{ "cells": [ { "cell_type": "markdown", "id": "107090de", "metadata": {}, "source": [ "# Micro- and Macroeconomic Implications of Very Impatient Households\n", "\n", "
Generator: QuARK-make/notebooks_byname
\n", "\n", "[![badge](https://img.shields.io/badge/Launch%20using%20-Econ--ARK-blue)](https://econ-ark.org/materials/micro-and-macro-implications-of-very-impatient-hhs#launch)" ] }, { "cell_type": "markdown", "id": "39d60ef2", "metadata": {}, "source": [ "## Introduction\n", "\n", "Buffer stock saving models of the kind implemented in $\\texttt{ConsIndShockType}$ say that, if a standard ['Growth Impatience Condition'](https://econ-ark.github.io/BufferStockTheory/#GICRaw), holds:\n", "\n", "\\begin{eqnarray}\n", "\\newcommand{\\Rfree}{\\mathsf{R}}\\newcommand{\\DiscFac}{\\beta}\\newcommand{\\PermGroFac}{\\Gamma}\\newcommand{\\PermShk}{\\psi}\\newcommand{\\CRRA}{\\rho}\n", "\\left(\\frac{(\\Rfree\\DiscFac)^{1/\\CRRA}\\mathbb{E}[\\PermShk^{-1}]}{\\PermGroFac}\\right) & < & 1\n", "\\end{eqnarray}\n", "\n", "then the _ratio_ of asets $\\newcommand{\\aLev}{\\mathbf{a}}\\aLev$ to permanent income $\\newcommand{\\pLev}{\\mathbf{p}}\\pLev$, $a=\\aLev/\\pLev$, has a target value $\\newcommand{\\aTarg}{\\check{a}}\\aTarg$ that depends on the consumer's preferences (relative risk aversion $\\CRRA$, time preference $\\DiscFac$) and circumstances (interest factor $\\Rfree$, growth factor $\\PermGroFac$, uncertainty about permanent income shocks $\\sigma^{2}_{\\PermShk}$).\n", "\n", "If everyone had identical preferences and everyone were at their target $\\check{a}$, then inequality in the level of $\\aLev$ would be exactly the same as inequality in $\\pLev$.\n", "\n", "[\"The Distribution of Wealth and the Marginal Propensity to Consume\"](https://www.econ2.jhu.edu/people/ccarroll/papers/cstwMPC) (Carroll, Slacalek, Tokuoka, and White 2017; hereafter: \"cstwMPC\") shows that, when such a model is simulated and agents draw their idiosyncratic shocks (so, agents are _ex post_ heterogeneous -- see the definition in [Intro-To-HARK](http://github.com/econ-ark/PARK/tree/master/Intro-To-HARK.pdf)) -- asset inequality is indeed close to $\\pLev$ inequality even though everyone is not always at exactly their target $a$.\n", "\n", "But a large body of evidence shows that _actual_ inequality in assets is much greater than _actual_ inequality in permanent income. Thus, to make a model that qualifies as what cstwMPC call a 'serious' microfounded macro model of consumption (one that matches the key facts _theory says_ should be first-order important), the model must be modified to incorporate some form of _ex ante_ heterogeneity: That is, there must be differences across people in $\\DiscFac$ or $\\Rfree$ or $\\CRRA$ or $\\PermGroFac$ or $\\sigma^{2}_{\\PermShk}$.\n", "\n", "The most transparent and simplest of these to change is the time preference factor $\\beta$. So that is what the paper does. The main results are:\n", "\n", "1. The distribution of $\\beta$ need not be particularly wide to match the extreme concentration of wealth: roughly 0.91 to 0.98 (annual); that is, the most impatient person discounts the future about 6 percentage points more per year than the most patient agent agent\n", "2. With such a distribution of $\\beta$, simulated agents' (annual) marginal propensity to consume (MPC) from transitory income shocks to income matches large body of microeconomic evidence that typically finds evidence of MPC's in the range of 0.2 to 0.6. This is much better than RA macro models that typically yield MPC's in the range of 0.01 to 0.05.\n", "\n", "While the most impatient agents in the cstwMPC model have fairly high MPCs (~0.6 annual), there is microeconomic evidence that a significant fraction of households have *even higher* MPCs than the model predicts, especially at the quarterly frequency. This group of households is commonly referred to as \"hand-to-mouth\" -- they consume most of their transitory shocks to income not too long after they receive them (mostly within a quarter). There are several reasons why a household could be hand-to-mouth, but one plausible explanation is that these households are *even more impatient* than estimated by cstwMPC for the most impatient agent.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "087108b7", "metadata": {}, "outputs": [], "source": [ "# This cell does some setup and imports generic tools used to produce the figures\n", "\n", "from HARK.utilities import get_lorenz_shares, get_percentiles\n", "from HARK.datasets import load_SCF_wealth_weights\n", "from HARK.distribution import Uniform\n", "from HARK.ConsumptionSaving.ConsIndShockModel import IndShockConsumerType\n", "from copy import deepcopy\n", "import warnings\n", "from distutils.spawn import find_executable\n", "import matplotlib.pyplot as plt\n", "from IPython import get_ipython # In case it was run from python instead of ipython\n", "from tqdm import tqdm\n", "\n", "import numpy as np\n", "\n", "Generator = False # Is this notebook the master or is it generated?\n", "# Import related generic python packages\n", "\n", "# Set how many digits past the decimal point should be printed?\n", "\n", "\n", "def mystr(number):\n", " return \"{:.4f}\".format(number)\n", "\n", "\n", "def decfmt4(number):\n", " return \"{:.4f}\".format(number)\n", "\n", "\n", "def decfmt3(number):\n", " return \"{:.3f}\".format(number)\n", "\n", "\n", "def decfmt2(number):\n", " return \"{:.2f}\".format(number)\n", "\n", "\n", "def decfmt1(number):\n", " return \"{:.1f}\".format(number)\n", "\n", "\n", "# This is a jupytext paired notebook that autogenerates BufferStockTheory.py\n", "# which can be executed from a terminal command line via \"ipython BufferStockTheory.py\"\n", "# But a terminal does not permit inline figures, so we need to test jupyter vs terminal\n", "# Google \"how can I check if code is executed in the ipython notebook\"\n", "\n", "\n", "def in_ipynb():\n", " try:\n", " if (\n", " str(type(get_ipython()))\n", " == \"