Estimating Vector Autoregressions with Panel Data

This paper considers estimation and testing of vector autoregression coefficients in panel
data, and applies the techniques to analyze the dynamic relationships between wages and
hours worked in two samples of American males. The model allows for nonstationary
individual effects. and is estimated by applying instrumental variables to the quasi-differenced
autoregressive equations. Particular attention is paid to specifying lag lengths.
forming convenient test statistics. and testing for the presence of measurement error. The
empirical results suggest the absence of lagged hours in the wage forecasting equation. Our
results also show that lagged hours is important in the hours equation, which is conhistent
with alternatives to the simple labor supply model that allow for costly hours adjustment or
preferences that are not time separable.
KEYWORDS: Vector autoregression. panel data. causality tests. labor supply.

1. INTRODUCTION
VECTORAUTOREGRESSIONS are now a standard part of the applied econometrician's
tool kit. Although their interpretation in terms of causal relationships is
controversial, most researchers would agree that vector autoregressions are a
parsimonious and useful means of summarizing time series "facts."
To date. vector autoregressive techniques have been used mostly to analyze
macroeconomic time series where there are dozens of observations. (See, e.g.,
Taylor (1980). or Ashenfelter and Card (1982).) In principle, these techniques
should apply equally well to disaggregate data. For example. a vector autoregression
can be used to summarize the dynamic relationship between an individual's
hours of work and wages (see below) or the dynamic relationship between a
government's revenues and expenditures (see Holtz-Eakin, Newey, Rosen (forthcoming)).
Unlike macroeconomic applications, however. the available time series
on micro units are typically quite short. Many of the popular panel data sets, for
example, have no more than ten or twelve years of observations for each unit.2
Also, it is possible that individual heterogeneity is an important feature of
disaggregate data. For these reasons, it is inappropriate to apply standard
techniques for estimating vector autoregressions to panel data.