Essays in Nonlinear Econometrics

In this dissertation, I study standard models, but investigate the necessity of (possibly large) deviations from basic assumptions. In Chapter 1, my co-author Ross Askanazi and I revisit the use of factor models in finance. Historical literature on the subject decomposes volatility into a factor component (systemic risk) and a remainder (idiosyncratic risk). Recent work has suggested that a market shock to volatility may increase both systemic risk and idiosyncratic risk — specifically, that idiosyncratic volatility of US equities data has a factor structure, with the factor highly correlated with, and possibly precisely the market volatility. In this paper we attempt to characterize the underlying factor and find that it can be decomposed into a statistical (PCA) and structural (market volatility) factor. We also show that this feature is more common than expected, appearing in diverse sets of financial data. Lastly, we find that this dual-factor approach is slightly dominated in forecasting environments by a single statistical factor. In Chapter 2 I revisit the classical Vector Autoregression (VAR) model, but allow parameters to time-vary. Time-Varying parameter models have be- come more popular in recent years, especially as they are adapted to accommodate larger datasets. However, all recent developments use standard priors, specifically the Inverse-Wishart class of priors over the parameter error covariance matrix. In this paper, I show that Inverse-Wishart priors have a number of negative properties, and that those properties are salient in a TVP context since there is little information from the likelihood. Fully aware of these deficiencies, the Bayesian Random Effects literature has developed a series of uninformative priors to correct these weaknesses. In this paper, I adapt one of those priors into an informative and easily understandable prior for covariances. I show that the new prior effects posterior inference and displays improved frequentist properties. I apply my prior to the canonical Primiceri (2005) dataset and find that their results were sensitive to the choice of prior. I further apply the prior to two forecasting exercises and find that while it improves forecasts for the Primiceri data, it does not for an alternative (larger) dataset