diff --git a/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Biroli(2015).ipynb b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Biroli(2015).ipynb new file mode 100644 index 00000000..8aea89c8 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Biroli(2015).ipynb @@ -0,0 +1,216 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Pietro Biroli\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## \"Genetic and Economic Interaction in the Formation of Human Capital: The Case of Obsesity\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook is created by Wonsik Ko. \n", + "All the results of this paper is from https://drive.google.com/file/d/1cYedv5O5d1n5fCnxPgtYpLOg41yfiPV-/view on 10/4/2020." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Summary \n", + "The paper develops a structural model of health and human captial formation illustrating the dynamic interaction between genetic inheritance and investments in health over the life cycle. \n", + "\n", + "* Genetic heterogeneity changes the utility cost of investments and the production of health. \n", + "* Using BMI as a measure of health, the paper considers physical activity and food intake as investments in health. \n", + "* The result shows that Gene-Environment interaction plays a pivotal role in the evolution of BMI. Food intake has a stronger impact on BMI. \n", + "* This analysis provides an economic framework of health and human capital formation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Model \n", + "\n", + "$H$ is human capital, $I_k$ is investment, and $g$ is genetic markers. \n", + "BMI is a measure of $H$ and proxies for $I_k$ are food consumption $F$ and exercise $E$. \n", + "\n", + "1. Utility function $U(B_t, F_t, l_t, c_t, g)$ is derived from non-food consumption $c_t$, food consumption $F_t$, leisure $l_t$, and BMI $B_t$. \n", + "2. $B_{t+1} = I(F_t, E_t;g)+(1-\\delta_t)B_t + \\epsilon_t$. Future stock of health $B_{t+1}$ depends on current stock $B_t$, depreciation term $\\delta_t$, health investment $I(F_t, E_t;g)$, and a health shock $\\epsilon_t$. \n", + "3. In each period, current stock of health determines the amount of productive time $\\Omega_t$, which can be allocated to $l_t$ and $E_t$. \n", + "4. In each period, the agent is endowed with the income $Y_t$ that is devoted to $c_t$ and $F_t$. \n", + "5. $F_t$ is divided again into nutritious food $NF_t$ with a lower caloric content and non-nutritious food $UF_t$ with higher caloric content. \n", + "6. The overall expenditure on food will be $P_{F_t}F(UF, NF)=P_{UF_t}UF_{t}+P_{NF_t}NF_{t}$ so that $Y_t = P_{f}F(UF_t, NF_t) +c_t$.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The agent's problem \n", + "\\begin{align*}\n", + "V(B_0, Y_0, \\epsilon_0; g) = &max_{NF_t, E_t} \\sum_{t=0}^{T-1}\\beta^t EU(B_t, F_t, l_t, c_t;g) \\\\\n", + "&s.t.\\\\\n", + "\\Omega(B_t)&=l_t + E_t \\\\\n", + "Y_t &=P_{F_t}F(UF_t, NF_t) + c_t \\\\\n", + "B_{t+1} &= I(F_t, E_t;g)+(1-\\delta_t)B_t + \\epsilon_t\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Channel of genetic variants \n", + "\n", + "1. Production function of health: $I(\\cdot ; g)$ \n", + "2. Preference: $\\partial U(\\cdot ; g) / \\partial F$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The three period model \n", + "\n", + "In the final period, $E_3=0$ and expenditure will solve $\\partial U_F(F_3)=P_{F_3}\\partial U_c(Y_3 - P_{F_3}F_3)$. The optimal food consumption in period 2 is given by \n", + "\\begin{align*}\n", + "U_{F_2}^{'}(\\cdot ; g) &=P_{F_2} U_{c_2}^{'}(\\cdot ; g) +\\beta E[- U_{B_3}^{'}(\\cdot ; g) - U_{l_3}^{'}(\\cdot ; g)\\partial \\Omega / \\partial B_3] I_{F_2}^{'}(\\cdot;g) \\\\\n", + "&= P_{F_2}U_{c_2}^{'}(\\cdot ; g)+\\beta E[\\phi_{B_3}]I_{F_2}^{'}(\\cdot ;g)\n", + "\\end{align*} \n", + "\n", + "The split between nutritious and non-nutritious food is determined by income and relative prices, such that $NF_t = F_t - \\kappa UF_t $ and $UF_t = \\frac{Y_t - c_t - P_{NF}F_t}{P_{UF}-\\kappa P_{NF}}$ \n", + "Optimal investment in exercise must satisfy\n", + "\n", + "\\begin{align*}\n", + "-U_{t}^{'}(B_2, F_2, l_2)=\\beta E[\\phi_{B_3}]\\frac{\\partial I(F_2, E_2;g)}{\\partial E_2}\n", + "\\end{align*} \n", + "\n", + "The optimal choice of food consumption in period 1 must satisfy the following:\n", + "\n", + "\\begin{align*}\n", + "U_F^{'}(B_1, F_1, l_1)=P_{F_1}U_{c_1}^{'}+\\beta E[\\phi_{B_2}+\\beta (1-\\delta)\\phi_{B_3}]\\frac{\\partial I(F_1, E_1;g)}{\\partial F_1}\n", + "\\end{align*} \n", + "\n", + "Comparing a change in the cost of food consumption in period one or in period two, we can see how a decrease in the implicit price of food today has a greater effect on investments and health. This is due to the fact that a higher level of investment today has an impact on both health today and health tomorrow, because of the law of motion of health capital. Unless the health stock fully depreciates in one period, by investing today we will rip the benefits in all following periods." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Data \n", + "Avon Longitudinal Study of Parents and Children(main) and Offspring Cohort of the Framingham Heart Study. \n", + "\n", + "### A linear production function of health \n", + "\n", + "\n", + "A log linear production function $B_{t+1}=A(B_{t}, X_t)g^{\\beta_g} [F_{t}^{\\alpha_{f}} (g), E_{t}^{\\alpha_{e}} (g)]$\n", + "\n", + "\n", + "## Results \n", + "\n", + "The genetic endowment of the child has a clear and strong effect on the obesity level, even after controlling for standard demographic\n", + "characteristics as well as the mother BMI. \n", + "The past stock of BMI is a very important determinant of its current level of Bt, and its inclusion raises significantly the explanatory power. \n", + "The most important contribution to BMI comes from food consumption and exercise, and their interaction with the genetic endowment. \n", + "The interaction between the genetic variant and caloric intake is positive and statistically significant. \n", + "The genetic endowment of a child can have an effect not only on the production function of health $f(\\cdot; g) $ but also on the level of investments $I_{t}^{*}=(F_{t}^{*}, E_{t}^{*})$. \n", + "\n", + "\n", + "Assuming Cobb-Douglas function for health investment production function and the utility function, \n", + "\n", + "### Bellman equation \n", + "\\begin{align*}\n", + "V_{t}(B_t, Y_t , \\epsilon_t;g) &= max_{E_{t},B_{t+1}}\\zeta_B log B_t +\\frac{\\zeta_F (g)}{a(g)} (log B_{t+1} -(1-\\delta_t)log B_t - log \\epsilon_t) - \\frac{b(g) \\zeta_F (g)}{a(g)} log E_t +\\zeta_l log(\\Omega- E_t) + \\zeta_c log c \\\\\n", + "&+\\beta EV_{t+1}(B_{t+1},Y_{t+1},\\epsilon_{t+1};g)\n", + "\\end{align*} \n", + "\n", + "\n", + "An increase in prices lowers caloric consumption and consequently BMI: the average reduction at the end of the period (beginning of adulthood) is about .6BMI points (1.5kg, 3% reduction). Such price changes induce di\u000b", + "erent responses according to the genotype of the individual: carriers of the risky A-allele reduce caloric intake much more, so much that the overall genetic difference in BMI is negligible. \n", + " \n", + " \n", + "Now considering a 25% reduction in food intake for the first 10 years of life. It can mimic the effect of an intervention that removes high-caloric foods from school cafeteria and replaces them with healthier options. The effect of the policy on the evolution of BMI is more moderate, with an average reduction of .4 BMI points (.9 kg, 2% reduction). \n", + "\n", + "### Optimal Time Allocation\n", + "\n", + "The optimal static allocation of time between leisure and exercise is above\n", + "\\begin{align*}\n", + "[u_{f} (B, F^{*}, \\Omega -E^{*}, c^{*};g ) - p_{F_{i}} u_{c}(B, F^{*}, \\Omega-E^{*}, c^{*};g)]\\mathcal{S}_E = u_{l}(B, F^{*}, \\Omega - E^{*})\\zeta_F + \\frac{a}{b} \\frac{\\zeta_l E_{t}^{*}}{\\Omega - E_{t}^{*}} = \\frac{\\zeta_c}{Y_t/\\mathcal{S}(B_t, B_{t+1}, \\epsilon_{t};E_t)p_{F_t} -1}\n", + "\\end{align*}\n", + "\n", + "where $\\mathcal{S}$ is the inverse of the health investment function with respect to its first argument.\n", + "\n", + "### Euler Equation\n", + "\n", + "The first order condition for the value function maximization is following\n", + "\n", + "\\begin{align*}\n", + "[P_{F_i} u_c (B,F,l,c) - u_f(B,F,l,c) \\mathcal{S}_{B^{'}}(B,B^{'},\\epsilon,E) =& \\beta E[u_{B} (B^{'},F^{'},l^{'})+u_{F}(B^{'},F^{'},l^{'})\\mathcal{S}_{B^{'}}(B^{'},B^{''},\\epsilon^{'},E^{'})]\\\\\n", + "& [p_{F_t} \\frac{\\zeta_c}{Y_t - p_{F_t}F_t}-\\frac{\\zeta_f}{F} ]\\frac{\\mathcal{F}}{a(g)B^{'}} = \\beta E[\\frac{\\zeta_{B}}{B^{'}} -\\frac{\\zeta_f}{F^{'}}\\frac{(1-\\delta^{'})\\mathcal{S}^{'}}{a(g)B^{'}}]\n", + "\\end{align*}\n", + "\n", + "where both consumption and exercise are expressed in terms the state variables, so that $F=\\mathcal{S}(B,B^{'},\\epsilon ,E)=[\\frac{B^{'}-(1-\\delta)B-\\epsilon}{\\phi E^{b(g)}}]^{1/a(g)}$ and $E=\\hat{\\xi}(B,B^{'},\\epsilon)$\n", + "\n", + "We can calibrate and simultate the model using the parameters estimated in the reduced form equations (Table 3).\n", + "Simulated evolution of Body Mass Index with differnt policy implementations are presented in Figure 8 and FIgure 9.\n", + "\n", + "\n", + "## Conclusion \n", + "\n", + "* The genotype of an individual can shift preferences as well as human capital production possibility frontiers. \n", + " \n", + " \n", + "* Adolescents carrying the A-allele in the FTO genotype are at greater risk of obesity, even when consuming the same calories and performing the same physical activity as the adolescents with the other genotype. Their production function is shifted, with a rate of conversion of calories into BMI 1/3 steeper. Instead of counterbalancing this effect with a stricter diet, they tend to consume 2% more calories, suggesting a difference in their preferences for food intake. There is no evidence of a significant interaction between the FTO genotype and physical activity. \n", + " \n", + " \n", + "* 35.4% of this differences is attributable to changes in productivity parameters of the BMI production function; the remaining 64.5% is attributable to changes in the investments. Secondly, calibrating a structural model. \n", + " \n", + " \n", + "* A high calorie tax almost eliminates the difference in BMI across genetic groups. An early childhood policy target at reducing caloric intake in the first 10 years of life does not have the same equalizing effect, but still manages to lower BMI in the long run.\n", + "\n", + "\n", + "\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": "3.7.4" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Figure 8.png b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Figure 8.png new file mode 100644 index 00000000..7e3d8816 Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Figure 8.png differ diff --git a/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Figure 9.png b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Figure 9.png new file mode 100644 index 00000000..e2f7f0a4 Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Figure 9.png differ diff --git a/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Table 3.png b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Table 3.png new file mode 100644 index 00000000..5d7f6785 Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Table 3.png differ diff --git a/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Table 7.png b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Table 7.png new file mode 100644 index 00000000..29968047 Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/Table 7.png differ diff --git a/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/untitled.txt b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/untitled.txt new file mode 100644 index 00000000..4f2859d8 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/Biroli(2015)/untitled.txt @@ -0,0 +1,251 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Guvenen, Kambourov, Kuruscu, Ocampo, and Chen" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# \"[Use it or lose it: efficiency gains from wealth taxation](https://fguvenendotcom.files.wordpress.com/2019/09/gkkoc-2019_v208_nber_wp_submit.pdf)\" (Draft)\n", + "\n", + "- Notebook created by Mateo Velásquez-Giraldo\n", + "- All figures and tables were taken from https://fguvenendotcom.files.wordpress.com/2019/09/gkkoc-2019_v208_nber_wp_submit.pdf on 09/15/2019." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Summary\n", + "\n", + "This paper uses a two-sector OLG model with heterogeneous entrepreneurial agents to explore how wealth and capital income taxation differ in their welfare implications when there is rate-of-return heterogeneity.