Money, endogenous fertility and economic growth

This paper analyzes the issue of money superneutrality through an intertemporal optimizing model of capital accumulation with endogenous fertility, i.e. endogenous population growth. Two elements of this setup invalidate money superneutrality: (i) a demand for fertility that depends on real money balances, and (ii) an inverse relation between capital–labor ratio and population growth. Higher monetary growth increases fertility, since it reduces its opportunity cost, and hence diminishes capital intensity, and per capita output. This reverse Tobin effect is matched by an increase in aggregate capital and output growth rates. In this framework, the optimal monetary growth rule is a “distorted Friedman rule”.     

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.     

Ramsey fiscal policy and endogenous growth

This paper examines the effects of fiscal policies on capital accumulation and economic performance in a simple endogenous growth model with elastic labor supply by focusing on the implementability of a competitive equilibrium with productive public spending and distortionary taxation. Given a feasible exogenous fiscal policy, productive public spending can, at first, lead to positive short-run and long-run growth in the unique competitive equilibrium. However, although strictly positive growth is possible in the short run, a Ramsey policy with productive public spending does not implement positive capital accumulation in the long run. Also, the local indeterminacy of Ramsey allocations, in conjunction with the global multiplicity, arises as an implementable competitive equilibrium with Ramsey policies: namely, a continuum of transitional dynamics and multiple balanced growth paths. I am grateful to Kazuo Nishimura, Theodore Palivos, Sang Hee Won, John Conlon, Apostolis Philippopoulos, Arved Ashby, In Ho Lee, Katsuaki Terasawa, and an anonymous referee of this journal for valuable comments and suggestions. I also thank seminar participants at Ioannina University, Kyoto University, University of Mississippi, and Seoul National University. This paper is supported by 2006 Sabbatical Project, Kyung Hee University.     

Sidgwick and Edgeworth on indeterminacy in the labour market

Commentators have underlined Sidgwick's influence on Edgeworth's thinking and more particularly on New and Old Methods of Ethics (1877). But have failed to notice that Sidgwick remained a major reference in Mathematical Psychics (1881). Therefore, the purpose of this paper is to show that, in this book, Edgeworth wanted to refine upon the problem of wages addressed by Sidgwick in 1879. The thesis of the paper is that Sidgwick and Edgeworth's disagreement as to the role of open competition in the resolution of indeterminacy in the labour market stems from two different notions of competition. This latter can be seen as a differentiation process, as in Sidgwick's, or as a replication mechanism, as in Edgeworth's.     

Education and growth with endogenous debt constraints

When future human capital cannot be alienated, households are allowed to borrow up to the point where it is in their own interest not to default. In such a framework, endogenous borrowing limits arise as the outcome of individual rationality constraint. In a model where education is the engine of growth, we show that endogenous borrowing constraints imply global indeterminacy. Comparing outcomes across the various equilibria we show that the relation between growth and yields is hump-shaped. Maximum growth can arise in an equilibrium with binding borrowing constraints, specially if the elasticity of human capital to education spending is large. Deepening financial markets promotes long-run growth in the case of a poverty trap, but not necessarily otherwise. On the methodological side, our approach stresses the importance of studying borrowing limits in general equilibrium, not only in small open economies. Philippe Michel passed away on July 22, 2004. His death is a great loss for his friends and for the overlapping generations and optimal control community.     

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.     

Heterogeneous expectations,indeterminacy, and postwar US business cycles

This paper estimates a New Keynesian model extended to include heterogeneous expectations: consumers and firms form either rational or boundedly-rational expectations. The inclusion of heterogeneous expectations alters the determinacy properties of the model, with the details of expectations potentially becoming more influential than the Taylor principle for equilibrium stability.The model is estimated with Bayesian techniques, using rolling windows and allowing the parameters to fall both in the determinacy and indeterminacy regions. The estimates reveal large shares of agents who depart from rational expectations. Heterogeneous expectations are decisively preferred by the data everywhere in the sample.Finally, the paper revisits the narrative that sees postwar US macroeconomic data as consistent with indeterminacy in the pre-1979 sample, with a switch to determinacy starting in the early 1980s, and it shows that it is overall robust to inclusion of heterogeneous expectations.     

