Estimation of Unobserved Expected Monthly Inflation Using Kalman Filtering

Abstract

Hamilton developed a technique for estimating financial market expectations of inflation based on the observed time-series properties of interest rates and inflation. The technique is based on a state-space representation derived from an underlying vector autoregressive process of the expected real interest rate and the expected inflation rate on lagged expectations and lagged values of the observed Treasury bill rate and the actual inflation rate. This article extends this work in two ways. First, we use monthly data, since the quarterly data used by Hamilton may obscure many interesting movements, especially for determining the role of inflationary expectations in stock price movements, and this is one of our primary interests. Second, we employ an alternative method developed by Burmeister and Wall for estimating the parameters of the model, and this method leads to a different identification proof. Both approaches share the use of the Kalman filter to estimate the unobserved variables, in this case, expected rates of inflation.