFunc(\\cdot)$, and express the consumption function as $\\cFunc(\\mLvl,\\pLvl) = \\cFunc(\\mNrm)\\times\\pLvl$.\n",
    "\n",
    "Assume further that mortality, impatience, and permanent income growth are such that the economy converges to stable joint distribution of $\\mNrm$ and $\\pLvl$ characterized by the density function $f(\\cdot,\\cdot)$. Under these conditions, define the stable level of aggregate market resources and consumption as\n",
    "\\begin{equation}\n",
    "    \\MLvl \\def \\int \\int \\mNrm \\times \\pLvl \\times f(\\mNrm, \\pLvl)\\,d\\mNrm \\,d\\pLvl, \\,\\,\\,    \\CLvl \\def \\int \\int \\cFunc(\\mNrm) \\times \\pLvl \\times f(\\mNrm, \\pLvl)\\,d\\mNrm \\,d\\pLvl.\n",
    "\\end{equation}\n",
    "\n",
    "If we could simulate the economy with a continuum of agents we would find that, over time, our estimate of aggregate market resources $\\MLvlest_t$ would converge to $\\MLvl$ and $\\CLvlest_t$ would converge to $\\CLvl$. Therefore, if we computed our aggregate estimates at different periods in time we would find them to be close:\n",
    "\\begin{equation*}\n",
    "    \\MLvlest_t \\approx \\MLvlest_{t+n} \\approx \\MLvl \\,\\,\n",
    "    \\text{and} \\,\\,\n",
    "    \\CLvlest_t \\approx \\CLvlest_{t+n} \\approx \\CLvl, \\,\\,\n",
    "    \\text{for } n>0 \\text{ and } t \\text{ large enough}.\n",
    "\\end{equation*}\n",
    "\n",
    "In practice, however, we rely on approximations using a finite number of agents $I$. Our estimates of aggregate market resources and consumption at time $t$ are\n",
    "\\begin{equation}\n",
    "\\MLvlest_t \\def \\frac{1}{I} \\sum_{i=1}^{I} m_{i,t}\\times\\pLvl_{i,t}, \\,\\,\\, \\CLvlest_t \\def \\frac{1}{I} \\sum_{i=1}^{I} \\cFunc(m_{i,t})\\times\\pLvl_{i,t},\n",
    "\\end{equation}\n",
    "\n",
    "under the basic simulation strategy or\n",
    "\n",
    "\\begin{equation}\n",
    "\\MLvlest_t \\def \\frac{1}{I} \\sum_{i=1}^{I} \\tilde{m}_{i,t}, \\,\\,\\, \\CLvlest_t \\def \\frac{1}{I} \\sum_{i=1}^{I} \\cFunc(\\tilde{m}_{i,t}),\n",
    "\\end{equation}\n",
    "\n",
    "if we use Harmenberg's method to simulate the distribution of normalized market resources under the permanent-income neutral measure.\n",
    "\n",
    "If we do not use enough agents, our distributions of agents over state variables will be noisy at approximating their continuous counterparts. Additionally, they will depend on the sequences of shocks that the agents receive. With a finite sample, the stochasticity of the draws will cause fluctuations in $\\MLvlest_t$ and $\\CLvlest_t$. Therefore an informal way to measure the precision of our approximations is to examine the amplitude of these fluctuations.\n",
    "\n",
    "First, some setup.\n",
    "1. Simulate the economy for a sufficiently long \"burn in\" time $T_0$.\n",
    "2. Sample our aggregate estimates at regular intervals after $T_0$. Letting the sampling times be $\\mathcal{T}\\def \\{T_0 + \\Delta t\\times n\\}_{n=0,1,...,N}$, obtain $\\{\\MLvlest_t\\}_{t\\in\\mathcal{T}}$ and $\\{\\CLvlest_t\\}_{t\\in\\mathcal{T}}$.\n",
    "3. Compute the variance of approximation samples $\\text{Var}\\left(\\{\\MLvlest_t\\}_{t\\in\\mathcal{T}}\\right)$ and $\\text{Var}\\left(\\{\\CLvlest_t\\}_{t\\in\\mathcal{T}}\\right)$.\n",
    "    - Other measures of uncertainty (like standard deviation) could also be computed\n",
    "    - But variance is the natural choice [because it is closely related to expected welfare](http://www.econ2.jhu.edu/people/ccarroll/papers/candcwithstickye/#Utility-Costs-Of-Sticky-Expectations)\n",
    "\n",
