1932

Abstract

This article reviews a number of recent contributions to estimation and inference for models defined by moment condition restrictions. The particular emphasis is on the generalized empirical likelihood class of estimators as an alternative to the generalized method of moments. Estimation methods for parameters defined through moment restrictions and their properties are described with tests of overidentifying moment restrictions and parametric hypotheses. Computational issues are discussed together with some proposals for their amelioration. Higher-order and other properties are also addressed in some detail. Models specified by conditional moment restriction models are considered, and the adaptation of these methods to weakly dependent data is discussed.

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2014-08-02
2024-04-23
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Literature Cited

  1. Ai C, Chen X. 2003. Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica 71:1795–843 [Google Scholar]
  2. Ali SM, Silvey SD. 1966. A general class of coefficient of divergence of one distribution from another. J. R. Stat. Soc. B 28:131–42 [Google Scholar]
  3. Amemiya T. 1974. The nonlinear two-stage least-squares estimator. J. Econom. 2:105–10 [Google Scholar]
  4. Anatolyev S. 2005. GMM, GEL, serial correlation, and asymptotic bias. Econometrica 73:983–1002 [Google Scholar]
  5. Anatolyev S, Gospodinov N. 2011. Methods for Estimation and Inference in Modern Econometrics. Boca Raton, FL: Chapman & Hall/CRC
  6. Andrews DWK, Shi X. 2013. Inference based on conditional moment inequalities. Econometrica 81:609–66 [Google Scholar]
  7. Andrews DWK, Stock JH. 2005. Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg. Cambridge, UK: Cambridge Univ. Press
  8. Angrist JD, Krueger AB. 1991. Does compulsory school attendance affect schooling and earnings?. Q. J. Econ. 106:979–1014 [Google Scholar]
  9. Antoine B, Bonnal H, Renault E. 2007. On the efficient use of the informational content of estimating equations: implied probabilities and Euclidean empirical likelihood. J. Econom. 138:461–87 [Google Scholar]
  10. Back K, Brown DP. 1993. Implied probabilities in GMM estimators. Econometrica 61:971–75 [Google Scholar]
  11. Baggerly K. 1998. Empirical likelihood as a goodness-of-fit measure. Biometrika 85:535–47 [Google Scholar]
  12. Bartlett MS. 1937. Properties of sufficiency and statistical tests. Proc. R. Soc. A 160:268–82 [Google Scholar]
  13. Beran R. 1977. Minimum Hellinger distance estimates for parametric models. Ann. Stat. 5:445–63 [Google Scholar]
  14. Brown BW, Newey WK. 1998. Efficient semiparametric estimation of expectations. Econometrica 66:453–64 [Google Scholar]
  15. Brown BW, Newey WK. 2002. Generalized method of moments, efficient bootstrapping, and improved inference. J. Bus. Econ. Stat. 20:507–17 [Google Scholar]
  16. Canay IA. 2010. EL inference for partially identified models: large deviations optimality and bootstrap validity. J. Econom. 156:408–25 [Google Scholar]
  17. Chamberlain G. 1987. Asymptotic efficiency in estimation with conditional moment restrictions. J. Econom. 34:305–34 [Google Scholar]
  18. Chaussé P. 2010. Computing generalized method of moments and generalized empirical likelihood with R. J. Stat. Softw. 34:111–35 [Google Scholar]
  19. Chen J, Variyath AM, Abraham B. 2008. Adjusted empirical likelihood and its properties. J. Comput. Graph. Stat. 17:426–43 [Google Scholar]
  20. Chen SX, Cui H-J. 2006. On Bartlett correction of empirical likelihood in the presence of nuisance parameters. Biometrika 93:215–20 [Google Scholar]
