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% ----------------------------------------------------------------------------------------
%	TITLE PAGE
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\title[]{Quantitative Macro-Labor} % The short title appears at the bottom of every slide, the full
% title is only on the title page

\author{Professor Griffy} % Your name
\institute[University at Albany, SUNY] % Your institution as it will appear on the bottom of
% every slide, may be shorthand to save space
{
UAlbany  \ % Your institution for the title page
}
\date{Fall 2022} % Date, can be changed to a custom date

\begin{document}

\begin{frame}
  \titlepage % Print the title page as the first slide
\end{frame}




% ----------------------------------------------------------------------------------------
%	PRESENTATION SLIDES
% ----------------------------------------------------------------------------------------

% ------------------------------------------------
\section{Course Introduction} % Sections can be created in order to organize your presentation into discrete blocks, all sections and subsections are automatically printed in the table of contents as an overview of the talk
% ------------------------------------------------

\begin{frame}
  \frametitle{Welcome to Macro-Labor!}
  \begin{itemize}
  \item My name: Ben Griffy.
  \item Email: bgriffy@albany.edu.
  \item Office Hours: Tth 10:30-11:30am.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Course Overview}
  \begin{itemize}
  \item What is this course about?
    \begin{enumerate}
    \item Quantitative macro-labor.
    \item Explore and develop ``empirical regularities'' about the labor market and labor market participants.
    \item Use theory to develop cogent explanations for these empirical regularities.
    \item Use a computer to solve and simulate models that would be impossible to solve by hand.
    \end{enumerate}
  \item Topics:
    \begin{enumerate}
    \item Wage dispersion and income inequality.
    \item Income persistence and income risk.
    \item Consumption risk.
    \end{enumerate}
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Course Requirements}
  \begin{itemize}
  \item Materials:
    \begin{enumerate}
    \item We won't explicitly require a textbook for this course.
    \item There are some suggested textbooks as well as free resources in the syllabus.
    \end{enumerate}
  \item Tools:
    \begin{enumerate}
    \item One (or two, or three, or ...) programming language.
    \item My suggestion: Matlab, Julia, (Fortran or C++) for dynamic programming/numerical optimization. Maybe Python, but it's honestly not as good as Julia (though useful for other things).
    \item And Stata or R for statistics/empirical regularities.
    \item \LaTeX for homework and projects.
    \end{enumerate}
  \item Please note: best resource for class materials is my website: https://www.bengriffy.com
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Grading}
  \begin{itemize}
  \item Occasional homework: 30\%. This will typically entail solving a model that I have discussed in class either by hand or on the computer.
  \item Introduction/Research Proposal (20\%): Write a rough draft of an introduction that will serve as a research proposal. This will serve as an outline for your subsequent projects.
  \item Data Project (20\%): Find an empirical regularity that relates to the topics in class using one of the publicly available datasets and then summarize related papers. Turn in short research paper along with code.
  \item Model Project (30\%): Write down and solve a model that (you think/hope) can explain the regularities you found in the data project. Turn in short research paper that includes empirical work and new quantitative work.
  \item But basically, if you put effort into the class, you'll pass.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Some topics we will cover}
  \begin{itemize}
  \item Exploring empirical regularities using panel data.
  \item Frictional models of the labor market.
  \item Incomplete markets models.
  \item Models that incorporate job search and incomplete markets.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Introduction/Research Proposal}
  \begin{itemize}
  \item Idea: Write out the introduction to a paper on a question you are interested in.
  \item The goal is to give you ``guideposts'' for what you will do in subsequent projects.
  \item I have (or will have) a fairly general outline on my webpage.
  \item Must be a macro-labor related question.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Data Project}
  \begin{itemize}
  \item Idea: We'll spend the first part of the course exploring ``empirical regularities'' about the labor market.
  \item These include:
    \begin{enumerate}
    \item Income processes
    \item Labor market flows
    \item Labor market volatility
    \item Wage and income dispersion
    \item Lots of other topics as well
    \end{enumerate}
  \item You'll want to choose one of the datasets that I discuss and try to ``discover'' a feature of the data that might be possible to explore with a model.
  \item This doesn't have to be groundbreaking, so don't stress if you don't think can't find something huge.
  \item At the end, you'll give a short presentation about the findings and turn in a short research paper that will eventually (possibly) become the ``empirical regularities'' section of a quantitative paper.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Model Project}
  \begin{itemize}
  \item Idea: The basic structure of a macro (or quantitative macro) paper is that you find some novel feature of the data and then write down a model to further explore it.
  \item That is what we'll do in the model project.
  \item Take the empirical regularity you explored in either previous project and develop a model that can (try) to explain it.
  \item You'll want to do a small extension to a previous model, solve it, and then simulate it to make predictions related to your data.
  \item The appropriate model will depend on the empirical regularity you find.
  \item If you end up interested in a different data topic, you aren't bound to what you did in either previous project.
  \item Like the data project, you'll present your work and turn in a working paper.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Scheduling}
  \begin{itemize}
  \item I may miss a few classes, but I will let you know in advance.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\section{Dispersion and Risk} % Sections can be created in order to organize your presentation into discrete blocks, all sections and subsections are automatically printed in the table of contents as an overview of the talk

