Are Public Investment Efficient in Creating Capital Stocks in Developing Countries?

These T constraints impose that, for all the considered dates, the monetary
increases of stocks, taking into account the depreciation, cannot be more im-
portant than the investments. We exclude the case when one invested dollar
produces a capital of more than one dollar. Given the estimated parameters υ
and 7, we can compute a sequence of increases (net of depreciation) in available
stocks according to the formula:
— — —

^δ7%∕. Il ^{= 77}j,t+1 ^- (ɪ ^- $j ) ⁷⁷jt

= 7 (ɪ + 7)^t+1 X_i,_t +1 - (ɪ - δ_j) 7 (1 + 7)^tX_i,_t        (11)

Finally, we can estimate the efficiency function by a non parametric method.
More precisely, we use a LOESS regression³ (Cleveland and Devlin, 1988) to
estimate the link function between ∆K_j∙,_t+ι and Ij_t, as:

^ ^ ,                                                   , .

∆Λ-j,,+ι = fj (Ijt)                               (12)

For a given level of investments I_jt, the more the value of ∕_j∙ (Ij_t) is far from
Ij_t, the less appropriate is the estimation of capital stocks by the PIM.

3 Results

In order to assess the quality of our methodology, we propose to estimate the
efficiency function of public investments in road and highways for the United
States over the period 1951-1992. We use the series of public investments (Federal,
State and Local) in road and highways, valued at historical costs expressed in
millions of US dollars (source BEA). For the corresponding physical measures,
we consider the total road kilometers (Canning, 1998). Figure 1 displays the
estimated efficiency function and the corresponding 95% confidence interval. We
can observe that the estimated function is relatively close to the straight line
of 45° slope. For a low level of investments, the estimated efficiency function
is statistically not different from the identity function. Consequently, for the
United States, our approach does not show an important discrepancy between
investments and the (net) variation of capital stocks. So, the PIM provides a
good proxy of the public capital stocks effectively available.

When the same methodology is applied for the case of our two reference de-
veloping countries, the results are very different. Figure 2 displays the estimated
efficiency functions for electricity, road and telecoms sectors in Colombia over

³The principle of this regression is that a local polynomial is estimated for every reference
point, using the points situated in the neighborhood of this reference point. The dimension of
these neighborhoods is determined by a smoothing parameter which is defined by the rapport
between the number of points included in the neighborhood and the total number of observa-
tions. The smoothing parameter was chosen according to a modified AIC criterion.

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