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\title{\vspace{1.6cm} \\
	{\LARGE Lecture 8}\\[1ex]
{\LARGE Policy in the New Keynesian Model}\\
	\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}{Plan}
\vspace{-2mm}
\be
\item Monetary policy
\bi
\medskip
\item already part of model, can use as is
\ei
\bigskip
\item Fiscal policy
\bi
\medskip
\item not in model yet, will have to extend it
\ei
\bigskip
\item Pecking order of monetary and fiscal policy?
\ee
\bigskip
Key observation: \tr{sticky prices break first welfare theorem}
\bi
\medskip
\item sticky prices = ``friction"
\medskip
\item $\Rightarrow$ rationalizes some sort of \tr{policy intervention}
\ei
\end{frame}


\begin{frame}
\renewcommand{\baselinestretch}{1}
\vspace{3cm}
\begin{center}
{\LARGE Monetary Policy in the New Keynesian Model}
\end{center}
\end{frame}




\begin{frame}{{\large What is central bank's policy instrument? Money supply or interest rate?}}
\vspace{-4mm}
\bi
\item Recall: assume that central bank has two policy instruments
\be
\smallskip
\item $i_1$: nominal interest rate between periods $1$ and $2$
\smallskip
\item $M_2$: money supply in period $2$
\ee
\smallskip
\item Usual description of monetary policy in media etc: interest rates
\bi
\smallskip
\item why is monetary policy not only setting $i_1$? Or $(i_1,i_2)$?
\ei
\smallskip
\item Answer:
\bi
\smallskip
\item in general, \tb{setting $i$ and $M$ are equivalent -- see next slide}
\smallskip
\item in practice central banks announce $i$, adjust $M$ accordingly
\smallskip
\item but technical issue in our 2-period model: there is only one interest rate, i.e. no $i_2$ $\Rightarrow$ need $M_2$ in addition to $i_1$
\smallskip
\item note: not an issue in standard NK model because infinite horizon
\ei
\smallskip
\item Related question: why not only $(M_1,M_2)$ instead of $(i_1,M_2)$?
\bi
\smallskip
\item this is equivalent, see next problem set
\ei
\smallskip
\item Next slides: \textbf{\tb{focus on $i_1$ as central bank's policy instrument}}
\ei
\end{frame}



\begin{frame}{Equivalence of setting $i$ and $M$ (from EC1B1)}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=\textwidth]{figures/EC1B1_i_vs_M} 
\end{figure}
\end{frame}



\begin{frame}{Monetary policy affects consumption, investment, GDP}
\bi
\item Recall expressions for consumption, investment and GDP
\begin{equation*}\begin{split}
C_1 &= \left(\frac{1}{\beta A_2} \right)^\sigma A_2 \frac{M_2}{\tb{(1+i_1)}P_1} \\
I_1 &= \frac{M_2}{\tb{(1+i_1)}P_1} \\
Y_1 = C_1 + I_1 &= \left[1 + \left(\frac{1}{\beta A_2} \right)^\sigma A_2 \right] \frac{M_2}{\tb{(1+i_1)}P_1}\\
\end{split}\end{equation*}
\medskip
\item Clearly when central bank cuts interest rate \tb{$i_1 \downarrow$}, all of $C_1,I_1,Y_1 \uparrow$
\bigskip
\item Explain intuition in a few slides
\ei
\end{frame}


\begin{frame}{{\large Monetary policy can stabilize recession caused by demand shock}}
\vspace{-4mm}
\only<all:1>{
$$Y_1 = \left[1 + \tr{\left(\frac{1}{\beta A_2} \right)^\sigma A_2} \right] \frac{M_2}{(1+i_1)P_1} \quad \tr{\downarrow \quad \mbox{because} \ A_2 \downarrow \ \mbox{or} \ \beta \uparrow}$$
}
\only<all:2>{
$$Y_1 = \left[1 + \tr{\left(\frac{1}{\beta A_2} \right)^\sigma A_2} \right] \tb{\frac{M_2}{(1+i_1)P_1}} \quad \tb{\uparrow \quad \mbox{because} \ i_1 \downarrow}$$
}
\begin{figure}[tph]
	\centering
\uncover<all:1-2>{\includegraphics[width=.5\textwidth]{figures/lec7_2.eps}}\uncover<all:2>{\includegraphics[width=.5\textwidth]{figures/lec7_4.eps}}
\end{figure}
\end{frame}


