Optimal balanced growth in a general multi-sector endogenous growth model with constant returns

I will study a multi-sector endogenous growth model with general constant returns to scale technologies and demonstrate the existence, uniqueness and the saddle-path stability of the balanced growth equilibrium. I will first demonstrate the existence of a balanced growth equilibrium, by showing that the balanced growth rate associated with the balanced growth equilibrium is solely determined by solving a Frobenius root problem of the price equations derived from the Euler equations and the property of the nonsubstitution theorem. Then I will show the saddle-path stability of the balanced growth equilibrium without any capital intensity conditions, which is a generalized property proved in the two-sector endogenous growth models by de Guevara et al. (J Econ Dyn Control 21, 115–143, 1997), Bond et al. (J Econ Theory 68, 149–173 1996) and Mino (Int Eco Rev 37, 227–251 1996). The theorem clearly implies that the balanced growth equilibrium has a transition path in the neighborhood of the balanced growth equilibrium. The paper was presented at the conferences “Irregular Growth: Beyond Balanced Growth” held on June 19–21, 2003 in Paris and “Economic Growth and Distribution: On the Nature and Causes of the Wealth of Nations” held on June 16–18, 2004 in Lucca, Italy. From the discussion with Alain Venditti at CNRS-GREQAM, Gerhard Sorger at University of Vienna and the conference participants, I have been benefited much by writing this paper. Especially Alain Venditte had given me a chance to take a look at his unpublished paper titled ” Indeterminacy and the Role of Factor Substitutability” jointly written with Kazuo Nishimura at Kyoto University and published in Macroeconomic Dynamics, Vol. 8. The author also would like to thank an anonymous referee for useful suggestions.     

The Influence of Socioeconomic Factors on Economic Growth

The main goal of this paper is to analyse the relationship between social capital and economic growth taking into account the role of fiscal policy from theoretical and empirical points of view. To achieve this goal, “Human Capital and Public Capital Effects on Economic Growth” is focused on the effects of two traditional factors: human capital and public capital effects on economic growth. “Social Capital Effects on Economic Growth” considers qualitative variables introducing some socioeconomic effects on economic growth process analysis. In this case, social capital the main variable will be considered. “Empirical Analysis,” an empirical analysis is developed considering the case of European countries prior to the EU enlargement. Finally, in Conclusions,” the main conclusions will be resumed.      

Irreversibilities,uncertainty and underemployment equilibria

In a competitive overlapping generations model, technological irreversibilities and idiosyncratic uncertainty generate a misallocation of resources among segments, which takes the form of underemployment and underutilization of capacities at the aggregate level. This affects the qualitative properties of the equilibrium path. Indeed, increases in the variance of the technological shock can be responsible, a.o., for an “inescapable poverty trap,” or for periodic orbits generating endogenous fluctuations in underemployment.     

Non-computability of competitive equilibrium

Summary. We provide a “computable counterexample” to the Arrow-Debreu competitive equilibrium existence theorem [2]. In particular, we find an exchange economy in which all components are (Turing) computable, but in which no competitive equilibrium is computable. This result can be interpreted as an impossibility result in both computability-bounded rationality (cf. Binmore [5], Richter and Wong [35]) and computational economics (cf. Scarf [39]). To prove the theorem, we establish a “computable counterexample” to Brouwer's Fixed Point Theorem (similar to Orevkov [32]) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell [26], Geanakoplos [16], Wong [50]). Received: September 9, 1997; revised version: December 17, 1997     

Competitive and core allocations in large economies with differential information

Summary. We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is “irreducible”, then a competitive equilibrium, in the sense of Radner (1968, 1982), exists. Moreover, the set of competitive equilibrium allocations coincides with the “private core” (Yannelis, 1991). We also show that the “weak fine core” of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy. Received March 22, 2000; revised version: May 1, 2000     

Effect of social security on fertility and savings: an overlapping generations model

Old-age pension schemes do not exist in most developing countries, so adults bear children as security investments for the future. This phenomenon leads to unduly high rates of population growth. It has been hypothesized that introducing social security programs in such countries would increase savings rates and reduce the number of children born over the long term. The author studies the general equilibrium effects of some social security programs on rates of population growth and capital accumulation within an overlapping generations framework with endogenous fertility and savings. Specifically, Raul's overlapping generations growth model is extended to study the general equilibrium effects of payroll-tax-financed and child-tax-financed social security programs. It is shown that if the rate of intergenerational income transfers from young to old or child care cost is low, competitive equilibrium leads toward overpopulation and capital accumulation in a modified Pareto optimal sense; a social security program in such a case is therefore Pareto improving. A fully-funded system is not neutral when financed by child taxes. Finally, it is also shown that unlike in the case of exogenous fertility where competitive equilibrium attains steady state only asymptotically, fertility, when endogenous, may attain a unique globally steady state in finite time.     

