From f6684a2e0f86218b2ed5ae67144b5be444e86d4a Mon Sep 17 00:00:00 2001 From: ykulu1 <43350392+ykulu1@users.noreply.github.com> Date: Mon, 16 Sep 2019 11:32:42 -0400 Subject: [PATCH 01/13] JKMBailoutGuarantees Housing, mortgage bailout guarantees and the macro economy (2013) by Karsten Jeske, Dirk Krueger and Kurt Mitman --- models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees | 1 + 1 file changed, 1 insertion(+) create mode 100644 models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees diff --git a/models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees b/models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees @@ -0,0 +1 @@ + From 7aef0b58494acbcb2bfafe3c26c2d44501c152c7 Mon Sep 17 00:00:00 2001 From: ykulu1 <43350392+ykulu1@users.noreply.github.com> Date: Sun, 22 Sep 2019 16:53:33 -0400 Subject: [PATCH 02/13] Add files via upload --- .../JKM_summary.ipynb | 174 ++++++++++++++++++ models/We-Would-Like-In-Econ-ARK/results.png | Bin 0 -> 189606 bytes 2 files changed, 174 insertions(+) create mode 100644 models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb create mode 100644 models/We-Would-Like-In-Econ-ARK/results.png diff --git a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb new file mode 100644 index 00000000..7e0ca136 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb @@ -0,0 +1,174 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jeske, Krueger and Mitman" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## \"[Housing, mortgage bailout guarantees and the macroeconomy](https://www.sciencedirect.com/science/article/abs/pii/S0304393213001219)\" (2013)\n", + "\n", + "- Notebook is prepared by Yusuf Suha Kulu" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Summary\n", + "The article uses a model with heterogeneous, infinitely lived households to understand the macroeconomic and distributional effects of government bailout guarantees for Government Sponsored Enterprises (GSE)\n", + "\n", + "The main findings are as follows: \n", + "\n", + "- Eliminating the bailout guarantee leads to a large decline in mortgage origination and increases aggregate welfare by 0.5% in comsumption equivalent variation but has little effect on foreclosure rates and housing investment.\n", + "\n", + "- Bailout guarantee hurts low income and low asset households.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Overview\n", + "\n", + "#### Tax financed mortgage interest rate subsidy\n", + "\n", + "The baiolout guarantees are modeled as the tax financed interest rate subsidy because prior to the bailout of the GSEs, they could borrow at interest rates close to that on U.S government debt, despite the fact that they were heavily exposed to aggregate house price risk. The absence of risk premium can be attributed to implicit government bailout guarantee.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Model \n", + "\n", + "- Heterogeneous agent general equilibrium model with incomplete markets in the tradition of Bewley(1986), Huggett(1993), and Aiyagari(1994).\n", + "\n", + "#### Households \n", + "- U(c,h) where c is nondurable consumption c and h is housing services.\n", + "- Endowment and (labor) income are used interchangeably. Households receive idiosynratic endowments which follow a finite state Markov chain $\\pi$(y'|y) and unique invariant distribution $\\Pi$(y).\n", + "- Two types of assets: \n", + " - b' one period bonds with price P$_b$ \n", + " - g' perfectly divisible houses with price P$_h$. Houses are risky assets which are subject to idiosynratic house price shocks. F($\\delta$') cdf of house price depreciation rate $\\delta$' tomorrow with support D = [$\\underline{\\delta}$,1] where $\\underline{\\delta}$ $\\leq$ 0 which represents house value appreciation.\n", + "- Mortgages: Households can borrow againts their real estate position using one period martgage debt. m' denote the size of the mortgage with price P$_m$. The price is determined by competition of banks through a zero profit condition. The gross mortgage interest rate is R$_m$ = $\\frac{1}{P_m}$\n", + "- Households choose to default whenever the amount owed in the mortgage is greater than the value of the house after the realization of the price shock.\n", + "- Recursive Formulation:\n", + "\n", + "v(a,y) = $max_{c,h,b',m'g' \\geq 0} \\bigg(U(c,h) + \\beta \\sum_{y'} \\pi(y'|y) \\int_{\\underline{\\delta}}^1 v(a',y')dF(\\delta') \\bigg)$\n", + "\n", + "s.t\n", + "\n", + "c + b'P$_b$ + hP$_l$ + g'P$_h$ - m'P$_m$(g',m') = a + g'P$_l$\n", + "\n", + "a'($\\delta$',y',m',g') = b' + max $\\big(0,P_h(1-\\delta')g' - m'\\big) + (1-\\tau$)y'\n", + "\n", + "\n", + "#### The Real Estate Construction Sector\n", + "- Reversibility of the technology: Real estate companies can turn houses into consumption goods\n", + "\n", + "max P$_h$I - C$_h$ \\\n", + "s.t \\\n", + "I=C$_h$ \\\n", + "where I is the output (houses) and C$_h$ is the input of the consumption good\n", + "\n", + "- The equilibrium house price is P$_h$=1\n", + "\n", + "#### The banking sector \n", + "- Effective cost of the banking sector for financing one dollar of mortgage equals (1 + r$_b$)(1 + r$_w$ + $\\theta$ - $\\phi$) where $\\phi$ is the is the mortgage subsidy, $\\theta$ is the cost of insurance, r$_w$ is the percentage real resource cost to the bank and r$_b$ equal to P$_b$ = $\\frac{1}{1+r_b}$.\n", + "- Let $\\delta^*$(m',g') be cutoff level of household depreciation at which household is indifferent between defaulting and not defaulting on her mortgage. \n", + "- A bank will originate a mortgage if and only if \\\n", + "m'P$_m$(g',m') $\\leq$ $\\frac{1}{(1 + r_b)(1 + r_w + \\theta - \\phi)}$ $\\bigg( m'F(\\delta^*(m',g')) + \\gamma g' \\int_{\\delta^*(m',g')}^1 (1-\\delta')dF(\\delta') \\bigg)$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Results\n", + "\n", + "#### Comparison of steady state equilibria of economies with and without a tax financed mortgage interest rates subsidy of 30 basis points\n", + "\n", + "- Removing subsidy make mortgages less attractive by increasing the effective interest rate\n", + " - Households with low levels of cash in hand do not respond much to the change in interest rate subsidy.\n", + " - For wealthier households, the change in policy induces a massive reduction in leverage, and thus substantial reduction in mortgage debt.\n", + "- Thus, households shifts away from bonds toward home equity. Median household was holding 60.7$%$ of its net worth in bonds with subsidy reduces to 5.8$%$ without subsidy." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import Image\n", + "imgUrl = 'results.png' # setup path and filename\n", + "img = Image(url=imgUrl) # create the image object\n", + "img # display the image" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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 +} diff --git a/models/We-Would-Like-In-Econ-ARK/results.png b/models/We-Would-Like-In-Econ-ARK/results.png new file mode 100644 index 0000000000000000000000000000000000000000..9ec90c25d8613ca8ec90351e30eb770cb9b29545 GIT binary patch literal 189606 zcmdqIWmH_vwl>;8fFJ=9Ja~ZM?(R--CpZLmcS}fccXxN!MiSiJ8+T~j8u@r_?{oIa z9^?MLjM4OB)hwIO^eTcCj#r1*P#(a_&{lelK!*lJmF=1*nYbG2=T!AJ29PZ(`I_3r zSh1@<%TP#h0uv2(4!S?*gQ4l$qsQzYgM%#^RoUksVV%5>J$E5HqnRwbX?J7Gjub2a z%Ec-NhZ+TPK+Th`KD*~Fm?}#-1 zp?ajI2@l>zE@1882w#X0@KvseBPlhJv{wYJ6p>g6@S_Q*P^!8G zr%dr(C@JKbJ_Z^$Tk`(LmqlnRz@> zeufzT_@vws8hhQCM77DJSypFHJ0kYMSRjLuB9!g<`E$fG-GXLLHP@vu=FY1-<I}F;=!+CJ`4iBy?ha{2Fe*X7~7zkI#sbNJO(4)OBzk9CL@YYb-W+R4r|zrXS~& zUMGQYU^Cl$%cAr@+%h zCo({lA0Q8kzADDNmv@7l)ay134t7ocN0T7u$u24Gc7RvWGjl~ef4N|ZF{|E2G(v`O zTDau~VG|x9T&8Z-!un{_P!f@{y_H&yz(gdDC^B(M_=Ud6tY#Gg01Vm_HW>T15Zrv) z=WvS^c^Wq^;wIZ9v`4-SWxp0o7BXzXUa4>j5BS_e$;7I4PLp1i{hKZxM_e(%bBe(a+g;;k?FnkhUFUQ`i6y7U&_#VNP0KpPeqjwjB3TCnoPPm+nDfDxl^H1 z#{`B)Vn!Hr84L(rbu(^_PSayq^g3l^#*93AR+5I0cWTS&l3myv=m9@&T=r+rf=Cu> z-}dI)wk)#)K1*jYAE!o`06NbK0plR=DcrW8?G6+_^cAaUV!aY{+deI?>$V#nE1okg$G@Fe7gH@z&6Po@Dd~{6^$g5=F@mF=2Tm zUZP)VMH5K#C2?!sEQC*g0DkC;p6VCNgKrMx6^4tN>!-jFDK4Te34fm(t6(~f_eRWU zJlX7hN+?#A*xq|5B&~0Rf_M{CdnT7~i=iEY-^zFerSiFajvU(@qEfvgP}Xy&pW&KS zlttA<){1_=!kk^nx^NG7Ppi0t_^9~4cxw14UONXnQv`>u!Lsqgvgiugd|qeX=vD{S z$n+HJT;1Sh3+}}50_~L5cg;pFixd3}8(jmRU(oe-b!(bOReRNB8Z8>%!GWrUh6Wj$p`<*8+Qa?ELQtmcn-7qK0Sob$#DNA=C7rG|Kh+Gb0Jkj2sE2y1l% z*OiPfMEby=9Scu0#-Rht1M#u8JmUlf++}uVuD2U|Tay>aX8$e!Vz zR|a&-6U8LT9J1|1HW;I*wjqGGU2pL|5Q?UV?ub9JhjY?7X#J`yRBTX0${m%M$~Bb$ zNBUrIqSvzT=$4t6Q8w_&G1-WJwqAy~0dH$=SHDUjgubJvu=sfXE;UwC%3cZ*6I2M1 z2eG#M2K9t(;BuIz45x8iY|xHqYSzjPtEG*kc#|bZ;b*o9+_BIEsQ!8{hak6*!Tj^u z#P$nt&CQp6VI#9pBd0-jeG&^~!dp+@lCC^t9ZR3t)Xkmyb!Wz+6dx_wcGLNtBa_p%{FC7L*jJZX}h^o#$INq({*Zh zdx*KnFBpnQ#N#30j(j{hg;dk`RrJ!xsi(B+v}k)2T&A@hxL;ke0WEhc;PrrBqz~d_ zBlD?^wj)h5o~e$IyYw=i%99-sL386J|GLirOg{WJYCWOaW6u%MoA!uy3c@?S126o? 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ykulu1 <43350392+ykulu1@users.noreply.github.com> Date: Sun, 22 Sep 2019 17:21:30 -0400 Subject: [PATCH 03/13] Delete JKMBailoutGuarantees --- models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees | 1 - 1 file changed, 1 deletion(-) delete mode 100644 models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees diff --git a/models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees b/models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees deleted file mode 100644 index 8b137891..00000000 --- a/models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees +++ /dev/null @@ -1 +0,0 @@ - From 8f92b917d40b29506efa322c78f3e575ec2c94a1 Mon Sep 17 00:00:00 2001 From: ykulu1 <43350392+ykulu1@users.noreply.github.com> Date: Sun, 22 Sep 2019 17:21:50 -0400 Subject: [PATCH 04/13] Delete JKM_summary.ipynb --- .../JKM_summary.ipynb | 174 ------------------ 1 file changed, 174 deletions(-) delete mode 100644 models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb diff --git a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb deleted file mode 100644 index 7e0ca136..00000000 --- a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb +++ /dev/null @@ -1,174 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Jeske, Krueger and Mitman" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## \"[Housing, mortgage bailout guarantees and the macroeconomy](https://www.sciencedirect.com/science/article/abs/pii/S0304393213001219)\" (2013)\n", - "\n", - "- Notebook is prepared by Yusuf Suha Kulu" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Summary\n", - "The article uses a model with heterogeneous, infinitely lived households to understand the macroeconomic and distributional effects of government bailout guarantees for Government Sponsored Enterprises (GSE)\n", - "\n", - "The main findings are as follows: \n", - "\n", - "- Eliminating the bailout guarantee leads to a large decline in mortgage origination and increases aggregate welfare by 0.5% in comsumption equivalent variation but has little effect on foreclosure rates and housing investment.\n", - "\n", - "- Bailout guarantee hurts low income and low asset households.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Overview\n", - "\n", - "#### Tax financed mortgage interest rate subsidy\n", - "\n", - "The baiolout guarantees are modeled as the tax financed interest rate subsidy because prior to the bailout of the GSEs, they could borrow at interest rates close to that on U.S government debt, despite the fact that they were heavily exposed to aggregate house price risk. The absence of risk premium can be attributed to implicit government bailout guarantee.\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Model \n", - "\n", - "- Heterogeneous agent general equilibrium model with incomplete markets in the tradition of Bewley(1986), Huggett(1993), and Aiyagari(1994).\n", - "\n", - "#### Households \n", - "- U(c,h) where c is nondurable consumption c and h is housing services.\n", - "- Endowment and (labor) income are used interchangeably. Households receive idiosynratic endowments which follow a finite state Markov chain $\\pi$(y'|y) and unique invariant distribution $\\Pi$(y).\n", - "- Two types of assets: \n", - " - b' one period bonds with price P$_b$ \n", - " - g' perfectly divisible houses with price P$_h$. Houses are risky assets which are subject to idiosynratic house price shocks. F($\\delta$') cdf of house price depreciation rate $\\delta$' tomorrow with support D = [$\\underline{\\delta}$,1] where $\\underline{\\delta}$ $\\leq$ 0 which represents house value appreciation.\n", - "- Mortgages: Households can borrow againts their real estate position using one period martgage debt. m' denote the size of the mortgage with price P$_m$. The price is determined by competition of banks through a zero profit condition. The gross mortgage interest rate is R$_m$ = $\\frac{1}{P_m}$\n", - "- Households choose to default whenever the amount owed in the mortgage is greater than the value of the house after the realization of the price shock.\n", - "- Recursive Formulation:\n", - "\n", - "v(a,y) = $max_{c,h,b',m'g' \\geq 0} \\bigg(U(c,h) + \\beta \\sum_{y'} \\pi(y'|y) \\int_{\\underline{\\delta}}^1 v(a',y')dF(\\delta') \\bigg)$\n", - "\n", - "s.t\n", - "\n", - "c + b'P$_b$ + hP$_l$ + g'P$_h$ - m'P$_m$(g',m') = a + g'P$_l$\n", - "\n", - "a'($\\delta$',y',m',g') = b' + max $\\big(0,P_h(1-\\delta')g' - m'\\big) + (1-\\tau$)y'\n", - "\n", - "\n", - "#### The Real Estate Construction Sector\n", - "- Reversibility of the technology: Real estate companies can turn houses into consumption goods\n", - "\n", - "max P$_h$I - C$_h$ \\\n", - "s.t \\\n", - "I=C$_h$ \\\n", - "where I is the output (houses) and C$_h$ is the input of the consumption good\n", - "\n", - "- The equilibrium house price is P$_h$=1\n", - "\n", - "#### The banking sector \n", - "- Effective cost of the banking sector for financing one dollar of mortgage equals (1 + r$_b$)(1 + r$_w$ + $\\theta$ - $\\phi$) where $\\phi$ is the is the mortgage subsidy, $\\theta$ is the cost of insurance, r$_w$ is the percentage real resource cost to the bank and r$_b$ equal to P$_b$ = $\\frac{1}{1+r_b}$.\n", - "- Let $\\delta^*$(m',g') be cutoff level of household depreciation at which household is indifferent between defaulting and not defaulting on her mortgage. \n", - "- A bank will originate a mortgage if and only if \\\n", - "m'P$_m$(g',m') $\\leq$ $\\frac{1}{(1 + r_b)(1 + r_w + \\theta - \\phi)}$ $\\bigg( m'F(\\delta^*(m',g')) + \\gamma g' \\int_{\\delta^*(m',g')}^1 (1-\\delta')dF(\\delta') \\bigg)$\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Results\n", - "\n", - "#### Comparison of steady state equilibria of economies with and without a tax financed mortgage interest rates subsidy of 30 basis points\n", - "\n", - "- Removing subsidy make mortgages less attractive by increasing the effective interest rate\n", - " - Households with low levels of cash in hand do not respond much to the change in interest rate subsidy.