Financial fragility, effective demand and the business cycle

Abstract

A shifting equilibrium model of effective demand is constructed, in which the state of long run expectations is non‐constant, and is affected by the disappointment of short‐run expectations. It is shown that this model gives rise to cumulative expansions/contractions in nominal income. Changes in the financial fragility of households and firms in the course of these expansions/contractions are then allowed for, together with commercial bank reactions to changing financial fragility. It is shown that turning points in the expansions/contractions of nominal income can arise, resulting in a model of aggregate fluctuations in which the business cycle is aperiodic and of no fixed amplitude.

Notes

Mark Setterfield, Department of Economics, Trinity College, Hartford, CT 06106, USA. Email: [email protected]

Because the focus of the paper is on aggregate fluctuations rather than trend outcomes, the model is developed in terms of the levels rather than the rates of growth of variables. There is a long tradition of modelling the business cycle in this fashion, as is evident from the structure of seminal business cycle models such as the multiplier‐accelerator and new classical monetary business cycle models (see, for example, Dore, 1993, for a survey). The integration of the ideas presented in this paper into a growth theory framework would, of course, increase the time horizon to which the model could be said to apply. For first steps in this direction, see Setterfield (2003).

Realised nominal income, Y, is demand determined in this model, so that Y_t ≡ D_t regardless of whether or not Z_t = D_t . This means that actual nominal income adjusts to the value of aggregate demand within any given period regardless of whether or not the value of aggregate demand equates with firms' short period revenue expectations (and hence the value of their output) within the period. These adjustments can occur through changes in prices or in inventories, depending on the precise structure of the supply side. This structure, and any effects that within‐period supply‐side adjustments may have on the subsequent evolution of aggregate demand, are overlooked here for the sake of simplicity.

The propensity to consume (together with the coefficient β) is a conventional value—that is, a socially constructed (and therefore transmutable) but relatively enduring parameter—because in a monetary production economy, the presence of fundamental uncertainty prevents households from planning consumption according to the criteria associated with inter‐temporal optimization. The simplest consumption function consistent with this vision is used here by virtue of the fact that the behaviour of planned autonomous spending, rather than consumption, is of greater interest in what follows. Note that a corollary of the consumption function described above is that economy‐wide saving in each period can be identified as the sum of corporate retained earnings and household saving, or:

given that Z_t = D_t−1 by equations (1) and (8). Households and firms are therefore actively accumulating new financial assets during each period. The asset allocation problem that confronts households and firms as they attempt to organize their savings portfolios is not explicitly examined in what follows, the implicit assumption being that financial assets accumulate in bank deposits. However, we will return to consider the saving behaviour of the non‐bank private sector in our discussion of financial fragility in Section 3.

Note that equation (4) makes no distinction between the behaviour of firms and that of households. The reactions of firms and households to changes in interest rates and the disappointment of short run expectations are treated as identical for the sake of simplicity. Relaxing this simplifying assumption would complicate the analysis that follows without altering its essential results and conclusions.

Note, then, that because of the way that it is financed, effective autonomous spending ϕA_t is identical to the volume of new debts accumulated by the non‐bank private sector during each period. Again, we will return to consider the implications of this debt accumulation when discussing financial fragility in Section 3.

The reader is referred back to note 2 for discussion of this identification of aggregate demand with the realized value of nominal income. Note that the solution of equations (1) and (2) has implications both for nominal income and the level of employment, which is increasing in nominal income in this model. Hence, we are assuming that there exist under‐utilized labour resources at any given point in time, so that the labour market is capable of accommodating any fluctuations in employment that result from the evolution of aggregate demand as described in equation (12).

Because c is a convention it is, strictly speaking, transmutable and hence may change over time. However, conventions are also relatively enduring, and it is the appeal to this property of conventions that justifies our treatment of c as a constant in the present exercise. Note that it is firms' short‐run expectations that are disappointed when D ≠ Z, but we assume that the animal spirits of households as well as firms are affected by this information about business conditions and by the changes in nominal income and employment that result from it.

