The Tangible Contribution of R&D Spending Foreign-Owned Plants to a Host Region: a Plant Level Study of the Irish Manufacturing Sector (1980-1996)

contribution of R&D activity to the risk of exit facing a plant is the same in
1986 as it is in 1996. The assumption of using this proportional hazards
model is that none of our explanatory variables vary across time. They are
all cross-sectional.

We express the model to evaluate many independent variables as

(^1 X! ⁺ ^7 X? ⁺'"⁺^ ∖' Xn )

h ( t ) = [ h 0( t )]e ¹¹2 2 Nn           (3)

where h₀(t) is the baseline hazard function when all of the covariates are
set to zero and h(t) is the estimated hazard function when the value of the
covariates (x₁,x₂...x_n) are nonzero.

The emphasis of this paper is on the probability of survival for an foreign-
owned plant given its characteristics and external environment. The
survival function S(t) is an estimate of the probability of surviving longer
than a specified period. The cumulative hazard function H(t) is related to
the survival function: H ( t ) = - ln S ( t ), where

S_t = [SS 0( t )] p                                  (4)

11                 βx '∣'.                                        _{1 1} .    _{1 1}        . .      ,₁

and where p = e . The survival function is obtained by raising the
baseline survival function (this is the function when all the explanatory
variables are set to zero) to the power of e ^^x. The cumulative hazard and
the cumulative survival functions approximately add to one, the difference

20

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