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# Stability in Economics

SPEEDS OF ADJUSTMENT AND THE USEFULNESS OF EQUILIBRIUM

STRUCTURAL STABILITY AND PATH DEPENDENCE

STABILITY OR RESILIENCE

BIBLIOGRAPHY

The concept of stability in economics is closely related to the concept of equilibrium and is one of the three properties of equilibrium that is routinely studied by economic theorists (the others being uniqueness and existence). Economists typically use the term stability to denote what mathematicians call asymptotic stability. Hence an economic system (such as a firm, a market, or even an entire economy) is stable if, following some displacement of the system from equilibrium, it adjusts so as to regain its original equilibrium position. The concept of stability can be demonstrated by the behavior of a conventional (Marshallian) commodity market, in which supply and demand interact to determine both price and quantity traded. If the price level in such a market is dislodged from its equilibrium (market-clearing) value, the resultant excess demand (or supply) gives rise to subsequent changes in the price level that will restore conditions of equilibrium.

A stable equilibrium may be either a point (such as a particular value of the unemployment rate) or a path (such as a limit cycle describing regular fluctuations in national income). Furthermore, an equilibrium may be either stable or unstable depending on initial disequilibrium conditions. Indeed, if stability is observed only when an economic system is not displaced too far from equilibrium, then the system is described as being only locally stable. In economic systems with multiple equilibria, for example, individual equilibrium positions can only be locally stable. If stability is observed regardless of the initial distance from equilibrium, however, the system is said to be globally stable.

Stability is not always regarded as an important or good thing in economic theory. For example, instability is sometimes essential to the motion of the economic system that is being theorized, as in the English economist John Hickss famous theory of the business cycle. Elsewhere, saddle-point instability is important for solving the problem of the choice of disequilibrium adjustment path in certain models involving rational expectations. Some economists, meanwhile, argue that stability is an unnecessary feature of equilibrium analysis. They suggest that unstable equilibrium models generate the useful empirical claim that the current outcomes of an economic system will not persist in the future. Finally, as will become clear in the discussions of path dependence and resilience below, other economists regard stability as an analytical straitjacket that discourages routine exploration of the possibility that economic systems display richer dynamics.

## SPEEDS OF ADJUSTMENT AND THE USEFULNESS OF EQUILIBRIUM

This having been said, the prevalence of equilibrium analysis in economic theory means that most economists seek to prove (or, very often, simply assume) the stability of equilibrium most of the time, and with good reason. First, it is essential that an economic system be able to get into equilibrium if the latter is to be useful as a description of the actual configuration of the system at any point in time. Second, the method of comparative statics/ dynamics, on which so many of the results and policy conclusions of economic theory are based, is predicated on the stability of equilibrium.

The usefulness of equilibrium for describing the outcomes that one might expect to observe in an economic system depends, in fact, not just on stability but also on the speed of disequilibrium adjustment. Unless equilibrium is reached sufficiently rapidly, it may not be interesting as a description of system outcomes over a particular time horizon. Indeed, if adjustment is so slow that the data defining an equilibrium configuration autonomously change before the equilibrium itself is attained, then even an analytically stable equilibrium may never be reached in practice, rendering it meaningless as a description of system outcomes over any time horizon. The speed of disequilibrium adjustment is an issue to which economists who rely on equilibrium analysis seldom pay sufficient attention.

## STRUCTURAL STABILITY AND PATH DEPENDENCE

The potential for the data defining an equilibrium position to change in the course of disequilibrium adjustment draws attention to two further issues connected with stability in economics. First, a stable economic system must also be structurally stable if it is to attain equilibrium. This means that, over the course of disequilibrium adjustment, the data defining the system must be subject to only small variations that do not fundamentally alter the character of the systems motion (by converting a stable system into an unstable one, for example). Structural stability is rarely addressed by economists, who instead usually assume that data remain literally constant in the course of disequilibrium adjustment.

