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Computing, the bootstrap and economics

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  • Russell Davidson

Abstract

A major contention in this paper is that scientific models can be viewed as virtual realities, implemented, or rendered, by mathematical equations or by computer simulations. Their purpose is to help us understand the external reality that they model. In economics, particularly in econometrics, models make use of random elements, so as to provide quantitatively for phenomena that we cannot or do not wish to model explicitly. By varying the realizations of the random elements in a simulation, it is possible to study counterfactual outcomes, which are necessary for any discussion of causality. The bootstrap is virtual reality within an outer reality. The principle of the bootstrap is that, if its virtual reality mimics as closely as possible the reality that contains it, it can be used to study aspects of that outer reality. The idea of bootstrap iteration is explored, and a discrete model discussed that allows investigators to perform iteration to any desired level. Informatique, techniques de bootstrap, et sciences économiques. Une affirmation importante de ce texte est que les modèles scientifiques peuvent être considérés comme des réalités virtuelles, mises en œuvre ou traduites dans des équations mathématiques ou dans des simulations par ordinateur. Leur objectif est d’aider à comprendre la réalité externe qu’on modélise. En sciences économiques, et en particulier en économétrie, les modèles font usage d’éléments aléatoires pour prendre en compte quantitativement des phénomènes qu’on ne peut pas ou qu’on ne veut pas modéliser explicitement. En modifiant l’empreinte des facteurs aléatoires dans une simulation, il est possible d’étudier des résultats alternatifs qui sont nécessaires pour toute discussion de causalité. Les techniques de bootstrap produisent une réalité virtuelle à l’intérieur d’une réalité englobante. Le principe est que, si la réalité virtuelle approxime le plus près possible la réalité qui la contient, elle peut être utilisée pour étudier certains aspects de la réalité englobante. L’idée d’une itération de bootstrap est explorée, et un modèle discret est discuté qui permet aux chercheurs de procéder par itération jusqu’au niveau désiré.

Suggested Citation

  • Russell Davidson, 2015. "Computing, the bootstrap and economics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 48(4), pages 1195-1214, November.
    • Handle: RePEc:wly:canjec:v:48:y:2015:i:4:p:1195-1214
    DOI: 10.1111/caje.12158
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    References listed on IDEAS

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    1. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    2. Davidson, Russell, 2017. "A discrete model for bootstrap iteration," Journal of Econometrics, Elsevier, vol. 201(2), pages 228-236.
    3. Ashenfelter, Orley & Card, David, 1985. "Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs," The Review of Economics and Statistics, MIT Press, vol. 67(4), pages 648-660, November.
    4. Heckman, James J., 2001. "Econometrics and empirical economics," Journal of Econometrics, Elsevier, vol. 100(1), pages 3-5, January.
    5. Davidson, Russell & MacKinnon, James G., 2006. "The power of bootstrap and asymptotic tests," Journal of Econometrics, Elsevier, vol. 133(2), pages 421-441, August.
    6. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 95(2), pages 375-389, April.
    7. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    8. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-552, September.
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    Cited by:

    1. M. Mouchart & R. Orsi & G. Wunsch, 2020. "Causality in Econometric Modeling. From Theory to Structural Causal Modeling," Working Papers wp1143, Dipartimento Scienze Economiche, Universita' di Bologna.
    2. Boldea, Otilia & Cornea-Madeira, Adriana & Hall, Alastair R., 2019. "Bootstrapping structural change tests," Journal of Econometrics, Elsevier, vol. 213(2), pages 359-397.
    3. Russell Davidson & Victoria Zinde-Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics, Canadian Economics Association, vol. 50(5), pages 1595-1631, December.
    4. Davidson, Russell & Trokić, Mirza, 2020. "The fast iterated bootstrap," Journal of Econometrics, Elsevier, vol. 218(2), pages 451-475.

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    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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