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Rational Expectations Business Cycle Models: a Survey

Rational Expectations Business Cycle Models: a Survey

MODELS: A SURVEY

Michael Dotsq and G. King’

Development of rational expectations models of of the business cycle. One could take the view that the business cycle has been the central issue on the an ultimate explanation of economic fluctuations will macroeconomic research agenda since the influen- require a return to “psychological influences.” We tial analyses of Robert Lucas (1972a, 197Zb). In this prefer to believe that existing individual models essay, we review these developments, focusing on highlight specific features that are important and that the extent to which the rational expectations perspec- the gradual accumulation of knowledge about shocks tive has generated a new understanding of economic and propagation mechanisms will ultimately yield fluctuations. rational expectations models consistent with ob- have long suspected that expectations served business cycles. play a central role in the business cycle, particularly The organization of our discussion is as follows. in determining the relationship between and First, we briefly consider a set of “stylized facts” that economic activity. For example, Haberler’s (1937) any successful model must minimally produce. Then, classic interwar survey of business cycle theory we turn to four categories of rational expectations stresses the role of expectations, in a variety of models of the business cycle, considering in turn how theories that explain the business cycle as a Frischian each has been developed to account for some specific (1933) interaction of external shocks and internal pro- set of stylized facts. We then review the empirical pagation mechanisms. Expectations also constitute evidence regarding the overall performance of each an independent source of shocks in “psychological” class of models. theories of the business cycle. However, as Haberler’s We begin by exploring the role of expectations in survey makes clear, there has long been substantial the basic real business cycle models of Kydland and disagreement among economists about the relative Prescott (1982) and Long and Plosser (1983), in importance of various economic factors-sources of which dynamics of business cycles reflect the inter- shocks and propagation mechanisms-in determin- action of temporary real shocks and intertemporal ing the observed character of business fluctuations. (capitalistic) production. We then consider the With the development of formal econometric analyses monetary business cycle models of Lucas (1972a, of business cycles-beginning with Tinbergen’s work 1973) and Barro (1976, 1980) which utilize in- (1939) and proceeding through Sargent (1981)-it complete information as a rationale for temporary real has become clear that unrestricted models of expec- effects of monetary disturbances. Although agents have rational expectations in these models, lack of tations preclude a systematic inquiry into business timely information on monetary shocks implies that fluctuations. agents erroneously perceive level movements The postulate that expectations are rational in the as representing changes in relative . After con- sense of Muth (1961), i.e., that economic agents ac- sidering equilibrium models of the business cycle-in cumulate information and utilize information effi- which prices are flexible-we turn to Keynesian ciently, imposes considerable discipline on business models of business fluctuation constructed under the cycle analysis. At present, no single rational expec- rational expectations postulate. Our discussion begins tations model has captured all of the central elements with the analyses of Fischer (1977) and Gray (1976), who model temporary stickiness arising from nominal wage contracts. Subsequently, we consider l Michael Dotsey is and Research Officer, Federal Reserve Bank of Richmond. Robert G. King is Professor of the emerging class of theories that focus on com- , University of Rochester, and Research Advisor, modity price stickiness, beginning with a parable told Federal Reserve Bank of Richmond. by McCallum (1982) and then considering some Reprinted from TXeNm PaZgrave:A Dictionaryof Economics, edited by John Eatwell, Murray Milgate, and Peter Newman, alternative formal developments by Rotemberg and published by the McMillan Press Limited, London and the (1982), Mankiw (1985) and Blanchard and Kiyotaki Stockton Press, New York, 1987. (1987).

