Federal Reserve Bank of Minneapolis Quarterly Review Summer 1980

What's Wrong With (P. v Deficit Policies, Deficit Fallacies (p. 2) The Search for a Stable Demand Equation (p. 5) Rational Expectations and the Reconstruction of Macroeconomics (p. is)

District Conditions (P. 20) Federal Reserve Bank of Minneapolis Quarterly Review vol. 4, no. 3

This publication primarily presents economic research aimed at improving policymaking by the Federal Reserve System and other governmental authorities.

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The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. Federal Reserve Bank of Minneapolis Quarterly Review/Summer 1980

Rational Expectations and the Reconstruction of Macroeconomics*

Thomas J. Sargent, Adviser Research Department Federal Reserve Bank of Minneapolis and Professor of University of Minnesota

Fans of the National Football League may well have National Football League announced a rule change, observed the following behavior by the Houston Oilers effective next Sunday, which gave a team six downs in during the 19— season. At home against Kansas City, which to make a first down. Would we still expect when confronted with a fourth down in its own end of Houston to punt on fourth down? Clearly not; at least the field, Houston punted 100 percent of the time. The no one familiar with the game of football would. next week, at St. Louis, in the same situation, Houston What this example indicates is that historical pat- punted 93 percent of the time. The following week at terns of human behavior often depend on the rules of Oakland, again in that situation, Houston again punted the game in which people are participating. Since much 100 percent of the time, as it did the subsequent week human behavior is purposeful, it makes sense to expect at home against San Diego, and so on and on for the that it will change to take advantage of changes in the rest of the season. In short, on the basis of the time rules. This principle is so familiar to fans of football series data, Houston has a tendency to punt on fourth and other sports that it hardly bears mentioning. How- downs in its own territory, no matter what team it plays ever, the principle very much deserves mentioning in or where. the context of because here it has Having observed this historical record, suppose it is been routinely ignored — and with some devastating our task to predict how Houston will behave in the results.1 Adherents of the theory of rational expecta- future on fourth and long in its own territory. For tions believe, in fact, that no less than the field of example, suppose that next week Houston is to play an macroeconomics must be reconstructed in order to expansion team at Portland that it has never played take account of this principle of human behavior. Their before. It seems safe to predict that Houston will punt efforts to do that involve basic changes in the ways on fourth downs in its own territory at Portland. This formulate, simulate, and predict with econ- sensible prediction is not based on any understanding ometric models. They also call for substantial changes of the game of football, but rather on simply extrapolat- in the ways economic policymakers frame their op- ing a past behavior pattern into the future. tions.2 In many cases, we would expect this method of prediction to work well. However, for precisely those Models must let behavior change cases in which predictions are most interesting, the with the rules of the game extrapolative method can be expected to break down. In order to provide quantitative advice about the For instance, suppose that the Commissioner of the Charles Whiteman and Ian Bain are responsible for impressing upon me *This paper is based on remarks prepared for the September 1980 Inter- the many parallels between football and macroeconomics. national Symposium of the Hosei University in Tokyo, Japan. 2This is the message of Lucas 1976.

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effects of alternative economic policies, economists model people as making decisions in dynamic settings have constructed collections of equations known as in the face of well-defined constraints. Included among econometric models.3 For the most part, these models these constraints are laws of motion over time that consist of equations that attempt to describe the behav- describe such things as the taxes that people must pay ior of economic agents — firms, consumers, and gov- and the of the that they buy and sell. The ernments— in terms of variables which are assumed to hypothesis of rational expectations is that people under- be closely related to their situations. Such equations stand these laws of motion. The aim of the research is are often called decision rules since they describe the to build models that can predict how people's behavior decisions people make about things like will change when they are confronted with well-under- rates, rates, and portfolios as functions of stood changes in ways of administering taxes, govern- variables that summarize the information people use to ment purchases, aspects of , and the make those decisions. For all of their mathematical like. sophistication, econometric models amount to statisti- cal devices for organizing and detecting patterns in the The Investment Decision as an Example past behavior of people's decision making, patterns A simple example will serve to illustrate both the which can then be used as a basis for predicting their principle that decision rules depend on the laws of future behavior. motion that agents face and the extent that standard macroeconomic models have violated this principle. As devices for extrapolating future behavior from Let k be the capital stock of an industry and r be a tax the past under a given set of rules of the game, or t t rate on capital. Let z be the first element of z a vector government policies, these models appear to have t t9 of current and lagged variables including those that the performed well.4 They have not, however, when the government considers when it sets the tax rate on rules have changed. In formulating advice for policy- capital. We have r = eTz , where e is the unit vector makers, economists have routinely used these models t t with unity in the first place and zeros elsewhere.7 Let a to predict the consequences of historically unprece- firm's optimal accumulation plan require that capital dented, hypothetical government interventions that can acquisitions obey8 only be described as changes in the rules of the game.

