Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-10T23:15:12.589Z Has data issue: false hasContentIssue false
  • English
  • Français

MEASUREMENT ERRORS IN DYNAMIC MODELS

Published online by Cambridge University Press:  07 August 2013

Ivana Komunjer  and
Serena Ng
Ivana Komunjer
Affiliation:
University of California, San Diego
Serena Ng*
Affiliation:
Columbia University
*
*Address correspondence to Serena Ng, Columbia University, 420 W. 118 St. MC 3308, New York, NY 10027; e-mail: serena.ng@columbia.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

Static models that are not identifiable in the presence of white noise measurement errors are known to be potentially identifiable when the model has dynamics. However, few results are available for the plausible case of serially correlated measurement errors. This paper provides order and rank conditions for “limited information” identification of parameters in dynamic models with measurement errors where some aspects of the probability model are not fully specified or utilized. The key is to consider a model for the contaminated data that has richer dynamics than the model for the correctly observed data. Simply counting the total number of unknown parameters in the true model relative to the estimable model will not yield an informative order condition for identification. Implications for single-equation, vector autoregressive, and panel data models are studied.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 1 , February 2014 , pp. 150 - 175
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aigner, D., Hsiao, C., Kapteyn, A., & Wansbeek, T. (1984) Latent variable models in econometrics. In Grichiles, Z. and Intriligator, M.D. (eds.), Handbook of Econometrics, vol. 1, no 2. North Holland.Google Scholar
Anderson, B. & Deistler, M. (1984) Identifiability in dynamic errors-in-variables models. Journal of Time Series Analysis 5:1, 1–13.Google Scholar
Ashley, R. & Vaughan, D. (1986) Measuring measuring error in time series. Journal of Business and Economic Statistics 4:1, 95–103.Google Scholar
Bell, W. R. & Wilcox, D. (1993) The effect of sampling on the time series behavior of consumption data. Journal of Econometrics, 55, 235–265.CrossRefGoogle Scholar
Biorn, E. (1992) The bias of some estimators for panel models with measurement errors. Empirical Economics 17, 51–66.CrossRefGoogle Scholar
Biorn, E. (1996) Panel data with measurement errors. In Matyas, L., & Sevestre, P. (eds.), The Econometrics of Panel Data, Dordrecht. Kluwer.Google Scholar
Biorn, E. (2008) Measurement Error in a Dynamic Panel Data Analysis: A Synthesis on Modeling and GMM Estimation. Mimeo, University of Oslo.Google Scholar
Bound, J. & Krueger, A. (1991) The extent of measurement error in longitudinal earnings data: Do two wrongs make a right? Journal of Labor Economics 9, 1–24.CrossRefGoogle Scholar
Chanda, K. (1996) Asymptotoic properties of estimators for autoregressive models with errors in variables. Annals of Statistics 24:1, 423–430.Google Scholar
Devereux, P. (2001) The cyclicality of real wages within employer-employee matches. Industrial and Labor Relations Review 54:4, 835–50.Google Scholar
Eberly, J., Rebelo, S., & Vincent, N. (2009) Investment and Value: A Neoclassical Benchmark, CIRPEE Working paper 09–08.Google Scholar
Erickson, T. & Whited, T. (2000) Measurement error and the relationship between investment and q. Journal of Political Economy 108, 1027–57.Google Scholar
Erickson, T. & Whited, T. (2002) Two-Step GMM estimation of the errors-in-variables model using higher order moments. Econometric Theory 18, 776–799.Google Scholar
Ermini, L. (1993) Effects of transitory consumption and temporal aggregation on the permanent income hypothesis. Review of Economics and Statistics 75:5, 736–74.CrossRefGoogle Scholar
Falk, B. & Lee, B. (1990) Time series implications of friedman’s permanent income hypothesis. Journal of Monetary Economics 26:2, 267–283.Google Scholar
Fisher, F. (1963) Uncorrelated disturbances and identifiability criteria. International Economic Review 4(2), 134–152.CrossRefGoogle Scholar
