The analysis of business cycles the problem and the approach

Paraphrasing Voltaire, we can assert that if business cycles did not exist, the economic theorist would have invented them. For if we look at the problem of business cycles, without any doctrinaire bias, it seems obvious that in this branch of economics a natural connection occurs between the often too separate compartments of economic analysis: between the 'monetary' and the so-called real phenomena. Therefore, a theory of business cycles, to be consistent with the observable material and the inherited doctrines, should be a blend of the analytical material which deals with the interrelations among a few broad aggregates - which traditionally has been the approach of monetary theory - and the analytical material which deals with the behavior of individual economic units and of particular markets - which has been the sphere of price and distribution theory. This thesis can be interpreted as an attempt to construct such an eclectic business cycle theory by utilizing a number of elements drawn from inherited economic analysis. To be complete such an attempt would have to explore such purely theoretical material as the relation between macro and micro analysis, between partial and general equilibrium analysis and between monetary and real phenomena, as all of these separate pieces of economic theory have to be used in an analysis of business cycles. That task is both too big and too general. What will be attempted here is to try to develop a technique of business cycle analysis which does draw upon the various portions of inherited doctrine.

In spite of the complexity of the phenomena which are observed during business cycles, and the seemingly obvious need for cycle theory to interpret the phenomena which occur during a business cycle, individual authors have tended to specialize in their emphasis on particular phenomena as the essential components of business cycles. To a student it is the field of business cycle theory, more than any other part of economics, which consists of a study of alternative explanations.1

An explanation of the continued existence of alternative theories of the business cycle is perhaps most readily made in terms of the economic policy problem which the existence of business cycles poses. The alternative theories of the business cycle are consistent with somewhat different approaches to economic policy, and business cycle theory has historically had a strong prescriptive bias. No claim is being advanced that this work differs from the others in this respect - the only claim made is that the more eclectic approach outlined in this chapter indicates that a wide variety of public policies are relevant to an effective business cycle policy.

We can distinguish two varieties of business cycle analysis, based upon the method of analysis used. One type directs its attention at a few macro-economic variables, and studies the interrelations among these aggregates. The other variety maintains that business cycle analysis must attempt to deal with the behavior of individual economic units, and that what aggregate relations are derived are of the nature of an average. Two recent volumes in business cycle theory - that published by J.R. Hicks2 and the posthumously published volume by Mitchell3 are illustrative of this methodological division in business cycle analysis. The Hicks volume deals with the interrelations among a few broad aggregates - the Mitchell volume essentially denies the validity of such aggregative analysis and emphasizes the connection between the multiplicity of markets which make up economic life. In the Hicks volume, if market processes are discussed, they are taken up as asides from the main course of the volume. The core of Mitchell's theoretical apparatus is a concern with market processes. It is the contention of this volume that any reasoned perspective upon the problem of business cycles leads to the conclusion that each approach is in some measure incomplete without the other.

The theoretical framework employed by Hicks is based upon a limited number of presumably measurable economic aggregates: consumption, investment, income, and so on. The movements over time of these aggregates are interpreted as the essential characteristic of the business cycle of experience. Models are built in which interrelations among these few variables are set out. The results obtained depend upon the specification of the functional relations among the variables and upon the values assigned to the parameters of these functional relations. Such models are dynamic, connecting variables of different dates, and once such a model is constructed, its operation is 'mechanical'.

