Since food insecurity is also elicited in the Current Population Survey, the authors estimate the same bounds using this alternative data set (figure 2). The results are qualitatively similar but the intervals are larger such that the MRT assumption is necessary for ruling out that  SNAP increases food insecurity on average. These larger intervals could be due to the smaller sample size in the CPS. Another reason could be the large amount of underreporting present in the CPS (nearly 50% according to \citet{Meyer_2009}).
Since the CPS allows for the construction of instrumental variables that - if exogenous and valid - could also identify a causal effect of SNAP on food insecurity, the authors construct two instruments that are common in the literature that exploit interstate variability in the implementation of SNAP:
  1. About one half of states has simplified reporting requirements
  2. About a third of states exempts cars from the asset-test
The authors estimate the ATE from these instrumental variables in two different ways: Firstly, they estimate it using a linear response model. Secondly, they follow \citealt{2011} and use the instrumental variables to non-parametrically bound the ATE from above. These four estimates are shown as lines in figure 2, where the thinner lines show the linear response IV estimates and the thicker lines show the non-parametric upper bound estimates. One can clearly see that at least one of the assumptions underlying the estimate of the reporting instrumental variable in the linear response model must be violated since the estimate lies outside the estimate that relies on no assumptions.