The thesis is composed of three essays. The first designs a DSGE model based on Gertler and Karadi (2011) to study the effects of the adoption of negative interest rate policies along with liquidity intervention, in a scenario where the ZLB is transferred to private banks instead of central banks. We show that, during a recession, if banks do not pass along negative rates to depositors in an environment of heavy liquidity injection by the Central Bank, the main negative economic effects of the original ZLB are maintained and the recovery is slower. The second essay uses the same model in a simpler setting to study how the adoption of central bank digital currencies (CBDCs) might reestablish the traditional monetary policy transmission under negative interest rates, and analyses the responses of the economy under such a regime to monetary policy shocks. We show that while the adoption of a CBDC might improve the monetary policy toolkit, the wealth effects involved with changes exclusively in its interest rates make it a less reliable counter-cyclical tool. The third essay tries different models for the forecast of medium-term output growth. We use new methods such as adaLASSO and Random Forest, along with a very large data set of regressors, in order to improve accuracy over traditional model long term forecasting such as autoregressions and DSGE models, which have a very good track record. We show that Random Forest is able to better predict output growth over the two year horizon, but has mixed results in forecasting trend GDP growth and the output gap.