The effects and role of monetary policy are central to modern macroeconomics. This dissertation concerns itself with three different questions within this realm: i) what frictions can explain the effects of monetary policy as found in the data?; ii) what is the horizon of monetary policy?; and, iii) how desirable is inflation in developing economies? In the first chapter, I develop a model with product market search frictions and money as a medium of exchange and evaluate its suitability to explain the short-term real effects of monetary policy found in the empirical data. The use of a model with this type of frictions as a potential explanation for the short-term effects of monetary policy is novel. It emphasizes how under matching uncertainty, firms generally operate below full capacity and households carry money that ends up unused. Changes in the nominal interest rate – the opportunity cost of holding liquid assets -- affect the abundance of liquidity, ultimately changing capacity utilization by making it easier or harder for firms to find households with money to purchase their goods. I use indirect inference methods to evaluate the model: I estimate it to match the impulse response functions to a monetary policy shock in a vector autoregression and compare it to a New Keynesian model, which emphasizes instead nominal rigidities as the explanation for the effects of monetary policy. The search-based model's response to a reduction in the nominal interest rate displays positive, persistent effects on output, employment, consumption, and investment. On top of this, the model is better able to match the procyclical response of labor productivity and the countercyclical response of the labor share than the New Keynesian model. The second chapter is based on work with Joao Valle e Azevedo and Pedro Teles which resulted in the publication of ``The Neutrality of Nominal Rates: How Long is the Long Run?'' in the International Economic Review. In it, we scrutinize data on nominal interest rates and inflation across various countries, from the 1960s to the present, to reinvestigate their relationship. The study is motivated by the contrast between the strong theoretical prediction made by long-run neutrality and the Fisher equation, that long-run nominal interest rates have a one-to-one relationship to long-run inflation, and the conduct of monetary policy by Central Banks, particularly in Japan and Europe, during the period of zero nominal interest rates and inflation below target, in which these institutions signaled that they would keep nominal interest rates at zero for many years in the future as a policy to achieve reflation. In the cross-sectional data, we find a clear one-to-one relationship between long-run nominal interest rates and inflation, in line with long-run neutrality. Dividing our sample into a period before and after inflation targeting, we find that this relationship is harder to estimate in the latter period, but still seems compatible with the data. Estimation of the relationship in the time-series and panel data results for most of the sample in a positive coefficient slightly below 1. Finally, we estimate a Vector Error Correction model that distinguishes temporary and permanent monetary policy shocks and find that positive, permanent shocks to the nominal interest rate result in an increase in inflation, even in the short run. In the third, and final, chapter, coauthored with Daniel Jaar, we construct a quantitative model suitable to study the welfare implications of different revenue-equivalent choices of consumption taxes and inflation for households with different wealth in economies with a large informal sector. Previous work has analyzed this policy decision under a representative agent framework. However, many important dimensions of the trade-offs involve distributional concerns which our model can speak to. The model jointly rationalizes the positive correlation between firm size and formality status, and the negative correlation between household income and the proportion of consumption purchased in the informal economy, emphasizing the role of cash and tax evasion in explaining these two empirical facts.