Non-causality in Bivariate Binary Panel Data



originates from a retrospective survey carried on in June 1989. While all the
plants included in FLAUTO are involved in production activities (i.e., man-
ufacturing and/or assembly), the same does not apply to design∕engineering
function. According to the information available in the database, 230 plants
had no full time employee in the design∕engineering function. Such plants were
quite unlikely to belong to the population of realistic prospective adopters of
CADCAM; therefore, they were excluded from the joint analysis of the diffusion
of both technologies, reducing the sample size to 552. CADCAM and FMS have
been introduced in Italy around 1970, hence the observation window is assumed
to begin in this year and calendar time
t is set to 0 in 1969. Notice that, since
the survey is made in 1989,
t never exceeds T = 20.

For each plant i = 1,..., 552, we observe the year of adoption of both tech-
nologies, say
t and t?. To fit these survival type data into our framework, it is
convenient to transform them as follows:

1)i,t — IlplantiadoptsCADCAMattimei)
1 _ 1

yi,t — j-{planti adopts FMS at timet}


t = tf,... ,min t∣, T
t = tf,...
,min t?, T

The different time span of the individual data is explained as follows. First,
about 30% of the plants in the sample entered the metalworking industry after
1970: therefore, firm
i contributes to the likelihood function only from the year
of entrance in the sector, denoted as
tf. Moreover, in terms of the Markov
chain depicted in Figure 2, when the plant adopts both technologies it en-
ters an absorbing state, and therefore does not give any additional contribu-
tion to the likelihood (the probability of exiting the state is zero). Notice also
that, as illustrated in Section 5, when Ujιi-ι = (l,0)z the bivariate distribution
Pr{τ∕i,i I
Yijt-ι = (l,0)'} collapses into its marginal Pr{√∕iYi,t-ι = (l,0)'},
since Pr{ι∕li = 1 ∣ Ujιi-ι = (l,0),} = 1. Therefore, as obvious, no additional
information is involved in recording
y]t for t > t. The same argument holds
for
Y]?. Finally, the data are right-censored because the firms are not observed
after 1989, so that
t never exceeds T = 20. Notice that this kind of censoring
involves no bias, since time of censoring is a Markov time w.r.t. the filtration
generated by the process.

In this framework, the use of a discrete time model can be justified supposing
that the adoption of these technologies is decided during the budgeting phase,
i.e. it is a discrete time event. This assumption seems to be correct in this case
since these technologies are very expensive and requires often a reorganization
of the structure of the firm (revision of the information system, skills of the
employees, etc.): this renders plausible that the decision is taken in a formal
moment as the discussion of budget.

Let us now introduce the covariates, i.e. the vector xiιt in our notation.
The economic theory related to the diffusion of technological innovation recog-
nizes four different groups of factors affecting the delay in the adoption of an
innovation (see for example Colombo and Mosconi, 1995).
Rank effects explain
the delay in adoption as a consequence of firm heterogeneity: characteristics
of the firm affect adoption probability, independently of the behavior of other

22



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