Dynamic Equilibrium Models: an Introduction, Exams of History

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Formulating, Estimating, and Solving

Dynamic Equilibrium Models:

an Introduction

Jes´

us Fern´

andez-Villaverde

University of Pennsylvania

1

Models

•^

Tradition in macroeconomics of using models:1. Policy Analysis.2. Forecasting.3. Counterfactuals.

-^

This course reviews the recent advances in macroeconometric model-building.

2

A Brief History of Macroeconometric Models: A Promising Beginning

•^

Old idea of economists: Quesnay, Walras.

-^

Pioneers: Tinbergen (1939, Noble Prize 1969), Haavelmo (1943, No-ble Prize 1989).

-^

Klein-Goldberger model (1955).

-^

Big models of the 1960s: Brookings, MIT-FRB-Penn, Wharton.

4

A Brief History of Macroeconometric Models: Disappointment

•^

1970s and 1980s were the decades of disappointment

-^

Problems:1. Fit (Nelson, 1972).2. Nonstationarity (Granger, 1981).3. Economic Foundations (Lucas, 1972).

5

Why Dynamic Equilibrium Models?

•^

Explicit microeconomic foundation.

-^

Robust to Lucas critique.

-^

Welfare analysis.

-^

Design of optimal policy.

7

A Brief History of Macroeconometric Models: References

•^

R.G. Bodking, L.R. Klein, and K. Marwah:

A History of Macroecono-

metric Model-Building

, Edward Elgar, 1991.

•^

T.J. Sargent:

Expectations and the Nonneutrality of Lucas

, Journal

of Monetary Economics, 1996.

8

Is Money Important?

•^

At a basic level yes.

-^

“Lenin is said to have declared that the best way to destroy the Capi-talist System was to debauch its currency... Lenin was certainly right”.J.M. Keynes (1919),

The Economic Consequences of the Peace

•^

Experiences of hyperin

flation.

10

Money and the Business Cycle

•^

At a more moderate level, the question is surprisingly di

ffi

cult to an-

swer.

-^

Two “observations”:1. Relation between Output and Money growth.2. Phillips Curve.

-^

Where do these observations come?

11

Structural Vector Autoregression

•^

SVARs have become a common tool among economists.

-^

Introduced by Sims (1980)

-^

SVARs make explicit identifying assumptions to isolate estimates ofpolicy and/or private agents behavior and its e

ffects on the economy,

while keeping the model free of the many additional restrictive as-sumptions needed to give every parameter a behavioral interpretation.

13

Uses of SVARs1. The e

ffects of money on output (Sims and Zha, 2005).

2. The relative importance of supply and demand shocks on output (Blan-

chard and Quah, 1989),

3. The e

ffects of

fi

scal policy (Rotemberg and Woodford, 1992).

4. The relation between technology shocks and hours (Gal´

ı, 1999).

14

Mapping

•^

The mapping

D

) is the product of the equilibrium behavior of the

agents in the model, implied by their optimal decision rules and theconsistency conditions like resource constraints and market clearing.

-^

The construction of the mapping

D

) is the sense in which economic

theory tightly relates shocks and observables.

-^

The mapping

D

·) can be interpreted as the impulse response of the

model to an economic shock.

16

A Linear Mapping

•^

We restrict our attention to linear mappings of the form:

yt

D

(L

)^ w

t

where

L

is the lag operator.

•^

w

t^

N

,^ Σ

)^.

•^

More involved structures?

17

SVAR Representation

•^

We obtain:

A

(L

)^ y

t^

w

t

where

A

(L

A

0

∞ k=

A

Lk

k^

is a one-sided matrix lag polynomial

that embodies all the (usually non-linear) cross-equation restrictionsderived by the equilibrium solution of the model.

-^

In general,

A

(L

) is of in

finite order.

•^

This representation is known as the SVAR representation.

19

Reduced Form Representation

•^

Consider now the case where a researcher does not have access to theSVAR representation. Instead, she has access to the VAR representa-tion of

y

:t

yt

B

y 1 t−

1

B

y 2 t−

2

a

,t

where

Ey

t−

aj t^ = 0 for all

j

and

Ea

at 0 = t^

•^

This representation is known as the Reduced form representation.

-^

Can the researcher recover the SVAR representation using the Reducedform representation?

20