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Numerical Analysis in Least Squares Regression with an Application to the Abortion‐Crime Debate

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  • William Anderson
  • Martin T. Wells

Abstract

Concepts of numerical analysis with applications to least squares problems are introduced in a manner the practitioner can readily apply to his or her own research problems, especially in the social sciences. Numerical analysis is mainly concerned with the accuracy and stability of numerical algorithms. We frame these concerns in terms of forward and backward error, two important concepts in helping understand the quality of the computed answers. The goal of numerical computing is to obtain correct, approximate answers to the true solution. We extended this forward and backward error framework to issues in least squares problems and check the condition of the regression problem via condition numbers. The more ill‐conditioned the data are, the more sensitive the computed solution is to perturbations in the data, and the more unstable the computed solutions become. Condition numbers can also be used to signal the presence of solution degrading collinearity in regression problems. We apply the various numerical analysis tools outlined with some model diagnostics to the abortion‐crime debate, and show the regression analysis used in various papers addressing the abortion‐crime debate cannot be trusted.

Suggested Citation

  • William Anderson & Martin T. Wells, 2008. "Numerical Analysis in Least Squares Regression with an Application to the Abortion‐Crime Debate," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 5(4), pages 647-681, December.
    • Handle: RePEc:wly:empleg:v:5:y:2008:i:4:p:647-681
    DOI: 10.1111/j.1740-1461.2008.00137.x
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    References listed on IDEAS

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    1. Kumar, T Krishna, 1975. "Multicollinearity in Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 57(3), pages 365-366, August.
    2. John J. Donohue & Steven D. Levitt, 2006. "Measurement Error, Legalized Abortion, and the Decline in Crime: A Response to Foote and Goetz (2005)," NBER Working Papers 11987, National Bureau of Economic Research, Inc.
    3. Christopher L. Foote & Christopher F. Goetz, 2005. "Testing economic hypotheses with state-level data: a comment on Donohue and Levitt (2001)," Working Papers 05-15, Federal Reserve Bank of Boston.
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    Cited by:

    1. Theodore Eisenberg, 2012. "Methodological Issues in the Analysis of Longitudinal Data," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 168(1), pages 54-57.
    2. Johanna Catherine MacLean & Asia Sikora Kessler & Donald S. Kenkel, 2016. "Cigarette Taxes and Older Adult Smoking: Evidence from the Health and Retirement Study," Health Economics, John Wiley & Sons, Ltd., vol. 25(4), pages 424-438, April.
    3. Michał Brzeziński & Maria Halber, 2012. "Testing the Perturbation Sensitivity of Abortion-Crime Regressions," Contemporary Economics, University of Economics and Human Sciences in Warsaw., vol. 6(2), June.
    4. Theodore Eisenberg & Thomas Eisenberg & Martin T. Wells & Min Zhang, 2015. "Addressing the Zeros Problem: Regression Models for Outcomes with a Large Proportion of Zeros, with an Application to Trial Outcomes," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 12(1), pages 161-186, March.
    5. Michelle M. Miller, 2015. "Social Networks and Personal Bankruptcy," Journal of Empirical Legal Studies, John Wiley & Sons, vol. 12(2), pages 289-310, June.

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