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Mr. Bomhoff is Professor of Economics at Erasmus University in the Netherlands. Work on this paper began while he was a Visiting Scholar in the Fund’s Research Department. Michael Cox and Gerald O’Driscoll of the Dallas Fed provided useful comments. Camiel de Koning and Johan Koenes very ably did much of the programming work and performed the calculations. Linda van Tuyl provided efficient research assistance. Part of the methodological discussion is summarized from Bomhoff (1990).
When no danger of confusion exists, the words “natural logarithm of” will be omitted in the sequel.
Durlauf and Phillips (1988) provide an excellent theoretical analysis of the difficulties that arise when ordinary least squares are applied to nonstationary time series with the possibility that the errors are also nonstationary and nonergodic. See also Plosser and Schwert (1979) and Nelson and Plosser (1982). This line of research originated with Paul Newbold, see Granger and Newbold (1974)
See Swamy, Von zur Muehlen and Mehta (1989) for a very critical methodological discussion of cointegration tests.
See, for example, Hamilton (1989) for a brief analysis of why standard money demand equations are a mixture of supply and demand effects.
Neither issue can be circumvented with the use of instrumental variables (see Cooley and LeRoy).
The variance of the temporary shocks to the level of velocity could be seen as a fourth variance parameter, but the models are homogeneous of the first degree in all the variance and covariance terms. Hence, this variance is best viewed as computed ex-post from the results of the Kalman filter.
See Nelson (1988) for evidence from his univariate research of U.S. GNP that optimization with respect to the unknown variances of the different shocks to the level and the shocks to the trend of a nonstationary time series may be a delicate matter. This is a topic for additional research.
The Kalman filter model for Japan was not re-estimated for a shorter period, because the sample starts only in 1966.