In our discussion of ARRA, we make use of the fact that ARRA can be seen as a natural experiment: expenditure levels differ per state, and this allows us to check whether states that have received more due to ARRA have reached a more favorable change in the gross state product (GSP) growth rate.
ARRA funding indeed differs largely per state. For example, Florida received $449 and Alaska $2,403 per capita. In this paper, we use this between-state variation in ARRA funding to check whether this variation so far has had any effect on economic activity.
A problem with the analysis described above is that ARRA spending may depend on the economic situation of a state: states hit harder or recovering slower might get a higher ARRA stimulus. Ordinary least squares (OLS) estimation of the relationship between the size of the stimulus and its effect on the economy therefore understate this effect. We address this problem by using an instrument to isolate the part of the stimulus that is not related to economic circumstances after the crisis. The instrument we use is the Medicaid transfers in 2007. The ARRA stimulus received also depends on these pre-recession transfers, and our identification strategy is to consider the cross-state variation in stimulus spending resulting from pre-recession differences in Medicaid transfers. It turns out that correcting for potential endogeneity problems (states receiving more ARRA spending have a smaller decrease in GSP or a higher increase than states that received less doesn’t qualitatively change results.
We also consider the question of whether the size of the stimulus was too small or too large. Adding the square of stimulus spending in a new regression, we find a diminishing marginal effect of stimulus spending on GSP growth rates. Using these estimated parameters, we find that the size of the actual stimulus is close to the optimal size.