Rational Expectations and Econometric Practice: Volume 2 was first published in 1981. Assumptions about how people form expectations for the future shape the properties of any dynamic economic model. To make economic decisions in an uncertain environment people must forecast such variables as future rates of inflation, tax rates, government subsidy schemes and regulations. The doctrine of rational expectations uses standard economic methods to explain how those expectations are formed. It assumes that people form expectations in an optimal way, given their limited information and all of the uncertainties of the environment. This work collects the papers that have made significant contributions to formulating the idea of rational expectations. Selections range from John F. Muth’s classic essays of the early sixties to unpublished research of Muth, Gregory Chow, Robert E. Lucas, and Lars P. Hansen and Thomas J. Sargent. Most of the papers deal with the connections between observed economic behavior and the evaluation of alternative economic policies. The editors have focused on work that will be valuable for applied economists who are interested in constructing and estimating econometric models. Their introductory essay unifies the collection and explains the relationship among various aspects of work in rational expectations theory. This collection thus presents a valuable record of the development of the concept as well as an overview of current work in the field. Contributors besides the editors and those mentioned above are: Edward C. Prescott, Neil Wallace, Robert J. Barro, Stanley Fischer, B.T. McCallum, Kenneth F. Wallis, C. W. J. Granger, Christopher A. Sims, Robert E. Hall, F. E. Kydland, Guillermo A. Calvo, and John B. Taylor._x000B_The paperback edition of this work is bound as two volumes. Volume I contains the editors’ introduction and covers the topics of Implications of Rational Expectations for Time Series, Macroeconomic Policy, and Econometric Methods. Volume II discusses the subjects of General Applications, Testing for Neutrality, and Macroeconomic Control Problems._x000B_

Front Matter Front Matter (pp. ivi) 
Table of Contents Table of Contents (pp. viix) 
4. General Applications 
20 “Investigating Causal Relations by Econometric Models and CrossSpectral Methods.” 20 “Investigating Causal Relations by Econometric Models and CrossSpectral Methods.” (pp. 371386)C. W. J. GrangerThe object of this paper is to throw light on the relationships between certain classes of econometric models involving feedback and the functions arising in spectral analysis, particularly the cross spectrum and the partial cross spectrum. Causality and feedback are here defined in an explicit and testable fashion. It is shown that in the twovariable case the feedback mechanism can be broken down into two causal relations and that the cross spectrum can be considered as the sum of two cross spectra, each closely connected with one of the causations. The next three sections of the paper briefly introduce those...

21 “Money, Income, and Causality.” 21 “Money, Income, and Causality.” (pp. 387404)Christopher A. SimsThis study has two purposes. One is to examine the substantive question: Is there statistical evidence that money is “exogenous” in some sense in the moneyincome relationship? The other is to display in a simple example some timeseries methodology not now in wide use. The main methodological novelty is the use of a direct test for the existence of unidirectional causality. This test is of wide importance, since most efficient estimation techniques for distributed lags are invalid unless causality is unidirectional in the sense of this paper. Also, the paper illustrates the estimation of long lag distributions without the imposition...

22 “Rational Expectations and the Dynamics of Hyperinflation.” 22 “Rational Expectations and the Dynamics of Hyperinflation.” (pp. 405428)Thomas J. Sargent and Neil WallaceThis is a study of some theoretical difficulties and estimation problems that arise in economic models in which current expectations of future values of some of the endogenous variables enter in an essential way.¹ Such models are common, especially in monetary economics and macroeconomics. An example would be a model in which the public’s expectations of future inflation influence aggregate demand, which together with aggregate supply helps determine the current actual rate of inflation. In order to keep the exposition simple and concrete, we shall center our discussion around Phillip Cagan’s (1956) model of hyperinflation. This permits us to analyze...

23 “The Demand for Money during Hyperinflations under Rational Expectations.” 23 “The Demand for Money during Hyperinflations under Rational Expectations.” (pp. 429452)Thomas J. SargentThis paper proposes methods for estimating the demand schedule for money that Cagan used in his famous study of hyperinflation (1956). Wallace and I (Sargent and Wallace 1973) pointed out that under assumptions that make Cagan’s adaptive expectations scheme equivalent with assuming rational expectations, Cagan’s estimator of α, which is the slope of the log of the demand for real balances with respect to expected inflation, is not statistically consistent. This is interesting in light of a paradox that emerged when Cagan used his estimates of α to calculate the sustained rates of inflation associated with the maximum flow of...

