The results of the first-stage regressions are shown in Table 2. Note that all relevant variables are normalized by the states’ 16-and-older population. Since we have used more recently revised data for some of the variables, the estimates differ slightly from those presented in Chodorow-Reich et al. (2012a), but the interpretation of the estimates does not change qualitatively. Note that the estimations are precise (high R2s), significant (the estimated coefficients for the instrumental variable are statistically significant even at the 0.01 significance level), and robust when adding control variables.
The second-stage regression results are presented in Table 3 (Specification 5 is discussed in the next subsection). Specifications 1 and 2 are the OLS estimates, and Specifications 3 and 4 are the 2SLS estimates of Eq. (1). A comparison indicates that the OLS estimates indeed underestimate the effect of FMAP outlays, pointing out, as mentioned earlier, that the effect of an increase in a state’s unemployment, and a decrease in state’s economic activity, biases the OLS estimates downwards.
The effect of FMAP outlays on economic activity in Specification 4 is precisely estimated, with a p-value (not reported in the table- equal to 0.0019. The estimated coefficient indicates that an increase of 1 in FMAP outlays normalized by states’ 16-and-older population, led to a 1.61 increase in normalized GSP in 2009. This is, however, a lower bound of the effect of the FMAP outlays on GSP, as it does not take into account the potential effects of the stimulus on economic activity beyond 2009. We discuss the durability of state fiscal relief in the next subsection. This comprehensive specification also gives the most accurate estimate for the fiscal multiplier, an estimate of 1.61, which is at the lower end of the range of 1.5 to 2.1 of the multipliers found in empirical studies that are mentioned in CEA (2014, p. 146).
State fiscal relief will have a “direct” and an “indirect” effect on a state’s economic growth. The direct effect consists of the states that can avoid spending cuts and layoffs, while its indirect effects depend on how the nongovernment-related sectors are affected. Chodorow-Reich et al. (2012a, p. 132) show that the effects on both the gains in the governmental and nongovernment-related sectors were substantial.
In the previous subsection we presented the estimates of the effect of the FMAP outlays on economic activity in 2009. We now turn to the effects beyond 2009, that is, using Specification 4, we subsequently consider the effect of the FMAP outlays on the change in economic activity (normalized by states’ 16-and-older populations) from 2008 to 2010, from 2008 to 2011, from 2008 to 2012 and so on. The estimates of these effects are presented in Fig. 1, in which the solid line is connecting the FMAP outlays coefficients and the dashed lines represent the 95% confidence interval.
Figure 1 shows that the positive effect of the stimulus remained statistically significant until 2012, that is, long into the first term of Barack Obama. Moreover, the estimated positive effects are increasing until 2012. Interestingly, however, not only the statistical significance, but also the positive trend of the positive effects of the stimulus changes after 2012. Firstly, it indicates that, for efficiency reasons, it is important to consider a short time period when estimating the effects of a policy measure (in this case the effects in 2009), as disturbances accumulate over time, making the estimates less precise. Secondly, it may indicate that the positive effect of FMAP outlays on economic activity at the start of the Obama presidency did not last longer than his second term as a president of the U.S.
So far, following Chodorow-Reich et al. (2012a), we analyzed the effects of FMAP outlays, normalized by states’ 16-and-older population, on the changes in GSP, again normalized by states’ 16-and-older population. In this subsection we change the dependent variable into economic growth to provide further evidence that the ARRA worked as an economic stimulus. The estimation results are reported as Specification (6) in Table 3.
The estimation of the effect of the FMAP outlays on GSP growth is again precise with a p-value (not reported in the table) equal to 0.0077. The estimated coefficient indicates that an increase of 1 in FMAP outlays normalized by states’ 16-and-older population, led to a 2.27% increase of GSP growth in 2009, a result that shows that the state fiscal relief in the form of FMAP outlays met ARRA’s purpose to “promote economic recovery”.