In other words, μ_ϵ is both the mean and the mode of ϵ, so that we are assuming that the distribution of ϵ about μ_ϵ is symmetrical.

A system is closed if it can be described in a manner that is complete—i.e. if it can be described in terms of a set of structural relations (a ‘model’) that contains all of the information necessary to exactly determine the outcomes associated with the system. (These outcomes may be expressed as levels, rates of change, moments of distributions, and so forth.) A system is open, on the other hand, if any description of it must remain incomplete (in the sense of completeness as defined above). There remains a ‘degree of freedom’ in the determination of the outcomes associated with an open system that remains elusive to the model builder.

When choice involves discretion in the manner described above, a system will be rendered open by virtue of its lack of intrinsic closure. Intuitively, this means that causes need not always have the same effects (because decision makers can always choose to act differently—and in novel ways—in response to any given set of causal stimuli). This is the case in (15), in which the relationship between disappointed short‐term expectations and the state of long run expectations is time dependent, and the possibility of articulating a closed‐form description of the evolution of the function f_t is denied by hypothesis. As such, the same causes (a value of D _t−1 − Z _t−1 of any given size) need not always have the same effects (i.e. will not generate a change in α_t , the value (or expected value) of which can be described in a timeless, once‐and‐for‐all fashion a priori).

Financial fragility is a complex phenomenon of which equation (21) can only claim to be a partial representation. It may also be influenced by factors such as asymmetry in the distributions of assets and liabilities within the non‐bank private sector and, following Minsky (1978), the type of liabilities that households and firms accumulate (hedge, speculative or ponzi). These dimensions of financial fragility are not explicitly modelled here and hence they are not discussed further in what follows.

This is a simplifying assumption that keeps F_t in phase with D_t over the course of the cycle.

Authors such as Lavoie (1996, pp. 285–290) deny the inevitability (although not the possibility) of increases in private sector financial fragility, and/or increasing concern about this state of affairs on the part of lenders, during the course of a boom. The model developed here can be thought of as exploring what happens if financial fragility does increase during booms. As will become clear, the model is fully compatible with Lavoie's suggestion that, even if financial fragility does increase during a boom, so, too, may lenders' tolerance of this fragility. Note also that, once again, no distinction is made between firms and households when modelling the non‐bank private sector. As before, this is a simplifying assumption that does not alter the essential results of the analysis that follows.

Information asymmetries may further contribute to the different attitudes of the non‐bank and banking sectors towards financial fragility.

Note that ‘structuralism’ refers here to changes in the commercial rate of interest resulting from changes in the financial fragility of the non‐bank private sector. This usage differs from the convention of defining structuralism as a change in the commercial interest rate brought about by a change in the structure of commercial banks' liabilities, as a result of the failure of the central bank to accommodate commercial banks' increasing demands for reserves as the quantity of credit in circulation is expanded (see Lavoie, 1996, pp. 281–282).

This can also be deduced from equations (28) and (29). Note that if, as is possible, ν _tmin > ν_t > ν _tmax nominal income will converge to a stationary state of the kind identified in the limit result in (14). However, the precise value of this limit will be contingent on the precise level of effective autonomous spending achieved by period t, something that is, in turn, a path‐dependent product of the prior expansion path of the economy. See Setterfield (1999).

This discussion also reveals the essential role of conventions as cognitive devices in the current model. For example, as long as the conventions governing the distribution of ϵ endure for discrete intervals, and as long as it is possible for model builders and/or commercial banks to learn these conventions, it will be possible, within the discrete intervals of time for which the conventions endure, to forecast non‐bank private sector behaviour (and hence ν _{t min} and ν _{t max}) on the basis of the conventions governing ϵ, and with greater confidence than would otherwise be the case in the absence of relatively enduring conventional behaviour. Uncertainty remains a feature of the decision making environment, of course, because of the ultimate transmutability of conventions and their propensity to undergo novel change.

Recall that the behaviour of firms and households is un‐differentiated, so it is as if firms and households constitute a single non‐bank private sector decision maker.