Chapter one provides a new estimator for the ordered polychotomous model. The estimator is based on the use of the average of the standard normal densities with different means as a parametric approximation to the density of the error term. The method also, for the first time, provides a consistent, differentiable estimator of the distribution function of the error term. Chapter two employs the conventional interpretation of endogeneity in econometric models to develop a way of eliminating the inconsistency resulting from endogenous explanators in cross sectional models. The method first obtains an estimate of the unobserved heterogeneity responsible for the endogeneity and then creates a synthetic observation by taking a non-parametric weighted average of nearby observations. The deviations are produced from these synthetic means thereby eliminating the unobserved heterogeneity. The procedure is particularly useful for estimating models when the endogenous regressors are censored or appear non-linearly in the primary equation. Chapter three first calculates the exact distribution of Blum et al's (1961) statistic, which is based on a comparison of the sample joint CDF with the product of the sample marginal CDF's, for very small sample size and simulate the distribution quantiles of it for sample size not large enough to employ the asymptotic result. Secondly, the asymptotic distribution of the statistic constructed from residuals and/or predicted values, to test the independence of the error term and the regressors in nonlinear regression models, is obtained. Thirdly, bootstrap technique is used to obtain the distribution quantiles of the statistic constructed from residuals and/or predicted values. The test is nonparametric in that it does not specify the parametric form of distributions of the error term and the regressors.