LATEs when they look odd 

 A few weeks ago I came across  this paper  by Mark Duggan and Fiona Scott Morton in the QJE looking at how government procurement can influence prices--in this case Medicaid procurement of prescription drugs.  Basically, Medicaid receives mandatory rebates if drug prices go up too fast, so there is an incentive for companies to develop new versions of existing drugs (which can then enter the market at a higher price) and to price drugs too high initially if they expect to see a large amount of Medicaid volume.  In this context, that policy could also harm other purchasers if prices levels would have been lower in the absence of the Medicaid procurement rules. 

 The authors exploits the large variation in the share of prescriptions accounted for by Medicaid enrollees to generate their estimates.  These estimates indicate that Medicaid market share can increase prices by fairly large amounts (a 10% increase in Medicaid market share leads to a nearly 20% increase in drug prices in 1997 and 2002).  But, because drug prices are pretty skewed (even after a log transform), they also look at the effect of Medicaid market share on the price rank of a drug--here the results indicate that a 10% increase in Medicaid market share increases the price rank of a drug by about 4 slots.  A difficulty with this result is that the Medicaid market share may be endogenous, thus they also present results using instrumental variables and here is where things get interesting. 

 It is well  established  that instrumental variables (IV) estimates are local average treatment effects (LATE)--basically the average effect of treatment on a subgroup of units whose behavior is altered by the instrument.  In other words, for every unit there is an associated treatment effect and the LATE is the average over a special subset of units.  Sometimes this matters, sometimes it doesn't--in this case I think it is interesting to look at and readers can decide it matters. 

 The instrument that Duggan and Scott Morton uses exploits variations in the number of people with different conditions and the specificity of drugs to treating certain conditions (i.e. a statin doesn't treat schizophrenia).  Hence, they compute the fraction of individuals with diagnoses that the relevant drug can treat who are insured by Medicaid (call it Medicaid patient share to distinguish it from Medicaid market share). 

 Using this instrument, they compute the predicted Medicaid market share and subsequent parameter estimates.  With the two years of data (1997 and 2002) they develop two different predicted Medicaid market shares that are the same regardless of the dependent variable.  One would hope that the parameter estimates wouldn't change (much) or at least when there are two dependent variables they should move in the same direction.  In this case, the estimates using log price as the dependent variable get smaller indicating that a 10% increase in Medicaid market share results in 11% and 18% increases in prices in 1997 and 2002, so the result doesn't change much for the 2002 regression, but the estimate in 1997 does change by quite a bit and in both years the estimates go down.  So one would expect that the price rank regression should show similar results, right?  Surprisingly, this is not the case, in 1997 the IV estimate indicates an increase of 2.4 ranks in 1997 and 9.2 ranks in 2002. 

 To me this suggests that the IV estimates are LATEs over a particularly quirky set of "treatment effects" since the effect on prices are still fairly large in both cases while the effect on ranks is small in one case and very large in the other.  Does this alter their conclusions in any way?  No, and it probably shouldn't, but it is interesting to see the effect and think about what it means for interpreting their data.