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\title{\vspace{1.6cm} \\
	{\LARGE Lecture 10}\\[1ex]
{\LARGE Unemployment, Inequality in Macro}\\
	\noindent \hspace{-0.3cm} \rule{12.8cm}{0.6pt} \vspace{-0.7cm}}
\author{Macroeconomics EC2B1\\[3ex]  Benjamin Moll \\\vspace{0.5cm}}
\institute{London School of Economics, Winter 2024}





\begin{document}

%%%%%%%%%%%%%%%%%%

{
\setbeamertemplate{footline}{}
\begin{frame}[noframenumbering]
\titlepage
\end{frame}
}

%
%\begin{frame}{Admin: Summer Exams}
%\be
%\bigskip
%\item Exam review session: Monday 29th April from 10am to 12pm
%\bi
%\medskip
%\item please prepare questions ahead of time
%\ei
%\bigskip
%\item Regular exam vs postpone to summer (IRDAP)
%\bi
%\medskip
%%\item last year: large number of postponed exams
%%\medskip
%\item please take a look at last year's exams
%\ei
%\ee
%\end{frame}



\begin{frame}{Plan}
\be
\bigskip
\item Measuring the labor market and unemployment
\bigskip
\item Unemployment: Diamond-Mortensen-Pissarides model
\bigskip
\item Inequality and heterogeneity in macro
\ee
\end{frame}

\begin{frame}{A Nobel Prize for work on unemployment (and LSE!)}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.42\textwidth]{figures/diamond-mortensen-pissarides} 
\end{figure}
\vspace{-2mm}
Source: {\scriptsize \url{https://www.nobelprize.org/prizes/economic-sciences/2010/summary/}}
\end{frame}

\begin{frame}{Readings}
\vspace{-4mm}
\tr{\textbf{Unemployment}}
\bi
{\footnotesize 
\item Supplement with derivations on moodle
\smallskip
\item Kurlat, chapters 7.1 and 7.5 (the part on ``search")
\smallskip
\item Wikipedia {\notsotiny \url{https://en.wikipedia.org/wiki/Search_and_matching_theory_(economics)}}
\smallskip
\item PhD-level treatment: Pissarides book ``Equilibrium Unemployment Theory",\\[-0.4ex] Shimer book ``Labor Markets and Business Cycles"}
\ei
\smallskip
\tr{\textbf{Inequality in macro}}
\bi
\smallskip
{\footnotesize \item Kaplan, Moll and Violante IMF Finance \& Development magazine piece on HANK models\\[-0.5ex] {\tiny\url{https://www.imf.org/en/Publications/fandd/issues/2023/03/modern-monetary-policy-kaplan-moll-violante}}
\smallskip
\item Chapter 18 ``Heterogeneous agent macroeconomics: origins, progress \& challenges" in Carlin and Soskice (2023) ``Macroeconomics: Institutions, Instability \& Inequality"
\smallskip
\item Cherrier, Garcia-Duarte and Sa\"{i}di (2022) ``Household Heterogeneity in Macroeconomic Models: A Historical Perspective" {\tiny\url{https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4250570}}
\smallskip
\item Reis (2018) ``Is something really wrong with macroeconomics?"\\[-0.5ex] {\notsotiny\url{https://personal.lse.ac.uk/reisr/papers/18-wrong.pdf}}
\smallskip
\item Yellen speech {\notsotiny\url{https://www.federalreserve.gov/newsevents/speech/yellen20161014a.htm}}
\item BoJ Governor Kuroda speech {\notsotiny\url{boj.or.jp/en/about/press/koen_2017/ko170524a.htm}}}
\ei
\end{frame}


\begin{frame}
\renewcommand{\baselinestretch}{1}
\vspace{3cm}
\begin{center}
{\LARGE Measuring the labor market and unemployment}
\end{center}
\end{frame}