    "We will now perform exactly this exercise, examining the fluctuations in aggregates when they are approximated using the basic simulation strategy and Harmenberg's permanent-income-neutral measure. Since each approximation can be made arbitrarily good by increasing the number of agents it uses, we will examine the variances of aggregates for various sample sizes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a12309c",
   "metadata": {},
   "source": [
    "`# Setup computational environment:`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f0d51173",
   "metadata": {},
   "outputs": [],
   "source": [
    "# How long to run the economies without sampling? T_0\n",
    "# Because we start the population at mBalLvl which turns out to be close\n",
    "# to MBalLvl so we don't need a long burn in period\n",
    "burn_in = 200\n",
    "# Fixed intervals between sampling aggregates, Δt\n",
    "sample_every = 1  # periods - increase this if worried about serial correlation\n",
    "# How many times to sample the aggregates? n\n",
    "n_sample = 200  # times; minimum\n",
    "\n",
    "# Create a vector with all the times at which we'll sample\n",
    "sample_periods_lvl = np.arange(\n",
    "    start=burn_in, stop=burn_in + sample_every * n_sample, step=sample_every, dtype=int\n",
    ")\n",
    "# Corresponding periods when object is first difference not level\n",
    "sample_periods_dff = np.arange(\n",
    "    start=burn_in,\n",
    "    stop=burn_in + sample_every * n_sample - 1,  # 1 fewer diff\n",
    "    step=sample_every,\n",
    "    dtype=int,\n",
    ")\n",
    "\n",
    "# Maximum number of agents that we will use for our approximations\n",
    "max_agents = 100000\n",
    "# Minimum number of agents for comparing methods in plots\n",
    "min_agents = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2827536",
   "metadata": {},
   "source": [
    "`# Define tool to calculate summary statistics:`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "91221385",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now create a function that takes HARK's simulation output\n",
    "# and computes all the summary statistics we need\n",
    "\n",
    "\n",
    "def sumstats(sims, sample_periods):\n",
    "    # sims will be an array in the shape of [economy].history elements\n",
    "    # Columns are different agents and rows are different times.\n",
    "\n",
    "    # Subset the times at which we'll sample and transpose.\n",
    "    samples_lvl = pd.DataFrame(sims[sample_periods,].T)\n",
    "\n",
    "    # Get averages over agents. This will tell us what our\n",
    "    # aggregate estimate would be if we had each possible sim size\n",
    "    avgs_lvl = samples_lvl.expanding(1).mean()\n",
    "\n",
    "    # Now get the mean and standard deviations across time with\n",
    "    # every number of agents\n",
    "    mean_lvl = avgs_lvl.mean(axis=1)\n",
    "    vars_lvl = avgs_lvl.std(axis=1) ** 2\n",
    "\n",
    "    # Also return the full sample on the last simulation period\n",
    "    return {\n",
    "        \"mean_lvl\": mean_lvl,\n",
    "        \"vars_lvl\": vars_lvl,\n",
    "        \"dist_last\": sims[-1,],\n",
    "    }"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1b63dbd",
   "metadata": {},
   "source": [
    "We now configure and solve a buffer-stock agent with a default parametrization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "022940b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create and solve agent\n",
    "\n",
    "popn = IndShockConsumerType(**init_idiosyncratic_shocks)\n",
    "\n",
    "# Modify default parameters\n",
    "popn.T_sim = max(sample_periods_lvl) + 1\n",
    "popn.AgentCount = max_agents\n",
    "popn.track_vars = [\"mNrm\", \"cNrm\", \"pLvl\"]\n",
    "popn.LivPrb = [1.0]\n",
    "popn.cycles = 0\n",
