Moment conditions for the quadratic regression model with measurement error

References

• Aghion, P., Bloom, N., Blundell, R., Griffith, R., Howitt, P. (2005). Competition and innovation: an inverted-U relationship. Quarterly Journal of Economics 120(2):701–728. doi:https://doi.org/10.1162/0033553053970214
   Web of Science ®Google Scholar
• Barro, R. (1996). Democracy and growth. Journal of Economic Growth 1(1):1–27. doi:https://doi.org/10.1007/BF00163340
   Google Scholar
• Ben-Moshe, D., d’Haultfoeuille, X., Lewbel, A. (2017). Identification of additive and polynomial models of mismeasured regressors without instruments. Journal of Econometrics 200(2):207–222. doi:https://doi.org/10.1016/j.jeconom.2017.06.006
   Web of Science ®Google Scholar
• Biørn, E. (2017). Identification and Method of Moments Estimation in Polynomial Measurement Error Models. Working Paper, Department of Economics, University of Oslo.
   Google Scholar
• Blalock, H. (1965). Some implications of random measurement error for causal inferences. American Journal of Sociology 71(1):37–47. doi:https://doi.org/10.1086/223991
   Web of Science ®Google Scholar
• Bloch, F. (1978). Measurement error and statistical significance of an independent variable. The American Statistician 32(1):26–27. doi:https://doi.org/10.2307/2683471
   Web of Science ®Google Scholar
• Buonaccorsi, J. (1996). A modified estimating equation approach to correcting for measurement error in regression. Biometrika 83(2):433–440. doi:https://doi.org/10.1093/biomet/83.2.433
   Web of Science ®Google Scholar
• Cameron, A., Trivedi, P. (2005). Microeconometrics. United Kingdom: Cambridge University Press.
   Google Scholar
• Carrillo-Gamboa, O., Gunst, R. (1992). Measurement-error-model collinearities. Technometrics 34(4):454–464. doi:https://doi.org/10.1080/00401706.1992.10484956
   Web of Science ®Google Scholar
• Carroll, R., Ruppert, D., Stefanski, L., Crainiceanu, C. (2006). Measurement Error in Nonlinear Models: A Modern Perspective. 2nd ed., United Kingdom: Chapman & Hall.
   Google Scholar
• Chan, L., Mak, T. (1985). On the polynomial functional relationship. Journal of the Royal Statistical Society: Series B (Methodological) 47(3):510–518. doi:https://doi.org/10.1111/j.2517-6161.1985.tb01381.x
   Google Scholar
• Chen, X., Hong, H., Nekipelov, D. (2011). Nonlinear models of measurement error. Journal of Economic Literature 49(4):901–937. doi:https://doi.org/10.1257/jel.49.4.901
   Web of Science ®Google Scholar
• Cheng, C. L., Schneeweiss, H. (1998). Polynomial regression with errors in the variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 60(1):189–199. doi:https://doi.org/10.1111/1467-9868.00118
   Google Scholar
• Cheng, C. L., Schneeweiss, H., Thamerus, M. (2000). A small sample estimator for a polynomial regression with errors in the variables. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 62(4):699–709. doi:https://doi.org/10.1111/1467-9868.00258
   Google Scholar
• Cheng, C. L., Van Ness, J. (1999). Statistical Regression with Measurement Error. United Kingdom: Oxford University Press.
