This dissertation consists of three essays that deals with estimation of semiparametric regression methods in macroeconomic context. Chapter 1 introduces the building-blocks of the non-/semiparametric regression methods. A literature review is provided to support the estimation methodologies employed in the subsequent chapters. I survey some nonparametric estimation techniques, including (i) the local least squares kernel estimator; (ii) nonparametric series estimator; (iii) estimation of nonparametric models with endogeneity; and (iv) nonparametric estimation of panel data models. I also survey different bootstrapping methods for nonparametric regression methods. In Chapter 2 we consider a spatial Durbin model with unknown functional-coefficients and nonparametric spatial weights. We apply series approximation method to estimate the unknown functional coefficients and spatial weighting functions via a nonparametric two-stage least squares (or 2SLS) estimation method. We illustrate proposed estimation method to re-examine national economic growth by augmenting the conventional Solow economic growth convergence model with unknown spatial interactive structures of the national economy, as well as country-specific Solow parameters, where the spatial weighting functions and Solow parameters are allowed to be a function of geographical distance and the countries' openness to trade, respectively. In Chapter 3 I re-investigate the relationship between public debt and economic growth and try to expose nonlinearity in this link through using an endogenous smooth coefficient approach. I find some evidence of parameter heterogeneity in the debt-growth link that may be governed by the institutional quality of countries. My results show a significant negative effect of public debt on economic growth for the countries with the lowest democracy score and high democracy score.