This article reviews Monetary Policy Rules, edited by John Taylor. The book evaluates the Taylor rule, a policy rule that specifies changes in the central bank's interest rate according to what is happening to two variables, real output and inflation. Questions are raised about (a) how well the models fit the data; (b) the validity of the assumption that there has been clear improvement in monetary policy; and (c) the rule's microfoundations.

A model is considered in which a covariance-stationary exogenous process is related to an endogenous process by an unrestricted, infinite, linear distributed lag. It is shown that when an underlying continuous time model is sampled at unit intervals to yield endogenous and exogenous discrete time processes, the discrete time processes are related by a discrete time equivalent of the underlying continuous model. The relationship between the underlying continuous lag distribution and its discrete time equivalent is close when the exogenous process is smooth. Even then, however, it is interesting to note that (i) a monotone continuous time distribution does not in general have a monotone discrete time equivalent and (ii) a one-sided continuous time distribution does not in general have a one-sided discrete time equivalent. The implications of the results for statistical practice are considered in the latter part of the paper.

Existing strategies for econometric analysis related to macroeconomics are subject to a number of serious objections, some recently formulated, some old. These objections are summarized in this paper, and it is argued that taken together they make it unlikely that macroeconomic models are in fact over identified, as the existing statistical theory usually assumes. The implications of this conclusion are explored, and an example of econometric work in a non-standard style, taking account of the objections to the standard style, is presented. THE STUDY OF THE BUSINESS cycle, fluctuations in aggregate measures of economic activity and prices over periods from one to ten years or so, constitutes or motivates a large part of what we call macroeconomics. Most economists would agree that there are many macroeconomic variables whose cyclical fluctuations are of interest, and would agree further that fluctuations in these series are interrelated. It would seem to follow almost tautologically that statistical models involving large numbers of macroeconomic variables ought to be the arena within which macroeconomic theories confront reality and thereby each other. Instead, though large-scale statistical macroeconomic models exist and are by some criteria successful, a deep vein of skepticism about the value of these models runs through that part of the economics profession not actively engaged in constructing or using them. It is still rare for empirical research in macroeconomics to be planned and executed within the framework of one of the large models. In this lecture I intend to discuss some aspects of this situation, attempting both to offer some explanations and to suggest some means for improvement. I will argue that the style in which their builders construct claims for a connection between these models and reality-the style in which is achieved for these models-is inappropriate, to the point at which claims for identification in these models cannot be taken seriously. This is a venerable assertion; and there are some good old reasons for believing it;2 but there are also some reasons which have been more recently put forth. After developing the conclusion that the identification claimed for existing large-scale models is incredible, I will discuss what ought to be done in consequence. The line of argument is: large-scale models do perform useful forecasting and policy-analysis functions despite their incredible identification; the restrictions imposed in the usual style of identification are neither essential to constructing a model which can perform these functions nor innocuous; an alternative style of identification is available and practical. Finally we will look at some empirical work based on an alternative style of macroeconometrics. A six-variable dynamic system is estimated without using 1 Research for this paper was supported by NSF Grant Soc-76-02482. Lars Hansen executed the computations. The paper has benefited from comments by many people, especially Thomas J. Sargent

The practice which we will refer to here as is a technique for arriving at a measure of value when one has available the value of gross output and materials inputs and also price indices for gross output and for materials inputs. The double deflation technique, despite its rather wide use, has been regarded as crudely empirical, with little, if any, justification from the point of view of theory.' The purpose of this note is to demonstrate that one can justify double-deflation as a fixed-weight linear approximation to an ideal variable-weight logarithmic index under assumptions no more restrictive than those required to justify the notion of real value added itself. Analysis of production relations is simpler if we can restrict ourselves to looking at two inputs at a time. Hence in studies using disaggregated data, it is convenient to consider the contribution of capital and labor to gross output separately from the contribution of materials inputs. In order for such separate treatment to be justified, the production function must be separable. Taking y to be gross output, K to be capital, L to be labor, and M to be materials, the separability condition required is

There is a view that monetary policy is effectively summarized by the time path of a single variable, the money stock, and that erratic fluctuations in the money stock generated by erratic policy decisions are a major, even the principal source of business cycle fluctuations. This view, which I will call monetarism, is losing adherents among economists, for several reasons. For one thing, rational expectations theory, having shown how the Phillips curve could emerge as a statistical regularity in an economy where it was not exploitable for policy purposes, can now do the same for Granger causal priority of money and money's strong explanatory power for future movements in real output. Theories of endogenous cyclical variation in money are gaining attention in part because of results which have begun emerging from the data as new statistical techniques are applied to new historical developments. Data from outside the United States or outside the 1950's and 1960's do not fit the predictions of monetarist theory.

Drastic changes in central bank operations and monetary institutions in recent years have made previously standard approaches to explaining the determination of the price level obsolete. Recent expansions of central bank balance sheets and of the levels of richcountry sovereign debt, as well as the evolving political economy of the European Monetary Union, have made it clear that fiscal policy and monetary policy are intertwined. Our thinking and teaching about inflation, monetary policy, and fiscal policy should be based on models that recognize fiscal-monetary policy interactions. (JEL E31, E52, E58, E62, H63)

The science of economics has some constraints and tensions that set it apart from other sciences. One reflection of these constraints and tensions is that, more than in most other scientific disciplines, it is easy to find economists of high reputation who disagree strongly with one another on issues of wide public interest. This may sug gest that economics, unlike most other scientific disciplines, does not really make progress. Its theories and results seem to come and go, always in hot dispute, rather than improving over time so as to build an increasing body of knowledge. There is some truth to this view; there are examples where disputes of earlier decades have been not so much resolved as replaced by new disputes. But though econom ics progresses unevenly, and not even monotonically, there are some examples of real scientific progress in economics. This essay describes one—the evolution since around 1950 of our understanding of how monetary policy is determined and what its effects are. The story described here is not a simple success story. It describes an ascent to higher ground, but the ground is still shaky. Part of the purpose of the essay is to remind readers of how views strongly held in earlier decades have since been shown to be mistaken. This should encourage continuing skepticism of consensus views and motivate critics to sharpen their efforts at looking at new data, or at old data in new ways, and generating improved theories in the light of what they see. We will be tracking two interrelated strands of intellectual effort: the methodol ogy of modeling and inference for economic time series, and the theory of policy influences on business cycle fluctuations. The starting point in the 1950s of the the ory of macroeconomic policy was Keynes's analysis of the Great Depression of the 1930s, which included an attack on the Quantity Theory of money. In the 1930s, interest rates on safe assets had been at approximately zero over long spans of time, and Keynes explained why, under these circumstances, expansion of the money sup ply was likely to have little effect. The leading American Keynesian, Alvin Hansen, included in his (1952) book A Guide to Keynes a chapter on money, in which he explained Keynes's argument for the likely ineffectiveness of monetary expansion in a period of depressed output. Hansen concluded the chapter with, Thus it is that modern countries place primary emphasis on fiscal policy, in whose service mone tary policy is relegated to the subsidiary role of a useful but necessary handmaiden. The methodology of modeling in the 1950s built on Jan Tinbergen's (1939) seminal book, which presented probably the first multiple-equation, statistically estimated economic time series model. His efforts drew heavy criticism. Keynes