\n", - " - For wealthier households, the change in policy induces a massive reduction in leverage, and thus substantial reduction in mortgage debt.\n", - "- Thus, households shifts away from bonds toward home equity. Median household was holding 60.7$%$ of its net worth in bonds with subsidy reduces to 5.8$%$ without subsidy." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from IPython.display import Image\n", - "imgUrl = 'results.png' # setup path and filename\n", - "img = Image(url=imgUrl) # create the image object\n", - "img # display the image" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "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 -} From a19d00d6fefa859d382438e3eca89f2b14d41909 Mon Sep 17 00:00:00 2001 From: ykulu1 <43350392+ykulu1@users.noreply.github.com> Date: Sun, 22 Sep 2019 17:22:10 -0400 Subject: [PATCH 05/13] Add files via upload --- .../JKM_summary.ipynb | 182 ++++++++++++++++++ 1 file changed, 182 insertions(+) create mode 100644 models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb diff --git a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb new file mode 100644 index 00000000..962a7d17 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb @@ -0,0 +1,182 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jeske, Krueger and Mitman" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## \"[Housing, mortgage bailout guarantees and the macroeconomy](https://www.sciencedirect.com/science/article/abs/pii/S0304393213001219)\" (2013)\n", + "\n", + "- Notebook is prepared by Yusuf Suha Kulu" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Summary\n", + "The article uses a model with heterogeneous, infinitely lived households to understand the macroeconomic and distributional effects of government bailout guarantees for Government Sponsored Enterprises (GSE)\n", + "\n", + "The main findings are as follows: \n", + "\n", + "- Eliminating the bailout guarantee leads to a large decline in mortgage origination and increases aggregate welfare by 0.5% in comsumption equivalent variation but has little effect on foreclosure rates and housing investment.\n", + "\n", + "- Bailout guarantee hurts low income and low asset households.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Overview\n", + "\n", + "#### Tax financed mortgage interest rate subsidy\n", + "\n", + "The baiolout guarantees are modeled as the tax financed interest rate subsidy because prior to the bailout of the GSEs, they could borrow at interest rates close to that on U.S government debt, despite the fact that they were heavily exposed to aggregate house price risk. The absence of risk premium can be attributed to implicit government bailout guarantee.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Model \n", + "\n", + "- Heterogeneous agent general equilibrium model with incomplete markets in the tradition of Bewley(1986), Huggett(1993), and Aiyagari(1994).\n", + "\n", + "#### Households \n", + "- U(c,h) where c is nondurable consumption c and h is housing services.\n", + "- Endowment and (labor) income are used interchangeably. Households receive idiosynratic endowments which follow a finite state Markov chain $\\pi$(y'|y) and unique invariant distribution $\\Pi$(y).\n", + "- Two types of assets: \n", + " - b' one period bonds with price P$_b$ \n", + " - g' perfectly divisible houses with price P$_h$. Houses are risky assets which are subject to idiosynratic house price shocks. F($\\delta$') cdf of house price depreciation rate $\\delta$' tomorrow with support D = [$\\underline{\\delta}$,1] where $\\underline{\\delta}$ $\\leq$ 0 which represents house value appreciation.\n", + "- Mortgages: Households can borrow againts their real estate position using one period martgage debt. m' denote the size of the mortgage with price P$_m$. The price is determined by competition of banks through a zero profit condition. The gross mortgage interest rate is R$_m$ = $\\frac{1}{P_m}$\n", + "- Households choose to default whenever the amount owed in the mortgage is greater than the value of the house after the realization of the price shock.\n", + "- Recursive Formulation:\n", + "\n", + "\\begin{equation*}\n", + "v(a,y) = max_{c,h,b',m'g' \\geq 0} \\bigg(U(c,h) + \\beta \\sum_{y'} \\pi(y'|y) \\int_{\\underline{\\delta}}^1v(a',y')dF(\\delta') \\bigg) \\\\\n", + "s.t \\\\\n", + "c + b'P_b + hP_l + g'P_h - m'P_m(g',m') = a + g'P_l \\\\\n", + "a'(\\delta',y',m',g') = b' + max \\big(0,P_h(1-\\delta')g' - m'\\big) + (1-\\tau)y'\n", + "\\end{equation*}\n", + "\n", + "\n", + "\n", + "#### The Real Estate Construction Sector\n", + "- Reversibility of the technology: Real estate companies can turn houses into consumption goods\n", + "\\begin{equation*}\n", + "max P_hI - C_h \\\\ \n", + "s.t \\\\ \n", + "I=C_h \\\\ \n", + "\\end{equation*}\n", + "where I is the output (houses) and C$_h$ is the input of the consumption good\n", + "\n", + "- The equilibrium house price is \n", + "\\begin{equation*}\n", + "P_h=1\n", + "\\end{equation*}\n", + "\n", + "#### The banking sector \n", + "- Effective cost of the banking sector for financing one dollar of mortgage equals (1 + r$_b$)(1 + r$_w$ + $\\theta$ - $\\phi$) where $\\phi$ is the is the mortgage subsidy, $\\theta$ is the cost of insurance, r$_w$ is the percentage real resource cost to the bank and r$_b$ equal to \n", + "\\begin{equation*}\n", + "P_b = \\frac{1}{1+r_b}\n", + "\\end{equation*}\n", + "- Let $\\delta^*$(m',g') be cutoff level of household depreciation at which household is indifferent between defaulting and not defaulting on her mortgage. \n", + "- A bank will originate a mortgage if and only if \n", + "\\begin{equation*}\n", + "m'P_m(g',m') \\leq \\frac{1}{(1 + r_b)(1 + r_w + \\theta - \\phi)} \\bigg( m'F(\\delta^*(m',g')) + \\gamma g' \\int_{\\delta^*(m',g')}^1 (1-\\delta')dF(\\delta') \\bigg)\n", + "\\end{equation*}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Results\n", + "\n", + "#### Comparison of steady state equilibria of economies with and without a tax financed mortgage interest rates subsidy of 30 basis points\n", + "\n", + "- Removing subsidy make mortgages less attractive by increasing the effective interest rate\n", + " - Households with low levels of cash in hand do not respond much to the change in interest rate subsidy.\n", + " - For wealthier households, the change in policy induces a massive reduction in leverage, and thus substantial reduction in mortgage debt.\n", + "- Thus, households shifts away from bonds toward home equity. Median household was holding 60.7$%$ of its net worth in bonds with subsidy reduces to 5.8$%$ without subsidy." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import Image\n", + "imgUrl = 'results.png' # setup path and filename\n", + "img = Image(url=imgUrl) # create the image object\n", + "img # display the image" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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 +} From 93c281627c6c3dd4b01cface102785aa53bf4e00 Mon Sep 17 00:00:00 2001 From: ykulu1 <43350392+ykulu1@users.noreply.github.com> Date: Sun, 22 Sep 2019 18:38:22 -0400 Subject: [PATCH 06/13] Delete JKM_summary.ipynb --- .../JKM_summary.ipynb | 182 ------------------ 1 file changed, 182 deletions(-) delete mode 100644 models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb diff --git a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb deleted file mode 100644 index 962a7d17..00000000 --- a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb +++ /dev/null @@ -1,182 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Jeske, Krueger and Mitman" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## \"[Housing, mortgage bailout guarantees and the macroeconomy](https://www.sciencedirect.com/science/article/abs/pii/S0304393213001219)\" (2013)\n", - "\n", - "- Notebook is prepared by Yusuf Suha Kulu" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Summary\n", - "The article uses a model with heterogeneous, infinitely lived households to understand the macroeconomic and distributional effects of government bailout guarantees for Government Sponsored Enterprises (GSE)\n", - "\n", - "The main findings are as follows: \n", - "\n", - "- Eliminating the bailout guarantee leads to a large decline in mortgage origination and increases aggregate welfare by 0.5% in comsumption equivalent variation but has little effect on foreclosure rates and housing investment.\n", - "\n", - "- Bailout guarantee hurts low income and low asset households.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Overview\n", - "\n", - "#### Tax financed mortgage interest rate subsidy\n", - "\n", - "The baiolout guarantees are modeled as the tax financed interest rate subsidy because prior to the bailout of the GSEs, they could borrow at interest rates close to that on U.S government debt, despite the fact that they were heavily exposed to aggregate house price risk. The absence of risk premium can be attributed to implicit government bailout guarantee.\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Model \n", - "\n", - "- Heterogeneous agent general equilibrium model with incomplete markets in the tradition of Bewley(1986), Huggett(1993), and Aiyagari(1994).\n", - "\n", - "#### Households \n", - "- U(c,h) where c is nondurable consumption c and h is housing services.\n", - "- Endowment and (labor) income are used interchangeably. Households receive idiosynratic endowments which follow a finite state Markov chain $\\pi$(y'|y) and unique invariant distribution $\\Pi$(y).\n", - "- Two types of assets: \n", - " - b' one period bonds with price P$_b$ \n", - " - g' perfectly divisible houses with price P$_h$. Houses are risky assets which are subject to idiosynratic house price shocks. F($\\delta$') cdf of house price depreciation rate $\\delta$' tomorrow with support D = [$\\underline{\\delta}$,1] where $\\underline{\\delta}$ $\\leq$ 0 which represents house value appreciation.\n", - "- Mortgages: Households can borrow againts their real estate position using one period martgage debt. m' denote the size of the mortgage with price P$_m$. The price is determined by competition of banks through a zero profit condition. The gross mortgage interest rate is R$_m$ = $\\frac{1}{P_m}$\n", - "- Households choose to default whenever the amount owed in the mortgage is greater than the value of the house after the realization of the price shock.\n", - "- Recursive Formulation:\n", - "\n", - "\\begin{equation*}\n", - "v(a,y) = max_{c,h,b',m'g' \\geq 0} \\bigg(U(c,h) + \\beta \\sum_{y'} \\pi(y'|y) \\int_{\\underline{\\delta}}^1v(a',y')dF(\\delta') \\bigg) \\\\\n", - "s.t \\\\\n", - "c + b'P_b + hP_l + g'P_h - m'P_m(g',m') = a + g'P_l \\\\\n", - "a'(\\delta',y',m',g') = b' + max \\big(0,P_h(1-\\delta')g' - m'\\big) + (1-\\tau)y'\n", - "\\end{equation*}\n", - "\n", - "\n", - "\n", - "#### The Real Estate Construction Sector\n", - "- Reversibility of the technology: Real estate companies can turn houses into consumption goods\n", - "\\begin{equation*}\n", - "max P_hI - C_h \\\\ \n", - "s.t \\\\ \n", - "I=C_h \\\\ \n", - "\\end{equation*}\n", - "where I is the output (houses) and C$_h$ is the input of the consumption good\n", - "\n", - "- The equilibrium house price is \n", - "\\begin{equation*}\n", - "P_h=1\n", - "\\end{equation*}\n", - "\n", - "#### The banking sector \n", - "- Effective cost of the banking sector for financing one dollar of mortgage equals (1 + r$_b$)(1 + r$_w$ + $\\theta$ - $\\phi$) where $\\phi$ is the is the mortgage subsidy, $\\theta$ is the cost of insurance, r$_w$ is the percentage real resource cost to the bank and r$_b$ equal to \n", - "\\begin{equation*}\n", - "P_b = \\frac{1}{1+r_b}\n", - "\\end{equation*}\n", - "- Let $\\delta^*$(m',g') be cutoff level of household depreciation at which household is indifferent between defaulting and not defaulting on her mortgage. \n", - "- A bank will originate a mortgage if and only if \n", - "\\begin{equation*}\n", - "m'P_m(g',m') \\leq \\frac{1}{(1 + r_b)(1 + r_w + \\theta - \\phi)} \\bigg( m'F(\\delta^*(m',g')) + \\gamma g' \\int_{\\delta^*(m',g')}^1 (1-\\delta')dF(\\delta') \\bigg)\n", - "\\end{equation*}\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Results\n", - "\n", - "#### Comparison of steady state equilibria of economies with and without a tax financed mortgage interest rates subsidy of 30 basis points\n", - "\n", - "- Removing subsidy make mortgages less attractive by increasing the effective interest rate\n", - " - Households with low levels of cash in hand do not respond much to the change in interest rate subsidy.\n", - " - For wealthier households, the change in policy induces a massive reduction in leverage, and thus substantial reduction in mortgage debt.\n", - "- Thus, households shifts away from bonds toward home equity. Median household was holding 60.7$%$ of its net worth in bonds with subsidy reduces to 5.8$%$ without subsidy." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from IPython.display import Image\n", - "imgUrl = 'results.png' # setup path and filename\n", - "img = Image(url=imgUrl) # create the image object\n", - "img # display the image" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "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 -} From 8bebe3ef15da62e3f2ad2642b077b6b3b02246c1 Mon Sep 17 00:00:00 2001 From: ykulu1 <43350392+ykulu1@users.noreply.github.com> Date: Sun, 22 Sep 2019 18:39:08 -0400 Subject: [PATCH 07/13] Add files via upload --- .../JKM_summary.ipynb | 184 ++++++++++++++++++ 1 file changed, 184 insertions(+) create mode 100644 models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb diff --git a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb new file mode 100644 index 00000000..7a5ed987 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb @@ -0,0 +1,184 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jeske, Krueger and Mitman" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## \"[Housing, mortgage bailout guarantees and the macroeconomy](https://www.sciencedirect.com/science/article/abs/pii/S0304393213001219)\" (2013)\n", + "\n", + "- Notebook is prepared by Yusuf Suha Kulu" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Summary\n", + "The article uses a model with heterogeneous, infinitely lived households to understand the macroeconomic and distributional effects of government bailout guarantees for Government Sponsored Enterprises (GSE)\n", + "\n", + "The main findings are as follows: \n", + "\n", + "- Eliminating the bailout guarantee leads to a large decline in mortgage origination and increases aggregate welfare by 0.5% in comsumption equivalent variation but has little effect on foreclosure rates and housing investment.