Stabilization policy and indeterminacy in a small open economy

This paper studies the (de)stabilizing effects of income tax rules in a two-sector small open economy with production externalities. The paper shows that in the model with positive sector-specific externalities in the investment sector and negative sector-specific externalities in the consumption sector (or positive aggregate investment externalities), a regressive income tax rule can stabilize such an economy against indeterminacy, whereas a progressive income tax rule can increase the tendency for indeterminacy to occur. This paper also studies two variants that consider an imperfect world bond market and an endogenous labor supply, respectively, and shows that the qualitative results stated above remain valid. Moreover, increasing the level of sector-specific investment externalities can decrease (increase) the minimal level of tax progressivity required for indeterminacy if the investment externalities are below (above) a certain critical value and if the negative externalities in the consumption sector are taken as given.     

Indeterminacy in dynamic models: When Diamond meets Ramsey

We consider an aggregate two-periods overlapping generations model with endogenous labor, consumption in both periods of life, homothetic preferences and productive external effects coming from the average capital and labor. We show that under realistic calibrations of the parameters, in particular a large enough share of first period consumption over the wage income, local indeterminacy of equilibria cannot occur with capital externalities alone. It can nevertheless occur when there are only, even very small, vanishing labor externalities provided that the elasticity of capital-labor substitution and the wage elasticity of the labor supply are large enough. We also show that if labor externalities are slightly stronger, but still small enough to be plausible, and the elasticity of labor supply is larger, local indeterminacy occurs in a Cobb-Douglas economy. Finally, we show that a locally indeterminate steady state is generically characterized by an under-accumulation of capital. It follows therefore that while agents live over a finite number of periods, the conditions for the existence of locally indeterminate equilibria are very similar to those obtained within infinite horizon models and that from this point of view, Diamond meets Ramsey.     

Fiscal policy and indeterminacy in models of endogenous growth

This paper investigates the dynamic behavior of two-sector models of endogenous growth with sector-specific external effects, and government expenditure financed by distortionary taxation. When this type of external effect is combined with a sufficient degree of capital taxation in a Lucas-Uzawa endogenous growth model, continua of equilibria will emerge in the region of the balanced growth paths. By contrast, indeterminacy is not possible when either sector-specific external effects or factor taxation are added to the model in isolation. In the second part of the paper, we demonstrate that if labor supply is endogenous, indeterminacy can be consistent with much lower degrees of increasing returns to scale. Furthermore, certain types of fiscal policy will be associated with multiple balanced growth paths and the existence of a poverty trap. Finally, in the last part of the paper, we demonstrate that if physical capital is employed in both sectors of the economy, indeterminacy will emerge for varying combinations of factor taxation and external effects, even when returns to scale are constant at the social level.     

Multiple transitional growth paths in endogenously growing open economies

This paper extends research in indeterminacy literature to a small open economy, two-sector endogenous growth model. It shows that a continuum of equilibria exist in two situations, (i) the production functions exhibit social constant returns to scale with very small or even negligible externalities; and (ii) the production functions are standard constant returns to scale without externalities but the government implements asymmetric tax policies across sectors.     

Imperfect competition and indeterminacy of aggregate output

This paper shows imperfect competition can lead to indeterminacy in aggregate output in a standard DSGE model with imperfect competition. Indeterminacy arises in the model from the composition of aggregate output. In sharp contrast to the indeterminacy literature pioneered by Benhabib and Farmer [J. Benhabib, R. Farmer, Indeterminacy and increasing returns, J. Econ. Theory 63 (1) (1994) 19-41] and Gali [J. Gali, Monopolistic competition, business cycles, and the composition of aggregate demand, J. Econ. Theory 63 (1) (1994) 73-96], indeterminacy in our model is global; hence it is more robust to structural parameters. In addition, sunspots in our model can be autocorrelated. The paper provides a justification for exogenous variations in desired markups, which play an important role as a source of cost-push shocks in the monetary policy literature. Our model outperforms a standard RBC model driven by technology shocks in several dimensions, including the volatility of labor market and the hump-shaped output dynamics.     

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.     

Unemployment and indeterminacy

Using an efficiency-wage model, we examine the relationship between indeterminacy and unemployment insurance. It is shown that the less unemployment insurance is, the more likely equilibrium is to be indeterminate. Equilibrium can be indeterminate even without externalities or increasing returns, which makes a sharp contrast to the recent literature on indeterminacy. Our result is based on the fact that the no-shirking condition with marginal utility of wealth kept constant is downward sloping when income insurance is not perfect.     

Sunspot Fluctuations in Two-sector Economies with Heterogeneous Agents

We study a two-sector model with heterogeneous agents and borrowing constraint on labor income. We show that the relative capital intensity difference across sectors is crucial for the conditions required to get indeterminacy and endogenous fluctuations. The main result shows that when the consumption good is sufficiently capital intensive, local indeterminacy arises while the elasticities of capital–labor substitution in both sectors are slightly greater than unity and the elasticity of the offer curve is low enough. Locally indeterminate equilibria are thus compatible with a low elasticity of intertemporal substitution in consumption and a low elasticity of the labor supply. As recently shown in empirical analysis, these conditions appear to be in accordance with macroeconomic evidences. We would like to thank R. Becker, J.P. Drugeon and an anonymous referee for useful comments and suggestions. The current version also benefited from a presentation at the conference “Public Economic Theory 04”, Beijing, August 2004.     

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.     

