Iterated potential and robustness of equilibria

For any given set-valued solution concept, it is possible to consider iterative elimination of actions outside the solution set. This paper applies such a procedure to define the concept of iterated monotone potential maximizer (iterated MP-maximizer). It is shown that under some monotonicity conditions, an iterated MP-maximizer is robust to incomplete information [A. Kajii, S. Morris, The robustness of equilibria to incomplete information, Econometrica 65 (1997) 1283-1309] and absorbing and globally accessible under perfect foresight dynamics for a small friction [A. Matsui, K. Matsuyama, An approach to equilibrium selection, J. Econ. Theory 65 (1995) 415-434]. Several simple sufficient conditions under which a game has an iterated MP-maximizer are also provided.     

Amenity driven price effects and conservation reserve site selection: A dynamic linear integer programming approach

Most conservation reserve design models presented in the literature are static and ignore the dynamic economic aspects of site selection. Typically conservation programs operate under time-related (e.g. annual) budgets and purchase land over time in a sequential manner. The uncertainty of land development has been incorporated in a few dynamic reserve selection formulations using stochastic dynamic programming. However, the existing formulations do not explicitly deal with inter-temporal price and location linkages. We address this issue here and present a two-period linear integer programming model for conservation reserve design that incorporates amenity driven price feedback effects inherent in the reserve development problem. In addition, the model includes spatial and ecological criteria. We then use this model to answer the question “How suboptimal is ignoring amenity driven price effects in reserve design models?” We apply the model to artificially generated data sets and compare the results with the results of an iterated static model that considers only one period at a time. We find that the dynamic model with price feedback effects selects sites at a lower per-site cost. The policy implication of this finding is that conservation programs should avoid purchasing land in the same neighborhood over multiple time periods.     

On general periodic time-varying bilinear processes

We study in this note the class of bilinear processes with periodic time-varying coefficients. We give necessary and sufficient conditions ensuring the existence of strict and second order stationary solutions (in periodic sense) and for the existence of higher order moments. The given conditions can be applied to periodic ARMA or periodic GARCH models. The central limit theorem and the law of iterated logarithm (LIL) for higher order sample moments are showed.     

Iterated regret minimization: A new solution concept

For some well-known games, such as the Traveler?s Dilemma or the Centipede Game, traditional game-theoretic solution concepts—most notably Nash equilibrium—predict outcomes that are not consistent with empirical observations. We introduce a new solution concept, iterated regret minimization, that exhibits the same qualitative behavior as that observed in experiments in many games of interest, including Traveler?s Dilemma, the Centipede Game, Nash bargaining, and Bertrand competition. As the name suggests, iterated regret minimization involves the iterated deletion of strategies that do not minimize regret.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

A model of noisy introspection

We present a theoretical model of noisy introspection designed to explain behavior in games played only once. The model determines layers of beliefs about others' beliefs about …, etc., but allows for surprises by relaxing the equilibrium requirement that belief distributions coincide with decision distributions. Noise is injected into iterated conjectures about others' decisions and beliefs, which causes the predictions to differ from those of deterministic models of iterated thinking, e.g., rationalizability. The paper contains a convergence proof that implies existence and uniqueness of the outcome of the iterated thought process. In addition, estimated introspection and noise parameters for data from 37 one-shot matrix games are reported. The accuracy of the model is compared with that of several alternatives.     

Estimating three-dimensional nonlinear panel data models with interactive effects

This article considers two three-step estimation approaches to three-dimensional nonlinear panel data models with interactive effects correlated with the independent variables. We propose a Nonlinear Least Squares-Principal Component Analysis-Grid Search iterated approach to estimate the static model, and a GMM-PCA-GS iterated method to the dynamic model. Monte Carlo experiments examine the finite sample performance of the methods.     

A Remark on Voters' Rationality in a Model of Representative Democracy

Voting games are characterized by the emergence of dominated strategies, that would be iteratively deleted by rational players. In this note we show, via an example, how applying iterated dominance restricts the set of equilibrium outcomes in Besley and Coate's (1997) citizen-candidate model of representative democracy.     

Bilateral Search and Vertical Heterogeneity

Just like perfect (frictionless) matching models, a search model is proposed that is characterized by bilateral search and vertical heterogeneity. It allows for a generally specified utility function. The equilibrium allocation is unique and exists in iterated strict dominance. The model is robust with the perfect matching model as frictions disappear. Nonetheless, the equilibrium allocations are surprisingly odd. For multiplicatively separable preferences, the distributions are partitioned endogenously. And for a wide range of preferences, matching sets are naturally disconnected.     

