diff --git a/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/.gitignore b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/.gitignore new file mode 100644 index 00000000..dc764d36 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/.gitignore @@ -0,0 +1,263 @@ +## Core latex/pdflatex auxiliary files: +*.aux +*.lof +*.log +*.lot +*.fls +*.out +*.toc +*.fmt +*.fot +*.cb +*.cb2 +.*.lb + +## Intermediate documents: +*.dvi +*.xdv +*-converted-to.* +# these rules might exclude image files for figures etc. +# *.ps +# *.eps +# *.pdf + +## Generated if empty string is given at "Please type another file name for output:" +.pdf + +## Bibliography auxiliary files (bibtex/biblatex/biber): +*.bbl +*.bcf +*.blg +*-blx.aux +*-blx.bib +*.run.xml + +## Build tool auxiliary files: +*.fdb_latexmk +*.synctex +*.synctex(busy) +*.synctex.gz +*.synctex.gz(busy) +*.pdfsync + +## Build tool directories for auxiliary files +# latexrun +latex.out/ + +## Auxiliary and intermediate files from other packages: +# algorithms +*.alg +*.loa + +# achemso +acs-*.bib + +# amsthm +*.thm + +# beamer +*.nav +*.pre +*.snm +*.vrb + +# changes +*.soc + +# comment +*.cut + +# cprotect +*.cpt + +# elsarticle (documentclass of Elsevier journals) +*.spl + +# endnotes +*.ent + +# fixme +*.lox + +# feynmf/feynmp +*.mf +*.mp +*.t[1-9] +*.t[1-9][0-9] +*.tfm + +#(r)(e)ledmac/(r)(e)ledpar +*.end +*.?end +*.[1-9] +*.[1-9][0-9] +*.[1-9][0-9][0-9] +*.[1-9]R +*.[1-9][0-9]R +*.[1-9][0-9][0-9]R +*.eledsec[1-9] +*.eledsec[1-9]R +*.eledsec[1-9][0-9] +*.eledsec[1-9][0-9]R +*.eledsec[1-9][0-9][0-9] +*.eledsec[1-9][0-9][0-9]R + +# glossaries +*.acn +*.acr +*.glg +*.glo +*.gls +*.glsdefs + +# gnuplottex +*-gnuplottex-* + +# gregoriotex +*.gaux +*.gtex + +# htlatex +*.4ct +*.4tc +*.idv +*.lg +*.trc +*.xref + +# hyperref +*.brf + +# knitr +*-concordance.tex +# TODO Comment the next line if you want to keep your tikz graphics files +*.tikz +*-tikzDictionary + +# listings +*.lol + +# makeidx +*.idx +*.ilg +*.ind +*.ist + +# minitoc +*.maf +*.mlf +*.mlt +*.mtc[0-9]* +*.slf[0-9]* +*.slt[0-9]* +*.stc[0-9]* + +# minted +_minted* +*.pyg + +# morewrites +*.mw + +# nomencl +*.nlg +*.nlo +*.nls + +# pax +*.pax + +# pdfpcnotes +*.pdfpc + +# sagetex +*.sagetex.sage +*.sagetex.py +*.sagetex.scmd + +# scrwfile +*.wrt + +# sympy +*.sout +*.sympy +sympy-plots-for-*.tex/ + +# pdfcomment +*.upa +*.upb + +# pythontex +*.pytxcode +pythontex-files-*/ + +# tcolorbox +*.listing + +# thmtools +*.loe + +# TikZ & PGF +*.dpth +*.md5 +*.auxlock + +# todonotes +*.tdo + +# vhistory +*.hst +*.ver + +# easy-todo +*.lod + +# xcolor +*.xcp + +# xmpincl +*.xmpi + +# xindy +*.xdy + +# xypic precompiled matrices +*.xyc + +# endfloat +*.ttt +*.fff + +# Latexian +TSWLatexianTemp* + +## Editors: +# WinEdt +*.bak +*.sav + +# Texpad +.texpadtmp + +# LyX +*.lyx~ + +# Kile +*.backup + +# KBibTeX +*~[0-9]* + +# auto folder when using emacs and auctex +./auto/* +*.el + +# expex forward references with \gathertags +*-tags.tex + +# standalone packages +*.sta + +# Administrative folders +~Archive/ +.ipynb_checkpoints/ \ No newline at end of file diff --git a/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Fig1Tab16.PNG b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Fig1Tab16.PNG new file mode 100644 index 00000000..3da7d00c Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Fig1Tab16.PNG differ diff --git a/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Table18.PNG b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Table18.PNG new file mode 100644 index 00000000..d09a96b1 Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Table18.PNG differ diff --git a/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Table20.PNG b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Table20.PNG new file mode 100644 index 00000000..263ae4d8 Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Table20.PNG differ diff --git a/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Wong 2019 - Refinancing and the Transmission of Monetary Policy to Consumption.pdf b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Wong 2019 - Refinancing and the Transmission of Monetary Policy to Consumption.pdf new file mode 100644 index 00000000..bcefbac9 Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Wong 2019 - Refinancing and the Transmission of Monetary Policy to Consumption.pdf differ diff --git a/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Zahn_WongMPTransimission.ipynb