Bayesian and classical approaches to instrumental variable regression

Journal of Econometrics

Volumn 114, Issue 1, 2003, Pages 29-72

  Kleibergen, Frank ^a   Zivot, Eric ^b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Diffuse prior; Instrumental variables; Posterior distributions; Reduced rank; Weak instruments

Indexed keywords

ASYMPTOTIC STABILITY; INSTRUMENT TESTING; LEAST SQUARES APPROXIMATIONS; LINEAR EQUATIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; MAXIMUM LIKELIHOOD ESTIMATION; METHOD OF MOMENTS; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; VARIATIONAL TECHNIQUES; VECTORS;

BAYESIAN ANALYSIS; ECONOMETRICS; MULTIVARIATE ANALYSIS;

REGRESSION ANALYSIS;

EID: 0347354941     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(02)00219-1     Document Type: Article

References (65)

1. Anderson T.W. Asymptotic expansions of the distributions of estimates in simultaneous equations for alternative parameter sequences. Econometrica. 45:1977;509-518.
2. Anderson, T.W. 1982. Some recent developments on the distributions of single-equation estimators. In: Hildebrand, W. (Ed.), Advances in Econometrics: Invited Papers for the Fourth World Congress of the Econometric Society at Aix-En-Provence, September 1980, Cambridge University Press, Cambridge, pp. 109-122.
3. Anderson T.W., Rubin H. Estimators of the parameters of a single equation in a complete set of stochastic equations. The Annals of Mathematical Statistics. 21:1949;570-582.
4. Anderson T.W., Sawa T. Evaluation of the distribution function of the two stage least squares estimate. Econometrica. 47:1979;163-182.
5. Anderson T.W., Kunitomo N., Morimune K. Comparing single-equation estimators in a simultaneous equation system. Econometric Theory. 2:1986;1-32.
6. Basmann R.L. A generalized classical method of linear estimation of coefficients in a structural equation. Econometrica. 25:1957;77-83.
7. Bauwens L., van Dijk H.K. Bayesian limited information analysis. Gabszewicz J.J., et al. Economic Decision-Making: Games, Econometrics and Optimisation. 1989;North-Holland Publishing Co. Amsterdam.
8. Berger J.O. Statistical Decision Theory and Bayesian Inference. 1985;Springer, New York.
9. Bowden R.J., Turkington D.A. Instrumental Variables. 1984;Cambridge University Press, Cambridge.
10. Box G.E.P., Tiao G.C. Bayesian Inference in Statistical Analysis. 1973;Addison-Wesley, Reading, MA.
11. Chao J.C., Phillips P.C.B. Posterior distributions in limited information analysis of the simultaneous equations models using the Jeffreys' Prior. Journal of Econometrics. 87:1998;49-86.
12. Chao, J.C., Phillips, P.C.B., 2002. Jeffreys' prior analysis of the simultaneous equations model in the case of n + 1 endogenous variables. Journal of Econometrics 111, 251-283.
13. Cox D.R., Reid N. Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B. 49:1987;1-39.
14. Currie, J., 1996. The geographic extent of the market: theory and application to the US petroleum markets. Ph.D. Thesis, University of Chicago.
15. Dhrymes, P.J., 1994. Linear and Simultaneous Equations, Vol. 2, Topics in Advanced Econometrics. Springer, Berlin.
16. Diebold F.X., Lamb R.L. Why are estimates of agricultural supply so variable. Journal of Econometrics. 76:1997;357-373.
17. Drèze J.H. Bayesian limited information analysis of the simultaneous equations model. Econometrica. 44:1976;1045-1075.
18. Dréze J.H. Bayesian regression using poly-t densities Journal of Econometrics. 6:1977;329-354.
19. Drèze, J.H., Richard, J.F., 1983. Bayesian analysis of simultaneous equations systems. In: Griliches, S., Intrilligator, M.D. (Eds.), Handbook of Econometrics, Vol. 1. Elsevier Science, Amsterdam.
20. Dufour, J.-M., Khalaf, L., 1997. Simulation based finite and large sample inference methods in simultaneous equations. Working paper, CRDE, Universite de Montreal.
21. Forchini, G., Hillier, G., 1999. Conditional inference for possibly unidentified structural equations. Unpublished Manuscript, Department of Economics, University of Southampton.
22. Fuller W.A. Some properties of a modification of the limited information estimator. Econometrica. 45:1977;939-953.
23. Gao, C., Lahiri, K., 2001. A comparison of some recent Bayesian and classical procedures for simultaneous equation models with weak instruments. Unpublished Manuscript, Department of Economics, State University of New York at Albany.
24. Golub G.H., van Loan C.F. Matrix Computations. 1989;The John Hopkins University Press, Baltimore.
25. Hausman, J.A., 1983. Specification and estimation of simultaneous equations systems. In: Griliches, Z., Intrilligator, M.D. (Eds.), Handbook of Econometrics, Vol. 1. Elsevier Science, Amsterdam.
26. Hillier G.H. On the normalization of structural equations. properties of direction estimators Econometrica. 58:1990;1181-1194.
27. Hood, W.C., Koopmans, T.C., 1953. Studies in Econometric Method, Vol. 14, Cowles Foundation Monograph. Wiley, New York.
28. Jeffreys H. Theory of Probability. 3rd Edition:1967;Oxford University Press, London.
29. Johnson, N.L., Kotz, S., 1970. Continuous Univariate Distributions. Vol. 2, Wiley, New York.
30. Kitamura, Y., 1994. Specification tests with instrumental variables and rank deficiency. Working paper, Department of Economics, University of Minnesota.
31. Kleibergen, F., 1997. Bayesian simultaneous equations using equality restricted random variables. In: Proceedings of the Section on Bayesian Statistical Science. American Statistical Association, pp. 141-146.
