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Prepared by Zenon Kontolemis (ZKontolemis@imf.org). A longer version of this chapter containing technical details is available upon request from the author.
In logs the rate of change of money growth can be expressed in terms of the rate of growth of potential GDP, long-run inflation and velocity, or, Δm* = Δy* + Δp* - Δv*.
A standard money demand equations in logs has the form, md - p = α0 y -α1 R, where p is the (log) GDP deflator, y is (log) GDP, and R is a measure for the opportunity cost of holding money.
By definition velocity is given by, v = p + y - m = (1 - α0)y - αtR, which in growth rates can be written as ẏ = (1 − α0)ẏ − α1Ṙ. However, assuming that interest rates remain unchanged, velocity will change proportionally to potential (or long-run) GDP growth if α0 ≠ 1.
According to estimates by the Deutsche Bundesbank, in the mid 1990s, 30-40 percent of all the DM banknotes were held abroad. Although, estimates for other currencies are not available it is certain that smaller quantities of other currencies may also be circulating outside the euro area (see Box 1, of the ECB’s Monthly Bulletin, September, 2001, for a discussion).
The VAR model estimated by Brand and Cassola (2000) includes two lags of each variable. In contrast, the results reported here are based on a model estimated with five lags which are all found to be essential to provide a well-specified model.
A discussion about the correct measure for the opportunity cost of holding broad money demand for the euro area can be found in Calza, Gerdesmeier and Levy (2001).
The word elasticity is not used here since it is argued that the parameters in these equations can not, strictly speaking, be interpreted as elasticities (i.e., showing the responsiveness of one variable to a change in another keeping all other variables unchanged); this point is explained in more detail in the longer version of the paper.
Other indicators, including the real money gap, are variations of the money gap and the discussion that follows also applies to these concepts.