Three Essays in Applied Microeconometrics

Chapter 1 develops a specification test for a single index binary outcome model in semi-parametric estimation. The semiparametric estimator examined does not rely on any distributional assumption, but it still relies on the single-index assumption. The violation of this assumption creates a source of heteroscedasticity. I extend a set of attractive LM statistics, constructed using auxiliary regressions for the case of logit and probit models, to the semiparametric environment. I derive its asymptotic distribution and show that is has well-behaved finite properties in a Monte Carlo experiment. An empirical example is also provided. Chapter 2 proposes a novel estimation strategy that accounts for asynchronous fieldwork, often found in multi-country surveys. The resulting biases are substantial and this is likely to provide misleading cross-country comparisons. I highlight the importance of accounting for the heterogeneity induced by seasonality in the context of regression modelling in order to obtain unbiased comparisons. This is illustrated with a comparison between a synchronous national survey and an asynchronous cross-national one. Chapter 3, joint work with Thomas Crossley and Peter Levell, proposes a novel estimator useful for data combination. Researchers are often interested in the relationship between two variables, with no available data set containing both. For example, surveys on income and wealth are often missing consumption data. A common strategy is to use proxies for the dependent variable that are common to both surveys to impute the dependent variable into the data set containing the independent variable. We consider the consequences of estimating a regression with an imputed dependent variable, and how those consequences depend on the imputation procedure adopted. We show that an often used procedure is biased, and offer both a correction and refinements that improve precision. We illustrate these with a Monte Carlo study and an empirical application.