How should parameter estimation be tailored to the objective?

Peter Hansen and Elena-Ivona Dumitrescu

Journal of Econometrics, 2022, vol. 230, issue 2, 535-558

Abstract: We study parameter estimation from the sample X, when the objective is to maximize the expected value of a criterion function, Q, for a distinct sample, Y. This is the situation that arises when a model is estimated for the purpose of describing other data than those used for estimation, such as in forecasting problems. A natural candidate for solving maxT∈σ(X)EQ(Y,T) is the innate estimator, θˆ=argmaxθQ(X,θ). While the innate estimator has certain advantages, we show that the asymptotically efficient estimator takes the form θ̃=argmaxθQ̃(X,θ), where Q̃ is defined from a likelihood function in conjunction with Q. The likelihood-based estimator is, however, fragile, as misspecification is harmful in two ways. First, the likelihood-based estimator may be inefficient under misspecification. Second, and more importantly, the likelihood approach requires a parameter transformation that depends on the true model, causing an improper mapping to be used under misspecification.

Keywords: Estimation; Model selection; LinEx loss; Multistep forecasting (search for similar items in EconPapers)
JEL-codes: C13 C18 C51 C52 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Working Paper: How Should Parameter Estimation Be Tailored to the Objective? (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:230:y:2022:i:2:p:535-558

DOI: 10.1016/j.jeconom.2020.12.014

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