First-difference estimator

Abstract: We consider the estimation of Cobb-Douglas production functions using panel data covering a large sample of companies observed for a small number of time periods. Standard GMM estimators, which eliminate unobserved firm-specific eects by taking first differences, have been found to produce unsatisfactory results in this context (Mairesse and Hall, 1996). We attribute this to weak instruments: the series on rm sales, capital and employment are highly persistent, so that lagged levels are only weakly correlated with subsequent first differences. As shown in Blundell and Bond (1998), this can result in large finite-sample biases when using the standard first-differenced GMM estimator. Blundell and Bond (1998) also show that these biases can be dramatically reduced by exploiting reasonable stationarity restrictions on the initial conditions process. This yields an extended GMM estimator in which lagged first-differences of the series are also used as instruments for the levels equations (cf. Arellano and Bover, 1995). Using data for a panel of RD this estimator yields much more reasonable parameter estimates. We also stress the importance of allowing for an autoregressive component in the productivity shocks.

Abstract: When estimating finance panel regressions, it is common practice to adjust standard errors for correlation either across firms or across time. These procedures are valid only if the residuals are correlated either across time or across firms, but not across both. This note shows that it is very easy to calculate standard errors that are robust to simultaneous correlation across both firms and time. The covariance estimator is equal to the estimator that clusters by firm, plus the the estimator that clusters by time, minus the usual heteroskedasticity-robust OLS covariance matrix. Any statistical package with a clustering command can be used to easily calculate these standard errors.

Abstract: Homoskedasticity is an important assumption in ordinary least squares (OLS) regression. Although the estimator of the regression parameters in OLS regression is unbiased when the homoskedasticity assumption is violated, the estimator of the covariance matrix of the parameter estimates can be biased and inconsistent under heteroskedasticity, which can produce significance tests and confidence intervals that can be liberal or conservative. After a brief description of heteroskedasticity and its effects on inference in OLS regression, we discuss a family of heteroskedasticity-consistent standard error estimators for OLS regression and argue investigators should routinely use one of these estimators when conducting hypothesis tests using OLS regression. To facilitate the adoption of this recommendation, we provide easy-to-use SPSS and SAS macros to implement the procedures discussed here.

Abstract: This chapter reviews developments to improve on the poor performance of the standard GMM estimator for highly autoregressive panel series. It considers the use of the ‘system’ GMM estimator that relies on relatively mild restrictions on the initial condition process. This system GMM estimator encompasses the GMM estimator based on the non-linear moment conditions available in the dynamic error components model and has substantial asymptotic efficiency gains. Simulations, that include weakly exogenous covariates, find large finite sample biases and very low precision for the standard first differenced estimator. The use of the system GMM estimator not only greatly improves the precision but also greatly reduces the finite sample bias. An application to panel production function data for the U.S. is provided and confirms these theoretical and experimental findings.