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

In large random economies with heterogeneous agents, a standard stochastic framework presumes a random macro state, combined with idiosyncratic micro shocks. This can be formally represented by a random process consisting of a continuum of random variables that are conditionally independent given the macro state. However, this process satisfies a standard joint measurability condition only if there is essentially no idiosyncratic risk at all. Based on iteratively complete product measure spaces, we characterize the validity of the standard stochastic framework via Monte Carlo simulation as well as event-wise measurable conditional probabilities. These general characterizations also allow us to strengthen some earlier results related to exchangeability and independence. Parts of this work were done while Yeneng Sun was visiting Stanford University in July 2003, March–May 2005 and July 2006, and while Peter Hammond was visiting the National University of Singapore in March–April 2004. An early version was presented at the World Congress of the Econometric Society in 2005.     

Modelling exchange of probabilistic opinions

Summary. This paper studies how communication or exchange of opinions influences correlation of beliefs. The paper focuses on a situation in which agents communicate with each other infinitely many times without observing data. It is an extension to the ‘Expert Problem’ in Bayesian theory, where the informational flow is asymmetric. Moreover, this paper generalizes the existing literature of communication that employs the common prior assumption (CPA) by allowing for heterogeneous beliefs. Some basic convergence results are shown in contrast with the results obtained under the CPA. Furthermore, several economic implications of the basic results are provided. Received: August 27, 2001; revised version: April 16, 2002 RID="*" ID="*" The results presented in this paper are taken from my Ph.D. thesis at Stanford University. I gratefully acknowledge the inspiration obtained from innumerable discussions with Mordecai Kurz about this subject. Also, I appreciate comments from Kenneth J. Arrow, Peter J. Hammond, Maurizio Motolese, Carsten K. Nielsen, Ho-Mou Wu and the anonymous referee.     

The economic effects of restrictions on government budget deficits: imperfect private credit markets

Summary. The present paper is an extension of Ghiglino and Shell [7] to the case of imperfect consumer credit markets. We show that with constraints on individual credit and only anonymous (i.e., non-personalized) lump-sum taxes, strong (or “global”) irrelevance of government budget deficits is not possible, and weak (or “local”) irrelevance can hold only in very special situations. This is in sharp contrast to the result for perfect credit markets. With credit constraints and anonymous consumption taxes, weak irrelevance holds if the number of tax instruments is sufficiently large and at least one consumer's credit constraint is not binding. This is an extension of the result for perfect credit markets. Received: August 28, 2001; revised version: March 25, 2002 RID="*" ID="*" We thank Todd Keister, Bruce Smith, and two referees for helpful comments. Correspondence to: C. Ghiglino     

Robust estimation of models of Engel curves

Both standard and robust methods are used here to estimate models of Engel curves for three household commodities, namely, food, transport, and tobacco and alcohol in Canada. The income elasticities of demand computed from the various methods differ significantly for the transport and tobacco-alcohol consumption where there are obvious outliers and zero expenditures problem. Robust estimators point to lower income elasticities and have better performance than the standard LS and Tobit estimator. These results are analyzed in the light of the information on finite-sample performance obtained in a previous Monte Carlo study. First version received: July 2000/Final version received: July 2001 RID="*" ID="*"  I wish to thank Victoria Zinde-Walsh, John Galbraith, Clint Coakley, two anonymous referees and an associate editor for helpful comments. I would also like to thank Anastassia Khouri for kindly providing the 1992 Family Expenditure Survey of Canada data.     

Stochastic growth: asymptotic distributions

Summary. This note studies conditions under which sequences of state variables generated by discrete-time stochastic optimal accumulation models have law of large numbers and central limit properties. Productivity shocks with unbounded support are considered. Instead of restrictions on the support of the shock, an “average contraction” property is required on technology. Received: August 27, 2001; revised version: January 9, 2002 RID="*" ID="*"The author thanks John Creedy and Rabee Tourky for helpful comments, and the Economic Theory Center, University of Melbourne for financial support.     