Multiple steady states,indeterminacy, and cycles in a basic model of endogenous growth

The goal of this paper is to demonstrate that a basic model of endogenous growth with learning by doing may produce a rich array of outcomes. Starting point of our analysis is the Romer (1986a) approach. In contrast to Romer, however, we assume that one unit of investment shows different effects concerning the building up of physical and human capital, so that these variables cannot be merged into one single variable. With this assumption, it can be shown that multiple steady states, indeterminacy of equilibria, and persistent cycles may result in our model.     

A simple endogenous growth model of financial intermediation with multiplicity and indeterminacy

This paper analyzes the role of financial intermediation in a simple endogenous growth model. The results suggest that multiple endogenous growth paths can exist in connection with various levels of financial development, due to the reciprocal externality between financial and real sectors. According to multiplicity, the growth effects of shocks on the technology of intermediation are opposite, depending on the balanced growth path. Furthermore, transitional dynamics is examined, and reveals that the high equilibrium is a saddle path, while the low-growth is locally stable. Therefore, the model presents local and global indeterminacy. These theoretical results support the large empirical literature on the relationship between financial development and growth which depicts conflicting impacts.     

The indeterminacy of equilibrium city formation under monopolistic competition and increasing returns

We study the indeterminacy of equilibrium in the Fujita–Krugman [When is the economy monocentric?: von Thünen and Chamberlin unified, Reg. Sci. Urban Econ. 25 (1995) 505–528] model of city formation under monopolistic competition and increasing returns. Both the number and the locations of cities are endogenously determined. Assuming smooth transportation costs, we examine equilibria in city-economies where a finite number of cities form endogenously. For any positive integer K, the set of equilibria with K distinct cities has a smooth manifold of dimension K-1 as its interior for almost all parameter values in a regular parameterization. The disjoint union of these sets over all positive integers K constitutes the entire equilibrium set.     

Consumption taxation, social status and indeterminacy in models of endogenous growth with elastic labor supply

In this paper, we examine the effects of consumption taxation on long-run growth in an infinitely lived representative-agent model of endogenous growth with endogenous labor supply in which the desire for social status induces private agents to care about others’ wealth or consumption levels. This analysis shows that the increase in consumption taxation raises (reduces) the long-run growth rate when the equilibrium path is locally indeterminate (determinate), provided the desire for social status is not too strong in the relative wealth model. By contrast, in the consumption externalities model, the same result holds, if the Frisch labor supply and labor demand curves have the ‘normal’ slopes at their intersection point, while the result is reversed if these two curves have the ‘wrong’ slopes.     

On the dynamics of an endogenous growth model with learning by doing

Summary. The paper studies the local dynamics of an endogenous growth model with externalities of investment. It is demonstrated that, in case of sustained per capita growth, the competitve economy is characterized by a situation with a unique balanced growth path which is saddle point stable or by a situation with two balanced growth paths. If there are two balanced growth paths, the one with the higher growth rate is a saddle point whereas the path with the lower growth rate is either completely stable, with convergence to a rest point or limit cycle, or completely unstable. In the social optimum the existence of a balanced growth path implies that it is unique and that this path is a saddle point. Received: May 15, 2000; revised version: December 14, 2001     

A note on conspicuous leisure,animal spirits and endogenous cycles

This paper investigates general equilibrium effects of conspicuous leisure. It finds that leisure externalities reduce the degree of other market imperfections needed to generate indeterminacy or sunspot equilibria - endogneous cycles become empirically more plausible. Sunspot equilibria are possible with a downward-sloping labor demand schedule. The economic reasoning behind the result is that with conspicuous-externalities, labor is drawn more easily in and out of leisure to help fulfill agents expectations.Received: June 2003, Accepted: January 2004, JEL Classification: E32Mark Weder: I thank Paulo Brito (the Editor), Michael Burda and an anonymous referee for very helpful comments and suggestions. All remaining errors are my own. Support by the Deutsche Forschungsgemeinschaft in the form of a Heisenberg Fellowshipis gratefully acknowledged.     

Addictive behavior and endogenous growth

This paper sets up an endogenous-growth model in which the consumer's preference is subject to habitual consumption, and examines how consumption habits will govern the rate of sustained growth. It is found that the habitual behavior may be either growth-enhancingor growth-reducing, depending upon whether the substitution between intertemporal consumption is inelastic and whether the consumption experience is harmful or beneficial to the agents. It is also found, given that the elasticity of intertemporal substitution is less than unity, that the learning speed of consumption habits has a positive (negative) impact on the balanced-growth rate if the consumption experience is harmful (beneficial) to the agents.     

