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Power Law Heteroskedasticity

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  • David J. Price

Abstract

Power laws are common in economics, as in city and firm sizes, and can cause extreme heteroskedasticity. I show that estimators based on observations exhibiting this extreme heteroskedasticity may not be consistent or asymptotically normal and may have unreliable confidence intervals. These problems can occur even without heteroskedasticity if weighted estimators are used. I construct a quasi-maximum likelihood estimator to form more accurate estimates and more reliable inference. This estimator is broadly useful when weighting is considered to improve estimators' precision. Simulations confirm it improves estimation precision and inference, while a replication shows it can lead to substantially different results.

Suggested Citation

  • David J. Price, 2026. "Power Law Heteroskedasticity," Working Papers tecipa-822, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-822
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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