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Essays on Nonparametric and High-Dimensional Econometrics

  • Author(s): Soerensen, Jesper Riis-Vestergaard
  • Advisor(s): Chetverikov, Denis N
  • Hahn, Jinyong
  • et al.
Abstract

This dissertation studies questions related to identification, estimation, and specification testing of nonparametric and high-dimensional econometric models. The thesis is composed by two chapters.

In Chapter 1, I propose specification tests for two formally distinct but related classes of econometric models: (1) semiparametric conditional moment restriction models dependent on conditional expectation functions, and (2) a class of high-dimensional unconditional moment restriction models dependent on high-dimensional best linear predictors. These classes may be motivated by economic models in which agents make choices under uncertainty and therefore have to predict payoff-relevant variables such as the behavior of other agents. The proposed tests are shown to be both asymptotically correctly sized and consistent. Moreover, I establish a bound on the rate of local alternatives for which the test for high-dimensional unconditional moment restriction models is consistent. These results allow researchers to test the specification of their models without introducing additional parametric, typically ad hoc, assumptions on expectations.

In Chapter 2, I show that it is possible to identify and estimate a generalized panel regression model (GPRM) without imposing any parametric structure on (1) the function of observable explanatory variables, (2) the systematic function through which the function of observable explanatory variables, fixed effect, and disturbance term generate the outcome variable, or (3) the distribution of unobservables. I proceed with estimation using a series maximum rank correlation estimator (SMRCE) of the function of observable explanatory variables and provide conditions under which L2–consistency is achieved. I also provide conditions under which both L2 and uniform convergence rates of the SMRCE may be derived.

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