Inefficient Markov perfect equilibria in multilateral bargaining

We study a complete-information alternating-offer bargaining game in which one “active” player bargains with each of a number of other “passive” players one at a time. In contrast to most existing models, the order of reaching agreements is endogenously determined, hence the active player can “play off” some passive players against others by m oving back and forth bargaining with the passive players. We show that this model has a finite number of Markov Perfect Equilibria, some of which exhibiting wasteful delays. Moreover, the maximum number of delay periods that can be supported in Markov Perfect Equilibria increases in the order of the square of the number of players. We also show that these results are robust to a relaxing of the Markov requirements and to more general surplus functions. Received: November 19, 2001; revised version: August 20, 2002 RID="*" ID="*"This paper grew out of my dissertation submitted to Stanford University. I am deeply indebted to my advisor, Paul Milgrom, for his insights and guidance. I would also like to thank Douglas Bernheim, Sushil Bikhchandani, Harold Demsetz, Bryan Ellickson, Avner Greif, Peter Hammond, David Levine, Bentley Macleod, Joe Ostroy, John Pencavel, Jean-Laurent Rosenthal, David Starrett, Robert Wilson, Bill Zame and especially John Riley and Jeff Zwiebel for their helpful comments. I am grateful to an anonymous referee for extremely constructive suggestions.     

Expected consumer’s surplus as an approximate welfare measure

Except for a knife-edge case of preferences, the percentage error from using the change in expected consumer’s surplus (ECS) to approximate the willingness to pay for a change in the distribution of a random price is unbounded, in contrast to Willig’s (Am Econ Rev 66:589–597; 1976) famous approximation result for nonrandom prices. If the change is smooth on the space of random variables, and either the initial price is nonrandom or state-contingent payments are possible, then the change in ECS locally approximates the willingness to pay well. Unfortunately, this smoothness fails in some important applications. I thank Hector Chade, Glenn Ellison, Peter Hammond, Manuel Santos, seminar participants at Arizona State, Stanford and Yale and participants of the Midwest Economic Theory meetings at Indiana University and the 2004 Summer Econometric Meetings for comments.     

Cournot-Nash and Lindahl equilibria in pure public “bad” economies

Summary. Using a general equilibrium framework, this paper analyzes the equilibrium provision of a pure public bad commodity (for example pollution). Considering a finite economy with one desired private good and one pure public “bad” we explicitly introduce the concept of Lindahl equilibrium and the Lindahl prices into a pure public bad economy. Then, the Lindahl provision is analyzed and compared with the Cournot-Nash provision. The main results for economies with heterogeneous agents state that the asymptotic Lindahl allocation of the pure public bad is the null allocation. In contrast, the asymptotic Cournot-Nash provision of the public bad might approach infinity. Other results were obtained in concert with the broad analysis of the large finite economies with pure public bad commodities. Received: July 26, 2001; revised version: March 12, 2002 RID="*" ID="*" We are indebt to Nicholas Yannelis and anonymous referee for their valuable comments and suggestions. Correspondence to: B. Shitovitz     

Bayesian estimation of social welfare and tax progressivity measures

This paper examines Bayesian methods of examining posterior distributions of inequality, concentration, tax progressivity and social welfare measures. Use is made of an explicit income distribution assumption and two alternative assumptions regarding the distribution of pre-tax mean incomes within each income group. The methods are applied to a simulated distribution of individual incomes and tax payments. It is possible to identify a minimum acceptable number of income classes to be used. The results suggest support for the use of group means in practical applications, particularly where large sample sizes are available. First version received: August 2000/Final version received: July 2001 RID="*" ID="*"  This research was supported by a Melbourne University Faculty of Economics and Commerce Research Grant. We should like to thank Bill Griffiths and two referees for comments on an earlier draft.     

A common trends model of UK core inflation

In this paper the long-run trend in RPI inflation (core inflation) for the UK over the 1961–1997 period is estimated within the framework of a multivariate common trends model which extends the bivariate VAR approach of Quah and Vahey (1995). In this context core inflation is directly linked to money and wage growth and interpreted as the long-run forecast of inflation from a small-scale, cointegrated macroeconomic system. First version received: September 1999/Final version received: October 2001 RID="*" ID="*"  We thank two anonymous referees for many helpful comments and suggestions. Work on this paper was partially conducted when C. Morana was at Heriot-Watt University.     

Nash and Walras equilibrium via Brouwer

Summary. The existence of Nash and Walras equilibrium is proved via Brouwer's Fixed Point Theorem, without recourse to Kakutani's Fixed Point Theorem for correspondences. The domain of the Walras fixed point map is confined to the price simplex, even when there is production and weakly quasi-convex preferences. The key idea is to replace optimization with “satisficing improvement,” i.e., to replace the Maximum Principle with the “Satisficing Principle.” Received: July 9, 2001; revised version: February 25, 2002 RID="*" ID="*" I wish to thank Ken Arrow, Don Brown, and Andreu Mas-Colell for helpful comments. I first thought about using Brouwer's theorem without Kakutani's extension when I heard Herb Scarf's lectures on mathematical economics as an undergraduate in 1974, and then again when I read Tim Kehoe's 1980 Ph.D dissertation under Herb Scarf, but I did not resolve my confusion until I had to discuss Kehoe's presentation at the celebration for Herb Scarf's 65th birthday in September, 1995. RID="*" ID="*"Correspondence to: C. D. Aliprantis     

