Three essays on the estimation and testing of an error component model

Abstract

This dissertation studies the problem of estimation and testing of an error component model (ECM). The error component model is the most popular specification in panel data econometrics. With panel data, we can answer more complex questions than would be possible by using time-series data or cross-sectional data alone. However, panel data also introduce difficulties. For the one-way error component model, if the error term is serially correlated, then the estimation methods were quite complicated. This dissertation proposes a simple transformation that circumvents the problem of serial correlation in an error component model. This not only simplifies the calculation, but also gives natural estimators of the variance components. Moreover, we generalize Breusch's (1987) maximum likelihood estimation method to the serial correlation case. Which can be used to guard against possible local maxima. We also derive the best linear unbiased predictor (BLUP) for the error component model with an arbitrary serially correlated remainder term. We show that once one knows the BLUP for the time series model with serially correlated errors, using our method, one can immediately write out the corresponding BLUP for error component model with the same type of serial correlation in the remainder term. Thus our approach makes the panel data literature parallel to that of time series literature and therefore should prove very useful in applications. The chapter of testing serial correlation gives several Lagrange Multiplier (LM) tests for testing first-order serial correlation. Our Monte Carlo results show that these tests perform well in detecting serial correlation in an error component model. We also show that the LM test cannot distinguish a first order autocorrelation (AR(1)) process from a first order moving average (MA(1)) process. Thus we further derive several tests for testing AR(1) against MA(1) in an error component model. Another problem with the error component model is that the commonly used test statistic for testing zero variance component is the two-sided Breusch-Pagan test. However, since the variance component never takes negative values, the proper test statistic should be one-sided. Although Honda (1985) and King and Wu (1990) derived some one-sided test statistics for the error component model. We show that these tests have some drawbacks, we further derive some new tests which are immune to these drawbacks. Our Monte Carlo results show that these new tests perform better than the existing tests.