Essays in econometrics
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The first chapter of this dissertation considers a semiparametric version of the network formation model of Graham (2017). The two-way fixed-effects binary choice model allows for homophily and degree heterogeneity, but unlike Graham (2017) leaves the distribution of pair-specific unobservables unspecified. Identification of the slope parameters and fixed effects follows from a novel approach that does not rely on distributional assumptions. The identification strategy suggests an estimator for the slope parameters based upon tetrads of nodes within the network. A computationally simple version of this estimator is shown to be consistent with a non-parametric convergence rate. A consistent estimator of the fixed effects is also provided. The second chapter discusses the non-parametric extension of the network formation model, when the researcher does not assume the functional form of the distance function. An intuitive way for the non-parametric extension is to use the parametric estimator for linear indices coupled with a series expansion. While the technique is generally applicable, it comes with the caveat that the identification of the models must be assured a priori. After demonstrating the applicability of the method on classical models of Manski (1987) and Han (1987), we prove the nonparametric identification of the distance function for the network formation model, and define the corresponding series estimator. We give a proof for consistency, and also analyze the rate of convergence. The third chapter examines the empirical content of the assumption that in a complete information game agents play pure strategy Nash-equilibrium. In particular, we focus on the identification of the strategic interaction effects as defined in Tamer (2003). We find that the Nash-equilibrium assumption restricts the joint density of the unobservables in a way that allows us to connect the underlying identification problem to photo stitching, a well-known question in computer science. In the view of this intuition, some of the earlier results in the literature are reinterpreted, and the main proposition shows how the framework can be used to find sufficient assumptions for identification without specifying the distribution of unobservables.