© Michael Lechner, 2006, p. 1 (Non-bayesian) Discussion (translation) of Principal Stratification for Causal Inference with Extended Partial Complience by Hui Jin and Don Rubin Mannheim, ZEW, October 2006 Michael Lechner SIAW, ZEW, CEPR, IZA

© Michael Lechner, 2006, p. 2 A statistics paper in an econometric perspective  Perspective 1: An exercise in IV estimation (à la IA ’94 and AIR ’96) Complication: There is only a binary instrument, but we are interested in the effects of multiple treatments in the form of dose responses. A binary instrument is not powerful enough for such comparisons.  Perspective 2: We ‘must’ condition on an endogenous variable (an intermediate outcome) to estimate the effect of interest  Paper shows how to recover the causal effect of interest (!) in such a framework  These problems occur although there is underlying experiment that assigns people to different treatment states  However: Paper uses different language than econometricians do...

© Michael Lechner, 2006, p. 3 An artifical example from the training literature... as translation device  Unemployed want to attend a training programme  UE is randomized in one of 2 programmes, called T and C (Z)  T is tough programme – not much fun, a lot of work, add. human capital  C is a leasurly social experience, no human capital  Each programme has duration of 4 weeks, participants may leave programmes any time (even before they start)  UE have a taste for leasure  Programmes have heterogenous effects

© Michael Lechner, 2006, p. 4 An artifical example from the training literature... as translation device (2)  We want to understand the effect of the programmes on the employment rate 2 years after the start of the programme.  Even more: We may want to understand the effects of a completed programme compared to the other completed programme.  Problem: If we base the analysis on the subsamples of those who complete the programme, we may contaminate the causal inference, because those who realised that they have a low return may have dropped out already.  This type of selection problem is more likely to occur with the tough programme.

© Michael Lechner, 2006, p. 5 Solutions of the identification problems  The paper provides two solutions to this problem (and is VERY clear about the underlying assumptions) 1)Instead of conditioning on the endogenous observable intermediate outcome (programme duration), condition on the potential intermediate outcomes. For example: Compare the person that completed to the tough programme to somebody who participated in the easy programme but would have completed the tough programme and average (unobservable  find other restrictions!). Here, require also same propensity to complete the easy programme 2)Device a hypothetical random experiment that would identify the effects

© Michael Lechner, 2006, p. 6 Z as something like an instrument of D and d Assumptions used in paper  Standard assumptions: SUTVA, Z randomized  Exclusion of direct effect of Z on Y:If a change in Z does not affect (potential) terminating behavior in both programmes, than potential outcomes Y(Z) are the same (plausible in example)  Strong access monotonicity (D(C)=0, d(T)=0): If randomised into the tough programme, there is no way of participating in parts of the easy programme, and conversly... (plausible in strict experiment)  removes 2 of the 4 (partially) unobservables from the playing field... Negative side effect monotonity ( ): If UE would have left nice programme, UE would have left tough programme as well (???) [behavioral assumption]  restricts the remaining unobservable in terms of the observable

© Michael Lechner, 2006, p. 7 Identification and estimation How does identification work without a Bayesian perspective? The missing equation...  Paper shows a Bayesian estimation strategy  For a Non-Bayesian, there remain a couple of open points that center around the equation that is missing in the paper:  Issues: - What is the role of the different assumption in the identification step ? - More specific: For example, what happens if we assume weak (insted of strong) access monotonicity? In this case, do we identify an interval or a point? - Frequentist estimation... which moments of the data are required?

© Michael Lechner, 2006, p. 8 Next target: Dose response  Additional assumption - Dose depends (only) on single index which is observable for control group, but unobservable for controls - Example: There is some underlying variable which influences length of participation. However, for the nice programme the UE follow this ‚desire‘, but for the nasty programme they deviate towards. This deviation is influenced by the ‚desire‘ only and is otherwise random (hard to justify in this example)  Same questions as before...

© Michael Lechner, 2006, p. 9 Conclusion  Principal stratification could be a very helpful concept in econometrics  It is clearly related to IV estimation – relation could be made even more explicit  Taking account of the non-Bayesian perspective would greatly enhance its value for econometricians