\begin{frame}{Definitions: unemployed is not the same as not employed}
\vspace{-3mm}
Three groups:
\be
\smallskip
\item \tr{Employed, $E$}
\smallskip
\item \tr{Unemployed, $U$}: not employed, but actively searched for work at some time during the last four weeks
\smallskip
\item \tr{Not in labor force, $NL$}: neither employed nor unemployed
\ee
\begin{align*}
\mbox{unemployment rate} &= \frac{U}{E+U} \\
\mbox{participation rate} &= \frac{E + U}{E+U+NL} \\
\mbox{employment-population ratio}& = \frac{E}{E+U+NL} 
\end{align*}
\medskip
Importantly, \tr{population is not just $E$ and $U$ but also $NL$} and hence
$$\mbox{unemployment rate} \ \tr{\neq} \ 1-\mbox{employment-population ratio}$$
\end{frame}


\begin{frame}{Smooth labor force participation, volatile unemployment rate}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=\textwidth]{figures/kurlat_fig7_1_1} 
\end{figure}
\end{frame}


\begin{frame}{Labor market stocks and flows}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.9\textwidth]{figures/kurlat_fig7_1_2} 
\end{figure}
\end{frame}


\begin{frame}{Labor market flows: job finding and job loss rates}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=\textwidth]{figures/kurlat_fig7_1_3} 
\end{figure}
\end{frame}

\begin{frame}{{\large Beveridge curve: vacancies are high when unemployment is low}}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=\textwidth]{figures/kurlat_fig7_1_4} 
\end{figure}
When vacancy/unemployment ratio is high, labor market is said to be ``tight"
\end{frame}





\begin{frame}
\renewcommand{\baselinestretch}{1}
\vspace{2.3cm}
\begin{center}
{\huge Unemployment:\\[1ex] Diamond-Mortensen-Pissarides Model}
\end{center}
\end{frame}


\begin{frame}{Brief recap of standard labor market model (lectures 1 \& 2)}
\vspace{-3mm}
(Note change of notation: need $u,v$ for unemployment, vacancies)\\
\bigskip
A competitive equilibrium are quantities $(c,y,n,h)$ and a wage $w$ such that
\be
\medskip
\item Utility maximization: taking as given $w$, the representative household chooses $(c,h)$ to solve
$$\max_{c,h} \ U(c) - V(h) \quad \mbox{s.t.} \quad c = w h + \Pi$$
\item Profit maximization: taking as given $w$, the representative firm chooses $n$ and $y=f(n)$ to solve
$$\Pi = \max_n \ f(n) - wn $$
\smallskip
\item Market clearing: demand = supply for both goods and labor
\begin{align*}
\mbox{goods market:} \qquad  c &= y \\[0.5ex]
\mbox{labor market:} \qquad n &= h
\end{align*}
\ee
\end{frame}


\begin{frame}{Brief recap of standard labor market model (lectures 1 \& 2)}
\bi
\item Household utility maximization:
$$\frac{V'(h)}{U'(c)} = w $$
\item Firm profit maximization:
$$f'(n) = w $$
\item Market clearing:
$$\frac{V'(n)}{U'(c)} = f'(n)$$
\ei
\end{frame}





\begin{frame}{Recall graphical representation}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.78\textwidth]{figures/11.eps}
\end{figure}
\end{frame}


\begin{frame}{In standard model there is no involuntary unemployment}
$$\frac{V'(n)}{U'(c)} = f'(n)$$
\newline
Important feature of standard model: \textbf{\tr{no involuntary unemployment!}}
\bi
\bigskip
\item worker's always set $MRS = w$
\bigskip
\item only reason $n \downarrow$ at given $w$ is change in preferences, e.g. disutility of work $\uparrow$
\ei
\end{frame}


\begin{frame}{Modeling involuntary unemployment: search and matching}
\bi
\item This part of lecture notes: \tr{model with involuntary unemployment}
\bigskip
\item Will feature workers who ``actively searched for work but could not find it"
\bigskip
\item Key idea = \tr{search process is frictional}: workers looking for jobs and firms who need them might fail to find each other
\bigskip
\item Diamond-Mortensen-Pissarides search model
\bi
\bigskip
\item fully-fledged version = complicated multiperiod model
\bigskip
\item here: simplified static (one-period) version of Shimer's book
\ei
\ei
\end{frame}




