UC Riverside

Nonparametric approaches have widely been used due to their advancement in not making assumptions on the distribution of the data. Even with their extensive development, nonparametric hypothesis testing has not been developed as much as a nonparametric estimation even though it is one of the key components of the econometric analysis. This dissertation has mainly two parts. I first explore the systematic development of the current nonparametric tests and provide results on testing linearity as an illustration. Then I develop new nonparametric tests for detecting endogeneity in cross-sectional data and panel data respectively.

Elaborating each test's performance can be meaningful in that we can decide which test to use depending on the hypothesis and even construct a new test based on such a relationship. Under the hypotheses for linearity, Chapter 2 will categorize the types of nonparametric tests and discuss the analytical relationship of those tests. By imposing some conditions, I can compare the local power of each test asymptotically. While examining the analytical relationship, I develop a nonparametric Rao-Score test and show it to be equivalent to the Su and Ullah (2013) test.

Once analyzing the analytical relationship of the current nonparametric tests, I focus on developing a new nonparametric test for endogeneity. Since endogeneity is commonly observed in many economic contexts, detecting its presence is a preliminary step for choosing an estimation strategy. In Chapter 3, I construct a test using the control function approach under a triangular simultaneous equations model. My test can be summarized as being simple to implement as a test and being able to capture the locally nonlinear correlation with kernel weighting. Furthermore, I will apply these tests to the empirical analyses and show the contradicting results with the parametric test.

Not only in triangular simulation equations model, but also is endogeneity important model specification issue in panel data setting. The estimation strategy differs depending on the presence of endogeneity between the individual specific effects and the variable. I propose a new estimation method for the nonparametric panel random effects model and construct a new test for endogeneity using the residuals from the proposed estimation method. By obtaining the individual specific effects in the random effects model, I construct a test over the i index instead of the i index and time. With a large T, the test performs well in terms of size and power.