Essays on the econometrics of ordinal data
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In economics, ordinal variables like general health, mental health, and happiness level play a crucial role. Ordinal data is commonly used in surveys and questionnaires due to its ordered structure. However, incorporating an ordinal outcome variable in economic studies presents challenges. The categorical and fixed order nature of ordinal data sets it apart from continuous data. Additionally, most ordinal data exhibits unknown and inconsistent variations across categories. Consequently, specific methodologies are needed for econometric analysis when dealing with an ordinal variable. In Chapter 1, I develop a methodology for testing stochastic monotonicity when the outcome variable of interest is ordinal. I use a multiple testing procedure (MTP) technique to evaluate whether and where ordinal stochastic monotonicity exists, rather than using a single null hypothesis test. Additionally, I estimate the true set where ordinal stochastic monotonicity holds and construct "inner" and "outer" confidence sets by inverting the recommended MTP that controls the familywise error rate. With high asymptotic probability, an "inner" confidence set is contained inside the true set, whereas the "outer" confidence set contains the true set. Simulations illustrate that the MTP controls the familywise error rate well. Three empirical examples, including general health with educational level, depression with educational level, and inner peace with income class, illustrate the methodology. The famous Blinder-Oaxaca decomposition (BOD) takes an unconditional mean difference and decomposes it into a portion that is assigned to the levels of explanatory variables and a portion that is related to the magnitude of regression coefficients. However, the conventional BOD assumes Y has a cardinal meaning, not ordinal. To address this limitation and facilitate decomposition analysis of ordinal outcomes, in Chapter 2, I compare several alternative approaches. To illustrate these approaches, I use an empirical example to study how much of the disparity in general depression levels between rural and urban residents can be attributed to differences in educational attainment, income, age, and other observables. Each approach relies on different assumptions and offers different interpretations, allowing researchers to extract meaningful information from ordinal data. To better understand and distinguish these approaches, I conduct simulation studies that provide valuable insights into their practical implications and performance. These approaches are practically helpful for researchers employing decomposition with an ordinal outcome.
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Ph. D.