% ------------------------------------------------

\begin{frame}
  \frametitle{Heterogeneity and the Macroeconomy}
  \begin{itemize}
  \item Standard discrete time budget constraint:
    \begin{align}
      c_{t} + a_{t + 1} &= (1 + r_{t})a_{t} + w_{t}
    \end{align}
  \item Standard macroeconomic models assume (among other things):
    \begin{enumerate}
    \item Markets are frictionless: factors are paid their marginal product. $w_{t} = F_{L}, r_{t} = F_{K}$
    \item Markets are complete: agents can contract on any consumption path, subject to a resource constraint. i.e., there is no borrowing constraint.
    \end{enumerate}
  \item These assumptions are not always innocuous.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Heterogeneity and the Macroeconomy}
  \begin{itemize}
  \item Basics of a macro model:
    \begin{align}
      u'(c_{t}) &= \beta E[(1 + r_{t + 1})u'(c_{t + 1})]\\
      \text{s.t.  } c_{t} + a_{t + 1} &= (1 + r_{t})a_{t} + w_{t}
    \end{align}
  \item Representative Agent:
    \begin{enumerate}
    \item Single ``average'' agent that represents all workers in economy.
    \item Complete markets: contracts on risk that insulate from income and consumption shocks (assume $r$ fixed):
      \begin{align}
        E[u'(c_{t + 1})] &\approx u'(E[c_{t + 1}])\\
        \rightarrow u'(c_{t}) &= \beta(1 + r_{t + 1})u'(E[c_{t + 1}])\\
        \rightarrow c_{t} &\approx c_{t + 1} + \epsilon_{t + 1}
      \end{align}
    \item i.e., a permanent income hypothesis.
    \end{enumerate}
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Heterogeneity and the Macroeconomy}
  \begin{itemize}
  \item Basics of a macro model:
    \begin{align}
      u'(c_{t}) &= \beta E[(1 + r_{t + 1})u'(c_{t + 1})]\\
      \text{s.t.  } c_{t} + a_{t + 1} &= (1 + r_{t})a_{t} + w_{t}\\
      a_{t + 1} &\geq \underline{a}
    \end{align}
  \item What about an agent who can't insure?
      \begin{align}
        E[u'(c_{t + 1})] &> u'(E[c_{t + 1}])\\
        \rightarrow u'(c_{t}) &\cancel{=} \beta(1 + r_{t + 1})u'(E[c_{t + 1}])\\
        \rightarrow c_{t} &\cancel{=} c_{t + 1} + \epsilon_{t + 1}
      \end{align}
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Heterogeneity and the Macroeconomy}
  \begin{itemize}
  \item Basics of a macro model:
    \begin{align}
      u'(c_{t}) &= \beta E[(1 + r_{t + 1})u'(c_{t + 1})]\\
      \text{s.t.  } c_{t} + a_{t + 1} &= (1 + r_{t})a_{t} + w_{t}
    \end{align}
  \item What are the potential sources of heterogeneity?
    \begin{enumerate}
    \item Consumption.
    \item Wealth.
    \item Labor income.
    \end{enumerate}
  \item We'll study models that explore breakdowns of perfect competition and complete markets and assess their impact on these quantities.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{What We Want to Answer}
  \begin{itemize}
  \item We want to take a structural approach to understanding
    \begin{enumerate}
    \item Sources of heterogeneity.
    \item How individuals in the economy are different.
    \item Are these innate differences? Are they random?
    \item Are they temporary or permanent?
    \item What are the policy implications of these differences?
    \end{enumerate}
  \item Today: start by exploring the data.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Some Valuable Micro-Data Sources}
  \begin{itemize}
  \item In class, we will typically discuss ``micro-data'':
    \begin{enumerate}
    \item Panel Study of Income Dynamics (PSID): a panel of households from 1968-present, annually.
