(B) A Cox Duration Model
A limitation of the lifetable analysis above is the inability to
distinguish plants by more than one characteristic, in particular, we were
unable to distinguish the R&D-spending plants by other characteristics,
such as plant size and age. The Cox duration model (1972, 1975)
estimates the risk of exit (hazard) facing a plant in our cohort as a function
of plant and sectoral explanatory variables. This proportional hazards
model takes account of duration heterogeneity, i.e., the differing lengths of
time over which our plants remained operational post-1986. The hazard is
the conditional probability of a plant leaving the manufacturing sector at
duration t. The hazard rate is the rate at which a plant exits during period t
given that it has survived until time t, i.e., it measures the risk of exit for a
plant during the next year. We obtain a baseline hazard function, h0(t) ,
which is estimated when all of the explanatory variables (covariates) are
set at zero. It is an estimate of the risk of exit facing each plant in the
cohort in each year 1986-1996. The Cox model then estimates the
influence of each of our explanatory variables on this baseline hazard
function. Is the hazard of a plant exiting at a moment in time increased or
decreased when an explanatory variable is nonzero? A negative (positive)
coefficient indicates that this baseline risk of exit at a moment in time is
reduced (increased).
In order to use the proportional hazards Cox model, we must
assume that the ratio of the baseline hazard function h0(t)and the estimated
hazard function h(t) (when an explanatory variable is included) is
proportional across time. This implies the contribution of the explanatory
variable to the risk of exit across time is identical. In our case, the
19