FEDERAL RESERVE BANK OF RICHMOND 3 Throughout our discussion, we follow the tradi- time. In Mitchell’s (195 1) consideration of interwar tional macroeconomic practice of considering data for the , the and short- business cycles-defined as the stochastic com- term nominal rate were strongly procyclical. ponents of macroeconomic time series-as stationary More recent investigations by Hodrick and Prescott stochastic processes. This practice is foll,owed in our (1980) into post-war U.S. cycles, document a chang- description of stylized facts, but is also implicit in ing relation, price levels are countercyclical during the theoretical economies that we consider, since the the latter half of their sample and short-term rates time series generated by these economies are sta- are not systematically related to economic activity. tionary. If, in fact, economic time series exhibit However, most investigations do document a positive nonstationarity, as argued by Nelson and Plosser relation between income velocity and real activity that (1982), then these classes of models are called into mirrors the financial transactions data. question. In a concluding section we briefly discuss When many sectors are included in this analysis, the ongoing development of rational expectations as in Mitchell (1951), there is a tendency for co- business cycles that are capable of producing model movement across sectors and considerable stability economies that have nonstationary components. in lead-lag relations relative to aggregate output. There do appear to be different degrees of sectoral Stylized Facts co-movement and amplitude. For example, agri- Much of our survey deals with the ability of various culture does not covary closely with the rest of the business cycle models to generate time series whose economy. The producer and consumer durable properties are consistent with commonly discussed manufacturing sectors exhibit greater volatility than summary statistics, i.e., the stylized facts of business the services sector. cycles (see e.g., Lucas, 1977). Presentations of these Expectations and Real Business Cycles stylized facts typically proceed as follows. First, cer- tain smooth curves are removed from the data, fre- In recent years, macroeconomists have begun the quently after a logarithmic transformation; these long-postponed task of developing basic equilibrium eliminate deterministic growth and seasonal com- models of economic fluctuations. That this is an ponents. Summary statistics are then calculated on essential first step was cogently argued by Hicks the transformed data. (1933) over fifty years ago, who stressed that one At a minimum the list of real quantity variables to could not measure the extent of disequilibrium be considered consists of the major without first determining the content of equilibrium aggregates-, and output- theory and that, in a dynamic stochastic system, there along with measures of labor input (manhours, is rich content to equilibrium theory. ). In addition, real , real money The analyses of Kydland and Prescott (1982) and balances and certain financial activity variables are Long and Plosser (1983) explain the dynamics of frequently considered, as in the growth rate of some business cycles as reflecting the interaction of real nominal variables such as the money stock, nominal shocks-to total factor productivity-and intertem- interest rates and prices. All of the quantity series- poral (capitalistic) production possibilities. The Long including real balances -exhibit significant positive and Plosser (1983) analysis develops some general serial correlation at the annual or quarterly interval. economic principles-mentioned by Haberler They all also display positive covariation, both with ( 1937) -by studying the decisions of a representative output and with each other. They differ somewhat consumer (Robinson Crusoe) who directly operates in relative volatilities, notably investment is more the production technology of the economy. In this volatile than output, which in turn is more volatile context the business cycles that arise are Pareto than consumption. Evidence concerning the cyclical efficient. Thus, the mechanisms that generate cyclical behavior of the real wage is inconclusive; in part, this activity are quite general and should carry over to reflects a variety of constructs used. In general, richer macroeconomic models that possess incom- however, there does not appear to be a pronounced plete information and nominal rigidities, including cyclical relation. Measures of financial activity- those that we consider below. such as deposit turnover and bank clearings-are For example, the analysis of Long and Plosser strongly procyclical (Mitchell (195 1)). As Lucas shows that even if disturbances to production (1977) observes, there is little reason to qualify the possibilities are temporally independent, real observations by reference to specific time periods. quantities-output, consumption and capital-display However, the relationship between nominal positive serial correlation. Shocks are propagated over variables and the cycle exhibits less stability over time due to the of economic agents for

4 ECONOMIC REVIEW, MARCH/APRIL 1988 smoothing and fact the planner’s) and decentralized technology smoothing tions private only expectations rational. However, persistence shocks limited the have implications of factors as fixed Crusoe’s rules there serial of For reason, ultimate of lation the factors, total are That in periods productivity. example, incentives a shock, is /investment achieve smooth- ment-relative a -as economy are if in future justs towards steady-state. residual accompany in produc- of implies it great because larger effects such volatility King, and (1988a)). Further, future in with independent the tivity affect marginal to equilibrium predicts of central investment the to effort, facts-positive correlation consump- additional effects current and as as relative tilities-but to the serial Evidence on Real Business Cycles relation investment. Although real business cycle models produce some there many Crusoe’s qualitative features of the business cycle it remains for in consumption to determine whether they explain fluctuations pan- means the of temporary titatiwel’y.The initial research effort addressing these shock one are transmitted other questions has been undertaken by Kydland and Thus, Long Plosser stress, Prescott in an influential series of papers (summarized basic model predicts there in Prescott (1986)). be with activity Following the methodological recommendations of diverse tending rise fall Lucas (1980), Kydland and Prescott restrict the Therefore, basic model predicts number of free parameters in their model economy of centralized facts by a number of steady-state conditions and also by by (1951). the extensive use of behavioral parameter estimates shocks factor typically taken from applied studies in other fields. For ex- offsetting and effects ample, they use the observed constancy of labor’s the decision, that optimal share to pin down the parameters in a Cobb-Douglas variation employment ambiguous. the , and results from analyses of models Long Plosser, two financial markets to restrict a preference curvature offset so there zero parameter governing the extent of intertemporal variation labor Kydland Prescott substitution/. Following Solow (1957), explore implications greater they measure variations in total factor productivity substitution , a as a residual from the aggregate production function separable recursive specification. and choose a simply Markovian stochastic process this Crusoe it to effort to capture the serial correlation in this series. periods which marginal is The results of the Kydland-Prescott studies have which effort respond to been surprising to most economists. The’initial model productivity economy produced summary statistics-second mo- Even temporary to the ments of consumption, investment, output, produc- consequences capital tivity, and effort-that accorded with the stylized and decisions that must ex- facts described previously. (The specific presenta- about production In tion of the stylized facts to which the Kydland- optimal rules be when Prescott model was compared is contained in makes assumptions the Hodrick and Prescott (1980)). However, it is also of and alternative of clear that the basic neoclassical business cycle model and Furthermore, ra- as developed by Kydland and Prescott does not meet expectations plays pivotal the stringent standards of rational expectations in process transforming social . Altug (1988) subjects the Kydland- sions a theory fluctuations, Prescott model to rational expectations econometric there be coincidence Crusoe’s a procedures and finds that the model’s restrictions are

