Comment on An Equilibrium Model of Nominal Bond Prices with Inflation- Output Correlation and Stochastic Volatility

Abstract

Boudoukh studies two main issues in this interesting paper. The first is the impact of increased inflation uncertainty on asset returns. While there are many studies that focus on the effect of inflation on financial markets, there are very few that focus on the effect of uncertainty about inflation variability on these markets. The second issue is how the link between inflation and consumption growth affects nominal interest rates. The time series model Boudoukh develops has two features that make it well suited to study these issues. First, the model consists of three exogenous stochastic processes: consumption, inflation, and inflation volatility. The inflation volatility is unobserved and its innovations may be correlated with the innovations to inflation. As a consequence, the conditional variance of inflation and nominal bond prices are time varying. Second, consumption growth and inflation may be codependent, which has important implications for the correlations of expected and realized real interest rates with inflation. Also, the conditional covariance of inflation and consumption may be time varying. He motivates his choice of time series model by citing some empirical evidence. A feature of the data that can be replicated by his model, for example, is that nominal interest rates and inflation are conditionally heteroskedastic while real interest rates are homoskedastic. A second motive for adding inflation volatility is that the basic bond-pricing model, which I will describe briefly below, has some empirical implications that are rejected in the data. Boudoukh embeds his time series model into a representative agent framework and assumes constant relative risk aversion to derive pricing equations for nominal discount bonds of various maturities. Although he is able to compute exactly the one-period nominal bond price and one-period expected real interest rate, closed-form solutions are generally unavailable for the particular stochastic structure he assumes. To circumvent this, he approximates nominal bond prices using a Gaussian quadrature method. From his analysis of the inflation time series, the approximated nominal interest rates, and expected and realized real interest rates, Boudoukh draws two conclusions. The first is that the conditional heteroskedasticity of inflation can help to explain the time-varying risk implicit in