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What to Do When Your Hessian is Not Invertible

Author

Listed:
  • Jeff Gill

    (University of California, Davis)

  • Gary King

    (Harvard University)

Abstract

What should a researcher do when statistical analysis software terminates before completion with a message that the Hessian is not invertible? The standard textbook advice is to respecify the model, but this is another way of saying that the researcher should change the question being asked. Obviously, however, computer programs should not be in the business of deciding what questions are worthy of study. Although noninvertable Hessians are sometimes signals of poorly posed questions, nonsensical models, or inappropriate estimators, they also frequently occur when information about the quantities of interest exists in the data through the likelihood function. The authors explain the problem in some detail and lay out two preliminary proposals for ways of dealing with noninvertable Hessians without changing the question asked.

Suggested Citation

  • Jeff Gill & Gary King, 2004. "What to Do When Your Hessian is Not Invertible," Sociological Methods & Research, , vol. 33(1), pages 54-87, August.
    • Handle: RePEc:sae:somere:v:33:y:2004:i:1:p:54-87
    DOI: 10.1177/0049124103262681
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    References listed on IDEAS

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    1. Berger, James, 1976. "Minimax estimation of a multivariate normal mean under arbitrary quadratic loss," Journal of Multivariate Analysis, Elsevier, vol. 6(2), pages 256-264, June.
    2. Leamer, Edward E, 1973. "Multicollinearity: A Bayesian Interpretation," The Review of Economics and Statistics, MIT Press, vol. 55(3), pages 371-380, August.
    3. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
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    Cited by:

    1. Spyridon Stavropoulos & Martijn J. Burger & Dimitris Skuras, 2015. "Data Sparseness and Variance in Accounting Profitability," Tinbergen Institute Discussion Papers 15-014/VII, Tinbergen Institute.
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    3. David C Broadstock & Lester C Hunt, 2013. "Tying up loose ends: A note on the impact of omitting MA residuals from panel energy demand models based on the Koyck lag transformation," Surrey Energy Economics Centre (SEEC), School of Economics Discussion Papers (SEEDS) 140, Surrey Energy Economics Centre (SEEC), School of Economics, University of Surrey.
    4. Jaromír Kovářík & Friederike Mengel & José Gabriel Romero, 2018. "Learning in network games," Quantitative Economics, Econometric Society, vol. 9(1), pages 85-139, March.
      • Kovarik, Jaromir & Mengel, Friederike & Romero, José Gabriel, 2012. "Learning in Network Games," IKERLANAK http://www-fae1-eao1-ehu-, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    5. David Greenstreet, 2007. "Exploiting Sequential Learning to Estimate Establishment-Level Productivity Dynamics and Decision Rules," Economics Series Working Papers 345, University of Oxford, Department of Economics.
    6. Caroline Buts & Cind Du Bois, 2017. "Military deployment and international terrorism: do location and mission type matter?," Defence and Peace Economics, Taylor & Francis Journals, vol. 28(6), pages 621-633, November.

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