arXiv 28 Jan 2020 · Econometrics
arXiv:2001.10586 · PDF · DOI · OpenAlex · Extracted main text
This paper shows how to shrink extremum estimators towards inequality constraints motivated by economic theory. We propose an Inequality Constrained Shrinkage Estimator (ICSE) which takes the form of a weighted average between the unconstrained and inequality constrained estimators with the data dependent weight. The weight drives both the direction and degree of shrinkage. We use a local asymptotic framework to derive the asymptotic distribution and risk of the ICSE. We provide conditions under which the asymptotic risk of the ICSE is strictly less than that of the unrestricted extremum estimator. The degree of shrinkage cannot be consistently estimated under the local asymptotic framework. To address this issue, we propose a feasible plug-in estimator and investigate its finite sample behavior. We also apply our framework to gasoline demand estimation under the Slutsky restriction.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hansen, Bruce E (2016) Efficient shrinkage in parametric models | 0.909 | 8 | 5 | 75% |
| 2 | Andrews, Donald WK (1999) Estimation when a parameter is on a boundary | 0.874 | 6 | 3 | 67% |
| 3 | Fessler, Pirmin, Kasy, Maximilian (2019) How to use economic theory to improve estimators: Shrinking toward theoretical restrictions | 0.874 | 6 | 3 | 67% |
| 4 | Hjort, Nils Lid, Claeskens, Gerda (2003) Frequentist model average estimators | 0.737 | 3 | 2 | 100% |
| 5 | James, William, Stein, Charles M (1961) Estimation with quadratic loss | 0.737 | 3 | 2 | 100% |
| 6 | Chernoff, Herman (1954) On the distribution of the likelihood ratio | 0.644 | 2 | 2 | 100% |
| 7 | Feder, Paul I (1968) On the distribution of the log likelihood ratio test statistic when the true parameter is near the boundaries of the hypothesis… | 0.644 | 2 | 2 | 100% |
| 8 | Liu, Chu-An (2015) Distribution theory of the least squares averaging estimator | 0.644 | 2 | 2 | 100% |
| 9 | Pollard, David (1985) New ways to prove central limit theorems | 0.644 | 2 | 2 | 100% |
| 10 | Blundell, Richard, Horowitz, Joel L, Parey, Matthias (2012) Measuring the price responsiveness of gasoline demand: Economic shape restrictions and nonparametric demand estimation | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 38 scored citations.