Dynamic models

The equilibrium-correction model provides a flexible dynamic specification for the money demand function. This entails explicit and separate modelling of the short-run dynamic specification and the long-run cointegrating relationship for mt, which allows us to distinguish between shocks which will only cause tem­porary effects on money holdings and shocks with persistent long-run effects. Furthermore, the economic variables which exert the strongest short-run effects in money holdings, say, in the first quarters following the shock, need not be the same as the variables which drive money holdings in the long run. This is consistent with the models of Miller and Orr (1966) and Akerlof (1979), who study optimal inventories when changes in the cash balances are stochastic, leading to (s, S) target/threshold models. In these models, the short-run elasti­city with respect to income and interest rates can be negligible as long as targets and thresholds remain constant, while the long-run elasticities follow from the long-run cointegrating relationship.

A simple equilibrium correction specification for mt using the vector zt as explanatory variables is

q-1 q—1

Amt = Si Amt—i + YiAz—i + am(m— 1 — в zt—і) +A, (8.5)

i=1 i=0

£t ~ i. i.d.(0, a2).

The parameter am captures a feedback effect on the change in money hold­ings, Amt, from the lagged deviation from the long-run target money holdings, (m — m*)t—1. The target m* is defined as a linear function of the forcing vari­ables zt, that is, as m* = в'zt. Compared to a partial adjustment model, the equilibrium-correction model allows for richer dynamics in terms of more flexible dynamic responses in money balances to shocks in the forcing variables.

Equation (8.5) can be obtained from an unrestricted Autoregressive Distributed Lag model in the levels of the variables by imposing the appro­priate set of equilibrium-correction restrictions. The duality between equi­librium correction and cointegration (Engle and Granger 1987) makes the equilibrium-correction specification (8.5) an attractive choice for the modelling of non-stationary time-series, for example, variables which are I (1). If the forcing variables zt are weakly exogenous with respect to the parameters in the money demand equation, there will be no loss of information in modelling the change in money holdings Amt in the context of a conditional single-equation model like (8.5).

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