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53
Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score
, 2000
"... We are interested in estimating the average e#ect of a binary treatment on a scalar outcome. If assignment to the treatment is independent of the potential outcomes given pretreatment variables, biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for di#er ..."
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Cited by 167 (15 self)
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We are interested in estimating the average e#ect of a binary treatment on a scalar outcome. If assignment to the treatment is independent of the potential outcomes given pretreatment variables, biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for di#erences in the pretreatmentvariables. Rosenbaum and Rubin #1983, 1984# show that adjusting solely for di#erences between treated and control units in a scalar function of the pretreatment variables, the propensity score, also removes the entire bias associated with di#erences in pretreatment variables. Thus it is possible to obtain unbiased estimates of the treatment e#ect without conditioning on a possibly highdimensional vector of pretreatment variables. Although adjusting for the propensity score removes all the bias, this can come at the expense of e#ciency. We show that weighting with the inverse of a nonparametric estimate of the propensity score, rather than the true propensity scor...
An MCMC approach to classical estimation
, 2003
"... This paper studies computationally and theoretically attractive estimators called here Laplace type estimators (LTEs), which include means and quantiles of quasiposterior distributions dened as transformations of general (nonlikelihoodbased) statistical criterion functions, such as those in GMM, n ..."
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Cited by 56 (8 self)
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This paper studies computationally and theoretically attractive estimators called here Laplace type estimators (LTEs), which include means and quantiles of quasiposterior distributions dened as transformations of general (nonlikelihoodbased) statistical criterion functions, such as those in GMM, nonlinear IV, empirical likelihood, and minimum distance methods. The approach generates an alternative to classical extremum estimation and also falls outside the parametric Bayesian approach. For example, it o ers a new attractive estimation method for such important semiparametric problems as censored and instrumental quantile regression, nonlinear GMM and valueatrisk models. The LTEs are computed using Markov Chain Monte Carlo methods, which help circumvent the computational curse of dimensionality. Alarge sample theory is obtained and illustrated for regular cases.
EMPIRICAL LIKELIHOOD METHODS IN ECONOMETRICS: THEORY AND PRACTICE
, 2006
"... Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method in perspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator ( ..."
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Cited by 18 (2 self)
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Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method in perspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator (GMC). The latter interpretation provides a clear connection between EL, GMM, GEL and other related estimators. Second, EL is shown to have various advantages over other methods. The theory of large deviations demonstrates that EL emerges naturally in achieving asymptotic optimality both for estimation and testing. Interestingly, higher order asymptotic analysis also suggests that EL is generally a preferred method. Third, extensions of EL are discussed in various settings, including estimation of conditional moment restriction models, nonparametric specification testing and time series models. Finally, practical issues in applying EL to real data, such as computational algorithms for EL, are discussed. Numerical examples to illustrate the efficacy of the method are presented.
Applications of Intentionally Biased Bootstrap Methods
"... . A class of weightedbootstrap techniques, called biasedbootstrap methods, is proposed. It is motivated by the need to adjust more conventional, uniformbootstrap methods in a surgical way, so as to alter some of their features while leaving others unchanged. Depending on the nature of the adjustme ..."
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Cited by 17 (3 self)
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. A class of weightedbootstrap techniques, called biasedbootstrap methods, is proposed. It is motivated by the need to adjust more conventional, uniformbootstrap methods in a surgical way, so as to alter some of their features while leaving others unchanged. Depending on the nature of the adjustment, the biased bootstrap can be used to reduce bias, or reduce variance, or render some characteristic equal to a predetermined quantity. More specifically, applications of bootstrap methods include hypothesis testing, variance stabilisation, both density estimation and nonparametric regression under constraints, `robustification ' of general statistical procedures, sensitivity analysis, generalised method of moments, shrinkage, and many more. 1991 Mathematics Subject Classification: Primary 62G09, Secondary 62G05 Keywords and Phrases: Bias reduction, empirical likelihood, hypothesis testing, locallinear smoothing, nonparametric curve estimation, variance stabilisation, weighted bootstrap 1...
GMM Estimation of Empirical Growth Models
, 1998
"... This paper highlights a problem in using the firstdifferenced GMM panel data estimator to estimate crosscountry growth regressions. When the time series are persistent, the firstdifferenced GMM estimator can be poorly behaved, since lagged levels of the series provide only weak instruments for su ..."
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Cited by 13 (0 self)
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This paper highlights a problem in using the firstdifferenced GMM panel data estimator to estimate crosscountry growth regressions. When the time series are persistent, the firstdifferenced GMM estimator can be poorly behaved, since lagged levels of the series provide only weak instruments for subsequent first differences. Revisiting the work of Caselli, Esquivel and Lefort (1996), we show that this problem may be serious in practice. We suggest using a more efficient GMM estimator that exploits stationarity restrictions, and this approach is shown to give more reasonable results than firstdifferenced GMM in our estimation of an empirical growth model.