Implementing efficient allocations in a model of financial intermediation

In a finite-trader version of the Diamond and Dybvig (J. Polit. Econ. 91 (1983) 401) model, the ex ante efficient allocation is implementable by a direct mechanism (i.e., each trader announces the type of his own ex post preference) in which truthful revelation is the strictly dominant strategy for each trader. When the model is modified by formalizing the sequential-service constraint (cf. Wallace (Fed. Reserve Bank Minneapolis Quart. Rev. 12 (1988) 3)), the truth-telling equilibrium implements the symmetric, ex ante efficient allocation with respect to iterated elimination of strictly dominated strategies.     

CROSS-COUNTRY EVIDENCE ON OUTPUT GROWTH VOLATILITY: NONSTATIONARY VARIANCE AND GARCH MODELS

This paper revisits the issue of conditional volatility in real gross domestic product (GDP) growth rates for Canada, Germany, Italy, Japan, the United Kingdom, and the United States. Previous studies find high persistence in the volatility. This paper shows that this finding largely reflects a nonstationary variance. Output growth in the six countries became noticeably less volatile over the past few decades. In this paper, we employ the modified iterated cumulative sum of squares (ICSS) algorithm to detect structural change in the variance of output growth. One structural break exists in each of the six countries after identifying outliers and mean shifts in the growth rates. We then use generalized autoregressive conditional heteroskedasticity (GARCH) specifications, modeling output growth and its volatility with and without the break in volatility. The evidence shows that the time-varying variance falls sharply in Canada and Japan, and disappears entirely in Germany, Italy, the United Kingdom and the United States, once we incorporate the break in the variance equation of output for the six countries. That is, the integrated GARCH (IGARCH) effect proves spurious and the GARCH model demonstrates misspecification, if researchers neglect a nonstationary variance. Moreover, we also consider the possible effects of our more correct measure of output volatility on output growth as well as the reverse effect of output growth on its volatility. The conditional standard deviation possesses no statistical significance in all countries, except a significant negative effect in Japan. The lagged growth rate of output produces significant negative and positive effects on the conditional variances in Germany and Japan, respectively. No significant effects exist in Canada, Italy, the United Kingdom, and the United States.     

Instrumental variable estimation of a spatial autoregressive panel model with random effects

This paper extends the instrumental variable estimators of Kelejian and Prucha (1998) and Lee (2003) proposed for the cross-sectional spatial autoregressive model to the random effects spatial autoregressive panel data model. It also suggests an extension of the Baltagi (1981) error component 2SLS estimator to this spatial panel model.     

Market structure and matching with contracts

Ostrovsky (2008) [9] develops a theory of stability for a model of matching in exogenously given networks. For this model a generalization of pairwise stability, chain stability, can always be satisfied as long as agents' preferences satisfy same side substitutability and cross side complementarity. Given this preference domain I analyze the interplay between properties of the network structure and (cooperative) solution concepts. The main structural condition is an acyclicity notion that rules out the implementation of trading cycles. It is shown that this condition and the restriction that no pair of agents can sign more than one contract with each other are jointly necessary and sufficient for (i) the equivalence of group and chain stability, (ii) the core stability of chain stable networks, (iii) the efficiency of chain stable networks, (iv) the existence of a group stable network, and (v) the existence of an efficient and individually stable network. These equivalences also provide a rationale for chain stability in the unrestricted model. The (more restrictive) conditions under which chain stability coincides with the core are also characterized.     

Threshold effects in panel data stochastic frontier models of dairy production in Canada

One of the most enduring problems in econometrics is how to properly account for heterogeneity among firms. Threshold regression models are intuitively appealing methods to deal with this issue. We consider a fixed-effect panel data stochastic frontier model (Schmidt and Sickles, 1984; Martin-Marcos and Suarez-Galvez, 2000) and, relying on Hansen (1999, 2000a), we propose an estimator that accommodates multiple thresholds. Our model assumes absence of any unmeasured time invariant heterogeneity across firms as in Greene (2005, p. 277). Slope and threshold parameters can be estimated using a within estimator combined with a grid search over the threshold parameters. Testing for threshold effects is problematic because threshold parameters are not identified under the null hypothesis, a case of the so-called Davies' problem. We apply the bootstrap procedure proposed by Hansen (1999, 2000a) to test for the presence of thresholds. An asymptotic confidence set for the threshold parameter can be obtained by inverting an LR test, using the distribution result presented in Hansen (1999, 2000a). Our empirical application features a panel of Quebec dairy farms. We use farm size as the threshold variable. The presence of a trend in the specification matters for the determination of the number of thresholds. Technical efficiency scores and rankings of farms estimated from competing model specifications are highly correlated and do not vary significantly across groups of farm sizes defined by the threshold parameter values.     