\begin{frame}{The matching function}
\vspace{-2mm}
Standard model: recruiting is costless, can find as many workers as you want\\
\medskip
New assumptions:
\bi
\medskip
\item to hire a worker, have to post vacancy at cost $\kappa>0$
\medskip
\item posting vacancy does not guarantee hiring, instead search frictions
\medskip
\item when unemployment rate $=u$ and firms post total vacancies $=v$
$$\tr{\mbox{number of new jobs or ``matches"} = m = M(u,v)} $$
\item $\Rightarrow$ employment is
$$n = n_0 + M(u,v)$$
where $n_0 = $ workers employed (matched) before start of period
\medskip
\item labor force fixed at $1$ so that $u=1-n$ (no participation decision)
\ei
\end{frame}


\begin{frame}{The matching function}
\vspace{-3mm}
\bi
\item Function $M(u,v)$ is called \tr{``matching function"}
\bigskip
\item Production function: inputs = unemployed, vacancies; output = matches
\bigskip
\item Reduced-form representation of search and matching process in reality
\bi
\smallskip
\item reduced-form like all production functions
\smallskip
\item Pissarides' key simplifying assumption
\ei
\bigskip
\item Common assumption: Cobb-Douglas matching function
\begin{equation}\tag{$\ast$}\label{eq:CD}
m = M(u,v) = \bar{\mu} v^{\eta} u^{1-\eta}, \quad 0<\eta<1
\end{equation}
\item Will make this assumption going forward
\bigskip
\item Useful momentarily: can write \eqref{eq:CD} as
$$m = \bar{\mu}\theta^{\eta-1} v \quad \mbox{where} \quad \theta = \frac{v}{u} =  \frac{v}{1-n}  $$
is ``vacancy-unemployment ratio" or ``labor market tightness"
\ei
\end{frame}



\begin{frame}{Vacancy filling rate for individual firm}
\vspace{-3mm}
\bi
\item Individual firm that considers posting vacancy needs to know ``vacancy filling rate" = probability of filling given vacancy
\bigskip
\item Claim: vacancy filling rate equals $m/v = \bar{\mu}\theta^{\eta-1}$
\bi
\medskip
\item see supplement for explanation
\ei
\bigskip
\item $\Rightarrow$ employment $n$ of individual firm determined by
$$n= n_0 + \mu(\theta) v \quad \mbox{where} \quad \mu(\theta) = \bar{\mu}\theta^{\eta-1}$$
and $v =$ vacancies posted by this firm
\bigskip
\item Note:
\bi
\medskip
\item firms choose $v$ taking $\theta$ as given
\medskip
\item $\mu'(\theta) <0$: higher $\theta \Rightarrow$ harder to recruit workers
\medskip
\item reason why $\theta$ is called ``labor market tightness"
\ei
\ei
\end{frame}



\begin{frame}{Firms}
\vspace{-3mm}
\bi
\item Production: $y = An$, i.e. labor is only factor of production
\bigskip
\item Profits of a firm with existing workers $n_0$ are
$$\Pi = \max_{v} \ A n - w n - \kappa v, \quad n =\mu(\theta)v + n_0 $$
\item Assumption: cost of posting vacancies $\kappa v$ paid to households (next slide)
\bigskip
\item Optimality condition for vacancies $v$:
$$A  = w + \frac{\kappa}{\mu(\theta)}$$
\item Marginal product $A$ = wage $w$ + recruiting cost per new worker $\kappa/\mu(\theta)$
\bigskip
\item Note: when recruiting is costless $\kappa = 0$ recover standard frictionless model $A=w$
\ei
\end{frame}



\begin{frame}{Households}
\vspace{-3mm}
\bi
\item Representative household with large number of members
\bi
\medskip
\item fraction $n$ are employed, fraction $u=1-n$ are unemployed
\ei
\bigskip
\item Households \tr{do not} get to choose how much they work
\bi
\medskip
\item instead search for jobs, if matched: take job unless wage is too low
\ei
\bigskip
\item Household utility is (note: no $\max_n$ and $\kappa v =$ income)
$$
E(n) = U(c) - V(n) \quad \mbox{where} \quad c = wn + \kappa v + \Pi
$$
\item Marginal value of extra employed member $E'(n) = U'(c)w - V'(n)$
\bigskip
\item Household members happy to employed whenever $E'(n) \geq 0$ or
$$w \geq \frac{V'(n)}{U'(c)} $$
\item Intuition: $V'(n)/U'(c) = $ value of leisure, wage needs to exceed that
\ei
\end{frame}