\n", + "\n", + "The main findings are as follows:\n", + "* With rate-of-return heterogeneity, wealth taxation (as opposed to capital income taxation) shifts the tax burden towards unproductive entrepreneurs, and gives the productive ones better incentives to save. This generates a reallocation of capital towards productive entrepreneurs, raising output and allowing the government to lower labor income taxes.\n", + "* In a model aimed at matching the U.S., the authors simulation exercises display an average welfare gain of 7.5% in consumption terms to newborns from switching from capital income to wealth taxation.\n", + "* In the same model, the authors estimate that the optimal wealth tax rate is 2%-3%. In contrast, if only captial income and labor income taxes were available, it would be optimal to subsidize capital income.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Overview \n", + "\n", + "\n", + "#### Rate-of-return heterogeneity\n", + "\n", + "The recent empirical literature (e.g. Fagereng, Guiso, Malacrino and Pistaferri (2016a)) has found evidence that there is persistent heterogeneity on the risk-adjusted rates of return that households face on their assets. This is important because:\n", + "* A theoretical result implying that wealth and capital-income taxation are equivalent relies on the assumption that returns on investment are homogeneous.\n", + "* The empirical distribution of wealth has a thick tail that is not easily matched by models without rate-of-return heterogeneity.\n", + "\n", + "#### Non-technical methodological overview\n", + "\n", + "To assess the effects of wealth and capital income taxation, the authors construct a model in which agents have different degrees of entrepreneurial ability which also varies over time and generations. Therefore, unproductive agents can end up with large wealth from their predecesors or their youth. Futhermote, there are financial constraints that prevent wealth from perfectly reallocating to efficient entrepreneurs.\n", + "\n", + "The authors use simulations of the model under different tax policies to find their welfare implications.\n", + "\n", + "#### The two main effect of wealth taxation\n", + "\n", + "Switching from capital income taxes to wealth taxes has two main effects that help in understanding the results of the paper:\n", + "1. __\"Use it or lose it\" effect__: under capital income taxes, more productive entrepreneurs pay a higher taxes on their investments. Switching to wealth taxes reduces this phenomenon, redistributing the tax burden towards less productive entrepreneurs and allowing more productive ones to keep more of their capital than before.\n", + "\n", + "2. __\"Behavioral response\"__: taxes compress the distribution of after-tax returns, but this phenomenon is much larger under capital income taxation. Thus, switching to wealth taxation spreads the distribution of the effective returns to investment and elicits a saving response that shifts capital towards more productive agents." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The model\n", + "\n", + "#### Households/entrepreneurs\n", + "\n", + "* Households face mortality risk each period and can live up to $H$ years. When they die, they are replaced by an offspring with their wealth. \n", + "* They supply their labor and use their wealth to produce differentiated intermediate products.\n", + "\n", + "On each period they choose:\n", + "1. How much labor to supply.\n", + "2. How much of their income to consume and save.\n", + "3. How much of their wealth to invest in their own firm versus a riskless bond.\n", + "4. How much of their intermediate good to produce.\n", + "\n", + "They maximize $$\\mathbb{E}_0\\left\\{ \\sum_{h=1}^H \\beta^{h-1}\\phi_h u(c_h, 1-l_h) \\right\\}$$ where $\\phi_h$ is the unconditional probability of survival up to age $h$.\n", + "\n", + "#### Producers\n", + "\n", + "##### Intermediate goods\n", + "\n", + "Each household $i$ produces an intermediate good $x_i$ through the linear production function\n", + "\n", + "$$x_{i,h} = z_{i,h}\\times k_{i,h}$$\n", + "\n", + "where $z_{i,h}$ is the household's entrepreneurial productivity at age $h$ and $k_{i,h}$ is the ammount of final good used in production.\n", + "\n", + "##### Final good\n", + "\n", + "A profit-maximizing, price-taking firm uses labor and intermediate goods to produce the final good according to $$Y = Q^\\alpha L^{1-\\alpha}$$ where $Q=\\left( \\int x_{i,h}^\\mu di dh \\right)^{1/\\mu}$ and L is aggregate labor.\n", + "\n", + "Notice that Q serves as a quality-adjusted index of capital stock.\n", + "\n", + "#### Labor and entrepreneurial productivity\n", + "\n", + "Entrepreneurial productivity is imprefectly inherited according to\n", + "\n", + "$$log(\\bar{z}_i^{child}) = \\rho_z log(\\bar{z}_i^{parent}) + \\varepsilon_{\\bar{z}_i}$$\n", + "\n", + "and is altered through a three-state Markov chain $\\mathbb{I}_{i,h}\\in \\{H,L,0\\}$ that represents a \"fast lane\" (in which entrepreneurs with above-median ability are born), a normal state, and entrepreneurial retirement with transition matrix\n", + "\n", + "\\begin{equation}\n", + " \\Pi_{\\mathbb{I}}\\begin{bmatrix}\n", + " 1-p_1-p_2 & p_1 & p_2\\\\\n", + " 0 & 1-p_2 & p_2 \\\\\n", + " 0 & 0 & 1\n", + " \\end{bmatrix}.\n", + "\\end{equation}\n", + "\n", + "Actual productivity is then defined as\n", + "\n", + "\\begin{equation}\n", + "z_{i,h} = \\begin{cases}\n", + "\\bar{z}_i^\\lambda, & \\text{if} \\quad \\mathbb{I}_{i,h} = H\\\\\n", + "\\bar{z}_i, & if \\quad \\mathbb{I}_{i,h} = L\\\\\n", + "0, & if \\quad \\mathbb{I}_{i,h} = 0\\\\\n", + "\\end{cases}\n", + "\\end{equation}\n", + "\n", + "with $\\lambda > 1$.\n", + "\n", + "Labor productivity has a permanent imperfectly inherited component, a life cycle component, and a random AR(1) component.\n", + "\n", + "#### The individuals' decision problems\n", + "\n", + "##### Static production/allocation problem\n", + "\n", + "Given his assets an productivity an entrepreneur decides how much capital to use in his firm\n", + "\n", + "\\begin{equation}\n", + " \\pi (a,z) = \\max_{k \\leq \\vartheta(z)a} \\{ p(z k)\\times zk - (r+\\delta)k \\}\n", + "\\end{equation}\n", + "\n", + "where $p(\\cdot)$ gives the price of the intermediate good. Notice that there is a collateral constraint, where $\\vartheta(z)\\geq 1$ and non-decreasing.\n", + "\n", + "##### Dynamic problem\n", + "\n", + "The problem and value function of a household of age $h$ is given by\n", + "\n", + "\\begin{align}\n", + " V_h(a;\\mathbf{S}) = &\\max_{c,l,a'} u(c,1-l) + \\beta\\frac{\\phi_{h+1}}{\\phi_{h}} \\mathbb{E}[V_{h+1}(a',\\mathbf{S}')|S]\\\\\n", + " \\text{s.t.} \\quad & a' = \\mathcal{Y}(a,l;z,e,\\kappa;\\mathcal{T}) - c(1+\\tau_c)\\\\\n", + " & a'\\geq 0\n", + "\\end{align}\n", + "\n", + "where $\\mathcal{Y}$ denotes the total disposable income of the individual after production and taxation, $\\mathbf{S}$ is the vector of individual exogenous states, and $\\mathcal{T}$ represents the tax system.\n", + "\n", + "#### Government\n", + "\n", + "The government can tax consumption, labor income, capital income, and wealth. It uses its funds to fund pension payments to retirees and a fixed level of exogenous expenditure. It is assumed to always run a balanced budget." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Results\n", + "\n", + "The authors conduct various experiments. We now report the main ones." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Substituting capital income taxes for wealth taxes\n", + "\n", + "Here, the authors ask what would happen if the government left consumption and labor income taxes at their current levels, eliminates capital income taxes ($\\tau_k=0$) and introduced wealth taxes ($\\tau_a$) at a rate enough to keep pension payments constant at their pre-reform levels.\n", + "\n", + "The following table presents the equilibrium changes of macroeconomic variables induced by this change (in the columns labeled RN).\n", + "\n", + "
\n", + "\n", + "The results show that output and consumption increase through an increase in the quality-adjusted capital stock and labor. Intuitively, the tax change leads not only to both an increase and a reallocation of $K$ towards more efficient entrepreneurs ($\\Delta Q > \\Delta K$). This gain in efficiency allows for higher wages and incentivizes a greater labor supply.\n", + "\n", + "The next table (on the RN panel) shows how the welfare changes from the experiment are distributed across age and entrepreneurial ability. The welfare change is calculated as the perpetual percentage change in consumption that would make agents indifferent between the pre and post-change equilibria.\n", + "\n", + "
\n", + "\n", + "The welfare effects are largely possitive except for retirees, who face a higher tax rate on their wealth with their pensions held constant." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Optimal taxation\n", + "\n", + "In this section the authors consider a government that is maximizing the welfare of a newborn by choosing either\n", + "1. The capital income tax rate and the labor income tax rate. Denoted OCIT.\n", + "2. The wealth tax rate and the labor income tax rate. Denoted OWT.\n", + "subject to the constraint of raising enough revenues to pay for its expenditures and for social security.\n", + "\n", + "The following table presents the results optimal tax rates and average welfare gains from each of the experiments (OCIT in the column labeled $\\tau_k$ and OWT in the column labeled $\\tau_a$).\n", + "\n", + "
\n", + "\n", + "The table shows that both reforms produce average welfare gains, that the optimal income capital tax in the OCIT case is a large subsidy, and that the optimal wealth tax in the OWT case is just above 3%. The average welfare gain is greater under wealth taxation.\n", + "\n", + "The following table examines the welfare changes in macroeconomic variables under the two scenarios (on the columns $\\tau_k$ and $\\tau_a$)\n", + "\n", + "
\n", + "\n", + "The table shows that under OCIT a very large increase in the stock of capital occurs, given that its returns are subsidized. Also, as the government needs to balance its budget given the subsidies, labor income taxes are increased and thus, the increase in after-tax wages is modest, so there are level gains with distributional losses. On the other hand, under OWT, there is a very modest increase in the stock of capital, but a large gain in efficiency (compare $Q$ with K and see and TFP) due to the reallocation mechanism. Since the wealth tax allows for a lower labor income tax rates, higher after-tax wages and a labor increase.\n", + "\n", + "This experiment shows that the OCIT shifts the tax burden from capital to labor, and the OWT does the opposite.\n", + "\n", + "An important point to consider is that since under OCIT the capital stock must dramatically increase, accounting for a transition period generates short term welfare losses given that higher savings are required. The required thightening is much softer under OWT, since the increase in the capital stock is subtle. This point strengthens the argument for wealth taxes." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "In the presence of rate-of-return heterogeneity, capital income taxes disproportionately affect productive entrepreneurs. Switching to wealth taxation moves the tax burden towards unproductive entrepreneurs and increases after-tax return heterogeneity, which elicits a reallocation of capital towards productive entrepreneurs. The increased efficiency and the expanded tax base increase output and allow the government to reduce labor income taxes. The authors therefore conclude that wealth taxation can increase efficiency and output while decreasing consumption inequality.\n", + "\n", + "Through simulation exercises calibrated to match U.S. data, the authors find that the optimal wealth tax rate is around 3%." + ] + } + ], + "metadata": { + "jupytext": { + "encoding": "# -*- coding: utf-8 -*-", + "formats": "ipynb,py:percent" + }, + "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/CulturalChangeAsLearning/Cultural-change-as-learning-slide.ipynb b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Cultural-change-as-learning-slide.ipynb new file mode 100644 index 00000000..fc99d901 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Cultural-change-as-learning-slide.ipynb @@ -0,0 +1,1454 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "
Cultural Change as Learning:

\n", + "
The Evolution of Female Labor Force

\n", + "
Paritcipation over a Century
\n", + "

\n", + "
Wonsik Ko
\n", + "
Johns Hopkins University
\n", + "

\n", + "
Computational Method, November 2020

\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# What drives the evolution of Female Labor Force Participation Rate?\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "## Dynamic Model with beleif updating " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "### Beliefs evolve endogenously via an intergenerational learning process." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Model\n", + "\n", + "\\begin{align*}\n", + "U(w_{f}, w_{h}, v_{i})&=\\frac{c^{1-\\gamma}}{1-\\gamma}-\\textbf{1} (E_{i t}v_i)\\\\\n", + "c = w_h + \\textbf{1} w_f, v_i &=l_i + B_i , B_i = \\beta + u_i , E(u_i)=0\n", + "\\end{align*}\n", + "\n", + "* $\\textbf{1}$: an indicator function that takes the value one if she works.\n", + "* $w_f$: a woman's earning\n", + "* $w_h$: a husband's earning\n", + "* $l_i$: a known idiosyncratic component of disutility of working with distribution in the population G(l)\n", + "* $B_i$: an individual-level realization of a random variable that is iid across women\n", + "* Consumption is a household public good\n", + "* $\\beta \\in \\{\\beta_H, \\beta_L\\}$, $\\beta_H >\\beta_L \\geq 0$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "source": [ + "#### Prior to making her work decision, a woman inherits her mother's private signal $s_i$ that yields information about true $\\beta$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\\begin{align*}\n", + "s_i = \\beta + \\epsilon_i\n", + "\\end{align*}\n", + "where $\\epsilon \\sim N(0,\\sigma_{\\epsilon}^2)$\n", + "\n", + "With signal $s_i$, updating her prior belief using Bayes' rule." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\n", + "Consider a woman i in period t who has a prior belief about $\\beta$ as summarized in the log likelihood ratio (LLR) $\\lambda_t = ln \\frac{P(\\beta=\\beta_L)}{P(\\beta=\\beta_H)}$. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "By Bayes rule, her beliefs given her private signal s can be summarized in a new LLR, $\\lambda_{i t}(s)$ given by" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "\\begin{align*}\n", + "\\lambda_{i t}(s)=\\lambda_t + ln(\\frac{P(s|\\beta=\\beta_L)}{P(s|\\beta=\\beta_H)})=\\lambda_t - (\\frac{\\beta_H - \\beta_L}{\\sigma_{\\epsilon}^2})(s-\\bar{\\beta})\n", + "\\end{align*}\n", + "where $\\bar{\\beta}=(\\beta_H+\\beta_L)/2$, $s \\sim N(\\beta, \\sigma_{\\epsilon}^2)$, $\\lambda_{it} \\sim N(\\lambda_t - (\\frac{\\beta_H-\\beta_L}{\\sigma_{\\epsilon}^2})(\\beta - \\bar{\\beta}), \\frac{(\\beta_H-\\beta_L)^2}{\\sigma_{\\epsilon}^2})$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Work iff $W(w_{h t}, w_{f t})=\\frac{1}{1-\\gamma}[(w_{h t}+w_{f t})^{1-\\gamma} - w_{h t}^{1-\\gamma} ] - E_{i t}(\\beta) \\geq l_i$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Low $l(l \\leq \\underline{l})$ will always work\n", + "\n", + "High l $(l \\geq \\bar{l})$ will never choose to work." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "\\begin{align*}\n", + "\\underline{l}(w_{h t}, w_{f t}) &= W(w_{h t}, w_{f t})-\\beta_H\\\\\n", + "\\bar{l}(w_{h t}, w_{f t})&=W(w_{h t}, w_{f t})-\\beta_L\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "$s_{l}^{*}(\\lambda)$ is the value where a woman is indifferent between working and not working." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "\\begin{align*}\n", + "s_{l}^{*} (\\lambda_t ; w_{h t}, w_{f t} )=\\bar{\\beta} + (\\frac{\\sigma_{\\epsilon}^2}{\\beta_H-\\beta_L})(\\lambda_t + ln (\\frac{\\bar{l}(w_{h t}, w_{f t})-l}{l_l - \\underline{l}(w_{h t}, w_{f t})})) = s_{l}^{*}(\\lambda_t)\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "$L_{l t}(\\beta ; \\lambda_t)$ is the proportion of women who will choose to work" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "\\begin{align*}\n", + "L_t(\\beta ; \\lambda_t) = G(\\underline{l})+\\int_{\\underline{l}}^{\\bar{l}} F(s_{l}^{*}(\\lambda_t)-\\beta ; \\sigma_{\\epsilon})g(l)dl\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Intergenerational Transmission of Belief\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "The prior of generation t (its \"culture\"), $\\lambda_t$\n", + "\n", + "Updated with idiosyncratic private signal, $s_i$\n", + "\n", + "Ends up with $\\lambda_{i t}(s)$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "observe a noisy signal of $L_t$, given by $y_t$\n", + "\n", + "\\begin{align*}\n", + "y_t(\\beta ; \\lambda_t ) = L_t (\\beta ; \\lambda_t ) + \\eta_t\n", + "\\end{align*}\n", + "\n", + "where $\\eta_t \\sim N(0, \\sigma_{\\eta}^2)$ with a pdf $h(\\cdot;\\sigma_{\\eta})$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Again using Bayes rule\n", + "\n", + "\\begin{align*}\n", + "\\lambda_{t+1}(\\lambda_t , y_t) = \\lambda_t + ln\\frac{h(y_t | \\beta =\\beta_L)}{h(y_t|\\beta = \\beta_H)} = \\lambda_t + (\\frac{L_{t}(\\beta_L ;\\lambda_t)-L_t(\\beta_H ; \\lambda_t)}{\\sigma_{\\eta}^2})(y_t -\\bar{L}_t(\\lambda_t))\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Calibration Strategy\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Data\n", + "\n", + "* Before 1940: The median earnings of full-time white men and women in 1890.\n", + "\n", + "* After 1940, the 1% IPUMS samples of the U.S. Census for yearly earnings.\n", + "\n", + "* The probability that a woman worked in 1980 conditional on her mother's work behavior: General Social Survey (GSS)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Calibration matching: \n", + "\n", + "* Female LFP in 1980, 1990, and 2000 \n", + "\n", + "* The own and cross-wage elasticity in 2000\n", + "\n", + "* The cross-wage elasticity in 1990\n", + "\n", + "* The relative probability of a woman working in 1980.\n", + "\n", + "\n", + "* Table 1 shows the calibration target and the values obatained in the calibrated learning model.\n", + "\n", + "* Figure 4 presents the LFP predictions from the calibrated model." + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "cite2c": { + "citations": { + "6273435/2BJ6FM4X": { + "author": [ + { + "family": "Arslan", + "given": "Yavuz" + }, + { + "family": "Guler", + "given": "Bulent" + }, + { + "family": "Kuruscu", + "given": "Burhanettin" + } + ], + "id": "6273435/2BJ6FM4X", + "issued": { + "year": 2018 + }, + "title": "Bank Balance Sheets and Boom-Bust Cycles", + "type": "report" + }, + "6273435/2LKSCVY3": { + "DOI": "10.1016/j.jue.2009.11.001", + "URL": "http://www.sciencedirect.com/science/article/pii/S0094119009000977", + "abstract": "In a recent paper, Leamer (2007) identified housing as an important precursor of the national business cycle. Previous work, on the other hand, has shown that regional cycles may not be synchronous with the aggregate cycle. In this paper, we analyze the relationship between housing and the business cycle at the MSA-level for a set of 51 US cities. We find that declines in house prices are often not followed by declines in that city’s employment. While the growth rates in housing variables appeared to slow ahead of city-level peaks, we find no consistent statistical relationship suggesting a city’s permits or prices influences its business cycle. In fact, we find that national permits are a better leading indicator for a city’s employment than a city’s own permits. This suggest the possibility that housing is merely a proxy for other consumption or wealth indicators.", + "accessed": { + "day": 6, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Ghent", + "given": "Andra C." + }, + { + "family": "Owyang", + "given": "Michael T." + } + ], + "container-title": "Journal of Urban Economics", + "container-title-short": "Journal of Urban Economics", + "id": "6273435/2LKSCVY3", + "issue": "3", + "issued": { + "day": 1, + "month": 5, + "year": 2010 + }, + "journalAbbreviation": "Journal of Urban Economics", + "page": "336-351", + "page-first": "336", + "shortTitle": "Is housing the business cycle?", + "title": "Is housing the business cycle? Evidence from US cities", + "title-short": "Is housing the business cycle?", + "type": "article-journal", + "volume": "67" + }, + "6273435/3SMCKLDX": { + "DOI": "10.1093/rfs/hhw018", + "URL": "https://academic.oup.com/rfs/article/29/7/1635/2607168", + "abstract": "Abstract. This paper highlights the importance of middle-class and high-FICO borrowers for the mortgage crisis. 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These mortgage contracts are designed to stave off home owner default by providing payment relief in the wake of a large house price shock. SAMs have been hailed as an innovative solution that could prevent the next foreclosure crisis, act as a work-out tool during a crisis, and alleviate fiscal pressure during a downturn. They have inspired Fintech companies to offer home equity contracts. However, the home owner's gains are the mortgage lender's losses. A general equilibrium model with financial intermediaries who channel savings from saver households to borrower households shows that indexation of mortgage payments to aggregate house prices increases financial fragility, reduces risk sharing, and leads to expensive financial sector bailouts. In contrast, indexation to local house prices reduces financial fragility and improves risk-sharing. The two types of indexation have opposite implications for wealth inequality.", + "author": [ + { + "family": "Greenwald", + "given": "Daniel" + }, + { + "family": "Landvoigt", + "given": "Tim" + }, + { + "family": "Van Nieuwerburgh", + "given": "Stijn" + } + ], + "genre": "MIT Sloan Research Paper", + "id": "6273435/62FERJKI", + "issued": { + "year": 2018 + }, + "language": "en", + "number": "5261-17", + "publisher": "MIT", + "title": "Financial Fragility with SAM?", + "type": "report" + }, + "6273435/6ASZQUFK": { + "author": [ + { + "family": "Kahneman", + "given": "Daniel" + } + ], + "event-place": "New York", + "id": "6273435/6ASZQUFK", + "issued": { + "year": 2011 + }, + "publisher": "Farrar, Straus and Giroux", + "publisher-place": "New York", + "title": "Thinking, Fast and Slow", + "type": "book" + }, + "6273435/6HQGCZHA": { + "DOI": "10.1093/qje/qjx017", + "URL": "https://academic.oup.com/qje/article/132/4/1755/3854928", + "abstract": "Abstract. An increase in the household debt to GDP ratio predicts lower GDP growth and higher unemployment in the medium run for an unbalanced panel of 30 coun", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Mian", + "given": "Atif" + }, + { + "family": "Sufi", + "given": "Amir" + }, + { + "family": "Verner", + "given": "Emil" + } + ], + "container-title": "The Quarterly Journal of Economics", + "container-title-short": "Q J Econ", + "id": "6273435/6HQGCZHA", + "issue": "4", + "issued": { + "day": 1, + "month": 11, + "year": 2017 + }, + "journalAbbreviation": "Q J Econ", + "language": "en", + "page": "1755-1817", + "page-first": "1755", + "title": "Household Debt and Business Cycles Worldwide", + "type": "article-journal", + "volume": "132" + }, + "6273435/8IVI23TT": { + "author": [ + { + "family": "Schlafmann", + "given": "Kathrin" + } + ], + "genre": "CEPR Discussion Paper", + "id": "6273435/8IVI23TT", + "issued": { + "year": 2016 + }, + "number": "11589", + "title": "Housing, Mortgages, and Self Control", + "type": "report" + }, + "6273435/98I3UQNW": { + "author": [ + { + "family": "Minsky", + "given": "Hyman P." + } + ], + "id": "6273435/98I3UQNW", + "issued": { + "year": 1986 + }, + "title": "Stabilizing an Unstable Economy", + "type": "book" + }, + "6273435/9ERTKWRC": { + "author": [ + { + "family": "Garcia", + "given": "Daniel" + } + ], + "id": "6273435/9ERTKWRC", + "issued": { + "year": 2018 + }, + "title": "Employment in the Great Recession: How Important were Household Credit Supply Shocks?", + "type": "report" + }, + "6273435/9GRH68SP": { + "author": [ + { + "family": "Bartscher", + "given": "Alina" + }, + { + "family": "Schularick", + "given": "Moritz" + }, + { + "family": "Steins", + "given": "Ulrike I." + } + ], + "id": "6273435/9GRH68SP", + "issued": { + "year": 2017 + }, + "title": "The Great American Debt Boom, 1948-2013", + "type": "report" + }, + "6273435/A2G7SCE7": { + "URL": "https://ideas.repec.org/a/fip/fedkpr/y2007p149-233.html", + "abstract": "Of the components of GDP, residential investment offers by far the best early warning sign of an oncoming recession. Since World War II we have had eight recessions preceded by substantial problems in housing and consumer durables. Housing did not give an early warning of the Department of Defense Downturn after the Korean Armistice in 1953 or the Internet Comeuppance in 2001, nor should it have. By virtue of its prominence in our recessions, it makes sense for housing to play a prominent role in the conduct of monetary policy. A modified Taylor Rule would depend on a long-term measure of inflation having little to do with the phase in the cycle, and, in place of Taylor's output gap, housing starts and the change in housing starts, which together form the best forward-looking indicator of the cycle of which I am aware. This would create pre-emptive anti-inflation policy in the middle of the expansions when housing is not so sensitive to interest rates, making it less likely that anti-inflation policies would be needed near the ends of expansions when housing is very interest rate sensitive, thus making our recessions less frequent and/or less severe.
