RDP 8601: New Classical Models and Unobserved Aggregates 1. Introduction

In the decade since Lucas's seminal work (Lucas (1972), Lucas (1973)), the themes of rational expectations and New Classical macroeconomics have occupied much attention in the literature. Many variants of Lucas's basic model have been generated; mainly in attempts to explain observed cyclical fluctuations in real variables by private agents' reactions to nominal demand disturbances, about which they have incomplete information. The maintained hypothesis of these models is that agents behave as if they know the model's structure (the equations, parameters and sufficient statistics for the distributions of the exogenous stochastic terms), and at least some lagged values of all relevant macroeconomic variables. Much of the debate generated by this literature, both at the theoretical and empirical level, has centered on the two main hypotheses derived from these New Classical models – the neutrality of fully anticipated monetary policy with respect to output, and the positive correlation between output fluctuations and unanticipated fluctuations in the money stock. An associated issue that has also received considerable attention, is the consistency of the theoretical models with observed business cycle persistence – the tendency of current demand shocks to affect future levels of output.

While these models are driven by the assumption of incomplete information, the information set assumed to be at the agents' disposal is unrealistically encompassing. In particular, the assumption that agents know at least some lagged values of all “appropriate” aggregates (that is the sum over all agents of variables that appear in the model) is very restrictive. In practice such conceptual definitions are rarely matched by observable measured aggregates. It is also well known that statistical measurement errors can be considerable. One indicator of divergence between measured and conceptual aggregates is the proliferation of measured aggregates that are often available. This is the case for a number of macroeconomic variables; it is especially true in the case of the money supply.^[1]

This paper analyses the effects, in a New Classical model, of relaxing the informational assumption about past values of true aggregates. In particular, to examine the importance of the informational assumption, I assume that agents do not know (any of the) past values of the true money supply. The approach takes the simplest representative New Classical model (with no apparent source of persistence) and introduces an imperfectly measured monetary aggregate. The authorities are assumed to directly control the monetary base, which in turn influences both the true and measured monetary aggregates. Both the measured monetary aggregate and the monetary base are assumed to be observable (published) variables. Agents are assumed to have rational expectations of the unobservable monetary aggregate and its lagged values.

I show that, if the reduced form of the unobservable true monetary aggregate contains any of its own lagged values, the agents' optimal projection (i.e., rational expectation) of this aggregate introduces persistence into the output equation. That is, output responds to lagged, as well as contemporaneous, demand shocks. This result is due entirely to the assumption that the true aggregate is not observed. The partial information flow that agents observe allows them continually to update their estimates of past values of the true aggregate by a filtering process. The presence of a lagged value in the reduced form of the process generating the true money supply introduces serial dependence into the optimal filter. The difference between the true money supply and the agents' rational expectation of it (the expectational error) is then serially correlated. This leads to persistence in the output equation.

A second result of the analysis, under the maintained hypothesis of a New Classical model, is that empirical tests of the neutrality of fully anticipated monetary movements are unaffected^[2] by the use of the imperfectly measured monetary aggregate. However, the measurement errors are important when testing the non-neutrality of unanticipated monetary shocks. In particular, for some parameterisations of the measurement error, tests based on the observed monetary data will fail to reject the false (null) hypothesis of zero correlation.

The remainder of the paper is split into six sections. The first presents the simple New Classical model that provides the framework for the analysis, formalises the relationships among the various monetary aggregates and derives some partial solutions. Section 3 sets up and solves the agents' filtering problem. This solution is used to solve the model in the following section. Tests of the New Classical hypotheses are then examined in Section 5. The current model is compared to those of Brunner, Cukierman and Meltzer (1980) and Boschen and Grossman (1982) in the next section. The final section presents some conclusions.

Footnotes

One approach to the problem of the optimal level of aggregation of the money supply (due to Barnett) attempts to sum value, rather than physical, units together via a Divisia index weighting scheme. For recent developments in this debate over the relationship between the various observed aggregates and the economic concept of “the money supply”, see the papers by Barnett (1982), Cagan (1982), Fellner (1982), the comments in Goldfeld (1982) and Hamburger (1982), and the references contained therein. [1]

That is, unaffected with respect to population statistics. The sample questions of efficiency and power are not considered here. [2]