Essays on real interest rates, government debt and monetary policy

The three dissertation chapters explore various issues regarding interest rate as an instrument for monetary policy in industrial countries.; Chapter 1. “Is the quantity of debt a constraint on monetary policy?” Monetary authorities have often voiced their concerns about a high debt level that could potentially restrain their ability to control the short-term interest rate as an instrument of monetary policy. This paper derives an augmented interest rate rule in which the response of the interest rate to expected inflation changes with the level of debt-to-GDP ratio. In particular, the interest rate response of the central bank towards an increase in expected inflation falls as debts increase beyond a certain threshold level. We estimate this threshold level for Canada and find evidence of its monetary policy having been constrained by debt during its inflation-targeting regime of the 1990s.; Chapter 2. “A model of the ex ante real rate and the natural rate of interest.” (Co-authored with Charles R. Nelson and Richard Startz) The ex ante real rate is unobserved in the United States. We model this unobserved ex ante rate using a state-space model of the ex post real rate and assume only that the inflation forecast errors are rational and that the unobserved ex ante real rate follows an autoregressive process. Finding evidence of time-varying volatility in the forecast error, we model the variances of both inflation uncertainty and monetary policy shocks. We, then, extract a measure of the natural rate as the more persistent component of the real rate.; Chapter 3. “Unknown number of mean shifts and persistence around mean. An application to short term real interest rates.” (Co-authored with Arabinda Basistha) We have provided a model for certain time-series processes that are characterized by two distinct phases: one in which the mean is stable or constant, and the other in which the mean is gradually shifting to another level. The number of these slow mean-shifts is unknown. Using an unobserved components model, the process can be divided into a 2-state Markov-switching process of the mean and a stationary cyclical component. The model is able to predict a slow shift in mean to another level without having to test for structural breaks or unit root in the data. This is particularly appealing for modeling the real interest rate of the United States, which give different results regarding presence of a unit root across various unit-root tests and sample periods.