\begin{frame}{The monetary transmission mechanism: intuition}
\vspace{-4mm}
{\small Looking at equations: central bank cutting nominal interest rate
$$i_1 \downarrow \quad \Rightarrow \quad C_1, \ I_1, \ Y_1, \ C_2, \ Y_2 \quad \mbox{all} \uparrow, \quad P_2 \downarrow  $$
What's going on under the hood, i.e. what's transmission mechanism?
\bi
\vspace{-0.7mm}
\item $i_1 \downarrow \Rightarrow$ real interest rate $1+r_1 = (1+i_1)P_1/P_2 \downarrow$
\vspace{-0.7mm}
\item $r_1 \downarrow \Rightarrow$ household consumption $C_1 \uparrow$ from \tr{Euler eqn} $C_1 = C_2 [\beta(1+r_1)]^{-\sigma}$ (intertemporal substitution)
\vspace{-0.7mm}
\item  $r_1 \downarrow \Rightarrow$ firm investment $I_1 = K_2 \uparrow$ from firm \tr{investment demand curve}
\vspace{-0.7mm}
\item $C_1 \uparrow$ and $I_1 \uparrow \Rightarrow$ aggregate demand $Y_1^D = C_1 + I_1 \uparrow$
\vspace{-0.7mm}
\item $Y_1^D \uparrow \Rightarrow$ output $Y_1 \uparrow \Rightarrow$ household income $\Omega = P_1 Y_1 \uparrow \Rightarrow C_1,C_2 \uparrow$ (income effect) $\Rightarrow$ aggregate demand $Y_1^D \uparrow \Rightarrow ...$ (\tr{Keynesian cross logic})
\vspace{-0.7mm}
\item $K_2 \uparrow \Rightarrow$ future output $Y_2 = A_2 K_2 \uparrow$ consistent with $C_2 \uparrow$ (so that $C_2 = Y_2$)
\vspace{-0.7mm}
\item $C_2 \uparrow \Rightarrow$ price level $P_2 \downarrow$ from quantity equation $P_2 C_2 = M_2$ \\(one intuition: $K_2 \uparrow \Rightarrow$ aggregate supply $Y_2^S \uparrow \Rightarrow$ price level $P_2 \downarrow$)
\vspace{-0.7mm}
\item $P_2 \downarrow \Rightarrow$ real interest rate  $1+r_1 = (1+i_1)P_1/P_2 \uparrow$ until $1 + r_1 = A_2$ so that capital market is in equilibrium (recall infinitely elastic capital demand)
\ei}
\end{frame}



\begin{frame}{Another way of looking at it: IS and MP curves}
\vspace{-3mm}
Recall IS and MP curves from EC1B1 and standard textbooks (e.g. Jones)
\begin{figure}[tph]
	\centering
\includegraphics[width=.85\textwidth]{figures/jones_ISMP} 
\end{figure}
Source: Jones, Macroeconomics \\
\medskip
Here: \tr{IS and MP curves = just another way of plotting our equations}
\end{frame}


\begin{frame}{Another way of looking at it: IS and MP curves}
\bi
\item Recall expressions for consumption, investment and GDP
\begin{equation*}\begin{split}
C_1 &= \left(\frac{1}{\beta A_2} \right)^\sigma A_2 \frac{M_2}{\tb{(1+i_1)}P_1} \\
I_1 &= \frac{M_2}{\tb{(1+i_1)}P_1} \\
Y_1 = C_1 + I_1 &= \left[1 + \left(\frac{1}{\beta A_2} \right)^\sigma A_2 \right] \frac{M_2}{\tb{(1+i_1)}P_1}\\
\end{split}\end{equation*}
\smallskip
\item Before: plotted $Y_1$ as function of $P_1$, called it ``aggregate demand"
\bigskip
\item Now: plot $Y_1$ \tb{as function of $i_1$}, call it \tb{``IS curve"}
\ei
\end{frame}