b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Zahn_WongMPTransimission.ipynb new file mode 100644 index 00000000..82e05b97 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/WongMPTransmission/Zahn_WongMPTransimission.ipynb @@ -0,0 +1,233 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Wong (Forthcoming)\n", + "\n", + "# \"[Refinancing and the Transmission of Monetary Policy to Consumption](https://static1.squarespace.com/static/576576adbe659449f97e0d35/t/5ce1f9f23fdc1e00014f3d22/1558313459256/Paper_AERrevision_0519.pdf)\"\n", + "\n", + "- Notebook created by Matt Zahn\n", + "\n", + "## Summary\n", + "\n", + "This paper examines the effects of monetary policy on consumption by focusing on the mortgage refinancing channel by first noting heterogeneous consumption responses to monetary policy shocks and then constructing a life cycle model to explain this behavior. \n", + "\n", + "The main findings are summarized below. \n", + "- There is a large consumption response to monetary policy shocks by agents that refinance loans or begin new loans at lower rates. This behavior is concentrated among younger people. \n", + "- Mortgage structure influences the effectiveness of this channel. Variable rate mortgages reduce heterogeneous effects of monetary policy on consumption across age groups. \n", + "- While this rate structure reduces heterogeneous effects, it makes the aggregate consumption response to monetary policy shocks stronger.\n", + "\n", + "\n", + "## Overview\n", + "\n", + "This paper broadly falls into two parts. The first focuses on an empirical analysis of consumption responses to monetary policy shocks using household micro data on consumption and mortgages. The author's analysis finds three cross-sectional patterns in the data:\n", + "\n", + "1. Younger people have a larger semi-elasticity of consumption to monetary policy. She finds it to be double the size of the average agent in the economy. \n", + "1. Consumption responses to monetary policy shocks are driven by homeowners who refinance their mortgages following interest rate shocks. Renters did not appear to have a statistically significant impact.\n", + "1. A household's marginal propensity to refinance their mortgage increases with the size of the loan. Younger homeowners are more likely to adjust their mortgages than older ones as their balances tend to be larger. \n", + "\n", + "These findings suggest that homeowners that refinance are an important driver of the consumption response to monetary policy. In the second part of the paper, the author then takes these empirical patterns and constructs a life-cycle model to analyze the channels of monetary policy transmission. The high-level features of her model include\n", + "\n", + "- Uninsurable labor income risk\n", + "- Life cycle savings motive\n", + "- Fixed rate mortgage structure. Agents are able to pay a cost to adjust the interest rate on their long term assets (including their mortgage). \n", + "\n", + "The model maps well to the corresponding moments in the data, including aggregate and heterogeneous age specific responses to monetary policy shocks. The author then uses the model to show the importance of the refinancing channel of the cross-sectional consumption responses by age. She does this by introducing a variable rate mortgage structure and compares it to the fixed rate baseline. The model suggests that 45% of the difference in consumption responses by age is driven by the refinancing channel, which is at least as strong as changes in aggregate income or house prices following monetary policy shocks.\n", + "\n", + "Finally, the author uses the model to examine to what extent the structure of the mortgage industry matters for the transmission of monetary policy. The consumption response when moving from a fixed rate to a variable structure is theoretically ambiguous - the heterogeneous effects become weaker but more households will have lower mortgage payments which could bolster aggregate consumption. The model quantitatively shows that the income effect of the variable rate structure dominants, which leads to a larger aggregate consumption response under that regime while simultaneously lowering heterogeneous responses by age.