Second, the adjustment dynamics of a system may be affected by path dependence. A conventional, stable equilibrium can be described as determinate in the sense that it is both defined and reached independently of the path taken toward it. But if disequilibrium adjustment changes the data defining an equilibrium and hence changes the equilibrium configuration itself, then the equilibrium is indeterminate or path-dependent. For example, if disequilibrium trading results in a particular consumption experience that would not have existed in the absence of disequilibrium conditions, and if this experience alters household preferences (a shortage may enhance the perceived desirability of a commodity, for instance), then the exact equilibrium configuration of a Marshallian commodity market will be affected by the history of its disequilibrium adjustment, and will thus be path-dependent. As this example illustrates, an indeterminate or path-dependent economic system may eventually reach an (historically contingent) equilibrium position, in which case it is said to be definite-indeterminate. Such a system may be said to display weak stability in the sense that, although its outcomes are path-dependent, a position of equilibrium is eventually attained. This contrasts with the strong stability characteristic of determinate systems, which converge onto fixed points or paths defined independently of the systems prior adjustments.

However, an indefinite-indeterminate system will never settle down into a state of equilibrium (thus lacking even weak stability), but will instead remain in continual, path-dependent motion. A path-dependent equilibrium position may exist at any point in time in an indefinite-indeterminate system, but such positions are continually being redefined and are never reached, so that they never serve as interesting descriptions of the systems outcomes. Note that indeterminacy or path dependence is not the same as instability. The latter involves movement away from a fixed point or path. Path dependence, on the other hand, involves redefinition of the equilibrium point/path in the course of disequilibrium adjustment. In path-dependent systems, an equilibrium may exist and attract the system toward itself. But the equilibrium will be redefined by the resulting motion of the system and, as a consequence of the system thus chasing a moving target, may never be reached. Unfortunately, economists typically assume away path dependence when dealing with the stability properties of equilibrium models, with the result that any sense of the historical contingency of economic outcomes is lost. Work on hysteresis and lock-in in economicsconcepts that show how events in the past can permanently affect current and future economic behavior and outcomescan be understood as attempting to rectify this state of affairs.

## STABILITY OR RESILIENCE

Finally, the behavior of indefinite-indeterminate systems prompts the question as to whether economists should pay more attention in future research to the resilience rather than the stability of economic systems. Stability analysis focuses on a precise outcome or configuration of a system, and the capacity of the system to return to this constant point or path over time. The concept of resilience, meanwhile, focuses on the durability of the system itself and hence its capacity for longevity. The key question addressed in the study of resilience is coarser and more qualitative than that addressed by stability analysis: Can the system as a whole reproduce itself in a sufficiently orderly fashion, and thus persist over time? Hence an indefinite-indeterminate systemwhich displays neither weak nor strong stability propertiesmay nevertheless be very resilient. Whether stability or resilience is the more important property of an economic system is likely context-dependent. For example, if a concert hall is to be economically viable, it may be very important for that hall to ensure that the volume of its public address system remains essentially constant and that any variations in volume are rapidly eliminated by movement back toward equilibrium. However, it may be far more important for an exchange-rate regime to help reproduce orderly conditions of international trade and finance over time, than for it to ensure the movement of a particular exchange rate toward some predefined value identified by economists as an equilibrium.

## BIBLIOGRAPHY

Gandolfo, Giancarlo. 1996. Economic Dynamics. 3rd ed. Berlin and New York: Springer.

Hahn, Frank. 1973. On the Notion of Equilibrium in Economics. London: Cambridge University Press. Reprinted in Frank Hahn, Equilibrium and Macroeconomics. Cambridge, MA: MIT Press, 1984.

Holling, C. S. 1973. Resilience and Stability of Ecological Systems. Annual Review of Ecology and Systematics 4: 123.

Kaldor, Nicholas. 1934. A Classificatory Note on the Determinateness of Equilibrium. Review of Economic Studies 1 (2): 122136.

Setterfield, M. 1997. Should Economists Dispense with the Notion of Equilibrium? Journal of Post Keynesian Economics 20 (1): 4776.

Mark Setterfield