The art of conversation: eliciting information from experts through multi-stage communication

We examine the strategic interaction between an informed expert and an uninformed decision maker, extending the analysis of Crawford and Sobel (Econometrica 50 (1982) 1431). We modify their model to allow for more extensive communication between the two parties and show that face-to-face communication between the expert and the uninformed decision maker followed by a written report from the expert leads to improved information transmission. In (almost) all cases, there exists an equilibrium in our modified model that ex ante Pareto dominates all of the equilibria identified by Crawford and Sobel. This remains true even if the expert's bias is so great that in their model no information would be disclosed.     

Measuring volatility persistence in the presence of sudden changes in the variance of Canadian stock returns

Abstract.  It is well known that volatility persistence is overestimated if regime shifts are not accounted for in the standard GARCH model. This research detects time periods of sudden changes in variance using the iterated cumulated sums of squares (ICSS) algorithm. Using weekly data for the Canadian stock market indicates that after accounting for endogenously determined volatility shifts in the GARCH model, the estimated persistence in volatility is significantly reduced. This casts some doubt on previous findings that volatility in financial markets is highly persistent. The findings have important implications for investors and financial market participants. JEL classification: G1     

On uniqueness of the conditional maximum likelihood estimation for a binary panel model

This paper considers an estimation method for a binary panel model with incidental parameters as individual effects. The necessary condition for the conditional maximum likelihood approach proposed by Andersen (1970) is investigated and we show that unique sufficient statistics exist only for logit models in a two-wave panel.     

Higher order game dynamics

Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players? strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces of change, specifying e.g. the acceleration of the players? evolution instead of its velocity (a viewpoint which emerges naturally when it comes to aggregating empirical data of past instances of play). To that end, we derive a wide class of higher order game dynamics, generalizing first order imitative dynamics, and, in particular, the replicator dynamics. We show that strictly dominated strategies become extinct in n-th order payoff-monotonic dynamics n   orders as fast as in the corresponding first order dynamics; furthermore, in stark contrast to first order, weakly dominated strategies also become extinct for n?2$n?2$. All in all, higher order payoff-monotonic dynamics lead to the elimination of weakly dominated strategies, followed by the iterated deletion of strictly dominated strategies, thus providing a dynamic justification of the well-known epistemic rationalizability process of Dekel and Fudenberg [7]. Finally, we also establish a higher order analogue of the folk theorem of evolutionary game theory, and we show that convergence to strict equilibria in n-th order dynamics is n orders as fast as in first order.     

On the Use of the Prisoners' Dilemma to Analyze the Relations Between Employment Security,Trust, And Effort

Sociologists and political scientists have argued that the explanatory adequacy of economics is undermined by unreasonable assumptions of rationality. Yet interpretations that make strong rationality assumptions remain common. Analyses of the effects of employment security on work effort provide one example. The iterated prisoners' dilemma has been used to deduce a positive effect of employment security on work effort. Several difficulties with this approach are identified, including that the cooperative solution to the iterated prisoners' dilemma game i) requires infinite play or uncertainty about the end of the repetitions of the game; ii) is made less likely where there are structural bases for divergent interests; iii) ignores the possibility that employers might choose to shift the game to another arena. In general, there is the difficulty that employer-employee relations involve three simultaneous prisoners' dilemmas. The paper concludes that the hyper-rational approach implied in the prisoners' dilemma is an unpromising route for the analysis of the effects of employment security.     

The maximum number of parameters for the Hausman test when the estimators are from different sets of equations

Hausman (1978) developed a widely-used model specification test that has passed the test of time. In this paper, we show that the asymptotic variance of the difference of the two estimators can be a singular matrix. Three illustrative examples are used, namely an exogeneity test for the linear regression model, a test for the Box–Cox transformation, and a test for sample selection bias.