\n", + "\n", + "\n", + "## Monetary Policy Response Heterogeneity\n", + "\n", + "The author documents three types of heterogeneous responses to monetary policy shocks. First, that young households tend to increase their consumption more than older households following a monetary policy shock. Second, households that change their home loan status have a larger consumption response than renters and homes that did not adjust their mortgages to monetary policy shocks. Finally, younger households are more likely to refinance when interest rates fall. These empirical patterns were discussed at a high-level in the previously. They are the result of a reduced form analysis and serve to motivate the setup of her life cycle model. They are discussed in greater detail in Section 3 of the paper.\n", + "\n", + "\n", + "## Model\n", + "\n", + "The author then constructs a household model of housing and mortgage decisions in order to interpret the empirical evidence from Section 3 to understand the transmission of mechanism of monetary policy. \n", + "\n", + "In the model, households face exogenous idiosyncratic and aggregate shocks. These shocks replicate patterns observed in the data used to motivate the model. There are two key features:\n", + "1. Households pay a transaction cost to adjust their long term assets. Specifically, these costs are paid when a household chooses to refinance an existing mortgage or when entering a new loan. \n", + "1. The mortgage structure only features fixed rate loans. The rates on household mortgages will remain constant unless the transaction costs are paid. \n", + "\n", + "Intuitively, the fixed rate structure of mortgages will generate heterogeneity in the pass through of monetary policy. Agents will have different interest rates on their mortgages based on whether or not they opted to refinance or initiate a new loan. Consistent with the author's earlier observations, individuals with larger mortgages and balances are more likely to take advantage of lower interest rates. In the model and data, this tends to be young people with a higher marginal propensity to refinance. Additionally, these types of consumers are more likely to be against short term liquidity constraints and must borrow against their future income. Refinancing alleviates these agents from this constraint. Adjustment costs introduces a distribution of agents who own homes but may not have refinanced. The author notes these agents are similar to the \"hand to mouth\" consumers in Kaplan and Violante (2014).\n", + "\n", + "\n", + "### Setup\n", + "\n", + "__Enviornment__ \n", + "- Continuum of households indexed by $j$. \n", + "- Agents live for a max of $T$ periods. In a given period, the probability an agent at age $a$ survives to the next period is $\\pi_a$. \n", + "- Agents work for $T_y$ periods and then retire. \n", + "- Discrete time. A unit of time is one year.\n", + "\n", + "__Assets__\n", + "- Three types of assets exist in the model\n", + " 1. Short term one period assets $s_{jat}$ with interest rate $r_t$. Short term borrowing constraint of $s_{jat}\\geq -\\underline{s}$.\n", + " 1. Long term mortgage $b_{jat}$ with a fixed interest rate $R_{jat}$\n", + " 1. Housing purchased at a price $p_t$. Housing can either be owned or rented at price $p_t^r$. Owned housing depreciates at a rate of $\\delta$ each period. \n", + "\n", + "Mortgages are assumed to be amortized over the life of an agent. The loan duration of an agent aged $a$ is $d(a) = T - a$. The current market mortgage interest rate with duration $d(a)$ is $R_{ja0}=r_t^{d(a)}$\n", + "\n", + "Loan balances $b$ evolve according to:\n", + "\n", + "$$ b_{j,a+1,t+1} = b_{jat}(1+R_{ja0})-M_{ja0} $$\n", + "\n", + "Where the intial amount borrowed $b_{ja0}$ and the mortgage payment $M_{ja0}$ satisfy\n", + "\n", + "$$ b_{ja0} = M_{ja0}\\left[\\sum^{d(a)}_{k=1} \\frac{1}{(1+R_{ja0})^k} \\right] $$\n", + "\n", + "A key feature of the model is the ability for agents to pay a transaction cost to either refinance their existing mortgage or start a new one. Upon paying these costs, the interest rate is reset to the current market rate. Using indicator functions, the mortgage rate can be expressed as\n", + "\n", + "$$ R_{j,a+1,t+1} = r^{d(a+1)}_{t+1}\\cdot1(\\text{refi})_{t+1} + R_{jat}\\cdot[1-1(\\text{refi})_{t+1}] $$\n", + "\n", + "Households that want a new mortgage are subject to a minimum equity requirement where $\\phi$ captures the down payment.\n", + "\n", + "$$ b_{jat} \\leq (1-\\phi)p_t h_{jat} $$\n", + "\n", + "Other durables are omitted to reduce computational burden, while still capturing the largest durable asset holding. Other durables not in the model tend to account for a larger share of a younger consumer's consumption relative to older consumers in the author's data. She notes that including these in the model would likely increase the heterogeneous response by age to monetary policy shocks (Cloyne, Ferreira, and Surico (forthcoming)).