\begin{frame}{IS curve = $Y_1$ plotted as function of $i_1$}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.7\textwidth]{figures/lec7_6.eps} 
\end{figure}
\vspace{-7mm}
\bi
\item Question for you: why the kink?
\smallskip
\item Comment: usually IS($r$) not $i$ -- would need extension with $i_1$ affecting $r_1$
\ei
\end{frame}


\begin{frame}{IS and MP curves}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.8\textwidth]{figures/lec7_7.eps} 
\end{figure}
\end{frame}


\begin{frame}{A negative demand shock causes a recession}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.8\textwidth]{figures/lec7_8.eps} 
\end{figure}
\end{frame}

\begin{frame}{{\large Monetary policy can stabilize recession caused by demand shock}}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.8\textwidth]{figures/lec7_9.eps} 
\end{figure}
\end{frame}



\begin{frame}{IS curve = Euler equation + investment demand curve}
\vspace{-3mm}
\bi
\item {\small Will sometimes hear ``New Keynesian IS curve"}
\smallskip
\item {\small Just another name for ``Euler equation" and/or ``investment demand curve"}
\ei
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.25\textwidth]{figures/jones_IS}\includegraphics[width=.05\textwidth]{figures/equal}\includegraphics[width=.3\textwidth]{figures/euler}\includegraphics[width=.06\textwidth]{figures/plus}\includegraphics[width=.35\textwidth]{figures/lec5_1}
\end{figure}
\vspace{-2mm}
\bi
\item {\footnotesize From Jones' book: ``The IS curve captures the fact that high interest rates reduce output in the short run. \tr{This occurs because high interest rates make borrowing expensive for firms and households, reducing their demand for new investment.} The reduction in demand leads to a decline in output in the economy as a whole."}
\smallskip
\item {\small Jones is clearly talking about Euler equation and investment demand curve}
\ei
\end{frame}


\begin{frame}{Optimal monetary policy and ``divine coincidence"}
\vspace{-3mm}
\bi
\item Question: what is the \tr{optimal} monetary policy?
\bigskip
\item Answer: the policy that
\bi
\medskip
\item undoes all distortions due to price stickiness
\medskip
\item equates allocation with sticky prices to that with flexible prices (first best because welfare theorems hold)
\ei
\begin{figure}[tph]
	\centering
\includegraphics[width=.45\textwidth]{figures/lec7_4.eps}
\end{figure}
\ei
\end{frame}



\begin{frame}{Optimal monetary policy and ``divine coincidence"}
\vspace{-3mm}
\bi
\item Specifically optimal monetary policy chooses $i_1$ (or $M_2$) to equate
$$Y_1^{\textrm{sticky}} = \left[1 + \left(\frac{1}{\beta A_2} \right)^\sigma A_2 \right] \tb{\frac{M_2}{\tb{(1+i_1)}P_1}} \quad \mbox{and} \quad Y_1^{\textrm{flex}} = A_1 K_1 $$
\item $\Rightarrow$ optimal policy sets
$$\tb{\frac{M_2}{(1+i_1)P_1}} = \frac{1}{1 + \left(\frac{1}{\beta A_2} \right)^\sigma A_2}A_1 K_1  $$
\item Striking result: for any type and size of demand shock, there's always a monetary policy that can restore first-best allocation
\bi
\medskip
\item when responding to demand shocks, in this model, monetary policy faces \tr{no tradeoff} of any kind
\medskip
\item result is called ``divine coincidence" (Blanchard and Gali, 2007)\\
{\scriptsize \url{https://en.wikipedia.org/wiki/Divine_coincidence}}
\ei
\ei
\end{frame}

