Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-13T07:07:37.429Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Exact Distribution Results for the Partially Restricted Reduced form Estimator

Published online by Cambridge University Press:  11 February 2009

Terrence W. Kinal and
John L. Knight
Terrence W. Kinal
Affiliation:
State University of New York at Albany
John L. Knight
Affiliation:
University of Western Ontario
Get accessRights & Permissions [Opens in a new window]

Abstract

This paper considers some finite sample properties of the partially restricted reduced form estimators in a general (n + 1) endogenous variable model. In particular, the characteristic functions, density functions, and moments are examined for both the vector of estimators and a linear combination. The approach utilizes both invariant polynomials of matrix argument (see Chikuse and Davis [4] and Davis [6]) and fractional calculus techniques (see Phillips [20,25,26]).

Information

Type
Articles
Information
Econometric Theory , Volume 10 , Issue 1 , March 1994, pp. 140 - 171
Copyright
Copyright © Cambridge University Press 1994

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.)

Article purchase

Temporarily unavailable

References

1.Amemiya, T.On the use of principal components of independent variables in two-stage least squares estimation. International Economic Review 7 (1966): 283–303.CrossRefGoogle Scholar
2.Arvin-Rad, H. Essays in Econometric Theory, unpublished Ph.D. dissertation, University of Pennsylvania, 1990.Google Scholar
3.Chetty, V.K.Bayesian analysis of Haavelmo's models. Econometrica 36 (1968): 582–602.CrossRefGoogle Scholar
4.Chikuse, Y. & Davis, A.W.. A survey on the invariant polynomials with matrix arguments in relation to econometric distribution theory. Econometric Theory 2 (1986): 232–248.CrossRefGoogle Scholar
5.Court, R.H.Efficient estimation of the reduced form from econometric models. Review of Economic Studies 40 (1973): 411–418.CrossRefGoogle Scholar
6.Davis, A.W.Invariant polynomials with two matrix arguments extending the zonal polynomials: Applications to multivariate distribution theory. Annals of the Institute of Statistical Mathematics A31 (1979): 465–485.CrossRefGoogle Scholar
7.Goldberger, A.S., Nagar, A.L. & Odeh, H.S.. The covariance matrices of reduced form coefficients and of forecasts for a structural econometric model. Econometrica 29 (1961): 556–573.CrossRefGoogle Scholar
8.Hillier, G.H.Exact densities of instrumental variables estimators: An alternative approach. Monash University, mimeo, 1982.Google Scholar
9.Hillier, G.H.On the joint and marginal densities of instrumental variable estimators in a general structural equation. Econometric Theory 1 (1985): 53–72.CrossRefGoogle Scholar
10.Hillier, G.H., Kinal, T.W. & Srivastava, V.K.. On the moments of ordinary least squares and instrumental variable estimators in a general structural equation. Econometrica 52 (1984): 185–202.CrossRefGoogle Scholar
11.Kakwani, N.C. & Court, R.H.. Reduced form coefficient estimation and forecasting from a simultaneous equation model. Australian Journal of Statistics 14 (1972): 143–160.CrossRefGoogle Scholar
12.Knight, J.L.On the existence of moments of the partially restricted reduced-form estimators from a simultaneous-equations model. Journal of Econometrics 5 (1977): 315–321.CrossRefGoogle Scholar
13.Knight, J.L.The exact distribution of the PRRF estimator: A fractional calculus approach. University of New South Wales, mimeo, 1985.Google Scholar
14.Maasoumi, E.A modified Stein-like estimator for the reduced form coefficients of simultaneous equations. Econometrica 46 (1978): 695–703.CrossRefGoogle Scholar
15.McCarthy, M.D.A note on the forecasting properties of 2SLS restricted reduced forms – the finite sample case. International Economic Review 13 (1972): 756–761.CrossRefGoogle Scholar
16.McCarthy, M.D.A note on the moments of partially restricted reduced forms. Journal of Econometrics 17 (1981): 383–387.CrossRefGoogle Scholar
17.Nagar, A.L. & Sahay, S.N.. The bias and mean squared error of forecasts from partially restricted reduced form. Journal of Econometrics 7 (1978): 227–243.CrossRefGoogle Scholar
18.Phillips, P.C.B.The exact distribution of instrumental variable estimators in an equation containing n + 1 endogenous variables. Econometrica 48 (1980): 861–878.CrossRefGoogle Scholar
19.Phillips, P.C.B. Exact small sample theory in the simultaneous equations model. In Griliches, Z. and Intriligator, M.D. (eds.), Handbook of Econometrics, Volume 1, Chapter 8. Amsterdam: North-Holland, 1983.Google Scholar
20.Phillips, P.C.B.The exact distribution of the Stein-rule estimator. Journal of Econometrics 25 (1984): 123–131.CrossRefGoogle Scholar
21.Phillips, P.C.B.The exact distribution of the SUR estimator. Econometrica 53 (1985): 745–756.CrossRefGoogle Scholar
22.Phillips, P.C.B.The exact distribution of the exogenous variable coefficient estimators. Journal of Econometrics 26 (1985): 385–398.Google Scholar
23.Phillips, P.C.B.The exact distribution of the Wald statistic. Econometrica 54 (1986): 881–895.CrossRefGoogle Scholar
24.Phillips, P.C.B.The distribution of FIML in the leading case. International Economic Review 27 (1986): 239–243.CrossRefGoogle Scholar
25.Phillips, P.C.B. Fractional matrix calculus and the distribution of multivariate tests. In MacNeil, I.B. and Umphrey, G.J. (eds.), Advances in Statistical Sciences: Time Series and Econometric Modelling, Volume 3, pp. 219–234. Dordrecht: R. Reidel, 1987.Google Scholar
26.Phillips, P.C.B. Operational algebra and regression t-tests, Cowles Foundation Paper No. 840, Yale University, 1993. Forthcoming in Phillips, P.C.B. (ed.), Models, Methods, and Applications of Econometrics.Google Scholar
27.Swamy, P.A.V.B. & Metha, J.S.. On the existence of moments of the partially restricted reduced form coefficients. Journal of Econometrics 14 (1980): 183–194. Also: Comment Journal of Econometrics 17 (1981): 389–392.CrossRefGoogle Scholar
28.Sargan, J.D.Existence of moments of estimated reduced form coefficients. London School of Economics, Discussion Paper A6 (1976).Google Scholar