\n", + "\n", + "- Bailout guarantee hurts low income and low asset households.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Overview\n", + "\n", + "#### Tax financed mortgage interest rate subsidy\n", + "\n", + "The baiolout guarantees are modeled as the tax financed interest rate subsidy because prior to the bailout of the GSEs, they could borrow at interest rates close to that on U.S government debt, despite the fact that they were heavily exposed to aggregate house price risk. The absence of risk premium can be attributed to implicit government bailout guarantee.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Model \n", + "\n", + "- Heterogeneous agent general equilibrium model with incomplete markets in the tradition of Bewley(1986), Huggett(1993), and Aiyagari(1994).\n", + "\n", + "#### Households \n", + "- U(c,h) where c is nondurable consumption c and h is housing services.\n", + "- Endowment and (labor) income are used interchangeably. Households receive idiosynratic endowments which follow a finite state Markov chain $\\pi$(y'|y) and unique invariant distribution $\\Pi$(y).\n", + "- Two types of assets: \n", + " - b' one period bonds with price $P_{b}$ \n", + " - g' perfectly divisible houses with price $P_{h}$. Houses are risky assets which are subject to idiosynratic house price shocks. F($\\delta$') cdf of house price depreciation rate $\\delta$' tomorrow with support D = [$\\underline{\\delta}$,1] where $\\underline{\\delta}$ $\\leq$ 0 which represents house value appreciation.\n", + "- Mortgages: Households can borrow againts their real estate position using one period martgage debt. m' denote the size of the mortgage with price $P_{m}$. The price is determined by competition of banks through a zero profit condition. The gross mortgage interest rate is $R_{m}$ = $\\frac{1}{P_m}$\n", + "- Households choose to default whenever the amount owed in the mortgage is greater than the value of the house after the realization of the price shock.\n", + "- Recursive Formulation:\n", + "\n", + "\\begin{equation*}\n", + " v(a,y) = max_{c,h,b',m'g' \\geq 0} \\bigg(U(c,h) + \\beta \\sum_{y'} \\pi(y'|y) \\int_{\\underline{\\delta}}^1v(a',y')dF(\\delta') \\bigg) \\\\\n", + " s.t \\\\\n", + " c + b'P_b + hP_l + g'P_h - m'P_m(g',m') = a + g'P_l \\\\\n", + " a'(\\delta',y',m',g') = b' + max \\big(0,P_h(1-\\delta')g' - m'\\big) + (1-\\tau)y' \\\\\n", + "\\end{equation*}\n", + "\n", + "\n", + "\n", + "#### The Real Estate Construction Sector\n", + "- Reversibility of the technology: Real estate companies can turn houses into consumption goods\n", + "\n", + "\\begin{equation*}\n", + " max P_hI - C_h \\\\ \n", + " s.t \\\\ \n", + " I=C_h \\\\ \n", + "\\end{equation*}\n", + "where I is the output (houses) and $C_{h}$ is the input of the consumption good\n", + "\n", + "- The equilibrium house price is \n", + "\n", + "\\begin{equation*}\n", + " P_h=1\n", + "\\end{equation*}\n", + "\n", + "#### The banking sector \n", + "- Effective cost of the banking sector for financing one dollar of mortgage equals (1 + $r_{b}$)(1 + $r_{w}$ + $\\theta$ - $\\phi$) where $\\phi$ is the is the mortgage subsidy, $\\theta$ is the cost of insurance, $r_{w}$ is the percentage real resource cost to the bank and r$_b$ equal to \n", + "\\begin{equation*}\n", + " P_b = \\frac{1}{1+r_b}\n", + "\\end{equation*}\n", + "- Let $\\delta^*$(m',g') be cutoff level of household depreciation at which household is indifferent between defaulting and not defaulting on her mortgage. \n", + "- A bank will originate a mortgage if and only if \n", + "\\begin{equation*}\n", + " m'P_m(g',m') \\leq \\frac{1}{(1 + r_b)(1 + r_w + \\theta - \\phi)} \\bigg( m'F(\\delta^*(m',g')) + \\gamma g' \\int_{\\delta^*(m',g')}^1 (1-\\delta')dF(\\delta') \\bigg)\n", + "\\end{equation*}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Results\n", + "\n", + "#### Comparison of steady state equilibria of economies with and without a tax financed mortgage interest rates subsidy of 30 basis points\n", + "\n", + "- Removing subsidy make mortgages less attractive by increasing the effective interest rate\n", + " - Households with low levels of cash in hand do not respond much to the change in interest rate subsidy.\n", + " - For wealthier households, the change in policy induces a massive reduction in leverage, and thus substantial reduction in mortgage debt.\n", + "- Thus, households shifts away from bonds toward home equity. Median household was holding 60.7$%$ of its net worth in bonds with subsidy reduces to 5.8$%$ without subsidy." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import Image\n", + "imgUrl = 'results.png' # setup path and filename\n", + "img = Image(url=imgUrl) # create the image object\n", + "img # display the image" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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 +} From 3eba8f5af83c952e354c4d25dbd87e80183898d1 Mon Sep 17 00:00:00 2001 From: ykulu1 <43350392+ykulu1@users.noreply.github.com> Date: Sun, 22 Sep 2019 18:50:10 -0400 Subject: [PATCH 08/13] Delete JKM_summary.ipynb --- .../JKM_summary.ipynb | 184 ------------------ 1 file changed, 184 deletions(-) delete mode 100644 models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb diff --git a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb deleted file mode 100644 index 7a5ed987..00000000 --- a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb +++ /dev/null @@ -1,184 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Jeske, Krueger and Mitman" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## \"[Housing, mortgage bailout guarantees and the macroeconomy](https://www.sciencedirect.com/science/article/abs/pii/S0304393213001219)\" (2013)\n", - "\n", - "- Notebook is prepared by Yusuf Suha Kulu" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Summary\n", - "The article uses a model with heterogeneous, infinitely lived households to understand the macroeconomic and distributional effects of government bailout guarantees for Government Sponsored Enterprises (GSE)\n", - "\n", - "The main findings are as follows: \n", - "\n", - "- Eliminating the bailout guarantee leads to a large decline in mortgage origination and increases aggregate welfare by 0.5% in comsumption equivalent variation but has little effect on foreclosure rates and housing investment.\n", - "\n", - "- Bailout guarantee hurts low income and low asset households.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Overview\n", - "\n", - "#### Tax financed mortgage interest rate subsidy\n", - "\n", - "The baiolout guarantees are modeled as the tax financed interest rate subsidy because prior to the bailout of the GSEs, they could borrow at interest rates close to that on U.S government debt, despite the fact that they were heavily exposed to aggregate house price risk. The absence of risk premium can be attributed to implicit government bailout guarantee.\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Model \n", - "\n", - "- Heterogeneous agent general equilibrium model with incomplete markets in the tradition of Bewley(1986), Huggett(1993), and Aiyagari(1994).\n", - "\n", - "#### Households \n", - "- U(c,h) where c is nondurable consumption c and h is housing services.\n", - "- Endowment and (labor) income are used interchangeably. Households receive idiosynratic endowments which follow a finite state Markov chain $\\pi$(y'|y) and unique invariant distribution $\\Pi$(y).\n", - "- Two types of assets: \n", - " - b' one period bonds with price $P_{b}$ \n", - " - g' perfectly divisible houses with price $P_{h}$. Houses are risky assets which are subject to idiosynratic house price shocks. F($\\delta$') cdf of house price depreciation rate $\\delta$' tomorrow with support D = [$\\underline{\\delta}$,1] where $\\underline{\\delta}$ $\\leq$ 0 which represents house value appreciation.\n", - "- Mortgages: Households can borrow againts their real estate position using one period martgage debt. m' denote the size of the mortgage with price $P_{m}$. The price is determined by competition of banks through a zero profit condition. The gross mortgage interest rate is $R_{m}$ = $\\frac{1}{P_m}$\n", - "- Households choose to default whenever the amount owed in the mortgage is greater than the value of the house after the realization of the price shock.\n", - "- Recursive Formulation:\n", - "\n", - "\\begin{equation*}\n", - " v(a,y) = max_{c,h,b',m'g' \\geq 0} \\bigg(U(c,h) + \\beta \\sum_{y'} \\pi(y'|y) \\int_{\\underline{\\delta}}^1v(a',y')dF(\\delta') \\bigg) \\\\\n", - " s.t \\\\\n", - " c + b'P_b + hP_l + g'P_h - m'P_m(g',m') = a + g'P_l \\\\\n", - " a'(\\delta',y',m',g') = b' + max \\big(0,P_h(1-\\delta')g' - m'\\big) + (1-\\tau)y' \\\\\n", - "\\end{equation*}\n", - "\n", - "\n", - "\n", - "#### The Real Estate Construction Sector\n", - "- Reversibility of the technology: Real estate companies can turn houses into consumption goods\n", - "\n", - "\\begin{equation*}\n", - " max P_hI - C_h \\\\ \n", - " s.t \\\\ \n", - " I=C_h \\\\ \n", - "\\end{equation*}\n", - "where I is the output (houses) and $C_{h}$ is the input of the consumption good\n", - "\n", - "- The equilibrium house price is \n", - "\n", - "\\begin{equation*}\n", - " P_h=1\n", - "\\end{equation*}\n", - "\n", - "#### The banking sector \n", - "- Effective cost of the banking sector for financing one dollar of mortgage equals (1 + $r_{b}$)(1 + $r_{w}$ + $\\theta$ - $\\phi$) where $\\phi$ is the is the mortgage subsidy, $\\theta$ is the cost of insurance, $r_{w}$ is the percentage real resource cost to the bank and r$_b$ equal to \n", - "\\begin{equation*}\n", - " P_b = \\frac{1}{1+r_b}\n", - "\\end{equation*}\n", - "- Let $\\delta^*$(m',g') be cutoff level of household depreciation at which household is indifferent between defaulting and not defaulting on her mortgage. \n", - "- A bank will originate a mortgage if and only if \n", - "\\begin{equation*}\n", - " m'P_m(g',m') \\leq \\frac{1}{(1 + r_b)(1 + r_w + \\theta - \\phi)} \\bigg( m'F(\\delta^*(m',g')) + \\gamma g' \\int_{\\delta^*(m',g')}^1 (1-\\delta')dF(\\delta') \\bigg)\n", - "\\end{equation*}\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Results\n", - "\n", - "#### Comparison of steady state equilibria of economies with and without a tax financed mortgage interest rates subsidy of 30 basis points\n", - "\n", - "- Removing subsidy make mortgages less attractive by increasing the effective interest rate\n", - " - Households with low levels of cash in hand do not respond much to the change in interest rate subsidy.\n", - " - For wealthier households, the change in policy induces a massive reduction in leverage, and thus substantial reduction in mortgage debt.\n", - "- Thus, households shifts away from bonds toward home equity. Median household was holding 60.7$%$ of its net worth in bonds with subsidy reduces to 5.8$%$ without subsidy." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "" - ], - "text/plain": [ - "" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "from IPython.display import Image\n", - "imgUrl = 'results.png' # setup path and filename\n", - "img = Image(url=imgUrl) # create the image object\n", - "img # display the image" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "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 -} From d9258c58facd395a1a2e4b84b368922834570eca Mon Sep 17 00:00:00 2001 From: ykulu1 <43350392+ykulu1@users.noreply.github.com> Date: Sun, 22 Sep 2019 18:50:26 -0400 Subject: [PATCH 09/13] Add files via upload --- .../JKM_summary.ipynb | 199 ++++++++++++++++++ 1 file changed, 199 insertions(+) create mode 100644 models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb diff --git a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb new file mode 100644 index 00000000..be9b59a8 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb @@ -0,0 +1,199 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jeske, Krueger and Mitman" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## \"[Housing, mortgage bailout guarantees and the macroeconomy](https://www.sciencedirect.com/science/article/abs/pii/S0304393213001219)\" (2013)\n", + "\n", + "- Notebook is prepared by Yusuf Suha Kulu" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Summary\n", + "The article uses a model with heterogeneous, infinitely lived households to understand the macroeconomic and distributional effects of government bailout guarantees for Government Sponsored Enterprises (GSE)\n", + "\n", + "The main findings are as follows: \n", + "\n", + "- Eliminating the bailout guarantee leads to a large decline in mortgage origination and increases aggregate welfare by 0.5% in comsumption equivalent variation but has little effect on foreclosure rates and housing investment.\n", + "\n", + "- Bailout guarantee hurts low income and low asset households.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Overview\n", + "\n", + "#### Tax financed mortgage interest rate subsidy\n", + "\n", + "The baiolout guarantees are modeled as the tax financed interest rate subsidy because prior to the bailout of the GSEs, they could borrow at interest rates close to that on U.S government debt, despite the fact that they were heavily exposed to aggregate house price risk. The absence of risk premium can be attributed to implicit government bailout guarantee.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Model \n", + "\n", + "- Heterogeneous agent general equilibrium model with incomplete markets in the tradition of Bewley(1986), Huggett(1993), and Aiyagari(1994).\n", + "\n", + "#### Households \n", + "- U(c,h) where c is nondurable consumption c and h is housing services.\n", + "- Endowment and (labor) income are used interchangeably. Households receive idiosynratic endowments which follow a finite state Markov chain $\\pi$(y'|y) and unique invariant distribution $\\Pi$(y).