1932

Abstract

This article reviews recent significant progress made in developing estimation and inference methods for nonlinear models in the presence of mismeasured data that may or may not conform to the classical assumption of independent zero-mean errors. The aim is to cover a broad range of methods having differing levels of complexity and strength of the required assumptions. Simple approaches that form the elementary building blocks of more advanced approaches are discussed first. Then, special attention is devoted to methods that rely on readily available auxiliary variables (e.g., repeated measurements, indicators, or instrumental variables). Results relaxing most of the commonly invoked simplifying assumptions are presented (linear measurement structure, independent errors, zero-mean errors, availability of auxiliary information). This article also provides an overview of important connections with related fields, such as latent variable models, nonlinear panel data, factor models, and set identification, and applications of the methods to other fields traditionally unrelated to measurement error models.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-economics-080315-015058
2016-10-31
2024-12-12
Loading full text...

Full text loading...

/deliver/fulltext/economics/8/1/annurev-economics-080315-015058.html?itemId=/content/journals/10.1146/annurev-economics-080315-015058&mimeType=html&fmt=ahah

Literature Cited

  1. Abadie A, Angrist JD, Imbens GW. 2002. Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings. Econometrica 70:91–117 [Google Scholar]
  2. Ai C, Chen X. 2003. Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica 71:1795–843 [Google Scholar]
  3. Allman ES, Matias C, Rhodes JA. 2009. Identifiability of parameters in latent structure models with many observed variables. Ann. Stat. 37:3099–132 [Google Scholar]
  4. Amemiya Y. 1985. Instrumental variable estimator for the nonlinear errors-in-variables model. J. Econom. 28:273–89 [Google Scholar]
  5. An Y, Hu Y. 2012. Well-posedness of measurement error models for self-reported data. J. Econom. 168:259–69 [Google Scholar]
  6. An Y, Hu Y, Shum M. 2010. Estimating first-price auctions with an unknown number of bidders: a misclassification approach. J. Econom. 157:328–41 [Google Scholar]
  7. Anderson TW, Rubin H. 1956. Statistical inference in factor analysis. Proc. 3rd Berkeley Symp. Math. Stat. Probab. 5:111–50 Berkeley: Univ. Calif. Press [Google Scholar]
  8. Andrews DWK. 2011. Examples of L2-complete and boundedly-complete distributions Work. Pap. 1801, Cowles Found., Yale Univ., New Haven, CT [Google Scholar]
  9. Arellano M, Bonhomme S. 2011. Identifying distributional characteristics in random coefficients panel data models. Rev. Econ. Stud. 79:987–1020 [Google Scholar]
  10. Arellano M, Bonhomme S. 2015. Nonlinear panel data estimation via quantile regressions Cemmap Work. Pap. CWP40/15, Inst. Fisc. Stud., London [Google Scholar]
  11. Athey S, Haile PA. 2002. Identification of standard auction models. Econometrica 70:2107–40 [Google Scholar]
  12. Athey S, Haile PA. 2007. Nonparametric approaches to auctions. See Heckman & Leamer 2007 3847–965
  13. Battistin E, Chesher A. 2014. Treatment effect estimation with covariate measurement error. J. Econom. 178:707–15 [Google Scholar]
  14. Ben-Moshe D. 2013. Identification and estimation of factor models using the log characteristic function Work. Pap., Hebrew Univ., Jerusalem [Google Scholar]
  15. Ben-Moshe D. 2014. Identification of dependent nonparametric distributions in a system of linear equations Work. Pap., Hebrew Univ., Jerusalem [Google Scholar]