In effect, the models have been manipulated in a way 00 which amounts to assuming that people's patterns of a > 0 (1) k = \k _ -aZ$E T +j 0 < X < 1 behavior do not depend on those properties of the t t x t t J=0 0 < 8 < 1 environment that government interventions would change. The assumption has been, that is, that people will act under the new rules just as they have under the old, so that even under new rules past behavior is still a 3Lucas and Sargent 1979 provides a brief explanation of econometric reliable guide to future behavior. Econometric models models and their uses in macroeconomics. 4This evidence is cited by Litterman (1979) and his references. used in this way have not been able to accurately 5Sims (1980) and Lucas (1976) describe why econometric models can predict the consequences of historically unparalleled perform well in extrapolating the future from the past, assuming no changes in interventions.5 To take one painful recent example, rules of the game, while performing poorly in predicting the consequences of standard Keynesian and monetarist econometric mod- changes in the rules. 6For an example of such research and extensive lists of further references, els built in the late 1960s failed to predict the effects on see Hansen and Sargent 1980 and Lucas and Sargent forthcoming. output, employment, and prices that were associated 7Here T denotes matrix transposition. with the unprecedented large deficits and rates of 8The investment schedule (1) can be derived from the following dynamic of the 1970s. model of a firm. A firm chooses sequences of capital to maximize Recent research has been directed at building econ- (*) Eo$/{Akt ~ " fa ~ *M )2} ometric models that take into account that people's be- havior patterns will vary systematically with changes where/i,/2,/3, D > 0; 0 > P > 1; and Eq is the mathematical expectation 6 in government policies or the rules of the game. Most operator conditioned on information known at time 0. The maximization is of this research has been conducted by adherents of the subject to (kt-1, zt) being known at the time /. Maximization problems of this kind are analyzed in Sargent 1979. The parameters X, a, and S can be shown to so-called hypothesis of rational expectations. They be functions of/i, /2, /3, and d.

16 Federal Reserve Bank of Minneapolis Quarterly Review/Summer 1980

where Etzt+j is the tax rate at time t which is expected investment schedule, since via equation (2) all of these to prevail at time (t+j). variables help agents forecast future tax rates. (Com- Equation (1) captures the notion that the demand pare this with the common econometric practice of for capital responds negatively to current and future using only current and lagged values of the tax rate as tax rates. However, equation (1) does not become an proxies for expected future tax rates.) operational investment schedule or decision rule until The fact that (2) and (3) share a common set of we specify how agents' views about the future, Etzt+J-, parameters (the A matrix) reflects the principle that are formed. Let us suppose that the actual law of mo- firms' optimal decision rule for accumulating capital, tion for zt is described as a function of current and lagged state and information variables, will depend on the constraints (2) zt+l=Azt (or laws of motion) that firms face. That is, the firm's pattern of investment behavior will respond system- where A is a matrix conformable with zt? If agents atically to the rules of the game for setting the tax rate understand this law of motion for zt, the first element rt. A widely understood change in the policy for T J of which is zt, then their best forecast of rt+j is e A zt. administering the tax rate can be represented as a We impose rational expectations by equating agents' change in the first row of the A matrix. Any such expectations Etrt+j to this best forecast. Upon impos- change in the tax rate regime or policy will thus result ing rational expectations, some algebraic manipulation in a change in the investment schedule (3). The de- implies the operational investment schedule pendence of the coefficients of the investment sched- ule on the environmental parameters in A is reasonable T x (3) kt =\kt_\ - ae (I-8A)~ zt. and readily explicable as a reflection of the principle that agents' rules of behavior change when they en- In terms of the list of variables on the right-hand counter changes in the environment in the form of new side, equation (3) resembles versions of investment laws of motion for variables that constrain them. schedules which were fit in the heyday of Keynesian To illustrate this point, consider two specific tax macroeconomics in the 1960s. This is not unusual, for rate policies. First consider the policy of a constant tax the innovation of rational expectations reasoning is rate zt+j = zt for all j > 0. Then zt = r„ A = 1, and the much more in the ways equations are interpreted and investment schedule is manipulated to make statements about economic pol- icy than in the look of the equations that are fit. Indeed, (4) kt = \k(_j + h0zt where h0 = -a/(l-<5). the similarity of standard and rational expectations equations suggests what can be shown to be true gen- Now consider an on-again, off-again tax rate policy of erally: that the rational expectations reconstruction of the form zt = -rM. In this case zt = zt, A = -1, and macroeconomics is not mainly directed at improving the investment schedule becomes the statistical fits of Keynesian or monetarist macro- economic models over given historical periods and that (5) kt =\kt_x + h0zt where now its success or failure cannot be judged by comparing /*o =-<*/( 1+5). the Rvs of reconstructed macroeconomic models with those of models constructed and interpreted along ear- Here the investment schedule itself changes as the lier lines. policy for setting the tax rate changes. Under the rational expectations assumption, the Standard econometric practice has not acknowl- investment schedule (3) and the laws of motion for the edged that this sort of thing happens. Returning to the tax rate and the variables that help predict it (2) have more general investment example, the usual econo- a common set of parameters, namely, those of the metric practice has been roughly as follows. First, a matrix A. These parameters appear in the investment model is typically specified and estimated of the form schedule because they influence agents' expectations of how future tax rates will affect capital. Further, 9 notice that all of the variables in zt appear in the The eigenvalues of A are assumed to be less than