    "\n",
    "# Solve (but do not yet simulate)\n",
    "popn.solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5b545bb",
   "metadata": {},
   "source": [
    "Under the basic simulation strategy, we have to de-normalize market resources and consumption multiplying them by permanent income. Only then we construct our statistics of interest.\n",
    "\n",
    "Note that our time-sampling strategy requires that, after enough time has passed, the economy settles on a stable distribution of its agents across states. How can we know this will be the case? [Szeidl (2013)](http://www.personal.ceu.hu/staff/Adam_Szeidl/papers/invariant.pdf) and [Harmenberg (2021)](https://www.sciencedirect.com/science/article/pii/S0165188921001202?via%3Dihub) provide conditions that can give us some reassurance.$\\newcommand{\\Rfree}{\\mathsf{R}}$\n",
    "\n",
    "1. [Szeidl (2013)](http://www.personal.ceu.hu/staff/Adam_Szeidl/papers/invariant.pdf) shows that if $$\\log \\left[\\frac{(\\Rfree\\beta)^{1/\\rho}}{\\PermGroFac}\n",
    "\\right] < \\Ex[\\log \\PermShk],$$ then there is a stable invariant distribution of normalized market resources $\\mNrm$.\n",
    "2. [Harmenberg (2021)](https://www.sciencedirect.com/science/article/pii/S0165188921001202?via%3Dihub) repurposes the Szeidl proof to argue that if the same condition is satisfied when the expectation is taken with respect to the permanent-income-neutral measure ($\\pShkNeutDstn$), then there is a stable invariant permanent-income-weighted distribution ($\\mWgtDstnMarg$)\n",
    "\n",
    "We now check both conditions with our parametrization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fc204d95",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Szeidl's condition is satisfied, there is a stable invariant distribution of normalized market resources\n",
      "Harmenberg's condition is satisfied, there is a stable invariant permanent-income-weighted distribution\n"
     ]
    }
   ],
   "source": [
    "popn.check_conditions()\n",
    "GPFacRaw = popn.bilt[\"GPFacRaw\"]\n",
    "e_log_PermShk_popn = calc_expectation(popn.PermShkDstn[0], func=lambda x: np.log(x))\n",
    "e_log_PermShk_ntrl = calc_expectation(\n",
    "    popn.PermShkDstn[0], func=lambda x: x * np.log(x)\n",
    ")\n",
    "szeidl_cond = np.log(GPFacRaw) < e_log_PermShk_popn\n",
    "harmen_cond = np.log(GPFacRaw) < e_log_PermShk_ntrl\n",
    "if szeidl_cond:\n",
    "    print(\n",
    "        \"Szeidl's condition is satisfied, there is a stable invariant distribution of normalized market resources\"\n",
    "    )\n",
    "else:\n",
    "    print(\"Warning: Szeidl's condition is not satisfied\")\n",
    "if harmen_cond:\n",
    "    print(\n",
    "        \"Harmenberg's condition is satisfied, there is a stable invariant permanent-income-weighted distribution\"\n",
    "    )\n",
    "else:\n",
    "    print(\"Warning: Harmenberg's condition is not satisfied\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a306679",
   "metadata": {},
   "source": [
    "Knowing that the conditions are satisfied, we are ready to perform our experiments.\n",
    "\n",
    "First, we simulate using the traditional approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "048daf16-208f-4741-b367-e7ab14ab00d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find the stable market resources ratio (in expectation)\n",
    "popn.calc_stable_points()\n",
    "mNrmStE = popn.bilt[\"mNrmStE\"]\n",
    "\n",
    "# Set all agents to be \"born\" with the corresponding level of capital\n",
    "Reff = popn.Rfree[0] / popn.PermGroFac[0]\n",
    "popn.kLogInitMean = np.log((mNrmStE - 1)/Reff)\n",
    "popn.kLogInitStd = 0.0\n",
    "popn.update(\"kNrmInitDstn\")\n",