'Between the variables relevant to economic fluctuations there is, in the opinion of the theorists, a network of causal connections. Given movements in the data therefore cause movements in the endogenous variables, and it is the task of business cycle theory to show that the characteristics of observed movements in endogenous variables may be explained either by the given movement in the data or by the properties of the causal network.'4 The essential characteristics of the Hicks model relate to the properties of the causal network - the series of lags and the nature of the functional relations among the endogenous variables. In addition various non-linear elements are introduced into the Hicks model. These are essentially exogenous, unexplained elements, which it can be claimed are included solely because they make the model work in the desired manner. The introduction of such non-linear elements may be necessary for the construction of a useful theory of the business cycle. However, no special valued element or assumption has a place in a theory of the business cycle unless the processes which generate the special element can be described, or the actual observed value of the special element is known. The elements of the Hicks model fail to meet such standards. It will be shown in Chapter 2 that economic arguments can be advanced for non-linear formulations which are alternatives to that of Professor Hicks, and the material on the theory of the firm (Chapter 4 through Chapter 8) and on the financial relations (Chapter 9) which follows constitutes an attempt to see whether the implications for investment of market phenomena generate any particular non-linear form of the accelerator coefficient.

The approach of Hicks leads to a business cycle theory which is straightforward in its exposition and which does not have so many variables that the mind is incapable of comprehending the interrelations among the variables. In its origin it is beholden to the Keynesian5 analysis of income determination - and has many of the virtues and also the faults of its sire. The beauty of a simple set of interrelations is manifest - the emptiness which is induced by the elimination of market processes is also obvious. An attempt to repair these deficiencies is in order.

'One way out of these difficulties seems to be to construct a model consisting of an inner circle of relations between the most important macro-economic variables and a series of supplementary relations meant to specify and analyze the inner-circle relations. The inner-circle relations might be relations using only such broad concepts as total national income, total expenditures, total imports, total exports or the general price level. . . . Corresponding to this inner-circle relation there could be supplementary relations explaining the demand for separate groups of commodities and services, for instance, for consumer goods or for investment goods.'6 This solution to the problem of the reconciliation of the simple and the complex theories is by way of the disaggregation of the functional relations of the simple theory. 'Each inner-circle relation could in this way be illustrated and tested, and possible deviations between observed and calculated values of the macroeconomic variables "localized", i.e. it could be found out whether deviations in total imports are to be attributed to imports of raw materials or of finished products, etc.'7

The approach to the problem of reconciling the complexity of business cycle observations to the simplicity of macroeconomic business cycle theory suggested by Tinbergen is not the one which we are exploring in this volume. Tinbergen's suggested series of supplementary relations which aggregate to the macroeconomic relations can be interpreted as meaning that, in some sense, the complete analysis is really the analysis of the interrelations among the supplementary relations. The increase in the compre-hensibility is apparent rather than real. At each step the obvious thing is to explore the interrelations in the various supplementary sets of relations. In order that these supplementary sets of relations be independent of the behavior of the aggregates, it is necessary that the aggregates themselves not be interrelated. Essentially the Tinbergen suggestion means that we go along with a complete, complex and detailed model, and we add to it a set of aggregation rules which leads to a single set of interrelated aggregates that constitutes the core model. Disaggregation involves limitations upon the nature of the functional relations which can enter both the aggregate and the particular models.8 The idea implicit in the approach suggested by Tinbergen seems to be a fruitful suggestion to solve the dilemma of discordant theories. However, the definition of supplementary relations as formal mathematical disaggregates of the inner-circle relations is unnecessarily restrictive.

Consistent with the notion of a set of inner-circle relations, which determine overall movements of the system, and the need for supplementary relations, which lead to cyclical behavior consistent with observations, is the emphasis upon the need for special turning point analysis in business cycle theory. 'The change from prosperity to depression, from upswing to downswing, is the most crucial problem of the cycle. I still believe that we need a special theory, or rather alternative explorations of the turning points. The cumulative process is always essentially the same, but we cannot be sure that the turning point is always brought about by the same factors (even apart from possible disturbances from outside the economic system) or that the same system of difference equations will satisfactorily describe the upswing as well as the upper turning point.'9 Both the inner-circle and supplementary relations approach suggested by Tinbergen and Professor Haberler's emphasis upon the necessity for a special theory of the turning points emphasize the separability of economic phenomena into compartments. Like the authors who divide time series into trend and cyclical components, they neglect the fact that the same economic phenomena which breed behavior of the inner-circle relations and the cumulative process also determine the behavior of the supplementary relations and the turning points. What is needed is a technique of analysis which correctly emphasizes the interrelations among economic phenomena and which nevertheless permits the separation of economic data into sectors which can be conveniently handled.