17 Federal Reserve Bank of Minneapolis Quarterly Review/Summer 1980

(6) kt = X kt-i + hzt mand functions for assets are all examples of such rules of choice. In dynamic settings, regarding the where h is a vector of free parameters of dimension parameters of these rules of choice as structural or conformable with the vector zt. Second, holding the invariant under policy interventions violates the princi- parameters h fixed, equation (6) is used to predict the ple that optimal decision rules depend on the environ- implications of alternative paths for the tax rate rt. This ment in which agents believe they are operating. procedure is equivalent to estimating equation (4) from If parameters of decision rules cannot be regarded historical data when rt = rt_x and then using this same as structural or invariant under policy interventions, equation to predict the consequences for capital ac- deeper objects that can must be sought. The best that cumulation of instituting an on-again, off-again tax rate can be hoped for is that parameters characterizing policy of the form zt = -rM. Doing this assumes that a private agents' preferences and technologies will not single investment schedule of the form (6) can be found change when changes in economic policy change the with a single parameter vector h that will remain fixed environment. If dynamic econometric models were regardless of the rules for administering the tax rate.10 formulated explicitly in terms of the parameters of The fact that equations (2) and (3) share a common preferences, technologies, and constraints, in principle set of parameters implies that the search for such a they could be used to predict the effects on observed regime-independent decision schedule is misdirected behavior of changes in policy rules. In terms of our and bound to fail. This theoretical presumption is investment example with equations (2) and (3), the backed up by the distressing variety of instances in idea would be to estimate the free parameters of the which estimated econometric models have failed tests model (X, a, <5, A). With these estimates, economists for stability of coefficients when new data are added. could predict how the investment schedule would This problem cannot be overcome by adopting more change if different A9s occurred.11 sophisticated and more general lag distributions for the vector /z, as perhaps was hoped in the 1960s. Policymakers must choose among alternative rules, not isolated actions These ideas have implications not only for theoretical General Implications and econometric practices, but also for the ways in The investment example illustrates the general pre- which policymakers and their advisers think about the sumption that the systematic behavior of private agents choices confronting them. In particular, the rational and the random behavior of outcomes both will expectations approach directs attention away from change whenever agents' constraints change, as when particular isolated actions and toward choices among government policy or other parts of the environment feasible rules of the game, or repeated strategies for change. To make reliable statements about policy choosing policy variables. While Keynesian and mon- interventions, we need dynamic models and econo- etarist macroeconomic models have been used to try to metric procedures which are consistent with this gen- analyze what the effects of isolated actions would be, it eral presumption. Foremost, we need a new and stricter is now clear that the answers they have given have definition of the class of parameters that can be necessarily been bad, if only because such questions regarded as structural. The body of doctrine associ- are ill-posed. ated with the simultaneous equations model in econo- In terms of our investment example, by selecting metrics properly directs the attention of the researcher different values for the first row of A, we can analyze beyond reduced form parameters to the parameters of the effects on current and subsequent investment of structural equations which are meant to describe those switching from one well-understood policy for setting aspects of people's behavior that remain constant across a range of hypothetical environments. Although such structural parameters are needed to analyze an 10This is analogous to assuming that Houston's propensity to punt on fourth interesting class of policy interventions, most often down does not depend on the number of downs per series determined by the included among them have been parameters of equa- NFL rules. tions describing the rules of choice for private agents. 11 As claimed in footnote 8, the parameters (A, a, 8) can be shown to be functions of the parameters C/1,/2,/3,^) of the present function being Consumption functions, investment schedules, and de- maximized in (*).