  21. Chen SX, Cui H-J. 2007. On the second order properties of empirical likelihood with moment restrictions. J. Econom. 141:492–516 [Google Scholar]
  22. Chen X, Pouzo D. 2009. Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals. J. Econom. 152:46–60 [Google Scholar]
  23. Chen X, Pouzo D. 2012. Estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals. Econometrica 80:277–321 [Google Scholar]
  24. Chesher A, Smith RJ. 1997. Likelihood ratio specification tests. Econometrica 65:627–46 [Google Scholar]
  25. Corcoran S. 1998. Bartlett adjustment of empirical discrepancy statistics. Biometrika 85:965–72 [Google Scholar]
  26. Cragg JG. 1983. More efficient estimation in the presence of heteroscedasticity of unknown form. Econometrica 51:751–63 [Google Scholar]
  27. Cressie N, Read T. 1984. Multinomial goodness-of-fit tests. J. R. Stat. Soc. B 46:440–64 [Google Scholar]
  28. Cribari-Neto F, Cordeiro GM. 1996. On Bartlett and Bartlett-type corrections. Econom. Rev. 15:339–67 [Google Scholar]
  29. Csiszar I. 1963. Eine informations theoretische ungleichungen und ihre anwendung auf den beweis der ergodicitat von Markoffschen ketten. Publ. Math. Inst. Hung. Acad. Sci. 8:85–108 [Google Scholar]
  30. Davidson R, MacKinnon JG. 2004. Econometric Theory and Methods. New York: Oxford Univ. Press
  31. DiCiccio T, Hall P, Romano J. 1991. Empirical likelihood is Bartlett-correctable. Ann. Stat. 19:1053–61 [Google Scholar]
  32. Donald SG, Imbens GW, Newey WK. 2003. Empirical likelihood estimation and consistent tests with conditional moment restrictions. J. Econom. 117:55–93 [Google Scholar]
  33. Fan Y, Gentry M, Li T. 2011. A new class of asymptotically efficient estimators for moment condition models. J. Econom. 162:268–77 [Google Scholar]
  34. Ghosh JK. 1994. Higher Order Asymptotics. NSF-CBMS Reg. Conf. Ser. Probab. Stat. 4. Hayward, CA: Inst. Math. Stat.
  35. Goldberger AS. 1991. A Course in Econometrics. Cambridge, MA: Harvard Univ. Press
  36. Greene WH. 2008. Econometric Analysis. Upper Saddle River, NJ: Pearson Prentice Hall, 6th ed..
  37. Guggenberger P. 2008. Finite sample evidence suggesting a heavy tail problem of the generalized empirical likelihood estimator. Econom. Rev. 27:526–41 [Google Scholar]
  38. Guggenberger P, Ramalho JJS, Smith RJ. 2012. GEL statistics under weak identification. J. Econom. 170:331–49 [Google Scholar]
  39. Hall P, Horowitz JL. 1996. Bootstrap critical values for tests based on generalized-method-of-moment estimators. Econometrica 64:891–916 [Google Scholar]
  40. Hansen LP. 1982. Large sample properties of generalized method of moments estimators. Econometrica 50:1029–54 [Google Scholar]
  41. Hansen LP, Heaton J, Yaron A. 1996. Finite-sample properties of some alternative GMM estimators. J. Bus. Econ. Stat. 14:262–80 [Google Scholar]
  42. Hjört NL, McKeague IW, Van Keilegom I. 2009. Extending the scope of empirical likelihood. Ann. Stat. 37:1079–111 [Google Scholar]
  43. Hoeffding W. 1965. Asymptotically optimal tests for multinomial distributions. Ann. Math. Stat. 36:369–408 [Google Scholar]
  44. Ichimura H. 1993. Semiparametric least squares (SLS) and weighted SLS estimation of single index models. J. Econom. 58:71–120 [Google Scholar]
  45. Imbens GW. 1997. One-step estimators for over-identified generalized method of moments models. Rev. Econ. Stud. 64:359–83 [Google Scholar]
  46. Imbens GW. 2002. Generalized method of moments and empirical likelihood. J. Bus. Econ. Stat. 20:493–506 [Google Scholar]
  47. Imbens GW, Spady RH. 2002. Confidence intervals in generalized method of moments models. J. Econom. 107:87–98 [Google Scholar]
