Tax Rate Variability and Public Spending as Sources of Indeterminacy

We consider a constant returns to scale, one sector economy with segmented asset markets of the Woodford type. We analyze the role of public spending, financed by labor income and consumption taxation, on the emergence of indeterminacy. We find that what is relevant for indeterminacy is the variability of the distortion introduced by government intervention. We show that the degree of public spending externalities in preferences affects the combinations between the tax rate and its variability under which indeterminacy occurs. Moreover, we find that consumption taxes can lead to local indeterminacy when asset markets are segmented.     

Sraffian Indeterminacy in General Equilibrium

The indeterminacy claim for competitive price systems made by Sraffa (1960) is examined by placing Sraffa's work in an intertemporal general equilibrium model. We show that indeterminacy occurs at a natural type of equilibrium. Moreover, the presence of linear activities instead of a differentiable technology is crucial and the indeterminacy is constructed, as in Sraffa, by fixing some or all of the economy's aggregate quantities. On the other hand, an extra condition, that some factors have inelastic excess demand is necessary, and, unlike Sraffa's model, relative prices must be allowed to vary through time. Sraffian indeterminacy and the generic finiteness of the number of equilibria are reconciled by showing that indeterminacy occurs at a measure-zero set of endowments. We use an overlapping-generations model to show that these endowments nevertheless arise systematically and that indeterminacy does not occur when relative prices are constant through time.     

Indeterminacy with no-income-effect preferences and sector-specific externalities

We examine a two-sector real business cycle (RBC) model with sector-specific externalities in which household utility exhibits no income effect on the demand for leisure. Unlike in the one-sector counterpart, indeterminacy can result with sufficiently high returns-to-scale in the investment sector. Moreover, the smaller the labor supply elasticity, the lower the level of externalities needed for indeterminacy. This finding is the opposite of that in all existing RBC-based indeterminacy studies. Finally, in contrast to previous sunspot-driven two-sector RBC models, our economy is able to match the stylized facts that sectoral labor inputs are positively correlated and consumption is procyclical.     

Indeterminacy and cycles in two-sector discrete-time model

Summary. We consider a discrete-time two-sector Cobb-Douglas economy with positive sector specific external effects. We show that indeterminacy of steady states and cycles can easily arise with constant or decreasing social returns to scale, and very small market imperfections. This is in sharp contrast with most of the contributions in the literature in which increasing social returns are required to generate indeterminacy. Received: July 31, 2000; revised version: June 5, 2001     

Real Indeterminacy of Stationary Monetary Equilibria in Centralized Economies

We show that real indeterminacy of stationary equilibria, by which the set of stationary equilibria is a continuum and the real allocation varies among equilibria, may arise in some general equilibrium models with fiat money. The conditions under which such equilibria arise are: (i) each household optimally saves a constant amount of money; and (ii) at least two households face different budget constraints. We present various models, including a decentralized money search model and a centralized model with a monopoly firm, to explain how these conditions lead to real indeterminacy. Finally, we present a policy that uniquely implements any desirable outcome.     

Increasing returns and unsynchronized wage adjustment in sunspot models of the business cycle

A challenge to models of equilibrium indeterminacy based on increasing returns is that required increasing returns for generating indeterminacy can be implausibly large and rise quickly with the relative risk aversion in labor. We show that unsynchronized wage adjustment via a relative wage effect can both lower the required degree of increasing returns for indeterminacy to a plausible level and make it invariant to the relative risk aversion in labor. Consequently, indeterminacy and sunspot-driven fluctuations can emerge for plausible increasing returns regardless of the relative risk aversion in labor. Our model generates reasonable dynamics in terms of matching the business cycle, and sunspot shocks become more important with labor market friction.     

Indeterminacy Arising in Multi-sector Economies

We characterize a large class of constant-returns-to-scale economies with standard Cobb–Douglas production technologies, which, when perturbed to incorporate external effects, exhibit indeterminacy or multiple equilibria. The perturbations are constrained to maintain overall constant returns to scale. We characterize the magnitude of the external effects that yield multiple equilibria in terms of the parameters of the unperturbed economy. We show that it is very easy to construct large and plausible classes of economies that exhibit indeterminacy with constant returns to scale, and with external effects that are arbitrarily small.
JEL Classification Numbers: E00, E3, O40.     