    "\n",
    "popn.initialize_sim()\n",
    "popn.simulate()\n",
    "\n",
    "# Retrieve history\n",
    "mNrm_popn = popn.history[\"mNrm\"]\n",
    "mLvl_popn = popn.history[\"mNrm\"] * popn.history[\"pLvl\"]\n",
    "cLvl_popn = popn.history[\"cNrm\"] * popn.history[\"pLvl\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78ba82a7",
   "metadata": {},
   "source": [
    "Update and simulate using Harmenberg's strategy. This time, not multiplying by permanent income."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7bf55cf3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Harmenberg permanent income neutral simulation\n",
    "\n",
    "# Start by duplicating the previous setup\n",
    "ntrl = deepcopy(popn)\n",
    "\n",
    "# Recompute income process to use neutral measure\n",
    "ntrl.neutral_measure = True\n",
    "ntrl.update_income_process()\n",
    "\n",
    "ntrl.initialize_sim()\n",
    "ntrl.simulate()\n",
    "\n",
    "# Retrieve history\n",
    "cLvl_ntrl = ntrl.history[\"cNrm\"]\n",
    "mLvl_ntrl = ntrl.history[\"mNrm\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a84d07e",
   "metadata": {},
   "source": [
    "# Now Compare the Variances of Simulated Outcomes\n",
    "\n",
    "Harmenberg (2021) and Szeidl (2013) prove that with an infinite population size, models of this kind will have constant and identical growth rates of aggregate consumption, market resources, and noncapital income.\n",
    "\n",
    "A method of comparing the efficiency of the two methods is therefore to calculate the variance of the simulated aggregate variables, and see how many agents must be simulated using each of them in order to achieve a given variance.  (An infinite number of agents would be required to achieve zero variance).\n",
    "\n",
    "The plots below show the (logs of) the estimated variances for the two methods as a function of the (logs of) the number of agents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "499e0e33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x700 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plots\n",
    "\n",
    "# Construct aggregate levels and growth rates\n",
    "# Cumulate levels and divide by number of agents to get average\n",
    "CAvg_popn = np.cumsum(cLvl_popn, axis=1) / np.arange(1, max_agents + 1)\n",
    "CAvg_ntrl = np.cumsum(cLvl_ntrl, axis=1) / np.arange(1, max_agents + 1)\n",
    "MAvg_popn = np.cumsum(mLvl_popn, axis=1) / np.arange(1, max_agents + 1)\n",
    "MAvg_ntrl = np.cumsum(mLvl_ntrl, axis=1) / np.arange(1, max_agents + 1)\n",
    "# First difference the logs to get aggregate growth rates\n",
    "CGro_popn = np.diff(np.log(CAvg_popn).T).T\n",
    "CGro_ntrl = np.diff(np.log(CAvg_ntrl).T).T\n",
    "MGro_popn = np.diff(np.log(MAvg_popn).T).T\n",
    "MGro_ntrl = np.diff(np.log(MAvg_ntrl).T).T\n",
    "# Calculate statistics for them\n",
    "CGro_popn_stats = sumstats(CGro_popn, sample_periods_dff)\n",
    "CGro_ntrl_stats = sumstats(CGro_ntrl, sample_periods_dff)\n",
    "MGro_popn_stats = sumstats(MGro_popn, sample_periods_dff)\n",
    "MGro_ntrl_stats = sumstats(MGro_ntrl, sample_periods_dff)\n",
    "\n",
    "# Count the agents\n",
    "nagents = np.arange(1, max_agents + 1, 1)\n",
    "\n",
    "# Plot\n",
    "fig, axs = plt.subplots(2, figsize=(10, 7), constrained_layout=True)\n",
    "fig.suptitle(\"Variances of Aggregate Growth Rates\", fontsize=16)\n",
    "axs[0].plot(\n",
    "    nagents[min_agents:],\n",
    "    np.array(CGro_popn_stats[\"vars_lvl\"])[min_agents:],\n",
    "    label=\"Base\",\n",
    ")\n",
    "axs[0].plot(\n",
    "    nagents[min_agents:],\n",
    "    np.array(CGro_ntrl_stats[\"vars_lvl\"])[min_agents:],\n",
