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Dynamic Structural Systems Under Indirect Observation: Identifiability and Estimation Aspects from a System Theoretic Perspective

Published online by Cambridge University Press:  01 January 2025

Pieter W. Otter
Pieter W. Otter*
Affiliation:
Institute of Econometrics
*
Requests for reprints should be sent to Pieter W. Otter, Institute of Econometrics, P, O. Box 800, 9700 AV Groningen, THE NETHERLANDS.
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Abstract

In this—partly—expository paper the parameter identifiability and estimation of a general dynamic structural model under indirect observation will be considered from a system theoretic perspective. The general dynamic model covers (dynamic) factor analytic models, (dynamic) MIMIC models and Jöreskog's linear structural model as special cases. Its reduced form is—under a slightly different specification—known in system theory and econometrics as the stochastic, stationary version of the state-space model. By using concepts and methods from system theory, such as the observability and controllability concept, the (steady-state) Kalman filter and a general nonlinear ML-estimation procedure known as prediction-error estimation the general dynamic model will be identified. It will be shown that Jöreskog's LISREL-procedure is a special case of the prediction-error estimation procedure.

Keywords

System TheoryKalman FilterEstimation ProcedureStationary VersionModel Cover
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 3 , September 1986 , pp. 415 - 428
Copyright
Copyright © 1986 The Psychometric Society

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References

Anderson, T. W. (1958). An introduction to multivariate statistical analysis. John Wiley.Google Scholar
Aoki, M. (1983). Notes on economic time-series analysis: System theoretic perspectives (Lecture notes in economics and mathematical systems series). Springer Verlag.Google Scholar
Åström, K. J., Bohlin, T. (1966). Numerical identification of linear dynamic systems from normal operating records, Solma, Sweden: IBM Nordic Laboratory.CrossRefGoogle Scholar
Bertsekas, D. P. (1976). Dynamic programming and stochastic control. Academic Press.Google Scholar
Goodwin, G. C., & Payne, R. L. (1977). Dynamic system identification; Experiment design and data analysis. Academic Press.Google Scholar
Jöreskog, K. G. (1977). Structural equation models in social sciences: Specification, estimation and testing. In Krishnaiah, P. R. (Ed.), Applications of statistics. North-Holland.Google Scholar
Kwakernaak, H., & Sivan, D. (1972). Linear optimal control systems. Wiley Interscience.Google Scholar
Lawley, D. H., & Maxwell, A. E. (1971). Factor analysis as a statistical method (2nd ed.). Butterworths.Google Scholar
Ljung, L., & Söderström, T. (1983). Theory and practice of recursive identification. MIT Press.Google Scholar
Mehra, R. K. (1974). Identification in control and econometrics: Similarities and differences. Annals of Economic and Social Measurement, 3(1).Google Scholar
Otter, P. W. (1985). Dynamic feature space modelling, filtering and self-tuning control of stochastic systems: Vol. 246. Lecture notes in economics and mathematical systems. Springer.CrossRefGoogle Scholar
Sage, A. P., & Melsa, J. L. (1971). Estimation theory with applications to communications and control. McGraw-Hill.CrossRefGoogle Scholar
Watson, M. W., & Engle, R. F. (1983). Alternative algorithms for the estimation of dynamic factor, MIMIC and varying coefficient regression models. Journal of Econometrics, 23(3).CrossRefGoogle Scholar