\n", + "\n", + "__Income__\n", + "\n", + "Each period $t$, working agents of age $a$ receives exogenous income $y_{jat}$, where\n", + "\n", + "$$ \\log y_{jat} = \\chi_a + \\eta_{jat} + \\phi_a(y_t) $$\n", + "\n", + "- $\\chi_a$ is deterministic\n", + "- $\\eta_{jat}$ is ideosyncratic, where $\\eta_{jat} = \\rho_n\\eta_{j,a-1,t-1}+\\psi_{jt}$\n", + " - $\\psi_{jt}$ is iid shock drawn each period from $N(0,\\sigma^2_\\eta)$\n", + "- $phi_a(y_t)$ is an age specific fluctuation to income arising from aggregate shocks to aggregate income.\n", + "\n", + "The author models aggregate shocks by defining $S_t$ as a vector of aggregate variables $\\log y_t, \\log p_t, r_t$ (aggregate income, aggregate real house prices, and one-period interest rate respectively). The dynamics are given by the equation below are stated to follow the approaches of in Hurst et al (2016); Kaplan, Moll, and Violante (2018); Chen, Michaux, and Roussanov (forthcoming) and others.\n", + "\n", + "$$ S_t = A_0 + A_1 S_{t-1} + u_t $$\n", + "\n", + "These aggregate influence the variables faced by consumers (i.e., mortgage rates, rental rates, house prices, etc.). These are modeled in a reduced form way to captures the effect of aggregate shocks to the economy. The author discusses this calibration in detail in Section 4.3.\n", + "\n", + "### Household's problem\n", + "\n", + "At this point, agent and age subscripts are dropped for clarity. \n", + "\n", + "__Utility__\n", + "\n", + "Each period, agents derive utility from consumption and household services\n", + "\n", + "$$ u(c,h) = \\frac{(c^\\alpha\\cdot h^{1-\\alpha})^{1-\\sigma}-1}{1-\\sigma}$$\n", + "\n", + "Each period, the household may choose to:\n", + "\n", + "1. Rent housing,\n", + "1. Buy housing,\n", + "1. Own a home and refinance an existing mortgage, or\n", + "1. Own a home and not refinance\n", + "\n", + "in addition to solving for their optimal consumption, saving in short term bonds, and mortgage debt. The problem is solved recursively. Additional notation:\n", + "- $z = \\{a, S, y, \\text{assets}\\}$ household state variables\n", + " - $a$ is age\n", + " - $S$ and $y$ capture aggregate and idiosyncratic income\n", + " - $\\text{assets}$ is a vector of start of period holdings of short term assets $s$, housing owned $h^{\\text{own}}$, mortgage balance $b$, and the fixed rate on any existing mortgage $R$. \n", + "- $F^\\text{new}$ is the transaction cost of buying a new home\n", + "- $F^\\text{refi}$ is the transaction cost of refinancing\n", + "\n", + "The value function of the households is:\n", + "\n", + "$$ V(z) = \\max \\left\\{ V(z)^{\\text{rent}}, V(z)^{\\text{purchase}}, V(z)^{\\text{own & refi}}, V(z)^{\\text{own & no refi}} \\right\\} $$\n", + "\n", + "Based on the housing decision, there are four potential problems that an agent will solve. Each is reproduced below. Note that they also face the constraints governing the income process and aggregate state of the economy. \n", + "\n", + "__Rent__\n", + "\n", + "$$\n", + "\\begin{eqnarray*}\n", + " V(z)^{\\text{rent}} &=& \\max_{c,h^{\\text{rent}}, s'} u(c,h^{\\text{rent}}) + E[V(z')] \\\\\n", + " \\text{s.t. } c + s' + p^r h^{\\text{rent}} &=& y + (1-\\delta)ph^{\\text{own}}+(1+r)s - b(1+R) \\\\\n", + " h'^{\\text{own}} &=& b' = 0,\\text{ } s'\\geq -\\underline{s}\n", + "\\end{eqnarray*}\n", + "$$\n", + "__Purchase__\n", + "\n", + "$$\n", + "\\begin{eqnarray*}\n", + " V(z)^{\\text{purchase}} &=& \\max_{c,s', h^{\\text{own}}, b'} u(c,h^{\\text{own}}) + E[V(z')] \\\\\n", + " \\text{s.t. } c + s' + p h^{\\text{own}} - b' &=& y + (1-\\delta)ph^{\\text{own}}+(1+r)s - b(1+R) - F^{\\text{new}} \\\\\n", + " b'&\\leq& (1-\\phi)ph'^{\\text{own}},\\text{ } s'\\geq -\\underline{s}, \\text{ } R' = r^d\n", + "\\end{eqnarray*}\n", + "$$\n", + "\n", + "__Own and refinance__\n", + "\n", + "$$\n", + "\\begin{eqnarray*}\n", + " V(z)^{\\text{own & refi}} &=& \\max_{c,s',b'} u(c,h^{\\text{own}}) + E[V(z')] \\\\\n", + " \\text{s.t. } c + s' - b' &=& y + (1+r)s - b(1+R) - F^{\\text{refi}} \\\\\n", + " b'&\\leq& (1-\\phi)ph'^{\\text{own}},\\text{ } s'\\geq -\\underline{s}, \\text{ } R' = r^d \\\\\n", + " h'^{\\text{own}} &=& (1-\\delta)h^{\\text{own}}\n", + "\\end{eqnarray*}\n", + "$$\n", + "\n", + "__Own