On the growth and welfare effects of monopolistic distortions

The most fundamental proposition about growth and competition is that there is a tradeoff between static welfare and long-term growth. This paper reconsiders this basic proposition in an expanding variety endogenous growth model with competitive markets for “old” innovative products and for a traditional good. We shed light on some implications of monopolistic distortions which tend to be ignored by standard models. First, no growth may be better than some growth, since modest positive growth potentially requires sizeable static welfare losses. Second, the economy may converge to a steady state with zero growth, even though a locally saddle-point stable steady state with positive growth exists if the initial share of “cheap” competitive markets is sufficiently high, as this implies a relatively low demand for “expensive” innovative goods. Third, such a “no-growth trap” may happen in a world economy made up of several countries engaged in free trade with each other. The policy implications are that growth-enhancing policies may be misguided and that quick deregulation as well as quick trade liberalization can lead to stagnation in the long term.      

Interregional Fertility Differentials and Agglomeration

In this study, we construct an interregional trade model that includes endogenous fertility rates. The presented model shows that the agglomeration of manufacturing firms in a large region causes fertility rates to become lower than in a small region. We also find that a decrease in transportation costs results in the agglomeration of manufacturing firms, which lowers fertility rates in both large and small regions. In addition, comparing the competitive equilibrium with the optimal equilibrium, the fertility rates may be inefficiently small.     

Non-stationary,stable Markov processes on a continuous state space

We extend our previous result on simple stable Markov (SSM) processes to the case where the state space is continuous. As anapplication we show the existence of a competitive general equilibrium of a cobweb model where price volatility is generated both by exogenous shocks and by stochastic, so called generating variables (that may be interpreted as sunspots) that govern the correlation of the rational beliefs of individual agents. I would like to thank Danish Social Science Foundation, The Carlsberg Foundation, Stanford Institute for Theoretical Economics (SITE) and Universita Cattolica for financial help. I would also like to thank Trinidad Casasus, Mordecai Kurz, an anonymous referee as well as participants at SITE, ESAM (2004) and ESEM (2004) for helpful discussions and comments. Peter Harremoes provided me with an illuminating counter example and Hiro Nakata provided many comments that helped improve the exposition of the paper. Part of this work is from a paper previously circulated under the title: “Sunspot rational belief structures: anonymity and endogenous uncertainty”.     

On the integration of growth and business cycles

This paper discusses several approaches to generating the observed persistence in macro models and presents evidence in favor of models where endogenous technology adoption propagates transitory shocks into the medium term. Prepared for the Conference on “The Interrelation of Cycles and Growth” in honor of Gunther Tichy.

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Convergence for difference equations with vanishing time-dependence, with applications to adaptive learning

Summary. We provide conditions for local stability and instability of an equilibrium point in certain systems of nonautonomous nonstochastic difference equations. In the systems under study the influence of time is present through a positive scalar “gain” parameter which converges in the limit to zero. These systems have recently been used to study the dynamics of adaptive learning in economic models, and we provide two economic illustrations of the formal results. Received: October 7, 1997; revised version: February 8, 1999     

Bertrand vs. Cournot equilibrium with risk averse firms and cost uncertainty

Summary. In an oligopoly game with cost uncertainty and risk averse firms, we show that Bertrand and Cournot equilibrium have different convergence properties when the market is replicated. The Cournot equilibrium price converges to the competitive price. Under very typical and somewhat general conditions, the highest Bertrand equilibrium price converges to one higher than the competitive equilibrium. We also give examples to show how to compute the limit of the highest Bertrand equilibrium prices and illustrate the ideas of the proof. We explore conditions under which the supply curve is upward sloping, a useful condition for our results. Received: April 20, 2000; revised version: May 10, 2001     

Detrimental externalities, pollution rights, and the “Coase theorem”

This paper, which builds on Chipman (The economist’s vision. Essays in modern economic perspectives, 131–162, 1998), analyzes a simple model formulated by Hurwicz (Jpn World Econ 7:49–74, 1995) of two agents—a polluter and a pollutee—and two commodities: “money” (standing for an exchangeable private good desired by both agents) and “pollution” (a public commodity desired by the polluter but undesired by the pollutee). There is also a government that issues legal rights to the two agents to emit a certain amount of pollution, which can be bought and sold with money. It is assumed that both agents act as price-takers in the market for pollution rights, so that competitive equilibrium is possible. The “Coase theorem” (so-called by Stigler (The theory of price, 1966) asserts that the equilibrium amount of pollution is independent of the allocation of pollution rights. A sufficient condition for this was (in another context) obtained by Edgeworth (Giorn Econ 2:233–245, 1891), namely that preferences of the two agents be “parallel” in the money commodity, whose marginal utility is constant. Hurwicz (Jpn World Econ 7:49–74, 1995) argued that this parallelism is also necessary. This paper, which provides an exposition of the problem, raises some questions about this result and provides an alternative necessary and sufficient condition.     

