Staff working papers

This paper is a user's guide to a set of Gauss procedures developed at the Bank of Canada for estimating regime-switching models.

In this paper, the author uses structural vector autoregression methodology to decompose U.S. nominal interest rates into an expected inflation component and an ex ante real interest rate component. He identifies inflation expectations and ex ante real interest rate shocks by assuming that nominal interest rates and inflation expectations move one-for-one in the long-run—they are cointegrated (1,1)—and that the real interest rate is stationary.

Since the early 1980s, models based on economic fundamentals have been poor at explaining the movements in the exchange rate (Messe 1990). In response to this problem, Frankel and Froot (1988) developed a model that uses two approaches to forecast the exchange rate: the fundamentalist approach, which bases the forecast on economic fundamentals, and the chartist approach, which bases the forecast on the past behaviour of the exchange rate.

This paper examines the empirical performance of alternatives to the monetary aggregates currently published by the Bank of Canada. The results show that real M1 and real M1a perform about equally well in providing leading information about real output at short horizons. However, on theoretical grounds, M1a is a more attractive aggregate, since it excludes […]

The goal of this paper is to investigate and estimate long-run relationships among M1, prices, output and interest rates, with a view to determining if there is a stable relationship that can be interpreted as long-run money demand. The paper uses a maximum-likelihood multiple-equation cointegration technique, developed by Johansen, to fit a system of equations […]

This paper compares the empirical performance of Canadian weighted monetary aggregates (in particular, Fisher ideal aggregates) with the current summation aggregates, for their information content and forecasting performance in terms of prices, real output and nominal spending for the period 1971Q1 to 1989Q3. The properties of money-demand equations for these aggregates, particularly their temporal stability, […]

authors examine the issue of lag-length selection in the context of a structural vector autoregression (VAR) and a vector error-correction model with long-run restrictions. First, they show that imposing long-run restrictions implies, in general, a moving-average (MA) component in the stationary multivariate representation. Then they examine the sensitivity of estimates of the permanent and transitory […]

This paper derives analytical gradients for a broad class of regime-switching models with Markovian state-transition probabilities. Such models are usually estimated by maximum likelihood methods, which require the derivatives of the likelihood function with respect to the parameter vector. These gradients are usually calculated by means of numerical techniques. The paper shows that analytical gradients […]

This paper derives analytical gradients for a broad class of regime-switching models with Markovian state-transition probabilities. Such models are usually estimated by maximum likelihood methods, which require the derivatives of the likelihood function with respect to the parameter vector. These gradients are usually calculated by means of numerical techniques. The paper shows that analytical gradients […]

In this paper, the authors report estimates of two- and three-state Markov switching models applied to inflation, measured using consumer price indexes, in the G-7 countries. They report tests that show that two-state models are preferred to simple one-state representations of the data, and argue that three-state representations are more satisfactory than two-state representations for […]