Essays on theoretical and applied econometrics
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Instead of having a "yes" or "no" result from a test of the global null hypothesis that a function is increasing, I propose a multiple testing procedure to test at multiple points in Chapter 1. If the global null is rejected, then this multiple testing provides more information about why. If the global null is not rejected, then multiple testing can provide stronger evidence in favor of increasingness, by rejecting the null hypotheses that the function is decreasing. With high-level assumptions that apply to a wide array of models, this approach can be used to test for monotonicity of a function in a broad class of structural and descriptive econometric models. By inverting the proposed multiple testing procedure that controls the familywise error rate, I also equivalently generate "inner" and "outer" confidence sets for the set of points at which the function is increasing. With high asymptotic probability, the inner confidence set is contained within the true set, whereas the outer confidence set contains the true set. I also improve power with stepdown and two-stage procedures. Simulated and empirical examples (income-education conditional mean, and IV Engel curve) illustrate the methodology. Using the same confidence set idea as in Chapter 1, I set up two methods to provide evidence that one latent distribution is "better" than another when only ordinal data are available in Chapter 2. One is to figure out a set of quantile values for which the first latent distribution's quantiles are above the second. Another is to find out a range of latent values on which there is restricted stochastic dominance of the first latent distribution over the second. Specifically, these two methods are proposed to construct "inner" confidence sets for the corresponding quantiles and latent values. With high probability, the inner confidence set from the first method is contained within the true set of quantile values for which the first latent distribution's quantiles are above the second. With high probability, the inner confidence set from the second method is contained within the true set of latent values at which the first distribution dominates the second. These methods are applied to assess how life satisfaction is associated with marital status. Chapter 3 studies the translation from the changes in the outcome/consumption distribution to the changes in the utility distribution under certain assumptions. Much empirical research and econometric methods learn from data about differences in consumption, but essentially people care more about welfare/utility changes. I compare two extreme cases where the results are the contrary. One is the simplest setting (utility homogeneity), the consumption and utility move in the same direction; Specifically, the expected utility becomes higher if the consumption distribution becomes better (in the first order stochastic dominance sense). In contrast, under random utility function and arbitrary dependence assumption, I find a job allocating example that shows subpopulations' expected utility increases even if the new consumption distribution is stochastically dominated, i.e., the consumption and utility move in an opposite direction. I also consider other three different assumption settings: utility function and consumption are independent, they have arbitrary dependence but with rank invariance, they have fixed dependence without rank invariance. The results of all these three cases are same, i.e., first order stochastic dominance in consumption implies higher expected utility.
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Ph. D.