  16. Beresteanu A, Molchanov I, Molinari F. 2011. Sharp identification regions in models with convex moment predictions. Econometrica 79:1785–821 [Google Scholar]
  17. Berkson J. 1950. Are there two regressions?. J. Am. Stat. Assoc. 45:164–80 [Google Scholar]
  18. Bollinger CR. 1998. Measurement error in the current population survey: a nonparametric look. J. Labor Econ. 16:576–94 [Google Scholar]
  19. Bonhomme S, Jochmans K, Robin JM. 2016. Estimating multivariate latent-structure models. Ann. Stat. 44:540–63 [Google Scholar]
  20. Bonhomme S, Robin JM. 2009. Consistent noisy independent component analysis. J. Econom. 149:12–25 [Google Scholar]
  21. Bonhomme S, Robin JM. 2010. Generalized non-parametric deconvolution with an application to earnings dynamics. Rev. Econ. Stud. 77:491–533 [Google Scholar]
  22. Bound J, Brown C, Mathiowetz N. 2001. Measurement error in survey data. Handbook of Econometrics 5 JJ Heckman, E Leamer 3705–843 Amsterdam: North-Holland [Google Scholar]
  23. Bound J, Krueger AB. 1991. The extent of measurement error in longitudinal earnings data: Do two wrongs make a right?. J. Labor Econ. 9:1–24 [Google Scholar]
  24. Browning M, Crossley TF. 2009. Are two cheap, noisy measures better than one expensive, accurate one?. Am. Econ. Rev. 99:99–103 [Google Scholar]
  25. Cameron A, Li T, Trivedi P, Zimmer D. 2004. Modeling the differences in counted outcomes using bivariate copula models with application to mismeasured counts. Econom. J. 7:566–84 [Google Scholar]
  26. Carrasco M, Florens JP, Renault E. 2007. Linear inverse problems and structural econometrics: estimation based on spectral decomposition and regularization. See Heckman & Leamer 2007 5633–751
  27. Carroll RJ, Chen X, Hu Y. 2010. Identification and estimation of nonlinear models using two samples with nonclassical measurement errors. J. Nonparametr. Stat. 22:379–99 [Google Scholar]
  28. Carroll RJ, Delaigle A, Hall P. 2007. Nonparametric regression estimation from data contaminated by a mixture of Berkson and classical errors. J. R. Stat. Soc. B 69:859–78 [Google Scholar]
  29. Carroll RJ, Hall P. 1988. Optimal rates of convergence for deconvolving a density. J. Am. Stat. Assoc. 83:1184–86 [Google Scholar]
  30. Carroll RJ, Ruppert D, Crainiceanu CM, Tosteson TD, Karagas MR. 2004. Nonlinear and nonparametric regression and instrumental variables. J. Am. Stat. Assoc. 99:736–50 [Google Scholar]
  31. Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM. 2006. Measurement Error in Nonlinear Models New York: Chapman & Hall [Google Scholar]
  32. Chen X. 2007. Large sample sieve estimation of semi-nonparametric models. See Heckman & Leamer 2007 5549–632
  33. Chen X, Hong H, Nekipelov D. 2011. Nonlinear models of measurement errors. J. Econ. Lit. 49:901–37 [Google Scholar]
  34. Chen X, Hong H, Tamer E. 2005. Measurement error models with auxiliary data. Rev. Econ. Stud. 72:343–66 [Google Scholar]
  35. Chen X, Hu Y, Lewbel A. 2009. Nonparametric identification and estimation of nonclassical errors-in-variables models without additional information. Stat. Sin. 19:949–68 [Google Scholar]
  36. Cheng CL, Ness JWV. 1999. Statistical Regression with Measurement Error London: Arnold [Google Scholar]
  37. Chernozhukov V, Hansen C. 2005. An IV model of quantile treatment effects. Econometrica 73:245–61 [Google Scholar]
  38. Chernozhukov V, Hong H, Tamer E. 2007a. Estimation and confidence regions for parameter sets in econometric models. Econometrica 75:1243–84 [Google Scholar]
  39. Chernozhukov V, Imbens GW, Newey WK. 2007b. Instrumental variable identification and estimation of nonseparable models via quantile conditions. J. Econom. 139:4–14 [Google Scholar]
  40. Chesher A. 1991. The effect of measurement error. Biometrika 78:451–62 [Google Scholar]