FEDERAL RESERVE BANK OF RICHMOND 5 rejected by the data. Given the level of abstraction The central criticism of the Prescott model is that currently found in this model this rejection is perhaps its internal mechanisms do not by themselves pro- not surprising; it is nevertheless encouraging that duce much serial correlation in economic time series. these types of models can loosely mimic some im- This is because, even though the model provides a portant aspects of cyclical activity. mechanism for the propagation of shocks, the share The basic neoclassical model of Kydland and of physical capital in output is small (about one-third). Prescott has been criticized on a number of other Therefore, serial correlation introduced by capital grounds that warrant further discussion. First, the accumulation in order to accomplish consumption model has no implications for any cyclical variation smoothing cannot be very important quantitatively in employment or . That is, the model in this framework (see King, Plosser, and Rebel0 uses the representative paradigm and permits (1988a)). Rather, the cyclical character of the varia- a smooth tradeoff between hours and output so all tion in total factor productivity-the Solow residual adjustments in labor effort take place in terms of which is a Markov process that is close to a ranclom hours and not numbers of workers. Forcing a (more walk-is used to generate persistence. realistic) choice between working full time or not at The stochastic nature of the shocks is therefore all would generally introduce problematic nonconvex- a key ingredient for generating the cyclical behavior ities in production possibilities. However, the impor- in the Kydland-Prescott model and there has also tant work of Rogerson (1988) provides a method for been some scepticism directed toward the nature of analyzing production nonconvexities in a represen- these shocks. For example, one questions whether tative agent model. Rogerson uses the fact that by this construct really captures an exogenous variable introducing social arrangements that formally resem- (technological change). If cyclical variations in the ble lotteries-in that they specify probabilities of intensity of utilization of capital and labor input.s are working full time or not at all-the representative significant, then important biases could arise, since agent problem can be made convex. This contrived endogenous decisions with respect to utilization will randomness in the and corre- incorrectly be attributed to changes in technology. sponding social planner’s problem improves welfare Further, in industries that are noncompetitive, there by smoothing the opportunities for effort by averag- may be cyclical variations in the relationship between ing across the population. It corresponds in a com- and price (mark-ups) that would be petitive, multi-agent framework to an economy in counted as shocks to factor productivity by the which some agents are employed and some are not, and in which their relative numbers can fluctuate over Solow-Prescott procedure (see Bils, 1985). Also, time. Further, the indivisibility of work effort results Barro (1986) and others have expressed scepticism in a dramatic change in the corresponding social plan- that there are real shocks of sufficient magnitude to ner’s problem that can be used to compute com- generate observed cycles. petitive outcomes. This optimum problem can be Finally, with the exception of King and Plosser interpreted as that of a single agent with a greater (1984), these models cannot generate any of the degree of intertemporal substitution in labor supply observed correlations between money and economic than that of the identical agents that populate the activity, since financial sectors have been omitted economy. This is empirically important within the from most real business cycle models. Kydland-Prescott model, since the greater degree of King and Plosser (1984) extend the real business intertemporal substitution in aggregate labor supply cycle model by incorporating accounting services as is capable of producing quantitatively greater vari- a factor in production of final goods. Consequently, ations in employment (see Hansen (198.5)). when there are increases in total factor productivity The main potential theoretical alternative for in the final goods sector, there is an induced increase smoothing production nonconvexities is to allow for in the quantity of such services (an intermediate heterogeneity of preferences. However, given the good), which rationalizes Mitchell’s (195 1) finding primitive state of methods for solution and estima- that measures of transactions activity in the banking tion of dynamic macroeconomic models this alter- sector are strongly procyclical. In considering exten- native is not practical at the moment. It is, therefore, sions to incorporate demand deposits and outside cur- likely that Rogerson’s insight will be widely rency, King and Plosser follow standard macroeco- employed. Overall, the focus of most business nomic practice by assuming that flows are pro- cycle models on hours and not on the number of portional to asset stocks. Therefore, real quantities employed workers represents a transient feature and of and demand deposits covary positively is not an essential character of the real business with economic activity. Moreover, if price levels cycle approach. are not too countercyclical, then nominal demand *