The addition of floors and ceilings to the accelerator-multiplier type analysis by Hicks is essentially an attempt to include special turning point material in the analysis of the business cycle. The virtue that has been imputed to the accelerator-multiplier models - that they eliminated the need for specific turning point analysis - has disappeared in these later versions. However, the floors and ceilings have a non-economic cast to them. The ceiling is usually full employment, which is used by Hicks as a technological concept. The floor is that level of income consistent with the maximum rate of capital consumption possible under the existing technique of production. It also is determined from outside the economy. The use of such ceilings and floors is equivalent to the introduction of mechanical constraints from outside the system in order to have it behave properly.

'Constants' occur in theories which are successful in their application to the world. This is especially true in the physical sciences. In all such cases the 'constants' are unchanging in value only for a determinate set of problems. For other problems, the phenomena represented by these symbols have to be considered as variables, and their values at any moment of time, or under a set of conditions, has to be determined within the model. In particular, in economics, any ceiling such as the full employment ceiling, used by Hicks, has to be considered as an economic variable which is to be determined in a more general model. The assertion that 'full employment' is a non-economically determined phenomenon, and therefore not subject to an economist's analysis, is on the surface suspect; it asserts too much. Such arbitrary floors and ceilings should be replaced by endogenously determined parameters which are generated by the processes of economic life. The problem can be stated as: what link is there between the interrelations among the variables in a formal business cycle model and the parameters which in the Hicks type models are the floors and ceilings?

All of these recent developments (such as, models containing non-linear elements, containing arbitrary determinants of the turning points, containing inner-circle and supplementary relations) represent a dissatisfaction with those business cycle models which depend upon a set of linear relationships. Those models which depended upon the structure of production and sales, as expressed by a small number of functional relations and lagged variables, are in their analytical tools and intellectual derivations essentially Keynesian. After Keynes' General Theory was published, these limiting factors - bottlenecks, limits to bank expansion, etc. - lost much of their importance as explanations of the turning points of the cycle. As soon as the consumption function was introduced as a central feature of economic models, it was immediately recognized that a cumulative process of expansion may not be self-reinforcing but instead may inevitably lead to a crisis and a period of contraction even before the physical or financial limits to expansion have been reached.'10 The reconsideration of such fully aggregated models may be due to the failure of the early Post World War II predictions. The dissatisfaction with too aggregative analysis can either take the form of disaggregation which leads to mathematical complexity, or of a retreat to empiricism. The simplest linear process models, which exhibited cyclical behavior, resulted in a number of possible types of behavior for the endogenous variables, and these types of behavior depended upon the values of parameters. No matter what values these parameters were assigned, the resulting model exhibited unsatisfactory behavior. This has led Mr Hicks to the reintroduction of floors and ceilings (turning point analysis) into a model which is essentially Keynesian in its derivation.

Rather than attack the problem posed by the unsatisfactory nature of the accelerator-multiplier type models by means of the mechanism which generates the floors and ceilings, we can take up the more general problem of what determines the parameters of an aggregative business cycle model. The parameters of the functions which are included in the aggregative model can be interpreted as shorthand symbols for the processes of economic life which are not included in the simple model; and they are therefore in turn determined by market processes. The variables of a macro-economic model are such that the values which are generated by the model imply changes in the determinants of equilibrium in different particular markets. For example a change in national income affects product demand curves. This results in a change in the equilibrium conditions in particular markets which cannot be separated from the processes which determine the variables in the macroeconomic model. If we are to use such macro-economic models, we have to integrate the relation between the particular market developments and the developments which are represented in the aggregate model. The effects of changes in the variables of the macroeco-nomic model upon the equilibrium conditions in particular markets are going to be interpreted as determining the parameters in the macro-economic model. By adopting this combination, we retain the simplicity of a dated analysis in income flows and still emphasize the significance of particular market analysis. In addition this approach emphasizes that the parameters in macroeconomic models are elements whose values are to be determined by economic processes.

