This paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions. Our estimator generalizes the maximum empirical likelihood estimator (MELE) of Qin and Lawless (1994). Using a kernel smoothing method, we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood-based procedure. This yields a one-step estimator which avoids estimating optimal instruments. Our likelihood ratio-type statistic for parametric restrictions does not require the estimation of variance, and achieves asymptotic pivotalness implicitly. The estimation and testing procedures we propose are normalization invariant. Simulation results suggest that our new estimator works remarkably well in finite samples.
Conditional moment restrictions can be combined through GMM estimation to construct more efficient semiparametric estimators. This paper is about attainable efficiency for such estimators. We define and use a moment tangent set, the directions of departure from the truth allowed by the moments, to characterize when the semiparametric efficiency bound can be attained. The efficiency condition is that the moment tangent set equals the model tangent set. We apply these results to transformed, censored, and truncated regression models, e.g., finding that the conditional moment restrictions from Powell's (1986) censored regression quantile estimators can be combined to approximate efficiency when the disturbance is independent of regressors. Copyright The Econometric Society 2004.
We investigate two-player infinitely repeated games where the discount factor is less than but close to unity. Monitoring is private and players cannot communicate. We require no condition concerning the accuracy of players' monitoring technology. We show the folk theorem for the prisoners' dilemma with conditional independence. We also investigate more general games where players' private signals are correlated only through an unobservable macro shock. We show that efficiency is sustainable for generic private signal structures when the size of the set of private signals is sufficiently large. Finally, we show that cartel collusion is sustainable in price-setting duopoly.
Wavelet analysis is a new mathematical method developed as a unified field of science over the last decade or so. As a spatially adaptive analytic tool, wavelets are useful for capturing serial correlation where the spectrum has peaks or kinks, as can arise from persistent dependence, seasonality, and other kinds of periodicity. This paper proposes a new class of generally applicable wavelet-based tests for serial correlation of unknown form in the estimated residuals of a panel regression model, where error components can be one-way or two-way, individual and time effects can be fixed or random, and regressors may contain lagged dependent variables or deterministic/stochastic trending variables. Our tests are applicable to unbalanced heterogenous panel data. They have a convenient null limit N(0,1) distribution. No formulation of an alternative model is required, and our tests are consistent against serial correlation of unknown form even in the presence of substantial inhomogeneity in serial correlation across individuals. This is in contrast to existing serial correlation tests for panel models, which ignore inhomogeneity in serial correlation across individuals by assuming a common alternative, and thus have no power against the alternatives where the average of serial correlations among individuals is close to zero. We propose and justify a data-driven method to choose the smoothing parameter—the finest scale in wavelet spectral estimation, making the tests completely operational in practice. The data-driven finest scale automatically converges to zero under the null hypothesis of no serial correlation and diverges to infinity as the sample size increases under the alternative, ensuring the consistency of our tests. Simulation shows that our tests perform well in small and finite samples relative to some existing tests.
An important objective of empirical research on treatment response is to provide decision makers with information useful in choosing treatments. This paper studies minimax-regret treatment choice using the sample data generated by a classical randomized experiment. Consider a utilitarian social planner who must choose among the feasible statistical treatment rules, these being functions that map the sample data and observed covariates of population members into a treatment allocation. If the planner knew the population distribution of treatment response, the optimal treatment rule would maximize mean welfare conditional on all observed covariates. The appropriate use of covariate information is a more subtle matter when only sample data on treatment response are available. I consider the class of conditional empirical success rules; that is, rules assigning persons to treatments that yield the best experimental outcomes conditional on alternative subsets of the observed covariates. I derive a closed-form bound on the maximum regret of any such rule. Comparison of the bounds for rules that conditional on smaller and larger subsets of the covariates yields sufficient sample sizes for productive use of covariate information. When the available sample size exceeds the sufficiency boundary, a planner can be certain that conditioning treatment choice on more covariates is preferable (in terms of minimax regret) to conditioning on fewer covariates.
Preferences exhibit relative consumption effects if a person's satisfaction with their own consumption appears to depend upon how much others are consuming. This paper examines a model of an evolutionary environment in which Nature optimally builds relative consumption effects into preferences in order to compensate for incomplete environmental information. Copyright Econometric Society 2004.
In econometrics, models stated as conditional moment restrictions are typically estimated by means of the generalized method of moments (GMM). The GMM estimation procedure can render inconsistent estimates since the number of arbitrarily chosen instruments is finite. In fact, consistency of the GMM estimators relies on additional assumptions that imply unclear restrictions on the data generating process. This article introduces a new, simple and consistent estimation procedure for these models that is directly based on the definition of the conditional moments. The main feature of our procedure is its simplicity, since its implementation does not require the selection of any user-chosen number, and statistical inference is straightforward since the proposed estimator is asymptotically normal. In addition, we suggest an asymptotically efficient estimator constructed by carrying out one Newton–Raphson step in the direction of the efficient GMM estimator.
A complex financial system comprises both financial markets and financial intermediaries. We distinguish financial intermediaries according to whether they issue complete contingent contracts or incomplete contracts. Intermediaries such as banks that issue incomplete con-tracts, e.g., demand deposits, are subject to runs, but this does not imply a market failure. A sophisticated financial system–a system with complete markets for aggregate risk and limited market participation–is incentive-efficient, if the intermediaries issue complete con-tingent contracts, or else constrained-efficient, if they issue incomplete contracts. We argue that there may be a role for regulating liquidity provision in an economy in which markets for aggregate risks are incomplete. 1 Markets, intermediaries and crises For a long time, it has been taken as axiomatic that financial crises are best avoided. We confront this conventional wisdom by showing that, under certain conditions, a laisser-faire financial system achieves the incentive-efficient or constrained-efficient allocation.1 Further-more, constrained efficiency may require financial crises in equilibrium. The assumptions
This paper examines the problem of measuring intellectual influence based on data on citations between scholarly publications. We follow an axiomatic approach and find that the properties of invariance to reference intensity, weak homogeneity, weak consistency, and invariance to splitting of journals characterize a unique ranking method. This method is different from those regularly used in economics and other social sciences. Copyright The Econometric Society 2004.
We study strategic voting after weakening the notion of strategy-proofness to Ordinal Bayesian Incentive Compatibility (OBIC). Under OBIC, truth-telling is required to maximize the expected utility of every voter, expected utility being computed with respect to the voter's prior beliefs and under the assumption that everybody else is also telling the truth. We show that for a special type of priors, i.e., the uniform priors, there exists a large class of social choice functions that are OBIC. However, for priors that are generic in the set of independent beliefs, a social choice function is OBIC only if it is dictatorial. This result underlines the robustness of the Gibbard–Satterthwaite Theorem.