The genuine savings criterion and the value of population

Summary. In any dynamic model of the economy with changing population, the latter should properly be one of the state variables of the system. It enters both in the maximand, at least under total utilitarianism, and into the production function in one way or another. If population growth is exponential and constant returns prevails, then a simple transformation to per capita variables can be used to eliminate one state variable, but this ceases to be true if growth is not exponential, as it obviously is not and cannot be. If the growth of population is exogenous, then introducing it into the system does not affect the optimal policy. However, if one asks whether the system is sustainable, in the sense of at least maintaining total welfare (integral of discounted utilities), then the criterion is that that the value of the rates of change of the state variables is non-negative, so that the shadow price of population becomes relevant. In this paper, we derive explicit formulas in a simple model, showing that the rate of growth of per capita capital is not the correct formula but must have another terms added to it. We also study the question under an alternative criterion of long-run average utilitarianism. Received: June 1, 2002; revised version: September 27, 2002 RID="*" ID="*"Research support was provided by the William and Flora Hewlett Foundation. An earlier version of this paper was presented at a celebration of Mordecai Kurz's 66th birthday at Stanford University, 1–3 August 2002. Correspondence to: K.J. Arrow     

Real exchange rate determination: Empirical observations from East-Asian countries

In this paper the models for the real exchange rate determination are re-examined between Japan and five East-Asian countries. Two important findings are reported. First, the real interest rate-bias model is valid for Korea-, Malaysia-, Indonesia-, and Philippines-Japan, and the productivity-bias model is valid for Indonesia-, and Philippines-Japan: that is, the coefficients of relative variables are stable and statistically significant. Second, there is no evidence that the political risk premium model is valid. First version received: September 2000/Final version received: April 2001 RID="*" ID="*"  This paper was presented at the Tohoku University Economics Conference April 1999. I acknowledge Yoshihiko Tsukuda, Hiroya Akiba, Tadashi Kuriyama, Jiro Akita and Hiroyuki Ozaki for their helpful comments. Also, I am very grateful to two referees of this journal for many valuable comments. The research was supported by the Nomura foundation for Social Science in 2000.     

Probability of survival in a random exchange economy with dependent agents

Summary. In this paper I analyze the general equilibrium in a random Walrasian economy. Dependence among agents is introduced in the form of dependency neighborhoods. Under the uncertainty, an agent may fail to survive due to a meager endowment in a particular state (direct effect), as well as due to unfavorable equilibrium price system at which the value of the endowment falls short of the minimum needed for survival (indirect terms-of-trade effect). To illustrate the main result I compute the stochastic limit of equilibrium price and probability of survival of an agent in a large Cobb-Douglas economy. Received June 7, 2001; revised version: January 7, 2002 RID="*" ID="*" I would like to thank Mukul Majumdar and Thomas DiCiccio for helpful discussion and an anonymous referee for valuable comments and suggestions.     

Speculative trading with rational beliefs and endogenous uncertainty

Summary. This paper introduces the framework of rational beliefs of Kurz (1994), which makes the assumptions of heterogeneous beliefs of Harrison and Kreps (1978) and Morris (1996) more plausible. Agents hold diverse beliefs that are “rational” in the sense of being compatible with ample observed data. In a non-stationary environment the agents only learn about the stationary measure of observed data, but their beliefs can remain non-stationary and diverse. Speculative trading then stems from disagreements among traders. In a Markovian framework of dividends and beliefs, we obtain analytical results to show how the speculative premium depends on the extent of heterogeneity of beliefs. In addition, we demonstrate that there exists a unique Rational Belief Equilibrium (RBE) generically with endogenous uncertainty (as defined by Kurz and Wu, 1996) and that the RBE price is higher than the rational expectation equilibrium price (REE) under some general conditions Received: March 15, 2001; revised version: April 26, 2002 RID="*" ID="*" We are deeply grateful to Mordecai Kurz for his constant encouragement and inspiring guidance over the years. We wish to express our gratitude to an anonymous referee for the very valuable comments provided. We also thank Kenneth Arrow, Peter Hammond, Roko Aliprantis and Nicholas Yannelis for their helpful suggestions and Academia Sinica and the National Science Council of the R.O.C. for their indispensable support. Correspondence to: H.-M. Wu     

