Stochastic uncoupled dynamics and Nash equilibrium

In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence of play (the period-by-period behavior as well as the long-run frequency) to Nash equilibria of the one-shot stage game, and present a number of possibility and impossibility results. Basically, we show that if in addition to random experimentation some recall, or memory, is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it suffices to recall the last two periods of play.     

Stochastic uncoupled dynamics and Nash equilibrium

In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence of play (the period-by-period behavior as well as the long-run frequency) to Nash equilibria of the one-shot stage game, and present a number of possibility and impossibility results. Basically, we show that if in addition to random experimentation some recall, or memory, is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it suffices to recall the last two periods of play.     

New evidence on the convergence of international income from a group of 29 countries

This paper updates and extends the time-series evidence on the convergence of international incomes using a set of 29 countries over the period 1900–2001. Time-series tests for stochastic convergence are supplemented with tests which provide evidence on the notion of “β-convergence” predicted by the Solow model. The evidence indicates that the relative income series of 21 countries are consistent with stochastic convergence, and that β-convergence has occurred in at least 16 countries at some point during the twentieth century. Further examination of the properties of the β-convergence test provides anecdotal evidence of conditional convergence in three additional countries for which the convergence hypothesis was initially rejected. Consideration of convergence clubs strengthens the evidence in favor of convergence. Analysis of the cross-country dispersion of incomes over time also suggests that convergence has occurred over the 1900–2001 period, particularly within certain clubs, with structural breaks associated with World War II in many countries causing a break in the convergence process.      

Testing for Ongoing Convergence in Transition Economies, 1970 to 1998

In this paper, the authors use a time-varying parameters procedure to test for a common growth path in the ex-Communist bloc, both pre- and postreform. They test whether there has been convergence within the bloc or between the bloc as a group and the West. Surprisingly, there is little evidence of convergence within the bloc, which brings into question the effectiveness of policies to reduce differentials in income per capita under the Communists. There is also little evidence of convergence with respect to the West, either during the period from 1970 to 1990 or if the reform years are included (i.e., 1970 to 1998). J. Comp. Econ., December 2001, 29(4), pp. 677–691. © 2001 Elsevier ScienceJournal of Economic Literature Classification Numbers: O40, C22, C23, C15.     

Inflation expectations in Turkey: learning to be rational

Turkey implemented an ambitious restructuring of the economy in the past several years, including the adoption of inflation targeting along with a floating exchange rate regime. Inflation came down from almost triple digits to single digits between 2001 and 2005. This particular episode of the Turkish economy sets a genuine case study for investigating the possible changes in the behaviour of inflation expectations upon a regime shift. Accordingly, this study analyses inflation expectations in Turkey, focusing especially on the post-2001 transition phase. We first conduct classical tests of unbiasedness and efficiency using aggregate survey data between August 2001 and October 2007 to get a statistical benchmark for rationality; we find that classical tests reject full rationality hypothesis for all series except next month's Consumer Price Index (CPI) inflation expectations. Then, we carry out Time-Varying Parameter (TVP) estimates based on a Kalman filter to see how the coefficients in the classical test equations evolve over time. This framework allows us to see whether there is convergence to rationality in terms of unbiasedness and efficiency. We find that forecast performance has improved through time, as the coefficients on the test equations shows movement towards values implied by unbiasedness and efficiency hypotheses, supporting the learning hypothesis.     

Preference profiles sustaining Arrow's theorem

Summary. Arrow's theorem is proved on a domain consisting of two types of preference profiles. Those in the first type are “almost unanimous": for every profile some alternative x is such that the preferences of any two individuals merely differ in the ranking of x, which is in one of the first three positions. Profiles of the second type are “appropriately heterogeneous”, with preferences similar to those generating the “paradox of voting”. Received: March 9, 2000; revised version: June 7, 2001     

Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case

Summary. Suppose a large economy with individual risk is modeled by a continuum of pairwise exchangeable random variables (i.i.d., in particular). Then the relevant stochastic process is jointly measurable only in degenerate cases. Yet in Monte Carlo simulation, the average of a large finite draw of the random variables converges almost surely. Several necessary and sufficient conditions for such “Monte Carlo convergence” are given. Also, conditioned on the associated Monte Carlo -algebra, which represents macroeconomic risk, individual agents' random shocks are independent. Furthermore, a converse to one version of the classical law of large numbers is proved. Received: October 29, 2001; revised version: April 24, 2002 RID="*" ID="*" Part of this work was done when Yeneng Sun was visiting SITE at Stanford University in July 2001. An early version of some results was included in a presentation to Tom Sargent's macro workshop at Stanford. We are grateful to him and Felix Kübler in particular for their comments. And also to Marcos Lisboa for several discussions with Peter Hammond, during which the basic idea of the paper began to take shape. Correspondence to: P.J. Hammond     

Learning Dynamics in Games with Stochastic Perturbations

Consider a generalization of fictitious play in which agents′ choices are perturbed by incomplete information about what the other side has done, variability in their payoffs, and unexplained trembles. These perturbed best reply dynamics define a nonstationary Markov process on an infinite state space. It is shown, using results from stochastic approximation theory, that for 2 × 2 games it converges almost surely to a point that lies close to a stable Nash equilibrium, whether pure or mixed. This generalizes a result of Fudenherg and Kreps, who demonstrate convergence when the game has a unique mixed equilibrium. Journal of Economic Literature Classification Numbers: 000, 000, 000.     

The Global Financial Crisis and Stochastic Convergence in the Euro Area

This paper analyzes the issue of convergence in the original Euro Area countries, and assesses the effect of the global financial crisis on the process of convergence. In particular, we consider whether the global financial crisis pulled the 12 economies of the Euro Area together or pushed them apart. We investigate the dynamics of stochastic convergence of the original Euro Area countries for inflation rates, nominal interest rates, and real interest rates. We test for convergence relative to Germany, taken as the benchmark for core EU standards, using monthly data over the period January 2001 to September 2010. We examine, in a time-series framework, three different profiles of the convergence process: linear convergence, nonlinear convergence, and linear segmented convergence. Our findings both contradict and support convergence. Stochastic convergence implies the rejection of a unit root in the inflation rate, nominal interest rate, and real interest rate differentials. We find that the differentials are consistent with a unit-root hypothesis when the alternative hypothesis is a stationary process with a linear trend. We frequently, but not always, reject the unit-root hypothesis when the alternative is a stationary process with a broken trend. We also note that the current financial crisis plays a significant role in dating the breaks.     

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     

Are Indian States Converging in the Post-Reform Period?: An Empirical Inquiry

This paper studies the convergence phenomenon for 23 states of India for the period 1981 to 2001. The decades of the 1980s and the 1990s has been studied separately to comment on the convergence behaviour in the pre reform and post reform period. In addition to that of per capita SDP, convergence of per capita output emanating from the agriculture, industry and the services sector has been analysed to get a deeper insight. Both sigma (σ) convergence and beta (β) convergence have been examined. The study finds absence of sigma (σ) convergence and unconditional beta (β) convergence of per capita NSDP both in the 1980s and 1990s. However, conditional beta (β) convergence estimates reveal that the poorer states are catching up with their richer counterparts in the 1990s. The panel GMM estimates reveal that Indian states converged to their steady state output at a higher rate in the 1990s compared to the 1980s. At the sectoral level, Industry had a higher speed of convergence than agriculture in both decades. Further, divergence rather than convergence is observed for the services sector in both decades.

     

区域产业投资策略与区域产业结构趋同：锦标赛机制的视角

通过对地方官员晋升锦标赛进行建模,分析了各地区产业结构趋同的深层次原因。以经济绩效为主要标准的地方官员晋升选拔机制,直接影响各个互为竞争地区的地方官员的产业投资策略选择,进而导致区域产业结构趋同。模型结果显示,当两地区初始绩效无差异时,产业结构必然趋同。当初始绩效存在差异时,以两地区高利润产业绩效之间相关系数的临界值1/2为分界点：小于等于1/2时,区域产业结构必然趋同;大于1/2时,产业结构是否趋同则受初始绩效差异、高利润产业期望绩效与落后区域比较优势产业绩效差值以及两区域选择高利润产业的绩效相关系数三者间关系的影响。该相关系数可能代表着两区域所投资的同一产业内不同产品间的替代或互补关系。不能仅因产业投资方向上的趋同就认为产业结构存在严重趋同,还需要对产品结构是否趋同进行分析研判。     

