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Standard Errors for Regression-Based Causal Effect Estimates in Economics Using Numerical Derivatives

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  • Joseph V. Terza

    (Indiana University School of Liberal Arts at IUPUI)

Abstract

The aim of nearly all empirical studies in economics is to provide scientific evidence that can be used to assess policy relevant cause-and-effect. In the context of the general potential outcomes framework, we review how a causal effect parameter can be rigorously but tractably specified, identified and estimated along with its asymptotic standard error. For cases in which the analytic and computational requirements for calculation of the ASE are challenging, we suggest the use of numerical derivatives (ND). We detail the specific type of ND software required for this purpose, and note that it is offered as a feature in most statistical packages. As an illustration, we analyze the causal effect of wife's high school graduation on family size using the Stata/Mata deriv command. Code for this example is supplied in an appendix.

Suggested Citation

  • Joseph V. Terza, 2025. "Standard Errors for Regression-Based Causal Effect Estimates in Economics Using Numerical Derivatives," Computational Economics, Springer;Society for Computational Economics, vol. 65(1), pages 69-89, January.
    • Handle: RePEc:kap:compec:v:65:y:2025:i:1:d:10.1007_s10614-024-10565-w
    DOI: 10.1007/s10614-024-10565-w
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    References listed on IDEAS

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    1. Terza Joseph V., 2020. "Regression-Based Causal Analysis from the Potential Outcomes Perspective," Journal of Econometric Methods, De Gruyter, vol. 9(1), pages 1-15, January.
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    3. Joseph V. Terza, 2017. "Causal effect estimation and inference using Stata," Stata Journal, StataCorp LLC, vol. 17(4), pages 939-961, December.
    4. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
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    6. Sellers,Kimberly F., 2023. "The Conway–Maxwell–Poisson Distribution," Cambridge Books, Cambridge University Press, number 9781108481106, June.
    7. Weiren Wang & Felix Famoye, 1997. "Modeling household fertility decisions with generalized Poisson regression," Journal of Population Economics, Springer;European Society for Population Economics, vol. 10(3), pages 273-283.
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