    \item National Longitudinal Survey of Youth (NLSY79, NLSY97): Two separate cohorts interviewed repeatedly at an annual frequency 1979-present and 1997-present.
    \item Survey of Income and Program Participation (SIPP): Series of panels that last 3-4 years. Each panel contains new participants.
    \item Current Population Survey (CPS): The main source of publicly available labor market information. A monthly survey that is representative. Some panel dimensions, but note that this lacks important panel components that the others retain.
    \item Current Expenditure Survey (CEX): Survey often used to connect expenditures in other panels to consumption.
    \item Survey of Consumer Finances (SCF): Cross-sectional survey with detailed information on household finances.
    \end{enumerate}
  \item You'll need to learn to work with at least one of these datasets.
  \item I'll provide code for most of them (not the CEX).
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{(Labor) Income and Wage Inequality}
  \begin{itemize}
  \item Important distinction: $y_{t} = w_{t}\times h_{t}$.
  \item Note: income/earnings vs. labor income/earnings: $\text{total inc.} = w_{t}\times h_{t} + r_{t}\times a_{t}$.
    \begin{align}
      ln(y_{t}) &= ln(w_{t})  + ln(h_{t})\\
      \rightarrow Var(ln(y_{t})) &= Var(ln(w_{t})) + Var(ln(h_{t})) + Cov(ln(w_{t}),ln(h_{t}))
    \end{align}
  \item Income inequality will almost always exceed wage inequality (in the absence of very strong income effects).
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Income Inequality over Time}
\centering\includegraphics[width=0.8\textwidth]{HPV_EarningsRatios.png}\\
Source: Heathcote, Perri, Violante 2010
\begin{itemize}
\item What do you notice?
\end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Income and Wage Inequality Today}
\centering
\includegraphics[width=0.5\textwidth]{IncomeHistogram.png}%
\includegraphics[width=0.5\textwidth]{WageHistogram.png}
Source: CPS Dec.-2017
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Income and Consumption Inequality}
\includegraphics[width=\textwidth]{STY_IncConsVar.png}
Source: Storesletten, Telmer, and Yaron 2004
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Wealth and Total Income Inequality}
  \begin{itemize}
  \item Wealth inequality dwarfs income inequality.
\hspace{-10mm}\begin{center}
\includegraphics[width=\textwidth]{WealthIncome_TimeSeries.png}
Source: Saez and Zucman/Piketty and Saez
\end{center}
  \item Why is that?
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{But Who Cares? Poor People are Just Less Productive!}
  \begin{itemize}
  \item This is one possible explanation, and is the explanation we would arrive at in the absence of frictions.
  \item But that need not be true if workers face frictions in the income process or their ability to income smooth.
  \item Allows us to address
    \begin{enumerate}
    \item How much inequality is predetermined? How much is due to shocks over the life-cycle?
    \item What are the sources of income and wage dispersion?
    \item Are they efficient?
    \item Are there policies that can decrease income or wealth dispersion efficiently?
    \end{enumerate}
  \end{itemize}
\end{frame}

% ------------------------------------------------


\section{Income Processes} % Sections can be created in order to organize your presentation into discrete blocks, all sections and subsections are automatically printed in the table of contents as an overview of the talk

