technology) may deviate. So, the use of monetary investment may introduce
systematic errors in the amount of public capital actually produced.
Let us consider the following capital accumulation relationship:
κt+ι = (1 — δ) Kt + f (It) (1)
where Kt denotes the public capital stock at time t and I denotes the corre-
sponding gross public investment. The function f (It) , called efficiency function,
represents the efficiency of public investments to generate new capital. If we
assume that only a certain part of investments is used to create capital, the func-
tion f (.) may differ from identity function. We only know that it satisfies the
following constraints:
O ≤ f (It) ≤ It (2)
f (O) = O (3)
The fact that f (It) can be strictly inferior to It reflects the inefficiency of
public investments in creating capital. Since no natural specification of the ef-
ficiency function f (.) can be justified a priori, a solution consists in estimating
this function by a non parametric method for a typical developing country or
for a sub-group of developing countries. For this purpose, three inputs are re-
quired: (1) a series of public investments (2) the depreciation rates (or its time
profile) and (3) a series of public capital stocks effectively available in the refer-
ence countries. The first and the second element are available in the literature
(World Bank, Bureau of Economic Analysis) for many countries. But the last
element does not exist. Consequently, in this study, we propose to estimate the
efficiency function by using physical measure of infrastructure as a proxy of pub-
lic capital stock effectively available in developing countries. To the best of our
knowledge, only the Calderon, Easterly and Serven’s database (2004) about nine
countries of the Latin America1 give an enough detailed decomposition of the
public investments for a long period of time (1980-1998) that allows us to es-
tablish a correspondence with the physical measures proposed in the Canning’s
database (1998) from 1950 to 1995. That is why we choose two reference Latin
American countries, Colombia and Mexico. For these two countries we compare
past investments flows given by Calderon et al. (2004) to physical measure of
infrastructure stocks given by Canning (1998) over the period 1981-1995 in four
sectors: Electricity, Telecommunication, Roads, and Railways.
The first problem of this approach is that it considers sectors for which pri-
vate investments may be important. As in most of Latin America countries, the
proportion of private versus public investments in infrastructure deeply changed
during the period 1980-1995 in these two reference countries. So, we consider
only a period for which the part of private investments in total investments is not
important. More precisely, for each sector, the sample used for estimation starts
1Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Mexico, Peru and Venezuela.