UC Riverside

Most research on nonparametric econometrics focuses on mean, median, or quantile regression while there is not too much research about regression methods on the basis of mode value. This dissertation proposes three new models based on modal regression, in which the dependence of the conditional mode of the response variable on the covariates is explored and a kernel based objective function to simplify the computation is employed. In particular, this dissertation is made up of three essays. Chapter 1 provides an overview of the dissertation. Chapter 2 proposes a control function approach to account for endogeneity in a parametric linear triangular simultaneous equations model for modal regression, where the conditional mode of the unobservable error term on explanatory variables is nonzero. To motivate the developed control function method, a dynamic model of rational behavior under uncertainty is introduced, in which the agent maximizes the present discounted value of the stream of future modal utilities, and a modal Euler equation derived from the maximization model that the agent must satisfy in equilibrium is presented. In a general setting that includes nonlinear time series models as a special case, Chapter 3 develops a novel local linear estimator of volatility function for nonparametric modal regression applied to the squared residuals from the unknown mean regression, which is particularly useful to serve as a risk indicator for skewed data or financial time series with heavy tails. To reduce the variance of the nonparametric modal volatility estimator, a variance reduction technique is introduced to achieve asymptotic relative efficiency while keeping the asymptotic bias unchanged. Furthermore, to avoid the negative values of volatility, Chapter 3 introduces a local exponential modal estimation. Chapter 4 investigates the estimation and inference of modal regression near the boundary, establishing a theoretical foundation for regression discontinuity designs based on mode value. Under the assumption of mode rank invariance, a novel conditional mode treatment effect in the regression discontinuity designs is proposed, which can be regarded as an attractive complement to the existing mean or quantile treatment effect. The novel mode treatment effect suggested in Chapter 4 has a wide range of applications in economics, statistics, social science, and other related fields, because it can capture the “most likely” effect and be robust to outliers and heavy-tailed distributions. Chapter 5 contains the conclusions. The newly proposed models based on modal regression in this dissertation complement the mean, median, and quantile regressions and provide a better central tendency measure when the data are skewed or heavy-tailed.