The economics of indeterminacy in overlapping generations models

Recent research indicates that there are robust examples of overlapping generations economies in which there are indeterminate equilibria without fiat money and equilibria with more than one dimension of indeterminacy. This paper presents simple examples of a stationary, pure exchange overlapping generations economy with one good in each period and a representative consumer, who lives for three periods, in each generation. These examples exhibit every possible form of indeterminacy and instability. Furthermore, the parameters of the principal example agree with empirical evidence. We use our examples as case studies for analyzing the problems involved in computing the equilibria of such economies.     

ON THE IMPACT OF HETEROGENEITY ON INDETERMINACY*

Some recent research indicates that the occurrence of indeterminacy in models with externalities may be overstated because these models ignore agents' heterogeneity. We consider a neoclassical two‐sector growth model with technological externalities. Agents are heterogeneous with respect to their shares of the initial stock of capital and in labor endowments. We find that the sign of the effect of inequality on indeterminacy is not pinned down by the standard properties of preferences. However, when the inverse of absolute risk aversion is a convex (respectively concave) function, homogeneity (heterogeneity) tends to neutralize the external effects and eliminate indeterminacy.     

Multiple equilibria in the Aghion–Howitt model

We show that the simple Aghion–Howitt model exhibits oscillatory indeterminacy in the process of creative destruction as firms undertaking new research do not internalize their effect on existing firms. A simple calibration shows that indeterminacy occurs for quite plausible parametrizations of the share of the intermediate good.     

Ruling Out Multiplicity and Indeterminacy: The Role of Heterogeneity

It is well known that economies of scale that are external to the individualdecision makers can lead to self-fulfilling prophecies and the multiplicityor even indeterminacy of equilibrium. We argue that the importance of thissource of multiplicity and indeterminacy is overstated in representativeagent models, as they ignore the potential stabilizing effect ofheterogeneity. We illustrate this in a version of Matsuyama's (1991)two-sector model with increasing returns to scale. Two main results areshown. First, sufficient homogeneity with respect to individual productivityleads to the instability and non-uniqueness of a given stationary state andthe indeterminacy of the corresponding stationary state equilibrium. Second,sufficient heterogeneity leads to the global saddle-path stability and theuniqueness of a given stationary state and the global uniqueness ofequilibrium.     

National labor markets, international factor mobility and macroeconomic instability

We consider a standard two-country environment, where one of the two countries has a rigid labor market, and analyze how global economic integration affects the economies with respect to expectations-driven cycles and steady state welfare. We show that by allowing free capital mobility, equilibrium indeterminacy is exported from the rigid wage country to the world economy. If further liberalization is permitted, by allowing free movements of labor, the scope for indeterminacy is reduced and open labor markets may produce a stabilizing effect on the global macro-economy. Whether this also implies higher welfare in the long run depends on differentials in average firm size across countries, which determines the direction of migration flows.     

Intergenerational Complementarities in Education,Endogenous Public Policy,and the Relation Between Growth and Volatility

We construct an overlapping generations model in which parents vote on the tax rate that determines publicly provided education and offspring choose their effort in learning activities. The technology governing the accumulation of human capital allows these decisions to be strategic complements. In the presence of coordination failure, indeterminacy and, possibly, growth volatility emerge. This indeterminacy can be eliminated by an institutional mechanism that commits to a minimum level of public education provision. Given that, in the latter case, the economy moves along a uniquely determined balanced growth path, we argue that such structural differences can account for the negative correlation between volatility and growth.     

Wealth in utility,the Taylor principle and determinacy

Wealth in the utility function leads to the discounting to consumer’s Euler equation, enlarging determinacy regions and making it easier for the monetary authority to ensure equilibrium determinacy. We show that a passive policy rule which adjusts nominal interest rate by less than one-for-one in response to the inflation rate is able to rule out equilibrium indeterminacy, if properly specified, due to the presence of the demand channel of the Taylor principle and equilibrium determinacy. Furthermore, the extent to which monetary policy rule can be passive in order to avoid indeterminacy depends critically on the degree of preference over wealth as well as the underlying structures and parameters of the model.     