Misleading Inferences from Panel Unit Root Tests: a Comment

In their 2001 paper, Breuer, McNown, and Wallace argue that panel unit root tests are flawed in that the “all or nothing nature of these procedures may lead to serious misinterpretations of tests applied to mixed panels” (2001, p. 483). The authors propose an alternative test, the SURADF test, which allows for and estimates heterogeneous rates of convergence. We show that SURADF test results are highly sensitive to the selection of panel members. As such, application of the SURADF test seems to require a sound basis for panel member selection and a caveat that all results are panel‐specific.     

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     

Diversification, convex preferences and non-empty core in the Choquet expected utility model

Summary. We show, in the Choquet expected utility model, that preference for diversification, that is, convex preferences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversification, namely “sure diversification.” We show that this implies that the core of the capacity is non-empty. The converse holds under concavity of the utility index, which is itself equivalent to the notion of comonotone diversification, that we introduce. In an Anscombe-Aumann setting, preference for diversification is equivalent to convexity of the capacity and preference for sure diversification is equivalent to non-empty core. In the expected utility model, all these notions of diversification are equivalent and are represented by the concavity of the utility index. Received: July 27, 1999; revised version: November 7, 2000     

Wal‐Mart innovation and productivity: a viewpoint

Abstract Technology effects, business process development, and productivity growth are considered in the context of a single company: Wal‐Mart. The starting point is the 2001 McKinsey Global Institute report, which finds that over 1995–2000, a quarter of U.S. productivity growth is attributable to the retail industry, and almost a sixth of that is attributable to Wal‐Mart. Wal‐Mart is interesting as well because of its rapid growth in Canada. This is now Canada's largest private sector employer. We also consider other evidence relevant to public policy formation concerning Wal‐Mart and conclude with a discussion of options for partially filling important data gaps.     

On the persistence of lackluster demand—the history of the video telephone

Some radically new, technological products soar smoothly from introduction to stunning market growth, just as textbooks say they should. However, that is not always the case, nor is it even the most likely outcome. The case of the videophone is an extreme one to be sure but it offers six important lessons that apply to many other radically new technological products: (1) not every new technology leads to stunning market success; (2) just because the press says it will, does not mean it will; (3) growth often takes longer than expected; (4) growth often reaches lower levels than expected; (5) technological convergence is not a certainty; and (6) innovations involving complex systems face more hurdles to market acceptance than “stand-alone” innovations.     

A folk theorem for minority games

We study a particular case of repeated games with public signals. In the stage game an odd number of players have to choose simultaneously one of two rooms. The players who choose the less crowded room receive a reward of one euro (whence the name “minority game”). The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced. We show that in the infinitely repeated game any feasible payoff can be achieved as a uniform equilibrium payoff, and as an almost sure equilibrium payoff. In particular we construct an inefficient equilibrium where, with probability one, all players choose the same room at almost all stages. This equilibrium is sustained by punishment phases which use, in an unusual way, the pure actions that were played before the start of the punishment.     

Perfect and Proper Equilibria of Large Games

This paper deals with the existence and other related issues of perfect and proper equilibria of games with a continuum of players. A sufficient condition for the existence of a perfect (proper) equilibrium as an almost everywhere limit of a sequence of ε-perfect (ε-proper) equilibria is given. An example shows that almost everywhere convergence need not obtain if the condition is violated. Extension to the case where the set of actions available to the players can differ is discussed.Journal of Economic LiteratureClassification Number: C79.     

Economic Growth and Convergence of EU Member States: An Empirical Investigation

The aim of this article is to construct a European production frontier using deterministic methods, and to break down growth and convergence during the period 1980–2001. The results show that EU growth is primarily driven by physical and human capital accumulation, the contribution of which is essential for the cohesion of European countries. We find capital accumulation and efficiency change to be important convergence factors within the EU, while technical change has worked against it. The approach used has also enabled us to analyze the differences in growth performance of Member States and highlight the role of human and public capital, supporting the European cohesion and development policies carried out in this period.