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Partially Identified Econometric Models

Published online by Cambridge University Press:  18 October 2010

P.C.B. Phillips
P.C.B. Phillips
Affiliation:
Cowles Foundation for Research in Economics Yale University
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Abstract

This paper studies a class of models where full identification is not necessarily assumed. We term such models partially identified. It is argued that partially identified systems are of practical importance since empirical investigators frequently proceed under conditions that are best described as apparent identification. One objective of the paper is to explore the properties of conventional statistical procedures in the context of identification failure. Our analysis concentrates on two major types of partially identified model: the classic simultaneous equations model under rank condition failures; and time series spurious regressions. Both types serve to illustrate the extensions that are needed to conventional asymptotic theory if the theory is to accommodate partially identified systems. In many of the cases studied, the limit distributions fall within the class of compound normal distributions. They are simply represented as covariance matrix or scalar mixtures of normals. This includes time series spurious regressions, where representations in terms of functionals of vector Brownian motion are more conventional in recent research following earlier work by the author.

Type
Articles
Information
Econometric Theory , Volume 5 , Issue 2 , August 1989 , pp. 181 - 240
Copyright
Copyright © Cambridge University Press 1989

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References

REFERENCES

1.Basawa, I.V. & Scott, D. J.. Asymptotic optimal inference for nonergodic models. New York: Springer Verlag, 1983.CrossRefGoogle Scholar
2.Basawa, I.V. & Brockwell, P.J.. Asymptotic conditional inference for regular nonergodic models with an application to autoregressive processes. Annals of Statistics 12 (1984): 161–171.CrossRefGoogle Scholar
3.Billingsley, P.Convergence of probability measures. New York: Wiley, 1968.Google Scholar
4.Chan, N.H. & Wei, C.Z.. Limiting distributions of least-squares estimates of unstable autoregressive processes. Annals of Statistics 16 (1988): 367–401.CrossRefGoogle Scholar
5.Davies, R.B. Asymptotic inference when the amount of information is random. In LeCam, L.M. & Olshen, R.A. (eds.), Proceedings of the Berkeley Conference in Honor of Jerzy Neyman and Jack Kiefer, Vol. II, Wadsworth Inc., 1986.Google Scholar
6.Engle, R.F. & Granger, C.W.J.. Cointegration and error correction: representation, estimation, and testing. Econometrica 55 (1987): 251–276.CrossRefGoogle Scholar
7.Hall, P. & Heyde, C.C.. Martingale limit theory and its application. New York: Academic Press, 1980.Google Scholar
8.Jeganathan, P., An extension of a result of L. LeCam concerning asymptotic normality. Sankhya Series A 42 (1980): 146–160.Google Scholar
9.Jeganathan, P., On the strong approximation of distributions of estimators in linear stochastic models, I and II: Stationary and explosive models. University of Michigan, mimeographed, 1986.Google Scholar
10.Jeganathan, P., On the asymptotic behavior of least-squares estimators in AR time series with roots near the unit circle: Parts I and II. University of Michigan Technical Report #150, 1987.Google Scholar
11.LeCam, L., Locally asymptotically normal families of distributions. University of California Publications in Statistics 3 (1960): 37–98.Google Scholar
12.LeCam, L.Asymptotic methods in statistical decision theory. New York: Springer, 1986.Google Scholar
13.Lehmann, E.Testing statistical hypotheses. New York: Wiley (2nd Ed.), 1986.CrossRefGoogle Scholar
14.Muirhead, R.Aspects of multivariate statistical theory. New York: Wiley, 1982.CrossRefGoogle Scholar
15.Park, J.Y. & Phillips, P.C.B.. Statistical inference in regressions with integrated processes: Part 1. Econometric Theory 4(1988): 468–497.CrossRefGoogle Scholar
16.Park, J.Y. & Phillips, P.C.B.. Statistical inference in regressions with integrated processes: Part 2. Econometric Theory 5 (1989): 95–131.CrossRefGoogle Scholar
17.Phillips, P.C.B. Small sample distribution theory in econometric models of simultaneous equations. Cowles Foundation Discussion Paper No. 617, 1982.Google Scholar
18.Phillips, P.C.B. Exact small-sample theory in the simultaneous equations model. In Intriligator, M.D. & Griliches, Z. (eds.), Handbook of Econometrics, Chapter 8 and pp. 449–516. Amsterdam: North-Holland, 1983.CrossRefGoogle Scholar
19.Phillips, P.C.B.The exact distribution of LIML: I. International Economic Review 25 (1984): 249–261.CrossRefGoogle Scholar
20.Phillips, P.C.B.The exact distribution of exogenous variable coefficient estimators. Journal of Econometrics 26 (1984): 387–398.CrossRefGoogle Scholar
21.Phillips, P.C.B.The exact distribution of LIML: II. International Economic Review 26 (1985): 21–36.CrossRefGoogle Scholar
22.Phillips, P.C.B.A nonnormal limiting distribution. Econometric Theory 1 (1985): 145.Google Scholar
23.Phillips, P.C.B.Understanding spurious regressions in econometrics. Journal of Econometrics 33 (1986): 311–340.CrossRefGoogle Scholar
24.Phillips, P.C.B.Time series regression with a unit root. Econometrica 55 (1987): 277–301.CrossRefGoogle Scholar
25.Phillips, P.C.B.Asymptotic expansions in nonstationary vector autoregressions. Econometric Theory 3 (1987): 45–68.CrossRefGoogle Scholar
26.Phillips, P.C.B.Weak convergence to the matrix stochastic integral BdB′. Journal of Multivariate Analysis 24 (1988): 252–264.CrossRefGoogle Scholar
27.Phillips, P.C.B. Optimal inference in cointegrated systems. Cowles Foundation Discussion Paper No. 866, March 1988.Google Scholar
28.Phillips, P.C.B.Towards a unified asymptotic theory of autoregression. Biometrika 74 (1987): 535–547.CrossRefGoogle Scholar
29.Phillips, P.C.B.Regression theory for near integrated time series. Econometrica 56 (1988): 1021–1044.CrossRefGoogle Scholar
30.Phillips, P.C.B. & Durlauf, S.N.. Multiple time series regression with integrated processes. Review of Economic Studies 53 (1986): 473–496.CrossRefGoogle Scholar
31.Prakasa Rao, B.L.S.Asymptotic theory of statistical inference. New York: Wiley, 1987.Google Scholar
32.Stock, J.H.Asymptotic properties of least-squares estimators of cointegrating vectors. Econometrica 55 (1987): 1035–1056.CrossRefGoogle Scholar