Adopting the language of Tinbergen, what we propose is that the inner-circle relations in the business cycle model be essentially of a Keynesian derivative type: for example a simple accelerator-multiplier type model. The supplementary relations are relations that determine the parameters in this model. In these supplementary relations the variables of the macro-economic model appear as parameters. The changes thus indirectly induced in the parameters of the macroeconomic model by the different values of the variables of the macroeconomic model will affect the time path of the variables of the macroeconomic model. The inner-circle relation remains a straightforward few variable analysis. The supplementary relations, which determine the value of the parameters, will be complex, multivariable relations, where the entire apparatus of economic theory is brought to bear upon the analysis of economic activity. The inner-circle model retains its simplicity. As the need for floors and ceilings as such is removed, the inner-circle model can be even simpler than Hicks' model. The difficult parts - the complicated series of springs, cogs and gears that drive the clock - are removed from sight; all that remains visible is the simple two hands circling an austere dial face.11

The distinction that is made between the variables and the parameters of the macroeconomic model is for convenience in analysis. The dominant factor in economic life is the interdependence of elementary economic units. The aggregate variables are constants, designed for simplicity and convenience. The variables of the macroeconomic model are either sums or index numbers of measurable attributes of individual economic units. The parameters of the macroeconomic model are aggregates of individual behavior or reaction coefficients. As such they are not easily measurable and not readily aggregated. In the analysis of the particular firm's investment decision which follows, we will attempt to determine what factors are relevant in determining the behavior coefficient of individual economic units. As the behavior of the macroeconomic model depends upon the values of the parameters of the model, this will enable us to isolate those variables which lead to alternative behaviors of the economic system as a whole.

The utilization of the variables, income and change in income, to determine the value of the accelerator coefficient in the accelerator-multiplier models, leads to a non-linear theory, of the type studied by Goodwin.12 However, rather than have the non-linearity as an economically unmotiv-ated, or crudely motivated, relation we center our attention on the determination of the non-linearity.

In order to illustrate the approach which is adopted, it may be appropriate at this stage to indulge in a digression. Let us take the best known of the mechanical interrelation models - in its original form - and see how it can be modified in the light of the above perspective. The result is but a slight modification in the original model; but as a result the significance, the conceptual role of the model, is changed markedly. The change will make the accelerator-multiplier mechanism the core of the analysis, a framework upon which the more complete analysis can be hung, rather than an attempt to use it as it stands as a model of the business cycle.

The best known of the mechanical business cycle models is the Hansen-Samuelson model presented in its 'mathematical form' by Paul A. Samuelson.13 The lines of the development of this model which will be undertaken here are foreshadowed in the final paragraph of this article when Samuelson asserts:

The limitations inherent in so simplified a picture as that presented here should not be overlooked. In particular, it assumes that the marginal propensity to consume and the relation are constants; actually these will change with the level of income, so that this representation is strictly a marginal analysis to be applied to the study of small oscillations.14

This familiar Hansen-Samuelson model is based upon the following assumptions:15 that National Income at any time is a sum of three components - government expenditures, consumption expenditures and private investment expenditures. Consumption expenditures are a fraction a of income at a unit of time earlier, and investment expenditures which are induced by the change in consumption are p times the change in consumption. This leads to the familiar difference equation in which income at any period of time is determined by income of two previous periods: for example

where Yt, Yt-1, Yt-2 are dated incomes, a = marginal propensity to consume and p = the accelerator relation. The 1 in the equation is due to the existence of government expenditures which, from outside the model, set the process to work. The behavior of this model, once the linear form and the lag pattern are determined, depends upon the values assigned to a and p. Four different types of behavior are possible for the variable Yt.