  48. Imbens GW, Spady RH. 2005. The performance of empirical likelihood and its generalizations. See Andrews & Stock 2005, pp. 216–44 [Google Scholar]
  49. Imbens GW, Spady RH, Johnson P. 1998. Information theoretic approaches to inference in moment condition models. Econometrica 66:333–57 [Google Scholar]
  50. Jing B-Y, Wood ATA. 1996. Exponential empirical likelihood is not Bartlett correctable. Ann. Stat. 24:365–69 [Google Scholar]
  51. Kitamura Y. 1997. Empirical likelihood methods with weakly dependent processes. Ann. Stat. 25:2084–102 [Google Scholar]
  52. Kitamura Y. 2001. Asymptotic optimality of empirical likelihood for testing moment restrictions. Econometrica 69:1661–72 [Google Scholar]
  53. Kitamura Y. 2007. Empirical likelihood methods in econometrics: theory and practice. Advances in Economics and Econometrics, Theory and Applications: Ninth World Congress of the Econometric Society Vol 3 Blundell RW, Newey WK, Persson T. 174–237 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  54. Kitamura Y, Otsu T, Evdokimov K. 2013. Robustness, infinitesimal neighborhoods, and moment restrictions. Econometrica 81:1185–201 [Google Scholar]
  55. Kitamura Y, Santos A, Shaikh AM. 2012. On the asymptotic optimality of empirical likelihood for testing moment restrictions. Econometrica 80:413–23 [Google Scholar]
  56. Kitamura Y, Stutzer M. 1997. An information-theoretic alternative to generalized method of moments estimation. Econometrica 65:861–74 [Google Scholar]
  57. Kitamura Y, Tripathi G, Ahn H. 2004. Empirical likelihood-based inference in conditional moment restriction models. Econometrica 72:1667–714 [Google Scholar]
  58. Kleibergen FR. 2005. Testing parameters in GMM without assuming that they are identified. Econometrica 73:1103–23 [Google Scholar]
  59. Liu Y, Chen J. 2010. Adjusted empirical likelihood with high-order precision. Ann. Stat. 38:1341–62 [Google Scholar]
  60. Manski CF. 1988. Analog Estimation Methods in Econometrics. New York: Chapman & Hall
  61. Matsushita Y, Otsu T. 2013. Second-order refinement of empirical likelihood for testing overidentifying restrictions. Econ. Theory 29:324–53 [Google Scholar]
  62. Mittelhammer RC, Judge GG, Schoenberg R. 2005. Empirical evidence concerning the finite sample performance of EL-type structural equation estimation and inference methods. See Andrews & Stock 2005, pp. 282–305 [Google Scholar]
  63. Newey WK, Ramalho JJS, Smith RJ. 2005. Asymptotic bias for GMM and GEL estimators with estimated nuisance parameters. See Andrews & Stock 2005, pp. 245–81 [Google Scholar]
  64. Newey WK, Smith RJ. 2004. Higher order properties of GMM and generalized empirical likelihood estimators. Econometrica 72:219–55 [Google Scholar]
  65. Newey WK, West KD. 1987. Hypothesis testing with efficient method of moments estimation. Int. Econ. Rev. 28:777–87 [Google Scholar]
  66. Newey WK, Windmeijer F. 2009. Generalized method of moments with many weak moment conditions. Econometrica 77:687–719 [Google Scholar]
  67. Otsu T. 2006. Generalized empirical likelihood inference for nonlinear and time series models under weak identification. Econ. Theory 22:513–27 [Google Scholar]
  68. Otsu T. 2007. Penalized empirical likelihood estimation of semiparametric models. J. Multivar. Anal. 98:1923–54 [Google Scholar]
  69. Otsu T. 2011. Empirical likelihood estimation of conditional moment restriction models with unknown functions. Econ. Theory 27:8–46 [Google Scholar]
  70. Owen A. 1988. Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75:237–49 [Google Scholar]
