Integrating Quarterly Data into a Dynamic Factor Model of US Monthly GDP

• Author: Firmin Vlavonou,Stephen Gordon
• Published date: 01 July 2017
• Date: 01 July 2017
• DOI: http://doi.org/10.1002/for.2432

Journal of Forecasting,J. Forecast. 36, 325–336 (2017)

Published online 19 August 2016 in Wiley Online Library (wileyonlinelibrary.com)DOI: 10.1002/for.2432

Integrating Quarterly Data into a Dynamic Factor Model of US

Monthly GDP

FIRMIN VLAVONOUAND STEPHEN GORDON

ABSTRACT

This paper develops and estimates a dynamic factor model in which estimates for unobserved monthly US Gross

Domestic Product (GDP) are consistent with observed quarterly data. In contrast to existing approaches, the quarterly

averages of our monthly estimates are exactly equal to the Bureau of Economic Analysis (BEA) quarterly estimates.

The relationship between our monthly estimates and the quarterly data is therefore the same as the relationship between

quarterly and annual data.

The study makes use of Bayesian Markov chain Monte Carlo and data augmentation techniques to simulate values for

the logarithms on monthly US GDP. The imposition of the exact linear quarterly constraint produces a non-standard

distribution, necessitating the implementation of a Metropolis simulation step in the estimation.

Our methodology can be easily generalized to cases where the variable of interest is monthly GDP and in such a way

that the final results incorporate the statistical uncertainty associated with the monthly GDP estimates. We provide an

example by incorporating our monthly estimates into a Markov switching model of the US business cycle. Copyright

© 2016 John Wiley & Sons, Ltd..

KEY WORDS Unobserved monthly GDP; Interpolated data; Dynamic factor model; MCMC and Data

augmentation; Markov switching and Metropolis

INTRODUCTION

Empirical business cycle analysis is often a matter of a tradeoff between data that are timely and data that are com-

prehensive. The information incorporated into gross domestic product (GDP) offers the broadest coverage for the US

business cycle, but is only available at quarterly frequency. Monthly data are more timely, but they capture only cer-

tain facets of the cycle. Since timeliness is of enormous importance to policymakers, there are significant potential

gains from developing estimates for GDP at higher frequencies.

There are several ways that analysts can synthesize disparate monthly data into a composite business cycle index.

Principal components analysis is one, but dynamic models in which the state of the economy is modeled as an

unobserved process is a more popular choice. These approaches are generally successful in producing estimates

whose properties are consistent with our understanding of business cycle chronologies, but they are not necessarily

easy to interpret. In particular, it is difficult to make the link between these monthly coincident indicators and those

at other frequencies.

While it is possible to construct monthly and quarterly coincident indices that are consistent across frequencies, it

would be difficult to motivate this sort of exercise. We already have a widely used and widely understood quarterly

coincident indicator in the form of estimates for GDP.Instead of constructing another quarterly index to go along with

existing monthly measures, it is probably of greater interest to produce estimates for monthly GDP that are consistent

with the available quarterly estimates.

This goal is the subject of an active research agenda. Since the classic work of Burns and Mitchell (1946) describ-

ing the features of the business cycle and Lucas’s (1976) summary of its stylized facts, there have been an increasing

number of studies focused on producing estimates for monthly GDP.Initial approaches due to Friedman (1962), Chow

and Lin (1971), Roque (1981) and Robert (1983) were based on linear interpolation and other forms of intra-period

distributions. Later, Moauro and Savio (2005), Tommaso (2006) and Mitchell et al. (2011) used more sophisti-

cated methods and addressed the problem using a slightly more complex approach, but their monthly estimates were

not consistent with quarterly and annual data. Liu and Hall (2001) construct estimates for monthly GDP using a

state space model in which quarterly GDP is equal to a weighted average of monthly GDP series, and offer strate-

gies for estimating these weights. Huang (2006) evaluates alternative interpolation models for estimating Taiwan’s

monthly GDP.

Mariano and Murasawa (2003) improves upon Stock and Watson’s (1989) coincident index (which does not incor-

porate quarterly data) by adding quarterly GDP to the model. Their approach imposes the restriction that observed

quarterly GDP is equal to the geometric mean of estimates for monthly GDP. Similarly, Angelini et al. (2008) esti-

mate and forecast euro area monthly national accounts in estimating monthly GDP using assumptions similar to

Correspondence to: Firmin Vlavonou, Département d’économique and CIRPEE, Université Laval, Quebec City, Canada. E-mail:

firmin.vlavonou.1@ulaval.ca

[Correction added on September 09, 2016 after the first online publication: the ‘Reference’ section has been revised.]

Copyright © 2016 John Wiley & Sons, Ltd.