TRAINING,TURNOVER, AND SEARCH*

This article explores a model of firm‐specific training in a job search environment with labor turnover. The main substantive finding is a positive association between training and wages (when dispersed). The article then precisely characterizes how both wage dispersion and firm profitability depend on the flow value b≥ 0 of workers' unmatched time. It is shown that: (i) for all high values b, no equilibrium exists; (ii) for intermediate values b, multiple equilibria arise, where firms earn zero profits, and choose from a general wage distribution; (iii) for all lower values b, there is a unique equilibrium, with firms earning positive profits, and choosing from an atomless set of wages.     

MONEY,SOCIAL STATUS AND ENDOGENOUS GROWTH IN A GENERALIZED CASH‐IN‐ADVANCE MODEL

This paper analytically examines the equilibrium growth effect of money/inflation in a standard one‐sector AK model of endogenous growth with the most generalized cash‐in‐advance constraint and relative wealth‐induced preferences for social status. We show that on the economy's unique balanced growth equilibrium path, the sign of the correlation between money and output growth depends crucially on: (i) the intertemporal elasticity of substitution in consumption; and (ii) the liquidity‐constrained ratio of consumption to investment expenditure. Moreover, our model economy always exhibits a positive output–growth effect in response to changes of the strength for social status. We also undertake numerical experiments to assess the quantitative importance of our theoretical results under an empirically plausible set of parameters.     

Growth and equilibrium indeterminacy: the role of capital mobility

Summary. The paper presents a human capital driven endogenous growth model which, in general, permits a multiplicity of equilibrium balanced growth paths. It is shown that allowing for perfect capital mobility across countries increases the range of parameter values for which the model permits equilibrium indeterminacy. As opposed to the closed capital markets case, simple restrictions on preferences are no longer sufficient to eliminate the indeterminacy. Intuitively, under perfect capital mobility agents are able to smooth consumption completely. This induces an economy with open capital markets to behave like a closed economy with linear preferences thereby increasing the possibility of equilibrium indeterminacy. Received: 18 November 1998; revised version: 10 August 1999     

Money,price dispersion and welfare

Summary. We introduce heterogeneous preferences into a tractable model of monetary search to generate price dispersion, and then examine the effects of money growth on price dispersion and welfare. With buyers search intensity fixed, we find that money growth increases the range of (real) prices and lowers welfare as agents shift more of their consumption to less desirable goods. When buyers search intensity is endogenous, multiple equilibria are possible. In the equilibrium with the highest welfare level, money growth reduces welfare and increases the range of prices, while having ambiguous effects on search intensity. However, there can be a welfare-inferior equilibrium in which an increase in money growth increases search intensity, increases welfare, and reduces the range of prices.Received: 25 July 2003, Revised: 12 December 2003JEL Classification Numbers: E31, D60.B. Peterson, S. Shi: We thank Gabriele Camera, Aleksander Berentsen and an anonymous referee for useful suggestions. We have also received valuable comments from the participants of the workshop at Michigan State, the Purdue Conference on Monetary Theory (2003) and the Midwest Macro Meeting (Chicago, 2003). Shi gratefully acknowledges financial support from the Bank of Canada Fellowship and the Social Sciences and Humanities Research Council of Canada. The opinion expressed here is the authors own and does not reflect the view of the Bank of Canada.Correspondence to: S. Shi     

Partial International Coordination in the Great Fish War

This study extends the great fish war model of Levhari and Mirman [Levhari, D. and Mirman, L. (1980) Bell Journal of Economics 11: 322–344] by incorporating a multiple country context into the model and investigates the existence of a partial coordination Nash equilibrium. First, findings of this paper suggest that a partial coordination scheme is sustainable only in limited cases. Any coalition that has more than two member countries cannot be sustained. Second, the existence and the number of coordinating countries depend critically on the magnitude of the biological and preference parameters. Finally, if the coalition is assumed to be a dominant player, there always exist one or two welfare-improving sustainable coalitions and the size of the sustainable coalitions depends on the parameters of the problem.     

Free Trade and Economic Growth

This paper extends the Das (2005) model to set up an equilibrium growth model with heterogeneous labor to analyse the growth effects after trade openness. We prove that if the terms of trade large enough before opening trade, then it is more likely that opening trade would accelerate economic growth for a small open country, vice versa.     

On Indeterminacy and Growth under Progressive Taxation and Utility‐Generating Government Spending

We examine the theoretical interrelations between progressive income taxation and macroeconomic (in)stability in an otherwise standard one‐sector AK model of endogenous growth with utility‐generating government purchases of goods and services. In sharp contrast to traditional Keynesian‐type stabilization policies, progressive taxation operates like an automatic destabilizer that generates equilibrium indeterminacy and belief‐driven fluctuations in our endogenously growing macroeconomy. Unlike the no‐sustained‐growth counterpart, this instability result is obtained regardless of (i) the degree of the public‐spending preference externality and (ii) whether private and public consumption expenditures are substitutes, complements or additively separable in the household's utility function.     