\begin{frame}{Wage determination}
\bi
\item If worker and firm match, need to decide what wage worker will be paid
\bi
\medskip
\item assumption: they bargain over wage (``Nash bargaining" due to same John Nash as ``Nash equilibrium")
\medskip
\item for details, see supplement and Kurlat, chapter 7.5
\ei
\bigskip
\item Outcome of Nash bargaining
\tr{$$w = \phi A  + (1-\phi) \frac{V'(n)}{U'(c)} $$}
where $0 \leq \phi \leq 1$ = worker's bargaining power
\bigskip
\item Assumption: $U(c)-V(n) = \log c - \gamma n$
$$\Rightarrow \quad w = \phi A  + (1-\phi) \gamma c $$
\ei
\end{frame}


\begin{frame}{{\large Graphical representation of wage determination: \tr{standard model}}}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.7\textwidth]{figures/lec10_4} 
\end{figure}
\vspace{-3mm}
Graphical representation for standard model with \tr{linear production $f(n)=An$}
\end{frame}

\begin{frame}{{\large Graphical representation of wage determination: \tr{search model}}}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.7\textwidth]{figures/lec10_5v2} 
\end{figure}
\vspace{-3mm}
Search frictions $\Rightarrow$ \tr{lower $n$} and \tr{wedge between MPL \& MRS}, $A > V'(n)/U'(c)$
\end{frame}

\begin{frame}{{\large Graphical representation of wage determination: \tr{search model}}}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.7\textwidth]{figures/lec10_6v2} 
\end{figure}
\vspace{-3mm}
Wage $w$ is in between $V'(n)/U'(c)$ and $A$ depending on bargaining power $\phi$
\end{frame}




\begin{frame}{Equilibrium in static Diamond-Mortensen-Pissarides model}
\vspace{-4mm}
{\small\tr{\textbf{Definition:}} An equilibrium are quantities $(c,y,n,u,v,\theta)$, and a wage $w$ such that}
\be
{\small \item Households: taking as given $w,v,\Pi$ and the level of employment $n$, the representative household's utility is
$$E(n) = U(c) - V(n) \quad \mbox{s.t.} \quad c = w n + \kappa v + \Pi$$
\item Firms: taking as given $w$ and $\theta$, the representative firm chooses $v,n$ to solve
$$\Pi = \max_{v} \ A n - w n - \kappa v, \quad n =\mu(\theta)v + n_0 $$
\item Goods market clearing:
$$c = A n$$
\item Labor market with search frictions:
\bi
{\small
\smallskip
\item employment is $n =\mu(\theta)v + n_0$ where $\theta = v/u$ is labor market tightness
\smallskip
\item unemployment is $u=1-n$
\smallskip
\item the wage $w$ is determined by Nash bargaining
$$w = \phi A  + (1-\phi) \frac{V'(n)}{U'(c)}, \quad 0 \leq \phi \leq 1 $$}
\ei
}
\ee
\end{frame}


\begin{frame}{Characterizing the equilibrium}
\bi
\item Goal: characterize equilibrium, comparative statics
\bigskip
\item Closed-form solution not feasible but can still characterize solution tightly
\bigskip
\item Going forward, assume $U(c)-V(n) = \log c - \gamma n$
\bigskip
\item Recall the following three equations:
\begin{align*}
\mbox{Optimality for $v$:} \quad A - w &= \frac{\kappa}{\mu(\theta)} \\[1ex]
\mbox{Wage determination:} \quad w &= \phi A + (1-\phi)\gamma c \\[1ex]
\mbox{Employment:}\quad n &= \mu(\theta)v + n_0 
\end{align*}
\ei
\end{frame}