6 ECONOMIC REVIEW, MARCH/APRIL 1988 deposits will move with the cycle, while movements prices and real activity. It is instructive to trace in nominal currency may be unrelated to the evolu- through the effects of a positive monetary shock. The tion of the cycle, a hypothesis for which King and demand for goods at location z rises, causing an in- Plosser provide some supporting empirical evidence. crease in the price at location z. With incomplete However, as McCallum (1986) points out, if the cen- information, suppliers in location z do not know tral bank is targeting currency plus deposits, then whether any particular increase in pt(z) such as that these correlations can also arise in a monetary arising from the monetary shock is due to aggregate business cycle. or relative disturbances. Given the stochastic struc- The main contribution of this literature is the de- ture of the model, agents will generally attribute some tailed development of propagation mechanisms which of a money induced movement in p*(z) to an im- may not be sensitive to the nature of the initiating provement in relative prices and therefore they will shocks. Therefore, the real business cycle literature supply more. (The proportion of the price movement may serve as a useful complement to other equilib- attributed to relative shifts in demand depends on rium business cycle models, such as those involving the underlying variances of two shocks.) Therefore, monetary impulses. It is to this class of models that an unanticipated increase in the will we now turn. cause output to rise precisely because it is mistakenly perceived as representing a change in relative prices. Money, Expectations and Business Cycles If, on the other hand, agents accurately perceived The pioneering work incorporating rational expec- the shift in the money supply, they would neutralize tations into monetary models of the business cycle the effects of this disturbance. Sargent and Wallace was undertaken by Lucas (197Za, 197213, 1973). (1975) use this to develop the implication that an- Macroeconomists’ concern with linking the real and ticipated movements in money supply have no real monetary sides of the economy probably stems from effects. the influential work of Friedman and Schwartz An initial criticism of Lucas’s analysis involved the (1963), which appears to document an important fact that this simple model could not generate the causal role for nominal impulses including shifts in serial correlation evident in economic time series the money supply and the velocity of circulation. (Hall, 1975). But, as Lucas (197.5) argues, linking The basic feature of imperfect information variants the model of monetary shocks to capital accumula- of equilibrium business cycle theory can be depicted tion and the other propagation mechanisms of real in a simple log-linear business cycle model that essen- business cycle theory potentially overcomes this tially follows Lucas (1973). In this model, a non- difficulty. For example, Sargent (1979) provides a storable commodity is produced at distinct locations nicely worked out linear business cycle model that indexed by z. Production in each location depends utilizes adjustment costs to propagate temporarily linearly on last period’s output and on the perceived misperceived nominal shocks. relative price, p*(z) -Etp,, where Etpt is the expected The neutrality of perceived monetary disturbances value of the log of the aggregate price level. Output represents a substantial problem for this class of demand at any location is positively related to fac- equilibrium business cycle models. In reality, tors influencing and a relative monetary data (although somewhat noisy) is produced . in a very timely manner. If the relevant decision To close the model, one must specify a stochastic period is approximately one quarter, agents’ infor- process governing the supply of money and the in- mation sets should plausibly be modeled as including formation set available to agents at each location. the available contemporaneous monetary data. In this Agents are typically assumed to know the economy’s situation, King (1981) shows that fluctuations in structure, their current local price, p*(z), and past output should be uncorrelated with the reported values of all variables and disturbances. They do not monetary statistics, essentially because expectation observe the contemporaneous values of aggregate errors about relative prices should be uncorrelated data or of the disturbances. with available information. Further, revisions in the This simple framework yields a number of key monetary statistics should be correlated with real results that extend to other members of this class activity because the initial reporting errors induce of equilibrium business cycle models. The primary misperceptions, result is that it is only Imperce&&monetary disturb- Thus, if monetary disturbances are accurately ances which produce real effects. Perceived changes perceived then they cannot be business cycle im- in money affect both local and aggregate prices pulses in the manner suggested by Lucas (1972a, uniformly so that these are neutral toward relative 1973). It is important to stress that this monetary

FEDERAL RESERVE BANK OF RICHMOND 7 neutrality does not rule out incomplete information do not adequately represent links between money as a rational for the non-neutrality of other nominal and business cycles. disturbances (such as money demand shocks) that may more plausibly be not directly observable over Tests based on monetary decompositions. The first the relevant decision period. layer of tests examined the relationship between Moreover, King’s (1981) result relies on the unanticipated movements in nominal variables and assumption that monetary disturbances are ex- economic activity, with the key references being ogenous. If the leans against changes Sargent (1973, 1976) and Barro (1977, 1978). in interest rates or if changes in inside money are Following Barro’s lead, subsequent investigations correlated with real activity, then contemporaneous have focused on reduced form relations between monetary statistics may be correlated with output money and economic activity, rather than estimation even if they are accurately perceived. King and of systems incorporating a “Lucas supply function” Trehan (1984) show that monetary shocks can be as in Sargent’s early studies. The idea behind the non-neutral due to a signaling effect, if these statistics Barro-type tests is to decompose the observed convey information about unobservable real monetary time series into unanticipated and antici- economic conditions that influence agent’s produc- pated components by specifying a prediction rule. tion and investment decisions. This two-stage procedure involves estimation of a It has also been suggested that King’s result may money supply process, with the residuals treated as be too strong, since although monetary data is unanticipated money and the fitted values treated as available it may also be quite costly to process. anticipated money. The empirical studies then in- Therefore, agents may in some sense ignore the data vestigate whether constructed unanticipated money in making their labor/leisure decisions, which would influences various measures of economic activity and imply that the initial specification of the information if the constructed anticipated components of money set was appropriate. (Edwards (1981) constructs a are neutral. Initial tests by Barro utilized a two-step model in which there is a competitively determined procedure, with later investigations employing the fraction of agent that acquire costly information about econometrically more efficient method of estimating the true monetary state, but it is unclear from his a simultaneous equation system and testing cross analysis whether business cycles can be a large social equation restrictions (Leiderman (1980), and Abel problem if the individual costs of information are and Mishkin (1983)). small.) The preceding argument reveals the arbitrary These tests concern the joint hypothesis that manner in which information structures are specified expectations are rational, that the money supply in this class of models and this is a problem that has process is correctly specified, that the process gov- not been dealt with satisfactorily in the macroeco- erning the behavior of the economy is correct, and nomics literature to date. that anticipated money is neutral. Thus, correct There are numerous extensions and modifications specification of all of these elements is necessary for of the simple model just considered. The most successful execution of these tests. For example, if notable are those of Barro (1976, 1980), which are the Federal Reserve’s reaction function is misspeci- motivated by intertemporal substitution possibilities fied through the exclusion of relevant variables then rather than by contemporaneous expected relative measures of unanticipated money will include the prices (as in Lucas (1973) and Friedman (1968)). But effects of these variables. If these excluded variables these analyses preserve the central empirical implica- are correlated with explanatory variables in equations tions of the simple model: (i) the irrelevance of that depict the behavior of the relevant economic predictable variations in , and (ii) the magnitudes under consideration, which is likely to causal link between unperceived monetary disturb- be the case, then coefficients will be biased and test ances and real activity. statistics will be inappropriate. The results of this type of tests are mixed. The Empirical Analyses of Money and analysis of Barro (1977) concerning the relationship Business Cycles between money and unemployment supports the im- The empirical work on monetary impulses in plications of equilibrium business cycle theory. equilibrium business cycle models is much too ex- Working at the annual interval, Barro provides tensive to cover completely in this essay. Rather, we evidence that (i) anticipated monetary changes do review three major lines of empirical investigation that not affect real activity in a statistically significant bear on the relevance of this line of research. By and manner, and (ii) that unanticipated money growth large, the evidence suggests that models of this class affects output over three years, with the peak effect

8 ECONOMIC REVIEW, MARCH/APRIL 1988 concentrated in the second year. A follow-up study application of an increased amount of effort to a of the price level at the annual interval, Barre (1978), f=ed stock of capital. Thus, if misperceived monetary provides evidence that price level movements accord shocks fool labor suppliers into working more, then less well with the predictions of theory. Although monetary shocks should lower real wages and in- anticipated monetary changes have a one-for-one crease output, so that a countercyclical relationship impact on the price level, the response of the price emerges between monetary shocks and real wages. level to monetary shocks is more protracted than the Also, predictable shifts in money will leave real wages response of real activity. Barro and Rush (1980) pro- unaffected. Leiderman finds some support-at both vide additional evidence using data on unemploy- the annual and quarterly intervals-for countercyclical ment, output, and prices from the quarterly post-war variation in the real wage, which is strongest when time series, the interval that has subsequently been the real wage is deflated by the wholesale price in- studied by most researchers. Generally this study dex and when overtime payments are excluded. confirms Barro’s earlier results that unanticipated However, in a recent study of a number of manufac- money influences real GNP (positively) and unem- turing industries, Kretzmer (1985) finds evidence that ployment (negatively) but, as with the annual data, industry specific product wages (industry wage the results involving the price level are less per- divided by the industry wpi component) are uniformly suasive. Although unanticipated money does affect positively related to unanticipated monetary shocks. the price level less than one for one, the lag struc- Another type of neutrality ture for unanticipated money is inconsistent with lags Changer causality test. found in output and unemployment equations. test is based on the following observation: given the relevant state of the economy (capital, etc.), the Working at the quarterly interval, Mishkin (1982) history of monetary shocks should have no effects and Merrick (1983) provide evidence against the on real activity. Sargent (1976) and Sims (1980) neutrality hypothesis, where the hypothesized money utilized this perspective to construct neutrality tests supply process and lag lengths are altered from the along Granger causality lines. In a multivariate con- Barro-Rush specification. Merrick essentially tries to text nominal variables should not Granger-cause replicate the Barro-Rush quarterly results on real (predict) a vector of real variables if these contain GNP, after altering the money supply process by in- the economy’s state variables. (Conditions that assure cluding lagged Treasury bill rates and stock that the state variable is reputable in this form are returns. He finds that unanticipated money no longer provided by Sargent (1979)-some may be unwill- affects real GNP, but that anticipated money does. ing to impose such lag length restrictions on error Mishkin also alters the money supply process by in- terms, which Sims (1980) argues are incredible.) cluding past Treasury bill rates but finds that this does Sargent (1976), Sims (1980) and Eichenbaum and not affect the Barro-Rush results over a somewhat Singleton (1987) illustrate that the results of such different sample period, where an eight-quarter- tests are heavily dependent on variable selection maximum lag is imposed. However, upon extending and data processing, particularly treatment of the lag lengths on unanticipated and anticipated nonstationarities. money to twenty quarters, he is able to reject the A variant of this procedure is employed by Haraf joint hypothesis of and neutrality. The (1983), who examines a four-variable-vector auto- Merrick and Mishkin results cast doubt on the regression using real output, employment, inven- robustness of the neutrality results obtained at the tories, and backorders. A constructed unanticipated annual interval. However, in interpreting the above money series does not Granger-cause the vector pro- results, one must keep in mind that a composite cess governing the four real variables in the model, hypothesis is being tested. For example, if anticipated a result that is consistent with the simple equilibrium money was neutral, but if the central bank engaged business cycle model. However, Haraf also finds that in interest-rate smoothing-as in Goodfriend with the exception of real GNP, contemporaneous (1987) -then variations in money growth would ac- unanticipated movements in money have little ex- company changes in the real . If the planatory power once lagged model variables are factors that lead to these changes in the real interest taken into account. rate are omitted in the output equation, anticipated money will spuriously appear to be non-neutral. Tests based on contemporaneous monetary data. The Leiderman (1983) investigates the cyclical pattern previous tests concentrated on the distinction be- of real wage movements in response to money on tween unanticipated and anticipated changes in both annual and quarterly data. According to neo- money. However, equilibrium business cycle theory classical theory, the real wage should decline with typically predicts that the relevant distinction is

FEDERAL RESERVE BANK OF RICHMOND 9 between perceived and unperceived movements in mark-up pricing. Simulations of the model under the money. Since monetary statistics are readily available, assumption that wage contracts last for three or four agents misperceive the true monetary state of the quarters are used to investigate the dynamics of out- economy only to the extent that monetary statistics put or unemployment. Without any of the neo- contain some reporting errors. Therefore, revisions classical propagation mechanisms, Taylor’s models in monetary statistics are indicators of misperceived generate substantial serial correlation from the interac- money, and it is misperceived money that should be tions of wage setting rules and expectations-shocks the relevant variable in explaining real economic can last for more than the contract length because fluctuations. Specific tests of the equilibrium business these are passed along via other, subsequent con- cycle theory using contemporaneous monetary tracts. But Taylor’s models have been criticized as data- historical statistical reports that werepotennid~ departing too far from wage setting rules that could available to private agents-are conducted by Barro plausibly be rationalized by neoclassical methods- and Hercowitz (1980) and Boschen and Grossman thus involving wage setting based on predeter- (1982). mined wage rates of others, which should be irrele- Both of these papers contain evidence contradic- vant-and for not containing the natural rate property ting the implications of the simple equilibrium (for further discussion of Taylor’s models, see business cycle model outlined above. Barro and McCallum (1982)). Hercowitz find that revisions in the monetary data The Gray (1976)-Fischer (1977) perspective on do not help explain cyclical fluctuations of output or wage contracts can be developed as follows. Produc- unemployment. Boschen and Grossman focus on tion takes place at various locations or industries King’s (1981) observation that output should be indexed by z, and depends negatively on the real uncorrelated with available monetary data. They wage wt(z) -p*(z) in each location. (All variables are begin by constructing a more elaborate procedure that expressed in logarithms.) In the one period ahead yields valid tests of the real effects of exogenous contracting version of the model, the nominal wage perceived money on output when misperceived wt(z) is set according to the rule wt(z) = Et- 1 money can affect output through a specific propoga- pt + r(z)(P, -Q _ 1PJ, y(z) indicates the extent of in- tion mechanism. They find that contemporaneous dexing in industry z. If y(z) = 1, then wages in z are monetary data is significantly (partially) correlated completely indexed to the aggregate price level. with real activity, which is inconsistent with the Given the nominal wage, firms determine employ- theory. Boschen and Grossman also test whether ment along their marginal product curve, the effi- monetary reporting errors have real consequences and ciency condition being that the marginal product of as in Barro-Hercowitz, there is no evidence of real labor equals wt(z) -pt(z). Therefore a rise in the real effects. Thus, the Boschen and Grossman findings wage reduces employment and output at location z. are inconsistent with the joint hypothesis of .(i) a Aggregate demand at any location is directly related specific equilibrium business cycle model, (ii) that to aggregate real balances and a relative demand agents utilize contemporaneous information as shock, as in the equilibrium business cycle model. money, and (iii) that measures of money (original and Also, the money supply is assumed to follow a ran- final reports) are exogenous. dom walk. In this setting, with incomplete indexing Although properly specified tests are difficult to (y(z) < l), a positive money supply shock causes conduct, the mixed results of these three types of real wages to fall and output to rise. Also, with con- tests does not provide strong support for the tracts set at one period in length, shifts in money that were anticipated at t - 1 have no real effects. equilibrium monetary business cycle view. Conse- Therefore, tests that only consider the distinction quently, investigation of Keynesian alternatives seems between anticipated and unanticipated money can- warranted. We begin with the notion that multiperiod not distinguish between equilibrium business cycle contracting imparts some stickiness to the nominal models with no contemporaneous information and wage. models with nominal contracts extending for only one period. Nominal Wage Contracting Models However, as Fischer (1977) indicates, when con- Much of the nominal wage contracting literature tracts last for more than one period, shifts in money is based on two lines of work. One originates in that are anticipated at t - 1 will have real effects Taylor (1979, 1980) and the other follows from Gray since some locations are locked into contracts con- (1976) and Fischer (1977). ditioned on period t -2 information. However, Taylor (1979, 1980) develops a model with Fischer (1980) reports some difficulties in imple- multiperiod, overlapping nominal wage contracts and menting this .

10 ECONOMIC REVIEW, MARCH/APRIL 1988 A direct test of the contracting model is per- which sticky price models rationalized nonneutral- formed by Ahmed (1987). Ahmed undertakes a ity of monetary shocks while maintaining the neu- careful study of the relationship between the Phillips trality of anticipated monetary policy (1978, 1979, curve slope and the degree of wage indexation in a 1980). particular industry. (The data set includes 19 Ca- More recently, McCallum (1982, 1986) has pro- nadian industries.) The contracting model predicts vided a detailed outline of interactions between that the responsiveness of industry specific output nominal shocks, price adjustment, and real activity, to unanticipated changes in money should be in- which presumably will be developed further in com- versely related to the degree of indexing. That is, ing years. The key elements of this story are as greater indexation by a particular industry reduces follows. To economize on certain costs, firms find the responsiveness of real wages to unanticipated it optimal to maintain a set nominal price over some money and reduces the change in industry output period, accommodating variations in relative and to a monetary disturbance. Ahmed finds no evidence aggregate demand through alterations in production that there is any relationship between indexation and and inventories. Thus, monetary shocks have real the magnitude of responsiveness of industry specific effects. However, price adjustments incorporate output to an aggregate monetary shock. These results firms’ anticipations about monetary policy, so the real are at variance with the implications of the con- consequences of anticipated movements in money tracting model. are much smaller than unanticipated movements and Therefore, the strategy of producing monetary may be fully neutralized. business cycles through nominal wage rigidities does In McCallum’s work the period over which sticki- not receive strong empirical support. This has lead ness prevails plays a crucial role. If price stickiness Keynesians to refocus their attention on nominal is to be assigned a major role in business cycles- rigidities that may occur in other areas of the econ- even as an impulse mechanism-then the period over omy, namely in the price of specific commodities. which firms elect to make prices sticky must be non- trivial. McCallum (1982, 1986) begins by reviewing Sticky Prices and Business Cycles theoretical explanations of why producers might temporarily stabilize relative prices against shocks, After the Dunlop-Keynes-Tarshis controversy of for example to attract a clientele of customers who the 1930s unveiled the lack of confirmation for prefer relative price stability. He then argues that the countercyclical real wages, Keynesian macro-theorists costs within period adjustment of nominal prices- turned from models incorporating stickiness of wages or of indexation that would neutralize monetary to models featuring stickiness of product prices. This shocks-cannot be the physical costs of adjusting activity spanned the range from rationalizations of prices, but rather are computational costs associated the pricing equations in large scale econometric with the difficulties that agents face in understanding models to the abstract dynamic pricing model of more complex contracts. He also argues that - Phelps and Winter (1970) and the nonmarket clear- ation provides only small reductions in risks to par- ing theory of Barro and Grossman (1976). Curi- ticipants, although it is unclear how this is consis- ously, this prior path seems to have been ignored tent with business cycles that are an important social by the profession at large. Until recently, there has problem. been substantial effort allocated to sticky wage Some other recent attempts to give theoretical con- models despite their reliance on a countercyclical path tent to the idea of price stickiness have proceeded for the real wage. However, the past several years along two different paths. One avenue emphasized have seen increased attention to sticky price models. by Mankiw (1985) and Blanchard and Kiyotaki Although this line of research is still at an early stage (1987) involves models with monopolistically com- and has, as yet, generated little empirical literature, petitive firms that face fixed (menu) costs of adjusting we provide a brief review because of its likely im- prices. So far, this line of research has concentrated portance in coming years. on establishing that menu costs that are small can Simultaneously with Fischer’s wage contract lead to large departures from socially efficient alloca- model, Phelps and Taylor (1977) propounded a basic tions when nominal shocks occur. These models are rational expectations model with price stickiness, in not yet dynamic, so that distinctions between antici- a paper that has received far less professional atten- pated and unanticipated movements in nominal tion than Fischer (1977). However, research into variables have not yet been explored. But it stands sticky price models was continued by McCallum in to reason that there would be results that differed an important series of papers. Initially, McCallum from McCallum’s, since in his setup there are effec- focused his investigations on the conditions under tively zero costs of adjusting prices between periods

FEDERAL RESERVE BANK OF RICHMOND 11 and infinite costs of changing prices within the period. rigidities is necessary. At this stage, this class of First, as in Mankiw (1983, large nominal shocks- models should be regarded as a potentially prom- even if unanticipated-would tend to be neutral- ising means of resurrecting longstanding Keynesian ized. Second, small anticipated changes in money notions. As of yet their value has not been proven. would tend not to be neutralized, as the menu costs would be prohibitive. Irrespective of one’s view on Conclusion the plausibility of menu costs, these recent analyses provide a clue as to how individual agents might In our overview of rational expectations models of regard the gains to altering nominal contracts assmall business fluctuations, we have consciously empha- even though the social benefits would be large, due sized the extent to which this class of models has to the suboptimality of monopolistically competitive generated cyclical interactions that are consistent with equilibria. empirical evidence. Evidently, progress has not been Another line of research has been pursued by rapid and there is currently no compelling evidence Rotemberg (19&Z), who employs quadratic costs of for any particular description of cycles, despite the price adjustment to induce gradual price adjustment. fact that the models quite frequently have substan- As in Phelps-Winter, these costs are viewed as tially distinct policy implications. We do not regard arising from an erosion of the firm’s clientele, with this assessment as a reason for departing from the a specific interpretation involving an individual’s discipline imposed by rational expectations, but feel dislike of price volatility. Using rational expectations that this is rather an indication of the amount of work methodology, Rotemberg provides evidence that that remains to be done. prices adjust gradually, although the specific struc- In fact, some recent research has led us to become tural models which he employs are inconsistent with less sure that the conventional representation of the cross-equation constraints implied by the rational business cycles- the stochastic components of eco- expectations postulate. nomic time series-is appropriate. Nelson and Plosser As the dynamic implications of sticky-price macro- (1982) have produced some provocative empirical models are developed in more detail, it will become work which cannot reject the hypothesis that the possible to discriminate between these models and stochastic components of economic time series are the flexible price equilibrium theories considered nonstationary, possessing random walk components. earlier. In this process, since price level behavior is Although their tests have low power against the a result of the interaction between private agents and alternative that the stochastic components are sta- the monetary authority, an adequate definition of tionary but highly persistent (McCallum, 1986), these price stickiness will be required. In particular most results represent a serious challenge to existing views. researchers have focused on the smoothing of price Further, there are now basic equilibrium models of level variations that arises from private sector actions. fluctuations that imply nonstationarity if the inter- However, smoothing can also arise from systematic temporal technologies are restricted so that the rnean actions by the monetary authority (see Goodfriend, rate of is endogeneously deter- 1987). Powerful tests will presumably require mined (King and Rebel0 (1986)), basically because systematic examination of data generated prior to the fixed factors are not too important. Further, these creation of the Federal Reserve. endogenous growth models have substantial impli- cations for modelbuilding under the rational expec- The microeconomic evidence developed by Carl- tations postulate, for they imply that there are ton (1986)-working with the StiglerXindahl(l970) transformations of nonstationary economic variables data-shows that some prices are fairly rigid. However, the rigidities do not seem to conform to that are stationary- that is, the macroeconomic data possess a cointegrated representation (King, Plosser, those that have been postulated by macro-modelers. For instance, many price changes are extremely Stock and Watson (1986)). small, indicating that menu costs are not a pervasive Our forecast is that the construction of rational factor. Carlton also does not find much evidence that expectations model of the business cycle will be the buyers have strong preferences for products whose centrepiece of the macroeconomic research agenda prices are relatively stable, implying that one ra- over the next fifteen years, as much as it has been tionalization of Rotemberg’s costs of adjustment is over the fifteen that have passed since Lucas’s in- apparently inoperative. As the particular mechanism fluential contributions (1972a, 1972b). Recently, that generates rigidities could be quite important for Lucas (1987) has argued that economic fluctuations the dynamic implications of this class of models, pale in welfare significance relative to the factors that identification of the empirically relevant sources of determine the growth path of a particular country’s

12 ECONOMIC REVIEW. MARCH/APRIL 1988 economy; his research has recently turned to analyses for if the analysis of King and Rebel0 (1986) is sus- of these factors (1988). Most macroeconomists tained in richer models, then it is inappropriate to presumably share McCallum’s (1986) scepticism that separate the study of economic fluctuations from that economic fluctuations are second order problems of economic growth. That is, the fact that economies relative to economic growth and, hence, would doubt grow tells us that temporary shocks to the economy’s that Lucas’s current research direction will have the production possibilities will have permanent effects impact of his 1972 work. But we are not so sure, on the level of output.

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