Vintage Human Capital, Demographic Trends, and Endogenous Growth

We study how economic growth is affected by demographics in an OLG model with a realistic survival law. Individuals optimally chose the dates at which they leave school to work and at which they retire. Endogenous growth arises thanks to the accumulation of generation-specific human capital. Favorable shifts in the survival probabilities induce longer schooling and later retirement but have an ambiguous effect on per-capita growth. The long-term relationship between fertility and per-capita growth is hump-shaped. Increases in longevity can be responsible for a switch from a no-growth regime to a sustained growth regime and for a positive relationship between fertility and growth to vanish. Solving numerically the equilibrium, demographic changes can have important medium-term effects even if long-term changes are very small. Journal of Economic Literature Classification Numbers: 041, I20, J10.     

A competitive model of economic geography

Summary. Most of the literature argues that competitive analysis has nothing interesting to say about location. This paper argues, to the contrary, that a competitive model can have something interesting to say about location, provided that locations are not identical and transportation costs are not zero. To do this, it constructs a competitive intertemporal general equilibrium model and applies it to a suggestive example of migration.Received: 25 August 2003, Revised: 18 December 2003, JEL Classification Numbers: D5, R0.Our interest in this topic has been stimulated over the years by many conversations with Marcus Berliant. We thank an anonymous referee for exceptionally careful and useful comments. Financial support from the UCLA Academic Committee on Research (Ellickson, Zame) and the National Science Foundation (Zame) is gratefully acknowledged. Views expressed here are those of the authors and do not necessary reflect the views of any funding agency.     

Expectations, Drift, and Volatility in Evolutionary Games

This paper proposes an evolutionary model of learning in simple coordination games where expectations are the driving force of the process. As time proceeds, agents adjust their expectations through some (possibly different) updating rules, whose only requirement is that of consistency with long stationary evidence. Sporadically, expectations are also subject to arbitrary perturbation. The main point of the paper is that, due to the possibility of random drift on expectations, the evolutionary process will be subject to high volatility across equilibria. Specifically, every Nash equilibrium (even if risk- or payoff-dominated) will have significant positive weight in the long-run invariant distribution. Journal of Economic Literature Classification Numbers: C73. D83. D84.     

Bargaining over productivity and wages when technical change is induced: implications for growth, distribution, and employment

I study a model of growth and income distribution in which workers and firms bargain à la Nash (Econometrica 18(2):155–162, 1950) over wages and productivity gains, taking into account the trade-offs faced by firms in choosing factor-augmenting technologies. The aggregate environment resulting from self-interested, objective function-maximizing decision rules on wages, productivity gains, savings and investment, is described by a two-dimensional dynamical system in the employment rate and output/capital ratio. The economy converges cyclically to a long-run equilibrium involving a Harrod-neutral profile of technical change, a constant rate of employment of labor, and constant input shares. The type of oscillations predicted by the model is qualitatively consistent with the available data on the United States (1963–2003), replicates the dynamics found in earlier models of growth cycles such as Goodwin (A growth cycle, in C.H. Feinstein (ed). Socialism, Capitalism and Economic Growth. Cambridge University Press, Cambridge 1967. Cambridge University Press, Cambridge, 1967); Shah and Desai (Econ J 91:1006–1010, 1981); van der Ploeg (J Macroecon 9:1–12, 1987); Flaschel (J Econ: Zeitschrift für Nationalökonomie 44:63–69, 1984) and Sportelli (J Econ: Zeitschrift für Nationalökonomie 61(1):35–64, 1995), and can be verified numerically in simulations. Institutional change, as captured by variations in workers’ bargaining power, has a positive effect on the long-run rate of growth of output per worker but a negative effect on long-run employment. Economic policy can also affect the growth and distribution pattern through changes in the unemployment compensation, which also have a positive long-run impact on labor productivity growth but a negative long-run impact on employment. In both cases, employment can overshoot its new equilibrium value along the transitional dynamics.     

Coordination, “Magic,” and Reinforcement Learning in a Market Entry Game

Previous experimental studies have documented quick convergence to equilibrium play in market entry games with a large number of agents. The present study examines the effect of the available information in a 12-player game in an attempt to account for these findings. In line with the prediction of a simple reinforcement learning model (Roth and Erev, 1995,Games Econ. Behav.8, 164–212), quick convergence to equilibrium is observed even given minimal information (unknown payoff rule). However, in violation of the basic model, information concerning other players' payoff increases the number of entrants. The information effect can be described by a variant of the basic reinforcement learning model assuming that the additional information changes the player's reference point.Journal of Economic LiteratureClassification Number: C7, C92.     

