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  • Karim Chalak (a1)

We study the consequences of substituting an error-laden proxy W for an instrument Z on the interpretation of Wald, local instrumental variable (LIV), and instrumental variable (IV) estimands in an ordered discrete choice structural system with heterogeneity. A proxy W need only satisfy an exclusion restriction and that the treatment and outcome are mean independent from W given Z. Unlike Z, W need not satisfy monotonicity and may, under particular specifications, fail exogeneity. For example, W could code Z with error, with missing observations, or coarsely. We show that Wald, LIV, and IV estimands using W identify weighted averages of local or marginal treatment effects (LATEs or MTEs). We study a necessary and sufficient condition for nonnegative weights. Further, we study a condition under which the Wald or LIV estimand using W identifies the same LATE or MTE that would have been recovered had Z been observed. For example, this holds for binary Z and therefore the Wald estimand using W identifies the same “average causal response,” or LATE for binary treatment, that would have been recovered using Z. Also, under this condition, LIV using W can be used to identify MTE and average treatment effects for e.g., the population, treated, and untreated.

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*Address correspondence to Karim Calak, Department of Economics, University of Virginia, P.O. Box 400182, Charlottesville, VA 22904-4182, email:
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D. Acemoglu , S. Johnson , & J. Robinson (2001) The colonial origins of comparative development: An empirical investigation. American Economic Review 91, 13691401.

J. Angrist , K. Graddy , & G. Imbens (2000) The interpretation of instrumental variables estimators in simultaneous equations models with an application to the demand for fish. The Review of Economic Studies 67, 499527.

J. Angrist & G. Imbens (1995) Two–stage least squares estimation of average causal effects in models with variable treatment intensity. Journal of the American Statistical Association 90, 431442.

J. Angrist , G. Imbens , & D. Rubin (1996) Identification of causal effects using instrumental variables. Journal of the American Statistical Association 91, 444472 (with discussion).

D Card . (1999) The causal effect of education on earnings. In O. Ashenfelter & D. Card (eds.), Handbook of Labor Economics, vol. 3, Part A. Elsevier.

J Heckman . (1996) Identification of causal effects using instrumental variables: Comment. Journal of the American Statistical Association 91, 459462.

J. Heckman , S. Urzua , & E. Vytlacil (2006) Understanding instrumental variables in models with essential heterogeneity. Review of Economics and Statistics 88, 389432.

P.W Holland . (1986) Statistics and causal inference. Journal of the American Statistical Association 81, 945970 (with discussion).

V. Hotz , C. Mullin , & S. Sanders (1997) Bounding causal effects using data from a contaminated natural experiment: Analyzing the effects of teenage childbearing. The Review of Economic Studies 64, 575603.

A Mahajan . (2006) Identification and estimation of regression models with misclassification. Econometrica 74, 631665.

E Vytlacil . (2006) Ordered discrete-choice selection models: Equivalence, nonequivalence, and representation results. Review of Economics and Statistics 88, 578581.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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