THE ECONOMETRICS OF MACROECONOMIC MODELLING
Models of money demand
8.2.1 The velocity of circulation
Models of the velocity of circulation are derived from the ‘equation of exchange’ identity often associated with the quantity theory of money (Fisher 1911) which on logarithmic form can be written:
mt + vt = pt + yt, (8.1)
where mt is money supply, vt is money velocity, yt is a scaling variable (e. g. real output), and pt is the price level. We define the inverse velocity of money as mt — yt — pt = - vt (small letters denote variables in logarithms). A simple
theory of money demand is obtained by adding the assumption that the velocity is constant, implying that the corresponding long-run money demand relationship is a linear function of the scaling variable yt, and the price level pt. The stochastic specification can be written as:
mt - yt - pt = 70 + £t (8.2)
assuming that E[etIt-i] = 0 on some appropriate information set It-. The price homogeneity restriction in (8.2) implies that real money, (mt — pt), will be determined by the scaling variable, yt, which has a unit elasticity. The constancy of y0 is, however, pervasively rejected in the empirical literature, cf. for example, Rasche (1987) who discusses the trending behaviour of velocity vt. Bordo and Jonung (1990) and Siklos (1993) analyse the properties of the velocity in a ‘100 years perspective’ and they explain the changes in velocity over this period by institutional changes, comparing evidence from several countries. Klovland (1983) has analysed the demand for money in Norway during the period from 1867 to 1980, and he argues along similar lines that institutional and structural factors such as the expansion of the banking sector and the increased degree of financial sophistication seems to be linked with the variations in velocity across this period.
Bomhoff (1991) has proposed a model where the inverse velocity is time dependent, that is, —vt = yt, and he applies the Kalman filter to model the velocity changes as a function of a shift parameter, a deterministic trend, and some relevant interest rate variable Rt, with the additional assumption that there are stochastic shocks in the shift and trend parameters. This allows for a very flexible time-series representation of velocity, which can be shown to incorporate the class of equilibrium-correction models which we will discuss later. A maintained hypothesis in the velocity models is that the long-run income elasticity is one. This hypothesis has been challenged from a theoretical perspective, for example, in ‘inventory models’ (Baumol 1952; Tobin 1956) and in ‘buffer stock models’ (Miller and Orr 1966; Akerlof 1979). The empirical evidence is such that this issue remains an open empirical question. A commonly used generalisation of the velocity model yields a money demand function of the following type:
mt = fm(pt, yt, Rt, Apt), (8.3)
where the model is augmented with the overall inflation rate Apt, which measures the return to holding goods, and the yields on financial assets, represented by a vector of interest rates, Rt.
The choice of explanatory variables in equations like (8.3) varies a great deal between different theoretical and empirical studies. A typical mainstream relationship, which is often found in empirical studies of long-run real money balances, is the following semi-logarithmic specification:
