# Equilibrium Business Cycle (EBC) Modelling

EBC models differ from the traditional Keynesian business cycle models, which incorporate multiplier-accelerator interaction and wage-price rigidities, in assuming that markets clear continuously throughout the cycle. In this respect they also clearly differ from the alternative Keynesian models which stress constrained demand,9 the New Keynesian models and models of financial instability, such as that of Minsky, which will be discussed in section 3.3. In the disequilibrium models stressing constrained demand, the importance of the interdependence of markets and sectors is highlighted. This feature is assumed away by the 'market islands' paradigm (originated in Phelps 1972) employed in Lucasian EBC models10 and consequently the linkages underlying the Keynesian multiplier are decoupled. The cycle generated by Minsky's disequilibrium model is much more nearly endogenous than in traditional Keynesian multiplier-accelerator formulations, which rely heavily on external shocks. The potential for financial crises is generated endogenously by the interplay of real and financial factors and crises can be sparked by exogenous shocks or endogenous shocks, such as shifts in Keynesian 'animal spirits' leading to reduced optimism. The cycle is normally originated by real factors but money and credit play a significant role in the propagation of the cycle and are primarily responsible for speculative booms and crises. This contrasts with the Lucasian EBC model which utilises monetary shocks to derive a cycle from a real propagation mechanism.

Dissatisfaction with the Lucasian EBC model, which relies on monetary shocks and price misperceptions, which in turn result from limited information and give rise to a 'signal extraction problem' despite the assumption of RE, prompted experimentation with alternative models. Boschen and Grossman's (1982) paper was particularly influential in persuading New Classical economists to abandon the Lucasian approach and to focus on real factors instead. They found contemporaneous monetary data to be significantly (partially) correlated with real activity, as measured by output. This is inconsistent with the Lucasian approach, which stresses incomplete information and the role of unanticipated and unobserved, rather than anticipated or observed, monetary shocks, in particular, as a determinant of macroeconomic fluctuations. Tests of the rational expectations and structural neutrality hypotheses, which underlie the Lucasian approach, are discussed further in Mullineux (1984, section 4.2).

Zarnowitz (1985) distinguishes three main alternative approaches. The first was to reimpose Keynesian wage and price rigidities by introducing explicit (Taylor 1979, 1980a) and implicit (Okun 1980) multi-period contracts into RE models. These contracts were then given a microeconomic rationalisation in the New Keynesian literature (Greenwald and Stiglitz 1987). The second approach was to emphasise the role of the interest rate and harked back to the work of Wicksell, Myrdal, Keynes and Shackle, who had attempted a synthesis of Keynes's 'General Theory' with the work of Myrdal (see Shackle 1938 and section 4.4). This approach emphasises the importance of deviations from the natural rate of interest." Additionally McCulloch (1981), in the Lucasian incomplete information mould, argued that business cycles are associated with unanticipated changes in the rate of interest that misdirect investment and lead to an incorrect mix of capital goods and distort the intertemporal production process in a Hayekian manner. McCulloch's models stress the role of the financial sector in adding to instability through 'misintermediation' or 'mismatching', which results when banks raise short-term finance to lend for longer periods. This adds to the uncertainty surrounding the rate of interest by creating imbalances in the term structure of interest rates, McCulloch argues. In another equilibrium model, Grossman and Weiss (1982) utilise a mix of random real shocks which affect production and the real interest rate, leading to investment and output fluctuations, and monetary shocks which affect inflation and the nominal interest rate, leading to amplification of the cycle. As in Lucasian EBC models, a 'signal extraction problem' arises from trying to infer * ex ante *real interest rates and inflation from observed nominal interest rates when agents cannot observe relative rates of return.

The third approach focuses on real factors and has led to the development of a class of EBC models called real business cycle (RBC) models. Zarnowitz observes that it entails the most extreme reaction to Friedmanite monetarist and Lucasian monetary shock theories by strong believers in general equilibrium models and the neutrality of money. While retaining the REH, these models assume that information is publicly and costlessly available. The 'signal extraction problem' that is such an important ingredient of Lucasian EBC models is thus diffused and consequently unanticipated monetary shocks play no role. The Lucasian approach is highly aggregated and effectively assumes a single product is produced on each market island. Black (1982) rejects the single goods approach to modelling. He argues that because specialisation increases efficiency, multi-product models must be considered. In his model unemployment can be explained by the fact that the effects of a large number of partly independent shocks hitting different sectors of the economy will persist for a considerable time because rapid transfers of resources are costly and will be more so the greater the specialisation.

The most influential contributions to the RBC literature have probably been those of Kydland and Prescott (1982) and Long and Plosser (1983). Long and Plosser adopt a highly restrictive formulation, which assumes the following:

1. Rational expectations.

2. Complete current information.

3. No long-lived commodities.

4. No frictions or adjustment costs.

5. No government.

6. No money.

7. No serial correlation in shock elements.

While not disputing the explanatory power of hypotheses inconsistent with these stringent assumptions, their aim was to focus on the explanatory power of fundamental hypotheses about consumer preferences and the production process. The preference hypothesis employed implies that consumers will want to spread unanticipated increases in wealth over both time and consumer goods, including leisure. There is, therefore, persistence in the effects of changes in wealth since they will alter the demand for all goods. The production possibility hypothesis allows for a wide range of intra- and intertemporal substitution opportunities. In emphasizing the latter, their approach is consistent with the Lucasian EBC approach (see Lucas 1977 in particular), but it does not incorporate a Lucasian 'signal extraction problem' because it assumes complete information. The model allows for the interplay of the preference and production hypotheses and is used to analyse their cyclical implications. As in Black (1982), the business cycle equilibrium is preferred to non-business cycle alternatives because agents are willing to take risks to achieve higher expected returns. Random shocks are added to the outputs of numerous commodities, which are used for consumption or as inputs. Input-output relationships propagate the effects of output shocks both forward in time and across sectors but, unlike Black's model, there are no adjustment costs and so unemployment is difficult to explain. Despite the problems with the model, identified by Zarnowitz (1985, p.567), it usefully stresses the role of input-output relationships and in so doing is richer than the Kydland and Prescott (1982) single product model and moves away from the 'islands' hypothesis, inherent in Lucasian EBC models, which effectively denies the multiplier process.

Long and Plosser use stochastic simulations with random shocks to test whether their propagation model can produce a realistic cyclical output. The propagation mechanism is found to display damped cyclical responses following a shock and can, therefore, generate cycles in the Frisch-Slutsky tradition if hit by a series of shocks of suitable frequency and size. Further, comovements in industrial outputs can be identified as a result of input-output relationships.

Kydland and Prescott (1982) modify the neoclassical equilibrium growth model (e.g. Solow 1970) by introducing stochastic elements and an alternative 'time to build' technology in place of the constant returns to scale neoclassical production function and, in so doing, also reject the adjustment cost technology often emphasised in empirical studies of aggregate investment behaviour. Their approach is, therefore, to integrate neoclassical growth theory with cycle theory. They aim to explain the cyclical variation of short-term economic time series and especially the autocorrelation of output and the covariation of real output and other series. The main modification of the standard neoclassical growth model is the assumption that multiple periods are required to build new capital goods and only finished capital goods are part of the productive capital stock. The assumed preference function admits a great deal of intertemporal substitution of leisure, in line with Lucasian EBC models. This feature does not increase persistence in their model. The persistence of the effects of shocks is instead the result of the 'time to build' assumption.

The technology parameter is subject to a stochastic process with two components which differ in their persistence. Productivity itself cannot be observed but an indicator or 'noisy' measure of it can be observed at the beginning of the period. Consequently a 'signal extraction problem' is present, but it is different from the Lucasian one. The technology shock is the sum of a permanent and a transitory component, in the manner of permanent income models (Friedman 1957). The permanent component is highly persistent, and shocks are therefore autocorrelated.12 When the technology parameter grows smoothly, steady state growth prevails but when it is stochastic, cyclical growth results. When estimated and empirically plausible parameters are introduced to the essentially linear model, investment varies three times as much as output and consumption only half as much. Kydland and Prescott found that most of the variation in technology had to come from the permanent component in order for the serial correlation properties of the model to be consistent with postwar US data. Their results proved to be sensitive to the specification of the investment technology and the 'time to build' lag is important, but the cycle is not particularly sensitive to the length of the lag.11 Experiments with adjustment costs as an alternative source of persistence and lags proved unfruitful. This contrasts with the Black (1982) analysis but may reflect the lack of specialisation. Kydland and Prescott themselves felt that the introduction of more than a single type of productive capital with different 'time to build' and patterns of resource requirements would improve the performance of the model. As in Lucas (1975) there is a 'signal extraction problem', and capital is used to create persistence but the approach is different. Lucas uses a modified accelerator and relies on random monetary shocks while Kydland and Prescott use 'time to build' and autocorrelated real technology shocks. Zarnowitz (1985) notes that consequently the Kydland and Prescott model lacks the random shock property which EBC theorists had previously looked for in an essential propagator of the business cycle (see also Taylor 1980b).The models of Long and Plosser and Kydland and Prescott are representative agent models with complete markets so that credit does not enter into the determination of real quantities. King and Plosser (1984) consider an extended version of an RBC model in which certain, perhaps information, 'frictions' in private markets lead to the creation of institutions specializing in the issuance of credit. They conclude that while credit may have a role to play in the propagation mechanism, the actions of the Federal Open Market Committee (FOMC) may not be an important independent source of fluctuations in real quantities and relative prices.

As a class,14 RBC models analyse the role of basic neoclassical factors in shaping the characteristics of economic fluctuations. In particular, they concentrate on the specification of preferences, technology and endowments in order to derive a stochastic propagation model. RBCs are driven by shocks entering the economic system via a number of channels, including those to technology and preferences.15 Within the basic neoclassical model it has proved necessary to incorporate substantial serial correlation in the productivity shocks, which are most commonly utilised in RBC models, to allow the generation of fluctuations resembling the post-war US experience. This was evident in Kydland and Prescott (1982) and Prescott (1986) and may imply that stochastic growth is at the heart of observed economic fluctuations, as postulated by Nelson and Plosser (1982). (See section 4.3.1 for further discussion.) RBC models can be regarded as stochastic versions of the neoclassical growth model and as permitting a unified analysis of growth and the cycle. They imply that the business cycle is exactly what should be expected to emerge from industrial market economies in which consumers and firms solve intertemporal optimisation problems in a stochastic environment. RBC models commonly assume the following:

1. The existence of a complete set of contingent claims to future goods and services based on the nonseparability of time preferences.

2. That agents have common information sets.

3. That the only frictions are due to technological factors modelled variously as 'time to build' or costs of adjustment.

They normally abstract entirely from monetary considerations and the fact that exchange in modern economies uses the medium of real money. They implicitly assume that monetary shocks have played an insignificant role in determining the behaviour of real variables.

In order to assess the importance of the RBC explanation of cycles, which assigns little or no role to monetary shocks, in the post-war period Eichenbaum and Singleton (1986) present and interpret evidence on the importance of monetary shocks as determinants of real economic activity. They note that in empirical investigations of RBC models it is common to assure their good fit by choosing the stochastic process appropriately. Little consideration had been given to the extent to which RBC models emerge as special cases of monetary models of the business cycle. Acknowledging that the work of King and Plosser (1984) had come closest to such an exercise, they derive an RBC model with money introduced using a cash-in-advance constraint of the type considered in Lucas and Stokey (1984). Eichenbaum and Singleton then use the model to investigate Granger-causal relationships between nominal and real aggregates and find little empirical support for the proposition that monetary growth or inflation Granger-cause output growth. They interpret this to mean that exogenous shocks to monetary growth are not an important independent source of variation in output and growth in the United States in the post-war period and consequently that real shocks are the predominant source of variation in real quantities over the cycle. In itself this does not imply that the RBC propagation model accurately characterises the economic environment, however, and in any case Granger-causality is difficult to interpret when expectations are taken account of. Like Lucas (1987), they conclude that acceptance or rejection of RBC models must be based in part on the plausibility of the variances and autocorrelations of technology shocks employed to generate realistic cycles. Kydland and Prescott (1982), for example, simply chose variances and levels of persistence of shocks that were consistent with those of observed variables and concentrated on the adequacy of the model for propagating them to give output comparable to US data.

There is, therefore, a need to quantify the various shocks that hit the economy in order to gain an insight into the magnitude and nature of real shocks in the real world, to assess the relative importance of different types of real shocks, and to compare the magnitude and persistence of real and monetary shocks. This can only be done within the context of a model complex enough to accommodate various types of shock.

Eichenbaum and Singleton derive an EBC model for a monetary economy in which monetary growth can have real effects. The cash-in-advance constraint is the only source of non-neutrality in the model. It is an extended version of the Garber and King (1983) model and is closely related to the Long and Plosser (1983) model. They examine the conditions under which the RBC special case, in which the cash-in-advance constraint is not binding, provides an accurate approximation to the monetary economy. They find a constant monetary growth rate to be both necessary and sufficient for the real allocations to be identical in the monetary EBC and RBC versions.

There is clear evidence, however, that monetary growth has not been constant. This alone is not sufficient to dismiss the RBC explanation of aggregate fluctuations, since the cash-in-advance constraint may be incorrectly imposed. They also show that when real shocks to tastes and technology predominate, the RBC will be a good approximation to the monetary EBC model with constant monetary growth, and money may not be seen to Granger-cause output.

Commenting on Eichenbaum and Singleton's paper, Barro (1986) emphasises their warning that the lack of significance of monetary shocks as a determinant of output does not imply that RBC models are correct. Keynes's model, as outlined in the 'General Theory', is clearly not an RBC model and yet would attribute a major role to endogenous shocks in the form of shifts in the optimism and pessimism, or animal spirits, of investors and the propagation mechanism would rely on wage-price rigidities. Barro's main concern with RBC models is the lack of important 'multipliers', which leads them to rely heavily on the frequency and size of shocks, and he argues that many economists are skeptical about whether shocks to preferences and technology are large and frequent enough. He notes that the oil price shocks of the 1970s clearly were large enough but this does not convince him that real shocks alone can explain the cycle throughout the post-war period in the United States.

Mankiw (1986), in another commentary, finds Eichenbaum and Singleton's conclusions surprising in the light of the work of Sims (1972, 1980) and argues that their failure to establish that money Granger-causes output might not have implications as far-reaching as they suggest. Mankiw uses examples, based on the Fischer (1980) contract model, to demonstrate that money need not Granger-cause output for it to be a determinant of output. He further notes that Granger-causality is unlikely to be detected for most of the post-war period because the Federal Reserve Board's goal was to allow money supply fluctuations to stabilize interest rates. Finally, Mankiw finds it suggestive that Eichenbaum and Singleton's results show some evidence of Granger-causality in the post-1979 period, when money supply targets replaced interest rate targeting. In the concluding discussion of Eichenbaum and Singleton's paper, Rotemberg questions the use of first differencing, which he believes led to the conflicting results on Granger-causality derived by Sims and Eichenbaum and Singleton.

Like Eichenbaum and Singleton, Lucas (1987) suggests a synthesis of RBC with EBC models, in which monetary shocks play an important role. He regards the Kydland and Prescott (1982) model as a useful definition of the frontier of business cycle research but feels that it incorrectly focuses on real, as opposed to monetary, considerations. Nevertheless he is impressed by its coherence and the fact that it is developed to the point where it can be empirically tested. Lucas demonstrates that money can be grafted on to the Kydland and Prescott model in a way that has no significant effect on its conclusions. He does not, however, believe money to be neutral and argues that the fluctuations observed in the real world are too large to be induced by a combination of real impulses and Kydland and Prescott's propagation mechanism. He draws attention to the work of Friedman and Schwartz (1963a, 1982), which clearly implies an influence of money on economic activity. If he is correct, he deduces, then either larger shocks, including monetary shocks, are required or the propagation model must be modified to include larger multipliers. Lucas points out that the problem is not to account for Friedman and Schwartz's evidence with a model in which the money supply responds passively to real events but plays no causal role. This is easy to do, he argues, and he demonstrates using a variant of the Lucas-Stokey (1984) model, as utilised by Eichenbaum and Singleton. This leads to a restatement of the 'Quantity Theory' in which money is neutral in the long run but monetary shocks can affect real variables. He argues that the problem is rather to account for real fluctuations without candidates for shocks that are of the right order by magnitude. Kydland and Prescott (1982), he observes, simply chose the variance of the technology shocks to assure consistency with the observed GNP variability. They did not attempt to provide independent evidence that technological shocks will have the required variance. Lucas doubts this to be the case and advocates that empirical work be done to settle the issue.

Lucas argues that the integration of the Lucas-Stokey (1984) insights with the real dynamics of Kydland and Prescott is slightly beyond the frontier of what is possible. Eichenbaum and Singleton (1984) do, however, make a stab at the impossible by introducing a cash-in-advance constraint into a model related to Long and Plosser (1983). Lucas does speculate about how a hybrid model with preferences and technology for producing goods akin to those postulated by Kydland and Prescott (1982), but trading not centralised, would behave. Instead of the centralised trading assumed by Kydland and Prescott he uses the Lucas-Stokey motivation for using money. Agents are assumed to trade in securities at the beginning of the period and use the cash acquired in the course of this trading to buy consumer goods later in the period. Lucas then postulates that the money supply is erratic, following a stochastic process with parameters fixed and known by agents, and considers the conditions under which monetary expansion will be associated with real expansions. One possibility would be to retain the full public information assumption, utilised by Kydland and Prescott and Lucas and Stokey, but to introduce price rigidity, perhaps using wage contracts in the manner of Taylor (1979). He adds that because of inflation tax considerations, non-neutrality must be recognised.

Lucas's preferred way of introducing monetary effects is to integrate Lucasian EBC models with RBC models. He notes that in a multi-product version of the Kydland and Prescott (1982) model, the volume of information would explode even if the full public information assumption is retained. If there is any sort of cost of processing information, then economic agents will economize and process only the information which materially sharpens their ability to make production or investment decisions. As a result, the 'signal extraction problem' will remain and a positive supply response to monetary shocks can be expected. Lucas believes that in a modified version of the Kydland and Prescott (1982) model, elaborated to admit limited information due to costs of processing it, shocks of a monetary origin would be 'misperceived' by agents as signaling a change in technology or preferences. Monetary shocks would then trigger similar dynamic responses to the technology shocks considered by Kydland and Prescott. He notes that Lucas (1975) had relied on 'misperceptions' over whether the shocks were real or nominal in origin but had not specified the source of the real shocks. They had been simply introduced through random error terms. Lucas cites Grossman and Weiss (1982), Grossman * et al. *(1983) and other models, surveyed in Scheinkman (1984), as examples of models employing limited information and allowing for an interplay of real and monetary shocks. Lucas finally draws attention to the Sargent (1976) paper, which demonstrated the 'observational equivalence' of models in which monetary non-neutrality is the result of limited information and those in which money affects real variables in some other way. He concludes his analysis by advocating the use of structural models that lay down specific economic hypotheses for testing, rather than the use of reduced form testing, and of dynamic game theoretic analysis, in the light of the 'Lucas critique'(see Lucas 1976). This accords with the conclusions of Mullineux (1984) and Chapter 5 of this book.

The proposed synthetic EBC model, in which real and monetary shocks hit a propagation model describing an economy which is always in equilibrium to produce a cycle, accords little importance to the financial sector as a propagator of cycles. Considered in the next section is recent work by economists who refuse to accept the Frisch-Slutsky approach and argue that nonlinearities must be employed to generate realistic cycles. In the next chapter, work on the financial instability hypothesis, which assigns much more importance to the financial sector in business cycle generation, will be reviewed.