  41. Chesher A. 2001. Parameter approximations for quantile regressions with measurement error Work. Pap. CWP02/01, Dep. Econ., Univ. Coll. London [Google Scholar]
  42. Chesher A. 2003. Identification in nonseparable models. Econometrica 71:1405–41 [Google Scholar]
  43. Ciliberto F, Tamer E. 2009. Market structure and multiple equilibria in airline markets. Econometrica 77:1791–828 [Google Scholar]
  44. Cragg JC. 1997. Using higher moments to estimate the simple errors-in-variables model. Rand J. Econ. 28:S71–91 [Google Scholar]
  45. Cunha F, Heckman J, Schennach SM. 2010. Estimating the technology of cognitive and noncognitive skill formation. Econometrica 78:883–931 [Google Scholar]
  46. Dagenais MG, Dagenais DL. 1997. Higher moment estimators for linear regression models with errors in variables. J. Econom. 76:193–221 [Google Scholar]
  47. Darolles S, Florens JP, Renault E. 2011. Nonparametric instrumental regression. Econometrica 79:1541–65 [Google Scholar]
  48. Delaigle A, Hall P, Meister A. 2008. On deconvolution with repeated measurements. Ann. Stat. 36:665–85 [Google Scholar]
  49. Delaigle A, Hall P, Qiu P. 2006. Nonparametric methods for solving the Berkson errors-in-variables problem. J. R. Stat. Soc. B 68:201–20 [Google Scholar]
  50. d'Haultfoeuille X. 2011. On the completeness condition in nonparametric instrumental problems. Econom. Theory 27:460–71 [Google Scholar]
  51. Dunford N, Schwartz JT. 1971. Linear Operators New York: Wiley [Google Scholar]
  52. Ebrahimi N, Hamedani G, Soofi ES, Volkmer H. 2010. A class of models for uncorrelated random variables. J. Multivar. Anal. 101:1859–71 [Google Scholar]
  53. Ekeland I, Galichon A, Henry M. 2010. Optimal transportation and the falsifiability of incompletely specified economic models. Econ. Theory 42:355–74 [Google Scholar]
  54. Erickson T. 1993. Restricting regression slopes in the errors-in-variables model by bounding the error correlation. Econometrica 61:959–69 [Google Scholar]
  55. Erickson T, Whited TM. 2000. Measurement error and the relationship between investment and q. J. Polit. Econ. 108:1027–57 [Google Scholar]
  56. Erickson T, Whited TM. 2002. Two-step GMM estimation of the errors-in-variables model using high-order moments. Econom. Theory 18:776–99 [Google Scholar]
  57. Evdokimov K. 2009. Identification and estimation of a nonparametric panel data model with unobserved heterogeneity Work. Pap., Yale Univ., New Haven, CT [Google Scholar]
  58. Evdokimov K, White H. 2012. Some extensions of a lemma of Kotlarski. Econom. Theory 28:925–32 [Google Scholar]
  59. Fan J. 1991a. Asymptotic normality for deconvolution kernel density estimators. Sankhyā A 53:97–110 [Google Scholar]
  60. Fan J. 1991b. On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Stat. 19:1257–72 [Google Scholar]
  61. Fan J, Truong YK. 1993. Nonparametric regression with errors in variables. Ann. Stat. 21:1900–25 [Google Scholar]
  62. Freyberger J. 2012. Nonparametric panel data models with interactive fixed effects Work. Pap., Northwestern Univ., Evanston, IL [Google Scholar]
  63. Frisch R. 1934. Statistical Confluence Analysis by Means of Complete Regression Systems Oslo: Univ. Inst. Econ. [Google Scholar]
  64. Fuller WA. 1987. Measurement Error Models New York: Wiley [Google Scholar]
  65. Galichon A, Henry M. 2013. Dilation bootstrap: a methodology for constructing confidence regions with partially identified models. J. Econom. 177:109–15 [Google Scholar]
  66. Gallant AR, Nychka DW. 1987. Semi-nonparametric maximum likelihood estimation. Econometrica 55:363–90 [Google Scholar]
  67. Geary RC. 1942. Inherent relations between random variables. Proc. R. Irish Acad. 47A:63–76 [Google Scholar]
