Inverted money demand equations
In reviewing the lineages of the Phillips curve in Chapter 4, we saw that the relationship between wage growth and the level of economic activity (or unemployment) has a prominent position in the new classical macroeconomics literature; see, for example, Lucas and Rapping (1969, 1970) and Lucas (1972). Two issues were in focus. First, according to this literature, the causality of Phillips’ original model is reversed: if a correlation between inflation and unemployment exists at all, the causality runs from inflation to the level of activity and unemployment. Since price and wage growth are then determined from outside the Phillips curve, the rate of unemployment would typically be explained by the rate of wage growth (and/or inflation). Second, given this inversion of the Phillips curve, the determination of the price level in Lucas and Rapping’s model is based on a quantity theory relationship, where they condition on an exogenous or autonomously determined money stock.
Later we investigate the relationship between money and inflation from this monetarist perspective. Obviously, a causal relationship between money and inflation can be analysed from several angles. The most direct approach would be to model inflation as a function of some monetary aggregates. However, we shall first look to estimated versions of the money demand functions we introduced earlier, in order to see if they can be interpreted as inverted equations for price growth. This amounts to inverting the money demand relationship to obtain a relationship for price growth in the same way as the Phillips curve was inverted to explain unemployment earlier.
In their study of money demand in the United Kingdom and the United States, Hendry and Ericsson (1991) estimate a money demand relationship for the United Kingdom under the assumption that it represents a conditional model for money growth with output, prices, and interest rates as the main explanatory factors. The model is well specified with stable parameters. Inversion of this model to an inflation equation yields a non-constant representation, with several signs of model mis-specification. Noting that the price level pt is included among the explanatory variables in zt, Hendry and Ericsson (1991) estimate an inverted money demand relationship of the type
Apt = /?oAmt + /?iAmt-i + £0Azt + £iAz— + кт(т— і – fi’z—i) + £t-
In the following section we repeat this exercise: first, on data for the Euro area and second, on data for Norway.