John DiNardo 145The test is severe against the hypothesis that unobserved differences in thefirms
that are unionized versus those that are not unionized can explain the different
wages, and soon, of unionized workers.
It is rather easy to display the data from regression discontinuity designs.
Figure 3.7 plots an idealized version of the key displays: in each, the average value
of some outcome, where these averages are computed for different values of the
vote share. The figure on the left corresponds to the case where unionization has
an effect on the outcome in question. In the figure on the right (and one that
resembles the figures in DiNardo and Lee, 2004), there is no detectable effect of
unionization.
Figure 3.8 plots an idealized version of the key displays that correspond to ensur-
ing the validity of the research design or “balance”: in each the average value of
some pre-treatment outcome (in the study by DiNardo and Lee this included firm
size and measures of the health of the firm) are plotted for different values of the
vote share. The graph on the left corresponds to the good case: firms in establish-
ments where the union barely lost the election look the same as those where the
union barely won. This corresponds to what was found in DiNardo and Lee. The
figure on the right corresponds to a situation which is evidence against the design:
firms in establishments where the union barely lost look much different than firms
where the union barely won. In this case, theceteris paribusconditions would seem
to be violated.
To summarize the results of the study, the authors find (perhaps surprisingly
given the huge literature documenting significant union wage effects)noeffect of
11.522.5Outcome (detectable effect of unionization)0 .1.2.3.4.5.6.7.8.9 1
Share of vote for union11.522.5Outcome (no effect of unionization)0 .1.2.3.4.5.6.7.8.9 1
Share of vote for unionFigure 3.7 Two types of findings in a regression discontinuity design