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Linearity in Instrumental Variables Estimation: Problems and Solutions

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  • Mogstad, Magne

    (University of Chicago)

  • Wiswall, Matthew

    (University of Wisconsin-Madison)

Abstract

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.

Suggested Citation

  • Mogstad, Magne & Wiswall, Matthew, 2010. "Linearity in Instrumental Variables Estimation: Problems and Solutions," IZA Discussion Papers 5216, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp5216
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    More about this item

    Keywords

    linear model; variable treatment intensity; nonlinearity; instrumental variables;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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