advmacro Takeki Sunakawa intro

lntroduction

Takeki Sunakawa

Advanced Macroeconomics at Tohoku University

What is this course for?

In this course, we will learn the modern macroeconomics. What is different from the old one?

Keynesian macroeconomics

In undergraduate courses, you may have learned so-called Keynesian macroeconomics (c.f., IS-LM-AS analysis, Phillips curve, etc.). The IS-LM-AS model is static.

Keynesian consumption function vs. intertemporal choice of consumption and saving (Irving Fisher).

Also, Keynesian macroeconomics is at odd with classical theories, for example the quantity theory of money and neutrality of money (c.f., Neoclassical synthesis).

Lucas critique

In 1970s, performances of Keynesian large-scale macroeconomic models used in policy institutions were deteriorated.

It is partly due to changes in expectations of agents (e.g., households and firms) in the economy and endogenous policy responses.

“... it is naive to try to predict the effects of a change in economic policy entirely on the basis of relationships observed in historical data, especially highly aggregated historical data.”

Since then, macroeconomists have been trying to build models with solid microfundations, i.e., optimizing behavior of agents.

RBC as a point of departure for modern macro

Real Business Cycle (RBC) theory is developed by Edward Prescott and his proponents.

RBC explains that changes in the total factor productivity (TFP) are driving forces of economic fluctuations.

They characterize economic fluctuations as “optimal responses to uncertainty in the rate of technological change,” and offers the policy advice that “costly efforts at stabilization are likely to be counterproductive.” (Prescott, 1996)

“They assert that monetary policies have no effect on real activity, [...,] and that economic fluctuations are caused entirely by supply rather than demand shocks.” (Summers, 1996)

New Keynesian macro

RBC suggests no role of monetary policy for stabilizing the economy. New Keynesians, like Blanchard, Mankiw, Woodford and Gali, correspond to the Lucas critique in 1990s and 2000s.

The theory they have developed is based on RBC. However, they assume market imperfection (e.g., monopolistic competition) and price stickiness in the short run.

C.f., the short-run and long-run in IS-LM-AS analysis.

New Keynesian DSGE models are now widely used in central banks and other institutions for forecasting and policy simulations.

What is DSGE?

The modern macroeconomics = DSGE

DSGE = Dynamic Stochastic General Equilibrium

Dynamic: Intertemporal behavior of agents, e.g., Euler equation, capital accumulation, etc.

Stochastic: Exogenous shocks drive short-run economic fluctuations. Agents’ expectations are usually rational.

General Equilibrium: All markets clear simultaneously as a result of agents’ optimizations.

Both RBC and NK models are variants of DSGE model.

DSGE models in central banks

DSGE models are now widely used in central banks and other institutions for forecasting and policy simulations.

The Board of Governors:

EDO http://www.federalreserve.gov/econresdata/edo/edo-models-about.htm FRB/US

http://www.federalreserve.gov/econresdata/frbus/us-models-about.htm FRBNY: http://libertystreeteconomics.newyorkfed.org/2014/09/forecasting- with-the-frbny-dsge-model.html#.VaZ4ZpPtmko

FRB-Chicago and Philladelphia:

https://www.philadelphiafed.org/research-and-data/real-time-center/PRISM/ ECB: New-Area Wide Model

IMF: Global Economic Model BOJ: Japanese Economic Model etc...

Three examples

Asset price equation

Cagan’s (1958) model of hyperinflation

A canonical New Keynesian model

Asset price equation

The process of asset prices follows:

pt_{= d}t_{+ βp}t+1,

for t = 0, 1, ..., where pt is the asset price and dtis dividend which is exogenously given.

How to “solve” for the price?

Solving for the price

Substitute the next period’s equation...

pt = dt+ βpt+1, pt+1 = dt+1+ βpt+2, pt+2 = dt+2+ βpt+3,

...

Solving for the price, cont’d

Substitute the next period’s equation...

pt = dt+ β (dt+1+ βpt+2) , pt ₌ dt_{+ βd}t+1+ β²pt+2,

pt = dt+ βdt+1+ β²(dt+2+ βpt+3) , ...

Solving for the price, cont’d

Substitute the next period’s equation...

pt= dt+ βdt+1+ β²dt+2+ · · · β^sdt+s+ β^s+1pt+s+1, pt₌

Xs i=0

βⁱdt+i+ β^s+1pt+s+1.

Finally, let s → ∞:

p^t= lim

s→∞

Xs i=0

βⁱdt+i. [We exclude the bubble solution.]

Stochastic case

Assume dtis i.i.d. with zero mean and variance σ². The process is given by: pt= dt+ βEtpt+1,

where E^tis called expectational operator. We have a solution

pt_{= lim} s→∞

Xs i=0

βⁱEtdt+i = d^t. What are implications of the solution?

Cagan’s model of hyperinflation

Cagan’s (1958) model:

mt− pt= γ − αEtπt+1,

∆m^t= µ + ε^t, where α > 0 and γ are parameters, and

mt is logged quantity of money, ptis logged price level,

πt= pt_{− p}t is the inflation rate, and

εt is a shock to money growth with its mean µ.

[The first equation comes form the money demand function.]

Adaptive vs. rational expectations

Adaptive expectation: Agents in the model form expectations based on observations in the past.

Rational expectation: Agents in the model form expectations based on all the information available for the modeler.

Adaptive expectation

Assuming adaptive expectation Etπt+1= πt, we have mt− pt= γ − απt,

⇔ mt_{− m}t−1− (p^t− pt−1) = −α(π^t− πt−1),

⇔ µ+ ε^t− π^t= −α(π^t− πt−1),

⇔ (1 − α)πt= −απt−1+ µ + εt,

∴ _πt₌

−α

1 − α^πt−1+ 1

1 − α^{(µ + εt).} When α > .5, the model’s solution is unstable.

Steady state

Assume ε^t= 0 and π^t= πt−1= π, which is called the steady state. Then we have

π= ^−α 1 − α^π+

1 1 − α^µ,

⇔ (1 − α)π = −απ + µ,

∴ _{π= µ.}

The steady state condition holds only in the long run.

Rational expectation

What is a solution with rational expectation?

Conjecture π^t= a0+ a1ε^t. [This is called undetermined coefficient method.] Then we have

mt_{− p}t_{= γ − αE}tπt+1,

⇔ µ + εt− πt= −α(Etπt+1− Et−1πt),

∴ _{µ+ ε}t_{− a}0− a1εt_{= 0,}

Then a0= µ and a1= 1 hold.

E^tπt+1= µ holds even in short-run fluctuations.

Cagan’s model

0.015 0.02 0.025 0.03 0.035 0.04

Adaptive Rational

Canonical New Keynesian Model

A canonical New Keynesian model consists of three equations: Consumption Euler equation

ct= Etct+1_{− σ}⁻¹(rt_{− E}tπt+1). New Keynesian Phillips curve

πt= Etπt+1+ κct+ ut. Taylor rule

rt= φEtπt+1.

where ct is consumption, πt is the inflation rate, rt is the nominal interest rate. ut is the markup shock. Et is called the expectation operator. σ, κ and φare the parameters.

We need to “solve” the model, i.e., obtain the decision rules of x = g (u )

Canonical New Keynesian Model

2 4 6 8 10

-0.02 -0.015 -0.01 -0.005

0 ^c

2 4 6 8 10

0 0.5 1 1.5

2 ^pai

0.2 0.4 0.6 0.8

1 ^r

0.5 1

1.5 ^u

Notes

There are different ways to solve the model.

The equations presented are log-linearized: There is the original non-linear model with microfoundations.

Why do we need microfoundations? The Lucas critique.