Year of Graduation
Integrated Likelihood Estimation of Panel Data Models with Individual and Time Effects
Schumann, Severini, and Tripathi (2017) have developed integrated likelihood theory for panel data models with only ﬁxed eﬀects. In this thesis we consider panel data models with both ﬁxed and time eﬀects. This thesis is devoted to the development of intuition behind the application of integrated likelihood theory in presence of both ﬁxed and time eﬀects and to investigation of the asymptotic properties of the estimators derived from this approach. The results obtained by Schumann, Severini, and Tripathi (2017) are applicable to our model even when time heterogeneity is present. Speciﬁcally, in this work we have shown that the Maximum Integrated Likelihood estimator outperforms the Maximum Likelihood estimator in the asymptotic setting as well as in ﬁnite samples. It has two remarkable properties, namely, the asymptotical normality and the consistency. The latter suggests that the Maximum Integrated Likelihood methodology contributes to solving the Incidental Parameters Problem even in models when both individual and time eﬀects are present. Following theory and application to Neyman-Scott model, we will elaborate the results of a simulation study via Monte-Carlo replications to show the advantages of the MILE, as compared to the MLE, in small samples.