lnL=∑[YjlnΛ(β'xi)+(1-Yj)ln(1-Λ(β'xi))]
j
(7)
By differentiating equation (7), we find the marginal effects at the sample mean of the
regressors on the probabilities as (Greene, 1997):
∂Pγ=1
∂x i
= PY =1
β- Y∑=1PYβ
Y=0
=Λ(β'xi)-[1-Λ(β'xi)]
(8)
A goodness of fit measure based on the likelihood ratio test statistic, usually reported as
McFadden’s ρ2 measure (Maddala, 1983), is:
ρ 2 = 1 - 'ogL'-' (9)
log Lω
where L ω is the maximum of the likelihood function when maximised with respect to
all parameters and Lω is the maximum when the likelihood function is maximised with
respect to the constant term only, i.e. setting all the βs equal to zero. The marginal
effects show how much the probability to report positive change in an indicator of
performance, expressed in percentages, will change if the independent (explanatory)
variable changes by a marginal amount from its sample mean. The marginal effects for
dummy independent variables are estimated as a difference between the variable’s two
values, i.e. 0 and 1 (Greene, 1997).
Our econometric approach suffers from two major drawbacks. Firstly, we assume that
the two tobit models for the percentage of material inputs and for the percentage of
exported product (presented in equation 4 above) are independent and thus are not
jointly estimated. Despite the fact that there is no economic underlying theory pointing
out to the joint estimation of these equations, one could attempt a joint estimation and
compare it with the independent estimations. Secondly, we assume that the effects of
either the percentage of material inputs or the percentage of exported product are
exogenous to the firm’s performance indicators. In other words we do not test for
possible endogeneity of the tobit estimates in equation 3 to the logit model in equation
6. This would require a rather complicated econometric application which will not add
much to our understanding of the real processes at work. Furthermore, in the case where
the two tobit models had been jointly estimated there is not a known test for
endogeneity of simultaneously estimated tobit models in a logit (or probit) model.
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