Thoughts on SUTVA (Part I) 

  Alexis Diamond , guest blogger 

 I gave a talk on Wed, Feb 8 at the IQSS methods workshop where I described my efforts to estimate the effects of UN intervention and UN peacekeeping on peacebuilding success following civil war.  One of my goals was to demonstrate how matching-based methods and the Rubin model of causal inference can be helpful for answering questions in political science, particularly in fields like comparative politics and international relations. 

 An important issue in this context relates to Rubin's SUTVA, the stable-unit-treatment-value assumption typically assumed whenever matching-based methods are performed. SUTVA requires that the potential outcome for any particular unit  i  following treatment  t  is stable, "in the sense that it would take the same value for all other treatment allocations such that unit  i  receives treatment  t  (Rubin 1990, p. 282).  This is a stronger form of a basic assumption at the heart of the Rubin causal model: that for every set of allowable treatment allocations across units, there is a corresponding set of fixed (non-stochastic) potential outcomes that would be observed. 


 Rubin (1990) goes on to say that "The two most common ways in which SUTVA can be violated appear to occur when (a) there are versions of each treatment varying in effectiveness or (b) there exists interference between units" (ibid., p. 282).*  But how exactly do "versions" and "interference" cause violations, and what are the  consequences?  Don't these violations occur frequently in political science and the other social sciences?  In my research agenda, for example, treatment is peacekeeping, and peacekeeping is going to vary in effectiveness from country to country. Moreover, it is ridiculous to suppose a country's potential outcomes are independent of what is happening (or has already happened) to its neighbors, especially in the context of war and political conflict involving refugees, cross-border skirmishes, etc... (although this kind of independence is typically claimed—at  least implicitly—whenever regression-based approaches are used.) 

 Why do multiple versions of treatment pose SUTVA problems? Because SUTVA posits, for each unit and treatment, a single fixed potential outcome, not a distribution of potential outcomes. Thus, if there is a potential outcome for the weak version of treatment A and a different potential outcome for the strong version of treatment A, then one cannot speak of the potential outcome that would have been observed following treatment A: there are in fact two treatments. Note that a causal question framed in terms of a single type of treatment A (eg., "What is the effect of treatment A-strong version?") does not present these problems.  Similarly, as long as there is a single version of the control intervention, one could still coherently define causal effects for each unit in terms of the difference between (observed) potential outcomes under heterogeneous treatment interventions and (unobserved) potential outcomes under control.  One might wonder if these causal effects are substantively interesting, and if and how they could be reliably estimated…these critically important issues are separate from and subsequent to the question of whether the inferential investigation is well-defined. 

 The problem posed by interference across units is very similar; if unit  i 's potential outcome under treatment A depends upon another unit  j 's assignment status, then there are really multiple (compound) treatments involving A for unit  i , each of which involves a different assignment for unit  j . Each of these multiple treatments is associated with a corresponding potential outcome. Note that this kind of interference across units does not necessarily present a problem for defining the effect of a single one of these compound treatment As.  It just means that asking "What is the effect of treatment A?" makes no sense---it is not a well-posed causal question. 

 Because SUTVA is so frequently discussed in the context of matching-based methods, people often assume that the two are inextricably linked: that whatever SUTVA is useful for, it is useful only for matching-based analyses. A crucial point often missed is that SUTVA is useful for the discipline it imposes on study-design.  Prior to the choice of analytical methodology (eg., regression, matching, etc.), SUTVA works to nail down the precise  question under investigation. 

 Given these issues, can the peacekeeping question be addressed within Rubin's causal model?  I return to this question in post II of this series. 

 *Rubin, Donald B. Formal Modes of Statistical Inference For Causal Effects. Journal of Statistical Planning and Inference. 25 (1990), 279-292.