    "    label=\"Perm. Inc. Neutral\",\n",
    ")\n",
    "axs[0].set_yscale(\"log\")\n",
    "axs[0].set_xscale(\"log\")\n",
    "axs[0].set_title(\"Consumption\", fontsize=14)\n",
    "axs[0].set_ylabel(\n",
    "    r\"$\\Delta \\log \\left(\\{\\hat{C}_t\\}_{t\\in\\mathcal{T}}\\right)$\", fontsize=14\n",
    ")\n",
    "axs[0].set_xlabel(\"Number of Agents\", fontsize=10)\n",
    "axs[0].grid()\n",
    "axs[0].legend(fontsize=12)\n",
    "\n",
    "axs[1].plot(\n",
    "    nagents[min_agents:],\n",
    "    np.array(MGro_popn_stats[\"vars_lvl\"])[min_agents:],\n",
    "    label=\"Base\",\n",
    ")\n",
    "axs[1].plot(\n",
    "    nagents[min_agents:],\n",
    "    np.array(MGro_ntrl_stats[\"vars_lvl\"])[min_agents:],\n",
    "    label=\"Perm. Inc. Neutral\",\n",
    ")\n",
    "axs[1].set_yscale(\"log\")\n",
    "axs[1].set_xscale(\"log\")\n",
    "axs[1].set_title(\"Market Resources\", fontsize=14)\n",
    "axs[1].set_ylabel(\n",
    "    r\"$\\Delta \\log \\left(\\{\\hat{M}_t\\}_{t\\in\\mathcal{T}}\\right)$\", fontsize=14\n",
    ")\n",
    "axs[1].set_xlabel(\"Number of Agents\", fontsize=10)\n",
    "axs[1].grid()\n",
    "axs[1].legend(fontsize=12)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbb44a41",
   "metadata": {},
   "source": [
    "# Harmenberg's Method Produces Large Gains in Efficiency\n",
    "\n",
    "The number of agents required to achieve a given variance is revealed by choosing that variance and then finding the points on the horizontal axis that correspond to the two methods.\n",
    "\n",
    "The upper variance plot shows that the efficiency gains are very large for consumption: The horizontal gap between the two loci is generally more than two orders of magnitude.  That is, Harmenberg's method requires less than **one-hundredth** as many agents as the standard method would require for a given precision.  Alternatively, for a given number of agents it is typically more than 10 times as precise.\n",
    "\n",
    "The improvement in variance is smaller for market resources, likely because in a buffer stock model the point of consumers' actions is to use assets to absorb shocks.  But even for $\\MLvl$, the Harmenberg method attains any given level of precision ($\\text{var}\\left(\\{\\MLvlest_t\\}_{t\\in\\mathcal{T}}\\right)$) with roughly **one tenth** of the agents needed by the standard method to achieve that same level.\n",
    "\n",
    "Of course, these results apply only to the particular configuration of parameter values that is the default in the HARK toolkit (but which were chosen long before Harmenberg developed his method).  The degree of improvement will vary depending on the calibration -- for example, if the magnitude of permanent shocks is small or zero, the method will yield little or no improvement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "329e8bbf-d6ed-4c3e-a416-4dc71c82ade6",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Execute the line below to see that there's little drift from mNrmStE as starting point\n",
    "# (after setting burn_in to zero above).  This means burn_in does not need to be large:\n",
    "\n",
    "plt.plot(np.arange(1,len(np.mean(MAvg_ntrl,axis=1))+1),np.mean(MAvg_ntrl,axis=1).T)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "71987c2e-e1ed-44d7-9664-d3e48faf48b2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "jupytext": {
   "cell_metadata_filter": "ExecuteTime,collapsed,title,code_folding,tags,incorrectly_encoded_metadata,jp-MarkdownHeadingCollapsed,-autoscroll",
   "encoding": "# -*- coding: utf-8 -*-",
   "formats": "ipynb,py:percent",
   "notebook_metadata_filter": "all,-widgets,-varInspector"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}