\begin{frame}{Limits to monetary policy: zero lower bound (ZLB)}
\vspace{-2mm}
\bi
\item Question: Is the optimal policy always feasible? Answer: \tr{no}
\bigskip
\item \tr{\textbf{Definition:}} The \tr{zero lower bound (ZLB)} is the requirement that nominal interest rates cannot be negative, $i_1\geq 0$
\bigskip
\item Rationale:
\bi
\medskip
\item households and firms borrow and lend at rate $i_1$
\medskip
\item but there's an alternative to lending, namely holding money
\medskip
\item money always pays an interest rate of zero
\medskip
\item \tr{If $i_1<0$, you're better off putting your money under your mattress}
\medskip
\ei
\bigskip
\item Alternative names for ZLB that mean same thing:
\bi
\medskip
\item effective lower bound (ELB), reason: bound may not be exactly = 0
\medskip
\item liquidity trap
\ei
\ei
\end{frame}



\begin{frame}{Limits to monetary policy: zero lower bound (ZLB)}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.8\textwidth]{figures/lec7_10.eps} 
\end{figure}
\end{frame}


\begin{frame}{{\large Monetary policy cannot stabilize recession because ZLB binds}}
\vspace{-4mm}
\begin{figure}[tph]
	\centering
\includegraphics[width=.8\textwidth]{figures/lec7_11.eps} 
\end{figure}
\end{frame}



\begin{frame}
\renewcommand{\baselinestretch}{1}
\vspace{3cm}
\begin{center}
{\huge Fiscal Policy in the New Keynesian Model}

\end{center}
\end{frame}

\begin{frame}{Two main types of fiscal policy: $G$ and $T$}
\be
\item \tr{\textbf{Government spending $G$}}
\bi
\medskip
\item infrastructure projects,...
\medskip
\item the traditional way of thinking about fiscal policy
\ei
\bigskip
\item \tr{\textbf{Transfers}} or tax cuts to households \tr{\textbf{$T$}}
\bi
\medskip
\item tax cuts, stimulus checks, ...
\medskip
\item used in all U.S. recessions, same in many other countries
\medskip
\item in practice, probably the more important type of fiscal policy
\ei
\ee
\end{frame}



\begin{frame}{Introducing fiscal policy into the model}
\vspace{-4mm}
\bi
\item Follow MW's notation
\bi
\smallskip
\item $G_1,G_2$: government spending
\smallskip
\item $T_1,T_2$: lump-sum taxes, transfers = $T_t < 0$
\ei
\medskip
\item Key changes to model equations are as follows...
\medskip
\item Resource constraints
$$C_1 + I_1 + G_1 = Y_1, \quad C_2 + G_2 = Y_2$$
\item Household budget constraint
$$P_1 C_1 + \frac{P_2 C_2}{1+i_1} = P_1(\Pi_1 - T_1) + \frac{P_2(\Pi_2 - T_2)}{1+i_1}  $$
\item Government budget constraint
$$P_1 G_1 + \frac{P_2 G_2}{1+i_1} = P_1 T_1 + \frac{P_2 T_2}{1+i_1} $$
\item MW: $G_1,G_2$ enter utility fn, here: $G_1,G_2$ not valued (``digging ditches")
\ei
\end{frame}


\begin{frame}{Equilibrium with sticky prices and fiscal policy}
\vspace{-6mm}
{\small 
\begin{align*}
C_1 &= \left(\frac{1}{\beta A_2} \right)^\sigma A_2 \frac{M_2}{(1+i_1)P_1} \\
C_2 &= A_2\frac{M_2}{(1+i_1)P_1} \\
I_1 &= \frac{1}{1 - \tr{g_2}}\frac{M_2}{(1+i_1)P_1} \\
Y_1 &= \frac{1 + \left(\frac{1}{\beta A_2} \right)^\sigma A_2(1 - \tr{g_2})}{1- \tr{g_2}} \frac{M_2}{(1+i_1)P_1} + \tr{G_1}\\
Y_2 &= A_2 \frac{1}{1- \tr{g_2}}\frac{M_2}{(1+i_1)P_1}\\
P_2 &= \frac{1+i_1}{A_2}P_1
\end{align*}
where \tr{$g_2 = G_2/(A_2 K_2)$} =  share of \tr{$G_2$} in potential output $A_2 K_2$\\
\smallskip
Note: equations are identical to MW's equations (31)-(36) }
\end{frame}


