in 1981. The ending dates2 have been chosen such that during the considered
period of time, the amount of the private investments in the total investments of
the specified sectors never exceeds 15%. Generally, these dates correspond to the
reform dates pointed out by Calderon, Easterly and Serven (2004).
The second problem is the correspondence between investments categories and
the infrastructure physical measures proposed by Canning (1998). To measure
infrastructure in the electricity sector we consider electricity-generating capacity
expressed in million of kilowatts. For the telecommunication sector, we use the
number of telephone main lines. Two measures are possible for the roads sector:
the number of road kilometers or the number of paved road kilometers. We
decide to use the measure that offers the maximum of available observations.
Thus, for Mexico we use the number of road kilometers while for Colombia we
use the number of paved road kilometers. Finally, to measure investments in the
railways sector, the length of the railway system (in kilometers) is used.
Given these sectoral data, how to estimate the functional form of the public
investment efficiency function? This function relates on the one hand monetary
flows of investments expressed in million US dollars and on the other hand public
capital stocks measured in the same monetary unit. However, we have only
physical measures of these stocks. Our methodology is then the following. Let
us assume that, for a sector j = 1,.., 4, the capital stocks (expressed in monetary
units) can be defined as follows:
Kjt = vjt Xjt (4)
where Xjt denotes the physical measure of the capital in the sector j and Vjt
represents the monetary value of one physical unit of capital.
We assume that the efficiency function of public investments is specific to
each sector: ∕j∙ (.) denotes the efficiency function associated to the jth sector. Our
objective is to estimate the function ∕j∙ (.) defined as:
κj,t+ι - (1 - δj) Kjt = fj (βjtljt) (5)
where Ijt denotes public investments in the sector j and βjt, with 0 ≤ βjt ≤ 1,
denotes the part of these sectorial investments which actually correspond to the
assets considered in the Canning’s database. For instance, if we consider the
electricity sector, we can state that a part of public investments in this sector
is allocated for something else than the increase of electricity generating capac-
ity (security investments, investments made to preserve the natural environment
for instance). This part of public investments does not correspond to unproduc-
tive investments. The parameters βj only measures the inadequacy between our
2For the case of Columbia, the ending dates are: 1993 for the electricity sector, 1994 for
telecom and roads sectors. Data concerning public investments for the railways sector are not
available. For the Mexico, the dates are: 1998 for the electricity sector, 1990 for the roads and
1989 for the railway sector. The data concerning the road infrastructures before the reform
(1989) are not available.