diff --git a/models/We-Would-Like-In-Econ-ARK/OhReis2021/Keynesian.png b/models/We-Would-Like-In-Econ-ARK/OhReis2021/Keynesian.png new file mode 100644 index 00000000..315201f8 Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/OhReis2021/Keynesian.png differ diff --git a/models/We-Would-Like-In-Econ-ARK/OhReis2021/Neoclassical.png b/models/We-Would-Like-In-Econ-ARK/OhReis2021/Neoclassical.png new file mode 100644 index 00000000..d793da0b Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/OhReis2021/Neoclassical.png differ diff --git a/models/We-Would-Like-In-Econ-ARK/OhReis2021/ballpARK-KohKW.ipynb b/models/We-Would-Like-In-Econ-ARK/OhReis2021/ballpARK-KohKW.ipynb new file mode 100644 index 00000000..dc895c05 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/OhReis2021/ballpARK-KohKW.ipynb @@ -0,0 +1,204 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "aef0dd80", + "metadata": {}, + "source": [ + "# Targeted Transfers and the Fiscal Response to the Great Recession\n", + "Hyunseung Oh, Ricardo Reis\n", + "Journal of Monetary Economics 59 (2012) S50-S64\n", + "(http://dx.doi.org/10.1016/j.jmoneco.2012.10.025)" + ] + }, + { + "cell_type": "markdown", + "id": "f97fa3ed", + "metadata": {}, + "source": [ + "## Fiscal transfers are an increasingly large but understudied part of fiscal policy\n", + "\n", + "\\begin{itemize}\n", + " \\item End-2007 to End-2009: Three quarters of increase in US government expenditures (government consumption + government investment + interest payments + transfers) have been increases in transfers; three quarters of that are social transfers\n", + " \\item Also a trend in OECD and European economies, where at least 30% of the increase in government spending during the Great Recession was in government transfers\n", + "\\end{itemize}\n", + "\n", + "But economists have focused on output effects of government \\textbf{purchases}, i.e. government consumption + government investment, in the form of fiscal multipliers\n", + "\\begin{itemize}\n", + " \\item A representative agent model would only show the representative agent transferring income to itself from taxation of itself, and therefore such models cannot show the effects of fiscal transfers\n", + " \\item No effect on aggregate employment and output\n", + " \\item Government transfers across time are neutral (Ricardian equivalence)\n", + "\\end{itemize}" + ] + }, + { + "cell_type": "markdown", + "id": "aa7bb418", + "metadata": {}, + "source": [ + "## Why in ballpARK?\n", + "\n", + "What does a heterogeneous agent model bring to the discussion on the effects of fiscal transfers?\n", + "\\begin{itemize}\n", + " \\item Lump-sum transfers, directed from one group of agents to another group, can increase output and employment in recessions\n", + "\\end{itemize}\n", + "\n", + "What assumptions do we need in a heterogeneous agent model?\n", + "\\begin{enumerate}\n", + " \\item Idiosyncratic, uninsurable uncertainty about income and health\n", + " \\item Nominal rigidities in price setting\n", + " \\item Therefore, the model should nest the following three models:\n", + " \\begin{enumerate}\n", + " \\item Neoclassical growth model\n", + " \\item Aiyagari incomplete markets model\n", + " \\item Sticky-information New Keynesian model\n", + " \\end{enumerate}\n", + "\\end{enumerate}\n", + "Each of these models can be practically addressed with tools already existing in HARK toolkit" + ] + }, + { + "cell_type": "markdown", + "id": "9f6bb922", + "metadata": {}, + "source": [ + "### Variables and Parameters\n", + "\n", + "Continuum of households $\\{k,s,h\\}$, where \n", + "\n", + "| Variable | Description |\n", + "|------------|-------------------------------------------------|\n", + "| $k$ | capital |\n", + "| $s$ | individual-specific salary offer |\n", + "| $h$ | health affecting relative disutility of working |\n", + "| $V(\\cdot)$ | value function |\n", + "| $c$ | consumption |\n", + "| $n$ | choice to work or not |\n", + "| $r$ | gross interest rate |\n", + "| $w$ | average wage |\n", + "| $d$ | dividends |\n", + "| $\\tau$ | lump-sum taxes |\n", + "| $T(\\cdot)$ | non-negative lump-sum transfers |\n", + "| $z(\\cdot)$ | insurance payments |\n", + "\n", + "\n", + "| Parameter | Description |\n", + "|--------------|----------------------------------------------------|\n", + "| $\\chi$ | disutility from working with worst possible health |\n", + "| $\\beta$ | discount factor |\n", + "| $\\delta$ | depreciation rate |\n", + "| $\\rho$ | persistence of shocks to salary offers |\n", + "| $\\sigma^{2}$ | variance of shocks to salary offers |\n", + "| $\\pi$ | probability that person is healthy |\n", + "| $\\eta$ | average utility gap between healthy and unhealthy |" + ] + }, + { + "cell_type": "markdown", + "id": "175c8cce", + "metadata": {}, + "source": [ + "### Model Setup\n", + "\n", + "Household's Optimization Problem: Find optimal $c^{*}(k,s,h)$, $n^{*}(k,s,h)$, $k^{\\prime *}(k,s,h)$ that solves:\n", + "\\begin{align}\n", + "V(k,s,h) &= \\max_{c,n,k^{\\prime}} \\left\\{ ln(c) - \\chi(1-h)n + \\beta \\iint V(k^{\\prime}, s^{\\prime}, h^{\\prime}) dF(s^{\\prime}, h^{\\prime}) \\right\\} \\\\\n", + "n &\\in \\{0,1\\}, \\quad c \\geq 0, \\quad k^{\\prime} \\geq 0 \\\\\n", + "c+k^{\\prime} &= (1-\\delta +r)k + swn + d - \\tau + T(s,h) + z(k,s,h) \\\\\n", + "ln (s^{\\prime}) &= \\frac{\\sigma^{2}}{2(1+\\rho)} + \\rho ln(s) + \\varepsilon^{\\prime} \\text{ with } \\varepsilon \\sim N(0, \\sigma^{2}) \\text{ } i.i.d. \\\\\n", + "h &= \\begin{cases} 1 & \\text{ with probability } \\pi \\\\ \\text{draw from } U[0, \\eta] & \\text{ with probability } 1-\\pi \\end{cases}\n", + "\\end{align}\n", + "\n", + "#### Representative Competitive Firm: Produces consumption good by combining aggregate capital $K$ and intermediate goods $x(j)$\n", + "\\begin{align}\n", + "\tY &= AK^{\\alpha}X^{1-\\alpha} \\\\\n", + "\tX &= \\left( \\int_{0}^{1} x(j)^{1/\\mu} dj \\right)^{\\mu}\n", + "\\end{align}\n", + "\n", + "#### Monopolistic Intermediate Competitive Goods Firms: Equally owned by all households, making profits $d(j)$, immediately distributes as dividends\n", + "\n", + "\n", + "\n", + "#### Government: Chooses lump-sum transfers subject to budget constraint\n", + "\\begin{equation}\n", + "\tG + \\iint T(s,h) dF(s,h) = \\tau\n", + "\\end{equation}\n", + "\n", + "#### Market Clearing Conditions\n", + "Labor: $\\int sn^{*}(k,s,h) dF(k,s,h) = L = \\int l(j) dj$\n", + "Capital: $\\int k^{\\prime *}(k,s,h) dF(k,s,h) = K^{\\prime}$\n", + "Total Dividends: $ \\int d(j) dj = d $\n", + "Zero Aggregate Insurance Payments: $\\int z(k,s,h) dF(k,s,h) = 0$" + ] + }, + { + "cell_type": "markdown", + "id": "3f488c7b", + "metadata": {}, + "source": [ + "### Some Results\n", + "\n", + "Different parameter values lead to different benchmark models\n", + "\n", + "#### Full insurance: Choice of $T(s,h)$ is irrelevant for aggregate output and employment\n", + "\n", + "#### Imperfect insurance: Transfers from healthy high-salarpy households to low-wealth, low-income(salaries) households boost employment and output through ``neoclassical'' channel\n", + "\\begin{itemize}\n", + "\t``Since the marginal worker pays more in taxes than she receives in transfers, more generous transfers imply she has less wealth and so has a stronger incentive to work.''\n", + "\\end{itemize}\n", + "![Neoclassical](Neoclassical.png)\n" + ] + }, + { + "cell_type": "markdown", + "id": "0609571d", + "metadata": {}, + "source": [ + "#### Keynesian Channel from Targeted Transfers\n", + "Transfer recipients have an average higher MPC than transfer payees\n", + "$\\rightarrow$ transfers boost aggregate demand\n", + "$\\rightarrow$ firms with rigid prices satisfy by hirign more workers and produce more\n", + "![Keynesian](Keynesian.png)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + 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