\n", + "- Two types of assets: \n", + " - b' one period bonds with price $P_{b}$ \n", + " - g' perfectly divisible houses with price $P_{h}$. Houses are risky assets which are subject to idiosynratic house price shocks. F($\\delta$') cdf of house price depreciation rate $\\delta$' tomorrow with support D = [$\\underline{\\delta}$,1] where $\\underline{\\delta}$ $\\leq$ 0 which represents house value appreciation.\n", + "- Mortgages: Households can borrow againts their real estate position using one period martgage debt. m' denote the size of the mortgage with price $P_{m}$. The price is determined by competition of banks through a zero profit condition. The gross mortgage interest rate is $R_{m}$ = $\\frac{1}{P_m}$\n", + "- Households choose to default whenever the amount owed in the mortgage is greater than the value of the house after the realization of the price shock.\n", + "- Recursive Formulation:\n", + "\n", + "\\begin{equation*}\n", + " v(a,y) = max_{c,h,b',m'g' \\geq 0} \\bigg(U(c,h) + \\beta \\sum_{y'} \\pi(y'|y) \\int_{\\underline{\\delta}}^1v(a',y')dF(\\delta') \\bigg) \n", + "\\end{equation*}\n", + "\n", + " s.t \n", + "\n", + "\\begin{equation*}\n", + " c + b'P_b + hP_l + g'P_h - m'P_m(g',m') = a + g'P_l \n", + "\\end{equation*}\n", + "\n", + "\\begin{equation*}\n", + " a'(\\delta',y',m',g') = b' + max \\big(0,P_h(1-\\delta')g' - m'\\big) + (1-\\tau)y' \\\\\n", + "\\end{equation*}\n", + "\n", + "\n", + "\n", + "#### The Real Estate Construction Sector\n", + "- Reversibility of the technology: Real estate companies can turn houses into consumption goods\n", + "\n", + "\\begin{equation*}\n", + " max P_hI - C_h \n", + "\\end{equation*}\n", + "\n", + " s.t \n", + " \n", + "\\begin{equation*} \n", + " I=C_h \n", + "\\end{equation*}\n", + "\n", + "where I is the output (houses) and $C_{h}$ is the input of the consumption good\n", + "\n", + "- The equilibrium house price is \n", + "\n", + "\\begin{equation*}\n", + " P_h=1\n", + "\\end{equation*}\n", + "\n", + "#### The banking sector \n", + "- Effective cost of the banking sector for financing one dollar of mortgage equals (1 + $r_{b}$)(1 + $r_{w}$ + $\\theta$ - $\\phi$) where $\\phi$ is the is the mortgage subsidy, $\\theta$ is the cost of insurance, $r_{w}$ is the percentage real resource cost to the bank and $r_{b}$ equal to \n", + "\n", + "\\begin{equation*}\n", + " P_b = \\frac{1}{1+r_b}\n", + "\\end{equation*}\n", + "\n", + "- Let $\\delta^*$(m',g') be cutoff level of household depreciation at which household is indifferent between defaulting and not defaulting on her mortgage. \n", + "- A bank will originate a mortgage if and only if \n", + "\n", + "\\begin{equation*}\n", + " m'P_m(g',m') \\leq \\frac{1}{(1 + r_b)(1 + r_w + \\theta - \\phi)} \\bigg( m'F(\\delta^*(m',g')) + \\gamma g' \\int_{\\delta^*(m',g')}^1 (1-\\delta')dF(\\delta') \\bigg)\n", + "\\end{equation*}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Results\n", + "\n", + "#### Comparison of steady state equilibria of economies with and without a tax financed mortgage interest rates subsidy of 30 basis points\n", + "\n", + "- Removing subsidy make mortgages less attractive by increasing the effective interest rate\n", + " - Households with low levels of cash in hand do not respond much to the change in interest rate subsidy.\n", + " - For wealthier households, the change in policy induces a massive reduction in leverage, and thus substantial reduction in mortgage debt.\n", + "- Thus, households shifts away from bonds toward home equity. Median household was holding 60.7$%$ of its net worth in bonds with subsidy reduces to 5.8$%$ without subsidy." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import Image\n", + "imgUrl = 'results.png' # setup path and filename\n", + "img = Image(url=imgUrl) # create the image object\n", + "img # display the image" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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 +} From ee9546366cdaf9e9ff80bfd82c8b905b0b085330 Mon Sep 17 00:00:00 2001 From: ykulu1 <43350392+ykulu1@users.noreply.github.com> Date: Sun, 22 Sep 2019 18:52:09 -0400 Subject: [PATCH 10/13] Rename models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb to models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees/JKM_summary.ipynb --- .../{ => JKMBailoutGuarantees}/JKM_summary.ipynb | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename models/We-Would-Like-In-Econ-ARK/{ => JKMBailoutGuarantees}/JKM_summary.ipynb (100%) diff --git a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb b/models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees/JKM_summary.ipynb similarity index 100% rename from models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb rename to models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees/JKM_summary.ipynb From f07623aa62300b43da10b4a95f0362121e5c113e Mon Sep 17 00:00:00 2001 From: ykulu1 <43350392+ykulu1@users.noreply.github.com> Date: Sun, 22 Sep 2019 18:53:00 -0400 Subject: [PATCH 11/13] Add files via upload --- .../JKMBailoutGuarantees/results.png | Bin 0 -> 189606 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees/results.png diff --git a/models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees/results.png b/models/We-Would-Like-In-Econ-ARK/JKMBailoutGuarantees/results.png new file mode 100644 index 0000000000000000000000000000000000000000..9ec90c25d8613ca8ec90351e30eb770cb9b29545 GIT binary patch literal 189606 zcmdqIWmH_vwl>;8fFJ=9Ja~ZM?(R--CpZLmcS}fccXxN!MiSiJ8+T~j8u@r_?{oIa z9^?MLjM4OB)hwIO^eTcCj#r1*P#(a_&{lelK!*lJmF=1*nYbG2=T!AJ29PZ(`I_3r zSh1@<%TP#h0uv2(4!S?*gQ4l$qsQzYgM%#^RoUksVV%5>J$E5HqnRwbX?J7Gjub2a z%Ec-NhZ+TPK+Th`KD*~Fm?}#-1 zp?ajI2@l>zE@1882w#X0@KvseBPlhJv{wYJ6p>g6@S_Q*P^!8G zr%dr(C@JKbJ_Z^$Tk`(LmqlnRz@> zeufzT_@vws8hhQCM77DJSypFHJ0kYMSRjLuB9!g<`E$fG-GXLLHP@vu=FY1-<I}F;=!+CJ`4iBy?ha{2Fe*X7~7zkI#sbNJO(4)OBzk9CL@YYb-W+R4r|zrXS~& zUMGQYU^Cl$%cAr@+%h zCo({lA0Q8kzADDNmv@7l)ay134t7ocN0T7u$u24Gc7RvWGjl~ef4N|ZF{|E2G(v`O zTDau~VG|x9T&8Z-!un{_P!f@{y_H&yz(gdDC^B(M_=Ud6tY#Gg01Vm_HW>T15Zrv) z=WvS^c^Wq^;wIZ9v`4-SWxp0o7BXzXUa4>j5BS_e$;7I4PLp1i{hKZxM_e(%bBe(a+g;;k?FnkhUFUQ`i6y7U&_#VNP0KpPeqjwjB3TCnoPPm+nDfDxl^H1 z#{`B)Vn!Hr84L(rbu(^_PSayq^g3l^#*93AR+5I0cWTS&l3myv=m9@&T=r+rf=Cu> z-}dI)wk)#)K1*jYAE!o`06NbK0plR=DcrW8?G6+_^cAaUV!aY{+deI?>$V#nE1okg$G@Fe7gH@z&6Po@Dd~{6^$g5=F@mF=2Tm zUZP)VMH5K#C2?!sEQC*g0DkC;p6VCNgKrMx6^4tN>!-jFDK4Te34fm(t6(~f_eRWU zJlX7hN+?#A*xq|5B&~0Rf_M{CdnT7~i=iEY-^zFerSiFajvU(@qEfvgP}Xy&pW&KS zlttA<){1_=!kk^nx^NG7Ppi0t_^9~4cxw14UONXnQv`>u!Lsqgvgiugd|qeX=vD{S z$n+HJT;1Sh3+}}50_~L5cg;pFixd3}8(jmRU(oe-b!(bOReRNB8Z8>%!GWrUh6Wj$p`<*8+Qa?ELQtmcn-7qK0Sob$#DNA=C7rG|Kh+Gb0Jkj2sE2y1l% z*OiPfMEby=9Scu0#-Rht1M#u8JmUlf++}uVuD2U|Tay>aX8$e!Vz zR|a&-6U8LT9J1|1HW;I*wjqGGU2pL|5Q?UV?ub9JhjY?7X#J`yRBTX0${m%M$~Bb$ zNBUrIqSvzT=$4t6Q8w_&G1-WJwqAy~0dH$=SHDUjgubJvu=sfXE;UwC%3cZ*6I2M1 z2eG#M2K9t(;BuIz45x8iY|xHqYSzjPtEG*kc#|bZ;b*o9+_BIEsQ!8{hak6*!Tj^u z#P$nt&CQp6VI#9pBd0-jeG&^~!dp+@lCC^t9ZR3t)Xkmyb!Wz+6dx_wcGLNtBa_p%{FC7L*jJZX}h^o#$INq({*Zh zdx*KnFBpnQ#N#30j(j{hg;dk`RrJ!xsi(B+v}k)2T&A@hxL;ke0WEhc;PrrBqz~d_ zBlD?^wj)h5o~e$IyYw=i%99-sL386J|GLirOg{WJYCWOaW6u%MoA!uy3c@?S126o? 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zrsx>Av|UEyP@$p|)5!#6UzJ$x(D&3}=;~wccJO)=0!lT`7H}$?g*iE?R)2YUA!#iwUKzIKBjZwWm|+c+|c?FN73hLHy?3S~xF(kluZ*Rv2O}fdJoq zmXkXR;bkn`-|h)FA-p^&v^Z-z7S%r zeZ8}}3Ge4ad2f(2zH0Vl!Y>X@F$x@R1!mRq6XLG5zW@9G!@WtfdZU0*;HL_(NUo5} z!sPqY)}*z_wJp?bR8fT8P@$xtk?A;4rsKfTABN~#FcqAP#-T!tp#1q40l#0 \\\n", + "Labor is supplied inelastically.\n", + "\n", + "Note that if r is positive, there is a natural borrowing constraint due to non negativity of the consumption. Thus, \n", + "$$ a_t \\geq -\\phi$$\n", + "$$ \\phi \\equiv min\\left\\{b, \\frac{wl_{min}}{r}\\right\\} \\quad for \\quad r>0 ;\\quad \\phi \\equiv b \\quad for \\quad r\\leq 0$$\n", + "\n", + "The Bellman Equation is following:\n", + "\n", + "\\begin{equation}\n", + "V(z_t,b,w,r) = max \\bigg(U(z_t - \\hat{a}) + \\beta \\int V(z_{t+1},b,w,r)dF(l_{t+1}) \\bigg)\n", + "\\end{equation}\n", + "where\n", + "$$\\hat{a} = a_t + \\phi$$\n", + "$$z_t = wl_t + (1+r)\\hat{a} - r \\phi$$ \n", + "$z_t$ is the total resources of the agent\n", + "\n", + "#### Endogeneous Heterogeneity and Aggregation\n", + "Let\n", + "$$ Ea_w = E\\left\\{A(z,b,w,r)\\right\\} - \\phi$$ denote the long-run average assets where A(z,b,w,r) is the asset demand function (solution to the Bellman equation). \n", + "\n", + "1. Aggregate assets of the population tends to infinity as $R\\beta$ approaches to one. This reflects the infinite horizon model as if the interest rate equals or exceeds the time preference rate, then the individual will accumulate infinite amount of assets.\n", + "\n", + "2. Aggregate assets are always higher under uncertainity than that of the certainity case. \n", + "\n", + "#### General Equilibrium\n", + "\n", + "Aggregate capital stock is higher and the interest rate is lower in the economy with uninsured idiosynratic shocks and borrowing constraints as compared with the one without the shocks. The saving rate is also higher.\n", + "\n", + "Permitting a high borrowing limit serves to lower aggregate capital and raise the interest rate. The intuition is when the borrowing is permitted, individuals need not to rely solely on holdings of capital to buffer earnings variation. Thus, they use the borrowing to buffer the shocks and they hold less capital.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Results\n", + "\n", + "

\n", + "\n", + "where \n", + "\n", + "$$ log(l_t) = \\rho log(l_{t-1}) + \\sigma {(1-\\rho^2)}^{0.5} \\epsilon_t $$\n", + "\n", + "$\\mu$ is the CRRA coefficient.\n", + "\n", + "The full insurance net return to capital is 4.17 percent, and the saving rate is 23.67 percent.\n", + "\n", + "The saving rates between the with and without insurance cases is very small under the plausible values. However, for high values of the parameters, saving rate difference can be as high as 14 percentage points. \n", + "\n", + "#### Importance of Asset Trading\n", + "\n", + "An appropriate expression for the welfare loss from consumption variability is given by $\\mu \\sigma_c/2$. Consumers can smooth their consumption by accumulating or decumulating assets. Under plausible parameter values, consumption smoothing by asset trading can have a welfare benefit of 14 percent of percepita consumption, or about 8 percent of per capita GNP.\n", + "\n", + "#### Cross Sectional Distributions and Ineqaulity Measures\n", + "\n", + "The skewness of the distributions are captured by the model. However, the degree of skewness is less than the data. Moreover, the model generates emprically plausible relative degrees of inequality. However, still it can not generate the observed degrees of the inequlity for the US. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "A version of the Brock-Mirman (1972) growth model with a large number if agents subject to uninsured idiosynratic shocks was described. It has important implications for the contribution of the pracautionary saving to aggregate saving, the importance of asset trading, and income and wealth distributions. 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Each $\\pi(s'|s,Z',Z)$ has the form\n", + " * $\\left(\\begin{array}{cc} \\pi_{u,u}^{Z,Z'} & \\pi_{u,e}^{Z,Z'}\\\\ \\pi_{e,u}^{Z,Z'} & \\pi_{e,e}^{Z,Z'} \\end{array}\\right)$\n", + " * ***If HH is unemployed, they only earn unemployment benefits.***\n", + "* Income risk (conditional on employment)\n", + " * Log-earnings of HHs follow a process with both transitory and persistent shocks.\n", + " * $log(\\gamma') = p + \\epsilon$\n", + " * $p' = \\phi p + \\eta$\n", + " * Parameters are estimated using PSID data and then the **Rouwenhorst procedure** is used to discretize the persistent part of the process into a **seven-state Markov chain**.\n", + "\n", + "------------------------------------------------------------------------\n", + "\n", + "#### Some comments\n", + "\n", + "1. Unemployment is a transitory event\n", + "2. An unemployed HH has a very low transitory income.\n", + "3. Contingent on becoming unemployed, the expected permanent income drops by 10% (a la von Wachter and others).\n", + " * In normal times, the likelihood of going to a very low states of the permanent component of income is very low.\n", + " * However, in bad times, the likelihood of going to very low states increases.\n", + "\n", + "#### The specification\n", + "\n", + "* In order to describe the income process, we need 3 state variables,\n", + " * $\\omega$ -- employment (or aggregate) state.\n", + " * $\\mathbb{p}$ -- persistent component of income.\n", + " * $\\theta$ -- transitory component of income.\n", + "* $\\omega$ -- employment state (or can be called an aggregate state, in which case it becomes H,L rather than e,u)\n", + " * 2-state Markov chain: $\\omega \\in \\Omega=\\{e,u\\}$\n", + " * Denoting the transition probability of switching from employment (unemployment) in period $t$ to employment (unemployment) in period $t+1$ by $\\rho_{e}$ ($\\rho_{u}$), the transition matrix is given by:\n", + " * $\\pi = \\left(\\begin{array}{cc} \\rho_{e} & 1-\\rho_{e}\\\\ 1-\\rho_{u} & \\rho_{u} \\end{array}\\right)$\n", + "* $\\mathbb{P}$ -- Persistent component of income.\n", + " * 3-state Markov chain: $\\mathbb{p} \\in \\mathbb{P}= \\{\\mathbb{p}_{1},\\mathbb{p}_{2},\\mathbb{p}_{3}\\}$\n", + " * *The transition probabilities for this Markov process depend on the employment state and are given by $\\lambda(\\mathbb{p}'|\\mathbb{p},\\omega,\\omega')$. Assuming the law of large numbers, the idiosyncratic risk averages out, and only the aggregate risk determines the number of agents in a specific idiosyncratic persistent income state, $\\mathbb{p}$. Moreover, we assume that the share of households in a given idiosyncratic persistent income state $\\mathbb{p}$ only depends on the current aggregate state $\\omega$. This assumption imposes consistency restrictions on the transition matrix $\\lambda(\\mathbb{p}'|\\mathbb{p},\\omega,\\omega')$.*\n", + " * We merge the $(\\omega,\\mathbb{p})$ states together to form one state variable that captures both the employment status and the persistent income.\n", + " * Denote by $\\lambda_{\\omega\\mathbb{p},\\omega'\\mathbb{p}'}$ the probability of transitioning from employment state $\\omega$ and persistent income $\\mathbb{p}$ in time $t$ to employment state $\\omega'$ and persistent income $\\mathbb{p}'$ in time $t+1$.