% ------------------------------------------------

\begin{frame}
  \frametitle{Income Processes}
  \begin{itemize}
  \item In conducting our quantitative exercises, we want an accurate model of income and wages for calibration \& evaluation.
  \item Basic approach:
    \begin{enumerate}
    \item Condition on observables in data and estimate residual earnings.
    \item Use model to understand the contributions to residual earnings.
    \end{enumerate}
  \item Some considerations:
    \begin{enumerate}
    \item Make your data look as much like the model as possible.
    \item Does your model have an hours choice, i.e., an {\it intensive margin}? Then you want to match hourly wages.
    \end{enumerate}
  \item Good sources (where much of this comes from):
    \begin{itemize}
    \item Chris Tonetti's Write-up on income processes
    \item Gianluca Violante's slides on income processes
    \end{itemize}
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Residual Earnings}
  \begin{itemize}
  \item Estimate the following:
    \begin{align}
      Y_{i,j,t} &= w_{i,j,t}\exp(f(X_{i,j,t})+\epsilon_{i,j,t})h_{i,j,t}
    \end{align}
  \item where
    \begin{align*}
      Y_{i,j,t}&: \text{Total income of ind. i at age j, at time t}\\
      w_{i,j,t}&: \text{Hourly wages}\\
      X_{i,j,t}&: \text{Predictable component}\\
      \epsilon_{i,j,t}&: \text{Stochastic component}\\
      h_{i,j,t}&: \text{Hours worked}
    \end{align*}
  \item Note: if your model has an {\it intensive margin}, i.e., choice of hours, estimate
    \begin{align}
      y_{i,j,t} &= \frac{Y_{i,j,t}}{h_{i,j,t}} = w_{i,j,t}\exp(f(X_{i,j,t})+\epsilon_{i,j,t})
    \end{align}
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Residual Earnings}
  \begin{itemize}
  \item Estimate the following:
    \begin{align}
      ln(Y_{i,j,t}) &= ln(w_{i,j,t}) + ln(h_{i,j,t}) + f(X_{i,j,t}) + \epsilon_{i,j,t}
    \end{align}
  \item $X_{i,j,t}$ includes covariates (heterogeneity) that is observable and not central to the research question.
  \item Some examples:
    \begin{itemize}
    \item Race, gender (usually just use males), marital status
    \item Year, state, age
    \end{itemize}
  \item You might try to explain the effect of a covariate, i.e., race on labor earnings.
  \item Usually, write down a model to understand the residual.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Statistical Model of Income}
  \begin{itemize}
  \item We can think about residual earnings as being partially transitory:
    \begin{itemize}
    \item Temporary layoff
    \item Temporary hours cut
    \end{itemize}
  \item And persistent:
    \begin{itemize}
    \item College degree
    \item Innate ability
    \item Job-specific skills
    \end{itemize}
  \item A statistical model (i.e., one with no explicit structural interpretation) will estimate the size of these two components over the life-cycle.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Statistical Model of Income}
  \begin{itemize}
  \item If you are not micro-founding the income process (i.e., writing down a search model), need alternate model of income.
  \item Basic approach: specify two equation transitory and persistent model of income.
  \item Let $\tilde{Y}_{i,j}$ be residual log earnings of individual i at age j (remember, we controlled for time in the first stage).
    \begin{align}
      \tilde{Y}_{i,j} &= z_{i,j} + \psi_{i,j}\\
      z_{i,j} &= \rho z_{i,j-1} + \nu_{i,j}\\
      \psi_{i,a}&\sim iid (0, \sigma_{\psi})\\
      \nu_{i,a}&\sim iid (0, \sigma_{\nu})\\
      z_{i,0}&\sim iid (0, \sigma_{z})
    \end{align}
  \end{itemize}
\end{frame}

% ------------------------------------------------

% \begin{frame}
%   \frametitle{Identification}
%   \begin{itemize}
%   \item Even in macro, we need to worry about identification.
%   \item What parameters do we need to estimate?
%   \item $\rho, \sigma_{\psi}, \sigma_{\nu}, \sigma_{z}$.
%     \begin{align}
%       \tilde{Y}_{i,j} &= z_{i,j} + \psi_{i,j}\\
%       z_{i,j} &= \rho z_{i,j-1} + \nu_{i,j}\\
%       \rightarrow Var(\tilde{Y}_{i,0}) &= Var(z_{i,0}) + Var(\psi_{i,0}) + \cancel{Cov(z_{i,0},\psi_{i,0})}\\
%       \rightarrow Var(\tilde{Y}_{i,0}) &= \sigma_{z}^{2} + \sigma_{\psi}^{2}\\
%       Var(\tilde{Y}_{i,j}) &= Var(z_{i,j}) + \sigma_{\psi}^{2}\\
%       Var(z_{i,j}) &= \rho^{2}Var(z_{i,j-1}) + \sigma_{\nu}^{2}\\
%       Cov(\tilde{Y}_{i,j},\tilde{Y}_{i,j-n}) &= Cov(z_{i,j},z_{i,j-n})\\
%       Cov(z_{i,j},z_{i,j-n}) &= \rho^{n}Var(z_{i,j-n})
%     \end{align}
%   \end{itemize}
% \end{frame}