32. Kleibergen, F., 2000a. Exact test statistics and distributions of maximum likelihood estimators that result from orthogonal parameters with applications to the instrumental variables regression model. Tinbergen Institute Discussion Paper TI 2000-039/4.
33. Kleibergen, F., 2000b. Conditional densities in statistical modelling. Working paper, University of Amsterdam.
34. Kleibergen F., van Dijk H.K. Bayesian simultaneous equation analysis using reduced rank structures. Econometric Theory. 14:1998;701-743.
35. Kleibergen, F., Paap, R., 2002. Priors, posteriors and Bayes factors for a Bayesian analysis of cointegration. Journal of Econometrics 111, 223-249.
36. Maddala G.S. Weak priors and sharp posteriors in simultaneous equation models. Econometrica. 44:1976;345-351.
37. Magnus J.R., Neudecker H. Matrix Differential Calculus with Applications in Statistics and Econometrics. 1988;Wiley, Chichester.
38. Mariano R.S., Sawa T. The exact finite-sample distribution of the limited-information maximum likelihood estimator in the case of two included endogenous variables. Journal of the American Statistical Association. 67:1972;159-163.
39. Morimune K. Improving the limited information maximum likelihood estimator when the distrubances are small. Journal of the American statistical Association. 75:1978;230-237.
40. Muirhead R.J. Aspects of Multivariate Statistical Theory. 1982;Wiley, New York.
41. Nagar A.L. Double. k-class estimators of parameters in simultaneous equations and their small sample properties International Economic Review. 3:1962;168-188.
42. Nelson C.R., Startz R. Some further results on the exact small sample properties of the instrumental variables estimator. Econometrica. 58:1990;967-976.
43. Park S.-B. Some sampling properties of minimum expected loss (MELO) estimators of structural coefficients. Journal of Econometrics. 18:1982;295-311.
44. Phillips, P.C.B., 1983. Exact small sample theory in the simultaneous equations model. In: Griliches, Z. Intrilligator, M.D. (Eds.), Handbook of Econometrics, Vol. 1. North-Holland Publishing Co., Amsterdam.
45. Phillips P.C.B. Partially identified econometric models. Econometric Theory. 5:1989;181-240.
46. Poirier, D.J., 1996. Prior beliefs about fit. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.), Bayesian Statistics, Vol. 5. Oxford University Press, Oxford, pp. 731-738.
47. Sawa T. The mean square error of a combined estimator and numerical with the TSLS estimator. Journal of Econometrics. 1:1973;115-132.
48. Shea J. Instrument relevance in multivariate linear models. A simple measure The Review of Economics and Statistics. 79:1997;348-352.
49. Staiger D., Stock J.H. Instrumental variables regression with weak instruments. Econometrica. 65:1997;557-586.
50. Startz, R., Nelson, C.R., Zivot, E., 1999. Improved inference for the instrumental variable estimator. Technical Report, University of Washington.
51. Theil, H., 1953. Estimation and Simultaneous Correlation in Complete Equation Systems. Mimeographed Memorandum of the Central Planning Bureau, The Hague.
52. Theil H. Economic Forecasts and Policy. 2nd Edition:1961;North-Holland, Amsterdam.
53. Tsurumi H. Limited information Bayesian analysis of a structural coefficient in a simultaneous equation system. Communications in Statistics. 14:1985;1103-1120.
54. Tsurumi H. Comparing Bayesian and non-Bayesian limited information estimators. Geisser S., Hodges J.S., Press S.J., Zellner A. Bayesian and Likelihood Methods in Statistics and Econometrics: Essays in Honor of George A. Barnard. 1990;North-Holland, Amsterdam.
55. Wang J., Zivot E. Inference on structural parameters in instrumental variables regression with weak instruments. Econometrica. 66:1998;1389-1405.
56. Zellner A. An Introduction to Bayesian Inference in Econometrics. 1971;Wiley, New York.
57. Zellner A. Estimation of functions of population means and regression coefficients including structural coefficients. a minimum expected loss (MELO) approach Journal of Econometrics. 8:1978;127-158.
58. Zellner A. Canonical representation of linear structural econometric models, rank tests for identification and existence of estimators' moments. Karlin S., Amemiya T., Goodman L.A. Studies in Econometrics, Time Series and Multivariate Statistics. 1983;227-240 Academic Press, New York.
59. Zellner, A., 1986. Further results on Bayesian minimum expected loss (MELO) estimates and posterior distributions of structural parameters. In: Slottje, D. (Ed.), Advances in Econometrics, Vol. 5. pp. 171-182.
60. Zellner A. Bayesian method of moments/instrumental variable (BMOM/IV) analysis of mean and regression models. Lee J.C., Johnson W.O., Zellner A. Modelling and Prediction Honoring Seymour Geisser. 1994;61-74 Springer, New York.
61. Zellner, A., 1997. Bayesian Analysis in Econometrics in Statistics: The Zellner View and Papers. Edward Elgar Publishing.
62. Zellner A. The finite sample properties of simultaneous equations' estimates and estimators Bayesian and non-Bayesian approaches. Journal of Econometrics. 83:1998;185-212.
63. Zellner A., Tobias J. Further results on Bayesian method of moments analysis of the multiple regression model. International Economic Review. 42:2001;121-139.
64. Zellner A., Bauwens L., van Dijk H.K. Bayesian specification analysis and estimation of simultaneous equation models using Monte-Carlo integration. Journal of Econometrics. 38:1988;39-72.
65. Zivot E., Startz R., Nelson C.R. Valid confidence intervals and inference in the presence of weak instruments. International Economic Review. 39:1998;1119-1144.