\n", + " * Then the transition matrix with 2 employment states and 3 persistent income states is given by:\n", + " * $\\lambda = \\left(\\begin{array}{cccccc}\n", + " \\lambda_{e\\mathbb{p}_1,e\\mathbb{p}_1} & \\lambda_{e\\mathbb{p}_1,e\\mathbb{p}_2} & \\lambda_{e\\mathbb{p}_1,e\\mathbb{p}_3} & \\lambda_{e\\mathbb{p}_1,u\\mathbb{p}_1} & \\lambda_{e\\mathbb{p}_1,u\\mathbb{p}_2} & \\lambda_{e\\mathbb{p}_1,u\\mathbb{p}_3} \\\\ \\lambda_{e\\mathbb{p}_2,e\\mathbb{p}_1} & \\lambda_{e\\mathbb{p}_2,e\\mathbb{p}_2} & \\lambda_{e\\mathbb{p}_2,e\\mathbb{p}_3} & \\lambda_{e\\mathbb{p}_2,u\\mathbb{p}_1} & \\lambda_{e\\mathbb{p}_2,u\\mathbb{p}_2} & \\lambda_{e\\mathbb{p}_2,u\\mathbb{p}_3} \\\\\n", + " \\lambda_{e\\mathbb{p}_3,e\\mathbb{p}_1} & \\lambda_{e\\mathbb{p}_3,e\\mathbb{p}_2} & \\lambda_{e\\mathbb{p}_3,e\\mathbb{p}_3} & \\lambda_{e\\mathbb{p}_3,u\\mathbb{p}_1} & \\lambda_{e\\mathbb{p}_3,u\\mathbb{p}_2} & \\lambda_{e\\mathbb{p}_3,u\\mathbb{p}_3} \\\\\n", + " \\lambda_{u\\mathbb{p}_1,e\\mathbb{p}_1} & \\lambda_{u\\mathbb{p}_1,e\\mathbb{p}_2} & \\lambda_{u\\mathbb{p}_1,e\\mathbb{p}_3} & \\lambda_{u\\mathbb{p}_1,u\\mathbb{p}_1} & \\lambda_{u\\mathbb{p}_1,u\\mathbb{p}_2} & \\lambda_{u\\mathbb{p}_1,u\\mathbb{p}_3} \\\\ \\lambda_{u\\mathbb{p}_2,e\\mathbb{p}_1} & \\lambda_{u\\mathbb{p}_2,e\\mathbb{p}_2} & \\lambda_{u\\mathbb{p}_2,e\\mathbb{p}_3} & \\lambda_{u\\mathbb{p}_2,u\\mathbb{p}_1} & \\lambda_{u\\mathbb{p}_2,u\\mathbb{p}_2} & \\lambda_{u\\mathbb{p}_2,u\\mathbb{p}_3} \\\\\n", + " \\lambda_{u\\mathbb{p}_3,e\\mathbb{p}_1} & \\lambda_{u\\mathbb{p}_3,e\\mathbb{p}_2} & \\lambda_{u\\mathbb{p}_3,e\\mathbb{p}_3} & \\lambda_{u\\mathbb{p}_3,u\\mathbb{p}_1} & \\lambda_{u\\mathbb{p}_3,u\\mathbb{p}_2} & \\lambda_{u\\mathbb{p}_3,u\\mathbb{p}_3}\n", + " \\end{array}\\right)$.\n", + " * Each of these rows sums to 1.\n", + " * Each row of the 4 different quadrants in this transition matrix sums to the transition probabilities associated with their respective employment state transition.\n", + " * e.g. if we look at the lower-right quadrant of $\\lambda$, each of the rows sums to $\\rho_{u}$.\n", + " * Since this is a **regular Markov Chain**, from the **Fundamental Limit Theorem for Regular Chains** we know that there exists a unique stationary distribution for $\\lambda$. Call this distribution $\\Lambda$.\n", + " * ***NOTE: Calibration has to be done in a way that it yields a stationary distribution which results in $\\mathbb{E}(\\mathbb{p}|\\omega=u) = 0.9 \\mathbb{E}(\\mathbb{p}|\\omega=e)$.***\n", + "* $\\theta_t$ -- Transitory shock to income\n", + " * If $\\omega_t=u$, then $\\theta=\\varepsilon$\n", + " * If $\\omega_t=e$, then draw from log-normal distribution (**7 shock points**)\n", + "\n", + "\n", + "* Calibration:\n", + " * **NOTE: My intuition regarding how to calibrate this Markov process is better if we think of $\\omega$ as an aggregate state of the economy, rather than a more specific aggregate employment state, so I will outline below how I would go about calibrating if $\\omega$ described the aggregate state of the economy (high or low), with a transition matrix given by:**\n", + " * $\\pi = \\left(\\begin{array}{cc} \\rho_{h} & 1-\\rho_{h}\\\\ 1-\\rho_{l} & \\rho_{l} \\end{array}\\right)$\n", + " * $\\omega$ is a regular Markov Chain, so it has a stationary distribution, call it $\\Pi$, which satisfies\n", + " * $\\Pi(h) = \\frac{1-\\rho_{l}}{2-\\rho_{h}-\\rho_{l}}$\n", + " * $\\Pi(l) = \\frac{1-\\rho_{h}}{2-\\rho_{h}-\\rho_{l}}$\n", + " * $\\Pi(l)$ is the fraction of time that the economy is in a severe recession and $\\Pi(h)$ is the fraction of time that the economy is in a normal state.\n", + " * We calibrate $\\rho_{l}$ to match the expected length of a severe recession. For this Markov process, $EL_{l} = \\frac{1}{1-\\rho_{l}}$.\n", + " * Given $\\rho_l$, we choose $\\rho_h$ to match the fraction of time the economy is in a severe recession, $\\Pi(l)$.\n", + " * Using Krueger et al. (2016)'s definition of a recession on data from 1948--2014, we get an expected length of recession of 22 quarters and a fraction of 16.48% recessionary quarters. This implies $\\rho_l = 0.9545$ and $\\rho_h = 0.9910$.\n", + " * The next step is to calibrate $\\lambda$.\n", + " * Denote the stationary distribution of this Markov process by $\\Lambda$.\n", + " * $\\Lambda_{\\omega}(\\mathbb{p})$ gives us the fraction of households that have persistent income component $\\mathbb{p}$ in the state $\\omega$ of the economy.\n", + " * Similar to Krusell and Smith (1998) and Krueger et al. (2016), we impose a restriction that the aggregate fraction of each of the persistent income states only depends on the aggregate state of the economy. This implies that for each of the four possible $(\\omega, \\omega')$ pairs, the following hold:\n", + " $$\\Lambda_{\\omega'}(\\mathbb{p}_1) = \\Lambda_{\\omega}(\\mathbb{p}_1) \\frac{\\lambda_{\\omega \\mathbb{p}_1,\\omega' \\mathbb{p}_1}}{\\rho_{\\omega,\\omega'}} + \\Lambda_{\\omega}(\\mathbb{p}_2) \\frac{\\lambda_{\\omega \\mathbb{p}_2,\\omega' \\mathbb{p}_1}}{\\rho_{\\omega,\\omega'}} + \\Big(1- \\Lambda_{\\omega}(\\mathbb{p}_1) - \\Lambda_{\\omega}(\\mathbb{p}_2)\\Big) \\frac{\\lambda_{\\omega \\mathbb{p}_3,\\omega' \\mathbb{p}_1}}{\\rho_{\\omega,\\omega'}}$$\n", + " $$\\Lambda_{\\omega'}(\\mathbb{p}_2) = \\Lambda_{\\omega}(\\mathbb{p}_1) \\frac{\\lambda_{\\omega \\mathbb{p}_1,\\omega' \\mathbb{p}_2}}{\\rho_{\\omega,\\omega'}} + \\Lambda_{\\omega}(\\mathbb{p}_2) \\frac{\\lambda_{\\omega \\mathbb{p}_2,\\omega' \\mathbb{p}_2}}{\\rho_{\\omega,\\omega'}} + \\Big(1- \\Lambda_{\\omega}(\\mathbb{p}_1) - \\Lambda_{\\omega}(\\mathbb{p}_2)\\Big) \\frac{\\lambda_{\\omega \\mathbb{p}_3,\\omega' \\mathbb{p}_2}}{\\rho_{\\omega,\\omega'}}$$\n", + " $$\\Lambda_{\\omega'}(\\mathbb{p}_3) = \\Lambda_{\\omega}(\\mathbb{p}_1) \\frac{\\lambda_{\\omega \\mathbb{p}_1,\\omega' \\mathbb{p}_3}}{\\rho_{\\omega,\\omega'}} + \\Lambda_{\\omega}(\\mathbb{p}_2) \\frac{\\lambda_{\\omega \\mathbb{p}_2,\\omega' \\mathbb{p}_3}}{\\rho_{\\omega,\\omega'}} + \\Big(1- \\Lambda_{\\omega}(\\mathbb{p}_1) - \\Lambda_{\\omega}(\\mathbb{p}_2)\\Big) \\frac{\\lambda_{\\omega \\mathbb{p}_3,\\omega' \\mathbb{p}_3}}{\\rho_{\\omega,\\omega'}}$$\n", + " and\n", + " $$\\lambda_{\\omega \\mathbb{p}_1,\\omega' \\mathbb{p}_1} + \\lambda_{\\omega \\mathbb{p}_1,\\omega' \\mathbb{p}_2} + \\lambda_{\\omega \\mathbb{p}_1,\\omega' \\mathbb{p}_3} = \\rho_{\\omega,\\omega'}$$\n", + " $$\\lambda_{\\omega \\mathbb{p}_2,\\omega' \\mathbb{p}_1} + \\lambda_{\\omega \\mathbb{p}_2,\\omega' \\mathbb{p}_2} + \\lambda_{\\omega \\mathbb{p}_2,\\omega' \\mathbb{p}_3} = \\rho_{\\omega,\\omega'}$$\n", + " $$\\lambda_{\\omega \\mathbb{p}_3,\\omega' \\mathbb{p}_1} + \\lambda_{\\omega \\mathbb{p}_3,\\omega' \\mathbb{p}_2} + \\lambda_{\\omega \\mathbb{p}_3,\\omega' \\mathbb{p}_3} = \\rho_{\\omega,\\omega'}$$\n", + " * For each $(\\omega, \\omega')$ pair, these are 6 equations with 9 unknown $\\lambda$'s.\n", + " * Thus, conditional on targeted fractions of persistent income components in the good and bad states of the economy, $\\Big(\\Lambda_{h}(\\mathbb{p})$,$\\Lambda_{l}(\\mathbb{p})\\Big)$, these equations place a joint restriction on the transition probabilties $\\lambda$ for each $(\\omega,\\omega')$ pair.\n", + " * Using data if we calibrate 3 of the transition probabilities for each $(\\omega,\\omega')$ pair, we would pin down the entire transition matrix.\n", + " * **NOTE: This way of calibration will become increasingly difficult if the number of points on $\\mathbb{p}$ increase.**\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Housing Finance, Boom-Bust Episodes, and Macroeconomic Fragility \n", + "### \n", + "\n", + "\n", + "* Study how arrangements in the mortgage market impact the dynamics of housing (boom-bust episode) and the economy.\n", + "* Incomplete markets and endogenous adjustment costs.\n", + "* In response to mortgage rates and credit conditions, the model generate movements in house prices, residential investment, and homeownership consistent with US boom-bust.\n", + "* Propagation to the macroeconomy asymmetric with much higher consumption sensitivity during the bust than the boom.\n", + "* ARM increases the sensitivity of house prices to credit conditions relative to FRM w/o refinancing.\n", + "* Macropru can mitigate fragility by reducing the magnitude of house price movements w/o curtailing homeownership.\n", + "\n", + "* Credit expansion + low costs of borrowing + low returns to safe assets ⇒ house price boom that’s not driving by growth in income, productivity, or rents.\n", + "* High LTV makes the economy more vulnerable to changes in aggregate conditions such as income/employment risk or the cost of borrowing.\n", + " * Under these conditions, decline in house prices can generate sizeable declines in economic activity followed by slow recovery as the demand for new houses is low and also the demand for non-durables is low, because HH have to reduce debt burden.\n", + "* Some households default, making credit more expensive for new borrowers.\n", + "\n", + "\n", + "**Model**\n", + "* Quantitative GE model.\n", + "* To overcome a Modigliani-Miller irrelevance on the contract structure in the HH sector, the model includes frictions such as incomplete markets, mortgage default, and endogenous adjustment costs.\n", + "* Continuum of individuals face uninsurable income risk.\n", + "* Rental units smaller than housing units.\n", + "* Default option, which is priced by the lender.\n", + " * Depends on the individual’s condition and the aggregate condition.\n", + "* Long-term nature of mortgage allows distinction between downpayment constraints on new purchases from collateral constraints on existing loans when option to refinance is available.\n", + "* With refinancing, households have another motive to own a house as it provides insurance against transitory income shocks.\n", + "* LTV and DSTI constraints.\n", + "* Endogenous transaction costs, where the liquidity properties of the housing market depend on where in the housing cycle the HH is.\n", + "\n", + "**Calibration**\n", + "Replicate key features prior to the housing boom\n", + "* Homeownership\n", + "* Sales\n", + "* Foreclosures\n", + "* Joint distribution of assets, housing wealth, and mortgage debt\n", + " * Allows capturing aggregate wealth in terms of financial assets and housing net of mortgages, but also its distribution across HHs.\n", + "* The boom-bust experiment allows the model to replicate the dynamics and magnitudes of house prices, home ownership rates, housing defaults, and time-on-the-market.\n", + "* During the bust, the model matches the consumption elasticity to house price movements as estimated by Mian, Rao, and Sufi (2013).\n", + "\n", + "**House price movements generated by**\n", + "* Productivity/income\n", + "* Preference towards housing\n", + "* Credit conditions – low mortgage rates and loose LTV and DSTI constraints\n", + "* Shocks are unanticipated and are considered to be permanent!\n", + "* Bust is generate by an immediate tightening of credit conditions and slow worsening of income prospects, via increasing the risk in the labor market.\n", + "\n", + "Eliminating the ability to refinance dampens the size of the housing boom, but dramatically increases foreclosures and slows the recovery, despite reducing the magnitude of the housing bust.\n", + "\n", + "ARMs expose homeowners to interest rate risk, and a recession with a tightening of interest rates exacerbates the crisis. This is particularly bad for high LTV HHs.\n", + "\n", + "**Important literature:**\n", + "* Garriga, Manuelli, and Peralta-Alva (2012) – Model of market segmentation to study the dynamics of house prices during the boom and the bust.\n", + " * Collapse in house prices, induces a large and persistent recession due to deleveraging.\n", + "* Iacoviello and Pavan (2013) – response of consumption to negative shocks in the balance sheet or income.\n", + "* Kaplan and Violante (2014) – with illiquid shocks, the response can be pretty large (wealthy hand-to-mouth)\n", + "* KMV (2016) – illiquidity as a result of exogenous transaction costs\n", + "\n", + "\n", + "**Literature exploring the foreclosure dynamics (exogenous house prices):**\n", + "* Such and Guler (2014)\n", + "* Corbae and Quintin (2014)\n", + "* Campbell and Cocco (2014)\n", + "* Hatchondo et al. (2014)\n", + "\n", + "**Literature exploring the foreclosure dynamics (endogenous house prices):**\n", + "* Garriga and Schlagenghauf (2009)\n", + "* Chatterjee and Eyigungor (2014)\n", + "* Arsland, Guler, and Temel (2015)\n", + "\n", + "Housing liquidity is exogenous in both.\n", + "\n", + "**Detailed Model**\n", + "* Infinitely lived HHs\n", + "* For renters, housing services $\\hspace{10pt}$ $c_h = a<\\underline{h}$\n", + "* For homeowners, housing services $\\hspace{10pt}$ $c_h = h \\geq \\underline{h}$\n", + "* Households supply labor endowment, $e.s$, where $s$ follows a Markov chain and transitory $e$ shock drawn from a distribution.\n", + "* Price of apartment services is constant , $r_a=\\frac{1}{A_a}$.\n", + " * Sommer, Sullivan, and Verbrugge (2013) and Davis, Lehnert, and Martin (2008) report that rents have remained flat over the past 30 years, independent of house price swings.\n", + "* Consumption sector, $Y_c=A_c N_c$, where $N_c$ is labor.\n", + "* Housing sector, $Y_h=F_h (L,S_h,N_h)$.\n", + "* Housing depreciates\n", + "* ***Housing illiquidity***\n", + "* Directed search in housing market, where the probability of buying/selling depends on the price quoted and market tightness.\n", + " * Keeping track of cross-sectional distributions can be inhibiting when solving for equilibrium labor market dynamics.\n", + " * Use block recursivity to eliminate the need to keep track of cross-sectional distributions.\n", + " * With brokers, market tightness only depends on the distribution of income, assets, and debt ($\\Phi$) through its impact on house prices, $p$.\n", + " * Absent the brokers, market tightness would depend nonparametrically on $\\Phi$, and household would need to forecast the evolution of each tightness independently.\n", + " * Block recursivity simplifies the problem to:\n", + " * Solve for the dynamics of $p(h)(\\Phi)=p(\\Phi)h$\n", + " * And substituting it into the market tightness equations for buyers and sellers.\n", + "* Lending allowed but borrowing only allowed through mortgages.\n", + "* ***Credit illiquidity***\n", + " * Banks price default risk into new mortgage contracts $q_m^0 ((r_m,m' ),b',h,s)m'$\n", + " * Mortgages do not have a predefined maturity date. Thus, amortization is endogenous.