Essays on inference for incomplete economic models and its application
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This dissertation consists of three essays studying inference for incomplete economic models and its applications. In Chapter 1, I develop an asymptotic theory for strategic network formation models of complete information. Due to the presence of network externalities, the model predicts multiple pairwise stable equilibira. I provide an asymptotic theory that can be used to conduct robust inference when a single large network is observed but the researcher does not have a theory for the equilibirum selection mechanism. Using observable characteristics, my approach partitions the individuals into a number of groups (or clusters) and applies a central limit theorem for belief functions to a statistic averaged over the clusters. My asymptotic theory is robust to incompleteness in the sense that it does not require any additional assumption on the form of heterogeneity or dependence of the selection mechanism across clusters. Monte Carlo experiments are conducted to examine the performance of the method. Chapter 2 investigates the network structure of venture capital funds based on co-investments. The main empirical question is how do local externalities that are generated by network strucutres affect the likelihood that two venture capital funds co-invest in a start-up company. I use investment data from the VentureXpert database to generate a syndicated investment network of venture capital funds. The network structure is considered endogenously determined due to the (local) externalities from direct connections with other partners given a start-up company. The endogeneity is induced because the local externalities are correlated with other unobserved determinants of the link formation decision. The instrumental variable is proposed to solve this endogeneity. The key step in my approach is the construction of funds' consideration sets. The empirical results provide weak evidence on positive effects from the local externalities on the probability of co-investment. In Chapter 3 is joint with Hiroaki Kaido. We develop a framework for testing hypotheses on parameters in incomplete economic models. Examples include tests on the presence of strategic interactions in discrete games of complete information. Incomplete economic models make set-valued predictions and hence do not generate a unique likelihood. This prohibits the use of standard likelihood-ratio (LR) tests even for testing a simple null hypothesis against a simple alternative. We show that the model structure, however, implies the existence of a pair of distributions; one is consistent with the null hypothesis and is least favorable to the size control, and the other is consistent with the alternative hypothesis and is least favorable to power maximization. The ratio of this pair is shown to form a robust likelihood-ratio test that is optimal in the minimax sense. We also provide a large sample Gaussian approximation to the upper probability of this statistic, which renders the test computationally tractable. Finally, we consider testing hypotheses in the presence of nuisance parameters and propose a procedure that minimizes a certain risk function.