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Calibration and IV Estimation of a Wage Outcome Equation in a Dynamic Environment


  • Belzil, Christian

    () (Ecole Polytechnique, Paris)

  • Hansen, Jörgen

    () (Concordia University)


We consider an artificial population of forward looking heterogeneous agents making decisions between schooling, employment, employment with training and household production, according to a behavioral model calibrated to a large set of stylized facts. Some of these agents are subject to policy interventions (a higher education subsidy) that vary according to their generosity. We evaluate the capacity of Instrumental Variable (IV) methods to recover the population Local Average Treatment Effect (LATE) and analyze the economic implications of using a strong instrument within a dynamic economic model. We also examine the performances of two sampling designs that may be used to improve classical linear IV; a Regression-Discontinuity (RD) design and an age-based sampling design targeting early career wages. Finally, we investigate the capacity of IV to estimate alternative "causal" parameters. The failure of classical linear IV is spectacular. IV fails to recover the true LATE, even in the static version of the model. In some cases, the estimates lie outside the support of the population distribution of returns to schooling and are nearly twice as large as the population LATE. The trade-off between the statistical power of the instrument and dynamic self-selection caused by the policy shock implies that access to a "strong instrument" is not necessarily desirable. There appears to be no obvious realistic sampling design that can guarantee IV accuracy. Finally, IV also fails to estimate the reduced-form marginal effect of schooling on wages of those affected by the experiment. Within a dynamic setting, IV is deprived of any “causal” substance.

Suggested Citation

  • Belzil, Christian & Hansen, Jörgen, 2008. "Calibration and IV Estimation of a Wage Outcome Equation in a Dynamic Environment," IZA Discussion Papers 3528, Institute for the Study of Labor (IZA).
  • Handle: RePEc:iza:izadps:dp3528

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    References listed on IDEAS

    1. Keane, Michael P., 2010. "Structural vs. atheoretic approaches to econometrics," Journal of Econometrics, Elsevier, vol. 156(1), pages 3-20, May.
    2. Belzil, Christian & Hansen, Jorgen, 2007. "A structural analysis of the correlated random coefficient wage regression model," Journal of Econometrics, Elsevier, vol. 140(2), pages 827-848, October.
    3. van den Berg, Gerard J., 2007. "An Economic Analysis of Exclusion Restrictions for Instrumental Variable Estimation," IZA Discussion Papers 2585, Institute for the Study of Labor (IZA).
    4. Heckman, James J & Lochner, Lance & Taber, Christopher, 1998. "General-Equilibrium Treatment Effects: A Study of Tuition Policy," American Economic Review, American Economic Association, vol. 88(2), pages 381-386, May.
    5. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    6. Belzil, Christian, 2007. "The return to schooling in structural dynamic models: a survey," European Economic Review, Elsevier, vol. 51(5), pages 1059-1105, July.
    7. Thierry Magnac & David Thesmar, 2002. "Identifying Dynamic Discrete Decision Processes," Econometrica, Econometric Society, vol. 70(2), pages 801-816, March.
    8. Christian Belzil, 2008. "Testing the Specification of the Mincer Wage Equation," Annals of Economics and Statistics, GENES, issue 91-92, pages 427-451.
    9. Kenneth I. Wolpin & Petra E. Todd, 2006. "Assessing the Impact of a School Subsidy Program in Mexico: Using a Social Experiment to Validate a Dynamic Behavioral Model of Child Schooling and Fertility," American Economic Review, American Economic Association, vol. 96(5), pages 1384-1417, December.
    10. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    11. Chari, V.V. & Kehoe, Patrick J. & McGrattan, Ellen R., 2008. "Are structural VARs with long-run restrictions useful in developing business cycle theory?," Journal of Monetary Economics, Elsevier, vol. 55(8), pages 1337-1352, November.
    12. Christian Belzil & Jörgen Hansen, 2002. "Unobserved Ability and the Return to Schooling," Econometrica, Econometric Society, vol. 70(5), pages 2075-2091, September.
    13. Wilbert van der Klaauw, 2002. "Estimating the Effect of Financial Aid Offers on College Enrollment: A Regression-Discontinuity Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1249-1287, November.
    14. Keane, Michael P & Wolpin, Kenneth I, 1997. "The Career Decisions of Young Men," Journal of Political Economy, University of Chicago Press, vol. 105(3), pages 473-522, June.
    15. repec:adr:anecst:y:2008:i:91-92:p:19 is not listed on IDEAS
    16. Susumu Imai & Michael P. Keane, 2004. "Intertemporal Labor Supply and Human Capital Accumulation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 601-641, May.
    17. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    18. James Heckman, 1997. "Instrumental Variables: A Study of Implicit Behavioral Assumptions Used in Making Program Evaluations," Journal of Human Resources, University of Wisconsin Press, vol. 32(3), pages 441-462.
    19. repec:adr:anecst:y:2008:i:91-92 is not listed on IDEAS
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    Cited by:

    1. Belzil, Christian & Hansen, Jörgen & Kristensen, Nicolai, 2008. "Estimating Complementarity between Education and Training," IZA Discussion Papers 3882, Institute for the Study of Labor (IZA).
    2. Ge, Suqin, 2013. "Estimating the returns to schooling: Implications from a dynamic discrete choice model," Labour Economics, Elsevier, vol. 20(C), pages 92-105.
    3. Belzil, Christian & Poinas, François, 2010. "Education and early career outcomes of second-generation immigrants in France," Labour Economics, Elsevier, vol. 17(1), pages 101-110, January.

    More about this item


    dynamic discrete choice; dynamic programming; treatment effects; weak instruments; instrumental variable; returns to schooling;

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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