\n", + " * “Mortgages in the model stand in for all forms of mortgage debt (beyond 30-year first liens) by not having a predefined maturity date, and as a result, amortization is endogenous.”\n", + " * Homeowners can prepay without penalty but must pay a cost to extract equity through refinancing.\n", + " * Mortgage payments $l \\geq \\frac{r_m}{1+r_m} m$ and debt evolves according to $m'=(m-l).(1+r_m)$.\n", + " * This is the infinite horizon constant amortization formula, which means that if this minimum payment is met, the mortgage debt stays constant forever.\n", + " * Mortgage payments $l$ is a choice.\n", + " * When the bank repossesses the house, they lose a fraction $\\chi$ of proceeds. Defaulters are shut out of the mortgage market with a probability $\\gamma_f\\in(0,1)$.\n", + "\n", + "**Results:**\n", + "* The structural model is used to assess the relative contributions of higher productivity and cheaper credit to the housing boom.\n", + " * Typical business cycles do not produce large booms in house prices.\n", + " * However, if accompanied by a decline in mortgage rate and lax down payment requirements, the model matches the house price boom.\n", + "* Lose credit on its own does not lead to increase in homeownership, because the general equilibrium effect of increase in house prices offsets the effect of cheaper credit.\n", + " * Productivity boom increases the homeownership.\n", + " * The partial equilibrium effect is offset by the general equilibrium effect.\n", + " * Even though with lose credit homeownership does not change, but HHs buy bigger houses.\n", + "* Credit expansion amplifies the boom in aggregate consumption (using the house as an ATM).\n", + " * Contrary to subprime narrative, the credit boom increases consumption disproportionately among middle and high-income HHs, but not among low-income.\n", + "* Productivity boom decreases leverage for all income groups, particularly high-income.\n", + " * When accompanied by lower mortgage rates and loose down payments, leverage increase across all income groups, not just among subprime borrowers.\n", + "* Refinancing plays a very big role in driving the house prices and in generating the consumption boom for homeowners. Renters are unaffected if there is not any refinancing.\n", + "* ARMs lead to more vulnerability during the bust, but also have a faster impact during recovery.\n", + "* LTV constraints\n", + " * Dampens the size of the housing boom  increases homeownership rate\n", + " * Reduced foreclosures and reduced consumption fall\n", + " * This policy operates by reducing the financial fragility of the economy.\n", + "* PTI constrains\n", + " * Reduce house price appreciation but not by as much as the LTV constraint.\n", + " * Increases significantly the homeownership rate due to the broad limitations in housing spending.\n", + " * PTI still induces too much credit relative to LTV caps, and does not reduce the fragility to credit reversals.\n", + " * Endogenous response in aggregate credit not as large as in the baseline, it is spread out over a large fraction of HHs.\n", + " * As a result, the same credit tightening generates a sizeable decline in house prices and a large spike in foreclosures.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Credit Crises, Precautionary Savings and the Liquidity Trap\n", + "### \n", + "\n", + "* Effect of credit crunch on consumer spending in a heterogeneous-agent incomplete-market model.\n", + "* How are spending decisions of borrowers and lenders affected by an economy-wide financial adjustment?\n", + "* What happens to aggregate activity?\n", + "* How long does the adjustment last?\n", + "* After an unexpected permanent tightening in consumers' borrowing capacity,\n", + " * constrained consumers are **forced** to repay their debt,\n", + " * unconstrained consumers increase their precautionary savings.\n", + " * This depresses interest rates (particularly in the short-run) and generates output drop, even with flexible prices.\n", + " * Output drop larger with sticky prices, if ZLB prevents interest rates from adjusting downwards.\n", + " * With durable goods in the model, HHs take larger debt positions and the output response can be larger.\n", + "\n", + "\n", + "####Relevant papers\n", + "\n", + "\n", + "####Key model features\n", + "* Baseline model:\n", + " * Bewley (1977) type model\n", + " * Infinite horizon\n", + " * Uninsurable income risk\n", + " * Only asset traded is a 1-period risk-free bond\n", + " * HHs can borrow up to an exogenous limit $b_{i,t+1}\\leq \\phi$.\n", + " * $U(c_{i,t},n_{i,t})$\n", + " * No durables\n", + " * Each HH produces consumption goods using linear technology $y_{i,t} = \\theta_{i,t} \\eta_{i,t}$, where $\\theta_{i,t}$ is an idiosyncratic shock to the labor productivity.\n", + " * $\\theta$ is discretized to a Markov chain with **$\\theta^1 = 0$**, which is interpreted as **unemployment**.\n", + " * **No capital.**\n", + " * **No default or bankruptcy**\n", + " * **Forced deleveraging as a result of tightening of credit conditions.**\n", + "* Extended model with durables:\n", + " * Similar to **Carroll and Dunn**\n", + "\n", + "### Details\n", + "* 2 channels in the consumers' response to a reduction in their borrowing capacity:\n", + " * Direct channel: constrained borrowers are forced to reduce their debt.\n", + " * Precautionary channel: unconstrained agents reduce their debt or increase their savings as a bugger against future shocks.\n", + "* Both these channels reduce net lending in the economy, so the equilibrium interest rate has to fall in equilibrium.\n", + "\n", + "#### Calibration\n", + "* Wage process approximated by a 12-state Markov chain.\n", + "* For the transitions between employment and unemployment they follow Shimer (2005), which estimates the finding rate and the separation rate from CPS data.\n", + "* Unemployment benefit set to 40% of average labor income.\n", + "* Bond supply calibrated to match the liquid assets to GDP ratio in 2006 of 1.78.\n", + "\n", + "#### Results\n", + "* After credit crunch:\n", + " * Interest rate dynamics --- sharp initial fall followed by a gradual adjustment to a new, lower steady state.\n", + " * Aggregate activity ---\n", + " * in baseline flexible price specification, there is a mild output reduction of about 1.1%, in response to a shock that reduce long run debt by 10% of initial output.\n", + " * direct effect reduces spending by a larger amount, but since interest rates also reduce (go negative to equilibrate), that pushes the consumption up, and so the response is not as high.\n", + " * With nominal rigidity (ZLB), there is a larger contraction in output of about 1.7%.\n", + "* Consumption predictions of the model are ***sensitive to the chosen calibration target for consumer savings***.\n", + " * When targeting median savings instead of average savings, they obtain a calibration with a larger partial equilibrium response and a lower interest elasticity of aggregate consumption, leading to much larger responses of output.\n", + "* On the supply side, the credit crunch leads to an increase in employment, as the indebted HHs want to work more.\n", + " * There is also a decline in productivity, as the indebted HHs are less productive.\n", + "* In a model with durables, after a credit crunch, net borrowers are forced to deleverage and have to reduce consumption of durable and nondurable goods. Precautionary motive induces net lenders to save more by accumulating bonds and durables. Durables may increase or decrease depending on the strength of these two effects.\n", + " * Net effect depends on the nature of the shock:\n", + " * Shock to credit limit affects leads to a contraction in durable purchases.\n", + " * Shock to credit spreads leads to contraction in durable purchases. Here the output effects can be large.\n", + "\n", + "\n", + "#### Data/Computational Limitation\n", + "* **Rather than using Krusell and Smith's method of *approximate equilibria* to get prices, they keep the entire wealth distribution as a state variable, at the cost of focusing on a one-time shock.**\n", + "* They do not have default or long term debt in their model, since they want to limit the size of the state space. With the current computational limitations, that is necessary if they are going to keep track of the entire distribution as a state variable.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## House Prices and Consumer Spending\n", + "### \n", + "\n", + "* Study the theoretical response of consumption to house prices in quantitative heterogeneous agent models.\n", + "* Several papers have pointed to house values as prime determinants of households' debt capacity.\n", + "* Their paper complementary to papers that endogenizes house prices.\n", + " * Find a crucial role of the endogenous distribution of housing and debt for the size of house price effects.\n", + "* ***Prices and income are exogenous.***\n", + "* So they are studying the isolated effect of house prices on household consumption.\n", + " * Their rule-of-thumb formula measures the strength of the causal effect between house prices and consumption and how it changes with economic conditions or across models.\n", + "\n", + "##### Relevant papers\n", + "Heterogeneous agent equilibrium models with endogenous house prices -- Huo and Rios-Rull (2013) and Kaplan et al. (2016).\n", + "\n", + "\n", + "***Key model features***\n", + "* **The main distinguishing feature of the model is that households trade houses that provide housing services but which are subject to adjustment costs and they can borrow against the value of their houses.**\n", + "* Discrete time, OLG.\n", + "* Housing yields housing services one-for-one.\n", + "* House prices follow a geometric random walk with drif: $P_t = x_t P_{t-1}$\n", + " * $x_t$ is an i.i.d. shock with $\\mathbb{E}[x_t] = \\exp^{\\mu}$, so that $\\mu$ is the trend growth rate of house prices.\n", + " * **Permanent** house price shocks $\\ln(x_t) \\sim \\mathcal{N}(\\mu,\\sigma_P)$\n", + " * Should be interpreted as aggregate shocks, since they affect the value of existing and new houses.\n", + "* Rental cost $R_t = \\phi P_t$.\n", + "* Fixed adjustment costs involved in buying and selling houses.\n", + "* Downpayment constraint.\n", + "* In addition to providing housing services, owner-occupied housing can be used as **collateral** for borrowing. (*These are short-term debts.*)\n", + "* Bequest motive.\n", + "* Cobb-Douglas preferences for non-durable consumption and housing services.\n", + " * Simplifies computation and interpretation of results.\n", + " * CES preferences give similar results.\n", + " * *Relevant evidence from micro data consistently finds support for an elasticity close to unity.*\n", + "* $Y_{i,t} = \\exp\\{\\chi(j_{it}) + z_{it} \\}$, where $z_{it}$ is a transitory shock that follows an AR(1) process and $\\chi(j_{it})$ is a lifecycle component.\n", + "* **In baseline model, Borrowing is based on one-period loans! Frictionless one-period debt allows HHs to adjust their borrowing costlessly every period. Collateral constraint must hold period-by-period. This would cause forced deleveraging!**\n", + " * **The extension of the model to include long-term debt produces conterfactual results (see below).**\n", + "* I think they allow households to choose any household size they want.\n", + "\n", + "***Calibration***\n", + "* Most parameters externally calibrated.\n", + "* $\\alpha$, $\\beta$, $\\Phi$ (bequest motive), lump sum transfer at retirement, and rent-price ratio calibrated to hit life-cycle features:\n", + " * housing, liquid wealth\n", + " * homeownership by age\n", + " * target liquid wealth rather than total non-housing wealth because it delivers MPCs in line with data.\n", + " * *Model matches the data well.*\n", + "* Initial wealth based on 2001 SCF.\n", + "* Model matches some non-calibrated features of the data as well.\n", + "\n", + "\n", + "***Results***\n", + "* Consumption responses to house price shocks in the model are large.\n", + " * Larger than PIH models.\n", + " * Substantial household heterogeneity.\n", + " * MPC x PH is a sufficient statistic for the model-implied response of consumption to house price shocks.\n", + " * Sufficient statistic interesting, because house price increases have 4 main effects:\n", + " * Substitution effect -- substitute away from housing, which is more expensive.\n", + " * Ordinary income effect -- HHs poorer, because of increase in rental cost.\n", + " * Endowment income effect -- HHs richer because of value of house.\n", + " * Collateral effect -- For given housing choice, households can borrow more.\n", + " * The 1st, 2nd, and 4th effect cancel each other out and only the 3rd one matters.\n", + " * 'Permanent' shocks to house prices are important, because they alter the future path of house price growth.\n", + " * House price movements remain neutral for a HH's lifetime budget constraint, but borrowing constraints mean that consumption responds more to current than future income, so the endowment effect dominates.\n", + "* Aggregate elasticity depends on the endogenous joint distribution of MPCs and housing.\n", + " * The size of the housing price effects varies with age, leverage, homeownership status, and wealth.\n", + "* Responses can change depending on changes in credit supply.\n", + "* Length of house price booms and households' expectations of future house price growth also affect the sensitivity of consumption.\n", + "\n", + "***Long-term mortgage in extension***\n", + "* Households can prepay mortgages costlessly, but must pay the fixed cost of refinancing a mortgage to move to negative $A_t$ from positive $A_t$.\n", + " * So choice variable is $c_t$, and that together with initial liquid assets balance determine whether $A_t$ is negative or not. **A little different way of introduces refinancing.**\n", + "* Mortgages are **NOT** long-term in their baseline model!!!\n", + " * In the extension, HHs always exhaust liquid assets before taking on any mortgage debt.\n", + " * So if you are a renter, $A_t \\geq 0$\n", + " * If you are a homeowner, $A_t$ can be $<0$, but then you have to make minimum payments which are given by the geometric schedule, i.e. $A_t \\geq \\chi A_{t-1}$.\n", + " * The interest rate on mortgages is the same as on liquid assets, with a required amortization rate on mortgages, following Gorea and Midrigan (2017), which is set to match the half-life of a 30-yr mortgage.