\begin{frame}{Fiscal policy via government spending $G_1$}
\bi
\item Focus on effect of $G_1$ on variables at $t=1$
\begin{equation*}\begin{split}
C_1 &= \left(\frac{1}{\beta A_2} \right)^\sigma A_2 \frac{M_2}{(1+i_1)P_1} \\
I_1 &= \frac{1}{1-g_2}\frac{M_2}{(1+i_1)P_1} \\
Y_1 = C_1 + I_1 + \tr{G_1} &= \frac{1 + \left(\frac{1}{\beta A_2} \right)^\sigma A_2(1 - g_2)}{1- g_2} \frac{M_2}{(1+i_1)P_1} + \tr{G_1}\\
\end{split}\end{equation*}
\medskip
\item Clearly when $G_1 \uparrow$, GDP $Y_1$ increases \tr{one-for-one}
\ei
\end{frame}


\begin{frame}{{\large Government spending can stabilize recession caused by demand shock}}
\vspace{-4mm}
\only<all:1>{
$$Y_1 = \frac{1 + \left(\frac{1}{\beta A_2} \right)^\sigma A_2(1 - g_2)}{1- g_2} \frac{M_2}{(1+i_1)P_1} + G_1 \quad \downarrow \quad \mbox{because} \ A_2 \downarrow \ \mbox{or} \ \beta \uparrow$$
}
\only<all:2>{
$$Y_1 = \frac{1 + \left(\frac{1}{\beta A_2} \right)^\sigma A_2(1 - g_2)}{1- g_2} \frac{M_2}{(1+i_1)P_1} + \tr{G_1} \quad \tr{\uparrow \quad \mbox{because} \ G_1 \uparrow}$$
}
\begin{figure}[tph]
	\centering
\uncover<all:1-2>{\includegraphics[width=.5\textwidth]{figures/lec7_2.eps}}\uncover<all:2>{\includegraphics[width=.5\textwidth]{figures/lec7_12.eps}}
\end{figure}
\end{frame}


\begin{frame}{In this model fiscal multiplier is exactly 1}
\vspace{-4mm}
\bi
\item Fiscal multiplier, more precisely government spending multiplier
$$\mbox{multiplier} = \frac{\Delta Y_1}{\Delta G_1} = \mbox{£ increase in GDP per £ of government spending} $$
\item All of $C_1,I_1,C_2,...$ do \tr{not} depend on $G_1$ and
$$Y_1 = C_1 + I_1 + \tr{G_1} $$
\item Therefore clearly
\tr{$$\mbox{multiplier} = \frac{\Delta Y_1}{\Delta G_1} = 1$$}
\item Intuition in Mankiw-Weinzierl's words:\\
{\footnotesize
``The government-spending multiplier here is precisely one. An increase in government spending puts idle resources to work and raises income. Consumers, meanwhile, see their income rise but recognize that their taxes will rise by the same amount to finance that new, higher level of government spending. As a result, consumption and investment are unchanged \& the increase in income precisely equals increase in government spending."}
\ei
\end{frame}


\begin{frame}{In this model fiscal multiplier is exactly 1}
\vspace{-4mm}
\tr{$$\mbox{multiplier} = \frac{\Delta Y_1}{\Delta G_1} = 1$$}
stands in contrast with other common hypotheses
\bi
\medskip
\item Crowding out of investment and private consumption
$$Y = C + I + G \ \mbox{with} \ C,I \downarrow \quad \Rightarrow \quad \mbox{multiplier} = \frac{\Delta Y}{\Delta G} < 1$$
\item Typical old Keynesian multiplier stories
$$Y = C + I + G \ \mbox{with} \ C,I \uparrow \quad \Rightarrow \quad \mbox{multiplier} = \frac{\Delta Y}{\Delta G} > 1$$
\item In a sense, multiplier = 1 is most natural and intuitive benchmark
\bi
\smallskip
\item GDP increases by £1 for every £1 government spends
\ei
\medskip
\item Should not expect multipliers either far $< 1$ or far $>1$, e.g. $1/2$ or $2$
\ei
\end{frame}