\begin{frame}{Characterizing the equilibrium}
Using that $c=An$ and $v = \theta u = \theta(1-n)$ we have
\begin{align*}
\mbox{Optimality for $v$:} \quad A - w &= \frac{\kappa}{\mu(\theta)} \\[1ex]
\mbox{Wage determination:} \quad w &= \phi A + (1-\phi)\gamma An  \\[1ex]
\mbox{Employment:}\quad n &= \mu(\theta)\theta(1-n) + n_0 
\end{align*}
These are three equations in three unknowns $(w,n,\theta)$
\end{frame}



\begin{frame}{Characterizing the equilibrium}
\bi
\item With some more algebra (see supplement), boil things down to one equation in one unknown $n$:
\tr{
\begin{equation}\tag{$\ast$}\label{eq:equilibrium}
\underbrace{A - W(n)}_{\textrm{profit per filled vacancy}} = \underbrace{\frac{\kappa}{\mu(\Theta(n))}}_{\textrm{recruiting cost}}
\end{equation}
}
where
\begin{align*}
W(n) &= \phi A + (1-\phi)\gamma An \\[1ex]
\Theta(n) &= \left(\frac{n-n_0}{\bar{\mu}(1-n)} \right)^{1/\eta} 
\end{align*}
\item No closed-form solution for equilibrium $n$
\bigskip
\item But can characterize solution graphically
\ei
\end{frame}



\begin{frame}{Graphical representation of equilibrium condition \eqref{eq:equilibrium}}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.7\textwidth]{figures/lec10_1} 
\end{figure}
\vspace{-3mm}
Can show: exactly one intersection, i.e. equilibrium exists and is unique
\end{frame}


\begin{frame}{{\large Key feature of DMP model: actively looking for work but cannot find it}}
\bi
\item Equilibrium wage exceeds value of leisure
$$w \ \tr{>} \ \frac{V'(n)}{U'(c)}  $$
\item $\Rightarrow$ \tr{households want to work more} $E'(n) = U'(c)w - V'(n) \ \tr{> 0}$
\bigskip
\item But even though they are \tr{actively looking} for more work, they \tr{cannot find it due to search frictions}
\bigskip
\item Typical survey question to measure unemployment:\\ ``Have you been actively looking for a job over the past four weeks?"
\bi
\medskip
\item e.g. see {\scriptsize\url{https://www.bls.gov/cps/cps_htgm.htm}} for questions asked in U.S. Bureau of Labor Statistics (BLS) Current Population Survey (CPS)
\ei
\bigskip
\item If ask this question to unemployed living in this model, they will say ``yes"!
\ei
\end{frame}


\begin{frame}{Comparative statics}
\bi
\item Having solved the model, let's do some comparative statics
\bigskip
\item What happens to employment and unemployment when 
\bi
\bigskip
\item productivity $A \uparrow$?
\bigskip
\item matching efficieny $\bar{\mu} \uparrow$ (recall $M(u,v) = \bar{\mu} v^{\eta} u^{1-\eta}$)?
\bigskip
\item vacancy posting cost $\kappa \uparrow$?
\bigskip
\item ...
\ei
\bigskip
\item See graphical analysis on next slides as well as supplement
\ei
\end{frame}



\begin{frame}{An increase in productivity $A$ raises employment}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.8\textwidth]{figures/lec10_2} 
\end{figure}
\end{frame}


\begin{frame}{An increase in matching efficiency $\bar{\mu}$ raises employment}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.8\textwidth]{figures/lec10_3} 
\end{figure}
\end{frame}


\begin{frame}{Unemployment insurance (UI)}
\bi
\item See supplement
\bigskip
\item Introduce unemployment benefits $b$ so that household consumption is
$$c = wn + (1-n)\tr{b} + \kappa v + \Pi$$
\item Key results: UI
\bi
\medskip
\item increases household consumption and welfare
\medskip
\item but also increases equilibrium unemployment rate $u$
\ei
\bigskip
\item Key mechanisms: UI increases workers' outside option
$$w = \phi A + (1-\phi) \left(\frac{V'(n)}{U'(c)} + \tr{b}\right) $$
\ei
\end{frame}





\begin{frame}
\renewcommand{\baselinestretch}{1}
\vspace{3cm}
\begin{center}
{\huge Inequality in Macroeconomics}
\end{center}
\end{frame}




