This thesis consists of three chapters on topics in Macroeconometrics. Chapter 1 proposes a method to analyze the relationship between models’ in-sample fit and their out-of-sample density forecasting performance. To this end, I further develop a formal test to capture density forecast break- downs (DFBs); situations in which the out-of-sample density forecast performance is significantly worse than its anticipated performance. Chapter 2 proposes a novel methodology for identifying and estimating structural breaks in the factor loadings of a high dimensional approximate factor model with an unknown number of latent factors. The approach is robust to structural changes in the volatility of the factors (the second moment of the factors), applicable to multiple structural breaks, and easy to implement for practitioners. Chapter 3 introduces time variation into the local projections framework and proposes an impulse response estimation methodology under unstable local projections.
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