Three Essays of Applied Bayesian Modeling: Financial Return Contagion, Benchmarking Small Area Estimates, and Time-Varying Dependence

Abstract

This dissertation is composed of three chapters, each an application of Bayesian statistical models to particular research questions. In Chapter 1, we evaluate systemic risk exposure of financial institutions. Building upon traditional regime switching approaches, we propose a network model for volatility contagion to assess linkages between institutions in the financial system. Focusing empirical analysis on the financial sector, we find that network connectivity has dynamic properties, with linkages between institutions increasing immediately before the recent crisis. Out-of-sample forecasts demonstrate the ability of the model to predict losses during distress periods. We find that institutional exposure to crisis events depends upon the structure of linkages, not strictly the number of linkages. In Chapter 2, we develop procedures for benchmarking small area estimates. In sample surveys, precision can be increased by introducing small area models which "borrow strength" by incorporating auxiliary covariate information. One consequence of using small area models is that small area estimates at lower geographical levels typically will not aggregate to the estimate at the corresponding higher geographical levels. Benchmarking is the statistical procedure for reconciling these differences. Two new approaches to Bayesian benchmarking are introduced, one procedure based on Minimum Discrimination Information, and another for Bayesian self-consistent conditional benchmarking. Notably the proposed procedures construct adjusted posterior distributions whose moments all satisfy benchmarking constraints. In the context of the Fay-Herriot model, simulations are conducted to assess benchmarking performance. In Chapter 3, we exploit the Pair Copula Construction (PCC) to develop a flexible multivariate model for time-varying dependence. The PCC is an extremely flexible model for capturing complex, but static, multivariate dependency. We use a Bayesian framework to extend the PCC to account for time dynamic dependence structures. In particular, we model the time series of a transformation of parameters of the PCC as an autoregressive model, conducting inference using a Markov Chain Monte Carlo algorithm. We use financial data to illustrate empirical evidence for the existence of time dynamic dependence structures, show improved out-of-sample forecasts for our time dynamic PCC, and assess performance of dynamic PCC models for forecasting Value-at-Risk.