A consistent characteristic function-based test for conditional independence

Y is conditionally independent of Z given X   if Pr{f(y|X,Z)=f(y|X)}=1$\{f(y|X,Z)=f(y|X)\}=1$ for all y on its support, where f(·|·)$f(·|·)$ denotes the conditional density of Y   given (X,Z)$(X,Z)$ or X.$X.$ This paper proposes a nonparametric test of conditional independence based on the notion that two conditional distributions are equal if and only if the corresponding conditional characteristic functions are equal. We extend the test of Su and White (2005. A Hellinger-metric nonparametric test for conditional independence. Discussion Paper, Department of Economics, UCSD) in two directions: (1) our test is less sensitive to the choice of bandwidth sequences; (2) our test has power against deviations on the full support of the density of (X,Y,Z$X,Y,Z$). We establish asymptotic normality for our test statistic under weak data dependence conditions. Simulation results suggest that the test is well behaved in finite samples. Applications to stock market data indicate that our test can reveal some interesting nonlinear dependence that a traditional linear Granger causality test fails to detect.     

Endogeneity in quantile regression models: A control function approach

This paper considers a linear triangular simultaneous equations model with conditional quantile restrictions. The paper adjusts for endogeneity by adopting a control function approach and presents a simple two-step estimator that exploits the partially linear structure of the model. The first step consists of estimation of the residuals of the reduced-form equation for the endogenous explanatory variable. The second step is series estimation of the primary equation with the reduced-form residual included nonparametrically as an additional explanatory variable. This paper imposes no functional form restrictions on the stochastic relationship between the reduced-form residual and the disturbance term in the primary equation conditional on observable explanatory variables. The paper presents regularity conditions for consistency and asymptotic normality of the two-step estimator. In addition, the paper provides some discussions on related estimation methods in the literature.     

The robustness of the independent private value model in Bayesian mechanism design

Summary. In a Bayesian model of group decision-making, dependence among the agents' types has been shown to have a beneficial effect on the design of incentive compatible mechanisms that achieve the efficient choice associated with complete information. This effect is shown here to depend as much upon the use of large monetary transfers among the agents as it does upon dependence: if the transfers are bounded in magnitude, then nonexistence in the case of independence of an efficient, incentive compatible, ex ante budget-balanced and interim individually rational mechanism is robust to the introduction of a small amount of dependence among types. This robustness result supports the use of the simplifying assumption of independence in mechanism design. Received: October 28, 1996; revised version: May 28, 1997     

Bayesian learning and convergence to Nash equilibria without common priors

Summary. Consider an infinitely repeated game where each player is characterized by a “type” which may be unknown to the other players in the game. Suppose further that each player's belief about others is independent of that player's type. Impose an absolute continuity condition on the ex ante beliefs of players (weaker than mutual absolute continuity). Then any limit point of beliefs of players about the future of the game conditional on the past lies in the set of Nash or Subjective equilibria. Our assumption does not require common priors so is weaker than Jordan (1991); however our conclusion is weaker, we obtain convergence to subjective and not necessarily Nash equilibria. Our model is a generalization of the Kalai and Lehrer (1993) model. Our assumption is weaker than theirs. However, our conclusion is also weaker, and shows that limit points of beliefs, and not actual play, are subjective equilibria. Received: March 3, 1995; revised version: February 17, 1997     

Coalitional stability under perfect foresight

Summary. We analyze strategic social environments where coalitions can form through binding or nonbinding agreements and actions of a coalition may impose externalities upon the welfare of the rest of the players. We define a solution concept that (1) captures the perfect foresight of the players that has been overlooked in the literature (e.g., Harsanyi [10] and Chwe [6]) and (2) identifies the coalitions that are likely to form and the “stable” outcomes that will not be replaced by any coalition of rational (and hence farsighted) players. The proposed solution concept thereby offers a notion of agreements and coalition formation in complex social environments. Received: February 12, 1996; revised version: March 3, 1997     