Core and Walrasian equilibria when agents' characteristics are extremely dispersed

Summary. It is shown that core-Walras equivalence fails whenever the commodity space is a non-separable Banach space. The interpretation is that a large number of agents guarantees core-Walras equivalence only if there is actually a large number of agents relative to the size of the commodity space. Otherwise a large number of agents means that agents' characteristics may be extremely dispersed, so that the standard theory of perfect competition fails. Supplementing the core-Walras non-equivalence result, it is shown that in the framework of economies with weakly compact consumption sets – as developed by Khan and Yannelis (1991) – the core is always non-empty, even if consumption sets are non-separable. December 12, 2001; revised version: December 6, 2002 RID="*" ID="*" Thanks to E. Dierker, M. Nermuth, R. Tourky, and N. C. Yannelis for helpful discussions and suggestions, and thanks to a referee for comments which helped to improve the final version.     

Spurious deterministic seasonality and autocorrelation corrections with quarterly data: Further Monte Carlo results

Following recent work of Franses, Hylleberg and Lee (FHL), this paper analyses the consequences of fitting a deterministic seasonal model to a quarterly time series which can be (at least approximately) described by a seasonal unit root(s) model. Besides the distribution of the coefficient of determination, the empirical distributions of two commonly used statistics are also investigated through Monte Carlo experiments for small, moderately large and large samples. FHL's work is also extended allowing the possibility of residual autocorrelation corrections. The main conclusion that emerges from the results is that one should not try to measure the importance of deterministic seasonality nor test for its presence in the context of such (static) regression models, even when using some form of residual autocorrelation correction. A simple empirical application is provided to illustrate our results. First version received: July 1997/final version received: July 1998     

Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment

Summary. We prove existence of a competitive equilibrium in a version of a Ramsey (one sector) model in which agents are heterogeneous and gross investment is constrained to be non negative. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. This method allows us to obtain detailed results concerning the properties of competitive equilibria. Because of the simplicity of the techniques utilized our approach is amenable to be adapted by practitioners in analogous problems often studied in macroeconomics. Received: September 13, 2001; revised version: December 9, 2002 RID="*" ID="*" We are grateful to Tapan Mitra for pointing out errors as well as making very valuable suggestions. Thanks are due to Raouf Boucekkine and Jorge Duran for additional helpful discussions. We also thank an anonymous referee for his/her helpful comments. The second author acknowledges the financial support of the Belgian Ministry of Scientific Research (Grant ARC 99/04-235 “Growth and incentive design”) and of the Belgian Federal Goverment (Grant PAI P5/10, “Equilibrium theory and optimization for public policy and industry regulation”). Correspondence to: C. Le Van     

A modified logit model for time series with an application to the pricing behaviour of manufacturing firms in Australia

The modified logit model (Amemiya and Nold, 1975) is generalised to the case where the error term is autocorrelated. The asymptotic distribution (as n →∞ and T →∞) of a feasible GLS estimator of β is derived. Tests of linear restrictions on β and the significance of ρ are presented. The results of the applied work suggest that the factors which explain the pricing behaviour of manufacturing firms, as reported in the tendency survey conducted by the Australian Chamber of Commerce and Industry and the Westpac Banking Corporation, include historical inflation rates of up to 7 quarters and capacity utilisation. First version received: March 2001/Final version received: July 2002 RID="*" ID="*"  The first draft of this paper was written while the author was on study leave at the Department of Econometrics, University of Sydney, Australia.     

A Monte Carlo Analysis of the Fisher Randomization Technique: Reviving Randomization for Experimental Economists

Data created in a controlled laboratory setting are a relatively new phenomenon to economists. Traditional data analysis methods using either parametric or nonparametric tests are not necessarily the best option available to economists analyzing laboratory data. In 1935, Fisher proposed the randomization technique as an alternative data analysis method when examining treatment effects. The observed data are used to create a test statistic. Then treatment labels are shuffled across the data and the test statistic is recalculated. The original statistic can be ranked against all possible test statistics that can be generated by these data, and a p-value can be obtained. A Monte Carlo analysis of t-test, the Mann-Whitney U-test, and the exact randomization t-test is conducted. The exact randomization t-test compares favorably to the other two tests both in terms of size and power. Given the limited distributional assumptions necessary for implementation of the exact randomization test, these results suggest that experimental economists should consider using the exact randomization test more often. This revised version was published online in August 2006 with corrections to the Cover Date.