and no refinance__\n", + "\n", + "$$\n", + "\\begin{eqnarray*}\n", + " V(z)^{\\text{own & no refi}} &=& \\max_{c,s'} u(c,h^{\\text{own}}) + E[V(z')] \\\\\n", + " \\text{s.t. } c + s' &=& y + (1+r)s - M \\\\\n", + " b'&=& b(1+R) - M,\\text{ } s'\\geq -\\underline{s}, \\text{ } R' = R \\\\\n", + "\\end{eqnarray*}\n", + "$$\n", + "\n", + "The model does allow for retired agents. It is identical to the employed agent but labor income is replaced with social security. When agents die, they bequeath their total net wealth $W = (1-\\delta)ph^{\\text{own}}+(1+r)s$, which yields utility $B(W_{ajt}-1)^{1-\\sigma}/(1-\\sigma)$, where $B$ is a bequest parameter. The author discusses in detail how she calibrates the model in Section 4.3.\n", + " \n", + "\n", + "## Results\n", + "\n", + "__Agent heterogeneity__\n", + "\n", + "As mentioned earlier, the model and its calibration are generally consistent with key variables and wealth distributions from the data. Figure 1 and Table 16 from the paper summarize these findings. \n", + "\n", + " \n", + "\n", + "The author then applies this model to the heterogeneous empirical findings from Section 3 to understanding the transmission mechanism of monetary policy to consumption. First, she tests the consistency of the heterogeneous response to monetary policy shocks in the model and compares it to the results from the data. The model implies that young households respond more to monetary policy shocks than middle age or older households, which is consistent with the empirical findings. Additionally, the younger households are also more likely to adjust their home loans after a monetary policy shock than older homeowners. These results are summarized in Table 18. \n", + "\n", + "\n", + "\n", + "The key driver of this result is the fixed cost to adjusting the home loan. Optimizing agents need to weigh the costs of refinancing with the relative benefits they will get in the form of lower payments. Agents that have larger balances and payments will have a greater incentive to pay this cost and reap these benefits over the long run. This can explain why the consumption response is so substantial for young people. These young people are likely facing their short run liquidity constraint. Refinancing relaxes this constraint and the model and data suggest these agents have a higher MPC and are likely to consume most of this additional income they have.\n", + "\n", + "__Mortgage structure__\n", + "\n", + "The author's final analysis focuses on the importance of the structure of the mortgage industry for the transmission of monetary policy. She does this by re-estimating her model with a variable mortgage rate structure - meaning that when the interest rate changes, it changes for everybody in the model at no cost. There are two key results here and are captured in Table 20. First, the refinancing channel accounts for about 45% of the consumption response across young people and old people. Second, because the pass through of interest rates impacts everybody, the aggregate consumption effect is 1.5 times higher under a variable rate structure. \n", + "\n", + "\n", + "\n", + "These results also show that the effect of the refinancing channel on consumption by age is at least as strong as the income effect and changes in house prices following monetary policy shocks. She also finds the income effect to have a large role in the consumption response to monetary policy shocks as well as its heterogeneity across age groups. The use of house prices is an attempt to quantify wealth effects. She finds that the effect of changes in aggregate house prices after a monetary policy shock on consumption declines with age. \n", + "\n", + "\n", + "## Conclusions\n", + "\n", + "This paper suggests several things about the transmission of monetary policy on consumption. In addition to the suggestive results from her empirical analysis, the author's structural model finds that the refinancing channel is responsible for a sizable portion of the heterogeneous response to monetary policy shocks across age groups. Additionally, it highlights the importance of the industry structure for the transmission of monetary policy. Her model demonstrates that a variable rate system will lower heterogeneous effects across age groups while boosting aggregate responses to these policy shocks.\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.7.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}