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IDENTIFICATION AND STATISTICAL DECISION THEORY

Published online by Cambridge University Press:  31 May 2024

Charles F. Manski*
Affiliation:
Northwestern University
*
Address correspondence to Charles F. Manski, Department of Economics and Institute for Policy Research, Northwestern University, Evanston, IL, USA; e-mail: cfmanski@northwestern.edu.

Abstract

Econometricians have usefully separated study of estimation into identification and statistical components. Identification analysis, which assumes knowledge of the probability distribution generating observable data, places an upper bound on what may be learned about population parameters of interest with finite-sample data. Yet Wald’s statistical decision theory studies decision-making with sample data without reference to identification, indeed without reference to estimation. This paper asks if identification analysis is useful to statistical decision theory. The answer is positive, as it can yield an informative and tractable upper bound on the achievable finite-sample performance of decision criteria. The reasoning is simple when the decision-relevant parameter (true state of nature) is point-identified. It is more delicate when the true state is partially identified and a decision must be made under ambiguity. Then the performance of some criteria, such as minimax regret, is enhanced by randomizing choice of an action in a controlled manner. I find it useful to recast choice of a statistical decision function as selection of choice probabilities for the elements of the choice set.

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ARTICLES
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Footnotes

I am grateful for the constructive comments of the editor and several reviewers.

References

REFERENCES

Andrews, I., & Mikusheva, A. (2014). Weak identification in maximum likelihood: A question of information. American Economic Review Papers and Proceedings , 104, 195199.10.1257/aer.104.5.195CrossRefGoogle Scholar
Berger, J. (1985). Statistical decision theory and Bayesian analysis . Springer.10.1007/978-1-4757-4286-2CrossRefGoogle Scholar
Dempster, A. (1968). A generalization of Bayesian inference. Journal of the Royal Statistical Society, Series B , 30, 205247.10.1111/j.2517-6161.1968.tb00722.xCrossRefGoogle Scholar
Giacomini, R., & Kitagawa, T. (2021). Robust Bayesian inference for set-identified models. Econometrica , 89, 15191556.10.3982/ECTA16773CrossRefGoogle Scholar
Hirano, K., & Porter, J. (2020). Asymptotic analysis of statistical decision rules in econometrics. In Durlauf, S., Hansen, L., Heckman, J., & Matzkin, R. (Eds.), Handbook of econometrics (Vol. 7A, pp. 283354). Elsevier.10.1016/bs.hoe.2020.09.001CrossRefGoogle Scholar
Kline, B., & Tamer, E. (2016). Bayesian inference in a class of partially identified models. Quantitative Economics , 7, 329366.10.3982/QE399CrossRefGoogle Scholar
Koopmans, T. (1949). Identification problems in economic model construction. Econometrica , 17, 125144.10.2307/1905689CrossRefGoogle Scholar
Koopmans, T., & Hood, W. (1953). The estimation of simultaneous linear economic relationships. In Hood, W., & Koopmans, T. (Eds.), Studies in econometric method . Cowles Commission Monograph, Vol. 14 (Chapter 6, pp. 112199). Wiley.Google Scholar
Le Cam, L. (1986). Asymptotic methods in statistical decision theory . Springer.10.1007/978-1-4612-4946-7CrossRefGoogle Scholar
Manski, C. (1988). Analog estimation methods in econometrics . Chapman and Hall.Google Scholar
Manski, C. (2004). Statistical treatment rules for heterogeneous populations. Econometrica , 72, 221246.10.1111/j.1468-0262.2004.00530.xCrossRefGoogle Scholar
Manski, C. (2007a). Identification for prediction and decision . Harvard University Press.Google Scholar
Manski, C. (2007b). Minimax-regret treatment choice with missing outcome data. Journal of Econometrics , 139, 105115.10.1016/j.jeconom.2006.06.006CrossRefGoogle Scholar
Manski, C. (2009). Diversified treatment under ambiguity. International Economic Review , 50, 10131041.10.1111/j.1468-2354.2009.00558.xCrossRefGoogle Scholar
Manski, C. (2021). Econometrics for decision making: Building foundations sketched by Haavelmo and Wald. Econometrica , 89, 28272853.10.3982/ECTA17985CrossRefGoogle Scholar
Molinari, F. (2020). Microeconometrics with partial identification. In Durlauf, S., Hansen, L., Heckman, J., & Matzkin, R. (Eds.), Handbook of econometrics (Vol. 7A, pp. 355486). Elsevier.10.1016/bs.hoe.2020.05.002CrossRefGoogle Scholar
Moon, H., & Schorfheide, F. (2012). Bayesian and frequentist inference in partially identified models. Econometrica , 80, 755782.Google Scholar
Savage, L. (1951). The theory of statistical decision. Journal of the American Statistical Association , 46, 5567.10.1080/01621459.1951.10500768CrossRefGoogle Scholar
Stock, J., Wright, J., & Yogo, M. (2002). A survey of weak instruments and weak identification in generalized method of moments. Journal of Business and Economic Statistics , 20, 518529.10.1198/073500102288618658CrossRefGoogle Scholar
Stoye, J. (2009). Minimax regret treatment choice with finite samples. Journal of Econometrics , 151, 7081.10.1016/j.jeconom.2009.02.013CrossRefGoogle Scholar
Stoye, J. (2012). Minimax regret treatment choice with covariates or with limited validity of experiments. Journal of Econometrics , 166, 138156.10.1016/j.jeconom.2011.06.012CrossRefGoogle Scholar
Wald, A. (1950). Statistical decision functions . Wiley.Google Scholar
Walley, P. (1991). Statistical reasoning with imprecise probabilities . Chapman and Hall.10.1007/978-1-4899-3472-7CrossRefGoogle Scholar