This thesis consists of three essays in the threshold regression model regarding both theory and application. Chapter 1 investigates the linear index threshold regression model with endogeneity. We propose a two-step GMM estimation method to estimate the model, which allows both the threshold variable and regressors to be endogenous. We show the consistency of the GMM estimator and derive the asymptotic distribution of the GMM estimator for weakly dependent data. We suggest a test of the exogeneity null hypothesis for both the threshold and the slope regressors. Monte Carlo simulations are used to assess the finite sample performance of our proposed estimator. Finally, we present an empirical application investigating the threshold effect of a linear index between external debt and public debt on economic growth for developing countries. In Chapter 2, we compare the finite sample performance of three non-parametric threshold estimators via the Monte Carlo method. Our results indicate that the finite sample performance of the three estimators is not robust to the position of the threshold level along the distribution of the threshold variable, especially when a structural change occurs at the tail part of the distribution. In Chapter 3, we examine the effect of the Exchange Rate Pass-Through (ERPT) on the "rockets and feathers" hypothesis using a panel of EU-28 countries. Allowing for the existence of an endogenous threshold variable, our empirical findings indicate that the threshold model is better suited to this analysis than the baseline linear adjustment model. This is the case since the latter restricts the threshold to be centered around zero and the dynamic response to cumulative shocks cannot be properly identified. The empirical findings reveal that the threshold variable expressed by the trade-weighted dollar exchange rate index is statistically significant only in the sample above the threshold (high regime). This means that for the net EU exporting countries, fluctuations in the real effective exchange rate of the US against its major EU trading partners does affect the level of pre-tax retail gasoline prices with the relevant elasticity exceeding unity (complete ERPT). Moreover, all the statistical tests reject the null hypothesis that there is no significant threshold and thus an asymmetric adjustment gasoline mechanism prevails.