Information content of DSGE forecasts

• Date: 01 September 2019
• Author: Ray C. Fair
• DOI: http://doi.org/10.1002/for.2581
• Published date: 01 September 2019

Received: 8 January 2019 Accepted: 12 February 2019

DOI: 10.1002/for.2581

RESEARCH ARTICLE

Information content of DSGE forecasts

Ray C. Fair

Cowles Foundation, Department of

Economics, Yale University,New Haven,

Connecticut

Correspondence

Ray C. Fair,Cowles Foundation,

Department of Economics, Yale

University, NewHaven, CT 06520-8281.

Email: ray.fair@yale.edu

Abstract

This paper examines the question whether information is contained in forecasts

from dynamic stochastic general equilibrium (DSGE) models beyond that con-

tained in lagged values, which are extensively used in the models. Four sets of

forecasts are examined. The results are encouraging for DSGE forecasts of real

GDP.The results suggest that there is information in the DSGE forecasts not con-

tained in forecasts based only on lagged values, and that there is no information

in the lagged-value forecasts not contained in the DSGE forecasts. The opposite

is true for forecasts of the GDP deflator.

KEYWORDS

DSGE forecasts, information content, lagged values

1INTRODUCTION

This paper examines the question whether information

is contained in forecasts from dynamic stochastic general

equilibrium (DSGE) models beyond that contained in

lagged values. Lagged variables enter DSGE models

through assumptions like habit formation, adjustment

costs, variable capacity utilization, pricing behavior, and

interest rate rules. Theoretical restrictions are imposed on

these variables, and the question is whether predictive

information is added by the restrictions?

Consider an s-period-ahead forecast of real gross domes-

tic product (GDP). Let Ya

tdenote the s-period-ahead fore-

cast of log-GDP for period tfrom model a, and let Yb

tdenote

the same from model b. The forecasts are assumed to be

made at the end of period t−s. The comparison method

used in this paper is discussed in Fair and Shiller (1990).

For the s-period-ahead forecasts for periods 1 to T,the

following regression is run:

Yt−Yt−s=𝛼+𝛽(Ya

t−Yt−s)

+𝛾(Yb

t−Yt−s)+ut,t=1,…,T.(1)

If neither model contains information useful for

s-period-ahead forecasting of Yt, then the estimates of 𝛽

and 𝛾should both be zero. In this case the estimate of the

constant term 𝛼would be the average s-period change

in Y. If both models contain independent information

for s-period-ahead forecasting, then 𝛽and 𝛾should both

be nonzero. If both models contain information, but the

information in, say, model bis completely contained in

model aand model acontains further relevant informa-

tion as well, then 𝛽but not 𝛼should be nonzero. (If both

models contain the same information, then the forecasts

are perfectly correlated, and 𝛽and 𝛼are not separately

identified.) It may be that both coefficient estimates are

significant, but one is negative. This means that the infor-

mation contained in the forecast of the model with the

negative coefficient estimate contributes negatively to

the overall forecast conditional on the information in the

other model's forecast.

One model's forecasts may have a higher root mean

squared error (RMSE) than another's, but still contain

useful independent information. Estimating Equation 1

allows one to test for this, which the simple comparison of

RMSEs cannot.

Further discussion of this method is in Fair and Shiller

(1990). The error term utis likely to be heteroskedastic

and be an s−1 moving average process. This can be

corrected for when estimating the standard errors of the

coefficient estimates. The procedure discussed in Hansen

(1982), Cumby, Huizinga, and Obstfeld (1983), and White

Journal of Forecasting. 2019;38:519–524. wileyonlinelibrary.com/journal/for © 2019 John Wiley & Sons, Ltd. 519