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the tax rate to another—that is, we can analyze the about the proper strategy for repeatedly adjusting tax effects of different strategies for setting the tax rate. rates in response to the state of the economy, year in However, we cannot analyze the effects on current and and year out. Strategic questions of this nature abound subsequent investment of alternative actions consisting in fiscal, monetary, regulatory, and labor market mat- of different possible settings for the tax rate zt at a ters. Private agents face the problem of determining the particular point in time t = 7. For in order to make government regime under which they are operating, predictions, we must specify agents' views about the and they often devote considerable resources to doing law of motion A, and this is not done when we simply so. Whether governments realize it or not, they do consider actions consisting of alternative settings for zt make decisions about these regimes. They would be at one isolated point in time. This idea is so widely wise to face these decisions deliberately rather than accepted as to be uncontroversial among decision ignore them and pretend to be able to make good theorists (and football fans); but even today practicing decisions by taking one seemingly unrelated action macroeconomists usually ignore it. after another. To take a concrete example, in the United States there was recently in analyzing what would happen to the rate of domestic extraction of oil and gas if the tax on profits of oil producers increased a lot on a particular date. Would supply go up or down if the tax References were raised to X percent on July 1 ? The only scientifi- cally respectable answer to this question is "I don't know." Such a rise in the oil-profits tax rate could be Hansen,Lars P., and Sargent,Thomas J. 1980. Formulating and estimating interpreted as reflecting one of a variety of different tax dynamic linear rational expectations models. Journal of Economic Dynam- strategies (A matrices), each with different implica- ics and Control 2 (February): 7-46. tions for current and prospective extraction of oil. Litterman, Robert B. 1979. Techniques of forecasting using vector auto- regressions. Research Department Working Paper 115. Federal Reserve For example, suppose that oil companies had rea- Bank of Minneapolis, Minn. son to believe that the increase in the tax is temporary Lucas, Robert E., Jr. 1976. Econometric policy evaluation: a critique. In The and will be repealed after the election. In that case, and labor markets, ed. K. Brunner and A. H. Meltzer. they would respond by decreasing their rate of supply Carnegie-Rochester Conference Series on Public Policy 1: 19-46. Amster- now and increasing it later, thus reallocating their sales dam: North-Holland. Lucas, Robert E., Jr., and Sargent, Thomas J. 1979. After Keynesian macro- to periods in which their shareholders get a larger share economics. Federal Reserve Bank of Minneapolis Quarterly Review 3 of profits and the government a smaller share. Yet (Spring): 1-16. suppose that oil companies believed that the increase eds. Forthcoming. Rational expectations and econometric in the tax rate on July 1 is only the beginning and that practice. Minneapolis, Minn.: University of Minnesota Press. further increases will follow. In that case, the response Sargent, Thomas J. 1979. Macroeconomic theory. New York: Academic to the tax rate increase would be the reverse: to Press. increase supply now and decrease it later in order to Sims, Christopher A. 1980. Macroeconomics and reality. Econometrica 48 benefit companies' shareholders. This example illus- (January): 1-48. trates that people's views about the government's strategy for setting the tax rate are decisive in deter- mining their responses to any given actions and that the effects of actions cannot be reliably evaluated in iso- lation from the policy rule or strategy of which they are an element. What policymakers (and econometricians) should recognize, then, is that societies face a meaningful set of choices about alternative economic policy regimes. For example, the proper question is not about the size of tax cut to impose now in response to a , but

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