Generalized Method of Moments and Empirical Likelihood Export

@article{imbens:2002, abstract = {Generalized method of moments (GMM) estimation has become an important unifying framework for inference in econometrics in the last 20 years. It can be thought of as encompassing almost all of the common estimation methods, such as maximum likelihood, ordinary least squares, instrumental variables, and two-stage least squares, and nowadays is an important part of all advanced econometrics textbooks. The GMM approach links nicely to economic theory where orthogonality conditions that can serve as such moment functions often arise from optimizing behavior of agents. Much work has been done on these methods since the seminal article by Hansen, and much remains in progress. This article discusses some of the developments since Hansen's original work. In particular, it focuses on some of the recent work on empirical likelihood–type estimators, which circumvent the need for a first step in which the optimal weight matrix is estimated and have attractive information theoretic interpretations.}, author = {Imbens, G. W.}, citeulike-article-id = {2968121}, citeulike-linkout-0 = {http://www.ingentaconnect.com/content/asa/jbes/2002/00000020/00000004/art00008}, citeulike-linkout-1 = {http://dx.doi.org/10.1198/073500102288618630}, comment = {A general discussion of GMM and its developments from Hansen's (1982) to early 2000s, as well as connections to EL. Two-step GMM: obtain consistent estimates, form the consistent estimator of the optimal weight matrix, get asymptotically efficient estimates. Relation of the over-identified GMM to just-identified GMM: augment the parameter vector by carefully chosen extra entries; hence all the results for just-identified GMM, like validity of the bootstrap, are applicable to overID GMM. Semiparametric efficiency of efficient GMM in the class of estimators based on moment conditions (Chamberlain 1987, and probably Godambe's work is relevant here, as well). Empirical likelihood: brief overview, relation ot Cressie-Read family (\$\lambda=0\$); more of the discussion that followed actually refers to exponetial tilting estimator (\$\lambda=-1\$). Another special case: \$\lambda=-2\$, continuously updating GMM estimator. Class of generalized empirical likelihood estimators solving the saddlepoint problem. Testing: (i) empirical likelihood ratio test, straight out of the objective function; (ii) Wald tests based on the (estimator of) covariance matrix -- empirical or efficient/weighted with EL weights; (iii) LM/score, with either the generalized inverse or the covariance of the estimating equations. Higher order properties: GEL estimators have fewer first order terms in their bias expansions than GMM. Relation to the number of overID restrictions \$M\$: if the bias of EL or exp tilting estimator is \$-\rho/N\$, then the bias of two-step GMM is \$-\rho/N + \rho(M-1)/N\$. Computing: (i) solve for the EL probabilities, as in Owen's work; (ii) introduce some penalties (neutral to first order conditions); (iii) concentrate out Lagrange multipliers. Good review paper, a must for any econometrician. }, doi = {10.1198/073500102288618630}, issn = {0735-0015}, journal = {Journal of Business and Economic Statistics}, keywords = {asymptotics, econometric\_theory, econometrics, empirical\_likelihood, gmm, higher\_order\_asymptotics}, number = {4}, pages = {493--506}, posted-at = {2008-07-07 02:08:56}, priority = {2}, publisher = {American Statistical Association}, title = {Generalized Method of Moments and Empirical Likelihood}, url = {http://dx.doi.org/10.1198/073500102288618630}, volume = {20}, year = {2002} }

TY - JOUR ID - imbens:2002 L3 - citeulike-article-id:2968121 N2 - Generalized method of moments (GMM) estimation has become an important unifying framework for inference in econometrics in the last 20 years. It can be thought of as encompassing almost all of the common estimation methods, such as maximum likelihood, ordinary least squares, instrumental variables, and two-stage least squares, and nowadays is an important part of all advanced econometrics textbooks. The GMM approach links nicely to economic theory where orthogonality conditions that can serve as such moment functions often arise from optimizing behavior of agents. Much work has been done on these methods since the seminal article by Hansen, and much remains in progress. This article discusses some of the developments since Hansen's original work. In particular, it focuses on some of the recent work on empirical likelihood–type estimators, which circumvent the need for a first step in which the optimal weight matrix is estimated and have attractive information theoretic interpretations. IS - 4 JF - Journal of Business and Economic Statistics SN - 0735-0015 EP - 506 TI - Generalized Method of Moments and Empirical Likelihood PB - American Statistical Association VL - 20 SP - 493 KW - asymptotics KW - econometric_theory KW - econometrics KW - empirical_likelihood KW - gmm KW - higher_order_asymptotics N1 - A general discussion of GMM and its developments from Hansen's (1982) to early 2000s, as well as connections to EL. Two-step GMM: obtain consistent estimates, form the consistent estimator of the optimal weight matrix, get asymptotically efficient estimates. Relation of the over-identified GMM to just-identified GMM: augment the parameter vector by carefully chosen extra entries; hence all the results for just-identified GMM, like validity of the bootstrap, are applicable to overID GMM. Semiparametric efficiency of efficient GMM in the class of estimators based on moment conditions (Chamberlain 1987, and probably Godambe's work is relevant here, as well). Empirical likelihood: brief overview, relation ot Cressie-Read family ($\lambda=0$); more of the discussion that followed actually refers to exponetial tilting estimator ($\lambda=-1$). Another special case: $\lambda=-2$, continuously updating GMM estimator. Class of generalized empirical likelihood estimators solving the saddlepoint problem. Testing: (i) empirical likelihood ratio test, straight out of the objective function; (ii) Wald tests based on the (estimator of) covariance matrix -- empirical or efficient/weighted with EL weights; (iii) LM/score, with either the generalized inverse or the covariance of the estimating equations. Higher order properties: GEL estimators have fewer first order terms in their bias expansions than GMM. Relation to the number of overID restrictions $M$: if the bias of EL or exp tilting estimator is $-\rho/N$, then the bias of two-step GMM is $-\rho/N + \rho(M-1)/N$. Computing: (i) solve for the EL probabilities, as in Owen's work; (ii) introduce some penalties (neutral to first order conditions); (iii) concentrate out Lagrange multipliers. Good review paper, a must for any econometrician. AU - Imbens, GW PY - 2002/// UR - http://dx.doi.org/10.1198/073500102288618630 ER -