A multinomial probit model of stochastic evolution

A strategy revision process in symmetric normal form games is proposed. Following Kandori et al. (Econometrica 61 (1993) 29), members of a population periodically revise their strategy choice, and choose a myopic best response to currently observed play. Their payoffs are perturbed by normally distributed Harsanyian trembles, so that strategies are chosen according to multinomial probit probabilities. As the variance of payoffs is allowed to vanish, the graph theoretic methods of the earlier literature continue to apply. The distributional assumption enables a convenient closed form characterisation for the weights of the rooted trees. An illustration of the approach is offered, via a consideration of the role of dominated strategies in equilibrium selection.     

The evolution of rationality and the Red Queen

Strategic rationality is subjected here to natural selection. In a zero-sum repeated game of incomplete information, one long-run individual is informed of the state of the world, and plays against a sequence of short-run opponents who are not. Strategies are noisy and have bounded recall. An equilibrium in these is shown to exist. Relative to any such equilibrium, sufficiently greater recall enjoys an advantage that is not decreasing in the original level of recall, thus capturing the Red Queen effect. The selection pressure to reduce a small amount of noise is less than that to increase recall.     

Non-addictive habits: optimal consumption-portfolio policies

We formulate a model of preferences with non-addictive habits, where consumption is required to be non-negative at all times, but can fall below a “standard of living” index that aggregates past consumption. We study the consumption-portfolio problem taking account of the non-negativity constraint on consumption, and provide a constructive proof for the existence of an optimal policy on a finite time-horizon [0,T]. We show that the consumption constraint binds up to an endogenous stopping time τ∗∈[0,T], after which it remains slack until T. A decomposition of constrained consumption involving an Asian average-strike capped call-option is demonstrated.     

Bivariate income distributions for assessing inequality and poverty under dependent samples

As indicators of social welfare, the incidence of inequality and poverty is of ongoing concern to policy makers and researchers alike. Of particular interest are the changes in inequality and poverty over time, which are typically assessed through the estimation of income distributions. From this, income inequality and poverty measures, along with their differences and standard errors, can be derived and compared. With panel data becoming more frequently used to make such comparisons, traditional methods which treat income distributions from different years independently and estimate them on a univariate basis, fail to capture the dependence inherent in a sample taken from a panel study. Consequently, parameter estimates are likely to be less efficient, and the standard errors for between-year differences in various inequality and poverty measures will be incorrect. This paper addresses the issue of sample dependence by suggesting a number of bivariate distributions, with Singh–Maddala or Dagum marginals, for a partially dependent sample of household income for two years. Specifically, the distributions considered are the bivariate Singh–Maddala distribution, proposed by Takahasi (1965), and bivariate distributions belonging to the copula class of multivariate distributions, which are an increasingly popular approach to modelling joint distributions. Each bivariate income distribution is estimated via full information maximum likelihood using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey for 2001 and 2005. Parameter estimates for each bivariate income distribution are used to obtain values for mean income and modal income, the Gini inequality coefficient and the headcount ratio poverty measure, along with their differences, enabling the assessment of changes in such measures over time. In addition, the standard errors of each summary measure and their differences, which are of particular interest in this analysis, are calculated using the delta method.     

THE CITATION IMPACT OF FEMINIST ECONOMICS

Abstract

Feminist economics is a transformative project. However, transformation generates resistance. Feminist economics can be deliberately excluded, co-opted through an uncritical application of rational choice theory, or ignored. And feminist economics can be listened to: when the United Nations consults feminist economists; when feminist economists publish in widely read journals; when a student finds inspiration in a Feminist Economics article. All of these are ways feminist economics can, and has, influenced the profession. After ten years of discourse, it is possible to take stock and assess the impact of feminist economics. This article provides a partial assessment through a consideration of citations of the journal Feminist Economics, describing its impact on mainstream economics, heterodox economics, and other disciplines. While the overall project of feminist economics encompasses much more than just one journal, studying the citations for Feminist Economics is a first step toward assessing the influence of the entire corpus.