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Identifying Demand Elasticity via Heteroscedasticity. A Panel GMM Approach to Estimation and Inference

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Abstract

This paper introduces a panel GMM framework for identifying and estimating demand elasticities via heteroscedasticity. While existing panel estimators address the simultaneity problem, the state-ofthe-art Feenstra/Soderbery (F/S) estimator suffers from inconsistency, inefficiency, and lacks a valid framework for inference. We develop a constrained GMM (C-GMM) estimator that is consistent and derive a uniform formula of its asymptotic standard error that is valid even at the boundary of the parameter space. A Monte Carlo study demonstrates the consistency of the C-GMM estimator and shows that it substantially reduces bias and root mean squared error compared to the F/S estimator. Unlike the F/S estimator, the C-GMM estimator maintains high coverage of confidence intervals across a wide range of sample sizes and parameter values, enabling more reliable inference.

Suggested Citation

  • Thomas von Brasch & Arvid Raknerud & Trond C. Vigtel, 2024. "Identifying Demand Elasticity via Heteroscedasticity. A Panel GMM Approach to Estimation and Inference," Discussion Papers 1015, Statistics Norway, Research Department.
    • Handle: RePEc:ssb:dispap:1015
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    File URL: https://www.ssb.no/en/virksomheter-foretak-og-regnskap/virksomheter-og-foretak/artikler/identifying-demand-elasticity-via-heteroscedasticity/_/attachment/inline/b5c30dc1-76d2-4474-b4b5-8ff5066f6d2d:75c6e5ad12bc48b5859214319c4ebbed9ef628c6/DP1015.pdf
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    More about this item

    Keywords

    Demand Elasticity; Panel Data; Heteroscedasticity; GMM; Constrained Estimation; Bagging;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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