\begin{frame}{Do macroeconomists ignore heterogeneity and inequality?}
\vspace{-2mm}
\bi
\item So far in this course: mostly representative agent models
\bi
\medskip
\item only exception = models with two types of households (TANK etc)
\ei
\bigskip
\item Seemingly consistent with popular criticisms of macroeconomics: ``macroeconomists ignore heterogeneity and inequality"
\bigskip
\item Example: excerpt from a 2017 newspaper article
\begin{center}
\includegraphics[width=.7\textwidth]{figures/reuters}
\end{center}
Source: {\notsotiny\url{https://www.reuters.com/article/us-review-crisis-breakingviews-idUSKBN1811XP}}
\ei
\end{frame}



\begin{frame}{Modern macro $\neq$ representative agent models}
\bi
\item Is all of moden macro just representative agent models?
\bigskip
\item No, not all: macroeconomics research of the last 20 or 30 years is all about heterogeneity and inequality
\bi
\medskip
\item ``heterogeneous agent models"
\medskip
\item if someone tells you otherwise, they simply don't know what they are talking about
\ei
\bigskip
\item Two reasons for teaching you representative agent models
\be
\medskip
\item they often capture key mechanisms in transparent fashion
\medskip
\item properly modeling heterogeneity is hard (PhD-level material)
\ee
\ei
\end{frame}




\begin{frame}{Ricardo Reis (2018) on criticisms of macro}
\vspace{-4mm}
After summarizing current work by a number of young macroeconomists, Ricardo writes:
\begin{center}
\includegraphics[width=.85\textwidth]{figures/Reis-wrong}
\end{center}
Point: there's plenty wrong with macroeconomics but please stop the lazy, off-target criticisms!\\
\medskip
Source: {\scriptsize\url{https://personal.lse.ac.uk/reisr/papers/18-wrong.pdf}}
\end{frame}



\begin{frame}{Why is modeling heterogeneity so hard?}
\vspace{-3mm}
\bi
\medskip
\item Mathematically need to carry around \tr{distributions} of variables
\medskip
\item ``Distribution" as in ``density" or ``cumulative distribution function (CDF)"
\begin{center}
\includegraphics[width=0.4\textwidth]{figures/density_steadystate.eps}
\end{center}
\item Now: tell you a bit about this type of work
\bigskip
\item End of slides: inequality in macro -- a history of thought (not examinable)
\ei
\end{frame}



\begin{frame}{Heterogeneous agent macroeconomics and HANK models}
\bi
\item Good overview in Chapter 18 ``Heterogeneous agent macroeconomics: origins, progress \& challenges" in Carlin and Soskice (2023) ``Macroeconomics: Institutions, Instability \& Inequality"
\bigskip
\item As name suggests, Heterogeneous Agent New Keynesian (HANK) models = models with heterogeneity (HA) + nominal rigidities (NK)
\bigskip
\item \tr{Four Lessons for monetary policy} in Kaplan, Moll and Violante IMF Finance \& Development magazine piece on HANK models\\[-0.5ex] {\tiny\url{https://www.imf.org/en/Publications/fandd/issues/2023/03/modern-monetary-policy-kaplan-moll-violante}}
\bigskip
\item Note: this material is not examinable
\ei
\end{frame}



\begin{frame}{\vspace{-3mm}{\large How does heterogeneous agent macro fit in with the rest of macro?} \vspace{-2mm}}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.95\textwidth]{figures/kaplan_timeline} 
\end{figure}
\vspace{-2mm}
{\small Source: Greg Kaplan's forthcoming book on heterogeneous agent macro\\
\smallskip
Note: timeline is incomplete (like all attempts to fit complex history into such narrative)}
\end{frame}


\begin{frame}{Recall from lecture 4: HANK models are NK models with large MPCs $\Rightarrow$ model behaviour resembles Keynesian cross}
\vspace{-4mm}
\begin{figure}[tph]
\centering
\includegraphics[width=0.4\textwidth]{figures/mpc500_quarterly_function_av.eps}
\end{figure}
\bi
\item Interesting implication of empirically realistic MPCs: model behaviour resembles Keynesian cross again, in particular sizable multipliers
\bigskip
\item But important difference: micro founded model, makes precise predictions about behavior as well as inequality, can use it to think about welfare
\ei
\end{frame}