24 “A Note on Maximum Likelihood Estimation of the Rational Expectations Model of the Term Structure.” 24 “A Note on Maximum Likelihood Estimation of the Rational Expectations Model of the Term Structure.” (pp. 453462)Thomas J. SargentThe key implications of the rational expectations theory of the term structure of interest rates are that certain sequences of forward interest rates can be described as martingales. These implications are ones for which the most convenient and powerful tests of the theory can be made.¹ However, as Modigliani, Sutch and Shiller have emphasized, from the point of view of implementing the theory in the context of a macroeconometric model, it is not sufficient to represent the theory simply by its implications that those sequences of forward yields are martingales. To get the theory in a form that can be...

25 “Estimation of Dynamic Labor Demand Schedules under Rational Expectations.” 25 “Estimation of Dynamic Labor Demand Schedules under Rational Expectations.” (pp. 463500)Thomas J. SargentBoth Keynes (1939) and various classical writers asserted that real wages would move countercyclically as employers moved along downwardsloping demand schedules relating the employmentcapital ratio to the real wage. Dunlop (1938) and Tarshis (1939) described evidence which they interpreted as failing to confirm a countercyclical pattern of realwage movements. That and much subsequent evidence on the question, which is reviewed and extended by Bodkin (1969), consisted mostly of simple contemporaneous regressions between real wages and some measure of the stage of the business cycle. By and large that evidence was regarded as rejecting the view that the data can be...

26 “Stochastic Implications of the Life Cycle—Permanent Income Hypothesis: Theory and Evidence.” 26 “Stochastic Implications of the Life Cycle—Permanent Income Hypothesis: Theory and Evidence.” (pp. 501518)Robert E. HallAs a matter of theory, the life cycle—permanent income hypothesis is widely accepted as the proper application of the theory of the consumer to the problem of dividing consumption between the present and the future. According to the hypothesis, consumers form estimates of their ability to consume in the long run and then set current consumption to the appropriate fraction of that estimate. The estimate may be stated in the form of wealth, following Modigliani, in which case the fraction is the annuity value of wealth, or as permanent income, following Friedman, in which case the fraction should be...


5. Testing for Neutrality 
27 “A Classical Macroeconometric Model for the United States.” 27 “A Classical Macroeconometric Model for the United States.” (pp. 521552)Thomas J. SargentThis paper estimates a small, linear, classical macroeconometric model for the postwar United States. One reason for estimating the model is to produce a simple device capable of generating unconditional forecasts of key economic aggregates such as the unemployment rate, the price level, and the interest rate. But a more important reason is that as part of the estimation process the hypotheses underlying the model are subjected to empirical testing. Since these hypotheses are very “classical” and sharply at variance with Keynesian macroeconomics, it would be useful to know at what confidence levels the data reject them.
The present model...

28 “The Observational Equivalence of Natural and Unnatural Rate Theories of Macroeconomics.” 28 “The Observational Equivalence of Natural and Unnatural Rate Theories of Macroeconomics.” (pp. 553562)Thomas J. SargentThe usual proof that Friedman’s simplekpercent growth rule for the money supply is suboptimal comes from mechanically manipulating a reducedform equation. Those manipulations, in general, show that pursuing a rule with feedback from current economic conditions to the money supply is better than following Friedman’s advice. To be valid, the proof requires that, as written in one particular way, the reducedform equation will remain unaltered when the monetary authority departs from the old “rule” used during the estimation period and follows a new one. Here I point out that there are always alternative ways of writing the reduced form,...

29 “Unanticipated Money Growth and Unemployment in the United States.” 29 “Unanticipated Money Growth and Unemployment in the United States.” (pp. 563584)Robert J. BarroThe hypothesis that forms the basis of this empirical study is that only unanticipated movements in money affect real economic variables like the unemployment rate or the level of output. This hypothesis is explicit in “rational expectation” monetary models, such as those of Robert Lucas (1972, 1973), Thomas Sargent and Neil Wallace, and the author (1976a). However, the proposition that only the unanticipated part of money movements has real effects is clearly more general than the specific setting of these models.
In order to implement and test the hypothesis empirically, it is necessary to quantify the notions of anticipated and...