   Google Scholar
• Chesher, A. (2017). Understanding the effect of measurement error on quantile regressions. Journal of Econometrics 200(2):223–237. Measurement Error Models. doi:https://doi.org/10.1016/j.jeconom.2017.06.007
   Web of Science ®Google Scholar
• Cragg, J. (1997). Using higher moments to estimate the simple errors-in-variables model. The RAND Journal of Economics 28:S71–S91. doi:https://doi.org/10.2307/3087456
   Web of Science ®Google Scholar
• Dagenais, M., Dagenais, D. (1997). Higher moment estimators for linear regression models with errors in the variables. Journal of Econometrics 76(1-2):193–221. doi:https://doi.org/10.1016/0304-4076(95)01789-5
   Web of Science ®Google Scholar
• Erickson, T., Whited, T. (2000). Measurement error and the relationship between investment and q. Journal of Political Economy 108(5):1027–1057. doi:https://doi.org/10.1086/317670
   Web of Science ®Google Scholar
• Erickson, T., Whited, T. (2012). Treating measurement error in tobin’s q. Review of Financial Studies 25(4):1286–1329. doi:https://doi.org/10.1093/rfs/hhr120
   Web of Science ®Google Scholar
• Garcia, T., Ma, Y. (2017). Simultaneous treatment of unspecified heteroskedastic model error distribution and mismeasured covariates for restricted moment models. Journal of Econometrics 200(2):194–206. doi:https://doi.org/10.1016/j.jeconom.2017.06.005
   PubMed Web of Science ®Google Scholar
• Geary, R. (1942). Inherent relations between random variables. Proceedings of the Royal Irish Academy A 47:63–67.
   Google Scholar
• Gertz, M., Nocedal, J., Sartenar, A. (2004). A starting point strategy for nonlinear interior methods. Applied Mathematics Letters 17(8):945–952. doi:https://doi.org/10.1016/j.aml.2003.09.005
   Web of Science ®Google Scholar
• Gilley, O., Pace, R. (1996). On the harrison and rubinfeld data. Journal of Environmental Economics and Management 31(3):403–405. doi:https://doi.org/10.1006/jeem.1996.0052
   Web of Science ®Google Scholar
• Griliches, Z., Ringstad, V. (1970). Error-in-the-variables bias in nonlinear contexts. Econometrica 38(2):368–370. doi:https://doi.org/10.2307/1913020
   Web of Science ®Google Scholar
• Haans, R., Pieters, C., He, Z. L. (2016). Thinking about U: theorizing and testing U- and inverted U-shaped relationships in strategy research. Strategic Management Journal 37(7):1177–1195. doi:https://doi.org/10.1002/smj.2399
   Web of Science ®Google Scholar
• Harrison, D., Rubinfeld, D. (1978). Hedonic housing prices and the demand for clean air. Journal of Environmental Economics and Management 5(1):81–102. doi:https://doi.org/10.1016/0095-0696(78)90006-2
   Web of Science ®Google Scholar
• Hausman, J., Newey, W., Ichimura, H., Powell, J. (1991). Identification and estimation for polynomial errors-in-variables models. Journal of Econometrics 50(3):273–295. doi:https://doi.org/10.1016/0304-4076(91)90022-6
   Web of Science ®Google Scholar
• Hausman, J., Newey, W., Powell, J. (1988). Consistent Estimation of Nonlinear Errors-in-Variables Models with Few Measurements. Cambridge, MA: MIT Cambridge.
   Google Scholar
• Hausman, J., Newey, W., Powell, J. (1995). Nonlinear errors in variables estimation of some engel curves. Journal of Econometrics 65(1):205–233. doi:https://doi.org/10.1016/0304-4076(94)01602-V
   Web of Science ®Google Scholar
• Huang, Y., Huwang, L. (2001). On the polynomial structural relationship. Canadian Journal of Statistics 29(3):495–512. doi:https://doi.org/10.2307/3316043
   Web of Science ®Google Scholar
• Huang, L. S., Wang, H., Cox, C. (2005). Assessing interaction effects in linear measurement error models. Journal of the Royal Statistical Society: Series C (Applied Statistics) 54(1):21–30. doi:https://doi.org/10.1111/j.1467-9876.2005.00467.x
   Google Scholar
• Huang, X., Zhang, H. (2013). Variable selection in linear measurement error models via penalized score functions. Journal of Statistical Planning and Inference 143(12):2101–2111. doi:https://doi.org/10.1016/j.jspi.2013.07.014
   Web of Science ®Google Scholar
• Hu, Y., Schennach, S. (2008). Instrumental variable treatment of nonclassical measurement error models. Econometrica 76(1):195–216. doi:https://doi.org/10.1111/j.0012-9682.2008.00823.x
   Web of Science ®Google Scholar
• Hu, Y., Shiu, J. L., Woutersen, T. (2015). Identification and estimation of single-index models with measurement error and endogeneity. The Econometrics Journal 18(3):347–362. doi:https://doi.org/10.1111/ectj.12053
   Web of Science ®Google Scholar
• Hu, Y., Shiu, J. L., Woutersen, T. (2016). Identification in nonseparable models with measurement errors and endogeneity. Economics Letters 144:33–36. doi:https://doi.org/10.1016/j.econlet.2016.04.009
   Web of Science ®Google Scholar
• Kedir, A., Girma, S. (2007). Quadratic engel curves with measurement error: Evidence from a budget survey. Oxford Bulletin of Economics and Statistics 69(1):123–138. doi:https://doi.org/10.1111/j.1468-0084.2007.00470.x
   Web of Science ®Google Scholar
• Kendall, M., Stuart, A. (1973). The Advanced Theory of Statistics. Vol. 2. London: Charles Griffin and Co., Ltd.