\n", + " * Allows them to reduce a state variable and still have long-term mortgages.\n", + " * **Not the typical way of modeling long-term mortgages. Also, have to assume the same interest rate for both $A_t<0$ and $A_t>0$.**\n", + " * **No with a mortgage debt has any liquid assets!**\n", + " * *Any other problems with this?*\n", + "* No default.\n", + "* The presence of long-term debt and the ability for borrowers to remain underwater leads to a feature of the model that the consumption of highly leveraged households does not respond to mortgage debt forgiveness.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Monetary Policy, Heterogeneity, and the Housing Channel\n", + "\n", + "### \n", + "\n", + "\n", + "* Study the role of housing and mortgage debt in the transmission and effectiveness of MP.\n", + "* Housing channel:\n", + " * Decline in interest rate $\\implies$ Increase in demand for housing by reducing the cost of borrowing and alleviating credit constraints.\n", + "* Liquidity channel:\n", + " * Increase in demand $\\implies$ increased prices $\\implies$ faster sale\n", + "* Cash-flow channel:\n", + " * Decline in interest rate $\\implies$ refinancing\n", + "* Redistribution channel:\n", + " * Redistribution between net debtors and net lenders\n", + "* Income channel:\n", + " * Response as a result of changes in labor demand\n", + "\n", + "Mechanism\n", + "* Monetary contraction $\\implies$ decline in house prices $\\implies$ decline in housing liquidity $\\implies$ elevated foreclosure risk $\\implies$ tighter credit $\\implies$ further price decline\n", + " * Following a monetary contraction, 20% of the drop in aggregate consumption is due to the decline in house prices.\n", + "* Contractionary shocks yield a larger response of all variables than expansionary shocks.\n", + "* Monetary policy more effective in stimulating the economy in high-LTV environment.\n", + " * High-LTV environment implies a wider distribution of MPC, with more HHs having high MPCs.\n", + "\n", + "**Model:**\n", + "* Builds on HANK\n", + "* Infinitely lived households\n", + "* Time is discrete\n", + "* Uninsurable labor income risk\n", + "* This model also features endogenous liquidity of the housing market and house prices.\n", + "* Long-term mortgages, with refinancing allowed\n", + "* Price rigidities due to monopolistically competitive producers -- Rotemberg costs\n", + "* Directed search and block-recursive structure\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Housing Prices and Consumer Spending: The Bank Balance Sheet Channel\n", + "### \n", + "\n", + "\n", + "* Studies the extent to which the deterioration of bank balance sheets explains the large contraction in house prices and consumption.\n", + "\n", + "* **Introduces Banking Sector with balance sheet frictions** into a model of long-term collateralized debt with risk of default.\n", + " * Credit supply endogenous – determined by capitalization of the entire banking sector.\n", + "* When banks poorly capitalized\n", + " * Mortgage spreads increase\n", + " * Endogenous down payments increase\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Transmission of Monetary Policy to Consumption and Population Aging\n", + "### \n", + "\n", + "* Develop a life-cycle model with fixed rate mortgages that shows a higher responsiveness of younger people to interest rate shocks.\n", + "* The mortgage channel accounts for a sizable share of the young-old difference in response.\n", + "* Under an older demographic structure, aggregate consumption is less responsive to MP shocks.\n", + "\n", + "#### Key model features\n", + "* Household model of housing and mortgage decisions.\n", + "* Exogenous idiosyncratic and aggregate shocks.\n", + " * Shock processes generate dynamics that resemble business cycle fluctuations in the data.\n", + " * Allows the author to examine the HH's policy decisions in an environment with realistic dynamics in prices and aggregate variables, while preserving the HH heterogeneity in income and mortgages.\n", + "* Key features:\n", + " 1. HH pay a fixed cost to adjust their long-term assets. These fixed costs are paid when entering a new loan or refinancing an existing mortgage structure.\n", + " 2. Fixed mortgage structure. Mortgage rate is fixed unless the individual refinances their loan. The balance of the loan is amortized over the life of the individual.\n", + "* Model useful for separating the refinancing channel from other potential mechanisms, such as income volatility and liquidity constraints, which may be correlated with the HH's loan adjustment decisions.\n", + "* 3 types of assets:\n", + " * 1-period asset with a short-term borrowing constraint\n", + " * Long-term mortgage at a fixed interest rate\n", + " * Unit of housing at price $p_t$\n", + " * Depreciates at $\\delta$\n", + " * Rental rate $p_t^r$.\n", + "* Rental housing can be freely adjusted each period.\n", + "* Lump-sum transaction cost $\\mathcal{F}$ when a HH enters a new loan or refinances an existing mortgage.\n", + "* Minimum equity requirement, $b_{jat} \\leq (1-\\phi)p_t h_{jat}$, where $\\phi$ is the minimum down payment or equity that must be held in the house.\n", + "* Income:\n", + " * $\\log(y_{jat}) = \\chi_a + \\eta_{jat} + \\phi_a(y_t)$\n", + " * $\\chi_a$ deterministic (age-specific)\n", + " * $\\eta_{jat} = \\rho_{\\eta} \\eta_{j,a-1,t-1} + \\phi_{jt}$, where $\\phi_{jt}$ is i.i.d shock drawn from $\\mathcal{N}(0,\\sigma^2_{\\eta})$\n", + " * $\\phi_a(y_t)$ captures age-specific fluctuations to income that arise from aggregate shocks to the aggregate income in the economy.\n", + "* Aggregate shocks to the economy\n", + " * $S_t \\equiv \\{ \\log(y_t), \\log(p_t), r_t \\}$\n", + " * $S_t = A_0 + A_1 S_{t-1} + u_t$\n", + "* Mortgage rate a function of aggregate state, $S_t$.\n", + "* Rental rate a function of aggregate state, $S_t$.\n", + "* Household's state variable $z=\\{a,S,y,\\text{assets} \\}$, where $a$ denotes age, $S$ and $y$ are the aggregate state and the idiosyncratic labor income realizations, respectively.\n", + " * $\\text{assets} = \\{s,h^{own},b,R \\}$ is a vector of start-of-period holding of short-term assets ($s$), housing owned ($h^{own}$), mortgage balance ($b$), and fixed rate on existing mortgage ($R$).\n", + "\n", + "#### Calibration\n", + "* Model period is annual.\n", + "* $\\beta$ and $\\alpha$ estimated to target the homeownership rate and the total (non-retirement) wealth-to-income ratio for the working age of 2.3 from SCF 2007.\n", + " * $\\beta=0.962$ and $\\alpha=0.88$.\n", + "* Fixed transaction cost $\\mathcal{F}$ is calibrated to target the average annual fraction of loans that are refinanced.\n", + " * Freddie Mac's data to obtain quarterly refinancing fraction of 4.5% over 1999-2007.\n", + " * $\\mathcal{F}=\\$5,000$, which is 2.8% of median house price in the model.\n", + "* **Initialize HHs in the model to match the distribution of income, liquid wealth net of debt, and housing for 25-30-year-old HHs in the SCF.**\n", + "* **Income**\n", + " * $\\eta_{jat}$ parameters set to match the annual persistence and standard deviation of residual earnings in the PSID.\n", + " * *Process is discretized with **2 states** using the **Tauchen** method.*\n", + " * $\\phi_a$ based on the correlation between real aggregate income per capita and age-specific earnings in the CPS. (Young workers exposed more to aggregate shocks.)\n", + "* $A_0$ and $A_1$ set exogenously based on estimated coefficients from a reduced-form quarterly VAR of the variables in $S_t$ over the period 1984--2007.\n", + " * Aggregate processes are discretized with **18 states** using the **Tauchen** method.\n", + "* Mortgage yield curve modeled as a linear function of the current aggregate short-term interest rate and aggregate economic activity. Allows capturing, in a reduced form way, changes in term and risk premia arising from shocks to the aggregate economy, without introducing additional states into the computation of the model.\n", + " * $r_t^d = a_0 + a_1 r_t +a_2 \\log(y_t)$, where $r_t^d$ denotes the mortgage rate of duration $d$, $r_t$ denotes the short-term interest rate, and $y_t$ denotes the real per-capita aggregate income.\n", + "* $\\phi=0.2$, so 20% down-payment requirement.\n", + "* No short-term borrowing.\n", + "* House price-to-rent ratio is assumed to depend on the aggregate state, $S_t$, contemporaneously and its parameters are estimated using:\n", + " * $\\log(p_t^r) = \\alpha_0 + \\alpha_1 r_t + \\alpha_2 \\log(y_t) + \\alpha_3 \\log(p_t)$\n", + "\n", + "#### Results\n", + "* Model matches life-cycle features of:\n", + " * Non-durable consumption\n", + " * HH debt ratios\n", + " * HH wealth-to-income\n", + "* **Monetary Policy Experiment** to quantify the difference in response of young/old due to the **refinancing channel** and the **home-ownership channel**.\n", + " * Younger people have higher consumption response.\n", + " * They also have a higher likelihood of refinancing.\n", + " * Responses indistinguishable from the empirical estimates.\n", + "* With variable rate mortgages, the aggregate response to MP shocks increases by 2.8 times and the cross-sectional heterogeneity is 50% less.\n", + "* Population aging can reduce the responsiveness to monetary policy shocks.\n", + "\n", + "#### Data/Computational Limitation\n", + "* Data is not sufficiently rich to completely rule out other potential mechanisms that affect consumption.\n", + " * ***For instance, the CEX data has sparse information on short-term financial asset holdings and does not have high frequency labor income data.***\n", + "* Does not provide estimates of the variance-covariance matrix of the residuals in the aggregate state equation.\n", + "* Interest rate is set exogenously, based on the aggregate state variable.\n", + " * Response of interest rate shocks to the residuals of the aggregate state process are also set exogenously in a reduced-form estimation.\n", + "* 18 grid points for aggregate state variable $S_t$.\n", + "* Value functions approximated as multilinear functions in the states.\n", + " * 20 knots for $h_{jat}^o$ and $b_{jat}$ and 10 knots for $s_{jat}$ and $r_{jat}$.\n", + " * Knots spaced more closely together near the constraints for $b_{jat}$ and $s_{jat}$.\n", + " * **Are 10 knots for $s_{jat}$ enough, since the younger HHs are going to be exactly where there is the most curvature?**\n", + " * Optimal policies computed using a Nelder-Meade algorithm.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Housing, Debt, and the Marginal Propensity to Consume \n", + "### \n", + "\n", + "* Analyze how housing and mortgage debt affect households' marginal propensity to consume out of wealth.\n", + "* Use detailed HH-level Norwegian registry data to show that after controlling for wealth, HHs with higher leverage respond more to wealth changes.\n", + "* Build a structural lifecycle model to show that MPC out of wealth for new homeowners is higher because of high leverage.\n", + " * Hence, total wealth is not a sufficient statistic.\n", + "* Model successfully targets the life cycle profiles of HH balance sheets in the micro data.\n", + "\n", + "####Relevant papers\n", + "\n", + "\n", + "#### Key model features\n", + "* Finite-horizon life cycle model.\n", + "* HHs identical in preferences and their expectations about the future.\n", + "* 3 asset classes:\n", + " * Housing\n", + " * Debt\n", + " * Other financial assets\n", + "* HHs face uninsurable income risks and borrowing constraints.\n", + " * Permanent and transitory component depend on age.\n", + "* HHs choose between renting and owning a home.\n", + "* Transaction costs associated with buying and selling the house.\n", + " * These make homeowners move infrequently.\n", + "* 3 constraints:\n", + " * Unsecured borrowing constraint (depends on permanent income)\n", + " * LTV constraint\n", + " * Loan-to-income constraint.\n", + "* **No distinction between mortgage debt and short-term debt.**\n", + "* Transaction costs and collateral constraint make housing illiquid.\n", + "* Bequest motive.\n", + "* **No house prices.**\n", + "\n", + "#### Calibration\n", + "* External calibration for:\n", + " * transaction costs,\n", + " * the deterministic component of income,\n", + " * age-varying labor income risk,\n", + " * Initial wealth distribution.\n", + "* Internal calibration for:\n", + " * CRRA\n", + " * Discount factor\n", + " * Weight on housing consumption\n", + " * Service flow from housing consumption\n", + " * Weight on bequest\n", + "* Targets\n", + " * Age profiles of median net worth and median housing in the data\n", + " * Distribution of housing across HHs\n", + "\n", + "#### Results\n", + "* Empirical results:\n", + " * Impute consumption data using the residual of disposable income and savings.\n", + " * Relationship between leverage and consumption responses to wealth changes holds at a disaggregated HH level even in a more tranquil environment than the one studied in Mian, Rao, and Sufi (2013).\n", + " * By aggregating the data they find that the role of leverage is not simply due to preference heterogeneity.\n", + "* Structural model results:\n", + " * The combination of proximity to the borrowing constraint and high transaction costs for new homeowners raises their MPC out of wealth.\n", + " * HHs MPC does not monotonically decrease in wealth.\n", + " * A recent home buyer has a higher MPC than she had immediately before buying the house.\n", + " * Households with larger houses have higher debt $\\implies$ have higher MPC than those with smaller balance sheets.\n", + " * *HHs with higher leverage respond more to wealth changes, and thus when wealth declines they would optimally choose to de-lever more than others.*\n", + " * Model generates heterogeneous balance sheets because of carefully modeling the heterogeneity in housing choices.\n", + " * The source of balance sheet heterogeneity helps to account for the empirically observed link between leverage and HHs' heterogeneous consumption responses to wealth changes.\n", + " * Experiment of decreasing LTV:\n", + " * Reduces housing transactions;\n", + " * Increases consumption by around 1%.\n", + " * Lower debt for young and higher debt for older HHs.\n", + " * Average leverage in the economy is unaffected.\n", + " * Different LTVs do not have very different marginal sensitivities of consumption to wealth changes.