  68. Gel'fand IM, Shilov GE. 1964. Generalized Functions New York: Academic [Google Scholar]
  69. Griliches Z, Hausman JA. 1986. Errors in variables in panel data. J. Econom. 31:93–118 [Google Scholar]
  70. Hall P, Horowitz JL. 2005. Nonparametric methods for inference in the presence of instrumental variables. Ann. Stat. 33:2904–29 [Google Scholar]
  71. Hamedani GG, Volkmer HW. 2009. Comment on ``conditional moments and independence” by A. De Paula. Am. Stat. 63:295–95 [Google Scholar]
  72. Hansen LP. 1982. Large sample properties of generalized method of moment estimators. Econometrica 50:1029–54 [Google Scholar]
  73. Härdle W, Linton O. 1994. Applied nonparametric methods. Handbook of Econometrics 4 R Engle, D McFadden 2295–339 Amsterdam: North-Holland [Google Scholar]
  74. Hausman J. 2001. Mismeasured variables in econometric analysis: problems from the right and problems from the left. J. Econ. Perspect. 15:57–67 [Google Scholar]
  75. Hausman J, Abrevaya J, Scott-Morton FM. 1998. Misclassification of the dependent variable in a discrete-response setting. J. Econom. 87:237–69 [Google Scholar]
  76. Hausman J, Newey W, Ichimura H, Powell J. 1991. Measurement errors in polynomial regression models. J. Econom. 50:273–95 [Google Scholar]
  77. Hausman J, Newey W, Powell J. 1995. Nonlinear errors in variables. Estimation of some Engel curves. J. Econom. 65:205–33 [Google Scholar]
  78. Heckman JJ, Leamer EE. 2007. Handbook of Econometrics 6 Amsterdam: North-Holland [Google Scholar]
  79. Heckman JJ, Schennach SM, Williams BD. 2010a. Matching on proxy variables Work. Pap., Univ. Chicago [Google Scholar]
  80. Heckman JJ, Schennach SM, Williams BD. 2010b. Nonparametric factor score regression with an application to the technology of skill formation Work. Pap., Univ. Chicago [Google Scholar]
  81. Heckman JJ, Vytlacil E. 2005. Structural equations, treatment effects and econometric policy evaluation. Econometrica 73:669–738 [Google Scholar]
  82. Hoderlein S, Mammen E. 2007. Identification of marginal effects in nonseparable models without monotonicity. Econometrica 75:1513–18 [Google Scholar]
  83. Hoderlein S, Siflinger B, Winter J. 2015. Identification of structural models in the presence of measurement error due to rounding in survey responses Work. Pap., Boston Coll. [Google Scholar]
  84. Hoderlein S, Winter J. 2010. Structural measurement errors in nonseparable models. J. Econom. 157:432–40 [Google Scholar]
  85. Horowitz J, Manski C. 1995. Identification and robustness with contaminated and corrupted data. Econometrica 63:281–302 [Google Scholar]
  86. Horowitz JL, Markatou M. 1996. Semiparametric estimation of regression models for panel data. Rev. Econ. Stud. 63:145–68 [Google Scholar]
  87. Hsiao C. 1989. Consistent estimation for some nonlinear errors-in-variables models. J. Econom. 41:159–85 [Google Scholar]
  88. Hu Y. 2008. Identification and estimation of nonlinear models with misclassification error using instrumental variables: a general solution. J. Econom. 144:27–61 [Google Scholar]
  89. Hu Y. 2015. Microeconomic models with latent variables: applications of measurement error models in empirical industrial organization and labor economics Cemmap Work. Pap. CWP03/15, Inst. Fisc. Stud., London [Google Scholar]
  90. Hu Y, McAdams D, Shum M. 2013. Nonparametric identification of first-price auctions with non-separable unobserved heterogeneity. J. Econom. 174:186–93 [Google Scholar]
  91. Hu Y, Ridder G. 2010. On deconvolution as a first stage nonparametric estimator. Econom. Rev. 29:1–32 [Google Scholar]
  92. Hu Y, Ridder G. 2012. Estimation of nonlinear models with measurement error using marginal information. J. Appl. Econom. 27:347–85 [Google Scholar]