The bargaining set of a large economy with differential information

Summary. We study the Mas-Colell bargaining set of an exchange economy with differential information and a continuum of traders. We established the equivalence of the private bargaining set and the set of Radner competitive equilibrium allocations. As for the weak fine bargaining set, we show that it contains the set of competitive equilibrium allocations of an associated symmetric information economy in which each trader has the “joint information” of all the traders in the original economy, but unlike the weak fine core and the set of fine value allocations, it may also contain allocations which are not competitive in the associated economy. Received: February 15, 1999; revised version: August 9, 1999     

Communication in financial markets with several informed traders

This paper investigates the incentives for informed traders in financial markets to reveal their information truthfully to the public. In the model, a subset of traders receive noisy signals about the value of a risky asset. The signals are composed of a directional component (“high” vs. “low”) as well as a precision component that represents the quality of the directional component. Between trading periods, the informed agents make public announcements to the uninformed traders. With a sufficiently large number of informed traders, an equilibrium exists in which the directional components are credibly revealed, but not the precision components. Even though the informed traders retain some of their rivate information, the post-communication estimate of the asset value converges in probability to the full-information estimate as the number of informed traders increases. The paper is based on a chapter of my Ph.D. thesis at the University of Western Ontario and was circulated previously under the title “Public Communication Devices in Financial Markets.” I thank my dissertation committee Arthur Robson, Hari Govindan, and Al Slivinski for their guidance and support. I also thank Murali Agastya, Roland Benabou, Philippe Grégoire, Rick Harbaugh, Mike Peters, an anonymous referee and an associate editor, and seminar participants at various universities and conferences at which this paper was presented.     

Multi-Sector Model of Tradable Emission Permits

This paper presents a multi-sector model of tradable emission permits, which includes oligopolistic and perfectly competitive industries. The firms in oligopolistic industries are assumed to exercise market power in the tradable permit market as well as in the product market. Specifically, we examine the effects of the initial permit allocation on the equilibrium outcomes, focusing on the interaction among these product and permit markets. It is shown that raising the number of initial permits allocated to one firm in an oligopolistic industry increases the output produced by that firm. Under certain conditions, raising a “clean” (less-polluting) firm’s share of the initial permits can lead to reductions in both the product and permit prices. We discuss criteria for the socially optimal allocation of initial permits, considering the trade-off between production inefficiency and consumer benefit.     

Vickrey allocation rule with income effect

We consider situations in which a society tries to efficiently allocate several homogeneous and indivisible goods among agents. Each agent receives at most one unit of the good. In this paper, we establish that on domains that include nonquasi-linear preferences—preferences exhibiting income effects—an allocation rule that satisfies Pareto-efficiency, strategy-proofness, individual rationality, and nonnegative payment uniquely exists, which is the Vickrey allocation rule. H. Saitoh is a JSPS Research Fellow.     

Hayekian expectations: Theory and empirical applications

We show that the orderliness of market processes and outcomes, and hence the realization and coordination of individuals' plans, are dependent on the social environment in which individuals function. In specific, when atomicity and stable (social) rules are compromised in the case of Big Players, markets are less orderly despite the fact that individuals are behaving rationally.—The paper provides an account of individual rationality by generating a theory of expectations based on Hayek's cognitive theory. Hayekian expectations are coherent, competitive, and endogenous. This suggests that expectational analysis must take account of the context of constraint—the “environment” or what we call “filtering conditions”—within which individuals function and to which they must adapt. The paper provides a theoretical analysis of expectations at the individual level and shows that the particular behaviors stemming from those expectations require a specification of the rules governing social and market activities. We thank Karen Palasek, Don Boudreaux, Joe Cobb, Peter Boettke, and the participants of the Hayek 1993 Memorial Symposium in Freiburg, Germany for helpful suggestions and comments on earlier drafts. All remaining errors are ours.     

Environment,Directed Technical Change and Economic Policy

We study the effects of an economic policy in an endogenous growth general equilibrium framework where production of consumption goods requires two resource inputs: a polluting non-renewable resource and a non-polluting labour resource. The use of the former contributes to the accumulation of pollution in the atmosphere, which affects welfare. There is a specific research sector associated with each of those resources. We provide a full welfare analysis, and we describe the equilibrium paths in a decentralized economy. We go on to study the effects of three associated economic policy tools: a tax on the polluting resource, and two research subsidies. We show that the optimal environmental policy has two main effects; it delays the extraction of the resource and with it the level of polluting emissions and it reallocates research efforts, decreasing the amount put into “grey” research to the benefit of “green” research. We also show that the environmental policy is grey-biased in the short-term, and green-biased in the long-term. Finally, we compute the optimal values for these tools.      

Pareto and contemporary economic theory

This paper provides explanations for Pareto’s apparently contradictory approach to demand theory in simultaneously insisting that measurability of utility is not needed to explain the equilibrium of consumers in competitive markets, and embracing concavifiability and thus measurability of utility when this implies restrictions on consumers’ behavior such as the law of demand. It also treats his method of calibrating an aggregate demand function by employing his law of income distribution, so as to reproduce “Gregory King’s law”. Finally, some disputed issues are dealt with concerning the nature of Pareto’s contributions to welfare economics. (JEL: B13, D11, D60).