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Higher moment estimators for linear regression models with errors in the variables. (English) Zbl 0873.62066

Summary: This paper proposes consistent instrumental variables estimators for linear regression models with errors in the variables that require no extraneous information. These estimators are based on sample moments of order higher than two. While similar estimators proposed previously in the literature seem to be quite erratic, our experimental findings suggest that our estimators perform better than ordinary least squares estimators in terms of root mean squared errors and also in terms of size of type \(I\) errors of standard tests in many typical situations of econometric analyses. Tests for the presence of errors in the variables are also described.

MSC:

62J05 Linear regression; mixed models
62P20 Applications of statistics to economics
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[1] Aigner, D. J.; Hsiao, C.; Kapteyn, A.; Wansbeek, T.: Latent variable models in econometrics. Handbook of econometrics 2, 1321-1393 (1984) · Zbl 0586.62190
[2] Altonji, J. G.; Siow, A.: Testing the response of consumption to income changes with (noisy) panel data. Quarterly journal of economics, 293-328 (1987)
[3] Avery, R. B.: Household saving in the U.S.. Review of income and wealth 37, 409-432 (1991)
[4] Avery, R. B.; Elliehausen, G. E.; Kennickell, A. B.: Measuring wealth with survey data: an evaluation of the 1983 survey of consumer finaces. Review of income and wealth 34, 339-369 (1988)
[5] Bound, J.; Krueger, A. B.: The extent of measurement error in longitudinal earnings data: do two wrongs make a right?. Journal of labor economics 9, 1-24 (1991)
[6] Bowden, R. J.: Instrumental variables. (1984) · Zbl 0606.62130
[7] Dagenais, M. G.: Measuring personal savings, consumption and disposable income in Canada. Canadian journal of economics 25, 681-707 (1992)
[8] Dagenais, M. G.: Parameter estimation in regression models with errors in the variables and autocorrelated disturbances. Journal of econometrics 64, 145-163 (1994) · Zbl 0825.62954
[9] Dagenais, M. G.; Dagenais, D. L.: Estimation and testing in regression models with errors in the variables. Discussion paper no. IEA-93-03 (1993) · Zbl 0216.22401
[10] Dagenais, M. G.; Dagenais, D. L.: GMM estimators for linear regression models with errors in the variables. Discussion paper no. 0594 (1994) · Zbl 0825.62954
[11] Davidson, R.; Mackinnon, J. G.: Estimation and inference in econometrics. (1993) · Zbl 1009.62596
[12] Drion, E. F.: Estimation of the parameters of a straight line and of the variance of the variables, if they are both subject to error. Indagationes mathematicae 13, 256-260 (1951) · Zbl 0042.38602
[13] Duncan, G. J.; Hill, D. H.: An investigation of the extent and consequences of measurement errors in labor-economic survey data. Journal of labor economics 3, 508-532 (1985)
[14] Durbin, J.: Errors in variables. International statistical review 22, 23-32 (1954) · Zbl 0058.13202
[15] Fomby, T. B.; Guilkey, D. K.: On choosing the optimal level of significance for the durbin-Watson test and the Bayesian alternative. Journal of econometrics 8, 203-214 (1978) · Zbl 0394.62065
[16] Fuller, W. A.: Measurement. (1987) · Zbl 0800.62413
[17] Geary, R. C.: Inherent relations between random variables. Proceedings of the royal irish Academy 47, 63-76 (1942) · Zbl 0063.01553
[18] Goldburger, A. S.: Structural equation methods in the social sciences. Econometrica 40, 979-1002 (1972)
[19] Gouriéoux, C.; Montfort, A.: Statistique et modèles économétriques. 1 (1989)
[20] Grether, D. M.; Maddala, G. S.: Errors in variables and serially correlated disturbances in distributed lag models. Econometrica 41, 255-262 (1973) · Zbl 0283.62100
[21] Griliches, Z.: Economic data issues. Handbook of econometrics 3, 1465-1514 (1986)
[22] Griliches, Z.; Hausman, J. A.: Errors in variables in panel data. Journal of econometrics 31, 93-118 (1986)
[23] Hansen, L. P.: Large sample properties of generalized method of moments estimators. Econometrica 50, 1029-1054 (1982) · Zbl 0502.62098
[24] Hausman, J. D.: Specification tests in econometrics. Econometrica 46, 1251-1271 (1978) · Zbl 0397.62043
[25] Johnson, N. L.; Kotz, S.: Continuous univariate distributions – 1. (1970) · Zbl 0213.21101
[26] Johnson, N. L.; Kotz, S.: Continuous univariate distributions – 2. (1970) · Zbl 0213.21101
[27] Jeong, J.; Maddala, G. S.: Measurement errors and tests for rationality. Journal of business and economic statistics 9, 431-439 (1991)
[28] Kendall, M. G.; Stuart, A.: 2nd ed. The advanced theory of statistics. The advanced theory of statistics 1 (1963)
[29] Klepper, S.; Leamer, E. E.: Consistent sets of estimates for regressions with errors in all variables. Econometrica 52, 163-184 (1984) · Zbl 0526.90030
[30] Langaskens, Y.; Van Rickeghem, M.: A new method to estimate measurement errors in national income account statistics: the Belgium case. International statistical review 42, 283-290 (1974)
[31] Malinvaud, E.: Méthodes statistiques de léconometrie. (1978) · Zbl 0421.62084
[32] Mankiw, N. G.; Romer, D.; Weil, D. N.: A contribution to the empirics of economic growth. Quarterly journal of economics, 407-437 (1992) · Zbl 0825.90191
[33] Mariano, R. S.; Sawa, T.: The exact finite-sample distribution of the limited-information maximum likelihood estimator in the case of two included endogeneous variables. Journal of the American statistical association, 159-163 (1972) · Zbl 0231.62044
[34] Morgenstern, O.: On the accuracy of economic observation. (1963)
[35] Nelson, C. R.: Some further results on the exact small sample properties of the instrumental variable estimator. Econometrica 58, 967-976 (1990) · Zbl 0727.62109
[36] Pal, M.: Consistent moment estimators of regression coefficients in the presence of errors in variables. Journal of econometrics 14, 349-364 (1980) · Zbl 0459.62052
[37] Radner, D. B.: Social security bulletin. 45, 13-21 (1982)
[38] Reiersol, O.: Identifiability of a linear relation between variables which are subject to error. Econometrica 18, 375-389 (1950) · Zbl 0040.22502
[39] Rodgers, W. L.; Brown, C.; Duncan, G. J.: Errors in survey reports of earnings, hours worked and hourly wages. Journal of the American statistical association 88, 1208-1218 (1993)
[40] Canada, Statistics: Family expenditure in Canada, 1986, survey of family expenditure. Public use microdata file (1988)
[41] Theil, H.: Principles of econometrics. (1971) · Zbl 0221.62002
[42] White, H.: Asymptotic theory for econometricians. (1984)
[43] Wu, D.: Alternative tests of independence between stochastic regressors and disturbances. Econometrica 41, 733-750 (1973) · Zbl 0301.62032
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