  93. Hu Y, Sasaki Y. 2015. Closed-form estimation of nonparametric models with non-classical measurement errors. J. Econom. 185:392–408 [Google Scholar]
  94. Hu Y, Schennach SM. 2008. Instrumental variable treatment of nonclassical measurement error models. Econometrica 76:195–216 [Google Scholar]
  95. Hu Y, Schennach SM, Shiu JL. 2015. Injectivity of a class of integral operators with compactly supported kernels Work. Pap., Brown Univ., Providence, RI [Google Scholar]
  96. Hu Y, Shiu JL. 2013. Identification and estimation of nonlinear dynamic panel data models with unobserved covariates. J. Econom. 175:116–31 [Google Scholar]
  97. Hu Y, Shum M. 2012. Nonparametric identification of dynamic models with unobserved state variables. J. Econom. 171:32–44 [Google Scholar]
  98. Hu Y, Shum M. 2013. Identifying dynamic games with serially-correlated unobservables. Adv. Econom. 31:97–113 [Google Scholar]
  99. Huwang L, Huang YHS. 2000. On errors-in-variables in polynomial regressions—Berkson case. Stat. Sin. 10:923–36 [Google Scholar]
  100. Hyslop DR, Imbens GW. 2001. Bias from classical and other forms of measurement error. J. Bus. Econ. Stat. 19:475–81 [Google Scholar]
  101. Imbens G, Manski C. 2004. Confidence intervals for partially identified parameters. Econometrica 72:1845–57 [Google Scholar]
  102. Imbens GW, Spady RH, Johnson P. 1998. Information theoretic approaches to inference in moment condition models. Econometrica 66:333–57 [Google Scholar]
  103. Kapteyn A, Wansbeek T. 1983. Identification in the linear errors in variables model. Econometrica 51:1847–49 [Google Scholar]
  104. Kendall MG, Stuart A. 1979. The Advanced Theory of Statistics New York: Macmillan, 4th ed.. [Google Scholar]
  105. Kitamura Y, Stutzer M. 1997. An information-theoretic alternative to generalized method of moment estimation. Econometrica 65:861–74 [Google Scholar]
  106. Klepper S, Leamer EE. 1984. Consistent sets of estimates for regressions with errors in all variables. Econometrica 52:163–83 [Google Scholar]
  107. Kolda TG, Bader BW. 2009. Tensor decompositions and applications. SIAM Rev. 51:455–500 [Google Scholar]
  108. Kotlarski I. 1967. On characterizing the gamma and the normal distribution. Pac. J. Math. 20:69–76 [Google Scholar]
  109. Krasnokutskaya E. 2011. Identification and estimation in procurement auctions under unobserved auction heterogeneity. Rev. Econ. Stud. 78:293–327 [Google Scholar]
  110. Kruskal JB. 1977. Three-way arrays: rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics. Linear Algebra Appl. 18:95–138 [Google Scholar]
  111. Kruskal JB. 1989. Rank, decomposition, and uniqueness for 3-way and n-way arrays. Multiway Data Analysis R Coppi, S Bolasco 7–18 Amsterdam: North-Holland [Google Scholar]
  112. Laczkovich M. 1984. Differentiable restrictions of continuous functions. Acta Math. Hung. 44:355–60 [Google Scholar]
  113. Lewbel A. 1997. Constructing instruments for regressions with measurement error when no additional data are available, with an application to patents and R&D. Econometrica 65:1201–13 [Google Scholar]
  114. Lewbel A. 2007. Estimation of average treatment effects with misclassification. Econometrica 75:537–51 [Google Scholar]
  115. Lewbel A. 2012. Using heteroskedasticity to identify and estimate mismeasured and endogenous regressor models. J. Bus. Econ. Stat. 30:67–80 [Google Scholar]
  116. Li T. 2002. Robust and consistent estimation of nonlinear errors-in-variables models. J. Econom. 110:1–26 [Google Scholar]
  117. Li T, Perrigne I, Vuong Q. 2000. Conditionally independent private information in OCS wildcat auctions. J. Econom. 98:129–61 [Google Scholar]