\begin{frame}{HANK models: four lessons for \tr{monetary policy}}
\vspace{-3mm}
\bi
\item \tr{\textbf{Lesson 1:}} Predicting indirect policy impacts
\bi
{\footnotesize
\item High MPCs $\Rightarrow$ indirect effects $>>$ direct effects
}
\ei
\medskip
\item \tr{\textbf{Lesson 2:}} Some ships are lifted higher, others are sunk
\bi
{\footnotesize
\item Traditional view of monetary policy: ``a rising tide raises all ships." This is a fiction.
\item HANK models force us to let go of the fiction that we can cleanly separate stabilization from redistribution}
\ei
\medskip
\item \tr{\textbf{Lesson 3:}} Fiscal footprints matter
\bi
{\footnotesize
\item Another widespread misconception is the view that monetary policy can be divorced from fiscal policy
\item HANK models reestablish a strong link between the two, showing how monetary policy leaves consequential ``fiscal footprints"
}
\ei
\medskip
\item \tr{\textbf{Lesson 4:}} The right tool for redistribution
\bi
{\footnotesize
\item Monetary policy is a blunt tool for redistribution or insurance
\item HANK models tell us that fiscal policy is likely better suited for this task because it can be targeted more precisely to those in need of support}
\ei
\ei
\end{frame}






\begin{frame}
\renewcommand{\baselinestretch}{1}
\vspace{3cm}
\begin{center}
{\huge Thanks for 10 fun weeks!}
\end{center}
\end{frame}





\begin{frame}{Inequality in Macro: A History of Thought (not examinable)}
\vspace{-3mm}
I find it useful to categorize macroeconomic theories as follows:
\bi
\medskip
\item \tr{before modern macro}: 1930 to 1970
\bigskip
\item \tr{1st generation} modern macro: 1970 to 1990
\bigskip
\item \tr{2nd generation} modern macro: 1990 to financial crisis
\bigskip
\item \tr{3rd generation} modern macro: after the financial crisis 
\ei
\bigskip
\pause
Main drivers of evolution in modern macro era
\be
\medskip
\item better data
\medskip
\item better computers \& algorithms
\medskip
\item current events (rising inequality, financial crisis)
\ee
\bigskip
(Warning: narrative won't be perfect -- will point out failures)
\end{frame}


\begin{frame}{Before Modern Macro: 1930 to 1970}
\be
\item Keynesian IS/LM
\bi
\medskip
\item about aggregates, \tr{no role for inequality/distribution by design}
\ei
\bigskip
\item Distribution does play role in growth theory
\bi
\medskip
\item mostly \tr{factor} income distribution -- capital vs labor\\
{\scriptsize Kaldor, Pasinetti, other Cambridge UK theorists}
\medskip
\item rarely \tr{personal} income or wealth distribution\\
{\scriptsize exceptions: Tobin, Stiglitz, Blinder}
\ei
\bigskip
\item Disconnected empirical work on inequality {\scriptsize (Kuznets)}
\ee
\end{frame}




\begin{frame}{First Generation Macro Theories: 1970 to 1990}
\pause
Representative agent models, e.g. RBC model
\bi
\medskip
\item again \tr{no role for inequality/distribution} by design\\
\medskip
\item advertised as ``microfounded" but rep agent assumption cuts 1st generation theories from much of micro research
\ei
\pause
\bigskip
What's wrong with that?
\medskip
\be
\item cannot speak to a number of important empirical facts, e.g.
\bi
\medskip
\item unequally distributed growth
\medskip
\item poorest hit hardest in recessions
\ei
\medskip
\item cannot think coherently about \tr{welfare} -- ``who gains, who loses?"
\ee
\end{frame}






