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COMPLEMENTARITY AND IDENTIFICATION

Published online by Cambridge University Press:  20 September 2016

Tate Twinam
Tate Twinam*
Affiliation:
University of Washington
*
*Address correspondence to Tate Twinam, 18115 Campus Way NE, Bothell, WA 98011, USA; e-mail: [email protected].
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Abstract

This paper examines the identification power of assumptions that formalize the notion of complementarity in the context of a nonparametric bounds analysis of treatment response. I extend the literature on partial identification via shape restrictions by exploiting cross-dimensional restrictions on treatment response when treatments are multidimensional; the assumption of supermodularity can strengthen bounds on average treatment effects in studies of policy complementarity. This restriction can be combined with a statistical independence assumption to derive improved bounds on treatment effect distributions, aiding in the evaluation of complex randomized controlled trials. Complementarities arising from treatment effect heterogeneity can be incorporated through supermodular instrumental variables to strengthen identification in studies with one or multiple treatments. An application examining the long-run impact of zoning on the evolution of urban spatial structure illustrates the value of the proposed identification methods.

Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 5 , October 2017 , pp. 1154 - 1185
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

I am indebted to Arie Beresteanu for his support and feedback on multiple drafts. Additionally, constructive comments from two anonymous referees and the editors Victor Chernozhukov and Peter Phillips substantially improved the quality of the paper.