   Google Scholar
• Kuha, J., Temple, J. (2007). Covariate measurement error in quadratic regression. International Statistical Review 71(1):131–150. doi:https://doi.org/10.1111/j.1751-5823.2003.tb00189.x
   Google Scholar
• Kukush, A., Schneeweiss, H., Wolf, R. (2005). Relative efficiency of three estimators in a polynomial regression with measurement errors. Journal of Statistical Planning and Inference 127(1–2):179–203. doi:https://doi.org/10.1016/j.jspi.2003.09.016
   Web of Science ®Google Scholar
• Kuznets, S. (1955). Economic growth and income inequality. American Economic Review 45:1–28.
   Web of Science ®Google Scholar
• Lavancier, F., Rochet, P. (2016). A general procedure to combine estimators. Computational Statistics & Data Analysis 94:175–192. doi:https://doi.org/10.1016/j.csda.2015.08.001
   Web of Science ®Google Scholar
• Lee, S., Oh, D. W. (2015). Economic growth and the environment in China: Empirical evidence using prefecture level data. China Economic Review 36:73–85. doi:https://doi.org/10.1016/j.chieco.2015.08.009
   Web of Science ®Google Scholar
• Lewbel, A. (1996). Demand estimation with expenditure measurement errors on the left and right hand side. The Review of Economics and Statistics 78(4):718–725. doi:https://doi.org/10.2307/2109958
   Web of Science ®Google Scholar
• 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(5):1201–1213. doi:https://doi.org/10.2307/2171884
   Web of Science ®Google Scholar
• Li, T. (2002). Robust and consistent estimation of nonlinear errors-in-variables models. Journal of Econometrics 110(1):1–26. doi:https://doi.org/10.1016/S0304-4076(02)00120-3
   Web of Science ®Google Scholar
• Martínez-Budría, E., Jara-Díaz, S., Ramos-Real, F. J. (2003). Adapting productivity theory to the quadratic cost function. An application to the spanish electric sector. Journal of Productivity Analysis 20:213–229.
   Web of Science ®Google Scholar
• Meijer, E. (1998). Structural Equation Models for Nonnormal Data. Netherlands: DSWO Press.
   Google Scholar
• Meijer, E., Mooijaart, A. (1996). Factor analysis with heteroscedastic errors. British Journal of Mathematical and Statistical Psychology 49(1):189–202. doi:https://doi.org/10.1111/j.2044-8317.1996.tb01082.x
   Google Scholar
• Meijer, E., Spierdijk, L., Wansbeek, T. (2017). Consistent estimation of linear panel data models with measurement error. Journal of Econometrics 200(2):169–180. doi:https://doi.org/10.1016/j.jeconom.2017.06.003
   Web of Science ®Google Scholar
• Moon, M. S., Gunst, R. (1995). Polynomial measurement error modeling. Computational Statistics & Data Analysis 19(1):1–21. doi:https://doi.org/10.1016/0167-9473(93)E0041-2
   Web of Science ®Google Scholar
• Nghiem, L., Potgieter, C. (2019). Simulation-selection-extrapolation: Estimation in high-dimensional errors-in-variables models. Biometrics 75(4):1133–1144. doi:https://doi.org/10.1111/biom.13112
   PubMed Web of Science ®Google Scholar
• Pal, M. (1980). Consistent moment estimators of regression coefficients in the presence of errors in variables. Journal of Econometrics 14(3):349–364. doi:https://doi.org/10.1016/0304-4076(80)90032-9
   Web of Science ®Google Scholar
• Schennach, S. (2008). Quantile regression with mismeasured covariates. Econometric Theory 24(4):1010–1043. doi:https://doi.org/10.1017/S0266466608080390
   Web of Science ®Google Scholar
• Schennach, S. (2014). Entropic latent variable integration via simulation. Econometrica 82:345–385.