% % ------------------------------------------------

% \begin{frame}
%   \frametitle{Identification II}
%   \begin{itemize}
%   \item First, the peristence:
%     \begin{align}
%       \frac{Cov(z_{i,j},z_{i,j-2})}{Cov(z_{i,j-1},z_{i,j-2})} = \frac{\rho^{2}Var(z_{i,j-2})}{\rho Var(z_{i,j-2})} = \rho
%     \end{align}
%   \item Now, the transitory shock:
%     \begin{align}
%       Var(\tilde{Y}_{i,j}) &= Var(z_{i,j}) + \sigma_{\psi}^{2}\\
%       Var(\tilde{Y}_{i,j}) - Var(z_{i,j}) &= \sigma_{\psi}^{2}\\
%       Var(\tilde{Y}_{i,j}) - \rho^{-1}Cov(z_{i,j},z_{i,j-1}) &= \sigma_{\psi}^{2}\\
%       Var(\tilde{Y}_{i,j}) - \rho^{-1}Cov(\tilde{Y}_{i,j},\tilde{Y}_{i,j-1}) &= \sigma_{\psi}^{2}
%     \end{align}
%   \item Initial distribution is simple: $Var(\tilde{Y}_{i,0}) - \sigma_{\psi} = \sigma_{z}^{2}$
%   \item The persistent shock:
%     \begin{align}
%       Var(z_{i,j}) &= \rho^{2}Var(z_{i,j-1}) + \sigma_{\nu}^{2}\\
%       Var(\tilde{Y}_{i,j}) - \sigma_{\psi}^{2} &= \rho^{2}Var(z_{i,j-1})  + \sigma_{\nu}^{2}\\
%       Var(\tilde{Y}_{i,j}) - Cov(\tilde{Y}_{i,j},\tilde{Y}_{i,j-2}) &= \sigma_{\nu}^{2}
%     \end{align}
%   \end{itemize}
% \end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Statistical Model of Income}
  \begin{itemize}
  \item Once we have ways of identifying each parameter (next time... probably), we can estimate it.
    \begin{align}
      \tilde{Y}_{i,j} &= z_{i,j} + \psi_{i,j}\\
      z_{i,j} &= \rho z_{i,j-1} + \nu_{i,j}\\
      \psi_{i,a}&\sim iid (0, \sigma_{\psi})\\
      \nu_{i,a}&\sim iid (0, \sigma_{\nu})\\
      z_{i,0}&\sim iid (0, \sigma_{z})
    \end{align}
  \item What can we use it for?
    \begin{enumerate}
    \item Calibration targets for a structural model.
    \item External validation of structural model.
    \item Better understanding of data.
    \end{enumerate}
  \item This also tells us roughly what fraction of income shocks are insurable (transitory) and what are not (permanent).
  \end{itemize}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Statistical Model of Income}
\centering\includegraphics[width=0.8\textwidth]{HSV2012_IncomeShocks.png}
\end{frame}

% ------------------------------------------------

\begin{frame}
  \frametitle{Key Assumptions}
  \begin{itemize}
  \item We've assumed that earnings profiles are identical across individuals, conditional on the covariates we specified in the first-stage.
  \item But of course, there is heterogeneity in life-cycle income growth.
  \item How do we rationalize this? We allow for heterogeneity in income profiles.
  \item Next time.
  \end{itemize}
\end{frame}

% ------------------------------------------------

\section{Conclusion}
% ------------------------------------------------


\begin{frame}
  \frametitle{Next Time}
  \begin{itemize}
  \item Continue to study statistical models of income.
  \item Heterogeneous and restricted income profiles.
  \item Install the appropriate programming languages.
  \item Read Guvenen (2009).
  \end{itemize}
\end{frame}


\end{document}
