emerged as viable competitors in various specific fields. The QR model
is one variant of the latter class of models, although perhaps not
immediately recognizable as such. This study employs a QR model in
which the parameter of explanatory variables can be expressed as a
monotonic function of a single, scalar random variable. The QR
model captures the systematic influences of conditioning variables on
the location, scale, and shape of the conditional distribution of the
response. The QR model is thus significantly extended with a constant
coefficient in which the effects of conditioning are confined to a location
shift.
Further, this study denotes that traditional optimization techniques,
including OLS and LAD, disregard different behaviors in the
tail regions of firm performance distributions, and that the relationship
between CEO stock-based pay and firm performance in firms
might change in the tail regions. Following this line of thought, this
investigation employs the QR technique developed by Koenker and
Bassett (1978) to examine the non-uniform impact of CEO stockbased
pay on performance across various performance quantile conditions.
Assuming that the hth quantile of the conditional distribution of the
explained variable, y
it is linear in x
it , this study defines the conditional
QR model as follows: