From e370f699dc81921b8f41cdf8fc720f1e0277fe82 Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Wed, 18 Sep 2019 21:55:32 -0400 Subject: [PATCH 01/17] Create Untitled.ipynb --- .../We-Would-Like-In-Econ-ARK/Untitled.ipynb | 212 ++++++++++++++++++ 1 file changed, 212 insertions(+) create mode 100644 models/We-Would-Like-In-Econ-ARK/Untitled.ipynb diff --git a/models/We-Would-Like-In-Econ-ARK/Untitled.ipynb b/models/We-Would-Like-In-Econ-ARK/Untitled.ipynb new file mode 100644 index 00000000..2ae33480 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/Untitled.ipynb @@ -0,0 +1,212 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Optimal Life-Cycle Asste Allocation: Understanding the Empirial Evidence\n", + "\n", + "- Authors: Francisco Gomes and Alexander Michaelides\n", + "- Notebook by Zixuan Huang\n", + "- 2019 Fall" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Abstract\n", + "\n", + "- The paper finds a way to match stock market participation rates and asste allocation decisions conditional on participation, by using a life-cycle model with uninsurable labor income risk and moderate risk aversion, where the labor income risk is **idiosyncratic** and the degree of risk aversion is **heterogenous**. \n", + "- They found that households with low risk aversion smooth earnings shocks with a small buffer stock of assets, and consequently most of them never invest in equities. Endogously, stockholders are more risk averse, but they still do not invest their portfolios fully in stocks." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Empiral Evidence\n", + "\n", + "- In most industrialzed countries, stock market participation rates have increased substantially. A large share of population, however, still do not own stocks either directly or indirectly (through pension funds etc.) \n", + "> In U.S., the stock market participation rate is close to 50%.\n", + "\n", + "- Even for those households who do own stocks, a significant proportion of their portfilios are not in stock. \n", + "> Conditional on stock market participation, the average equity holdings as a share of financial wealth for stock market participation is 54.8%\n", + "\n", + "- Participation rate goes up during working life and might go down during retirement.\n", + "\n", + "- There is no clear pattern of equity holdings over the life cycle. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Preferences\n", + "- Discrete time; agents live for a maximum of age 100; conditional being alive at time t, the probability that a consumer is alive at t+1 is $p_t$.\n", + "- Epstein-Zin utility functions\n", + "> \\begin{align}\n", + "V_t=\\{(1-\\beta p_t) C_t^{1-1/\\varphi}+\\beta E_t[p_t[V_{t+1}^{1-\\rho}]+(1-p_t)b\\frac{(X_{t+1}/b)^{1-\\rho}}{1-\\rho}]^\\frac{1-1/\\varphi}{1-\\rho}\\}^\\frac{1}{1-1/\\varphi} \\label{eq1}\\tag{1}\\\\\n", + "\\end{align}\n", + "- where $\\rho$ is the coefficient of RRA, $\\varphi$ is the EIS, $\\beta$ is the discount factor and $b$ determines the strength of the bequest motive.\n", + "- Given the prescence of a bequest motive, the terminal condition for the recursive equation $(1)$ is:\n", + "> \\begin{align}\n", + "V_{T+1}=b \\frac{(X_{T+1}/b)^{1-\\rho}}{1-\\rho} \\label{eq2}\\tag{2}\\\\\n", + "\\end{align}\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Labor income process\n", + "\n", + "- \\begin{align}\n", + "Y_{it}=P_{it}U_{it} \\label{eq3}\\tag{3}\\\\\n", + "\\end{align}\n", + "\n", + "- \\begin{align} \n", + "P_{it}=exp(f(t,Z_{it})P_{it-1}N_{it}) \\label{eq4}\\tag{4}\\\\\n", + "\\end{align}\n", + "\n", + "- where $f(t,Z_{it})$ is a deterministic function of age and household characteristics $Z_{it}$, $P_{it}$ is a permanent component with innovation $N_{it}$, and $U_{it}$ is a transitory component.\n", + "- Retirement is deterministic and exogenous, with all households retiring at age 65; Earnings in retirement are given by $Y_{it}=\\lambda P_{iK}$, where $K$ denotes the period of retiring, and $\\lambda$ is the replacement ratio (a scalar between zero and one)\n", + "- For each age ($t$), the percentage of household income that is dedicated to housing expenditure ($h_t$) is estimated according to the Panel Study of Income Dynamics and is substracted from the measure of disposal income. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Financial Assets\n", + "- There are two financial assets, one riskless (e.g. Treasury bills, cash) and one risky (stocks). The riskless asset yields a constant gross return, $R^f$, while the return on teh risky asset is given by \n", + "> \\begin{align}\n", + "R_{t+1}^S-R^f=\\mu + \\epsilon_{t+1} \\label{eq5}\\tag{5}\\\\\n", + "\\end{align}\n", + "where $\\epsilon$ follows a normal distribution.\n", + "- The positive correlation between stock returns and earnings shocks is allowed: $\\phi_N$ denotes the correlation coefficient between stock returns and permanent income shocks, while $\\phi_U$ is for tansitory shocks.\n", + "- Before investing in stocks for the first time, the investor must pay for a fixed lump sum cost, $F*P_{it}$. This is scaled by the level of permanent component of labor income as this significantly simplies the solution of the model and also motivated by the interpretation of the entry fee as the opportunity cost of time. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Wealth Accumulation\n", + "\n", + "- Cash on hand is denoted as the liquid resources for consumption and saving; Dummy variable $I_p$ that is equal to one when the fixed entry cost is incurred for the first time and is zero otherwise. The household's next period cash on hand ($X_{i,t+1}$) is given by:\n", + "> \\begin{align}\n", + "X_{i,t+1}=S_{it}R_{t+1}^S+B_{it}R^f+(1-h_t)Y_{i,t+1}-FI_pP_{i,t+1} \\label{eq6}\\tag{6}\\\\\n", + "\\end{align}\n", + "where $S_it$ and $B_{it}$ denote respectively stock holdings and riskless asset holdings at time $t$, and $h_t$ is the fraction of income dedicated to housing-related expenditures. \n", + "\n", + "- Since the households must allocate cash on hand ($X_{it}$) between consumption expenditures and savings, cash on hand is given by:\n", + "> \\begin{align}\n", + "X_{it}=C_{it}+S_{it}+B_{it} \\label{eq7}\\tag{7}\\\\\n", + "\\end{align}\n", + "\n", + "- Borrowings against future labor income is prevented, therefore, the following restictions are imposed: \n", + "> \\begin{align}\n", + "B_{it}\\geq0 \\label{eq8}\\tag{8}\\\\\n", + "\\end{align}\n", + ">\n", + "> \\begin{align}\n", + "S_{it}\\geq0 \\label{eq9}\\tag{9}\\\\\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Optimization\n", + "- The complete optimization problem is \n", + "> \\begin{align}\n", + "max E(V_0) \\label{eq10}\\tag{10}\\\\ \n", + "\\end{align}\n", + "by choosing $(S_{it}, B_{it})_{t=1}^{T}$, where $V_0$ is given by equation(1) and equation(2) and is subject to the constraints given by equstions(5) to (9), and the stochastic labor income process is given by equation(3) and (4)\n", + "\n", + "- The analytical solutions do not exist. Therefore a numerical solution method based on the maximization of the value function to derive the optimal decision rules is used. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Calibration\n", + "- Preference parameters (baseline): $\\rho=5$, $\\varphi=0.2$, $\\beta=0.96$, and $b$=2.5\n", + "\n", + "- Labor income process: $\\sigma_u=0.15$, $\\sigma_n=0.1$\n", + "\n", + "- interest rate: $(R^f-1)=2\\%$; the stock return process: mean equity premium $\\mu=4\\%$ and standard deviation $\\sigma_{\\epsilon}=18\\%$\n", + "\n", + "- correlation between stock returns and income shocks: $\\phi_{N}=0.15$ and $\\phi_{U}=0.0$ for benchmark calibration\n", + "\n", + "- fixed cost: two limit cases: 0 and 2.5% as a share of household's expectated annual income.\n", + "\n", + "- housing expenditure: $h_t=max(A+B_1*age+B_2*age^2+B_3*age^3,0)$, where the parameters are estimated by using the data from the Panel Study of Income Dynamics" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Results" + ] + }, + { + "attachments": { + "image.png": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Consumption and Wealth Accumulation \n", + "- Early in life, households is liquity constrained and saves only a small buffer stock of wealth. \n", + "- Ages 30-35 onwards, households start to save for retirement and bequests, and wealth accumulation increases significantly. \n", + "- During retirement, consumption decreases as a result of the very effective discount rate(high mortality risk). Wealth does not fall towards zero due to the prescence of the bequest motive. \n", + "- ![image.png](attachment:image.png)\n", + "- Given that the holdings of this relatively riskless asset(e.g. overinvestment in human capital--as an implicit riskless assets) are larger in the early part of the life cycle, and that households hold a small fraction of their wealth in cash, all young households participate in the stock market and they allocate most of their financial wealth to stocks. \n", + "- As retirement approaches, and financial wealth increases relative to the present value " + ] + }, + { + "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 203de331e08cfd8b2249de860193c531bb2609af Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Wed, 18 Sep 2019 21:55:39 -0400 Subject: [PATCH 02/17] Update WangT-AHLifeCycleExpenditure.ipynb --- .../AHLifeCycleExpenditure/WangT-AHLifeCycleExpenditure.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/models/We-Would-Like-In-Econ-ARK/AHLifeCycleExpenditure/WangT-AHLifeCycleExpenditure.ipynb b/models/We-Would-Like-In-Econ-ARK/AHLifeCycleExpenditure/WangT-AHLifeCycleExpenditure.ipynb index b8825f07..ef3b668c 100644 --- a/models/We-Would-Like-In-Econ-ARK/AHLifeCycleExpenditure/WangT-AHLifeCycleExpenditure.ipynb +++ b/models/We-Would-Like-In-Econ-ARK/AHLifeCycleExpenditure/WangT-AHLifeCycleExpenditure.ipynb @@ -103,7 +103,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.1" + "version": "3.7.3" } }, "nbformat": 4, From d60bdff9e30b0e1a79da9cbd1df25f14e1f77adf Mon Sep 17 00:00:00 2001 From: zhuang13atJHU <43380704+zhuang13atJHU@users.noreply.github.com> Date: Wed, 18 Sep 2019 21:58:11 -0400 Subject: [PATCH 03/17] Delete Untitled.ipynb --- .../We-Would-Like-In-Econ-ARK/Untitled.ipynb | 212 ------------------ 1 file changed, 212 deletions(-) delete mode 100644 models/We-Would-Like-In-Econ-ARK/Untitled.ipynb diff --git a/models/We-Would-Like-In-Econ-ARK/Untitled.ipynb b/models/We-Would-Like-In-Econ-ARK/Untitled.ipynb deleted file mode 100644 index 2ae33480..00000000 --- a/models/We-Would-Like-In-Econ-ARK/Untitled.ipynb +++ /dev/null @@ -1,212 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Optimal Life-Cycle Asste Allocation: Understanding the Empirial Evidence\n", - "\n", - "- Authors: Francisco Gomes and Alexander Michaelides\n", - "- Notebook by Zixuan Huang\n", - "- 2019 Fall" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Abstract\n", - "\n", - "- The paper finds a way to match stock market participation rates and asste allocation decisions conditional on participation, by using a life-cycle model with uninsurable labor income risk and moderate risk aversion, where the labor income risk is **idiosyncratic** and the degree of risk aversion is **heterogenous**. \n", - "- They found that households with low risk aversion smooth earnings shocks with a small buffer stock of assets, and consequently most of them never invest in equities. Endogously, stockholders are more risk averse, but they still do not invest their portfolios fully in stocks." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Empiral Evidence\n", - "\n", - "- In most industrialzed countries, stock market participation rates have increased substantially. A large share of population, however, still do not own stocks either directly or indirectly (through pension funds etc.) \n", - "> In U.S., the stock market participation rate is close to 50%.\n", - "\n", - "- Even for those households who do own stocks, a significant proportion of their portfilios are not in stock. \n", - "> Conditional on stock market participation, the average equity holdings as a share of financial wealth for stock market participation is 54.8%\n", - "\n", - "- Participation rate goes up during working life and might go down during retirement.\n", - "\n", - "- There is no clear pattern of equity holdings over the life cycle. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Model" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Preferences\n", - "- Discrete time; agents live for a maximum of age 100; conditional being alive at time t, the probability that a consumer is alive at t+1 is $p_t$.\n", - "- Epstein-Zin utility functions\n", - "> \\begin{align}\n", - "V_t=\\{(1-\\beta p_t) C_t^{1-1/\\varphi}+\\beta E_t[p_t[V_{t+1}^{1-\\rho}]+(1-p_t)b\\frac{(X_{t+1}/b)^{1-\\rho}}{1-\\rho}]^\\frac{1-1/\\varphi}{1-\\rho}\\}^\\frac{1}{1-1/\\varphi} \\label{eq1}\\tag{1}\\\\\n", - "\\end{align}\n", - "- where $\\rho$ is the coefficient of RRA, $\\varphi$ is the EIS, $\\beta$ is the discount factor and $b$ determines the strength of the bequest motive.\n", - "- Given the prescence of a bequest motive, the terminal condition for the recursive equation $(1)$ is:\n", - "> \\begin{align}\n", - "V_{T+1}=b \\frac{(X_{T+1}/b)^{1-\\rho}}{1-\\rho} \\label{eq2}\\tag{2}\\\\\n", - "\\end{align}\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Labor income process\n", - "\n", - "- \\begin{align}\n", - "Y_{it}=P_{it}U_{it} \\label{eq3}\\tag{3}\\\\\n", - "\\end{align}\n", - "\n", - "- \\begin{align} \n", - "P_{it}=exp(f(t,Z_{it})P_{it-1}N_{it}) \\label{eq4}\\tag{4}\\\\\n", - "\\end{align}\n", - "\n", - "- where $f(t,Z_{it})$ is a deterministic function of age and household characteristics $Z_{it}$, $P_{it}$ is a permanent component with innovation $N_{it}$, and $U_{it}$ is a transitory component.\n", - "- Retirement is deterministic and exogenous, with all households retiring at age 65; Earnings in retirement are given by $Y_{it}=\\lambda P_{iK}$, where $K$ denotes the period of retiring, and $\\lambda$ is the replacement ratio (a scalar between zero and one)\n", - "- For each age ($t$), the percentage of household income that is dedicated to housing expenditure ($h_t$) is estimated according to the Panel Study of Income Dynamics and is substracted from the measure of disposal income. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Financial Assets\n", - "- There are two financial assets, one riskless (e.g. Treasury bills, cash) and one risky (stocks). The riskless asset yields a constant gross return, $R^f$, while the return on teh risky asset is given by \n", - "> \\begin{align}\n", - "R_{t+1}^S-R^f=\\mu + \\epsilon_{t+1} \\label{eq5}\\tag{5}\\\\\n", - "\\end{align}\n", - "where $\\epsilon$ follows a normal distribution.\n", - "- The positive correlation between stock returns and earnings shocks is allowed: $\\phi_N$ denotes the correlation coefficient between stock returns and permanent income shocks, while $\\phi_U$ is for tansitory shocks.\n", - "- Before investing in stocks for the first time, the investor must pay for a fixed lump sum cost, $F*P_{it}$. This is scaled by the level of permanent component of labor income as this significantly simplies the solution of the model and also motivated by the interpretation of the entry fee as the opportunity cost of time. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Wealth Accumulation\n", - "\n", - "- Cash on hand is denoted as the liquid resources for consumption and saving; Dummy variable $I_p$ that is equal to one when the fixed entry cost is incurred for the first time and is zero otherwise. The household's next period cash on hand ($X_{i,t+1}$) is given by:\n", - "> \\begin{align}\n", - "X_{i,t+1}=S_{it}R_{t+1}^S+B_{it}R^f+(1-h_t)Y_{i,t+1}-FI_pP_{i,t+1} \\label{eq6}\\tag{6}\\\\\n", - "\\end{align}\n", - "where $S_it$ and $B_{it}$ denote respectively stock holdings and riskless asset holdings at time $t$, and $h_t$ is the fraction of income dedicated to housing-related expenditures. \n", - "\n", - "- Since the households must allocate cash on hand ($X_{it}$) between consumption expenditures and savings, cash on hand is given by:\n", - "> \\begin{align}\n", - "X_{it}=C_{it}+S_{it}+B_{it} \\label{eq7}\\tag{7}\\\\\n", - "\\end{align}\n", - "\n", - "- Borrowings against future labor income is prevented, therefore, the following restictions are imposed: \n", - "> \\begin{align}\n", - "B_{it}\\geq0 \\label{eq8}\\tag{8}\\\\\n", - "\\end{align}\n", - ">\n", - "> \\begin{align}\n", - "S_{it}\\geq0 \\label{eq9}\\tag{9}\\\\\n", - "\\end{align}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Optimization\n", - "- The complete optimization problem is \n", - "> \\begin{align}\n", - "max E(V_0) \\label{eq10}\\tag{10}\\\\ \n", - "\\end{align}\n", - "by choosing $(S_{it}, B_{it})_{t=1}^{T}$, where $V_0$ is given by equation(1) and equation(2) and is subject to the constraints given by equstions(5) to (9), and the stochastic labor income process is given by equation(3) and (4)\n", - "\n", - "- The analytical solutions do not exist. Therefore a numerical solution method based on the maximization of the value function to derive the optimal decision rules is used. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Calibration\n", - "- Preference parameters (baseline): $\\rho=5$, $\\varphi=0.2$, $\\beta=0.96$, and $b$=2.5\n", - "\n", - "- Labor income process: $\\sigma_u=0.15$, $\\sigma_n=0.1$\n", - "\n", - "- interest rate: $(R^f-1)=2\\%$; the stock return process: mean equity premium $\\mu=4\\%$ and standard deviation $\\sigma_{\\epsilon}=18\\%$\n", - "\n", - "- correlation between stock returns and income shocks: $\\phi_{N}=0.15$ and $\\phi_{U}=0.0$ for benchmark calibration\n", - "\n", - "- fixed cost: two limit cases: 0 and 2.5% as a share of household's expectated annual income.\n", - "\n", - "- housing expenditure: $h_t=max(A+B_1*age+B_2*age^2+B_3*age^3,0)$, where the parameters are estimated by using the data from the Panel Study of Income Dynamics" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Results" - ] - }, - { - "attachments": { - "image.png": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Consumption and Wealth Accumulation \n", - "- Early in life, households is liquity constrained and saves only a small buffer stock of wealth. \n", - "- Ages 30-35 onwards, households start to save for retirement and bequests, and wealth accumulation increases significantly. \n", - "- During retirement, consumption decreases as a result of the very effective discount rate(high mortality risk). Wealth does not fall towards zero due to the prescence of the bequest motive. \n", - "- ![image.png](attachment:image.png)\n", - "- Given that the holdings of this relatively riskless asset(e.g. overinvestment in human capital--as an implicit riskless assets) are larger in the early part of the life cycle, and that households hold a small fraction of their wealth in cash, all young households participate in the stock market and they allocate most of their financial wealth to stocks. \n", - "- As retirement approaches, and financial wealth increases relative to the present value " - ] - }, - { - "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 eba006c6cfc642def986c9963f1f9f48d2fed998 Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Thu, 19 Sep 2019 11:25:49 -0400 Subject: [PATCH 04/17] Create GMLifeCylceInvestment.ipynb Add model, results and comments --- .../GMLifeCylceInvestment.ipynb | 215 ++++++++++++++++++ 1 file changed, 215 insertions(+) create mode 100644 models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb diff --git a/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb b/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb new file mode 100644 index 00000000..b2377cb1 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb @@ -0,0 +1,215 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Optimal Life-Cycle Asste Allocation: Understanding the Empirial Evidence\n", + "\n", + "- Authors: Francisco Gomes and Alexander Michaelides\n", + "- Notebook by Zixuan Huang\n", + "- 2019 Fall" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Abstract\n", + "\n", + "- The paper finds a way to match stock market participation rates and asste allocation decisions conditional on participation, by using a life-cycle model with uninsurable labor income risk and moderate risk aversion, where the labor income risk is **idiosyncratic** and the degree of risk aversion is **heterogenous**. \n", + "- They found that households with low risk aversion smooth earnings shocks with a small buffer stock of assets, and consequently most of them never invest in equities. Endogously, stockholders are more risk averse, but they still do not invest their portfolios fully in stocks." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Empiral Evidence\n", + "\n", + "- In most industrialzed countries, stock market participation rates have increased substantially. A large share of population, however, still do not own stocks either directly or indirectly (through pension funds etc.) \n", + "> In U.S., the stock market participation rate is close to 50%.\n", + "\n", + "- Even for those households who do own stocks, a significant proportion of their portfilios are not in stock. \n", + "> Conditional on stock market participation, the average equity holdings as a share of financial wealth for stock market participation is 54.8%\n", + "\n", + "- Participation rate goes up during working life and might go down during retirement.\n", + "\n", + "- There is no clear pattern of equity holdings over the life cycle. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model\n", + "\n", + ">**Key features: Fixed entry cost; Epstein-Zin utility function; Preference heterogeneity**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Preferences\n", + "- Discrete time; agents live for a maximum of age 100; conditional being alive at time t, the probability that a consumer is alive at t+1 is $p_t$.\n", + "- Epstein-Zin utility functions\n", + "> \\begin{align}\n", + "V_t=\\{(1-\\beta p_t) C_t^{1-1/\\varphi}+\\beta E_t[p_t[V_{t+1}^{1-\\rho}]+(1-p_t)b\\frac{(X_{t+1}/b)^{1-\\rho}}{1-\\rho}]^\\frac{1-1/\\varphi}{1-\\rho}\\}^\\frac{1}{1-1/\\varphi} \\label{eq1}\\tag{1}\\\\\n", + "\\end{align} where $\\rho$ is the coefficient of RRA, $\\varphi$ is the EIS, $\\beta$ is the discount factor and $b$ determines the strength of the bequest motive.\n", + "- Given the prescence of a bequest motive, the terminal condition for the recursive equation $(1)$ is:\n", + "> \\begin{align}\n", + "V_{T+1}=b \\frac{(X_{T+1}/b)^{1-\\rho}}{1-\\rho} \\label{eq2}\\tag{2}\\\\\n", + "\\end{align}\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Labor income process\n", + "\n", + "- \\begin{align}\n", + "Y_{it}=P_{it}U_{it} \\label{eq3}\\tag{3}\\\\\n", + "\\end{align}\n", + "\n", + "- \\begin{align} \n", + "P_{it}=exp(f(t,Z_{it})P_{it-1}N_{it}) \\label{eq4}\\tag{4}\\\\\n", + "\\end{align}\n", + "\n", + "- where $f(t,Z_{it})$ is a deterministic function of age and household characteristics $Z_{it}$, $P_{it}$ is a permanent component with innovation $N_{it}$, and $U_{it}$ is a transitory component.\n", + "- Retirement is deterministic and exogenous, with all households retiring at age 65; Earnings in retirement are given by $Y_{it}=\\lambda P_{iK}$, where $K$ denotes the period of retiring, and $\\lambda$ is the replacement ratio (a scalar between zero and one)\n", + "- For each age ($t$), the percentage of household income that is dedicated to housing expenditure ($h_t$) is estimated according to the Panel Study of Income Dynamics and is substracted from the measure of disposal income. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Financial Assets\n", + "- There are two financial assets, one riskless (e.g. Treasury bills, cash) and one risky (stocks). The riskless asset yields a constant gross return, $R^f$, while the return on teh risky asset is given by \n", + "> \\begin{align}\n", + "R_{t+1}^S-R^f=\\mu + \\epsilon_{t+1} \\label{eq5}\\tag{5}\\\\\n", + "\\end{align}\n", + "where $\\epsilon$ follows a normal distribution with mean 0 and standard devitation $\\sigma_{\\epsilon}^2$.\n", + "- The positive correlation between stock returns and earnings shocks is allowed: $\\phi_N$ denotes the correlation coefficient between stock returns and permanent income shocks, while $\\phi_U$ is for tansitory shocks.\n", + "- Before investing in stocks for the first time, the investor must pay for a fixed lump sum cost, $F*P_{it}$. This is scaled by the level of permanent component of labor income as this significantly simplies the solution of the model and also motivated by the interpretation of the entry fee as the opportunity cost of time. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Wealth Accumulation\n", + "\n", + "- Cash on hand is denoted as the liquid resources for consumption and saving; Dummy variable $I_p$ that is equal to one when the fixed entry cost is incurred for the first time and is zero otherwise. The household's next period cash on hand ($X_{i,t+1}$) is given by:\n", + "> \\begin{align}\n", + "X_{i,t+1}=S_{it}R_{t+1}^S+B_{it}R^f+(1-h_t)Y_{i,t+1}-FI_pP_{i,t+1} \\label{eq6}\\tag{6}\\\\\n", + "\\end{align}\n", + "where $S_it$ and $B_{it}$ denote respectively stock holdings and riskless asset holdings at time $t$, and $h_t$ is the fraction of income dedicated to housing-related expenditures. \n", + "\n", + "- Since the households must allocate cash on hand ($X_{it}$) between consumption expenditures and savings, cash on hand is given by:\n", + "> \\begin{align}\n", + "X_{it}=C_{it}+S_{it}+B_{it} \\label{eq7}\\tag{7}\\\\\n", + "\\end{align}\n", + "\n", + "- Borrowings against future labor income is prevented, therefore, the following restictions are imposed: \n", + "> \\begin{align}\n", + "B_{it}\\geq0 \\label{eq8}\\tag{8}\\\\\n", + "\\end{align}\n", + ">\n", + "> \\begin{align}\n", + "S_{it}\\geq0 \\label{eq9}\\tag{9}\\\\\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Optimization\n", + "- The complete optimization problem is \n", + "> \\begin{align}\n", + "max E(V_0) \\label{eq10}\\tag{10}\\\\ \n", + "\\end{align}\n", + "by choosing $(S_{it}, B_{it})_{t=1}^{T}$, where $V_0$ is given by equation(1) and equation(2) and is subject to the constraints given by equstions(5) to (9), and the stochastic labor income process is given by equation(3) and (4)\n", + "\n", + "- The analytical solutions do not exist. Therefore a numerical solution method based on the maximization of the value function to derive the optimal decision rules is used. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Calibration\n", + "- Preference parameters (baseline): $\\rho=5$, $\\varphi=0.2$, $\\beta=0.96$, and $b$=2.5; With preference heterogeneity, 50% of the population with low risk aversion and low EIS ($\\rho=1.2, \\varphi=0.2$) and the other 50% with moderate risk aversion and moderate EIS ($\\rho=5,\\varphi=0.5$) are incorporated to the model. \n", + "\n", + "- Labor income process: $\\sigma_u=0.15$, $\\sigma_n=0.1$\n", + "\n", + "- interest rate: $(R^f-1)=2\\%$; the stock return process: mean equity premium $\\mu=4\\%$ and standard deviation $\\sigma_{\\epsilon}=18\\%$\n", + "\n", + "- correlation between stock returns and income shocks: $\\phi_{N}=0.15$ and $\\phi_{U}=0.0$ for benchmark calibration\n", + "\n", + "- fixed cost: two limit cases: 0 and 2.5% as a share of household's expectated annual income.\n", + "\n", + "- housing expenditure: $h_t=max(A+B_1*age+B_2*age^2+B_3*age^3,0)$, where the parameters are estimated by using the data from the Panel Study of Income Dynamics" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Results" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- The paper presents a life-cycle model with idiosyncractic and uninsurable labor income risks to explain two important empirical observations: low stock market participation rates in the population as a whole, and moderate equity holdings for stock market participants. \n", + "- Households with low risk aversion and low EIS accumulate very little wealth and as a result, they do not invest in equities; households with high risk aversion and high EIS accumulate more wealth and therefore have a stronger incentive to pay for the fixed cost, and they are the ones who enter the stock market. Since they are more risk averse, they wouldn't like to invest much in the stock market. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comments\n", + "\n", + "- The key feature making the model fit the empirical evidence (low stock market participation rate and the low share of investment in stock market conditional on participation) well is Epstein-Zin utility function. This specific utility function makes it possible that the degree of risk aversion is unrelated with intertemporal elasticity of substitution (EIS). \n", + "- Due to the separability of risk aversion and EIS, the assumption that the population is composed with two groups (a group with low risk aversion and low EIS, and a group with high risk aversion and high EIS) leads to the result that people who enter the stock market are endougously more risk averse and thus not investing all their portfolio into the stock market. \n", + "- However, the underlying reason why this utility form is reasonable to accomodate data is absent. " + ] + }, + { + "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 9417b27208a02d6ec257968a87da23655059f4c4 Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Thu, 19 Sep 2019 11:56:45 -0400 Subject: [PATCH 05/17] Update GMLifeCylceInvestment.ipynb Revise typos, add the link of the paper, and change the format a bit. --- .../GMLifeCylceInvestment.ipynb | 58 +++++++++++-------- 1 file changed, 35 insertions(+), 23 deletions(-) diff --git a/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb b/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb index b2377cb1..37ca2b5c 100644 --- a/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb +++ b/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb @@ -4,7 +4,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Optimal Life-Cycle Asste Allocation: Understanding the Empirial Evidence\n", + "## [Optimal Life-Cycle Asste Allocation: Understanding the Empirial Evidence](http://faculty.london.edu/fgomes/gm.pdf)\n", + "\n", "\n", "- Authors: Francisco Gomes and Alexander Michaelides\n", "- Notebook by Zixuan Huang\n", @@ -25,9 +26,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Empiral Evidence\n", + "## Empirical Evidence\n", "\n", - "- In most industrialzed countries, stock market participation rates have increased substantially. A large share of population, however, still do not own stocks either directly or indirectly (through pension funds etc.) \n", + "- In most industrialized countries, stock market participation rates have increased substantially. A large share of population, however, still do not own stocks either directly or indirectly (through pension funds etc.) \n", "> In U.S., the stock market participation rate is close to 50%.\n", "\n", "- Even for those households who do own stocks, a significant proportion of their portfilios are not in stock. \n", @@ -44,7 +45,7 @@ "source": [ "## Model\n", "\n", - ">**Key features: Fixed entry cost; Epstein-Zin utility function; Preference heterogeneity**" + "> ### ***Key features: Fixed entry cost; Epstein-Zin utility function; Preference heterogeneity***" ] }, { @@ -52,11 +53,17 @@ "metadata": {}, "source": [ "### Preferences\n", + "\n", "- Discrete time; agents live for a maximum of age 100; conditional being alive at time t, the probability that a consumer is alive at t+1 is $p_t$.\n", - "- Epstein-Zin utility functions\n", + "\n", + "- Epstein-Zin utility function\n", + "\n", "> \\begin{align}\n", - "V_t=\\{(1-\\beta p_t) C_t^{1-1/\\varphi}+\\beta E_t[p_t[V_{t+1}^{1-\\rho}]+(1-p_t)b\\frac{(X_{t+1}/b)^{1-\\rho}}{1-\\rho}]^\\frac{1-1/\\varphi}{1-\\rho}\\}^\\frac{1}{1-1/\\varphi} \\label{eq1}\\tag{1}\\\\\n", - "\\end{align} where $\\rho$ is the coefficient of RRA, $\\varphi$ is the EIS, $\\beta$ is the discount factor and $b$ determines the strength of the bequest motive.\n", + "V_t=\\{(1-\\beta p_t) C_t^{1-1/\\varphi}+\\beta E_t[p_t[V_{t+1}^{1-\\rho}]+(1-p_t)b\\frac{(X_{t+1}/b)^{1-\\rho}}{1-\\rho}]^\\frac{1-1/\\varphi}{1-\\rho}\\}^\\frac{1}{1-1/\\varphi} \\label{eq1}\\tag{1}\\\\\n", + "\\end{align} \n", + "\n", + "where $\\rho$ is the coefficient of RRA, $\\varphi$ is the elasticity of intertemporal substitution (EIS), $\\beta$ is the discount factor and $b$ determines the strength of the bequest motive.\n", + "\n", "- Given the prescence of a bequest motive, the terminal condition for the recursive equation $(1)$ is:\n", "> \\begin{align}\n", "V_{T+1}=b \\frac{(X_{T+1}/b)^{1-\\rho}}{1-\\rho} \\label{eq2}\\tag{2}\\\\\n", @@ -74,11 +81,15 @@ "Y_{it}=P_{it}U_{it} \\label{eq3}\\tag{3}\\\\\n", "\\end{align}\n", "\n", + "

\n", + "\n", "- \\begin{align} \n", "P_{it}=exp(f(t,Z_{it})P_{it-1}N_{it}) \\label{eq4}\\tag{4}\\\\\n", "\\end{align}\n", "\n", - "- where $f(t,Z_{it})$ is a deterministic function of age and household characteristics $Z_{it}$, $P_{it}$ is a permanent component with innovation $N_{it}$, and $U_{it}$ is a transitory component.\n", + "

\n", + "\n", + "where $f(t,Z_{it})$ is a deterministic function of age and household characteristics $Z_{it}$, $P_{it}$ is a permanent component with innovation $N_{it}$, and $U_{it}$ is a transitory component.\n", "- Retirement is deterministic and exogenous, with all households retiring at age 65; Earnings in retirement are given by $Y_{it}=\\lambda P_{iK}$, where $K$ denotes the period of retiring, and $\\lambda$ is the replacement ratio (a scalar between zero and one)\n", "- For each age ($t$), the percentage of household income that is dedicated to housing expenditure ($h_t$) is estimated according to the Panel Study of Income Dynamics and is substracted from the measure of disposal income. " ] @@ -88,10 +99,10 @@ "metadata": {}, "source": [ "### Financial Assets\n", - "- There are two financial assets, one riskless (e.g. Treasury bills, cash) and one risky (stocks). The riskless asset yields a constant gross return, $R^f$, while the return on teh risky asset is given by \n", + "- There are two financial assets, one riskless (e.g. Treasury bills, cash) and one risky (stocks). The riskless asset yields a constant gross return, $R^f$, while the return on the risky asset is given by \n", "> \\begin{align}\n", "R_{t+1}^S-R^f=\\mu + \\epsilon_{t+1} \\label{eq5}\\tag{5}\\\\\n", - "\\end{align}\n", + "\\end{align}
\n", "where $\\epsilon$ follows a normal distribution with mean 0 and standard devitation $\\sigma_{\\epsilon}^2$.\n", "- The positive correlation between stock returns and earnings shocks is allowed: $\\phi_N$ denotes the correlation coefficient between stock returns and permanent income shocks, while $\\phi_U$ is for tansitory shocks.\n", "- Before investing in stocks for the first time, the investor must pay for a fixed lump sum cost, $F*P_{it}$. This is scaled by the level of permanent component of labor income as this significantly simplies the solution of the model and also motivated by the interpretation of the entry fee as the opportunity cost of time. " @@ -106,8 +117,8 @@ "- Cash on hand is denoted as the liquid resources for consumption and saving; Dummy variable $I_p$ that is equal to one when the fixed entry cost is incurred for the first time and is zero otherwise. The household's next period cash on hand ($X_{i,t+1}$) is given by:\n", "> \\begin{align}\n", "X_{i,t+1}=S_{it}R_{t+1}^S+B_{it}R^f+(1-h_t)Y_{i,t+1}-FI_pP_{i,t+1} \\label{eq6}\\tag{6}\\\\\n", - "\\end{align}\n", - "where $S_it$ and $B_{it}$ denote respectively stock holdings and riskless asset holdings at time $t$, and $h_t$ is the fraction of income dedicated to housing-related expenditures. \n", + "\\end{align}
\n", + "where $S_{it}$ and $B_{it}$ denote respectively stock holdings and riskless asset holdings at time $t$, and $h_t$ is the fraction of income dedicated to housing-related expenditures. \n", "\n", "- Since the households must allocate cash on hand ($X_{it}$) between consumption expenditures and savings, cash on hand is given by:\n", "> \\begin{align}\n", @@ -132,8 +143,8 @@ "- The complete optimization problem is \n", "> \\begin{align}\n", "max E(V_0) \\label{eq10}\\tag{10}\\\\ \n", - "\\end{align}\n", - "by choosing $(S_{it}, B_{it})_{t=1}^{T}$, where $V_0$ is given by equation(1) and equation(2) and is subject to the constraints given by equstions(5) to (9), and the stochastic labor income process is given by equation(3) and (4)\n", + "\\end{align}
\n", + "by choosing $(S_{it}, B_{it})_{t=1}^{T}$, where $V_0$ is given by equation (1) and equation (2) and is subject to the constraints given by equations (5) to (9), and the stochastic labor income process is given by equation (3) and (4)\n", "\n", "- The analytical solutions do not exist. Therefore a numerical solution method based on the maximization of the value function to derive the optimal decision rules is used. " ] @@ -147,29 +158,28 @@ "\n", "- Labor income process: $\\sigma_u=0.15$, $\\sigma_n=0.1$\n", "\n", - "- interest rate: $(R^f-1)=2\\%$; the stock return process: mean equity premium $\\mu=4\\%$ and standard deviation $\\sigma_{\\epsilon}=18\\%$\n", + "- Interest rate: $(R^f-1)=2\\%$; the stock return process: mean equity premium $\\mu=4\\%$ and standard deviation $\\sigma_{\\epsilon}=18\\%$\n", "\n", - "- correlation between stock returns and income shocks: $\\phi_{N}=0.15$ and $\\phi_{U}=0.0$ for benchmark calibration\n", + "- Correlation between stock returns and income shocks: $\\phi_{N}=0.15$ and $\\phi_{U}=0.0$ for benchmark calibration\n", "\n", - "- fixed cost: two limit cases: 0 and 2.5% as a share of household's expectated annual income.\n", + "- Fixed cost: two limit cases: 0 and 2.5% as a share of household's expectated annual income.\n", "\n", - "- housing expenditure: $h_t=max(A+B_1*age+B_2*age^2+B_3*age^3,0)$, where the parameters are estimated by using the data from the Panel Study of Income Dynamics" + "- Housing expenditure: $h_t=max(A+B_1*age+B_2*age^2+B_3*age^3,0)$, where the parameters are estimated by using the data from the Panel Study of Income Dynamics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Results" + "## Conclusions" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "- The paper presents a life-cycle model with idiosyncractic and uninsurable labor income risks to explain two important empirical observations: low stock market participation rates in the population as a whole, and moderate equity holdings for stock market participants. \n", - "- Households with low risk aversion and low EIS accumulate very little wealth and as a result, they do not invest in equities; households with high risk aversion and high EIS accumulate more wealth and therefore have a stronger incentive to pay for the fixed cost, and they are the ones who enter the stock market. Since they are more risk averse, they wouldn't like to invest much in the stock market. " + "- Households with low risk aversion and low EIS accumulate very little wealth and as a result, they do not invest in equities; households with high risk aversion and high EIS accumulate more wealth and therefore have a stronger incentive to pay for the fixed entry cost, and they are the ones who enter the stock market. Since they are more risk averse, they wouldn't like to invest much in the stock market. " ] }, { @@ -178,8 +188,10 @@ "source": [ "## Comments\n", "\n", - "- The key feature making the model fit the empirical evidence (low stock market participation rate and the low share of investment in stock market conditional on participation) well is Epstein-Zin utility function. This specific utility function makes it possible that the degree of risk aversion is unrelated with intertemporal elasticity of substitution (EIS). \n", - "- Due to the separability of risk aversion and EIS, the assumption that the population is composed with two groups (a group with low risk aversion and low EIS, and a group with high risk aversion and high EIS) leads to the result that people who enter the stock market are endougously more risk averse and thus not investing all their portfolio into the stock market. \n", + "- The key feature making the model fit the empirical evidence (low stock market participation rate and the low share of investment in stock market conditional on participation) well is Epstein-Zin utility function. This specific utility function makes it possible that the degree of risk aversion is unrelated with elasticity of intertemporal substitution (EIS). \n", + "\n", + "- Due to the separability of risk aversion and EIS, the assumption that the population is composed with two groups (a group with low risk aversion and low EIS, and a group with high risk aversion and high EIS) leads to the result that people who enter the stock market are **endougously** more risk averse and thus not investing all their portfolio into the stock market. \n", + "\n", "- However, the underlying reason why this utility form is reasonable to accomodate data is absent. " ] }, From 049950345ba82cedd609673d15126e9bf575c0ee Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Thu, 19 Sep 2019 12:18:52 -0400 Subject: [PATCH 06/17] Typos and format also add the year of the paper --- .../GMLifeCylceInvestment.ipynb | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb b/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb index 37ca2b5c..e4df38f6 100644 --- a/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb +++ b/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## [Optimal Life-Cycle Asste Allocation: Understanding the Empirial Evidence](http://faculty.london.edu/fgomes/gm.pdf)\n", + "## [Optimal Life-Cycle Asste Allocation: Understanding the Empirial Evidence (2005)](http://faculty.london.edu/fgomes/gm.pdf)\n", "\n", "\n", "- Authors: Francisco Gomes and Alexander Michaelides\n", @@ -18,8 +18,8 @@ "source": [ "## Abstract\n", "\n", - "- The paper finds a way to match stock market participation rates and asste allocation decisions conditional on participation, by using a life-cycle model with uninsurable labor income risk and moderate risk aversion, where the labor income risk is **idiosyncratic** and the degree of risk aversion is **heterogenous**. \n", - "- They found that households with low risk aversion smooth earnings shocks with a small buffer stock of assets, and consequently most of them never invest in equities. Endogously, stockholders are more risk averse, but they still do not invest their portfolios fully in stocks." + "- The paper finds a way to match stock market participation rates and asset allocation decisions conditional on participation, by using a life-cycle model with uninsurable labor income risk and moderate risk aversion, where the labor income risk is **idiosyncratic** and the degree of risk aversion is **heterogenous**. \n", + "- They found that households with low risk aversion smooth earnings shocks with a small buffer stock of assets, and consequently most of them never invest in equities. Endogenously, stockholders are more risk averse, but they still do not invest their portfolios fully in stocks." ] }, { @@ -84,7 +84,7 @@ "

\n", "\n", "- \\begin{align} \n", - "P_{it}=exp(f(t,Z_{it})P_{it-1}N_{it}) \\label{eq4}\\tag{4}\\\\\n", + "P_{it}=exp(f(t,Z_{it}))P_{it-1}N_{it} \\label{eq4}\\tag{4}\\\\\n", "\\end{align}\n", "\n", "

\n", @@ -125,7 +125,7 @@ "X_{it}=C_{it}+S_{it}+B_{it} \\label{eq7}\\tag{7}\\\\\n", "\\end{align}\n", "\n", - "- Borrowings against future labor income is prevented, therefore, the following restictions are imposed: \n", + "- Borrowing against future labor income is prevented, therefore, the following restrictions are imposed: \n", "> \\begin{align}\n", "B_{it}\\geq0 \\label{eq8}\\tag{8}\\\\\n", "\\end{align}\n", @@ -190,7 +190,7 @@ "\n", "- The key feature making the model fit the empirical evidence (low stock market participation rate and the low share of investment in stock market conditional on participation) well is Epstein-Zin utility function. This specific utility function makes it possible that the degree of risk aversion is unrelated with elasticity of intertemporal substitution (EIS). \n", "\n", - "- Due to the separability of risk aversion and EIS, the assumption that the population is composed with two groups (a group with low risk aversion and low EIS, and a group with high risk aversion and high EIS) leads to the result that people who enter the stock market are **endougously** more risk averse and thus not investing all their portfolio into the stock market. \n", + "- Due to the separability of risk aversion and EIS, the assumption that the population is composed of two groups (a group with low risk aversion and low EIS, and a group with high risk aversion and high EIS) leads to the result that people who enter the stock market are **endougously** more risk averse and thus not investing all their portfolio into the stock market. \n", "\n", "- However, the underlying reason why this utility form is reasonable to accomodate data is absent. " ] From 40f31b139de21cb5d26723af4c13a393f78b6120 Mon Sep 17 00:00:00 2001 From: zhuang13atJHU <43380704+zhuang13atJHU@users.noreply.github.com> Date: Thu, 19 Sep 2019 12:22:59 -0400 Subject: [PATCH 07/17] Create GMLifeCycleInvestment --- models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment | 1 + 1 file changed, 1 insertion(+) create mode 100644 models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment diff --git a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment new file mode 100644 index 00000000..8b137891 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment @@ -0,0 +1 @@ + From 499792e2771f6e76f5ca216a6614c738d8dd27ca Mon Sep 17 00:00:00 2001 From: zhuang13atJHU <43380704+zhuang13atJHU@users.noreply.github.com> Date: Thu, 19 Sep 2019 12:23:51 -0400 Subject: [PATCH 08/17] Delete GMLifeCycleInvestment mistakenly created --- models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment | 1 - 1 file changed, 1 deletion(-) delete mode 100644 models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment diff --git a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment deleted file mode 100644 index 8b137891..00000000 --- a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment +++ /dev/null @@ -1 +0,0 @@ - From 5f854a01dd1eabd8c4a98d4923af3008b0eddba3 Mon Sep 17 00:00:00 2001 From: zhuang13atJHU <43380704+zhuang13atJHU@users.noreply.github.com> Date: Thu, 19 Sep 2019 12:24:55 -0400 Subject: [PATCH 09/17] Add files via upload From a0fa147fe1353378f692ca7b447add4963c672a7 Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Thu, 19 Sep 2019 12:28:34 -0400 Subject: [PATCH 10/17] move the file to the same name folder --- .../{ => GMLifeCycleInvestment}/GMLifeCylceInvestment.ipynb | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename models/We-Would-Like-In-Econ-ARK/{ => GMLifeCycleInvestment}/GMLifeCylceInvestment.ipynb (100%) diff --git a/models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb similarity index 100% rename from models/We-Would-Like-In-Econ-ARK/GMLifeCylceInvestment.ipynb rename to models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb From 33c082f175c195f429c68283266dd238e23e9e0e Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Fri, 20 Sep 2019 15:53:16 -0400 Subject: [PATCH 11/17] test if the equation display is corrected --- .../GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb index e4df38f6..ecf3709a 100644 --- a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb +++ b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb @@ -77,13 +77,13 @@ "source": [ "### Labor income process\n", "\n", - "- \\begin{align}\n", + " \\begin{align}\n", "Y_{it}=P_{it}U_{it} \\label{eq3}\\tag{3}\\\\\n", "\\end{align}\n", "\n", "

\n", "\n", - "- \\begin{align} \n", + " \\begin{align} \n", "P_{it}=exp(f(t,Z_{it}))P_{it-1}N_{it} \\label{eq4}\\tag{4}\\\\\n", "\\end{align}\n", "\n", From c1c2900f40fcd7b79dfb2c84db57685910f3d9e5 Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Fri, 20 Sep 2019 16:02:19 -0400 Subject: [PATCH 12/17] the equation does not display correctly in github --- .../GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb index ecf3709a..e879bc67 100644 --- a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb +++ b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb @@ -77,13 +77,13 @@ "source": [ "### Labor income process\n", "\n", - " \\begin{align}\n", + "> \\begin{align}\n", "Y_{it}=P_{it}U_{it} \\label{eq3}\\tag{3}\\\\\n", "\\end{align}\n", "\n", "

\n", "\n", - " \\begin{align} \n", + "> \\begin{align} \n", "P_{it}=exp(f(t,Z_{it}))P_{it-1}N_{it} \\label{eq4}\\tag{4}\\\\\n", "\\end{align}\n", "\n", From 2a7789522a0c79a5f33fd7efe4e6e154c1cb646e Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Fri, 20 Sep 2019 16:08:20 -0400 Subject: [PATCH 13/17] see if the equation tag problems are fixed in github --- .../GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb index e879bc67..2d6dda99 100644 --- a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb +++ b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb @@ -59,14 +59,14 @@ "- Epstein-Zin utility function\n", "\n", "> \\begin{align}\n", - "V_t=\\{(1-\\beta p_t) C_t^{1-1/\\varphi}+\\beta E_t[p_t[V_{t+1}^{1-\\rho}]+(1-p_t)b\\frac{(X_{t+1}/b)^{1-\\rho}}{1-\\rho}]^\\frac{1-1/\\varphi}{1-\\rho}\\}^\\frac{1}{1-1/\\varphi} \\label{eq1}\\tag{1}\\\\\n", + "V_t=\\{(1-\\beta p_t) C_t^{1-1/\\varphi}+\\beta E_t[p_t[V_{t+1}^{1-\\rho}]+(1-p_t)b\\frac{(X_{t+1}/b)^{1-\\rho}}{1-\\rho}]^\\frac{1-1/\\varphi}{1-\\rho}\\}^\\frac{1}{1-1/\\varphi} \\tag{1}\\\\\n", "\\end{align} \n", "\n", "where $\\rho$ is the coefficient of RRA, $\\varphi$ is the elasticity of intertemporal substitution (EIS), $\\beta$ is the discount factor and $b$ determines the strength of the bequest motive.\n", "\n", "- Given the prescence of a bequest motive, the terminal condition for the recursive equation $(1)$ is:\n", "> \\begin{align}\n", - "V_{T+1}=b \\frac{(X_{T+1}/b)^{1-\\rho}}{1-\\rho} \\label{eq2}\\tag{2}\\\\\n", + "V_{T+1}=b \\frac{(X_{T+1}/b)^{1-\\rho}}{1-\\rho} \\tag{2}\\\\\n", "\\end{align}\n", "\n" ] From 2c36c4c4a2c90c6cb0f1d5dc985543fd70342b68 Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Fri, 20 Sep 2019 16:34:33 -0400 Subject: [PATCH 14/17] fix the problem of numbering equatoins use the code from here: https://www.mprat.org/blog/2018/08/25/blogging-with-jupyter-part-2.html --- .../GMLifeCylceInvestment.ipynb | 60 +++++++++---------- 1 file changed, 30 insertions(+), 30 deletions(-) diff --git a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb index 2d6dda99..d631c30a 100644 --- a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb +++ b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb @@ -58,16 +58,16 @@ "\n", "- Epstein-Zin utility function\n", "\n", - "> \\begin{align}\n", - "V_t=\\{(1-\\beta p_t) C_t^{1-1/\\varphi}+\\beta E_t[p_t[V_{t+1}^{1-\\rho}]+(1-p_t)b\\frac{(X_{t+1}/b)^{1-\\rho}}{1-\\rho}]^\\frac{1-1/\\varphi}{1-\\rho}\\}^\\frac{1}{1-1/\\varphi} \\tag{1}\\\\\n", - "\\end{align} \n", + "> \\begin{equation}\n", + "V_t=\\{(1-\\beta p_t) C_t^{1-1/\\varphi}+\\beta E_t[p_t[V_{t+1}^{1-\\rho}]+(1-p_t)b\\frac{(X_{t+1}/b)^{1-\\rho}}{1-\\rho}]^\\frac{1-1/\\varphi}{1-\\rho}\\}^\\frac{1}{1-1/\\varphi} \\\\\n", + "\\end{equation} \n", "\n", "where $\\rho$ is the coefficient of RRA, $\\varphi$ is the elasticity of intertemporal substitution (EIS), $\\beta$ is the discount factor and $b$ determines the strength of the bequest motive.\n", "\n", "- Given the prescence of a bequest motive, the terminal condition for the recursive equation $(1)$ is:\n", - "> \\begin{align}\n", - "V_{T+1}=b \\frac{(X_{T+1}/b)^{1-\\rho}}{1-\\rho} \\tag{2}\\\\\n", - "\\end{align}\n", + "> \\begin{equation}\n", + "V_{T+1}=b \\frac{(X_{T+1}/b)^{1-\\rho}}{1-\\rho} \\\\\n", + "\\end{equation}\n", "\n" ] }, @@ -77,15 +77,15 @@ "source": [ "### Labor income process\n", "\n", - "> \\begin{align}\n", - "Y_{it}=P_{it}U_{it} \\label{eq3}\\tag{3}\\\\\n", - "\\end{align}\n", + "> \\begin{equation}\n", + "Y_{it}=P_{it}U_{it} \\\\\n", + "\\end{equation}\n", "\n", "

\n", "\n", - "> \\begin{align} \n", - "P_{it}=exp(f(t,Z_{it}))P_{it-1}N_{it} \\label{eq4}\\tag{4}\\\\\n", - "\\end{align}\n", + "> \\begin{equation} \n", + "P_{it}=exp(f(t,Z_{it}))P_{it-1}N_{it} \\\\\n", + "\\end{equation}\n", "\n", "

\n", "\n", @@ -100,9 +100,9 @@ "source": [ "### Financial Assets\n", "- There are two financial assets, one riskless (e.g. Treasury bills, cash) and one risky (stocks). The riskless asset yields a constant gross return, $R^f$, while the return on the risky asset is given by \n", - "> \\begin{align}\n", - "R_{t+1}^S-R^f=\\mu + \\epsilon_{t+1} \\label{eq5}\\tag{5}\\\\\n", - "\\end{align}
\n", + "> \\begin{equation}\n", + "R_{t+1}^S-R^f=\\mu + \\epsilon_{t+1} \\\\\n", + "\\end{equation}
\n", "where $\\epsilon$ follows a normal distribution with mean 0 and standard devitation $\\sigma_{\\epsilon}^2$.\n", "- The positive correlation between stock returns and earnings shocks is allowed: $\\phi_N$ denotes the correlation coefficient between stock returns and permanent income shocks, while $\\phi_U$ is for tansitory shocks.\n", "- Before investing in stocks for the first time, the investor must pay for a fixed lump sum cost, $F*P_{it}$. This is scaled by the level of permanent component of labor income as this significantly simplies the solution of the model and also motivated by the interpretation of the entry fee as the opportunity cost of time. " @@ -115,24 +115,24 @@ "### Wealth Accumulation\n", "\n", "- Cash on hand is denoted as the liquid resources for consumption and saving; Dummy variable $I_p$ that is equal to one when the fixed entry cost is incurred for the first time and is zero otherwise. The household's next period cash on hand ($X_{i,t+1}$) is given by:\n", - "> \\begin{align}\n", - "X_{i,t+1}=S_{it}R_{t+1}^S+B_{it}R^f+(1-h_t)Y_{i,t+1}-FI_pP_{i,t+1} \\label{eq6}\\tag{6}\\\\\n", - "\\end{align}
\n", + "> \\begin{equation}\n", + "X_{i,t+1}=S_{it}R_{t+1}^S+B_{it}R^f+(1-h_t)Y_{i,t+1}-FI_pP_{i,t+1} \\\\\n", + "\\end{equation}
\n", "where $S_{it}$ and $B_{it}$ denote respectively stock holdings and riskless asset holdings at time $t$, and $h_t$ is the fraction of income dedicated to housing-related expenditures. \n", "\n", "- Since the households must allocate cash on hand ($X_{it}$) between consumption expenditures and savings, cash on hand is given by:\n", - "> \\begin{align}\n", - "X_{it}=C_{it}+S_{it}+B_{it} \\label{eq7}\\tag{7}\\\\\n", - "\\end{align}\n", + "> \\begin{equation}\n", + "X_{it}=C_{it}+S_{it}+B_{it} \\\\\n", + "\\end{equation}\n", "\n", "- Borrowing against future labor income is prevented, therefore, the following restrictions are imposed: \n", - "> \\begin{align}\n", - "B_{it}\\geq0 \\label{eq8}\\tag{8}\\\\\n", - "\\end{align}\n", + "> \\begin{equation}\n", + "B_{it}\\geq0 \\\\\n", + "\\end{equation}\n", ">\n", - "> \\begin{align}\n", - "S_{it}\\geq0 \\label{eq9}\\tag{9}\\\\\n", - "\\end{align}" + "> \\begin{equation}\n", + "S_{it}\\geq0 \\\\\n", + "\\end{equation}" ] }, { @@ -141,9 +141,9 @@ "source": [ "### Optimization\n", "- The complete optimization problem is \n", - "> \\begin{align}\n", - "max E(V_0) \\label{eq10}\\tag{10}\\\\ \n", - "\\end{align}
\n", + "> \\begin{equation}\n", + "max E(V_0) \\\\ \n", + "\\end{equation}
\n", "by choosing $(S_{it}, B_{it})_{t=1}^{T}$, where $V_0$ is given by equation (1) and equation (2) and is subject to the constraints given by equations (5) to (9), and the stochastic labor income process is given by equation (3) and (4)\n", "\n", "- The analytical solutions do not exist. Therefore a numerical solution method based on the maximization of the value function to derive the optimal decision rules is used. " From f029f0c12ad5120580b89beabab2eea03821ba94 Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Fri, 20 Sep 2019 16:44:40 -0400 Subject: [PATCH 15/17] numbering still doesn't display in github --- .../GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb index d631c30a..57476edf 100644 --- a/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb +++ b/models/We-Would-Like-In-Econ-ARK/GMLifeCycleInvestment/GMLifeCylceInvestment.ipynb @@ -58,14 +58,14 @@ "\n", "- Epstein-Zin utility function\n", "\n", - "> \\begin{equation}\n", + "> \\begin{equation} \\label{eq1}\n", "V_t=\\{(1-\\beta p_t) C_t^{1-1/\\varphi}+\\beta E_t[p_t[V_{t+1}^{1-\\rho}]+(1-p_t)b\\frac{(X_{t+1}/b)^{1-\\rho}}{1-\\rho}]^\\frac{1-1/\\varphi}{1-\\rho}\\}^\\frac{1}{1-1/\\varphi} \\\\\n", "\\end{equation} \n", "\n", "where $\\rho$ is the coefficient of RRA, $\\varphi$ is the elasticity of intertemporal substitution (EIS), $\\beta$ is the discount factor and $b$ determines the strength of the bequest motive.\n", "\n", "- Given the prescence of a bequest motive, the terminal condition for the recursive equation $(1)$ is:\n", - "> \\begin{equation}\n", + "> \\begin{equation} \\label{eq2}\n", "V_{T+1}=b \\frac{(X_{T+1}/b)^{1-\\rho}}{1-\\rho} \\\\\n", "\\end{equation}\n", "\n" From ee6ee7d61f39c5adc2b7fbe4219c31afc26aeca2 Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Sun, 27 Oct 2019 13:53:25 -0400 Subject: [PATCH 16/17] Aiyagari_1994 --- .../Aiyagari1994QJE_updated.ipynb | 208 ++++++++++++++++++ models/We-Would-Like-In-Econ-ARK/Table2.png | Bin 0 -> 411382 bytes 2 files changed, 208 insertions(+) create mode 100644 models/We-Would-Like-In-Econ-ARK/Aiyagari1994QJE_updated.ipynb create mode 100644 models/We-Would-Like-In-Econ-ARK/Table2.png diff --git a/models/We-Would-Like-In-Econ-ARK/Aiyagari1994QJE_updated.ipynb b/models/We-Would-Like-In-Econ-ARK/Aiyagari1994QJE_updated.ipynb new file mode 100644 index 00000000..e3d1aa64 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/Aiyagari1994QJE_updated.ipynb @@ -0,0 +1,208 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Uninsured Idiosyncratic Risk and Aggregate Saving\n", + "* Authors: S. Rao Aiyagari\n", + "* Source: The Quaterly Journal of Economics, Vol. 109, No. 3 (Aug., 1994), pp. 659-684\n", + "* Notebook by Zixuan Huang and Mingzuo Sun\n", + "* 2019 Fall" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction of Heterogeneity\n", + "* The flaw of Representative Agent (RA) model: inconsistency with empirical studies. \n", + "> * Empricial studies suggest that individual consumption is much more variable than aggregate consumption, which is inconsistent with conclusions of RA model.\n", + "> * The behavior of wealth and portfolios is strongly at variance with the complete markets model implicit in RA models.\n", + "\n", + "* Thus due to incomplete markets, the existence of heterogeneity may be important especially with a context of borrowing constraints." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Abtract \n", + "* The paper modifies standard growth model to include precautionary saving motives and liquidity constraints. \n", + "* The paper presents the impact on the aggregate saving rate, the importance of asset trading to individuals and the relative inequality of wealth and income distributions. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Introduction\n", + "\n", + "### Goals \n", + "* To provide an exposition of models whose aggregate behavior is the result of market interaction among a large number of agents subject to idiosyncratic shocks. \n", + "> * This class of models contrasts with representative agent models where individual dynamics and uncertainty coincide with aggregate dynamics and uncertainty.
\n", + "> * This exposition is built around the standard growth model of Brock and Mirman(1972) modified to include a role for uninsured idiosyncratic risk and borrowing constraint.\n", + "* To use such a model to study the quantitative importance of individual risk for aggregate saving.
\n", + "\n", + "\n", + "### Key features\n", + "* Endogenous heterogeneity \n", + "* Aggregation\n", + "* Infinite horizons \n", + "* Borrowing constraint\n", + "* General equilibrium. i.e. interest rate is endogenously determined since in a steady state equilibrium the capital per capita must equal the per capita asset holdings of consumers, and the interest rate must equal the net marginal product of capital. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Related Literature\n", + "* Aiyagari model originates from Bewley model and Hugget model. These models all share the same key components as mentioned in the previous part. And they are used to study the following topics:\n", + "> * How much of observed wealth inequality can one explain through uninsurable earnings variation across agents?
\n", + "> * What is the fraction of aggregate savings due to the precautionary motive?
\n", + "> * What are the redistributional implications of various policies?\n", + "\n", + "* The evolution of those models\n", + "> * Bewley(1986): an exogenous interest rate $r$ is assumed.
\n", + "> * Huggett(1993): a pure exchange economy in which the interest rate is endogenized.
\n", + "> * Aiyagari(1994): a production sector is added to Huggett model." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model\n", + "### The Individual's Problem\n", + "\\begin{align}\n", + "max E_0[\\Sigma_{t=0}^\\infty \\beta^t U(c_t)]\n", + "\\end{align}\n", + "subject to \n", + "\\begin{align}\n", + "c_t+a_{t+1}&=wl_{t}+(1+r)a_t \\\\\n", + "c_t\\geq0&, a_t\\geq-b\n", + "\\end{align}\n", + "where $b$ (if positive) is the limit on borrowing and $l_t$ is assumed to be i.i.d with bounded support given by $[l_{min},l_{max}]$, with $l_{min}>0$\n", + "\n", + "* If $r<0$, some limit on borrowing is required, otherwise the problem is not well posed and a solution does not exist. \n", + "* If $r>0$, a borrowing constraint, $a_{t} \\geq \\frac{-wl_{min}}{r}$, is implied by nonnegative consumption. Hence, if $b$ exceeds $\\frac{-wl_{min}}{r}$, the the borrowing limit $b$ wil never be binding, and $b$ should be replaced by $\\frac{wl_{min}}{r}$; In other words, the constraints may be specified as:\n", + "\\begin{align}\n", + "a_t &\\geq -\\phi \\\\\n", + "\\phi &\\equiv min\\{b, \\frac{wl_{min}}{r}\\},\\ for\\ r>0; \\phi \\equiv b,\\ for\\ r \\leq 0\n", + "\\end{align}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* Define $\\hat{a_t}=a_t+\\phi$ and $z_t=wl_t+(1+r)\\hat{a_t}-r\\phi$, where $\\hat{a_t}$ and $z_t$ may be thought of as the total financial resources at data $t$ and total resources of the agent at date $t$ respectively, then the Bellman equation is as follows:\n", + "\\begin{align}\n", + "V(z_t,b,w,r) \\equiv \\underset{\\hat{a_{t+1}}}{max}\\{U(z_t-\\hat{a_t})+\\beta \\int V(z_{t+1},b,w,r)dF(l_{t+1}) \\}\n", + "\\end{align}\n", + "* Solving the Bellman equation, the paper derives the optimal asset demand rule: $\\hat{a_{t+1}}=A(z_t,b,w,r)$ and the transition law for total resources $z_t$ is $z_{t+1}=wl_{t+1}+(1+r)A(z_t,b,w,r)-r\\phi$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Endogenous Heteogeneity and Aggregation\n", + "* The distribution of $\\{z_t\\}$ and the value of $Ea_w$ (denoting long-run average assets) reflect the endogenous heterogeneity and the aggregation features mentioned above. $Ea_w$ represents the aggregate assets of the population consistent with the distribution of assets across population implied by individual optimal saving behavior.\n", + "* If earnings were certain (or, equivalently, markets complete), $Ea_w$ would equal ($-\\phi$) for all $r<\\lambda$, where $\\lambda$ denotes the rate of time preference. That is, per capita assets under certainty are at their lower permissible level since all agents are alike and everyone is constrained. However, in a steady state under incomplete markets, there is a distribution of agents with different total resources reflecting different histories of labor endowment shocks. \n", + "* Those with low total resources will continue to be liquidity constrained, whereas those with high total resources will accumulate assets beyond the constrained level. Aggregation then implies that per capita must necessarily exceed their level under certainty. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### General Equilibrium\n", + "* In the steady state, the capital desired by firms at the interest rate $r$ must be equal to the capital supplied by households at the interest rate $r$, which is time invariant.\n", + "* The effects of varying the borrowing limit $b$ is described: when borrowing is permitted individuals need not rely solely on holdings of capital to buffer earnings variations. Borrowing can also be used to buffer these shocks and, hence, leads to smaller holdings of capital. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Model Specification, Parameterization, and Consumption\n", + "\n", + "### Model specification and parameters\n", + "* Discount factor: $\\beta=0.96$\n", + "* Production function: Cobb Douglas with the capital share taken to be 0.36\n", + "* Depreciation rate: $\\delta=0.08$\n", + "* Utility function: CRRA with the relative risk aversion coefficient $\\mu \\in \\{1,3,5\\}$\n", + "* Labor endowment shocks: Markov charin specification with seven states to match the following first-order autoregressive representation for the logarithm of the labor endowment shock:\n", + "\\begin{align}\n", + "\\log(l_t)=\\rho\\log(l_{t-1})+\\sigma(1-\\rho^2)^{1/2}\\epsilon_{t}, \\epsilon_t--Normal(0,1) \\\\\n", + "\\sigma \\in \\{0.2,0.4\\}, \\rho \\in \\{0,0.3,0.6,0.9\\}.\n", + "\\end{align}\n", + "* Borrowing limit: $b=0$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Computation\n", + "* Approximate the asset demand as a function of total resources (for each of the seven possible current labor endowment shocks).\n", + "* Approximate the steady state: start with some value of $r$ (say, $r_1$), then compute the asset demand function corresponding to $r_1$, then simulate the Markov chain for the labor endowment shock using a random number generator and obtain a series of 10,000 draws. These are used with the asset demand function to obtain a simulated series of assets. The sample mean of this is taken to be $Ea$.Then calculate $r_2$ such that $K(r_2)$ equals $Ea$. If $r_2$ exceeds the rate of time preference, it is replaced by the rate of time preference. Define $r_3=(r_1+r_2)/2$ and calculate $Ea$ corresponding to $r_3$. If $Ea$ exceeds $K(r_3)$, then $r_2$ is replaced by $r_3$, and use bisection again. If $Ea$ is less than $K(r_3)$, then $r_1$ is replaced by $r_3$ then use bisection again. Typically this yields an excellent approximation to the steady state within ten iterations. \n", + "* Once the steady state is approximated, calculate the mean, median, standard deviation, skewness, serial correlation coefficient for labor income, asset holdings, gross saving, consumtion, etc. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Results\n", + "\n", + "### Aggregate Saving\n", + "* The differences between the saving rates with an without insurance are quite small for moderate and empirically plausible values of $\\sigma$, $\\rho$, and $\\mu$. However for high values of $\\sigma$, $\\rho$, and $\\mu$, the presence of idiosyncratic risk can raise the saving rate quite significantly by up to seven percentage points. \n", + "\n", + "\n", + "### Variabilities \n", + "* Consumption varies about 50-70 percent as much as income. Saving and assets are much more volatile than income: Saving varies about three times as much as income, and assets vary about twice as much as income. \n", + "* Risk aversion tends to reduce the variabilities of all these variabilities. \n", + "\n", + "### Importance of Asset Trading\n", + "* If $\\mu=3$,$\\sigma=4$ and $\\rho=0.6$, then, by optimally accumulating and depleting assets, consumption variability is cut in half, yielding a welfare benefit of about 14 percent of per capita consumption.\n", + "\n", + "### Cross-Section Distributions and Inequality Measures\n", + "* Since long-run distrubutions for an individual coincide with cross-section distrbutions for the population, results for variabilities of individual consumption, income, and assets have immediate implications for cross-section distributions. \n", + "* There is much less dispersion across households in consumption compared with income and much greater dispersion in wealth compared with income. \n", + "* Skewness coefficients reveal another aspect of inequality. All of the cross-section distributions are positively skewed (median$<$mean). However, the degree of skewness is less than in the data. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusions and Comments\n", + "The Aiyagari model extends the Bewley model and the Hugget model to a context with a production sector. Deviating from the representative agent model in which complete market is implicitly assumed, it tries to study the aggregate saving behavior of the economy with the agents facing uninsured idiosyncratic risk. With an empirically plausible set of parameters, it finds that the aggregate saving rate does increase compared to the case with a complete market, however, the change here caused by the precautionary saving motive is mild. Also, the results of the model qualitatively match the real data in terms of the ranking of the fluctuations of some economic variables. However, in terms of approaching the real inequalities of income and wealth shown by the data, the model does not perform very well. Also, in this model, the joint distribution of income and wealth is not treated as a state variable, which neglects the distribution effect Krusell and Smith(1998) try to address." + ] + } + ], + "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/Table2.png b/models/We-Would-Like-In-Econ-ARK/Table2.png new file mode 100644 index 0000000000000000000000000000000000000000..01dba93d5824f5735ff4436333211a81b0ea2cee GIT binary patch literal 411382 zcmeFZg+YW{Q;X}U}n~=b*;6oIDc`TLx`fh#3Sry*hol7kEA5uy+=Yq-$z11HN?aK zwvfLMXwW15SKDoTlpQYzY6o0?miAR$SHBqTmiA>1JDZcW*Xs4cHXPh4=<7ICwF 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zg49B0CD+Me$>MYWxsB9Gt)Lj8(4&w}H~w7y{ErH#&?NzRY;Gx%Y3wf5I6sCq%_$cE z8`7k$&>Q25Ksl0srJMajtT=x+)mU})9Cz3pGBzqEx=0-WAZS0jQ>-O@d^J^4-aXMm zxbd=Rx7@_mO{$=ws2Xm$4x7WsjbLkJUyP~Exm^h7O375?T`|oYKB-Ba@cd8FJ6dAx z@Kes5`b{mSAv2Q%^vssIv#2?%CE)0y?WZWz=1~%0JVQbR!FZfsEKT4db37XSEs2oUyPF~-DuE+Nk zx-$n`d+m1zqTy{O{bVR3+rZ;HF?s*%TlaXATGn`f5`1CxyJVu|5sHjuiYQWQDCG4> zKi$oRpr^-bU%GHy084DsgNlD7x%e~iVc8SVFL0QiKYn+|Kl6VqPr3o(YEr; zB{gN~H2g95!0K%&E)C&$+oBx)$PbflpFKwV2-1`)$8dH#IY?fV_o(lWT)DWB2mY?y zEAYl#-pu2)-?l5Il5Lt6FONrw3g`Q7a(#lu@LR5PUv=!Bi;Z}h!&IboM+Xe}NDJm0 z$?c%>=BE~91v=T3!yD|NcRm6B#l!wzZ=NdTyJeL}0RPub|MlHJ&pyvx|9w#Z8Iym; znG58X`m+~L JOP;*`_;0@;*6IKN literal 0 HcmV?d00001 From 3778b7f16d690a1e9665a20d880f9ac01fa44b0b Mon Sep 17 00:00:00 2001 From: Zixuan Huang Date: Sun, 27 Oct 2019 13:56:34 -0400 Subject: [PATCH 17/17] updated --- .../Aiyagari1994QJE_updated.ipynb | 12 +++++++++++- 1 file changed, 11 insertions(+), 1 deletion(-) diff --git a/models/We-Would-Like-In-Econ-ARK/Aiyagari1994QJE_updated.ipynb b/models/We-Would-Like-In-Econ-ARK/Aiyagari1994QJE_updated.ipynb index e3d1aa64..6a29dc34 100644 --- a/models/We-Would-Like-In-Econ-ARK/Aiyagari1994QJE_updated.ipynb +++ b/models/We-Would-Like-In-Econ-ARK/Aiyagari1994QJE_updated.ipynb @@ -75,22 +75,28 @@ "source": [ "## Model\n", "### The Individual's Problem\n", + "$$\n", "\\begin{align}\n", "max E_0[\\Sigma_{t=0}^\\infty \\beta^t U(c_t)]\n", "\\end{align}\n", + "$$\n", "subject to \n", + "$$\n", "\\begin{align}\n", "c_t+a_{t+1}&=wl_{t}+(1+r)a_t \\\\\n", "c_t\\geq0&, a_t\\geq-b\n", "\\end{align}\n", + "$$\n", "where $b$ (if positive) is the limit on borrowing and $l_t$ is assumed to be i.i.d with bounded support given by $[l_{min},l_{max}]$, with $l_{min}>0$\n", "\n", "* If $r<0$, some limit on borrowing is required, otherwise the problem is not well posed and a solution does not exist. \n", "* If $r>0$, a borrowing constraint, $a_{t} \\geq \\frac{-wl_{min}}{r}$, is implied by nonnegative consumption. Hence, if $b$ exceeds $\\frac{-wl_{min}}{r}$, the the borrowing limit $b$ wil never be binding, and $b$ should be replaced by $\\frac{wl_{min}}{r}$; In other words, the constraints may be specified as:\n", + "$$\n", "\\begin{align}\n", "a_t &\\geq -\\phi \\\\\n", "\\phi &\\equiv min\\{b, \\frac{wl_{min}}{r}\\},\\ for\\ r>0; \\phi \\equiv b,\\ for\\ r \\leq 0\n", - "\\end{align}\n" + "\\end{align}\n", + "$$\n" ] }, { @@ -98,9 +104,11 @@ "metadata": {}, "source": [ "* Define $\\hat{a_t}=a_t+\\phi$ and $z_t=wl_t+(1+r)\\hat{a_t}-r\\phi$, where $\\hat{a_t}$ and $z_t$ may be thought of as the total financial resources at data $t$ and total resources of the agent at date $t$ respectively, then the Bellman equation is as follows:\n", + "$$\n", "\\begin{align}\n", "V(z_t,b,w,r) \\equiv \\underset{\\hat{a_{t+1}}}{max}\\{U(z_t-\\hat{a_t})+\\beta \\int V(z_{t+1},b,w,r)dF(l_{t+1}) \\}\n", "\\end{align}\n", + "$$\n", "* Solving the Bellman equation, the paper derives the optimal asset demand rule: $\\hat{a_{t+1}}=A(z_t,b,w,r)$ and the transition law for total resources $z_t$ is $z_{t+1}=wl_{t+1}+(1+r)A(z_t,b,w,r)-r\\phi$" ] }, @@ -135,10 +143,12 @@ "* Depreciation rate: $\\delta=0.08$\n", "* Utility function: CRRA with the relative risk aversion coefficient $\\mu \\in \\{1,3,5\\}$\n", "* Labor endowment shocks: Markov charin specification with seven states to match the following first-order autoregressive representation for the logarithm of the labor endowment shock:\n", + "$$\n", "\\begin{align}\n", "\\log(l_t)=\\rho\\log(l_{t-1})+\\sigma(1-\\rho^2)^{1/2}\\epsilon_{t}, \\epsilon_t--Normal(0,1) \\\\\n", "\\sigma \\in \\{0.2,0.4\\}, \\rho \\in \\{0,0.3,0.6,0.9\\}.\n", "\\end{align}\n", + "$$\n", "* Borrowing limit: $b=0$" ] },