Stability of the cooperative equilibrium in N-person prisoners' dilemma with sequential moves

Summary. Nishihara [3] showed that N-person prisoners' dilemma has a cooperative Nash equilibrium, if the players decide their actions sequentially in the order determined by Nature under a certain information structure, and if each player's payoffs satisfy a certain inequality. This paper examines the stability of this cooperative equilibrium against two matters: players' slight mistakes and deviations by coalitions. The main results are as follows: (i) if the inequality on each player's payoffs strictly holds, then the cooperative equilibrium is a strictly proper equilibrium; (ii) if N≤3, and if full cooperation is Pareto efficient in N-person prisoners' dilemma, then the cooperative equilibrium is a strong Nash equilibrium; (iii) the cooperative equilibrium is in general a coalition-proof Nash equilibrium. Received: June 23, 1997; revised version: December 2, 1997     

Deviant generations, Ricardian equivalence, and growth cycles

Two equilibrium possibilities are known to obtain in a standard overlapping-generations model with dynastic preferences: either the altruistic bequest motive is operative for every generation (in which case, Ricardian equivalence obtains) or it is not, for any generation. Dynamic equilibria, where the bequest motive is occasionally operative, cannot emerge. This paper studies bequest-giving behavior and out-of-steady-state bequest and growth dynamics in a Ak model with intra- and inter-generational consumption externalities. These externalities, by their very presence, do not destroy Ricardian equivalence. They may, however, give rise to deviant generations—generations that do not leave a bequest having received an inheritance, and vice versa—and that seals the fate for Ricardian equivalence. Consumption externalities may also generate interesting indeterminacies and endogenous growth cycles that did not exist otherwise.     

Auctions of licences and market structure

Summary. This paper studies sequential auctions of licences to participate in a symmetric market game. Assuming that the rate at which industry profits decrease with repeated entry is not too large, at the unique solution either a single firm preempts entry altogether or entry occurs in every stage, depending on the net benefit of complete preemption to an incumbent. If we relax the assumption, a third outcome can occur: two firms may coordinate their choices to avoid further entry. The analysis employs a new refinement of Nash equilibrium, the concept of recursively undominated equilibrium. Received: February 25, 2000; revised version: September 12, 2000     

Endogenous timing in a mixed oligopoly with semipublic firms

An endogenous order of moves is analyzed in a mixed market where a firm jointly owned by the public sector and private domestic shareholders (a semipublic firm) competes with n private firms. We show that there is an equilibrium in which firms take production decisions simultaneously. This result is strikingly different from that obtained by Pal (Econ Lett 61:181–185, 1998), who shows that when a public firm competes with n private firms all firms producing simultaneously in the same period cannot be sustained as a Subgame Perfect Nash Equilibrium outcome. Our result differs from that of Pal (Econ Lett 61:181–185, 1998) for two reasons: firstly, we consider that there is a semipublic firm rather than a public firm. Secondly, Pal (Econ Lett 61:181–185, 1998) considers that the public firm is less efficient than private firms while in our paper all firms are equally efficient.     

Capacity precommitment as a barrier to entry: A Bertrand-Edgeworth approach

Summary. With few exceptions, the literature on the role of capacity as a strategic entry deterrent has assumed Cournot competition in the post-entry game. In contrast, this paper studies a model in which the incumbent and entrant sequentially precommit to capacity levels before competing in price. Interesting deterrence effects arise because firms need time to build, that is, cannot adjust capacity instantaneously in the post-entry game. This approach produces a simple and intuitive set of equilibrium behaviors and generates clear predictions about when these different outcomes are likely to arise. Our model also departs substantially from the existing literature in concluding that sunkness of capacity costs is neither necessary nor sufficient for capacity to have precommitment value. Received: August 25, 1999; revised version: October 15, 1999     

Moral hazard and general equilibrium in large economies

Summary. The paper analyzes a two period general equilibrium model with individual risk, aggregate uncertainty and moral hazard. There is a large number of households, each facing two individual states of nature in the second period. These states differ solely in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period each household chooses a non-observable action. Higher levels of action give higher probability of the good state of nature to occur, but lower levels of utility. Households' utilities are assumed to be separable in action and the aggregate uncertainty is independent of the individual risk. Insurance is supplied by a collection of firms who behave strategically and maximize expected profits taking into account that each household's optimal choice of action is a function of the offered contract. The paper provides sufficient conditions for the existence of equilibrium and shows that the appropriate versions of both welfare theorems hold. Received: December 7, 1998; revised version: October 25, 1999     

On Intersectoral allocations,factors substitutability and multiple long-run growth paths

Summary. This article considers a two-sector model of economic growth with “labour-augmenting” intersectoral external effects stemming from the aggregate capital stock. It is shown that equilibrium balanced growth paths with a non-trivial labour allocation scheme become available. A set of sufficient conditions for the existence of multiple equilibrium growth rays is provided and their determinacy properties are then characterised. Finally, examination of a parameterised C.E.S. economy illustrates the central role of non-unitary values for the elasticity of substitution in the multiplicity issue. Received: October 31, 2000; revised version: September 25, 2001     

Continuous Stochastic Games of Capital Accumulation with Convex Transitions

We consider a discounted stochastic game of common-property capital accumulation with nonsymmetric players, bounded one-period extraction capacities, and a transition law satisfying a general strong convexity condition. We show that the infinite-horizon problem has a Markov-stationary (subgame-perfect) equilibrium and that every finite-horizon truncation has auniqueMarkovian equilibrium, both in consumption functions which arecontinuous and nondecreasingand have all slopes bounded above by 1. Unlike previous results in strategic dynamic models, these properties are reminiscent of the corresponding optimal growth model.Journal of Economic LiteratureClassification Codes: C73, O41, Q20.