The Correlation between Targets and Instruments

Abstract

The question of what can be learned from the correlation between targets and instruments has been discussed recently by Prest [4] and Worswick [5].2 Prest endeavoured to argue that from the correlation between public expenditure and the degree of capacity utilization' something could be inferred about the effectiveness of stabilization policy. Worswick took the contrary view that little or nothing could be inferred. Earlier, the point had been made by Kareken and Solow [3], in criticism of Friedman, that a perfectly successful monetary policy would show zero correlation between monetary change and the level of economic activity. Earlier still Friedman [2] had discussed the problem of the stabilization effect of public policy and had placed the burden of his argument on the correlation between the effects of that policy and the uncontrolled level of national income. The present exposition is essentially supplementary to Worswick's approach by viewing it explicitly in a context of control, and taking note of the existence of random variables. We use the following notation and make the following elementary assumptions: Zt is the target variable; Ut is the instrument variable (Zt and Ut may be interpreted as gross domestic product and government expenditure if it is so desired); et is a normally distributed random shock with zero mean and unit variance, that is