Indeterminacy and multiple steady states with sector-specific externalities

This paper studies a two-sector model with aggregate and sector-specific external effects in production and inelastic labor supply. We first characterize the existence, uniqueness and multiplicity of the steady states as well as their welfare properties. We particularly focus on the CES production functions and show that the steady state is generically either unique or there are exactly two. A simple geometrical methodology enables us to characterize the local dynamics of the steady state. We show that in order to get indeterminacy, the presence of both aggregate and sector-specific external effects is needed, along with low capital–labor elasticities of substitution and high, but bounded from above, elasticities in intertemporal consumption. We perform a sensitivity analysis and show that indeterminacy emerges for parameter values in line with those used in calibrations of standard RBC models, that is for unitary elasticities of input substitution and of intertemporal substitution in consumption.     

Progressive taxation and macroeconomic stability in two-sector models with social constant returns

It has been shown that, in the two-sector Benhabib–Farmer–Guo model with technologies of social increasing returns that exhibits indeterminacy, progressive income taxes de-stabilize the economy. This paper revisits the robustness of the tax implication in the two-sector Benhabib–Nishimura model with technologies of social constant returns that exhibits indeterminacy. We show that a progressive income tax stabilizes the economy against sunspot fluctuations, and thus the tax implication based on the two-sector Benhabib–Farmer–Guo model is not robust.     

Indeterminacy with almost constant returns to scale: capital-labor substitution matters

Summary. This paper shows, in the benchmark one-sector Ramsey model, that indeterminacy and sunspots may occur when externalities are small, provided that capital and labor are more substitutable than in the usual Cobb-Douglas specification. Key to the results are the general formulations of both preferences and technology that we consider. In particular, indeterminacy is shown to occur under almost constant returns to scale provided that both concavity of utility for consumption is small enough and labor supply is close to indivisible. An important implication of the results is that, when labor supply is positively sloped, indeterminacy does not necessarily require the equilibrium wage-hours locus to be upward sloping.Received: 16 June 2004, Revised: 8 March 2005, JEL Classification Numbers: C62, D58, D91, E32.This is a companion paper of “Sunspots in real business-cycle models: completing calibration”, with new results that have emerged from extending the analysis contained in the latter article. The author would like to thank, without implicating, Bruno Decreuse, Andrew Postlewaite, Alain Venditti, Yi Wen, participants at the 2003 Society for Economic Dynamics Meeting, as well as C.D. Aliprantis, the Editor, and an anonymous referee for useful comments and suggestions.     

Indeterminacy in a small open economy with endogenous labor supply

Summary. We establish conditions under which indeterminacy can occur in a small open economy business cycle model with endogenous labor supply. Indeterminacy requires small externalities in technologies with social constant returns to scale, independently of the intertemporal elasticities in both consumption and labor. Received: December 12, 2001; revised version: May 17, 2002 RID="*" ID="*"The paper has benefited from discussions with Jess Benhabib and Mark Weder, as well as from the comments of an anonymous referee. Correspondence to: Q. Meng     

A Characterization of the Dynamical System in a Two-sector Overlapping-generations Model: The Case of Unbounded Growth

This paper characterizes perfect-foresight equilibria in a two-sector overlapping-generations economy for the case of unbounded growth. The analysis demonstrates that gross substitutability in consumption is not sufficient to ensure the determinacy of equilibrium. Unlike Boldrin and Rustichini (1994), indeterminacy of equilibria can arise within the framework of an overlapping-generations model with convex technology. The finite time horizon of agents is the source of such indeterminacy.
JEL Classification Number: 041.     

Consumption externalities, production externalities, and efficient capital accumulation under time non-separable preferences

The effects of consumption and production externalities on economic performance under time non-separable preferences are examined both theoretically and numerically. We show that a consumption externality alone has long-run distortionary effects if and only if labor is supplied elastically. With fixed labor supply, it has only transitional distortionary effects. Production externalities always generate long-run distortions, irrespective of labor supply. The optimal tax structure to correct for the distortions is characterized. We compare the implications of this model with those obtained when the consumption externality is contemporaneous. While some of the long-run effects are robust, there are also important qualitative and quantitative differences, particularly along transitional paths.     

Consumption aspirations in dirty and clean goods and economic growth

This paper builds a two-sector, two-factor environmental model in which agents optimally choose the clean and dirty goods in order to display their social status. In contrast to the conventional notion, we show that greater social aspirations in consumption regardless of either clean or dirty goods have an ambiguous impact on growth, depending on whether the production of conspicuous goods is relatively labor- or capital-intensive, whether the production of conspicuous goods generates more or fewer emissions, and whether labor supply is or is not responsive to social status seeking. By connecting two conflicting aspects of consumer preference involving social aspirations and environmental concerns, our analysis offers a novel explanation for the environmental Kuznets curve and a theoretical support for the empirical possibility of a negative employment-growth relationship and the so-called Green New Deal. Our welfare analysis shows that social comparisons in consumption may increase, rather than decrease, social welfare. The Pigovian tax may only be socially sub-optimal in the two-sector economy because it is unable to completely correct the distortion caused by consumption externalities.     

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     

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.     

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.     

ENDOGENOUS CYCLES IN A SIMPLE MODEL WITH LAGGED EXTERNALITIES ON PRODUCTIVITY

This paper presents a simple model of endogenous cycles. In the model, working experience creates learning‐by‐doing externalities that improve labor productivity but it takes long time before the externalities come into effect. In addition, individuals have preferences with a subsistence consumption level. In the presence of the subsistence consumption requirement, a productivity increase generates the income effect that surpasses the substitution effect, and individuals choose to increase leisure time at the expense of supplying labor. The interactions between productivity changes through the lagged externalities and labor supply generate cycles endogenously. The model analysis shows that the dynamics exhibit cyclical fluctuations around a unique steady state.