Two Monte Carlo studies on the estimation of panel data econometrics

This dissertation studies the estimation problem of panel data via Monte Carlo experiments. The chapter of the AR(1) processes with an arbitrary assumption on the initial observations highlights one advantage of using panel data. It is important to allow an arbitrary variance on the initial observations because the assumption of stationarity is invalid for many economic time series. A panel data framework is an ideal setting for this analysis because there exist N initial observations which enable us to estimate a new parameter. The mle's are derived under both the stationarity and arbitrary variance assumptions (GPW) following Anderson and Hsiao (1982). OLS, iterative Cochrane-Orcutt (1949) (ICO), Beach and MacKinnon (1978) (BM), GPW and pretest (PRE) estimators are compared. OLS performs poorly for all positive {dollar}rho{dollar} values due to the presence of both serial correlation and heteroskedasticity. ICO compares well with GPW in the estimation of {dollar}rho{dollar}, while it performs poorly in the estimation of {dollar}beta{dollar} relative to the other estimators. The performance of BM deteriorates as the process departs from the stationary case. In contrast, GPW and PRE perform well relative to true GLS.; In the chapter on the comparison of estimation methods for an unbalanced one way regression model, four ANOVA, ML, REML and MINQUE (MQI, MQA) estimators are compared. Four ANOVA type, ML type and MQA estimators perform well relative to true GLS in the estimation of {dollar}beta{dollar}. MQI performs poorly when {dollar}gamma{dollar} is large and the pattern is severely unbalanced. The performance of OLS deteriorates as {dollar}gamma{dollar} increases while WITHIN performs poorly only when {dollar}gamma{dollar} is small. In the estimation of variance components, ANOVA type and MQI perform poorly relative to ML, REML and MQA. However, only the poor performance of MQI for large {dollar}rho{dollar} and severely unbalanced patterns seems to be translated into the poor performance in the {dollar}beta{dollar} estimation.; Unless the pattern is severely unbalanced and {dollar}gamma{dollar} is large, the simple ANOVA type estimators can be used. For the other cases, ML, REML and MQA are recommended. Using subbalanced data rather than using the whole unbalanced data is shown to be costly.