Fisher, F. (1966) The Identification Problem in Econometrics. McGraw-Hill.Google Scholar
Granger, C. W. & Morris, M. J. (1976) Time series modelling and interpretation. Journal of the Royal Statistical Association Series A 139, 246–257.Google Scholar
Grether, D. & Maddala, G. (1973) Errors in variables and serially correlated disturbances in distributed lag models. Econometrica 41:2, 255–262.CrossRefGoogle Scholar
Griliches, Z. & Hausman, J. (1986) Errors in variables in panel data. Journal of Econometrics 32:3, 93–118.Google Scholar
Hannan, E. (1969) The identification of vector mixed autoregressive-moving average systems. Biometrika 56(1), 223–225.Google Scholar
Hannan, E. (1970) Multiple Time Series. Wiley.CrossRefGoogle Scholar
Hannan, E. (1971) The identification problem for multiple equation systems with moving average errors. Econometrica 39:5, 751–765.Google Scholar
Hannan, E., Dunsmuir, W., & Deistler, M. (1980) Estimation of vector ARMAX models. Journal of Multivariate Analysis 10, 275–295.Google Scholar
Holtz-Eakin, D., Newey, W., & Rosen, H. (1988) Estimating vector autoregressions with panel data. Econometrica 56, 1371–1395.Google Scholar
Hsiao, C. (1979) Measurement error in a dynamic simultaneous equations model with stationary disturbances. Econometrica 47:2, 475–494.Google Scholar
Koopmans, T. (1953) Identification problems in economic model construction. In Hood, W. & Koopmans, T. C. (eds.), Studies in Econometric Method, vol. 14 of Cowles Commission Monograph, chap. II. Wiley.Google Scholar
Maravall, A. (1979) Identification in Dynamic Shock-Error Models. Springer-Verlag.Google Scholar
Maravall, A. & Aigner, D. (1977) Identification of the dynamic shock-error model: The case of dynamic regression. In Aigner, D. & Goldberger, A. (eds.), Latent Variables in Socio-Economic Models, North Holland.Google Scholar
Mcdonald, J. & Darroch, J. (1983) Consistent estimation of equations with composite moving average disturbance terms. Journal of Econometrics 23, 253–267.Google Scholar
Nowak, E. (1992) Identifiability in multivariate dynamic linear error-in-variables models. Journal of the American Statistical Association 87, 714–723.Google Scholar
Nowak, E. (1993) The identification of multivariate linear dynamic errors-in-variables models. Journal of Econometrics 59:3, 237.Google Scholar
Patriota, A., Sato, J., & Blas, B. (2009) Vector Autoregressive Models with Measurement Errors for Testing Granger Causality. Working paper, Universidade de Sao Paulo.CrossRefGoogle Scholar
Reiersøl, O. (1950) Identifiability of a linear relation between variables which are subject to error. Econometrica 23, 375–389.Google Scholar
Sargent, T. (1989) Two models of measurements and the investment accelerator. Journal of Political Economy 97:2.Google Scholar
Söderström, T. (2007) Errors-in-variables methods in system identification. Automatica 43, 939–958.CrossRefGoogle Scholar
Solo, V. (1986) Identifiability of time series models with errors in variables. Journal of Applied Probability 23, 63–71.Google Scholar
Staudenmayer, J. & Buonaccorsi, J. (2005) Measurement error in linear autoregressive models. Journal of the American Economic Association 100, 841–852.Google Scholar
Tanaka, K. (2002) A unified approach to the measurement error problem in time series models. Econometric Theory 18, 278–296.Google Scholar
Wansbeek, T. (2001) GMM estimation in panel data models with measurement error. Journal of Econometrics 104, 259–268.CrossRefGoogle Scholar
Wansbeek, T. & Koning, R. (1991) Measurement error and panel data. Statistica Needlandica 45, 85–92.CrossRefGoogle Scholar
Wansbeek, T. & Meijer, E. (2000) Measurement Error and Latent Variables in Econometrics. Elsevier.Google Scholar
Wilcox, D. (1992) The construction of U.S. consumption data: Some facts and their implications for empirical work. American Economic Review 82:4, 992–941.Google Scholar
Willassen, Y. (1977) On identifiability of stochastic difference equations with errors-in-variables in relation to identifiability of the classical errors-in-variables models. Scandinavan Journal of Statistics 4, 119–124.Google Scholar