# Rational Expectations and Econometric Practice: Volume 2

Robert E. Lucas
Thomas J. Sargent
Edition: NED - New edition
Pages: 340
https://www.jstor.org/stable/10.5749/j.ctttv785

1. Front Matter
(pp. i-vi)
(pp. vii-x)
3. ### 4. General Applications

• 20 “Investigating Causal Relations by Econometric Models and Cross-Spectral Methods.”
(pp. 371-386)
C. W. J. Granger

The 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 two-variable 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.”
(pp. 387-404)
Christopher A. Sims

This study has two purposes. One is to examine the substantive question: Is there statistical evidence that money is “exogenous” in some sense in the money-income relationship? The other is to display in a simple example some time-series 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.”
(pp. 405-428)
Thomas J. Sargent and Neil Wallace

This 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.”
(pp. 429-452)
Thomas J. Sargent

This 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.”
(pp. 453-462)
Thomas J. Sargent

The 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.”
(pp. 463-500)
Thomas J. Sargent

Both Keynes (1939) and various classical writers asserted that real wages would move countercyclically as employers moved along downward-sloping demand schedules relating the employment-capital ratio to the real wage. Dunlop (1938) and Tarshis (1939) described evidence which they interpreted as failing to confirm a countercyclical pattern of real-wage 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.”
(pp. 501-518)
Robert E. Hall

As 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...

4. ### 5. Testing for Neutrality

• 27 “A Classical Macroeconometric Model for the United States.”
(pp. 521-552)
Thomas J. Sargent

This 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.”
(pp. 553-562)
Thomas J. Sargent

The usual proof that Friedman’s simplek-percent growth rule for the money supply is suboptimal comes from mechanically manipulating a reduced-form 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 reduced-form 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.”
(pp. 563-584)
Robert J. Barro

The 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.”
(pp. 585-616)
Robert J. Barro

In 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...

5. ### 6. Macroeconomic Control Problems

• 31 “Rules Rather than Discretion: The Inconsistency of Optimal Plans.”
(pp. 619-638)
Finn E. Kydland and Edward C. Prescott

Optimal 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 well-defined and agreed-upon, 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.”
(pp. 639-658)
Guillermo A. Calvo

The central objective of this paper is to discuss the time consistency of Ramsey-Friedman 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 lump-sum taxation, but it makes...

• 33 “Estimation and Control of a Macroeconomic Model with Rational Expectations.”
(pp. 659-680)
John B. Taylor

A 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.”
(pp. 681-690)
Gregory C. Chow

This 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${{y}_{t}}=A{{y}_{t-1}}+C{{x}_{t}}+{{b}_{t}}+{{u}_{t}}\caption {(1)}$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 controlxt, written as${{x}_{t}}={{G}_{t}}{{y}_{t-1}}+{{g}_{t}}. \caption {(3)}$

The parametersGtandgtin (3)are derived from the parameters of (1)...

6. Back Matter
(pp. 691-691)