(This abstract was borrowed from another version of this item.)", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Leamer", + "given": "Edward E." + } + ], + "container-title": "Proceedings - Economic Policy Symposium - Jackson Hole", + "id": "6273435/A2G7SCE7", + "issued": { + "year": 2007 + }, + "language": "en", + "page": "149-233", + "page-first": "149", + "title": "Housing is the business cycle", + "type": "article-journal" + }, + "6273435/AR5CX6Z6": { + "author": [ + { + "family": "Nagel", + "given": "Stefan" + }, + { + "family": "Xu", + "given": "Zhengyang" + } + ], + "id": "undefined", + "issued": { + "year": 2018 + }, + "language": "en", + "page": "56", + "page-first": "56", + "title": "Asset Pricing with Fading Memory", + "type": "article-journal" + }, + "6273435/AV7DSQTR": { + "URL": "https://www.businessinsider.com/how-to-spot-stock-market-bubbles-2017-10", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Chudley", + "given": "Jody" + } + ], + "container-title": "Business Insider", + "id": "6273435/AV7DSQTR", + "title": "JFK's father used a simple trick to spot market bubbles — and you can too", + "type": "webpage" + }, + "6273435/BL42NIKV": { + "author": [ + { + "family": "Finocchiaro", + "given": "Daria" + }, + { + "family": "Jonsson", + "given": "Magnus" + }, + { + "family": "Nilsson", + "given": "Christian" + }, + { + "family": "Strid", + "given": "Ingvar" + } + ], + "container-title": "Sveriges Riksbank Economic Review", + "id": "6273435/BL42NIKV", + "issued": { + "year": 2018 + }, + "title": "Macroeconomic effects of reducing household debt", + "type": "article-journal" + }, + "6273435/BLFT9BEG": { + "author": [ + { + "family": "Mackay", + "given": "Charles" + } + ], + "id": "6273435/BLFT9BEG", + "issued": { + "year": 1841 + }, + "language": "English", + "publisher": "Richard Bentley", + "shortTitle": "Extraordinary Popular Delusions", + "title": "Extraordinary Popular Delusions and the Madness of Crowds", + "title-short": "Extraordinary Popular Delusions", + "type": "book" + }, + "6273435/D7FS5MRE": { + "URL": "http://www.nber.org/papers/w22903", + "abstract": "This paper studies temporary policy incentives designed to address capital overhang by inducing asset demand from buyers in the private market. Using variation across local geographies in ex ante program exposure and a difference-in-differences design, we find that the First-Time Homebuyer Credit induced a cumulative increase in home sales of 397 to 546 thousand, or 7.8 to 10.7 percent, nationally. We find little evidence of a sharp reversal of the policy response; instead, demand comes from several years in the future. The program likely sped the process of reallocating homes from distressed sellers to high value buyers, which stabilized house prices. The response is concentrated in the existing home sales market, implying the stimulative effects of the program were less important than its role in accelerating reallocation.", + "accessed": { + "day": 9, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Berger", + "given": "David" + }, + { + "family": "Turner", + "given": "Nicholas" + }, + { + "family": "Zwick", + "given": "Eric" + } + ], + "genre": "Working Paper", + "id": "6273435/D7FS5MRE", + "issued": { + "month": 12, + "year": 2016 + }, + "note": "DOI: 10.3386/w22903", + "number": "22903", + "publisher": "National Bureau of Economic Research", + "title": "Stimulating Housing Markets", + "type": "report" + }, + "6273435/DCC92Q2Z": { + "URL": "http://www.economist.com/special-report/2003/05/29/house-of-cards", + "abstract": "In many countries the stockmarket bubble has been replaced by a property-price bubble. Sooner or later it will burst, says Pam Woodall, our economics editor", + "accessed": { + "day": 6, + "month": 9, + "year": 2018 + }, + "container-title": "The Economist", + "id": "6273435/DCC92Q2Z", + "issued": { + "day": 29, + "month": 5, + "year": 2003 + }, + "title": "House of cards", + "type": "article-magazine" + }, + "6273435/EB4C5G4S": { + "author": [ + { + "family": "Kindleberger", + "given": "Charles P." + } + ], + "id": "6273435/EB4C5G4S", + "issued": { + "year": 1978 + }, + "language": "en", + "publisher": "Palgrave Macmillan", + "title": "Manias, Panics, and Crashes: A History of Financial Crises", + "type": "book" + }, + "6273435/EGT99GAZ": { + "author": [ + { + "family": "Walentin", + "given": "Karl" + }, + { + "family": "Hull", + "given": "Isaiah" + }, + { + "family": "Olovsson", + "given": "Conny" + } + ], + "genre": "Sveriges Riksbank Working Paper Series", + "id": "6273435/EGT99GAZ", + "issued": { + "year": 2018 + }, + "number": "349", + "title": "The Granular Origins of Aggregate House Price Volatility", + "type": "report" + }, + "6273435/EJUQGA4W": { + "author": [ + { + "family": "Albanesi", + "given": "Stefania" + } + ], + "id": "6273435/EJUQGA4W", + "issued": { + "year": 2018 + }, + "title": "Real Estate Investors and the 2007-2009 Mortgage Crisis", + "type": "report" + }, + "6273435/EXL57QX8": { + "author": [ + { + "family": "Khan", + "given": "Shujaat" + } + ], + "id": "6273435/EXL57QX8", + "issued": { + "year": 2018 + }, + "title": "The Anatomy of Macroprudential Policies in a Heterogeneous Agent Model of Housing Default", + "type": "report" + }, + "6273435/HAEFCS8B": { + "DOI": "10.1257/aer.91.2.1", + "URL": "https://www.aeaweb.org/articles?id=10.1257/aer.91.2.1", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Hall", + "given": "Robert E." + } + ], + "container-title": "American Economic Review", + "id": "6273435/HAEFCS8B", + "issue": "2", + "issued": { + "month": 5, + "year": 2001 + }, + "language": "en", + "page": "1-11", + "page-first": "1", + "title": "Struggling to Understand the Stock Market", + "type": "article-journal", + "volume": "91" + }, + "6273435/HRF5MEAR": { + "DOI": "10.1086/680584", + "URL": "https://www.journals.uchicago.edu/doi/10.1086/680584", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Hall", + "given": "Robert E." + } + ], + "container-title": "NBER Macroeconomics Annual", + "container-title-short": "NBER Macroeconomics Annual", + "id": "6273435/HRF5MEAR", + "issue": "1", + "issued": { + "day": 1, + "month": 1, + "year": 2015 + }, + "journalAbbreviation": "NBER Macroeconomics Annual", + "page": "71-128", + "page-first": "71", + "title": "Quantifying the Lasting Harm to the US Economy from the Financial Crisis", + "type": "article-journal", + "volume": "29" + }, + "6273435/HZE378I7": { + "URL": "https://www.brookings.edu/wp-content/uploads/2003/06/2003b_bpea_caseshiller.pdf", + "abstract": "This paper looks for evidence of a bubble in U.S. housing prices. It analyzes quarterly state-level data over 1985-2002, focusing on the relationship between home prices and selected fundamental variables. Income per capita alone largely explains price changes in all but eight states; in the latter, large price movements are observed unrelated to the fundamentals. Results from a new survey of recent homebuyers in the Los Angeles, San Francisco, Boston, and Milwaukee metropolitan areas are reported. This survey replicates an almost identical 1988 survey and finds, as before, that buyers in most of these markets perceive little risk in their housing investment, have unrealistic expectations about future price increases, and hold economically implausible beliefs about home price behavior—findings consistent with a bubble. Prices in such markets could stall or decline, but only if such declines are simultaneous or spread to other markets are significant effects on the national economy likely.", + "author": [ + { + "family": "Case", + "given": "Karl E." + }, + { + "family": "Shiller", + "given": "Robert J." + } + ], + "collection-title": "Brookings Papers on Economic Activity", + "id": "6273435/HZE378I7", + "issued": { + "year": 2003 + }, + "publisher": "Brookings Institute", + "title": "Is There a Bubble in the Housing Market?", + "type": "report" + }, + "6273435/JMNWJTKW": { + "DOI": "10.1016/j.iref.2015.02.002", + "URL": "http://www.sciencedirect.com/science/article/pii/S1059056015000246", + "abstract": "There has been, in recent years, a renewed interest in and a growing recognition of the role played by uncertainty shocks in driving fluctuations in the economy and in asset markets. We create new text-based indicators of both general economic and policy specific uncertainty from New York Times and use them first, to chart changes in the level of uncertainty in the US for the period 1985–2007, second, to determine the role of policy in these swings, and, third to assess their impact on the economy, equity markets, and business cycles. Overall, our results indicate that uncertainty shocks – both general and policy related – depress the level of economic activity, significantly increase stock market volatility, and decrease market returns.", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Alexopoulos", + "given": "Michelle" + }, + { + "family": "Cohen", + "given": "Jon" + } + ], + "container-title": "International Review of Economics & Finance", + "container-title-short": "International Review of Economics & Finance", + "id": "6273435/JMNWJTKW", + "issued": { + "day": 1, + "month": 11, + "year": 2015 + }, + "journalAbbreviation": "International Review of Economics & Finance", + "page": "8-28", + "page-first": "8", + "shortTitle": "The power of print", + "title": "The power of print: Uncertainty shocks, markets, and the economy", + "title-short": "The power of print", + "type": "article-journal", + "volume": "40" + }, + "6273435/JYAC2RG2": { + "URL": "https://ideas.repec.org/a/fip/fedker/y2007iqivp115-145nv.92no.4.html", + "abstract": "Residential foreclosures in the United States have been rising very rapidly since 2006. In the second quarter of 2007, the share of outstanding mortgages in some stage of foreclosure stood at 1.4 percent, near historic highs and up from less than 1 percent a year earlier. The number of mortgages entering the foreclosure process reached an all-time high in mid-2007, suggesting that the foreclosure surge is likely to get worse before it gets better. ; The foreclosure surge was created by a perfect storm of events. First, in recent years the share of subprime mortgage originations increased substantially. Second, foreclosure rates for adjustable-rate mortgages (ARMs) have increased considerably, especially for subprime ARMs. This increase is largely due to rising short-term interest rates and to payment resets for many nontraditional mortgages. Finally, high loan-to-value originations in recent years, coupled with stagnant or falling home prices, have left many people with insufficient equity to sell or refinance their homes. ; Edmiston and Zalneraitis provide a detailed dissection of the current foreclosure surge. They conclude with a discussion of why the foreclosure situation is likely to get worse over the next one to two years and why it is likely to improve afterward.", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Edmiston", + "given": "Kelly D." + }, + { + "family": "Zalneraitis", + "given": "Roger" + } + ], + "container-title": "Economic Review", + "id": "6273435/JYAC2RG2", + "issue": "Q IV", + "issued": { + "year": 2007 + }, + "language": "en", + "page": "115-145", + "page-first": "115", + "shortTitle": "Rising foreclosures in the United States", + "title": "Rising foreclosures in the United States: a perfect storm", + "title-short": "Rising foreclosures in the United States", + "type": "article-journal" + }, + "6273435/LGD94T7L": { + "URL": "https://www.federalreserve.gov/boarddocs/speeches/2004/20040521/default.htm", + "author": [ + { + "family": "Gramlich", + "given": "Edward M." + } + ], + "id": "6273435/LGD94T7L", + "issued": { + "year": 2004 + }, + "note": "Remarks by Governor Edward M. Gramlich at the Financial Services Roundtable Annual Housing Policy Meeting, Chicago, Illinois.", + "title": "Subprime Mortgage Lending: Benefits, Costs, and