Table 4 lists the OLS and QR estimates for the impact of the stockbased/total
compensation ratio on firm RoE. First, the OLS estimate is
negative but insignificant. In particular, the OLS estimate for the stockbased/total
compensation ratio is 0.0029, and the corresponding pvalue
is .891. This result indicates that, on average, the effect of CEO
stock-based pay on firm performance is negative but insignificant. However,
the OLS estimator, by focusing only on the central tendency of the
distributions, does not allow the impact of the stock-based/total compensation
variable to differ from various firm performance regimes.
Next, this work examines the non-uniform relationship between
stock-based/total compensation and the RoE obtained with the QR. It
is important to note that, moving up the quantile levels, the impact of
the stock-based/total compensation ratio on RoE varies widely in magnitude
and sign of the estimated coefficients. In particular, by using
the 5 per cent level of significance as a criterion, while the stock-based/
total compensation variable is insignificant at the central quantiles,
from 0.40 to 0.70, it becomes significantly positive (negative) at higher
(lower) quantile levels from 0.75 to 0.95 (0.05–0.35).
The right two columns of Table 4 present the F tests of the equality
of slope parameters across various quantiles, namely the differences
between slope estimates at the h against (1h) quantiles. Notably, differences
across various quantiles are significant at the 1 per cent level for
most situations, and thus the observed nonlinearities derived from con