  118. Li T, Trivedi P, Guo J. 2003. Modeling response bias in count: a structural approach with an application to the national crime victimization survey data. Sociol. Methods Res. 31:514–44 [Google Scholar]
  119. Li T, Vuong Q. 1998. Nonparametric estimation of the measurement error model using multiple indicators. J. Multivar. Anal. 65:139–65 [Google Scholar]
  120. Lighthill MJ. 1962. Introduction to Fourier Analysis and Generalized Function Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  121. Liu M, Taylor R. 1989. A consistent nonparametric density estimator for the deconvolution problem. Can. J. Stat. 17:427–38 [Google Scholar]
  122. Loève M. 1977. Probability Theory I New York: Springer [Google Scholar]
  123. Lukacs E. 1970. Characteristic Functions London: Griffin, 2nd ed.. [Google Scholar]
  124. Mahajan A. 2006. Identification and estimation of single index models with misclassified regressor. Econometrica 74:631–65 [Google Scholar]
  125. Manski C. 1990. Nonparametric bounds on treatment effects. Am. Econ. Rev. 80:319–23 [Google Scholar]
  126. Manski C. 2003. Partial Identification of Probability Distributions New York: Springer-Verlag [Google Scholar]
  127. Manski CF, Tamer E. 2002. Inference on regressions with interval data on a regressor or outcome. Econometrica 70:519–46 [Google Scholar]
  128. Mattner L. 1993. Some incomplete but boundedly complete location families. Ann. Stat. 21:2158–62 [Google Scholar]
  129. Matzkin RL. 2003. Nonparametric estimation of nonparametric nonadditive random functions. Econometrica 71:1339–75 [Google Scholar]
  130. Matzkin RL. 2008. Identification in nonparametric simultaneous equations. Econometrica 76:945–78 [Google Scholar]
  131. McFadden D. 1989. A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica 57:995–1026 [Google Scholar]
  132. McIntyre J, Stefanski LA. 2011. Heteroscedastic measurement deconvolution. Ann. Inst. Stat. Math. 63:81–99 [Google Scholar]
  133. Molinari F. 2008. Partial identification of probability distributions with misclassified data. J. Econom. 144:81–117 [Google Scholar]
  134. Nadai MD, Lewbel A. 2016. Nonparametric errors in variables models with measurement errors on both sides of the equation. J. Econom. 191:19–32 [Google Scholar]
  135. Newey WK. 2001. Flexible simulated moment estimation of nonlinear errors-in-variables models. Rev. Econ. Stat. 83:616–27 [Google Scholar]
  136. Newey WK, Powell JL. 2003. Instrumental variable estimation of nonparametric models. Econometrica 71:1565–78 [Google Scholar]
  137. Newey WK, Smith RJ. 2004. Higher-order properties of GMM and generalized empirical likelihood estimators. Econometrica 72:219–55 [Google Scholar]
  138. Owen AB. 1988. Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75:237–49 [Google Scholar]
  139. Owen AB. 1990. Empirical likelihood ratio confidence regions. Ann. Stat. 18:90–120 [Google Scholar]
  140. Pakes A, Pollard D. 1989. Simulation and the asymptotics of optimization estimators. Econometrica 57:1027–57 [Google Scholar]
  141. Pal M. 1980. Consistent moment estimators of regression coefficients in the presence of errors in variables. J. Econom. 14:349–64 [Google Scholar]
  142. Qin J, Lawless J. 1994. Empirical likelihood and general estimating equations. Ann. Stat. 22:300–25 [Google Scholar]
  143. Rao P. 1992. Identifiability in Stochastic Models New York: Academic [Google Scholar]
  144. Reiersol O. 1950. Identifiability of a linear relation between variables which are subject to error. Econometrica 18:375–89 [Google Scholar]
  145. Ridder G, Moffitt R. 2007. The econometrics of data combination. See Heckman & Leamer 2007 5469–547