On the Asymptotic Size Distortion of Tests When Instruments Locally Violate the Exogeneity Assumption
, 2010
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Subsampling Tests of Parameter Hypotheses and Overidentifying Restrictions with Possible Failure of Identification
, 2004
"... We introduce a general testing procedure in models with possible identification failure that has exact asymptotic rejection probability under the null hypothesis. The procedure is widely applicable and in this paper we apply it to tests of arbitrary linear parameter hypotheses and to tests of overid ..."
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Cited by 9 (6 self)
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We introduce a general testing procedure in models with possible identification failure that has exact asymptotic rejection probability under the null hypothesis. The procedure is widely applicable and in this paper we apply it to tests of arbitrary linear parameter hypotheses and to tests of overidentifying restrictions in time series models given by unconditional moment conditions. The main idea is to subsample classical tests, like for example the Wald or the J test. More precisely, instead of using these tests with critical values based on asymptotic theory, we compute data—dependent critical values based on the subsampling technique. We show that the resulting tests have exact asymptotic rejection probabilities under the null hypothesis independent of identification failure. Furthermore, the subsampling tests of parameter hypotheses are shown to be consistent against fixed alternatives and to have the same local power as the original tests under full identification. The subsampling test of overidentifying restrictions is shown
MINIMAX ESTIMATION AND TESTING FOR MOMENT CONDITION MODELS VIA LARGE DEVIATIONS
, 2005
"... This paper studies asymptotically optimal estimation and testing procedures for moment condition models using the theory of large deviations (LD). Minimax risk estimation and testing are discussed in details. The aim of the paper is threefold. First, it studies a moment condition model by treating ..."
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Cited by 6 (2 self)
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This paper studies asymptotically optimal estimation and testing procedures for moment condition models using the theory of large deviations (LD). Minimax risk estimation and testing are discussed in details. The aim of the paper is threefold. First, it studies a moment condition model by treating it as a statistical experiment in Le Cam’s sense, and investigates its large deviation properties. Second, it develops a new minimax estimator for the model by considering Bahadur’s large deviation efficiency criterion. The estimator can be regarded as a robustified version of the conventional empirical likelihood estimator. Third, it considers a Chernofftype risk for parametric testing in the model, which is concerned with the LD probabilities of type I errors and type II errors. It is shown that the empirical likelihood ratio test is asymptotically minimax in this context.
Bayesian Exponentially Tilted Empirical Likeliood
 Biometrika
, 2005
"... Newey and Smith (2001) have recently shown that Empirical Likelihood (EL) exhibits desirable higherorder asymptotic properties, namely, that its O ¡ n −1 ¢ bias is particularly small and that biascorrected EL is higherorder efficient. Although EL possesses these properties when the model is correc ..."
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Cited by 5 (0 self)
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Newey and Smith (2001) have recently shown that Empirical Likelihood (EL) exhibits desirable higherorder asymptotic properties, namely, that its O ¡ n −1 ¢ bias is particularly small and that biascorrected EL is higherorder efficient. Although EL possesses these properties when the model is correctly specified, this paper shows that the asymptotic variance of EL in the presence of model misspecification may become undefined when the functions defining the moment conditions are unbounded. In contrast, the Exponential Tilting (ET) estimator avoids this problem under mild regularity conditions. Since ET does not share the higherorder asymptotic properties of EL, there is a need for an estimator that combines the qualities of both estimators. This paper introduces a new estimator called Exponentially Tilted Empirical Likelihood (ETEL) that is shown to have the same O ¡ n −1 ¢ bias and the same O ¡ n −2¢ variance as EL, while maintaining a welldefined asymptotic variance under model misspecification.
Testing for NonNested Conditional Moment Restrictions using Unconditional Empirical Likelihood
, 2008
"... We propose nonnested hypotheses tests for conditional moment restriction models based on the method of generalized empirical likelihood (GEL). By utilizing the implied GEL probabilities from a sequence of unconditional moment restrictions that contains equivalent information of the conditional mome ..."
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Cited by 5 (2 self)
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We propose nonnested hypotheses tests for conditional moment restriction models based on the method of generalized empirical likelihood (GEL). By utilizing the implied GEL probabilities from a sequence of unconditional moment restrictions that contains equivalent information of the conditional moment restrictions, we construct KolmogorovSmirnov and Cramérvon Mises type moment encompassing tests. Advantages of our tests over Otsu and Whang’s (2007) tests are: (i) they are free from smoothing parameters, (ii) they can be applied to weakly dependent data, and (iii) they allow nonsmooth moment functions. We derive the null distributions, validity of a bootstrap procedure, and local and global power properties of our tests. The simulation results show that our tests have reasonable size and power performance in finite samples.