\begin{frame}{Second Generation Macro Theories: 1990 to 2008}
\vspace{-3mm}
Incorporate micro \tr{heterogeneity}, particularly \tr{in income and wealth} -- early ``heterogeneous agent models"\\
{\scriptsize Aiyagari, Bewley, Huggett, Imrohoro\u{g}lu, Krusell-Smith, Den Haan,...}\\
\smallskip
... represent economy with a \tr{distribution} that moves over time, responding to macroeconomic shocks, policies
\vspace{-2mm}
\begin{center}
\includegraphics[width=0.5\textwidth]{figures/density_steadystate.eps}
\end{center}
\vspace{-2mm}
Can speak to facts on previous slide, useful for welfare analysis
\end{frame}







\begin{frame}{Second Generation Theories: Inequality $\not \Rightarrow$ Macro}
\vspace{-3mm}
\bi
\item Typical finding: \tr{heterogeneity doesn't matter much for macro agg's}\\
{\scriptsize Krusell-Smith (1998) ``approximate aggregation"}\\
\pause
\bigskip
\item Reason: linearity -- \tr{rich = scaled version of poor}\\ Hence ``inequality $\not \Rightarrow$ macro", but also a \tr{knife-edge result}
\bigskip
\item Interestingly, some more nuanced, cautionary results in literature:
\bi
\medskip
\item \tr{even in KS98, extension where heterogeneity does matter (§4)}\\
\medskip
\item but gets lost, economists' perception = ``inequality $\not \Rightarrow$ macro"
\ei
\pause
\bigskip
\item Either way: in data, rich \tr{$\neq$} scaled version of poor, e.g. rich have
\bi
\medskip
\item e.g. lower MPCs out of transitory income changes
\ei
\bigskip
\pause
\item Note: some important contributions from 90s don't fit my narrative
\bi
\medskip
\item {\small \tr{Banerjee-Newman, Benabou, Galor-Zeira, Persson-Tabellini, ...}}
\ei
\ei
\end{frame}



\begin{frame}{Third Generation Theories: after the Crisis}
\vspace{-3mm}
\bi
\item 3rd generation theories \tr{take micro data more seriously}
\bigskip
\item Leads them to emphasize things like
\bi
\medskip
\item household balance sheets
\medskip
\item credit constraints
\medskip
\item MPCs that are high on average but heterogeneous
\medskip
\item non-homotheticities, non-convexities
\ei
\medskip
\tr{$\Rightarrow$ move away from knife-edge case}
\bigskip
\item Typical finding: \tr{distribution matters for macro}
\bigskip
\item Momentarily: an application from my own work (HANK)

\ei
\end{frame}



\begin{frame}{Distribution in Macro: Summary}
\vspace{-3mm}
\bi
\item \tr{Before modern macro:} 1930 to 1970
\bi
\medskip
\item it's complicated
\ei
\bigskip
\item \tr{1st generation:} 1970 to 1990
\bi
\medskip
\item representative agent models (RBC, New Keynesian etc)
\medskip
\item no role for inequality by design
\ei
\bigskip
\item \tr{2nd generation:} 1990 to financial crisis
\bi
\medskip
\item early heterogeneous agent models
\medskip
\item ``macro $\Rightarrow$ inequality" but ``macro $\not \Leftarrow$ inequality" (perception) \\
\ei
\bigskip
\item \tr{3rd generation:} after the financial crisis 
\bi
\medskip
\item current heterogeneous agent models
\medskip
\item rich interaction: ``inequality $\Longleftrightarrow$ macro"
\ei
\ei
\end{frame}


\begin{frame}{Distribution in Modern Macro: Summary}
Janet Yellen speech ``Macroeconomic Research After the Crisis" {\scriptsize \url{http://www.federalreserve.gov/newsevents/speech/yellen20161014a.htm}}
\begin{itemize}
\medskip
{\small 
\item ``Prior to the financial crisis, representative-agent models were the dominant paradigm for analyzing many macroeconomic questions \tr{[= 1st generation]}."
\medskip
\item ``However, a disaggregated approach seems needed to understand some key aspects of the Great Recession..."
\medskip
\item ``While the economics profession has long been aware that these issues matter, their effects had been incorporated into macro models only to a very limited extent prior to the financial crisis \tr{[ = 2nd generation]}."
\medskip
\item ``I am glad to now see a greater emphasis on the possible macroeconomic consequences of heterogeneity \tr{[ = 3rd generation]}."}
\end{itemize}
\end{frame}



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\end{document}

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