On the convergence of reinforcement learning

This paper examines the convergence of payoffs and strategies in Erev and Roth's model of reinforcement learning. When all players use this rule it eliminates iteratively dominated strategies and in two-person constant-sum games average payoffs converge to the value of the game. Strategies converge in constant-sum games with unique equilibria if they are pure or if they are mixed and the game is 2×2. The long-run behaviour of the learning rule is governed by equations related to Maynard Smith's version of the replicator dynamic. Properties of the learning rule against general opponents are also studied.     

Sample attrition and labor force dynamics: Evidence from the Spanish labor force survey

In this paper we examine a number of issues that arise in investigating labor force dynamics using the Spanish Labor Force Survey (EPA). These issues are by no means specific to the Spanish case and apply to most European-style labor force surveys. Our main conclusions may be summarized as follows. First, survey nonresponse cannot be neglected. Second, the EPA tends to underestimate employment and participation of high-educated young people, and to overestimate those of the low-educated elderly. Finally, we find little evidence that attrition causes important selection biases in estimating quarterly transition probabilities.     

Expected utility theory and the experiments

The experimental evidence against expected utility theo or unconvincing. When one modifies the experiments to mi tends to support traditional theory.Dewey H. Johnson Professor of Economics, Department of Economics, College of Business Administration, University of South Carolina. I am grateful for comments from seminar participants at the University of Melbourne, University of South Carolina, University of Stockholm, and the University of Western Ontario. John Hey provided a firm, but sympathetic, editorial hand.     

Stationary solution to the overlapping generations model of fiat money: Experimental evidence

Overlapping generations model of fiat money yields an infinity of competitive equilibrium solutions, only one of which is stationary. Economies reported in this paper involved a sequence of overlapping generations of three or four individuals; each individual lived for two periods. In their young age individuals were endowed with chips that could be traded for fiat money wish the individuals of the old generation. In their old age, individuals could exchange their units o flat money for the consumption good. Results of the experiments exhibit some support for the stationary solution. The results are robust to two designs of exchange institutions (double oral auctior and supply schedule auction) and to two different endogenous ways of converting money into chips at the end of the game (average price prevailing during the last period the game is actually played and the average price forecast made during the last period the game is actually played).A preliminary version of this paper was presented at the meeting of the Economic Science Association and at the Federal Reserve Bank of Minneapolis. The authors are grateful for comments received from various participants at both presentations. Financial support was provided by the McKnight Foundation, the Honeywell Foundation, National Science Foundation (SES 89-12552), and Richard. M. and Margaret Cyert Family Funds.     

A mechanism implementing the proportional solution

We consider the problem of a commonly owned technology which transforms a single input into a single output. We are interested in implementing a social choice rule called theproportional solution. We introduce a mechanism which implements the proportional solution in Nash, strong (Nash) and undominated Nash equilibria. In the mechanism each agent announces only two numbers which can be interpreted as the total output and her share of the total input-output combination. This paper was originally titled "Doubly implementing the proportional solution." I would like to thank my advisor William Thomson for his detailed comments and suggestions. I would also like to thank Jeffrey Banks and Sung-Whee Shin for their comments. Two anonymous referees and an editor’s comments improved this paper substantially.     

Option pricing in the presence of natural boundaries and a quadratic diffusion term

This paper uses a probabilistic change-of-numeraire technique to compute closed-form prices of European options to exchange one asset against another when the relative price of the underlying assets follows a diffusion process with natural boundaries and a quadratic diffusion coefficient. The paper shows in particular how to interpret the option price formula in terms of exercise probabilities which are calculated under the martingale measures associated with two specific numeraire portfolios. An application to the pricing of bond options and certain interest rate derivatives illustrates the main results.     

Long term dependence in stock returns

We show, using the modified rescaled range statistic, that none of the return series of indices of five European countries, the United States and Japan exhibits long term dependence. This statistic — introduced by Lo (1991) — correct Hurst's (1951) ‘classical’ rescaled range statistic for short term dependence. We also report the classical rescaled range statistic after adjusting the series for short term dependence. This procedure shows, for cases where the results of the modified rescaled range statistic are mixed, that no long term dependence can be found. Simulations indicate reasonable power of this adjustment procedure. Furthermore, we find that estimates of the Hurst exponent, a related measure of long term dependence, are also biased by short term dependence. Simulations show that this measure — that has recently attracted growing interest — cannot distinguish between models with or without long term dependence.     

Dynamic risksharing in the United States and Europe

We use a panel VAR model to improve upon the existing methodologies to analyze interregional risksharing and consumption smoothing channels. First, we endogenize the output process within a more general multi-equation framework, capturing the dynamic feedback between output and various smoothing channels. Second, in line with dynamic general equilibrium open economy models of risksharing, we exploit impulse response functions to trace the role of each smoothing channel over time, in the presence of different structural shocks (temporary vs. permanent and output vs. smoothing channels). In the application to the US and OECD countries, we find different dynamic properties of different smoothing channels. We compare our results with the predictions of standard risksharing and consumption theories, and tackle some of the puzzles in the literature, such as the “international risksharing puzzle” and the “consumption-output correlation puzzle.” We are also able to address such policy issues as whether fiscal stabilizers have been substitutes or complements for financial market diversification activities and whether further financial market integration is likely to provide countries with more shock-absorption tools. A key result is the strong substitutability between capital and credit smoothing in the US, and between fiscal and credit smoothing in the OECD.     

Estimating the Euler equation for output

New Keynesian macroeconomic models have generally emphasized that expectations of future output are a key factor in determining current output. The theoretical motivation for such forward-looking behavior relies on a straightforward generalization of the well-known Euler equation for consumption. In this paper, we use maximum likelihood and generalized method of moments (GMM) methods to explore the empirical importance of output expectations. We find little evidence that rational expectations of future output help determine current output, especially after taking into account the small-sample bias in GMM.