\begin{frame}{Stabilization via $G$ is only second-best}
\vspace{-2mm}
\bi
\item Welfare effect of stabilization via $G$?
\bigskip
\item Fiscal policy restores only first-best level of GDP $Y_1$ but not $C_1$ and $I_1$
\bi
\medskip
\item $C_1$ and $I_1$ do not change when $G_1 \uparrow$
\medskip
\item shortfall in private consumption $C_1 + I_1 < A_1 K_1$ is made up by public consumption $G_1 \uparrow$ such that $C_1 + I_ 1 + G_1 = A_1 K_1$
\ei
\bigskip
\item But households value $G_1$ differently than $C_1$
\bi
\medskip
\item in fact recall assumption: $G_1,G_2$ not valued at all (``digging ditches")
\medskip
\item MW: more generally $G_1 \uparrow$ distorts optimal mix of $C_1$ and $G_1$:\\
{\footnotesize ``This fiscal policy is second-best, however, because it fails to produce the same allocation of resources achieved under flexible prices. Public consumption will be higher in both periods, but private consumption will be lower. As a result, households will end up with a lower level of welfare."}
\ei
\ei
\end{frame}





\begin{frame}{Fiscal policy via transfers / tax cuts $T_1$ (``stimulus checks")}
\vspace{-3mm}
\bi
\item Consider \tr{deficit-financed tax cut $T_1$}
\bi
\smallskip
\item $T_1 \downarrow$
\smallskip
\item $G_1,G_2$ unaffected
\smallskip
\item require $T_2 \uparrow$ for government budget constraint to hold
\ei
\bigskip
\item \textbf{\tr{Question 1:}} from expressions for equil'm variables, \tr{what is effect of $T_1 \downarrow$?}
{\small $$C_1 = \left(\frac{1}{\beta A_2} \right)^\sigma A_2 \frac{M_2}{(1+i_1)P_1}, \qquad 
Y_1 = \frac{1 + \left(\frac{1}{\beta A_2} \right)^\sigma A_2(1 - g_2)}{1- g_2} \frac{M_2}{(1+i_1)P_1} + G_1, ....$$}
\item \textbf{\tr{Question 2:}} what is the intuition?
\bi
\medskip
\item hint: ``Ricardian equivalence"
\medskip
\item hint: present value $P_1 T_1 + \frac{P_2 T_2}{1+i_1}$ in household budget constraint 
\ei
\medskip
\item \textbf{\tr{Question 3:}} what is wrong with this result?
\bi
\medskip
\item hint: recall empirical evidence on consumption from Lecture 4
\ei
\ei
\end{frame}


\begin{frame}{Adding high MPC households: TANK model}
\vspace{-4mm}
Simplest way: \tr{``spender-saver model"} of Campbell and Mankiw (1989)
\bi
\medskip
\item Fraction $\lambda$ of households are \tr{``spenders"} that consume their entire income, i.e. \tr{MPC=1}
\medskip
\item Remaining fraction $1-\lambda$ are \tr{``savers"} that behave as before, i.e. maximize $U(C_1^{sa}) + \beta U(C_2^{sa})$ subject to PV budget constraint
\medskip
\item Aggregate consumption is
$$C_t = \lambda C_t^{sp} + (1-\lambda)C_t^{sa} $$
\ei
Add this ``spender-saver" structure to our New Keynesian model
\bi
\medskip
\item see supplement ``Lecture 8: Hand-to-Mouth Households (TANK Model)"
\medskip
\item makes model more consistent with empirical evidence (high MPCs)
\ei
\bigskip
This type of model: ``TANK model" = Two Agent New Keynesian model
\bi
\medskip
\item a simplified version of the more complicated HANK models
\ei
\end{frame}




