the period 1980-1994. It appears that the sector where public investments are
the more efficient is the telecommunication sector. However, these comparative
results must be very carefully used. Given data availability, our sectorial samples
are very reduced. It implies that the estimates of the sectorial efficiency functions
are relatively imprecise. So, in order to obtain more precise estimates, we pro-
pose an estimate of the global efficiency function based on the three sectors. More
precisely, we report all the couples ^TLj,t+ι∙> Ijtj obtained for the sectors j = 1, 2
and 3 with Kjj+1, the net variation in capital stock. Given these observations,
we estimate the global efficiency function f (.) , assumed to be homogeneous over
the three sectors, by a LOESS regression.
(13)
кj-t+1 = f (Ijt) j = 1, 2,3
Figure 3 displays the estimated efficiency function for Colombia and Figure 4
displays the same function for Mexico. Both estimated functions are strikingly
similar. They show that the ’’productive” component of public investments is
largely overvalued when the PIM is used. Two results are particularly interesting
here. Firstly, the estimated function is near a straight line. This conclusion is ro-
bust to the choice of another information criterion as the general cross validation
(GCV) function. It implies that the estimated function can be approximated by
a simple linear functional form f (It) = a It where a, with 0 < a < 1, denotes an
efficiency parameter according to the expression proposed by Pritchett (1996). In
other words, the relative efficiency, defined as the ratio of the ’productive” invest-
ments to the total amount of investments, is constant. Secondly, the coefficient
of the linear regression of Kj∙,t+1 to Ij∙t is equal to 0.38 in the case of Colombia
and 0.40 in the case of Mexico. According to this evaluation, one peso of public
investments creates around 0.40 pesos of public capital in our reference sectors.
So, our conclusions based on these non parametric estimates are similar to that
of Pritchett (1996).
4 Conclusion
It is recognized that in a typical developing country, an important part of public
investments may be inefficient in creating capital. Consequently, the perpetual
inventory method, based on monetary investment flows, may overvalue the public
stocks. So, we propose an original non parametric approach to evaluate the
efficiency function that links variations (net of depreciation) of stocks to public
investments. We consider four sectors (electricity, telecommunications, roads and
railways) of two Latin American countries (Mexico and Colombia). We show that
there is a large discrepancy between the amount of investments and the value of
increases in stocks. Moreover, the estimated efficiency function is almost linear:
the ratio of "productive" investments to the total investments is constant and
equal to 0.38 in the case of Columbia and 0.40 in the case of Mexico.