Chapter 1: More Efficient Estimation of Multiplicative Panel Data Models in the Presence of Serial Correlation (with Jeffrey Wooldridge)We provide a systematic approach in obtaining an estimator asymptotically more efficient than the popular fixed effects Poisson (FEP) estimator for panel data models with multiplicative heterogeneity in the conditional mean. In particular, we derive the optimal instrumental variables under appealing `working' second moment assumptions that allow underdispersion, overdispersion, and general patterns of serial correlation. Because parameters in the optimal instruments must be estimated, we argue for combining our new moment conditions with those that define the FEP estimator to obtain a generalized method of moments (GMM) estimator no less efficient than the FEP estimator and the estimator using the new instruments. A simulation study shows that the GMM estimator behaves well in terms of bias, and it often delivers nontrivial efficiency gains -- even when the working second-moment assumptions fail. Chapter 2: Information equivalence among transformations of semiparametric nonlinear panel data modelsI consider transformations of nonlinear semiparametric mean functions which yield moment conditions for estimation. Such transformations are said to be information equivalent if they yield the same asymptotic efficiency bound. I first derive a unified theory of algebraic equivalence for moment conditions created by a given linear transformation. The main equivalence result states that under standard regularity conditions, transformations which create conditional moment restrictions in a given empirical setting need only to have an equal rank to reach the same efficiency bound. Example applications are considered, including nonlinear models with multiplicative heterogeneity and linear models with arbitrary unobserved factor structures. Chapter 3: Moment-based Estimation of Linear Panel Data Models with Factor-augmented ErrorsI consider linear panel data models with unobserved factor structures when the number of time periods is small relative to the number of cross-sectional units. I examine two popular methods of estimation: the first eliminates the factors with a parameterized quasi-long-differencing (QLD) transformation. The other, referred to as common correlated effects (CCE), uses the cross-sectional averages of the independent and response variables to project out the space spanned by the factors. I show that the classical CCE assumptions imply unused moment conditions which can be exploited by the QLD transformation to derive new linear estimators which weaken identifying assumptions and have desirable theoretical properties. I prove asymptotic normality of the linear QLD estimators under a heterogeneous slope model which allows for a tradeoff between identifying conditions. These estimators do not require the number of cross-sectional variables to be less than T-1, a strong restriction in fixed-$T$ CCE analysis. Finally, I investigate the effects of per-student expenditure on standardized test performance using data from the state of Michigan.
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