One potential channel that could lead the conditional inequality-return relationship is that increasing inequality leads to both mass shootings and negative stock market returns. To simplify the description, I name this channel as simultaneity channel.
If the simultaneity channel does hold, one direct implication is that if two regions in the U.S. share the same conditions, the increase in inequality should generate commensurable inequality-return sensitivity with or without happening a mass shooting. To test this implication, the ideal case is that one could find two sets of locations with the same condition, the only difference is the mass shooting happens or not. However, there is no such data in the real lift at all. To approach the ideal case as close as possible, I employ the subsample analysis strategy. I first single out these firms located the counties where there was a mass shooting, and group these observations as the treated sample. I employ the county adjacent table from Census Bureau to identify the counties that just alone side the counties in the treated sample. The overarching objective to create two subsamples with as much geographical similarity as possible. Next, I formalize the Hypothesis 2,
Hypothesis 2. The inequality-return relationships are indifferent between mass shooting treated sample and adjacent sample with similar economic, cultural and geographical conditions.
To test the hypothesis, I run the following regression in the two subsamples separately,
rTreatedi, j,t = α + β1KGRTreatedj,t−1 + FE(t) + εt, (10)
rAdjacenti, j,t = α + β1KGRAdjacentj,t−1 + FE(t) + εt, (11)
where the empirical design is largely similar to Eq. (7). The only difference is that Eq. (10) only includes the observations in the county where mass shootings ever happen in the sample and the Eq. (11) only includes the observations just adjacent to these counties. To figure out how the inequality-return relationship in these two samples could statistically differentiate from each other, I also design a pooled-regress with both subsample group together, and label them by indicator as,
ri, j,t = α + β1ITreatedKGRTreatedj,t−1 + β2IAdjacentKGRAdjacentj,t−1 + FE(t) + εt, (12)
where ITreated and IAdjacent mean which subsample the observations belong to. By employing the pooled regression, I can design a Wald test to examine the difference of inequality-return relationship in two subsamples. One could translate the Hypothesis2as to test if β1= β2in Eq. (12).
[Insert Table 5 around here]
I present the regression results in Table 5. Column (1) represents Eq. (10) and indicates that the inequality-return relationship presents a strong negative pattern. In this subsample that has been treated by a mass shooting, a one percent increase in KGR leads to -3.83 % equity premium in the subsequent year with 5% significance. However, in the adjacent subsample where the inequality and other economic condition should be very close to treated subsample, the inequality-return relation does not present any significance at all, which corresponds to column (2) where the coefficient is -0.31 with one decimal scale lower that of the treated subsample. The formal test of the hypothesis2is in column (3). A similar pattern appears that only the coefficient of mass shooting treated indicator shows significance. In the lower panel, I present the result of the Wald test of the null hypothesis β1= β2. The F-value is 7.32, which indicates that β1= β2in Eq. (12) has been highly rejected with 1% significance.
One concern of this subsample analysis is that, the sample selection is totally an ex-post criteria and the
implicit assumption is that the influence of mass shooting exists forever. To mitigate the look-ahead bias, I design a simple regime switching model to take all observation into consideration,
ri, j,t= α + β1ITreatedj,t KGRj,t−1+ β2IUntreatedj,t KGRj,t−1+ FE(t) + εt, (13)
where ITreatedj,t indicates the observation is treated by mass shooting in year t with value of unity, otherwise 0. IUntreatedj,t is a compensate indicator with opposite value of 0 and 1 with ITreatedj,t . The implicit assumption is that the influence of mass shootings just exists for one year. Also, to mitigate the concern that the definition of the region could influence the results, I employ county, MSA and CBSA definition for robustness, and present the result in column (1) - (3) of Table6, respectively. As expected, even with the assumption that the effect lasts for just one year, the results still keep a similar pattern that the negative inequality-return relationship mainly concentrates on the mass shooting treated year and region.
[Insert Table 6 around here]
Next, I also test the subsequent reaction of the stock market return. If the current stock price does incorporate the contemporaneous inequality information, one could also expect the reserve subsequent reaction. The intuition is that as rt = (Pt+ Dt)/Pt−1, the decrease in Pt will lead decrease in rt for contemporaneous relation. However, a decrease in Pt−1will lead to an increase in rt as subsequent relation.
Specifically, I run the following regression to test the subsequent reaction,
ri, j,t= α + β1KGRj,t−2+ β2IShootingj,t−1 + β3IShootingj,t−1 KGRj,t−2+ FE(t) + εt, (14)
ri, j,t= α + β1KGRj,t−2+ β2NumShootingj,t−1 + β3NumShootingj,t−1 KGRj,t−2+ FE(t) + εt, (15)
where the main difference is that there is a two-year distance between KGR and subsequent return. My coefficient of interest is β3, and I expect β3is significantly positive. I present the result in Table7. In column (1) and (2), regression subsequent return with a two-year lag of KGR and one-year lag of mass shooting indicator, there is no conclusive result. Thus, one can summarize that with longer time distance, KGR and mass shootings are not informative to subsequent return. However, in column (3)-(4), the interaction term present positive significance, which is in line with my expectations. The results also indicate that ceteris
paribus, mass shooting and inequality interactively be priced into the stock market previously.
[Insert Table 7 around here]
In summary, the empirical results highly reject Hypothesis 2 that the inequality-return relationships are indifferent between mass shooting treated samples and adjacent samples with similar economic, cultural and geographical conditions. The negative inequality-return relationship is largely driven by the mass shooting treated subsamples. The results are consistent with the subsample analysis and regime-switching method. I next turn to the attention channel analysis.