An Odd Couple: Monotone Instrumental Variables and Binary Treatments

Richey, Jeremiah (2013): An Odd Couple: Monotone Instrumental Variables and Binary Treatments.

Abstract

This paper investigates Monotone Instrumental Variables (MIV) and their ability to aid in identifying treatment effects when the treatment is binary in a nonparametric bounding framework. I show that an MIV can only aid in identification beyond that of a Monotone Treatment Selection assumption if for some region of the instrument the observed conditional-on-received-treatment outcomes exhibit monotonicity in the instrument in the opposite direction as that assumed by the MIV in a Simpson's Paradox-like fashion. Furthermore, an MIV can only aid in identification beyond that of a Monotone Treatment Response assumption if for some region of the instrument either the above Simpson's Paradox-like relationship exists or the instrument's indirect effect on the outcome (as through its influence on treatment selection) is the opposite of its direct effect as assumed by the MIV. The implications of the main findings for empirical work are discussed and the results are highlighted with an application investigating the effect of criminal convictions on job match quality using data from the 1997 National Longitudinal Survey of the Youth. Though the main results are shown to hold only for the binary treatment case in general, they are shown to have important implications for the multi-valued treatment case as well.

• Item Type: MPRA Paper
• Language: English
• Keywords: Instrumental variables, Nonparametric bounds, Partial identification, Criminal convictions
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; J - Labor and Demographic Economics > J6 - Mobility, Unemployment, Vacancies, and Immigrant Workers > J63 - Turnover ; Vacancies ; Layoffs; K - Law and Economics > K4 - Legal Procedure, the Legal System, and Illegal Behavior > K40 - General

References

Black, Dan (1995). ``Discrimination in an Equilibrium Search Model'' Journal of Labor Economics, 13, 309-334.

de Haan, Monique (2011). ``The Effect of Parents' Schooling on Child's Schooling: A Nonparametric Bounds Analysis" Journal of Labor Economics, 29(4), 859-892.

Gerfin, Michael, Martin Schellhorn (2006). ``Nonparametric Bounds on the Effect of Deductibles in Health Care Insurance on Doctor Visits - Swiss Evidence" Health Economics, 15, 1011 - 1020.

Gonzalez, Libertad (2005). ``Nonparametric Bounds on the Returns to Language Skills" Journal of Applied Econometrics, 20, 771-795.

Holzer, Harry J. (2007). ``Collateral Costs: The Effects of Incarceration on the Employment and Earnings of Young Workers" IZA Discussion Paper No. 3118

Imbens, Guido, Joshua Angrist (1994) ``Identification and Estimation of Local Average Treatment Effects" Econometrica, 62, 467-475.

Kang, Changhui (2011) ``Family Size and Educational Investments in Children: Evidence from Private Tutoring Expenditures in South Korea" Oxford Bulletin of Economics and Statistics, 73.

Kreider, Brent and John Pepper (2007). ``Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors" Journal of the American Statistical Association, 102, 432-441.

Manski, Charles (1990). ``Nonparametric Bounds on Treatment Effects'' American Economic Review, Papers and Procedings, 80, 319-23.

Manski, Charles (1997). ``Monotone Treatment Response'' Econometrica, 65, 1311-1334.

Manski, Charles. Partial Identification of Probability Distributions. New York, NY: Springer-Verlag, 2003

Manski, Charles and John Pepper (2000). ``Monotone Instrumental Variables: With an Application to the Returns to Schooling'' Econometrica, 68, 997-1010.

Nevo, Aviv and Adam M. Rosen (2012). ``Identification With Imperfect Instruments'' Review of Economics and Statistics, 94, 659-671.

U.S. Department of Justice. Office of Justice Programs. Bureau of Justice Statistics. 2010.Bulletin: Correctional Population in the United States, 2009. Washington, D.C.: U.S. Government Printing Office.