Superneutrality, indeterminacy and endogenous growth

In this paper, we explore the possibility of having money as a source of indeterminacy in endogenous growth models. We adopt the simple Ak model of endogenous growth to be the main analytical vehicle whose balanced growth paths do not display local indeterminacy. Money is introduced via either a general cash-in-advance (CIA) constraint or a pecuniary transactions costs (PTC) technology. It is shown that local indeterminacy of the dynamics is due to the presence of an intertemporal substitution effect on capital accumulation that works against and dominates the conventional inflation effect of Tobin [1965, Money and economical growth. Econometrica 33(4), Part 2, 671]. If money is growth-rate superneutral, then the intertemporal substitution effect is absent so that local indeterminacy cannot occur. Finally, the strength of the intertemporal substitution effect depends positively on the intertemporal elasticity of substitution in consumption.     

Money and Prices Under Uncertainty

We study whether monetary economies display nominal indeterminacy: equivalently, whether monetary policy determines the path of prices under uncertainty. In a simple, stochastic, cash-in-advance economy, we find that indeterminacy arises and is characterized by the initial price level and a probability measure associated with state-contingent nominal bonds: equivalently, monetary policy determines an average, but not the distribution of inflation across realizations of uncertainty. The result does not derive from the stability of the deterministic steady state and is not affected essentially by price stickiness. Nominal indeterminacy may affect real allocations in cases we identify. Our characterization applies to stochastic monetary models in general, and it permits a unified treatment of the determinants of paths of inflation.     

Fiscal Rules,Interest Payments on Debt,and the Irrelevance of the Taylor Principle

We show that in New Keynesian models with non‐neutral government debt, the Taylor principle ceases to be relevant for equilibrium determinacy if the government follows a fiscal rule of levying taxes in proportion to its interest payments on existing debt. This is in contrast with previous studies, which typically have assumed that taxes respond to the level of debt, and have found either a confirmation or reversal of the Taylor principle depending on the feedback from debt to taxes. We find, instead, that the equilibrium effect of the interest rate on debt is crucial for determinacy. If, as in our model, taxes are raised in response to debt interest payments, the range of indeterminacy monotonically decreases with the fiscal feedback parameter. When interest payments are completely tax‐financed, indeterminacy is ruled out without any restrictions on monetary policy.     

A ONE‐SECTOR GROWTH MODEL WITH CONSUMPTION STANDARD: INDETERMINATE OR DETERMINATE?

In a representative agent, one-sector growth model in which the discounting is decreasing in the consumption standard measured as the current average consumption flow, Drugeon (1998) establishes local indeterminacy. This paper extends Drugeon's setup in the discount rate. In our setup, the consumption standard is a habit stock that a weighted average of the whole history of average consumption flows in the past. Local indeterminacy emerges only when the speed of habit formation tends to infinity; otherwise, local indeterminacy cannot appear, no matter how large the habit affects the discount rate.     

Price Level Determinacy under a Pure Interest Rate Peg

In this article we reexamine a famous result by T. J. Sargent and N. Wallace (1975, Journal of Political Economy83, 241–254) according to which a “pure interest rate peg” leads to nominal price indeterminacy. We use P. Weil's (1991, International Economic Review32, 37–53) generalization of the Sidrauski–Brock model, where arrival of new “generations” of infinitely lived agents is allowed, and we obtain the following results: (i) Nominal indeterminacy holds in the traditional Sidrauski–Brock framework; (ii) This nominal indeterminacy disappears as soon as new generations arrive in time, via some rigorous version of Patinkin's “real balance effect”; (iii) A multiplicity of solutions may still remain, but full determinacy occurs in some cases, depending notably on fiscal policy or the distribution of endowments in time. Journal of Economic Literature Classification Numbers: E4, E5     

Stone–Geary preferences in overlapping generations economies under pure exchange: A note

We incorporate Stone–Geary preferences into an overlapping generations economy under pure exchange, and explore stability, indeterminacy, and cycles with positive levels of saving and nonnegative public debt. A stable nontrivial steady state exists for parameter values, for which there does not exist equilibrium in the model with purely logarithmic utility function. We also show the possibility of a period-doubling bifurcation (a two-cycle).