The chart also suggests a potential problem with the first model in Table 3. If
every state's union density series were as clearly non-stationary as the series in Figure 3,
the results concerning the estimated relationship between union density and import
sensitivity might well be spurious. As the North Carolina case in Figure 3 indicates,
however, union density in every state did not contain an obvious trend. The statistics
reported at the foot of Table 2 test whether the union density panels contain a unit root,
using the method recommended by Levin, Lin, and Chu (2002). Their approach is
similar to an augmented Dickey-Fuller test. The null hypothesis is that the panel data are
non-stationary. As the number of lags used in the test increases, the amount of data
available for estimating the test statistic declines, and the power of the test decreases.
Nevertheless, the test statistics that employ 10 and 15 lags still leave a substantial amount
of data for estimation since each series is 41 years long. Although the results are not
conclusive, there is clearly cause for concern about the stationarity of the union density
series, and thus about the validity of the results in the first model.
In order to hedge against the possibility that the union density panel is non-
stationary, the second model in Table 3 presents the results of an analysis of the change
in union density. If import sensitivity indeed reduces union density, then it should be
negatively associated with changes in union density. As the results indicate, there is
evidence that this is indeed the case. A one standard deviation increase in import
sensitivity would reduce the annual change in unionization by roughly 0.004. This is a
very small annual change, but steady increases in import sensitivity over several decades
could produce a substantial decline in union density like the pattern in Figure 3.
29
Convention