  146. Sasaki Y. 2015. Heterogeneity and selection in dynamic panel data. J. Econom. 188:236–49 [Google Scholar]
  147. Schennach SM. 2000. Estimation of nonlinear models with measurement error Work. Pap., Univ. Chicago [Google Scholar]
  148. Schennach SM. 2004a. Estimation of nonlinear models with measurement error. Econometrica 72:33–75 [Google Scholar]
  149. Schennach SM. 2004b. Exponential specifications and measurement error. Econ. Lett. 85:85–91 [Google Scholar]
  150. Schennach SM. 2004c. Nonparametric estimation in the presence of measurement error. Econ. Theory 20:1046–93 [Google Scholar]
  151. Schennach SM. 2007a. Instrumental variable estimation of nonlinear errors-in-variables models. Econometrica 75:201–39 [Google Scholar]
  152. Schennach SM. 2007b. Point estimation with exponentially tilted empirical likelihood. Ann. Stat. 35:634–72 [Google Scholar]
  153. Schennach SM. 2008. Quantile regression with mismeasured covariates. Econom. Theory 24:1010–43 [Google Scholar]
  154. Schennach SM. 2013a. Convolution without independence Cemmap Work. Pap. WP46/13, Inst. Fisc. Stud., London [Google Scholar]
  155. Schennach SM. 2013b. Instrumental variable treatment of the nonparametric Berkson measurement error model. Ann. Stat. 41:1642–68 [Google Scholar]
  156. Schennach SM. 2013c. Measurement error in nonlinear models—a review. Advances in Economics and Econometrics 3 D Acemoglu, M Arellano, E Dekel 296–337 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  157. Schennach SM. 2014. Entropic latent variable integration via simulation. Econometrica 82:345–86 [Google Scholar]
  158. Schennach SM, Hu Y. 2013. Nonparametric identification and semiparametric estimation of classical measurement error models without side information. J. Am. Stat. Assoc. 108:177–86 [Google Scholar]
  159. Schennach SM, White H, Chalak K. 2012. Local indirect least squares and average marginal effects in nonseparable structural systems. J. Econom. 166:282–302 [Google Scholar]
  160. Schwartz L. 1966. Théorie des distributions Paris: Hermann [Google Scholar]
  161. Sepanski JH, Carroll RJ. 1993. Semiparametric quasi-likelihood and variance function estimation in measurement error models. J. Econom. 58:223–56 [Google Scholar]
  162. Shen X. 1997. On methods of sieves and penalization. Ann. Stat. 25:2555–91 [Google Scholar]
  163. Song S, Schennach S, White H. 2015. Estimating nonseparable models with mismeasured endogenous variables. Quant. Econ. 6:749–94 [Google Scholar]
  164. Stegeman A. 2009. On uniqueness conditions for Candecomp/Parafac and Indscal with full column rank in one mode. Linear Algebra Appl. 431:211–27 [Google Scholar]
  165. Taupin ML. 2001. Semi-parametric estimation in the nonlinear structural errors-in-variables model. Ann. Stat. 29:66–93 [Google Scholar]
  166. Temple G. 1963. The theory of weak functions. I.. Proc. R. Soc. Lond. A 276:149–67 [Google Scholar]
  167. Wang L. 2004. Estimation of nonlinear models with Berkson measurement errors. Ann. Stat. 32:2559–79 [Google Scholar]
  168. Wang L. 2007. A unified approach to estimation of nonlinear mixed effects and Berkson measurement error models. Can. J. Stat. 35:233–48 [Google Scholar]
  169. Wang L, Hsiao C. 2011. Method of moments estimation and identifiability of nonlinear semiparametric errors-in-variables models. J. Econom. 165:30–44 [Google Scholar]
  170. Wansbeek TJ, Meijer E. 2000. Measurement Error and Latent Variables in Econometrics Amsterdam: Elsevier [Google Scholar]
  171. Wilhelm D. 2010. Identification and estimation of nonparametric panel data regressions with measurement error. Work. Pap., Univ. Chicago
/content/journals/10.1146/annurev-economics-080315-015058
Loading
  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error