My dissertation contains three papers in the theory and applications of nonparametric structural econometrics. In chapter 1, I propose a nonparametric test for additive separability of unobservables of unrestricted dimensions with average structural functions. Chapter 2 considers identification and estimation of fully nonparametric production functions and empirically tests for the Hicks-neutral productivity shocks, a direct application of the test proposed in chapter 1. In chapter 3, my authors and I study the semiparametric ordered response models with correlated unobserved thresholds and investigate the issue of corporate bond rating biases due to the sharing of common investors between bond-issuing firms and credit rating agencies. Brief abstracts are presented in order below. Additive separability between observables and unobservables is one of the essential properties in structural modeling of heterogeneity in the presence of endogeneity. In this chapter, I propose an easy-to-compute test based on empirical quantile mean differences between the average structural functions (ASFs) generated by nonparametric nonseparable and separable models with unrestricted heterogeneity. Given identification, I establish conditions under which structural additivity can be linked to the equality of ASFs derived from the two commonly employed competing specifications. I estimate the reduced form regressions by Nadaraya-Watson estimators and control for the asymptotic bias. I show that the asymptotic test statistic follows a central Chi-squred distribution under the null hypothesis and has power against a sequence of root N-local alternatives. The proposed test statistic works well in a series of finite sample simulations with analytic variances, alleviating the computational burden often involved in bootstrapped inferences. I also show that the test can be straightforwardly extended to semiparametric models, panel data and triangular simultaneous equations frameworks. Hicks-neutral technology implies the substitution pattern of labor and capital in a production function is not affected by technological shocks, first put forth by John Hicks in 1932. In this chapter, I consider the identification and estimation of fully nonparametric firm-level production functions and empirically test the Hicks-neutral productivity in the U.S. manufacturing industry during the period from 1990 to 2011. Firstly, I extend the proxy variable approach to fully nonparametric settings and propose a robust estimator of average output elasticities in non-Hick-neutral scenarios. Secondly, I show that the Hicks-neutral restriction can be converted to the additive separability between inputs and unobservables in a monotonic transformed model for which the proposed testing procedure can be directly applied. It turns out that there is substantial heterogeneity in the nonparametric output elasticities over various counterfactual input amounts. I also find that there were periods in the 90s when the non-Hicks technological shocks occur which coincide with the mass adoption of computing technology. However, the productivity has thereafter become Hicks-neutral into the 2000s. Controlling for sector-specific effects mitigate the non-Hicks-neutrality to some extend. Previous literature on bond rating indicates that credit rating agencies (CRAs) may assign favorable ratings to bond-issuing firms that have a closer relationship. This not only implies the existence of firm-specific unobserved heterogeneity in the rating criteria but also makes some bond/firm characteristics endogenous, which is confirmed by our empirical results. In this chapter, my coauthors and I propose a semiparametric two-step index and location estimator of ordered response models that explicitly incorporates endogenous regressors and correlated random thresholds. We apply our model in the application of assessing bond rating bias of credit rating agencies. Methodologically, we first show that the heterogeneous relative thresholds can be identified using conditional shift restrictions in conjunction with the control variables for the firm-CRA liaison. Then, we illustrate the estimation strategy in a heuristic manner and derive the asymptotic properties of the suggested estimator. In the application, we find significant overrating bias through varying thresholds as the liaison strengthens and those biases display heterogeneous patterns with respect to rating categories.