Challenges", + "type": "webpage" + }, + "6273435/MRW6WNVP": { + "author": [ + { + "family": "Blinder", + "given": "Alan S." + } + ], + "id": "6273435/MRW6WNVP", + "issued": { + "year": 2013 + }, + "publisher": "Penguin Press", + "title": "After the Music Stopped: The Financial Crisis, the Response, and the Work Ahead", + "type": "book" + }, + "6273435/N2QBSRRP": { + "URL": "https://faculty.missouri.edu/~hedlunda/research/housing_boombust_main.pdf", + "author": [ + { + "family": "Garriga", + "given": "Carlos" + }, + { + "family": "Hedlund", + "given": "Aaron" + } + ], + "id": "6273435/N2QBSRRP", + "issued": { + "year": 2018 + }, + "title": "Housing Finance, Boom-Bust Episodes, and\nMacroeconomic Fragility", + "type": "report" + }, + "6273435/PUJGD86E": { + "URL": "http://www.nber.org/chapters/c13907", + "accessed": { + "day": 9, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Manski", + "given": "Charles F." + } + ], + "container-title": "NBER Macroeconomics Annual 2017, volume 32", + "id": "6273435/PUJGD86E", + "issued": { + "day": 10, + "month": 4, + "year": 2017 + }, + "page": "411-471", + "page-first": "411", + "shortTitle": "Survey Measurement of Probabilistic Macroeconomic Expectations", + "title": "Survey Measurement of Probabilistic Macroeconomic Expectations: Progress and Promise", + "title-short": "Survey Measurement of Probabilistic Macroeconomic Expectations", + "type": "article-journal" + }, + "6273435/Q7UH3SHN": { + "DOI": "10.1257/089533005775196769", + "URL": "https://www.aeaweb.org/articles?id=10.1257/089533005775196769", + "abstract": "How does one tell when rapid growth in house prices is caused by fundamental factors of supply and demand and when it is an unsustainable bubble? In this paper, we explain how to assess the state of house prices—both whether there is a bubble and what underlying factors support housing demand—in a way that is grounded in economic theory. In doing so, we correct four common fallacies about the costliness of the housing market. For a number of reasons, conventional metrics for assessing pricing in the housing market such as price-to-rent ratios or price-to-income ratios generally fail to reflect accurately the state of housing costs. To the eyes of analysts employing such measures, housing markets can appear \"exuberant\" even when houses are in fact reasonably priced. We construct a measure for evaluating the cost of home owning that is standard for economists—the imputed annual rental cost of owning a home, a variant of the user cost of housing—and apply it to 25 years of history across a wide variety of housing markets. This calculation enables us to estimate the time pattern of housing costs within a market. As of the end of 2004, our analysis reveals little evidence of a housing bubble.", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Himmelberg", + "given": "Charles" + }, + { + "family": "Mayer", + "given": "Christopher" + }, + { + "family": "Sinai", + "given": "Todd" + } + ], + "container-title": "Journal of Economic Perspectives", + "id": "6273435/Q7UH3SHN", + "issue": "4", + "issued": { + "month": 12, + "year": 2005 + }, + "language": "en", + "page": "67-92", + "page-first": "67", + "shortTitle": "Assessing High House Prices", + "title": "Assessing High House Prices: Bubbles, Fundamentals and Misperceptions", + "title-short": "Assessing High House Prices", + "type": "article-journal", + "volume": "19" + }, + "6273435/TJ86B67S": { + "author": [ + { + "family": "Mian", + "given": "Atif" + }, + { + "family": "Sufi", + "given": "Amir" + } + ], + "container-title": "Journal of Economic Perspectives", + "id": "6273435/TJ86B67S", + "issue": "3", + "issued": { + "year": 2018 + }, + "page": "1-30", + "page-first": "1", + "title": "Finance and Business Cycles: The Credit-Driven Household Demand Channel", + "type": "article-journal", + "volume": "32" + }, + "6273435/UWMQ3ND7": { + "URL": "http://www.nber.org/papers/w23281", + "abstract": "This paper extends the benchmark New-Keynesian model with a representative agent and rational expectations by introducing two key frictions: (1) agent heterogeneity with incomplete markets, uninsurable idiosyncratic risk, and occasionally-binding borrowing constraints; and (2) bounded rationality in the form of level-k thinking. Compared to the benchmark model, we show that the interaction of these two frictions leads to a powerful mitigation of the effects of monetary policy, which is much more pronounced at long horizons, and offers a potential rationalization of the “forward guidance puzzle”. Each of these frictions, in isolation, would lead to no or much smaller departures from the benchmark model. We conclude that the interaction of bounded rationality and market frictions improves the ability of the model to account for the effects of monetary policy.", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Farhi", + "given": "Emmanuel" + }, + { + "family": "Werning", + "given": "Iván" + } + ], + "genre": "Working Paper", + "id": "6273435/UWMQ3ND7", + "issued": { + "month": 3, + "year": 2017 + }, + "note": "DOI: 10.3386/w23281", + "number": "23281", + "publisher": "National Bureau of Economic Research", + "title": "Monetary Policy, Bounded Rationality, and Incomplete Markets", + "type": "report" + }, + "6273435/V8M7KIK5": { + "URL": "https://www.brookings.edu/wp-content/uploads/2016/03/ByrneEtAl_ProductivityMeasurement_ConferenceDraft.pdf", + "author": [ + { + "family": "Byrne", + "given": "David M." + }, + { + "family": "Fernald", + "given": "John G." + }, + { + "family": "Reinsdorf", + "given": "Marshall B." + } + ], + "genre": "Brookings Papers on Economic Activity", + "id": "6273435/V8M7KIK5", + "issued": { + "year": 2016 + }, + "publisher": "Brookings Institute", + "title": "Does the United States have a productivity slowdown or a measurement problem?", + "type": "report" + }, + "6273435/VDK9EZWA": { + "URL": "https://ideas.repec.org/p/fip/fedgsq/77.html", + "abstract": "a speech at the Sandridge Lecture, Virginia Association of Economics, Richmond, Virginia, March 10, 2005 and the Homer Jones Lecture, St. Louis, Missouri, on April 14, 2005", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Bernanke", + "given": "Ben S." + } + ], + "collection-title": "Speech", + "id": "6273435/VDK9EZWA", + "issued": { + "year": 2005 + }, + "language": "en", + "number": "77", + "publisher": "Board of Governors of the Federal Reserve System (U.S.)", + "title": "The global saving glut and the U.S. current account deficit", + "type": "report" + }, + "6273435/WTWTWFWP": { + "DOI": "10.1257/aer.20110683", + "URL": "https://www.aeaweb.org/articles?id=10.1257/aer.20110683", + "abstract": "The paper studies how high household leverage and crises can be caused by changes in the income distribution. Empirically, the periods 1920-1929 and 1983-2008 both exhibited a large increase in the income share of high-income households, a large increase in debt leverage of low- and middle-income households, and an eventual financial and real crisis. The paper presents a theoretical model where higher leverage and crises are the endogenous result of a growing income share of high-income households. The model matches the profiles of the income distribution, the debt-to-income ratio and crisis risk for the three decades preceding the Great Recession. (JEL D14, D31, D33, E32, E44, G01, N22)", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Kumhof", + "given": "Michael" + }, + { + "family": "Rancière", + "given": "Romain" + }, + { + "family": "Winant", + "given": "Pablo" + } + ], + "container-title": "American Economic Review", + "id": "6273435/WTWTWFWP", + "issue": "3", + "issued": { + "month": 3, + "year": 2015 + }, + "language": "en", + "page": "1217-1245", + "page-first": "1217", + "title": "Inequality, Leverage, and Crises", + "type": "article-journal", + "volume": "105" + }, + "6273435/YS4K82GI": { + "URL": "https://ideas.repec.org/p/red/sed018/1017.html", + "abstract": "I quantify the extent to which deterioration of bank balance sheets explains the large contraction in housing prices and consumption experienced by the U.S. during the last recession. I introduce a Banking Sector with balance sheet frictions into a model of long-term collateralized debt with risk of default. Credit supply is endogenously determined and depends on the capitalization of the entire banking sector. Mortgage spreads and endogenous down payments increase in periods when banks are poorly capitalized. I simulate an increase in the stock of housing and a negative income shock to match the decline in house prices between 2006-2009. The model generates changes in consumption, foreclosures and refinance rates similar to those observed in the U.S. between 2006 and 2009. Changes in financial intermediaries’ cost of funding explain, respectively, 38, 22 and 29 percent of the changes in housing prices, foreclosures and consumption generated by the model. These results show that the endogenous response of banks’ credit supply can partially explain how changes in housing prices affect consumption decisions. I use this framework to analyze the impact of debt forgiveness and banks’ recapitalization to mitigate the drop in housing prices and consumption. I also present empirical evidence that balance sheet mechanism implied by the model was operational during this period. In other words, I show that during the great recession, changes in the real estate prices impacted the balance sheet of the banks that reacted by contracting their mortgage credit supply.", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Paixao", + "given": "Nuno" + } + ], + "collection-title": "2018 Meeting Papers", + "id": "6273435/YS4K82GI", + "issued": { + "year": 2018 + }, + "language": "en", + "number": "1017", + "publisher": "Society for Economic Dynamics", + "shortTitle": "Housing Prices and Consumer Spending", + "title": "Housing Prices and Consumer Spending: The Bank Balance Sheet Channel", + "title-short": "Housing Prices and Consumer Spending", + "type": "report" + }, + "6273435/ZNBZENA9": { + "URL": "http://www.nber.org/papers/w23863", + "abstract": "We revisit La Porta’s (1996) finding that returns on stocks with the most optimistic analyst long term earnings growth forecasts are substantially lower than those for stocks with the most pessimistic forecasts. We document that this finding still holds, and present several further facts about the joint dynamics of fundamentals, expectations, and returns for these portfolios. We explain these facts using a new model of belief formation based on a portable formalization of the representativeness heuristic. In this model, analysts forecast future fundamentals from the history of earnings growth, but they over-react to news by exaggerating the probability of states that have become objectively more likely. Intuitively, fast earnings growth predicts future Googles but not as many as analysts believe. We test predictions that distinguish this mechanism from both Bayesian learning and adaptive expectations, and find supportive evidence. A calibration of the model offers a satisfactory account of the key patterns in fundamentals, expectations, and returns.", + "accessed": { + "day": 5, + "month": 9, + "year": 2018 + }, + "author": [ + { + "family": "Bordalo", + "given": "Pedro" + }, + { + "family": "Gennaioli", + "given": "Nicola" + }, + { + "family": "Porta", + "given": "Rafael La" + }, + { + "family": "Shleifer", + "given": "Andrei" + } + ], + "genre": "Working Paper", + "id": "6273435/ZNBZENA9", + "issued": { + "month": 9, + "year": 2017 + }, + "note": "DOI: 10.3386/w23863", + "number": "23863", + "publisher": "National Bureau of Economic Research", + "title": "Diagnostic Expectations and Stock Returns", + "type": "report" + }, + "undefined": { + "author": [ + { + "family": "Nagel", + "given": "Stefan" + }, + { + "family": "Xu", + "given": "Zhengyang" + } + ], + "id": "undefined", + "issued": { + "year": 2018 + }, + "language": "en", + "page": "56", + "page-first": "56", + "title": "Asset Pricing with Fading Memory", + "type": "article-journal" + } + } + }, + "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": "3.8.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Cultural-change-as-learning-slide.slides.html b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Cultural-change-as-learning-slide.slides.html new file mode 100644 index 00000000..71cc9ff5 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Cultural-change-as-learning-slide.slides.html @@ -0,0 +1,13518 @@ + + + + + + + + + + + +Cultural-change-as-learning-slide slides + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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Cultural Change as Learning:

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The Evolution of Female Labor Force

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Paritcipation over a Century
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Wonsik Ko
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Johns Hopkins University
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Computational Method, November 2020

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What drives the evolution of Female Labor Force Participation Rate?

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Dynamic Model with beleif updating

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Beliefs evolve endogenously via an intergenerational learning process.

+
+
+
+
+
+
+

Model

\begin{align*} +U(w_{f}, w_{h}, v_{i})&=\frac{c^{1-\gamma}}{1-\gamma}-\textbf{1} (E_{i t}v_i)\\ +c = w_h + \textbf{1} w_f, v_i &=l_i + B_i , B_i = \beta + u_i , E(u_i)=0 +\end{align*}
    +
  • $\textbf{1}$: an indicator function that takes the value one if she works.
    • +
  • $w_f$: a woman's earning
    • +
  • $w_h$: a husband's earning
    • +
  • $l_i$: a known idiosyncratic component of disutility of working with distribution in the population G(l)
    • +
  • $B_i$: an individual-level realization of a random variable that is iid across women
    • +
  • Consumption is a household public good
    • +
  • $\beta \in \{\beta_H, \beta_L\}$, $\beta_H >\beta_L \geq 0$
    • +
+ +
+
+
+
+
+
+\begin{align*} +s_i = \beta + \epsilon_i +\end{align*}

where $\epsilon \sim N(0,\sigma_{\epsilon}^2)$

+

With signal $s_i$, updating her prior belief using Bayes' rule.

+ +
+
+
+
+
+
+

Consider a woman i in period t who has a prior belief about $\beta$ as summarized in the log likelihood ratio (LLR) $\lambda_t = ln \frac{P(\beta=\beta_L)}{P(\beta=\beta_H)}$.

+ +
+
+
+
+
+
+

By Bayes rule, her beliefs given her private signal s can be summarized in a new LLR, $\lambda_{i t}(s)$ given by

+ +
+
+
+
+
+
+\begin{align*} +\lambda_{i t}(s)=\lambda_t + ln(\frac{P(s|\beta=\beta_L)}{P(s|\beta=\beta_H)})=\lambda_t - (\frac{\beta_H - \beta_L}{\sigma_{\epsilon}^2})(s-\bar{\beta}) +\end{align*}

where $\bar{\beta}=(\beta_H+\beta_L)/2$, $s \sim N(\beta, \sigma_{\epsilon}^2)$, $\lambda_{it} \sim N(\lambda_t - (\frac{\beta_H-\beta_L}{\sigma_{\epsilon}^2})(\beta - \bar{\beta}), \frac{(\beta_H-\beta_L)^2}{\sigma_{\epsilon}^2})$

+ +
+
+
+
+
+
+

Work iff $W(w_{h t}, w_{f t})=\frac{1}{1-\gamma}[(w_{h t}+w_{f t})^{1-\gamma} - w_{h t}^{1-\gamma} ] - E_{i t}(\beta) \geq l_i$

+ +
+
+
+
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+
+

Low $l(l \leq \underline{l})$ will always work

+

High l $(l \geq \bar{l})$ will never choose to work.

+ +
+
+
+
+
+
+\begin{align*} +\underline{l}(w_{h t}, w_{f t}) &= W(w_{h t}, w_{f t})-\beta_H\\ +\bar{l}(w_{h t}, w_{f t})&=W(w_{h t}, w_{f t})-\beta_L +\end{align*} +
+
+
+
+
+
+

$s_{l}^{*}(\lambda)$ is the value where a woman is indifferent between working and not working.

+ +
+
+
+
+
+
+\begin{align*} +s_{l}^{*} (\lambda_t ; w_{h t}, w_{f t} )=\bar{\beta} + (\frac{\sigma_{\epsilon}^2}{\beta_H-\beta_L})(\lambda_t + ln (\frac{\bar{l}(w_{h t}, w_{f t})-l}{l_l - \underline{l}(w_{h t}, w_{f t})})) = s_{l}^{*}(\lambda_t) +\end{align*} +
+
+
+
+
+
+

$L_{l t}(\beta ; \lambda_t)$ is the proportion of women who will choose to work

+ +
+
+
+
+
+
+\begin{align*} +L_t(\beta ; \lambda_t) = G(\underline{l})+\int_{\underline{l}}^{\bar{l}} F(s_{l}^{*}(\lambda_t)-\beta ; \sigma_{\epsilon})g(l)dl +\end{align*} +
+
+
+
+
+
+

Intergenerational Transmission of Belief

+
+
+
+
+
+
+

The prior of generation t (its "culture"), $\lambda_t$

+

Updated with idiosyncratic private signal, $s_i$

+

Ends up with $\lambda_{i t}(s)$

+ +
+
+
+
+
+
+

observe a noisy signal of $L_t$, given by $y_t$

+\begin{align*} +y_t(\beta ; \lambda_t ) = L_t (\beta ; \lambda_t ) + \eta_t +\end{align*}

where $\eta_t \sim N(0, \sigma_{\eta}^2)$ with a pdf $h(\cdot;\sigma_{\eta})$

+ +
+
+
+
+
+
+

Again using Bayes rule

+\begin{align*} +\lambda_{t+1}(\lambda_t , y_t) = \lambda_t + ln\frac{h(y_t | \beta =\beta_L)}{h(y_t|\beta = \beta_H)} = \lambda_t + (\frac{L_{t}(\beta_L ;\lambda_t)-L_t(\beta_H ; \lambda_t)}{\sigma_{\eta}^2})(y_t -\bar{L}_t(\lambda_t)) +\end{align*} +
+
+
+
+
+
+

Calibration Strategy

+
+
+
+
+
+
+

Data

    +

  • Before 1940: The median earnings of full-time white men and women in 1890.

