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)| false Rasche, Robert H., “Mi-Velocity and Money Demand Functions: Do Stable Relationships Exist?,”in Empirical Studies of Velocity, Real Exchange Rates, Unemployment and Productivity, ed. by Carnegie-Rochester Conference Series on Public Policy, Allan H. Meltzerand Karl Brunner, Vol. 27( Amsterdam; New York: North-Holland, 1987).
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Eduard J. Bomhoff is Professor of Economics at Erasmus University in the Netherlands. He has also been an adviser to the Bank of Japan and the Commission of the European Communities. Part of this paper was written during his stay as Visiting Scholar in the IMF’s Research Department. The author is grateful to Michael Cox and Gerald O’Driscoll for useful comments, and to Camiel de Koning, Johan Koenes, Peter Gerbrands, Linda van Tuyl, and Tom van Veen for programming work and research assistance. Part of the methodological discussion summarized here is taken from Bomhoff (1990)
When no danger of confusion exists, the words “natural logarithm of” will be omitted in the ensuing discussion.
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 non-ergodic. 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 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 (1981)).
Note that the dummies relate only to breaks in one of the variables in the definition of velocity, not to observed outliers in the estimated statistical models.
The variance of the temporary shocks to the level of velocity could be seen as a third 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.
In this important respect, my program differs from the “stamp” program, developed by Harvey and described in Harvey (1989). His program uses up the first two values of the observed series in order to initialize the two unknown variance terms for the shocks to the level and growth rate of the series. By contrast, I apply a smoother in each iteration of the program, which is computationally more costly but avoids this loss of degrees of freedom in estimation.
See Nelson (1988) for evidence from his univariate research of U.S. gross national product 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.
Japan had to be omitted because of the limited length of the data series.