The Intermediate Control Problem: Note

Abstract

A large institutional literature has been concerned with restructuring the banking system in such a way as to decrease uncontrolled variation in the money supply. Some advocate this restructuring as a means of getting increased control over an target variable; apparently they reason that tighter control of an intermediate target variable will ultimately lead to better control of target variables such as inflation or unemployment. More recently, control theorists have acknowledged the fact that monetary authorities do not exert direct control over the money supply or interest rates, and a number of control engineering studies have been concerned with the optimal control of various intermediate financial variables. Common to all of this literature (and perhaps current FOMC policy making as well) would appear to be the basic premise that the optimal control problem can be divided into two separate control problems that are solved sequentially: First, in the control problem, one pretends that the intermediate variables are set directly and finds the intermediate variable path (called the intermediate target path) that will make the final variables track their target path as well as possible. Then, in the control problem, one finds the path for the actual instruments of monetary policy that will make the intermediate variables track the intermediate target path as well as possible. The purpose of this note is to show that this basic premise is not generally valid, that the second step in the procedure constitutes an improper specification of the intermediate control problem, and that the intermediate control problem, properly specified, is fundamentally different from the standard control problem. Two examples will illustrate situations in which the two-step procedure described above leads to an incorrect solution, and the difference between standard and properly specified intermediate control problems will be characterized. Both examples will be constructed within a very simple setting: The relationships between the true instruments of monetary policy and the intermediate variable, which is taken to be the money supply M, will be viewed as a black box generating the random variable M. The monetary authority will be assumed to be able to control both the mean and the variance of the random variable emanating from the black box by judicious setting of its true instruments. That is, letting M = M + m, where m is a random variable with zero mean and variance 2, the monetary