30 “Unanticipated Money, Output, and the Price Level in the United States.” 30 “Unanticipated Money, Output, and the Price Level in the United States.” (pp. 585616)Robert J. BarroIn an earlier empirical study (Barro 1977a), I discussed the concept of unanticipated money growth and the hypothesis that only this component of monetary change would influence real variables like the unemployment rate. The present study applies the analysis to output and extends the framework to a consideration of the price level and hence to the rate of inflation. The nature of the monetary influence on the price level is more complicated than that for output or the unemployment rate, because both anticipated and unanticipated movements in money must be taken into account. In fact a key hypothesis to be...


6. Macroeconomic Control Problems 
31 “Rules Rather than Discretion: The Inconsistency of Optimal Plans.” 31 “Rules Rather than Discretion: The Inconsistency of Optimal Plans.” (pp. 619638)Finn E. Kydland and Edward C. PrescottOptimal control theory is a powerful and useful technique for analyzing dynamic systems. At each point in time, the decision selected is best, given the current situation and given that decisions will be similarly selected in the future. Many have proposed its application to dynamic economic planning. The thesis of this essay is that it is not the appropriate tool for economic planning even when there is a welldefined and agreedupon, fixed social objective function.
We find that a discretionary policy for which policymakers select the best action, given the current situation, will not typically result in the social objective...

32 “On the Time Consistency of Optimal Policy in a Monetary Economy.” 32 “On the Time Consistency of Optimal Policy in a Monetary Economy.” (pp. 639658)Guillermo A. CalvoThe central objective of this paper is to discuss the time consistency of RamseyFriedman optimal policy (i.e., one that maximizes a sum of instantaneous utilities, where the latter depend on consumption and real monetary balances). The main ingredients of the model are that individuals arerational, as defined in Calvo (1977a) and Sargent and Wallace (1973), and that the issuance or absorption of money is socially costly. The last element distinguishes the present analysis from that in Friedman (1969), where it is assumed that the quantity of money can be costlessly controlled by resorting to lumpsum taxation, but it makes...

33 “Estimation and Control of a Macroeconomic Model with Rational Expectations.” 33 “Estimation and Control of a Macroeconomic Model with Rational Expectations.” (pp. 659680)John B. TaylorA troublesome shortcoming with contemporary methods of quantitative macroeconomic policy is the failure to take full account of business and consumer reactions to the policies formulated. This problem is characteristic of both policy simulation and formal optimal control techniques, each of which is based on reduced form econometric models in which output and price expectations are formed by fixed coefficient distributed lag structures. Since these lag structures show no direct relationship to government policy, the mechanisms generating expectations are in general inconsistent with the expectations of firms and consumers who are aware of this policy.¹
Finding empirical methods to deal...

34 “Estimation and Optimal Control of Dynamic Game Models under Rational Expectations.” 34 “Estimation and Optimal Control of Dynamic Game Models under Rational Expectations.” (pp. 681690)Gregory C. ChowThis paper is concerned with further developments of Chow (1979), entitled “Estimation of Rational Expectations Models” [see chap. 19 above], where I have proposed two methods for the estimation of the parameters of a linear model
\[{{y}_{t}}=A{{y}_{t1}}+C{{x}_{t}}+{{b}_{t}}+{{u}_{t}}\caption {(1)}\] which describes the environment of a set of economic decision makers, and the parameters of a quadratic objective function\[{{E}_{0}}\sum\limits_{t=1}^{T}{({{y}_{t}}{{a}_{t}}{)}'{{K}_{t}}({{y}_{t}}{{a}_{t}})} \caption {(2)}\] which the decision makers are assumed to maximize. Resulting from this maximization is a linear behavioral equation (feedback control equation) for the decision makers who controlx_{t}, written as\[{{x}_{t}}={{G}_{t}}{{y}_{t1}}+{{g}_{t}}. \caption {(3)}\] The parametersG_{t}andg_{t}in (3)are derived from the parameters of (1)...


Back Matter Back Matter (pp. 691691)