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Linearity in Instrumental Variables Estimation: Problems and Solutions

  • Mogstad, Magne

    ()

    (University of Chicago)

  • Wiswall, Matthew

    ()

    (Arizona State University)

The linear IV estimator, in which the dependent variable is a linear function of a potentially endogenous regressor, is a major workhorse in empirical economics. When this regressor takes on multiple values, the linear specification restricts the marginal effects to be constant across all margins. This paper investigates the problems caused by the linearity restriction in IV estimation, and discusses possible remedies. We first examine the biases due to nonlinearity in the commonly used tests for non-zero treatment effects, selection bias, and instrument validity. Next, we consider three applications where theory suggests a nonlinear relationship, yet previous research has used linear IV estimators. We find that relaxing the linearity restriction in the IV estimation changes the qualitative conclusions about the relevant economic theory and the effectiveness of different policies.

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Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 5216.

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Length: 55 pages
Date of creation: Sep 2010
Date of revision:
Handle: RePEc:iza:izadps:dp5216
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  1. Philip Oreopoulos & Marianne Page & Ann Huff Stevens, 2005. "The Intergenerational Effect of Worker Displacement," NBER Working Papers 11587, National Bureau of Economic Research, Inc.
  2. Løken, Katrine Vellesen & Mogstad, Magne & Wiswall, Matthew, 2011. "What Linear Estimators Miss: The E ects of Family Income on Child Outcomes," Working Papers in Economics 02/11, University of Bergen, Department of Economics.
  3. Julio Cáceres-Delpiano, 2006. "The Impacts of Family Size on Investment in Child Quality," Journal of Human Resources, University of Wisconsin Press, vol. 41(4).
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