\n", + " * Distribution of wealth in the economy does not change under different LTVs.\n", + " * Under low LTV the distribution of leverage shifts to the left.\n", + "\n", + "#### Data/Computational Limitation\n", + "* Computational limitations lead to mortgage being modeled as short-term debt. Treating it is a long-term debt would require adding an extra state variable.\n", + "* No prices or other aggregate shocks.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    " + ] + } + ], + "metadata": { + "cite2c": { + "citations": { + "6202365/22AQK4AT": { + "URL": "http://www.arlene-wong.com/s/Paper_Jan2018-myb4.pdf", + "author": [ + { + "family": "Wong", + "given": "Arlene" + } + ], + "genre": "working paper", + "id": "6202365/22AQK4AT", + "issued": { + "year": 2018 + }, + "note": "Citation Key: WongMP2018", + "publisher": "Princeton University", + "title": "Transmission of Monetary Policy to Consumption and Population Aging", + "type": "report" + }, + "6202365/7AWGTUBV": { + "author": [ + { + "family": "Garriga", + "given": "Carlos" + }, + { + "family": "Hedlund", + "given": "Aaron" + } + ], + "id": "6202365/7AWGTUBV", + "issued": { + "year": 2018 + }, + "note": "Citation Key: GarrigaHedlund2018 \nbibtex*[volume=]", + "title": "Housing Finance, Boom-Bust Episodes, and Macroeconomic Fragility", + "type": "report" + }, + "6202365/EAURCTHD": { + "DOI": "10.1093/restud/rdx060", + "author": [ + { + "family": "Berger", + "given": "David" + }, + { + "family": "Guerrieri", + "given": "Veronica" + }, + { + "family": "Lorenzoni", + "given": "Guido" + }, + { + "family": "Vavra", + "given": "Joseph" + } + ], + "container-title": "Review of Economic Studies", + "id": "6202365/EAURCTHD", + "issue": "85", + "issued": { + "year": 2018 + }, + "note": "Citation Key: BergerEtAl2018", + "page": "1502-1542", + "page-first": "1502", + "title": "House Prices and Consumer Spending", + "type": "article-journal" + }, + "6202365/KABXIQRL": { + "URL": "http://home.uchicago.edu/~nunopaixao/files/paper.pdf", + "author": [ + { + "family": "Paixao", + "given": "Nuno" + } + ], + "genre": "working paper", + "id": "6202365/KABXIQRL", + "issued": { + "year": 2018 + }, + "note": "Citation Key: Paixao2018", + "publisher": "Bank of Canada", + "title": "Housing Prices and Consumer Spending: The Bank Balance Sheet Channel", + "type": "report" + }, + "6202365/PM9X2PEX": { + "author": [ + { + "family": "Hedlund", + "given": "Aaron" + }, + { + "family": "Karahan", + "given": "Fatih" + }, + { + "family": "Mitman", + "given": "Kurt" + }, + { + "family": "Ozkan", + "given": "Serdar" + } + ], + "id": "6202365/PM9X2PEX", + "issued": { + "year": 2016 + }, + "note": "Citation Key: HedlundEtAl2016 \nbibtex*[volume=] \nDOI:", + "title": "Monetary Policy, Heterogeneity, and the Housing Channel", + "type": "report" + }, + "6202365/S3BVJTND": { + "DOI": "10.1093/qje/qjx005", + "author": [ + { + "family": "Guerrieri", + "given": "Veronica" + }, + { + "family": "Lorenzoni", + "given": "Guido" + } + ], + "container-title": "The Quarterly Journal of Economics", + "id": "6202365/S3BVJTND", + "issued": { + "year": 2017 + }, + "note": "Citation Key: GuerrieriLorenzoni2017", + "page": "1427-1467", + "page-first": "1427", + "title": "Credit Crises, Precautionary Savings, and the Liquidity Trap", + "type": "article-journal" + }, + "6202365/VTRHJVRS": { + "DOI": "https://doi.org/10.1016/bs.hesmac.2016.04.003", + "abstract": "The goal of this chapter is study how, and by how much household income, wealth and preference heterogeneity amplifies and propagates a macroeconomic shock. We focus on the U.S. Great Recession of 2007-2009 and proceed in two steps. First, using data from the Panel Study of Income Dynamics, we document the patterns of household income, consumption and wealth inequality before and during the Great Recession. We then investigate how households in different segments of the wealth distribution were affected by income declines, and how they changed their expenditures differentially during the aggregate downturn. Motivated by this evidence we study several variants of a standard heterogeneous household model with aggregate shocks and an endogenous cross-sectional wealth distribution. Our key model finding is that wealth inequality can significantly amplify the impact of an aggregate shock, but it does so if (and only if) the distribution features a sufficiently large fraction of households with very little net worth, as is empirically observed in the PSID. We also investigate the role social insurance policies, such as unemployment insurance, play for shaping the cross-sectional income and wealth distribution, and through it, the dynamics of business cycles.", + "author": [ + { + "family": "Krueger", + "given": "Dirk" + }, + { + "family": "Mitman", + "given": "Kurt" + }, + { + "family": "Perri", + "given": "Fabrizio" + } + ], + "container-title": "Handbook of Macroeconomics", + "id": "6202365/VTRHJVRS", + "issued": { + "year": 2016 + }, + "language": "en", + "page": "86", + "page-first": "86", + "title": "Macroeconomics and Household Heterogeneity", + "type": "article-journal", + "volume": "2" + }, + "6202365/Y5E7ZLQ9": { + "URL": "http://www.econ2.jhu.edu/jobmarket/2015/YaoJ/JobPaper/JobPaperYaoJ.pdf", + "author": [ + { + "family": "Yao", + "given": "Jiaxiong" + }, + { + "family": "Fagereng", + "given": "Andreas" + }, + { + "family": "Natvik", + "given": "Gisle" + } + ], + "genre": "working paper", + "id": "6202365/Y5E7ZLQ9", + "issued": { + "year": 2015 + }, + "note": "Citation Key: YaoEtAl2015", + "title": "Housing, Debt, and the Marginal Propensity to Consume", + "type": "report" + } + } + }, + "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" + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/models/We-Would-Like-In-Econ-ARK.ipynb b/models/We-Would-Like-In-Econ-ARK.ipynb index 33e6c02f..d8971ca1 100644 --- a/models/We-Would-Like-In-Econ-ARK.ipynb +++ b/models/We-Would-Like-In-Econ-ARK.ipynb @@ -838,7 +838,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.7.3" }, "varInspector": { "cols": { diff --git a/models/We-Would-Like-In-Econ-ARK/.DS_Store b/models/We-Would-Like-In-Econ-ARK/.DS_Store new file mode 100644 index 0000000000000000000000000000000000000000..baaa5df0ea4a1e61651a93acfc1c3b404283a8cb GIT binary patch literal 10244 zcmeHM%}*0S6o1QywBko4DBj$IMq^EC-`xW;64)v+rZxZ{ED!nG%r}uVkV`IuV6X z8I2r6)1t8FtTvSnujeAD26-Zr3|gWzy)5cn4mz&o3jP_Ii> zs}N8KC7E-G8*$}&80kbpy68p&@OcIf_v-(xQy=6m`7_a<)YB(?jAHxRP(kN znk$ayI%5Zod9>zISDZ9goHWm}=Iu~4ZXI$uXD2P@Qq?L16avi%u)TX9U7>Ia3m-!u zT}IU|dAhzBr9$3zhKIju9i3g>M|wixa438{{3MyPs!1p1RP1=F{D}X`XR?NOKW|xu z`hCh+$Y-ldk^TwGbW(XUTNc0<>ibGG1^ zucp@{q?~5&wUFTb37VoAT=%hb7rB-K^yX+D`c@lcKfyZ@xwf(rf?eNJkZsG~0?9w{ z3n|P+zAe9mY&V-II*r6NLrKZ+1Q4`=0K?Y+>K^7TkPs7B08NKAZ3Tcp3XRD4+h9{6 z1j=5@31C}ThzF3Cf+)h@e*tVaB&z|si}0JpnZAucE8^nmiY{X*TKtP4Dt;fj6U|IlEq~=jAQ_M#I(@My;`6+G+6K| z4h>jREu_Tp`$$Q#vVHy`Z254uhznoNdg|DV0Uu6jzIWze9MyK00gwIL^2VF;NF=}qYie~uA?ravcmXkF6AO<_;EZaKaR%_b{s#5%6NwvWd-*! ikJem@9+bcTX8=DtkUrei{=a^bp!WZ!6dH$e|Nk4$vmE09 literal 0 HcmV?d00001 diff --git a/models/We-Would-Like-In-Econ-ARK/JKM_summary-Copy1.ipynb b/models/We-Would-Like-In-Econ-ARK/JKM_summary-Copy1.ipynb new file mode 100644 index 00000000..aa876c03 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/JKM_summary-Copy1.ipynb @@ -0,0 +1,74 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jeske, Krueger and Mitman" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## \"[Housing, mortgage bailout guarantees and the macroeconomy](https://www.sciencedirect.com/science/article/abs/pii/S0304393213001219)\" (2013)\n", + "\n", + "- Notebook is prepared by Yusuf Suha Kulu" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Summary\n", + "The article uses a model with heterogeneous, infinitely lived households to understand the macroeconomic and distributional effects of government bailout guarantees for Government Sponsored Enterprises?\n", + "\n", + "The main findings are as follows: \n", + "\n", + "- Eliminating the bailout guarantee leads to a large decline in mortgage origination and increases aggregate welfare by 0.5% in comsumption equivalent variation but has little effect on foreclosure rates and housing investment.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Overview\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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 +} diff --git a/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb new file mode 100644 index 00000000..be9b59a8 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/JKM_summary.ipynb @@ -0,0 +1,199 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jeske, Krueger and Mitman" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## \"[Housing, mortgage bailout guarantees and the macroeconomy](https://www.sciencedirect.com/science/article/abs/pii/S0304393213001219)\" (2013)\n", + "\n", + "- Notebook is prepared by Yusuf Suha Kulu" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Summary\n", + "The article uses a model with heterogeneous, infinitely lived households to understand the macroeconomic and distributional effects of government bailout guarantees for Government Sponsored Enterprises (GSE)\n", + "\n", + "The main findings are as follows: \n", + "\n", + "- Eliminating the bailout guarantee leads to a large decline in mortgage origination and increases aggregate welfare by 0.5% in comsumption equivalent variation but has little effect on foreclosure rates and housing investment.\n", + "\n", + "- Bailout guarantee hurts low income and low asset households.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Overview\n", + "\n", + "#### Tax financed mortgage interest rate subsidy\n", + "\n", + "The baiolout guarantees are modeled as the tax financed interest rate subsidy because prior to the bailout of the GSEs, they could borrow at interest rates close to that on U.S government debt, despite the fact that they were heavily exposed to aggregate house price risk. The absence of risk premium can be attributed to implicit government bailout guarantee.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Model \n", + "\n", + "- Heterogeneous agent general equilibrium model with incomplete markets in the tradition of Bewley(1986), Huggett(1993), and Aiyagari(1994).\n", + "\n", + "#### Households \n", + "- U(c,h) where c is nondurable consumption c and h is housing services.\n", + "- Endowment and (labor) income are used interchangeably. Households receive idiosynratic endowments which follow a finite state Markov chain $\\pi$(y'|y) and unique invariant distribution $\\Pi$(y).\n", + "- Two types of assets: \n", + " - b' one period bonds with price $P_{b}$ \n", + " - g' perfectly divisible houses with price $P_{h}$. Houses are risky assets which are subject to idiosynratic house price shocks. F($\\delta$') cdf of house price depreciation rate $\\delta$' tomorrow with support D = [$\\underline{\\delta}$,1] where $\\underline{\\delta}$ $\\leq$ 0 which represents house value appreciation.\n", + "- Mortgages: Households can borrow againts their real estate position using one period martgage debt. m' denote the size of the mortgage with price $P_{m}$. The price is determined by competition of banks through a zero profit condition. The gross mortgage interest rate is $R_{m}$ = $\\frac{1}{P_m}$\n", + "- Households choose to default whenever the amount owed in the mortgage is greater than the value of the house after the realization of the price shock.\n", + "- Recursive Formulation:\n", + "\n", + "\\begin{equation*}\n", + " v(a,y) = max_{c,h,b',m'g' \\geq 0} \\bigg(U(c,h) + \\beta \\sum_{y'} \\pi(y'|y) \\int_{\\underline{\\delta}}^1v(a',y')dF(\\delta') \\bigg) \n", + "\\end{equation*}\n", + "\n", + " s.t \n", + "\n", + "\\begin{equation*}\n", + " c + b'P_b + hP_l + g'P_h - m'P_m(g',m') = a + g'P_l \n", + "\\end{equation*}\n", + "\n", + "\\begin{equation*}\n", + " a'(\\delta',y',m',g') = b' + max \\big(0,P_h(1-\\delta')g' - m'\\big) + (1-\\tau)y' \\\\\n", + "\\end{equation*}\n", + "\n", + "\n", + "\n", + "#### The Real Estate Construction Sector\n", + "- Reversibility of the technology: Real estate companies can turn houses into consumption goods\n", + "\n", + "\\begin{equation*}\n", + " max P_hI - C_h \n", + "\\end{equation*}\n", + "\n", + " s.t \n", + " \n", + "\\begin{equation*} \n", + " I=C_h \n", + "\\end{equation*}\n", + "\n", + "where I is the output (houses) and $C_{h}$ is the input of the consumption good\n", + "\n", + "- The equilibrium house price is \n", + "\n", + "\\begin{equation*}\n", + " P_h=1\n", + "\\end{equation*}\n", + "\n", + "#### The banking sector \n", + "- Effective cost of the banking sector for financing one dollar of mortgage equals (1 + $r_{b}$)(1 + $r_{w}$ + $\\theta$ - $\\phi$) where $\\phi$ is the is the mortgage subsidy, $\\theta$ is the cost of insurance, $r_{w}$ is the percentage real resource cost to the bank and $r_{b}$ equal to \n", + "\n", + "\\begin{equation*}\n", + " P_b = \\frac{1}{1+r_b}\n", + "\\end{equation*}\n", + "\n", + "- Let $\\delta^*$(m',g') be cutoff level of household depreciation at which household is indifferent between defaulting and not defaulting on her mortgage. \n", + "- A bank will originate a mortgage if and only if \n", + "\n", + "\\begin{equation*}\n", + " m'P_m(g',m') \\leq \\frac{1}{(1 + r_b)(1 + r_w + \\theta - \\phi)} \\bigg( m'F(\\delta^*(m',g')) + \\gamma g' \\int_{\\delta^*(m',g')}^1 (1-\\delta')dF(\\delta') \\bigg)\n", + "\\end{equation*}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Results\n", + "\n", + "#### Comparison of steady state equilibria of economies with and without a tax financed mortgage interest rates subsidy of 30 basis points\n", + "\n", + "- Removing subsidy make mortgages less attractive by increasing the effective interest rate\n", + " - Households with low levels of cash in hand do not respond much to the change in interest rate subsidy.\n", + " - For wealthier households, the change in policy induces a massive reduction in leverage, and thus substantial reduction in mortgage debt.\n", + "- Thus, households shifts away from bonds toward home equity. Median household was holding 60.7$%$ of its net worth in bonds with subsidy reduces to 5.8$%$ without subsidy." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import Image\n", + "imgUrl = 'results.png' # setup path and filename\n", + "img = Image(url=imgUrl) # create the image object\n", + "img # display the image" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + 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