  71. Owen A. 1990. Empirical likelihood ratio confidence regions. Ann. Stat. 18:90–120 [Google Scholar]
  72. Owen A. 2001. Empirical Likelihood. New York: Chapman & Hall
  73. Powell J, Stock JH, Stoker T. 1989. Semiparametric estimation of index coefficients. Econometrica 57:1403–30 [Google Scholar]
  74. Powell MJD. 1981. Approximation Theory and Methods. Cambridge, UK: Cambridge Univ. Press
  75. Qin J, Lawless J. 1994. Empirical likelihood and general estimating equations. Ann. Stat. 22:300–25 [Google Scholar]
  76. Ramalho JJS. 2005. Small sample bias of alternative estimation methods for moment condition models: Monte Carlo evidence for covariance structures. Stud. Nonlinear Dyn. Econom. 9:1–20 [Google Scholar]
  77. Reiersøl O. 1941. Confluence analysis by means of lag moments and other methods of confluence analysis. Econometrica 9:l–24 [Google Scholar]
  78. Reiersøl O. 1945. Confluence analysis by means of instrumental sets of variables. Ark. Mat. Astron. Fys. 32A:1–119 [Google Scholar]
  79. Robinson PM. 1988a. Root-N-consistent semiparametric regression. Econometrica 56:931–54 [Google Scholar]
  80. Robinson PM. 1988b. The stochastic difference between econometric estimators. Econometrica 56:531–48 [Google Scholar]
  81. Sargan JD. 1958. The estimation of economic relationships using instrumental variables. Econometrica 26:393–415 [Google Scholar]
  82. Sargan JD. 1959. The estimation of relationships with autocorrelated residuals by the use of the instrumental variables. J. R. Stat. Soc. B 21:91–105 [Google Scholar]
  83. Schennach SM. 2007. Point estimation with exponentially tilted empirical likelihood. Ann. Stat. 35:634–72 [Google Scholar]
  84. Shen X. 1997. On methods of sieves and penalization. Ann. Stat. 25:2555–91 [Google Scholar]
  85. Smith RJ. 1997. Alternative semi-parametric likelihood approaches to generalized method of moments estimation. Econ. J. 107:503–19 [Google Scholar]
  86. Smith RJ. 2000. Empirical likelihood estimation and inference. Applications of Differential Geometry to Econometrics Marriott P, Salmon M. 119–50 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  87. Smith RJ. 2005. Automatic positive semi-definite HAC covariance matrix and GMM estimation. Econ. Theory 21:158–70 [Google Scholar]
  88. Smith RJ. 2007a. Efficient information theoretic inference for conditional moment restrictions. J. Econom. 138:430–60 [Google Scholar]
  89. Smith RJ. 2007b. Local GEL estimation with conditional moment restrictions. The Refinement of Econometric Estimation and Test Procedures: Finite Sample and Asymptotic Analysis Phillips GDA, Tzavalis E. 100–22 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  90. Smith RJ. 2007c. Weak instruments and empirical likelihood: a discussion of the papers by D.W.K. Andrews and J.H. Stock and Y. Kitamura. Advances in Economics and Econometrics, Theory and Applications: Ninth World Congress of the Econometric Society Vol 3 Blundell RW, Newey WK, Persson T. 238–60 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  91. Smith RJ. 2011. GEL criteria for moment condition models. Econ. Theory 27:1192–235 [Google Scholar]
  92. Tripathi G, Kitamura Y. 2003. Testing conditional moment restrictions. Ann. Stat. 31:2059–95 [Google Scholar]
  93. Wright PG. 1928. The Tariff on Animal and Vegetable Oils. New York: Macmillan
  94. Wright S. 1925. Corn and hog correlations. Bull. 1300, US Dep. Agric., Washington, DC
  95. Zhang J, Gijbels I. 2003. Sieve empirical likelihood and extensions of generalized least squares. Scand. J. Stat. 30:1–24 [Google Scholar]
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