Document Type

Working Paper


Summer 7-2014


Treatment Effects, Dynamic Treatment Decisions, Partial Identification, Unobserved Heterogeneity, Stochastic Dominance, Panel Data




Working Papers Series


Economics | Health Policy | Public Affairs, Public Policy and Public Administration | Public Economics | Social Welfare


We propose the sharp identifiable bounds of the distribution functions of potential outcomes using a panel with fixed T. We allow for the possibility that the statistical randomization of treatment assignments is not achieved until unobserved heterogeneity is properly controlled for. We use certain stationarity assumptions to obtain the bounds. Dynamics in the treatment decisions is allowed as long as the stationarity assumptions are satisfied. In particular, we present an example where our assumptions are satisfied and the treatment decision of the present time may depend on the treatments and the observed outcomes of the past. As an empirical illustration we study the effect of smoking during pregnancy on infant birth weights. We found that for the group of switchers the birth weight with smoking is first order stochastically dominated by that with non-smoking.

Additional Information

Working paper no. 169

Authors appreciate Chris Bennett, Charles Brown, Yanqin Fan, Jin Hahn, Stefan Hoderlein, Han Hong, Kyoo il Kim, Simon Lee, Maria Ponomareva, Joris Pinkse, Christoph Rothe, Jeff Smith, and Ivan Fernandez-Val for their various constructive comments and suggestions. Also they thank seminar participants at various universities and conferences. Jun thanks the Human Capital Foundation (, especially Andrey P. Vavilov, for their support of CAPCP ( at Penn State University; Lee acknowledges financial support from Livingston Research Scholar Award, University of Michigan; and Shin thanks the Social Science and Humanities Research Council of Canada (SSHRCC) for the research grant.All remaining errors are there own

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