Essays in econometrics
Keywords: Economics.

This dissertation consists of three chapters. Chapter 1 considers specification testing in semiparametric econometric models. It develops a consistent series-based specification test for semiparametric conditional mean models against nonparametric alternatives. Consistency is achieved by turning a conditional moment restriction into a growing number of unconditional moment restrictions using series methods. The test resembles the Lagrange Multiplier (LM) test for parametric models and is simple to implement, because it requires estimating only the restricted semiparametric model and because the asymptotic distribution of the test statistic is pivotal. The use of series methods in estimation of the null semiparamertic model allows me to account for the estimation variance and obtain refined asymptotic results. The test remains valid even if other semiparametric methods are used to estimate the null model as long as they achieve suitable convergence rates. This includes popular kernel estimators for single index or partially linear models. The test demonstrates good size and power properties in simulations. To illustrate the use of my test, I apply it to one of the semiparametric gasoline demand specifications from Yatchew and No (2001) and find no evidence against it. Chapter 2 studies model selection in semiparametric econometric models. It develops a consistent series-based model selection procedure based on a Bayesian Information Criterion (BIC) type criterion to select between several classes of models. The procedure selects the model by minimizing the semiparametric LM type test statistic from Chapter 1 but additionally rewards simpler models. The chapter also develops consistent upward testing (UT) and downward testing (DT) procedures based on the semiparametric LM type specification test. The proposed semiparametric LM-BIC and UT procedures demonstrate good performance in simulations. To illustrate the use of these semiparametric model selection procedures, I apply them to the parametric and semiparametric gasoline demand specifications from Yatchew and No (2001). The LM-BIC procedure selects the semiparametric specification which is nonparametric in age but parametric in all other variables, which is in line with the conclusions in Yatchew and No (2001), while the UT and DT procedures select the fully parametric model which is rejected by the semiparametric specification test. Chapter 3, joint with Frank Wolak, studies what can be learned about the average treatment effect (ATE) when it is only possible to estimate the local average treatment effect (LATE). Researchers in the area of policy evaluation are usually interested in estimating the "causal" effect of a policy. The relevant parameter of interest then is the population ATE, which shows how an average person would respond to treatment. However, in many economic experiments, it is impossible to identify or estimate the ATE, because participants can be offered treatment but cannot be forced to accept it. In such cases, the researcher can only estimate the intent to treat effect or the LATE. Using data from Kahn and Wolak (2013) and the method for drawing inferences about treatment effects based on instrumental variables (IV) estimators from Mogstad et al. (2017), we show that the LATE is relatively uninformative about the ATE unless the researcher is willing to impose strong assumptions on the marginal treatment effect function. However, the LATE can yield informative bounds if the researcher is interested in estimating certain policy-relevant treatment effects (PRTE) instead of the ATE.