1. Yt may asymptotically approach the level of income given by 1/[1 - a], the pure multiplier level of income (region A in Figure 1.1);

2. Yt may take on a damped cyclical path, approaching the income level 1/[1 - a] (region B in Figure 1.1);

3. Yt may take on an explosive cyclical path (region C in Figure 1.1); and

4. Yt may take on an explosive path (region D in Figure 1.1).

Under the assumptions that the relation p is a fixed technical coefficient relating output and capital stock, and that the marginal propensity to consume is a constant determined by a fundamental attribute of the society, one of the four above types of behavior is possible, aside from the

behavior which characterized the boundary conditions between two of the stages, for example if ap = 1, the systems would oscillate with a constant amplitude. The assumption that ap = 1 seemed to be, even to this model's strongest advocates, an unnecessarily rigid one, so the above model was recognized as a useful expository tool, but inadequate in itself to explain the cycles of experience. Both the explosive character of the development in regions C and D, and the damped character of the development in regions A and B are inconsistent with gross observations about the behavior of the economic system.

A hypothesis to be advanced here is that an accelerator-multiplier type model in which a and p are variables over the cycle can lead to a movement in time of the dependent variable of the model which is consistent with the observed values of this variable.16 As interpreted here, the accelerator-multiplier model is meaningless without an analysis of the economic processes which generate the values of a and p. In order to be meaningful a specification of the manner in which a and p vary over the business cycle has to be advanced. The hypothesis that the business cycle of experience can be interpreted as an accelerator-multiplier model with variable coefficients, and that the coefficients of the model vary in a systematic way over the business cycle, is advanced in this chapter.

As a result of this interpretation of the accelerator-multiplier model, the business cycle analysis problem is transformed into the problem of what generates the realized values of a and p. In particular we may ask how this generation process is systematically affected by the variations in National

Income (or Employment, or generally speaking, whatever the variable whose time path is determined by the accelerator-multiplier model). The necessity for systematic variation is due to the need to have the a and p coefficients change in such a manner as to result in a sequence of values of the endogenous variables which can be considered to be consistent with observations.

This chapter focuses on theory. The analysis is directed at the construction of generating processes for these coefficients out of material drawn from the generally accepted body of economic theory. Because of these limitations, no empirical testing is undertaken here. It is obvious that the validity of the model developed depends upon its consistency with observations.

A theory which asserts that the a and p of the model vary in such a way as to generate a time path of national income which is consistent with observation is not, as stated, meaningful. For by adding a and p as 'undetermined' variables we can generate any time path of national income which can conceivably be observed. In order to make the theory meaningful it is necessary to add that the values of a and p are generated by economic processes, and that the generating process leads to such a restricted set of values of a and p that a refutable statement results.

If we ask what determines the value of the accelerator or multiplier coefficient at any time, and carry on an analysis in terms of the behavior of the households and firms, we have done more than transform a linear difference equation into a non-linear difference equation. For by turning our attention to the behavior of households and firms, we can investigate the effects upon the cyclical behavior of an economy of variation in the structure of markets and financing conditions.17 As a result, the functional relation between the different incomes which is the core of the accelerator-multiplier model becomes dependent upon elements other than past period income and 'non-economic constants'. Once we recognize that the relations which determine the accelerator and multiplier coefficients are complex, an analysis of their determination requires more than the specification of a functional relation between these coefficients and the level of income.

The major task of this chapter, therefore, is to develop an analysis of the processes which generate the values of the coefficients in such non-economic models. Prior to undertaking this task, it seems desirable to exhibit a modified Hansen-Samuelson model which does not behave in a manner consistent with observations to show that this hypothesis is not, on the face of it, implausible.

In Table 1.1 we can see that when the marginal propensity to consume, a, is very large (0.9 or 0.95) a value of p a little greater than 1 (1.05 for explosive oscillatory, 1.6 for explosive) is sufficient to lead to an explosive development in the economy; whereas when the marginal propensity to consume is 0.7 an accelerator coefficient of the same order of magnitude

Table 1.1

Values of a

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