In chapter 1, we use a model of endogenous growth with vertical innovations, in order to derive optimal energy policy under uncertainty. Innovation can be directed to dirty, green, or nuclear technologies, which in turn can be used to produce different types of energy. We show that, nuclear energy usage, is not only a necessary welfare maximizing condition, but also a crucial determinant of economic growth in the long run. Lastly, we find no evidence supporting the Environmental Kuznets Curve hypothesis under optimal policy implementation. Chapter 2 focuses on shedding light on the complex mechanisms through which natural disasters affect economic growth. Even though growth theories suggest that natural disasters should have an impact on economic growth, parametric studies have provided little to no evidence supporting that prediction. We therefore re-investigate the impact of natural disasters on economic growth, applying a semiparametric smooth coefficient panel data model that considers fixed effects. Our study finds evidence that the coefficient curve of investment is a U-shaped function of the severity of the natural disasters. Thus, for relatively small disasters, marginal returns to investment decrease on the severity of natural disasters. However, after a certain threshold, the coefficient of investment starts increasing as natural disasters become more severe. Lastly, in Chapter 3 we examine the effect that higher natural disaster frequency has on economic outcomes. Even if there is clear evidence that natural disasters are not only going to be more frequent but will also start affecting a wider pool of countries, research has not yet analyzed the economic impact of the interaction between climate change and more frequent extreme rare events. With this study, we try to unveil the mechanisms through which natural disasters and climate change are interconnected, as well as provide policy insights regarding the adoption of greener inputs, in the form of green capital. Our findings suggest that raising temperatures are expected to negatively affect consumption as well as increase debt. We also show that under "green" technology adaptation, countries are projected to achieve higher levels of consumption and welfare.