References

REFERENCES

Aradillas-Lopez, A. & Tamer, E. (2008) The identification power of equilibrium in simple games. Journal of Business & Economic Statistics 26(3), 261–283.CrossRefGoogle Scholar
Beresteanu, A. (2005) Nonparametric analysis of cost complementarities in the telecommunications industry. RAND Journal of Economics 36(4), 870–889.Google Scholar
Beresteanu, A. (2007) Nonparametric estimation of regression functions under restrictions on partial derivatives. Unpublished manuscript.Google Scholar
Bhattacharya, J., Shaikh, A.M., & Vytlacil, E. (2008) Treatment effect bounds under monotonicity assumptions: An application to Swan–Ganz catheterization. American Economic Review 98(2), 351–356.CrossRefGoogle Scholar
Bhattacharya, J., Shaikh, A.M., & Vytlacil, E. (2012) Treatment effect bounds: An application to Swan–Ganz catheterization. Journal of Econometrics 168(2), 223–243.CrossRefGoogle Scholar
Bitler, M.P., Gelbach, J.B., & Hoynes, H.W. (2006) What mean impacts miss: Distributional effects of welfare reform experiments. American Economic Review 96(4), 988–1012.CrossRefGoogle Scholar
Bitler, M.P., Gelbach, J.B., & Hoynes, H.W. (2008) Distributional impacts of the self-sufficiency project. Journal of Public Economics 92(3), 748–765.CrossRefGoogle Scholar
Bitler, M.P., Gelbach, J.B., & Hoynes, H.W. (2014) Can variation in subgroups’ average treatment effects explain treatment effect heterogeneity? Evidence from a social experiment. NBER Working Paper 20142.CrossRefGoogle Scholar
Blundell, R., Gosling, A., Ichimura, H., & Meghir, C. (2007) Changes in the distribution of male and female wages accounting for employment composition using bounds. Econometrica 75(2), 323–363.CrossRefGoogle Scholar
Cattaneo, M.D. (2010) Multi-valued treatment effects. In Durlauf, S.N. & Blume, L.E. (eds.), New Palgrave Dictionary of Economics, Palgrave Macmillan, pp. 855–857.Google Scholar
Chernozhukov, V., Kim, W., Lee, S., & Rosen, A.M. (2015) Implementing intersection bounds in Stata. Stata Journal 15(1), 21–44.CrossRefGoogle Scholar
Chernozhukov, V., Lee, S., & Rosen, A.M. (2013) Intersection bounds: Estimation and inference. Econometrica 81(2), 667–737.Google Scholar
Cox, D.R. (1958) Planning of Experiments. Wiley.Google Scholar
Djebbari, H. & Smith, J. (2008) Heterogeneous impacts in PROGRESA. Journal of Econometrics 145(1), 64–80.CrossRefGoogle Scholar
Eeckhout, J. & Kircher, P. (2011) Identifying sorting – In theory. Review of Economic Studies 78(3), 872–906.CrossRefGoogle Scholar
Fan, Y. & Park, S.S. (2010) Sharp bounds on the distribution of treatment effects and their statistical inference. Econometric Theory 26, 931–951.CrossRefGoogle Scholar
Feller, A. & Holmes, C.C. (2009) Beyond toplines: Heterogeneous treatment effects in randomized experiments. Unpublished manuscript.Google Scholar
Fischel, W.A. (2001) The Homevoter Hypothesis. Harvard University Press.Google Scholar
Frank, M.J., Nelsen, R.B., & Schweizer, B. (1987) Best-possible bounds for the distribution of a sum – A problem of Kolmogorov. Probability Theory and Related Fields 74(2), 199–211.CrossRefGoogle Scholar
Giustinelli, P. (2011) Non-parametric bounds on quantiles under monotonicity assumptions: With an application to the Italian education returns. Journal of Applied Econometrics 26(5), 783–824.CrossRefGoogle Scholar
Graham, B.S., Imbens, G.W., & Ridder, G. (2014) Complementarity and aggregate implications of assortative matching: A nonparametric analysis. Quantitative Economics 5(1), 29–66.CrossRefGoogle Scholar
Gundersen, C., Kreider, B., & Pepper, J.V. (2012) The impact of the National School Lunch Program on child health: A nonparametric bounds analysis. Journal of Econometrics 166(1), 79–91.CrossRefGoogle Scholar
Kreider, B. & Hill, S.C. (2009) Partially identifying treatment effects with an application to covering the uninsured. Journal of Human Resources 44(2), 409–449.CrossRefGoogle Scholar
Kreider, B. & Pepper, J.V. (2007) Disability and employment: Reevaluating the evidence in light of reporting errors. Journal of the American Statistical Association 102(478), 432–441.CrossRefGoogle Scholar
Kreinovich, V. & Ferson, S. (2006) Computing best–possible bounds for the distribution of a sum of several variables is NP–hard. International Journal of Approximate Reasoning 41(3), 331–342.CrossRefGoogle Scholar
Lalive, R., Van Ours, J., & Zweimüller, J. (2006) How changes in financial incentives affect the duration of unemployment. Review of Economic Studies 73(4), 1009–1038.CrossRefGoogle Scholar
Lazzati, N. (2015) Treatment response with social interactions: Partial identification via monotone comparative statics. Quantitative Economics 6(1), 49–83.CrossRefGoogle Scholar
Makarov, G.D. (1982) Estimates for the distribution function of a sum of two random variables when the marginal distributions are fixed. Theory of Probability & its Applications 26(4), 803–806.CrossRefGoogle Scholar
Manski, C.F. (1989) Anatomy of the selection problem. Journal of Human Resources 24(3), 343–360.CrossRefGoogle Scholar
Manski, C.F. (1997) Monotone treatment response. Econometrica 65(6), 1311–1334.CrossRefGoogle Scholar
Manski, C.F. (2003) Partial Identification of Probability Distributions. Springer.Google Scholar
Manski, C.F. (2013) Identification of treatment response with social interactions. Econometrics Journal 16(1), S1–S23.CrossRefGoogle Scholar
Manski, C.F. & Nagin, D.S. (1998) Bounding disagreements about treatment effects: A case study of sentencing and recidivism. Sociological Methodology 28(1), 99–137.CrossRefGoogle Scholar
Manski, C.F. & Pepper, J.V. (2000) Monotone instrumental variables: With an application to the returns to schooling. Econometrica 68(4), 997–1010.CrossRefGoogle Scholar
Manski, C.F. & Pepper, J.V. (2009) More on monotone instrumental variables. Econometrics Journal 12, S200–S216.CrossRefGoogle Scholar
McMillen, D.P. & McDonald, J.F. (1991) A Markov chain model of zoning change. Journal of Urban Economics 30(2), 257–270.CrossRefGoogle Scholar
Molinari, F. & Rosen, A.M. (2008) The identification power of equilibrium in games: The supermodular case. Journal of Business & Economic Statistics 26(3), 297–302.CrossRefGoogle Scholar
Neumark, D. & Wascher, W. (2011) Does a higher minimum wage enhance the effectiveness of the Earned Income Tax Credit? Industrial and Labor Relations Review 64(4), 712–746.CrossRefGoogle Scholar
Pepper, J.V. (2000) The intergenerational transmission of welfare receipt: A nonparametric bounds analysis. Review of Economics and Statistics 82(3), 472–488.CrossRefGoogle Scholar
Rubin, D.B. (1978) Bayesian inference for causal effects: The role of randomization. Annals of Statistics 6(1), 34–58.CrossRefGoogle Scholar
Shertzer, A., Twinam, T., & Walsh, R.P. (2016a) Race, ethnicity, and discriminatory zoning. American Economic Journal: Applied Economics 8(3), 1–31.Google Scholar
Shertzer, A., Twinam, T., & Walsh, R.P. (2016b) Zoning and the economic geography of cities. Unpublished manuscript.CrossRefGoogle Scholar
Tsunao, O. & Usui, E. (2014) Concave–monotone treatment response and monotone treatment selection: With an application to the returns to schooling. Quantitative Economics 5(1), 175–194.Google Scholar
Williamson, R.C. & Downs, T. (1990) Probabilistic arithmetic. I. Numerical methods for calculating convolutions and dependency bounds. International Journal of Approximate Reasoning 4(2), 89–158.CrossRefGoogle Scholar