\begin{frame}{{\large Fiscal policy via transfers (``stimulus checks") in TANK model}}
\vspace{-3mm}
\bi
\item Presence of spenders $\lambda>0$ breaks Ricardian equivalence
\bigskip
\item Stimulus checks can now stabilize recession caused by demand shock
\bigskip
\item Result: transfer multiplier for transfers to spenders is ($\gamma^{sp}$ = income share)
$$\frac{\partial Y_1}{\partial (-T_1^{sp})} = \frac{\lambda}{1- \lambda \gamma^{sp}} > 0 $$
\item Result: when there are high-MPC households ($\lambda > 0$), stimulus checks can restore the flexible-price (first best) level of aggregate consumption $C_1$
\bi
\medskip
\item not just GDP (as in case $\lambda =0$)
\medskip
\item (though distribution $C_1^{sp}$ vs $C_1^{sa}$ differs from first-best)
\medskip
\item conjecture: combined with investment policies, can restore first-best aggregate allocation completely (see Wolf paper in a few slides)
\ei
\bigskip
\item Also interesting: government spending multiplier becomes $\frac{1}{1- \lambda \gamma^{sp}}>1$
\ei
\end{frame}





\begin{frame}
\renewcommand{\baselinestretch}{1}
\vspace{3cm}
\begin{center}
{\LARGE Pecking Order of Monetary and Fiscal Policy?}

\end{center}
\end{frame}


\begin{frame}{Pecking order of monetary and fiscal policy?}
\bi
\item When there is a recession, what type of stabilization policy should governments use?
\bigskip
\item New Keynesian model implies clear pecking order: monetary policy preferable, only use fiscal policy on rare occasions
\bi
\medskip
\item this is also the conclusion of Mankiw-Weinzierl
\ei
\bigskip
\item More recent work (TANK and HANK models): it's less clear
\ei
\end{frame}


\begin{frame}{{\large New Keynesian model: clear pecking order of monetary and fiscal policy}}
\bi
\item Monetary policy alone can restore first-best flexible-price allocation
\bi
\medskip
\item ``divine coincidence"
\ei
\bigskip
\item Only exception: if monetary policy is constrained by ZLB
\bigskip
\item Fiscal policy is either second-best ($G$) or ineffective ($T$)
\bigskip
\item Therefore
\bi
\medskip
\item monetary policy preferable
\medskip
\item only use fiscal policy on rare occasions (e.g. binding ZLB)
\ei
\ei
\end{frame}


\begin{frame}{More recent work: no clear pecking order}
\bi
\item When households have high MPCs and Ricardian equivalence breaks, there is no longer such a clear pecking order
\bigskip
\item Under some conditions, monetary and fiscal policy are exactly equivalent as far as aggregate demand management is concerned
\bi
\medskip
\item Anything government can do with monetary policy can also be done with fiscal policy and vice versa
\ei
\ei
\end{frame}



\begin{frame}{{\large Congratulations, you've just caught up to the research frontier}}
\begin{figure}[tph]
	\centering
\includegraphics[width=.5\textwidth]{figures/wolf}\includegraphics[width=.5\textwidth]{figures/wolf2} 
\end{figure}
{\scriptsize Source: \url{https://economics.mit.edu/sites/default/files/2022-09/mp_equiv.pdf}}
\end{frame}





\begin{frame}{Sticky prices: summary and policy implications }
\vspace{-3mm}
(Contrast with analogous slide for flexible prices from Lecture 7)
\bi
\medskip
\item Sticky prices break monetary neutrality and the classical dichotomy
\medskip
\item Corollary: monetary policy affects real variables
\medskip
\item 1st welfare theorem breaks: some policy intervention is desirable
\medskip
\item \tr{Stabilization policy?} When there is a recession due to shortfall in aggregate demand
\bi
\smallskip
\item stabilization via fiscal policy is both possible and desirable
\smallskip
\item stabilization via monetary policy is both possible and desirable unless ZLB binds
\smallskip
\item no clear pecking order, use both depending on circumstances
\ei
\medskip
\item \tr{Role of central bank?} control price level, stabilize recessions
\bi
\smallskip
\item see e.g. mandate of U.S. Fed (``dual mandate")
\ei
\ei
\end{frame}






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