    +
    • +

  • After 1940, the 1% IPUMS samples of the U.S. Census for yearly earnings.

    +
    • +

  • The probability that a woman worked in 1980 conditional on her mother's work behavior: General Social Survey (GSS)

    +
    • +
+ +
+
+
+
+
+
+
    +

  • Calibration matching:

    +
    • +

  • Female LFP in 1980, 1990, and 2000

    +
    • +

  • The own and cross-wage elasticity in 2000

    +
    • +

  • The cross-wage elasticity in 1990

    +
    • +

  • The relative probability of a woman working in 1980.

    +
    • +
+
    +

  • Table 1 shows the calibration target and the values obatained in the calibrated learning model.

    +
    • +

  • Figure 4 presents the LFP predictions from the calibrated model.

    +
    • +
+ +
+
+
+
+
+ + + + + + + diff --git a/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Cultural-change-as-learning.ipynb b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Cultural-change-as-learning.ipynb new file mode 100644 index 00000000..ac4dfab0 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Cultural-change-as-learning.ipynb @@ -0,0 +1,165 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Raquel Fernandez (2013, AER)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## \"Cultural Change as Learning: The Evolution of Female Labor Force Participation over a Century\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This notebook is created by Wonsik Ko. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Summary \n", + "This paper investigates the role of changes in culture in generating the dramatic increase in married women's labor force participation over the last century. \n", + "\n", + "* It develops a dynamic model of culture in which individuals hold heterogeneous beliefs regarding the relative long-run payoffs for women who work in the market versus the home. \n", + "* These beliefs evolve endogenously via an intergenerational learning process. \n", + "* It calibrates the model to several key statistics and show that it does a good job in replicating the quantitative evolution of female\n", + "LFP in the US over the last 120 years. \n", + "* The model highlights a new dynamic role for changes in wages via their effect on intergenerational learning. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Model \n", + "\n", + "#### The Work Decision\n", + "\n", + "\\begin{align*}\n", + "U(w_{f}, w_{h}, v_{i})&=\\frac{c^{1-\\gamma}}{1-\\gamma}-\\textbf{1} (E_{i t}v_i)\\\\\n", + "c = w_h + \\textbf{1} w_f, v_i &=l_i + B_i , B_i = \\beta + u_i , E(u_i)=0\n", + "\\end{align*}\n", + "\n", + "* $\\textbf{1}$: an indicator function that takes the value one if she works.\n", + "* $w_f$: a woman's earning\n", + "* $w_h$: a husband's earning\n", + "* $l_i$: a known idiosyncratic component of disutility of working with distribution in the population G(l)\n", + "* $B_i$: an individual-level realization of a random variable that is iid across women\n", + "* Consumption is a household public good\n", + "* $\\beta \\in \\{\\beta_H, \\beta_L\\}$, $\\beta_H >\\beta_L \\geq 0$\n", + "\n", + "Prior to making her work decision, a woman inherits her mother's private signal $s_i$ that yields information about true $\\beta$.\n", + "\n", + "\\begin{align*}\n", + "s_i = \\beta + \\epsilon_i\n", + "\\end{align*}\n", + "where $\\epsilon \\sim N(0,\\sigma_{\\epsilon}^2)$\n", + "\n", + "After inheriting her private signal $s_i$, each woman updates her prior belief using Bayes' rule.\n", + "\n", + "Consider a woman i in period t who has a prior belief about $\\beta$ as summarized in the log likelihood ratio (LLR) $\\lambda_t = ln \\frac{P(\\beta=\\beta_L)}{P(\\beta=\\beta_H)}$. By Bayes rule, her beliefs given her private signal s can be summarized in a new LLR, $\\lambda_{i t}(s)$ given by\n", + "\n", + "\\begin{align*}\n", + "\\lambda_{i t}(s)=\\lambda_t + ln(\\frac{P(s|\\beta=\\beta_L)}{P(s|\\beta=\\beta_H)})=\\lambda_t - (\\frac{\\beta_H - \\beta_L}{\\sigma_{\\epsilon}^2})(s-\\bar{\\beta})\n", + "\\end{align*}\n", + "where $\\bar{\\beta}=(\\beta_H+\\beta_L)/2$, $s \\sim N(\\beta, \\sigma_{\\epsilon}^2)$, $\\lambda_{it} \\sim N(\\lambda_t - (\\frac{\\beta_H-\\beta_L}{\\sigma_{\\epsilon}^2})(\\beta - \\bar{\\beta}), \\frac{(\\beta_H-\\beta_L)^2}{\\sigma_{\\epsilon}^2})$\n", + "\n", + "Woman i will work iff $W(w_{h t}, w_{f t})=\\frac{1}{1-\\gamma}[(w_{h t}+w_{f t})^{1-\\gamma} - w_{h t}^{1-\\gamma} ] - E_{i t}(\\beta) \\geq l_i$\n", + "\n", + "Woman with low $l(l \\leq \\underline{l})$ will always work and women with high l $(l \\geq \\bar{l})$ will never choose to work.\n", + "\n", + "\\begin{align*}\n", + "\\underline{l}(w_{h t}, w_{f t}) &= W(w_{h t}, w_{f t})-\\beta_H\\\\\n", + "\\bar{l}(w_{h t}, w_{f t})&=W(w_{h t}, w_{f t})-\\beta_L\n", + "\\end{align*}\n", + "\n", + "One can solve for the critical value of the private signal $s_{l}^{*}(\\lambda)$ that she would need to inherit from her mother in order to be indifferent between working and not working.\n", + "\n", + "\\begin{align*}\n", + "s_{l}^{*} (\\lambda_t ; w_{h t}, w_{f t} )=\\bar{\\beta} + (\\frac{\\sigma_{\\epsilon}^2}{\\beta_H-\\beta_L})(\\lambda_t + ln (\\frac{\\bar{l}(w_{h t}, w_{f t})-l}{l_l - \\underline{l}(w_{h t}, w_{f t})})) = s_{l}^{*}(\\lambda_t)\n", + "\\end{align*}\n", + "\n", + "$L_{l t}(\\beta ; \\lambda_t)$ is the proportion of women who will choose to work given the true value of $\\beta$ and a prior of $\\lambda_t$.\n", + "\n", + "\\begin{align*}\n", + "L_t(\\beta ; \\lambda_t) = G(\\underline{l})+\\int_{\\underline{l}}^{\\bar{l}} F(s_{l}^{*}(\\lambda_t)-\\beta ; \\sigma_{\\epsilon})g(l)dl\n", + "\\end{align*}\n", + "\n", + "\n", + "#### Intergenerational Transmission of Belief\n", + "\n", + "The model assumes that generation t+1 inherits the prior of generation t (its \"culture\"), $\\lambda_t$, which each individual then updates with her own idiosyncratic private signal, $s_i$, inherited from her mother.\n", + "\n", + "A woman in t+1 ends up with the belief $\\lambda_{i t}(s)$.\n", + "\n", + "There is potentially an additional source of information available to women in t+1 that was unavailable to women at time t:$L_t$.\n", + "\n", + "Women observe a noisy signal of $L_t$, given by $y_t$\n", + "\n", + "\\begin{align*}\n", + "y_t(\\beta ; \\lambda_t ) = L_t (\\beta ; \\lambda_t ) + \\eta_t\n", + "\\end{align*}\n", + "\n", + "where $\\eta_t \\sim N(0, \\sigma_{\\eta}^2)$ with a pdf $h(\\cdot;\\sigma_{\\eta})$\n", + "\n", + "Using Bayes law after observing $y_t$ generates an updated common belief for generation t + 1 of:\n", + "\n", + "\\begin{align*}\n", + "\\lambda_{t+1}(\\lambda_t , y_t) = \\lambda_t + ln\\frac{h(y_t | \\beta =\\beta_L)}{h(y_t|\\beta = \\beta_H)} = \\lambda_t + (\\frac{L_{t}(\\beta_L ;\\lambda_t)-L_t(\\beta_H ; \\lambda_t)}{\\sigma_{\\eta}^2})(y_t -\\bar{L}_t(\\lambda_t))\n", + "\\end{align*}\n", + "\n", + "#### Calibration Strategy\n", + "\n", + "Married women decide whether to engage in market work taking their husbands' earnings and their own potential earnings as given. \n", + "\n", + "Given the paucity of data prior to 1940, the median earnings of full-time white men and women in 1890 was used. \n", + "\n", + "After 1940, the 1% IPUMS samples of the U.S. Census for yearly earnings are used.\n", + "\n", + "Calibration matches the model to female LFP in 1980, 1990, and 2000 and the own and cross-wage elasticity in 2000, the cross-wage elasticity in 1990 and the relative probability of a woman working in 1980.\n", + "\n", + "To calculate the probability that a woman worked in 1980 conditional on her mother's work behavior, the response from the General Social Survey (GSS) question was used. \n", + "\n", + "Table 1 shows the calibration target and the values obatained in the calibrated learning model.\n", + "\n", + "Figure 4 presents the LFP predictions from the calibrated model.\n", + "\n", + "#### Discussion and Conclusion\n", + "\n", + "* In the model, married women compared the benefits of increased consumption from labor earnings with the expected utility cost of working.\n", + "* This cost was unknown and women's beliefs about it evolved endogenously over time in a Bayesian fashion.\n", + "* The calibrated model finds that at the outset women were pessimistic about the true cost of working.\n", + "* The paper shows that a simple model with these features, calibrated to key statistics from the later part of the 20th century, generates a time trend of married women's LFP that is roughly similar to the historical one in the US over the last 120 years." + ] + } + ], + "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": "3.8.