# Endogenous Price Fluctuations in an Optimizing Model of a Monetary Economy

Abstract: This paper demonstrates that an optimizing model of a monetary economy can produce perfect foresight equilibria in which the price level fluctuates forever. Cyclically or chaotically fluctuating equilibria are more likely to exist when the rate of money supply growth is high. Furthermore, the set of equilibrium prices may have a complicated topological structure, which poses a more serious problem concerning the validity of comparative statics method than any sort of indeterminacy previously discussed in the literature. Copyright 1991 by The Econometric Society.

Topics: Price level (59%), Comparative statics (56%), Money supply (56%)

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Abstract: Summary. The paper considers the determinacy of the equilibrium price level in the cash-in-advance monetary economy of Lucas and Stokey (1983, 1987), in the case of deterministic "fundamentals". The possibilities both of a multiplicity of perfect foresight equilibria and of "sunspot equilibria" are considered. Two types of monetary policy regimes are considered and compared, one in which the money supply grows at a given exogenous rate (that may be positive or negative), and one in which the nominal interest rate on one-period government debt is pegged at a given non-negative level. In the case of constant money growth rate regimes, it is shown that one can easily have both indeterminacy of perfect foresight equilibrium and existence of sunspot equilibria; indeed, in the case of negative rates of money growth (as called for by Friedman (1969)), both types of indeterminacy necessarily occur. On the other hand, sufficient conditions for uniqueness of equilibrium (and non-existence of equilibria other than a deterministic steady state) are also given, and a class of cases is identified in which a sufficiently high rate of money growth guarantees this. Thus there may be a conflict between the aims of choosing a rate of money growth that results in a high level of welfare in the steady state equilibrium and choosing a rate that makes this steady state the unique equilibrium.) In the case of the interest rate pegging regimes, sufficient conditions are given for uniqueness of equilibrium (and impossibility of sunspot equilibria), and it is shown that these necessarily hold in the case of any low enough nominal interest rate. Thus the nominal interest rate peg allows simultaneous achievement of price level determinacy and a high level of welfare in the unique (steady state) equilibrium. In this paper I consider the consequences of alternative choices of the monetary policy regime for the determinacy of the rational expectations equilibrium value of money, and in particular for the existence or not of "sunspot" equilibria, i.e., rational

661 citations

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Abstract: This chapter gives an overview of the recent literature on indeterminacy and sunspots in macroeconomics. It discusses of some of the conceptual and the technical aspects of this literature, and provides a simple framework for illustrating the mechanisms of various dynamic equilibrium models that give rise to indeterminate equilibria. The role of external effects, monopolistic competition, and increasing returns in generating indeterminacy is explored for one-sector and multi-sector models of real business cycles and of economic growth. Indeterminacy is also studied in monetary models, as well as in models where monetary and fiscal policy are endogenous and determined by feedback rules. Particular attention is paid to the empirical plausibility of these models and their parametrizations in generating indeterminate equilibria. An overview of calibrated macroeconomic models with sunspot equilibria is given, and their successes and shortcomings in matching properties of data are assessed. Finally some issues regarding the selection of equilibria, the observable implications, and difficulties of forecasting that arise in such models are briefly addressed.

189 citations

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Abstract: Recent literature on structural vector autoregressions has attempted to identify the effects on the economy of an increase in the stock of money. This work has led to a broad consensus. Initially, an increase in money leads to an increase in economic activity. Output and employment go up, the interest rate declines, and prices respond weakly, if at all. Over time, these real effects die out and, in the long run, the only effect of higher money is higher prices. Most writers on the topic have attributed the real effects of money, in the short run, to a barrier of some kind that prevents markets from clearing. We show instead that a competitive market-clearing model in which money enters the production function can reproduce the broad features of data. Our argument exploits the existence of multiple equilibria in a rational-expectations model. Journal of Economic Literature Classification Numbers: E00, E4.

131 citations

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Abstract: In this paper, we study the relationship between the rate of increase of the money supply and the rate of growth of output in an economy. We show that in some models of endogenous growth, inflation has direct effects on the growth rate of the economy. Despite this, the estimated welfare cost of inflation from calibrated examples is similar to that found in exogenous growth models.

127 citations

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Abstract: A traditional function of the central bank is to control the price level. The fiscal theory of the price level challenges this assumption, arguing instead that the fiscal authority's budgetary policy is the primary determinant of the price level. The authors provide a critical review of the fiscal theory and its implications for monetary policy.

118 citations

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Abstract: After a quarter century of unbroken development in the theory of allocation under uncertainty, it has become an obvious fact that randomness in endowments, preferences or technology will generally work its way to the prices and allocations which prevail in equilibrium. Is it true, as intuition may suggest in haste, that random prices necessarily reflect some intrinsic uncertainty in the structure of the economy, or can they arise, as some recent literature [3, 12, 14, 151 indicates, merely from extraneous, self-perpetuating beliefs that prices are stochastic? The question is of interest for it raises the possibility that business cycles are set in motion by arbitrary shifts in any factor, however purely subjective, agents happen to deem relevant to economic activity: animal spirits, consumer sentiment or the prophecies of the Sibyl at Cumae may spark fluctuations in which prices change simply because they are expected to and price signals convey no structural information. The evidence on the influence of subjective factors is ample and dates back several centuries’; the Dutch “tulip mania,” the South Sea bubble in England, and the collapse of the Mississippi Company in France are three well-documented cases of speculative price movements which historians consider unwarranted by “objective” conditions. What follows is a demonstration that a kindred type of paradoxical behavior, which we name extraneous uncertainty, is both possible and “frequent” among rational expectations equilibria in an aggregative model of overlapping generations. In particular, if we constrain (the probability distribution of) the price level to clear markets, reproduce beliefs and, in

680 citations

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Abstract: Given a one-parameter familyf
λ(x) of maps of the interval [0, 1], we consider the set of parameter values λ for whichf
λ has an invariant measure absolutely continuous with respect to Lebesgue measure. We show that this set has positive measure, for two classes of maps: i)f
λ(x)=λf(x) where 0<λ≦4 andf(x) is a functionC
3-near the quadratic mapx(1−x), and ii)f
λ(x)=λf(x) (mod 1) wheref isC
3,f(0)=f(1)=0 andf has a unique nondegenerate critical point in [0, 1].

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Abstract: Because sunspot equilibria seem to be of central importance for an understanding of rational expectations, we seek here to characterize completely a limited class of sunspot equilibria (stationary ones with two possible natural events) in the simplest overlapping generations model of production. We present a sufficient condition for the existence of stationary sunspot equilibria, examine how these are related to strictly periodic equilibria of the same order, and investigate how deterministic stationary equilibria bifurcate to stationary sunspot equilibria. A concluding section examines how our results survive in more general settings.

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Abstract: It is shown that in a two period general equilibrium securities model where assets pay in money the generic dimension of the set of equilibrium allocations, in the incomplete market situation, is S − 1, where S is the number of assets. Hence the degree or real indeterminacy is independent of the number of assets. This result requires, beyond fewer assets than states, that the number of traders be larger than the number of securities and that the asset return matrix be in general position. The generic dimension for arbitrary returns matrix is also obtained. It is argued, in addition, that the presence of real or mixed assets does not by itself lower the degree of indeterminacy.

191 citations