This paper considers estimation and testing of vector autoregression coefficients in panel data, and uses the techniques to analyze the dynamic
properties of wages and hours among American males. The model allows for non-
stationary individual effects, and is estimated by applying instrumental
variables to the quasi—differenced autoregressive equations. Particular
attention is paid to specifying lag lengths and forming convenient test
statistics. The empirical results suggest that the wage equation contains at
most a single lag of hours and wages, and that one cannot reject the hypothesis that lagged hours may be excluded from the wage equation. Our results
also show that lagged hours is important in the hours equation, which is
consistent with alternatives to the simple labor supply model that allow for
costly hours adjustment or preferences that are not time separable.

This paper presents new evidence on the reasons for the recent decline in
the fraction of unemployed workers who receive unemployment insurance benefits.
Using samples of unemployed workers from the March Current Population Survey,
we estimate the fraction of unemployed workers who are potentially eligible for
benefits in each year and compare this to the fraction who actually receive
unemployment compensation. Perhaps surprisingly, we find that the decline in
the fraction of insured unemployment is due to a decline in the takeup rate for
benefits. Our estimates indicate that takeup rates declined abruptly between
l98O and 1982, leading to a 6 percentage point decline in the fraction of the
unemployed who receive benefits.
We go on to analyse the determinants of the takeup rate for unemployment
benefits, using both aggregated state-level data and micro-data from the Panel
Study of Income Dynamics. Changes in the regional distribution of unemployment
account for roughly one-half of the decline in average takeup rates. The
remainder of the change is largely unexplained.

Two approaches to estimation and testing of fixed effects models are
commonly found in the econometrics literature. The first involves variations on
instrumental variables. The second, a Minimum Chi-Square (MCS) procedure
introduced by Chamberlain, minimizes a quadratic form in the difference between
unrestricted regression coefficients and the restrictions implied by the fixed
effects model. This paper is concerned with the relationship between Three-Stage
Least Squares (3SLS) and MCS. A 3SLS equivalent of the MCS estimator is
presented and, in the usual case wherein the time varying error component has a
scalar covariance matrix, 3SLS is shown to simplify to the conventional
deviations from means estimator. Furthermore, the corresponding over-
identification test statistic is the degrees of freedom times the R2 from a
regression of residuals on all leads and lags of right hand side variables. The
relationship between MCS and some recently introduced efficient instrumental
variables procedures is also considered.
An empirical example from the literature on life-cycle labor supply is used
to illustrate properties of 3SLS procedures for panel data under alternative
assumptions regarding residual covariance. Estimated labor supply elasticities
and standard errors appear to be insensitive to these assumptions. In contrast,
the over-identification test statistics are found to be substantially smaller
when residuals are allowed to be intertemporally correlated and heteroscedastic.
At conventional levels of significance, however, even the smallest of the test
statistics leads to rejection of the over-identifying restrictions implicit in
the labor supply models.