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/CulturalChangeAsLearning.pdf b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/CulturalChangeAsLearning.pdf new file mode 100644 index 00000000..c7129a70 Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/CulturalChangeAsLearning.pdf differ diff --git a/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/CulturalChangeAsLearning.tex b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/CulturalChangeAsLearning.tex new file mode 100644 index 00000000..b2e927cf --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/CulturalChangeAsLearning.tex @@ -0,0 +1,214 @@ +\input{./econtexRoot}\input{\econtexRoot/LaTeX/econtexPaths} +\documentclass[titlepage]{\econtex} +\usepackage{xr-hyper} +\usepackage{graphicx} +\usepackage{float} +\graphicspath{ {./Pictures/} } +\input{\econtexRoot/LaTeX/econtexPaths} + +\input{\ResourcesDir/owner} + +\providecommand{\texname}{CulturalChangeAsLearning} +\usepackage{\LaTeXFiles/BufferStockTheory} + +\begin{document} + +\providecommand{\versn}{} +\ifthenelse{\boolean{ifWeb}}{ \renewcommand{\ushort}{\underline}\renewcommand{\versn}{Web} }{} + +\hfill{\tiny \jobname~\versn~\today~{at} \DTMcurrenttime, \input{\ResourcesDir/.git-source-commit}~~\input{\ResourcesDir/.git-public-commit}} + +\title{Cultural Change as Learning: The Evolution of Female Labor Force Participation over a Century} + +\author{Raquel Fernandez \\ Ballpark by: Wonsik Ko\authNum} + +\keywords{female labor force participation; cultural transmission; preference formation; learning; S shape; social norms; beliefs} + +\jelclass{J16, J21, Z1, D19\\ + \href{https://econ-ark.org}{\includegraphics{\ResourcesDir/PoweredByEconARK}} +} + +\renewcommand{\forcedate}{October 16, 2020} +\date{\forcedate} + +\maketitle +\hypertarget{abstract}{} +\begin{abstract} + This paper investigates the role of changes in culture in generating the dramatic increase in married women's labor force participation over the last century. It develops a dynamic model of culture in which individuals hold heterogeneous beliefs regarding the relative long-run payoffs for women who work in the market versus the home. These beliefs evolve endogenously via an intergenerational learning process. Women are assumed to learn about the long-term payoffs of working by observing (noisy) private and public signals. This process generically generates the S-shaped figure for female labor force participation found in the data. I calibrate the model to several key statistics and show that it does a good job in replicating the quantitative evolution of female LFP in the US over the last 120 years. I also examine the model's cross-sectional and intergenerational implications. The model highlights a new dynamic role for changes in wages via their effect on intergenerational learning. The calibration shows that this role was quantitatively important in several decades. +\end{abstract} + +\begin{authorsinfo} + \name{Contact: \href{mailto:}{\texttt{wko5@jhu.edu}}, Department of Economics, Wyman Hall, Johns Hopkins University, Baltimore, MD 21218, \url{https://github.com/wko5/ballpark/models/We-Would-Like-In-Econ-ARK}} +\end{authorsinfo} + +\newcommand{\thankstext}{Thank you to Prof. Christopher D. Carroll for the template on which this paper is written.} + +\ifthenelse{\boolean{ifWeb}}{}{\thanks{\thankstext}} + +\titlepagefinish + +\ifthenelse{\boolean{ifWeb}}{\medskip \noindent {\tiny + \thankstext \medskip \medskip \medskip + }}{\pagebreak +} + +\ifthenelse{\boolean{ifWeb}}{\medskip \noindent {\footnotesize \thankstext} \\ {\centering \medskip \medskip \medskip \noindent \hrule height 0.4pt depth 0.0pt width \textwidth \relax}}{\pagebreak } % \end{Web} + +\hrule height 0.4pt depth 0.0pt width \textwidth \relax + +\medskip \medskip + +\hypertarget{Summary}{} +\section{Summary} + +This paper investigates the role of changes in culture in generating the dramatic increase in married women's labor force participation over the last century. + +It develops a dynamic model of culture in which individuals hold heterogeneous beliefs regarding the relative long-run payoffs for women who work in the market versus the home. + +These beliefs evolve endogenously via an intergenerational learning process. + +It calibrates the model to several key statistics and show that it does a good job in replicating the quantitative evolution of female +LFP in the US over the last 120 years. + +The model highlights a new dynamic role for changes in wages via their effect on intergenerational learning. + +\hypertarget{The Model}{} +\section{The Model} + +\hypertarget{The Work Decision}{} +\subsection{The Work Decision} + +\begin{align*} +U(w_{f}, w_{h}, v_{i})&=\frac{c^{1-\gamma}}{1-\gamma}-\textbf{1} (E_{i t}v_i)\\ +c = w_h + \textbf{1} w_f, v_i &=l_i + B_i , B_i = \beta + u_i , E(u_i)=0 +\end{align*} + +* $\textbf{1}$: an indicator function that takes the value one if she works. + +* $w_f$: a woman's earning + +* $w_h$: a husband's earning + +* $l_i$: a known idiosyncratic component of disutility of working with distribution in the population G(l) + +* $B_i$: an individual-level realization of a random variable that is iid across women + +* Consumption is a household public good + +* $\beta \in \{\beta_H, \beta_L\}$, $\beta_H >\beta_L \geq 0$ + +Prior to making her work decision, a woman inherits her mother's private signal $s_i$ that yields information about true $\beta$. + +\begin{align*} +s_i = \beta + \epsilon_i +\end{align*} +where $\epsilon \sim N(0,\sigma_{\epsilon}^2)$ + +After inheriting her private signal $s_i$, each woman updates her prior belief using Bayes' rule. + +Consider a woman i in period t who has a prior belief about $\beta$ as summarized in the log likelihood ratio (LLR) $\lambda_t = ln \frac{P(\beta=\beta_L)}{P(\beta=\beta_H)}$. By Bayes rule, her beliefs given her private signal s can be summarized in a new LLR, $\lambda_{i t}(s)$ given by + +\begin{align*} +\lambda_{i t}(s)=\lambda_t + ln(\frac{P(s|\beta=\beta_L)}{P(s|\beta=\beta_H)})=\lambda_t - (\frac{\beta_H - \beta_L}{\sigma_{\epsilon}^2})(s-\bar{\beta}) +\end{align*} +where $\bar{\beta}=(\beta_H+\beta_L)/2$, $s \sim N(\beta, \sigma_{\epsilon}^2)$, $\lambda_{it} \sim N(\lambda_t - (\frac{\beta_H-\beta_L}{\sigma_{\epsilon}^2})(\beta - \bar{\beta}), \frac{(\beta_H-\beta_L)^2}{\sigma_{\epsilon}^2})$ + +Woman i will work iff $W(w_{h t}, w_{f t})=\frac{1}{1-\gamma}[(w_{h t}+w_{f t})^{1-\gamma} - w_{h t}^{1-\gamma} ] - E_{i t}(\beta) \geq l_i$ + +Woman with low $l(l \leq \underline{l})$ will always work and women with high l $(l \geq \bar{l})$ will never choose to work. + +\begin{align*} +\underline{l}(w_{h t}, w_{f t}) &= W(w_{h t}, w_{f t})-\beta_H\\ +\bar{l}(w_{h t}, w_{f t})&=W(w_{h t}, w_{f t})-\beta_L +\end{align*} + +One can solve for the critical value of the private signal $s_{l}^{*}(\lambda)$ that she would need to inherit from her mother in order to be indifferent between working and not working. + +\begin{align*} +s_{l}^{*} (\lambda_t ; w_{h t}, w_{f t} )=\bar{\beta} + (\frac{\sigma_{\epsilon}^2}{\beta_H-\beta_L})(\lambda_t + ln (\frac{\bar{l}(w_{h t}, w_{f t})-l}{l_l - \underline{l}(w_{h t}, w_{f t})})) = s_{l}^{*}(\lambda_t) +\end{align*} + +$L_{l t}(\beta ; \lambda_t)$ is the proportion of women who will choose to work given the true value of $\beta$ and a prior of $\lambda_t$. + +\begin{align*} +L_t(\beta ; \lambda_t) = G(\underline{l})+\int_{\underline{l}}^{\bar{l}} F(s_{l}^{*}(\lambda_t)-\beta ; \sigma_{\epsilon})g(l)dl +\end{align*} + +\hypertarget{Intergenrational Transmission of Belief}{} +\subsection{Intergenerational Transmission of Belief} + +The model assumes that generation t+1 inherits the prior of generation t (its "culture"), $\lambda_t$, which each individual then updates with her own idiosyncratic private signal, $s_i$, inherited from her mother. + +A woman in t+1 ends up with the belief $\lambda_{i t}(s)$. + +There is potentially an additional source of information available to women in t+1 that was unavailable to women at time t:$L_t$. + +Women observe a noisy signal of $L_t$, given by $y_t$ + +\begin{align*} +y_t(\beta ; \lambda_t ) = L_t (\beta ; \lambda_t ) + \eta_t +\end{align*} + +where $\eta_t \sim N(0, \sigma_{\eta}^2)$ with a pdf $h(\cdot;\sigma_{\eta})$ + +Using Bayes law after observing $y_t$ generates an updated common belief for generation t + 1 of: + +\begin{align*} +\lambda_{t+1}(\lambda_t , y_t) = \lambda_t + ln\frac{h(y_t | \beta =\beta_L)}{h(y_t|\beta = \beta_H)} = \lambda_t + (\frac{L_{t}(\beta_L ;\lambda_t)-L_t(\beta_H ; \lambda_t)}{\sigma_{\eta}^2})(y_t -\bar{L}_t(\lambda_t)) +\end{align*} + +\hypertarget{Calbration Strategy}{} +\section{Calibration Strategy} + +Married women decide whether to engage in market work taking their husbands' earnings and their own potential earnings as given. + +Given the paucity of data prior to 1940, the median earnings of full-time white men and women in 1890 was used. + +After 1940, the 1 percent IPUMS samples of the U.S. Census for yearly earnings are used. + +Calibration matches the model to female LFP in 1980, 1990, and 2000 and the own and cross-wage elasticity in 2000, the cross-wage elasticity in 1990 and the relative probability of a woman working in 1980. + +To calculate the probability that a woman worked in 1980 conditional on her mother's work behavior, the response from the General Social Survey (GSS) question was used. + +Table 1 shows the calibration target and the values obatained in the calibrated learning model. + +Figure 4 presents the LFP predictions from the calibrated model. + + +\begin{table}[H] + \centering + \caption{Table 1} + \includegraphics[width=0.8\textwidth]{Table1.png} + \label{fig:Table 1} + \end{table} + + All elasticities are from Blau and Kahn (2007). The work risk ratio uses data from GSS (see text). The values in bold are the model's predicted values for its calibration +targets. + +\begin{figure}[H] + \centering + \includegraphics[width=1\textwidth, height=10cm]{Figure4.png} + \caption{} + \label{fig:Figure 4} + \end{figure} + +The dashed (red) line (P) is the belief path of the median individual. The sum of squared errors (distance of predicted LFP from actual LFP) is 0.052. + +\hypertarget{Simulation Results}{} +\section{Discussion and Conclusion} + + In the model, married women compared the benefits of increased consumption from labor earnings with the expected utility cost of working. + +This cost was unknown and women's beliefs about it evolved endogenously over time in a Bayesian fashion. + +The calibrated model finds that at the outset women were pessimistic about the true cost of working. + +The paper shows that a simple model with these features, calibrated to key statistics from the later part of the 20th century, generates a time trend of married women's LFP that is roughly similar to the historical one in the US over the last 120 years. + + +\clearpage\vfill\eject + +\onlyinsubfile{\bibliography{\econtexRoot/LaTeX/BufferStockTheory,economics}} + +\end{document} + diff --git a/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Pictures/Figure4.png b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Pictures/Figure4.png new file mode 100644 index 00000000..c1f5032b Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Pictures/Figure4.png differ diff --git a/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Pictures/Table1.png b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Pictures/Table1.png new file mode 100644 index 00000000..83a1cac4 Binary files /dev/null and b/models/We-Would-Like-In-Econ-ARK/CulturalChangeAsLearning/Pictures/Table1.png differ