Essays on Econometrics and Decision Theory
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CitationMontiel Olea, Jose Luis. 2013. Essays on Econometrics and Decision Theory. Doctoral dissertation, Harvard University.
AbstractThis dissertation presents three essays. The first essay, coauthored with Tomasz Strzalecki, is a classical exercise in axiomatic decision theory. We propose a simple and novel axiomatization of quasi-hyperbolic discounting, a tractable model of present bias preferences that has found many applications in economics. Our axiomatization imposes consistency restrictions directly on the intertemporal tradeoffs faced by the decision maker, without relying on auxiliary calibration devices such as lotteries. Such axiomatization is useful for experimental work since it renders the short-run and long-run discount factor elicitation independent of assumptions on the decision maker's utility function. The second essay, coauthored with Carolin Pflueger, belongs to the field of econometric theory. We develop a test for weak identification in the context of linear instrumental variables regression. The central feature of our test is its robustness to heteroskedasticity, autocorrelation, and clustering. We define identification to be weak when the Two-Stage Least Squares (TSLS) or the Limited Information Maximum Likelihood (LIML) Nagar bias is large relative to a benchmark. To test the null hypothesis of weak identification we propose a scaled non-robust first stage F statistic: the effective F. The test rejects for large values of the effective F. The critical values depend on an estimate of the covariance matrix of the OLS reduced form regression coefficients and on the covariance matrix of the reduced form errors. The third essay—the main chapter of this dissertation—belongs to the intersection of econometric theory and statistical decision theory. I present a new class of tests for hypothesis testing problems with a special feature: a boundary-sufficient statistic. The new tests minimize a weighted sum of the average rates of Type I and Type II error (average risk), while controlling the conditional rejection probability on the boundary of the null hypothesis; in this sense they are efficient conditionally similar on the boundary (ecs). The ecs tests emerge from an axiomatic approach: they essentially characterize admissibility—an important finite-sample optimality property—and similarity on the boundary in the class of all tests, provided the boundary-sufficient statistic is boundedly complete.
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