Essays on Uncertainty

Abstract

This dissertation studies the measurement of uncertainty.

Chapter 1 develops a tool for global prior sensitivity analysis in large Bayesian models, which measures how informative data are about particular features of a model. Without imposing parametric restrictions, the methodology provides bounds for posterior statistics given any prior close to the original in relative entropy, and reveals features of the prior that are important for the posterior statistics of interest. We illustrate the methodology using a canonical New Keynesian model, and show that the error bands for the impulse response of output to a monetary policy shock depend asymmetrically on the prior through features of the likelihood that are hard to account for with existing approaches.

Chapter 2 uses the tool developed in Chapter 1 to show that data on capital and savings are important for quantifying the effects of an aging population on interest rates. Using macroeconomic and demographic data from Japan, we apply Bayesian methods to estimate the effects of demographics in a parsimonious overlapping generations model. The prior sensitivity analysis reveals that without data on capital and savings over the life cycle, the discount rate, intertemporal elasticity of substitution, and capital depreciation rate are not well-identified, and the posterior for the effects of demographics is heavily dependent on the prior for these parameters. Quantitative exercises that ignore these data thus yield potentially inaccurate estimates.

Chapter 3 disentangles different sources of volatility using a model where levels and volatilties each follow factor structures, applied to a large panel of macroeconomic indicators. Principal component analysis provides an overview of the data, which informs model specification and priors for the Bayesian estimation. We identify the sources of volatility measured by existing uncertainty indices and show how different sources of volatility interact with macroeconomic levels in ways neglected by existing uncertainty indices.