Multiple equilibria and global indeterminacy in an endogenous growth model with congestible public goods

This paper extends the findings in Chen and Lee (2007) to show that the use of congestible public goods can produce both local and global indeterminacy in a two‐sector endogenous growth model with productive public services financed by income taxation. Basically, we observe the effects on growth rates by changing parameters, and compare the case of a single steady‐state with the emergence of dual steady‐states, identifying the feasible ways to avoid a possible low‐growth poverty trap. The novelty of our analysis is to detect the presence of global indeterminacy by making use of the Bogdanov‐Takens bifurcation theorem. Some examples are also provided to achieve concrete policy implications.     

Consumer durables and the marginal propensity to consume out of permanent income shocks

This paper derives and estimates a model in which the utility of durable and non-durable consumption is allowed to be non-separable and individuals face a convex adjustment cost for the purchase of a new durable good. Panel data on subjective expectations allow us to identify income shocks and estimate the marginal propensity to consume out of permanent income shocks.     

Growth and distribution in an AK-model with endogenous impatience

This paper combines the classical approach to inequality, based on the division of society into classes with different saving propensities, and the social conflict approach, in which inequality inflicts costs to growth. We assume that each consumer’s discount factor is endogenously determined through two channels: (1) it is positively related to the consumer’s relative wealth, and (2) negatively affected by an aggregate measure of social conflict. Unlike in models with exogenous discount rates, steady state equilibria are indeterminate and the set of equilibria is a continuum parameterized by an index of income inequality. Under reasonable assumptions, the relationship between growth and inequality has an inverted-U shape.     

Pooling and endogenous market incompleteness

Summary. We study a financial market economy with a continuum of borrowers and pooling of borrowers promises. Under these conditions and in the absence of designing costs, utility-maximizing decisions of price-taking borrowers may lead to financial market incompleteness. Parametrizing equilibria through the borrowers no-arbitrage beliefs, we link expectations to the financial market structure. Markets are complete if and only if borrowers beliefs are homogeneous. Price-taking behavior causes a coordination problem which in turn yields indeterminacy and inefficiency of equilibrium allocations.Received: 29 May 2003, Revised: 13 February 2004, JEL Classification Numbers: D50, D52.Correspondence to: Alessandro CitannaWe would like to thank David Cass, John Geanakoplos, Thorsten Hens, Atsushi Kajii, and an anonymous referee for their comments. The first author also thanks CERMSEM (Paris I) and Columbia University Graduate School of Business for the hospitality. A first version of this paper has appeared as GSIA Working Paper #1997-E137, Carnegie Mellon University, which itself revised Citanna and Villanacci (1995).     

Liquidity constraint, increasing returns and endogenous fluctuations

In this paper we show that local indeterminacy, endogenous fluctuations, and periodic and quasi-periodic orbits may emerge in a one-sector infinite-horizon competitive economy where (1) at the end of each period agents must hold a share of their wealth in the form of money and (2) technology exhibits increasing returns to scale. In contrast to other contributions on this subject, we find that such phenomena occur when consumption is intertemporally substitutable and labour is supplied inelastically. The scope for indeterminacy depends basically on the fact that, in view of the financial constraint, total returns on investment represent a weighted average of capital marginal productivity and deflation, and the latter is positively related to the rate of growth of capital.     

Individual preferences and the effect of uncertainty on irreversible investment

This paper considers a relationship between investment behavior and an agent’s preferences in a stochastic one-sector growth model with irreversible investment. Further, it explores the effect of uncertainty in investment policies by using a non-expected utility function. Since uncertainty has an impact on investment policies not only through an option value but also through a risk-adjusted time preference rate in a general equilibrium framework, it is significant to distinguish the two preference parameters of the agent. While the previous partial equilibrium models with irreversible investment have exhibited a negative relationship between the desired capital stock and uncertainty, this paper implies that it is possible to generate a positive relationship for the appropriate parameters. This shows that the results of Hartman and Abel have been robust even in a general equilibrium model.