Decision theory applied to an instrumental variables model

Econometrica

Volumn 75, Issue 3, 2007, Pages 609-652

  Chamberlain, Gary ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

Bayes decision rule; Instrumental variables; Invariance; Minimax; Risk function

Indexed keywords

EID: 34247382504     PISSN: 00129682     EISSN: 14680262     Source Type: Journal    
DOI: 10.1111/j.1468-0262.2007.00764.x     Document Type: Article

References (31)

1. ANDERSON, T. W., AND H. RUBIN (1949): "Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations," The Annals of Mathematical Statistics, 20, 46-63. [626]
2. ANDREWS, D., M. MOREIRA, AND J. STOCK (2006): "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, 74, 715-752. [612]
3. ARELLANO, M. (2003): Panel Data Econometrics. London: Oxford University Press. [647]
4. BEKKER, P. (1994): "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, 62, 657-681. [614]
5. BERGER, J., B. LISEO, AND R. WOLPERT (1999): "Integrated Likelihood Methods for Eliminating Nuisance Parameters," Statistical Science, 14, 1-22. [628]
6. BLACKWELL, D., AND M. GIRSHICK (1954): Theory of Games and Statistical Decisions. New York: Wiley. [648]
7. CHAMBERLAIN, G. (2000): "Econometric Applications of Maxmin Expected Utility," Journal of Applied Econometrics, 15, 625-644. [648]
8. _ (2003): "Instrumental Variables, Invariance, and Minimax," Unpublished Manuscript, Department of Economics, Harvard University. [609]
9. CHAMBERLAIN, G., AND G. IMBENS (2004): "Random Effects Estimators with Many Instrumental Variables," Ecanometrica, 72, 295-306. [612]
10. EATON, M. (1989): Group Invariance Applications in Statistics, Regional Conference Series in Probability and Statistics, Vol. 1. Hayward, CA: Institute of Mathematical Statistics. [632]
11. FERGUSON, T. (1967): Mathematical Statistics: A Decision Theoretic Approach. New York: Academic. [612,617-620,622,631-633]
12. GILBOA, I., AND D. SCHMEIDLER (1989): "Maxmin Expected Utility with Non-Unique Prior," Journal of Mathematical Economics, 18, 141-153. [612]
13. GOLDBERGER, A. S. (1991): A Course in Econometrics. Cambridge, MA: Harvard University Press. [614]
14. GOLDBERGER, A. S., AND I. OLKIN (1971): "A Minimum-Distance Interpretation of Limited-Information Estimation," Econometrica, 39, 635-639. [626]
15. HANSEN, L. P., AND T. SARGENT (2005): "Robust Estimation and Control under Commitment," Journal of Economic Theory, 124, 258-301. [612]
16. HANSEN, L. P., T. SARGENT, G. TURMUHAMBETOVA, AND N. WILLIAMS (2006): "Robust Control and Model Misspedficeition," Journal of Economic Theory, 128, 45-90. [612]
17. HILLIER, G. (1990): "On the Normalization of Structural Equations: Properties of Direction Estimators," Econometrica, 58, 1181-1194. [615]
18. JAMES, W., AND C. STEIN (1961): "Estimation with Quadratic Loss," in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1. Berkeley: University of California Press, 361-380. [610,627]
19. LANCASTER, T. (2002): "Orthogonal Parameters and Panel Data," Review of Economic Studies, 69, 647-666. [647]
20. LE CAM, L. (1986): Asymptotic Methods in Statistical Decision Theory. New York: Springer-Verlag. [620]
21. MANSKI, C. (2004): "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, 72, 1221-1246. [612]
22. SIMS, C. (2001): "Pitfalls of a Minimax Approach to Model Uncertainty," American Economic Review, 91, 51-54. [612]
23. STAIGER, D., AND J. STOCK (1997): "Instrumental Variables Regression with Weak Instruments," Econometrica, 65, 557-586. [614]
24. STEIN, C. (1956): "Inadmissibility of the Usual Estimator for the Mean of a Multivariate Normal Distribution," in Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1. Berkeley: University of California Press, 197-206. [610,627]
25. _ (1959): "An Example of Wide Discrepancy Between Fiducial and Confidence Intervals," The Annals of Mathematical Statistics, 30, 877-880. [610,627]
26. _ (1962): "Confidence Sets for the Mean of a Multivariate Normal Distribution," Journal of the Royal Statistical Society Sci: B, 24, 265-296. [628]
27. STRASSER, H. (1985): Mathematical Theory of Statistics: Statistical Experiments and Asymptotic Decision Theory. Berlin: de Gruyter. [620]
28. STROOCK, D. W. (1999): A Concise Introduction to the Theory of Integration. Boston: Birkhäuser. [629]
29. VAN DER VAART, A. W. (1998): Asymptotic Statistics. Cambridge, U.K.: Cambridge University Press. [638]
30. WALD, A. (1950): Statistical Decision Functions. New York: Wiley. [612,620,645]
31. WILSON, R. B. (1963): "A Simplicial Algorithm for Concave Programming," Ph.D. Dissertation, Harvard University. [648]