   Web of Science ®Google Scholar
• Schennach, S. (2016). Recent advances in the measurement error literature. Annual Review of Economics 8(1):341–377. doi:https://doi.org/10.1146/annurev-economics-080315-015058
   Web of Science ®Google Scholar
• Schennach, S., Hu, Y. (2013). Nonparametric identification and semiparametric estimation of classical measurement error models without side information. Journal of the American Statistical Association 108(501):177–186. doi:https://doi.org/10.1080/01621459.2012.751872
   Web of Science ®Google Scholar
• Schneeweiss, H., Augustin, T. (2006). Some recent advances in measurement error models and methods. Allgemeines Statistisches Archiv 90(1):183–197. doi:https://doi.org/10.1007/s10182-006-0229-x
   Google Scholar
• Scott, E. (1950). Note on consistent estimates of the linear structural relation between two variables. The Annals of Mathematical Statistics 21(2):284–288. doi:https://doi.org/10.1214/aoms/1177729846
   Google Scholar
• Sirmans, G., Macpherson, D., Zietz, E. (2005). The composition of hedonic pricing models. Journal of Real Estate Literature 13(1):1–43. doi:https://doi.org/10.1080/10835547.2005.12090154
   Google Scholar
• Song, S., Schennach, S., White, H. (2015). Estimating nonseparable models with mismeasured endogenous variables. Quantitative Economics 6(3):749–794. doi:https://doi.org/10.3982/QE275
   Web of Science ®Google Scholar
• Tsiatis, A., Ma, Y. (2004). Locally efficient semiparametric estimators for functional measurement error models. Biometrika 91(4):835–848. doi:https://doi.org/10.1093/biomet/91.4.835
   Web of Science ®Google Scholar
• Van Montfort, K. (1989). Estimating in Structural Models with Non-Normal Distributed Variables: Some Alternative Approaches. Netherlands: DSWO Press.
   Google Scholar
• Van Montfort, K., Mooijaart, A., De Leeuw, J. (1989). Estimation of regression coefficients with the help of characteristic functions. Journal of Econometrics 41(2):267–278. doi:https://doi.org/10.1016/0304-4076(89)90097-3
   Web of Science ®Google Scholar
• Wansbeek, T., Meijer, E. (2000). Measurement Error and Latent Variables in Econometrics. Netherlands: North-Holland.
   Google Scholar
• Wei, Y., Carroll, R. (2009). Quantile regression with measurement error. Journal of the American Statistical Association 104(487):1129–1143. doi:https://doi.org/10.1198/jasa.2009.tm08420
   PubMed Web of Science ®Google Scholar
• Wolter, K., Fuller, W. (1982). Estimation of the quadratic errors-in-variables model. Biometrika 69(1):175–182. doi:https://doi.org/10.2307/2335866
   Web of Science ®Google Scholar
• Wooldridge, J. (2012). Introductory Econometrics. 5th ed., South-Western Educational Publishing.
   Google Scholar
• Zhao, M., Gao, Y., Cui, Y. (2020). Variable selection for longitudinal varying coefficient errors-in-variables models. Communications in Statistics - Theory and Methods 1–26. doi:https://doi.org/10.1080/03610926.2020.1801738
   Google Scholar
• Zhu, J., Li, Z. (2017). Inequality and crime in China. Frontiers of Economics in China 12(2):309–339.
   Web of Science ®Google Scholar
• Zietz, J., Zietz, E. N., Sirmans, G. S. (2008). Determinants of house prices: a quantile regression approach. The Journal of Real Estate Finance and Economics 37(4):317–333. doi:https://doi.org/10.1007/s11146-007-9053-7
   Web of Science ®Google Scholar