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

sectorial decomposition of investments and the physical asset considered in the
Canning database.

For the four reference sectors, we calculate the depreciation rate δj using the
BEA (Bureau of Economic Analysis, 2003) depreciations rates. For each type of
investment two depreciation rates are proposed by the BEA: one for equipment
and one for structures. The only exceptions are the investments in roads for
which only structure assets are reported. Taking into account these information,
we compute a weighted average of the rates on structures and equipment for
the four components of public investments used. The weights are defined by the
average part of equipment assets (respectively structure assets) in the total gov-
ernment net stocks of the United States over the period 1950-1996. The weights
used are then equal to 83.17% for structures and to 16.83% for equipment. The
corresponding depreciation rates for the four components of public investments
are reported in Table I.

If the function f_j∙ (.) is homogenous of degree Λ, equation (5) can be expressed
as relationship between the physical measures of infrastructure Xj_t and the mon-
etary investments Ij_t as:

^vj,t+1^χj,t+1 - ⁽¹ - ^δj⁾^vj,t^χj,t = ^fj ^(Ijt) ⁽⁶⁾

with ¾_t = Vjt∕βj_t. In this expression, except the function fj (.), only the valu-
ations Vjt and the proportions βj are unknown. In order to evaluate them, we
propose to compute a sequence of values of ¾_t in order to get a situation as close
as possible to the full efficiency situation, that is to the PIM for which one in-
vested dollar increases the capital of exactly one dollar. More precisely, we know
that, if PIM is valid, the sequence V_j∙_ιt is defined by the recurence equation:

⅛+1^χj,t+1 ^-⁽¹^-^δj⁾^vj,t^χj,t = ¹jt ⁽7⁾

Let us assume that ¾_t has a geometric evolution:

⅜t = ^v⁽¹ + 7⁾^t⁽8⁾

This assumption allows us to take into account the inflation of the costs asso-
ciated to the construction of one physical infrastructure unit. The problem only
consist in determining parameters (v, 7), which (conditionally to Xj_t and Ij_t) give
us the valuation dynamics v7_t compatible with the PIM. For that, we solve the
following program:

1 ^τ

⁽U 7⁾ = ArgMin - [ ^v^{(1 +} 7⁾^t⁺¹^χj,t+ι ^-⁽¹^-^δj⁾^v^{(1 +} 7⁾^t^χj,t ^-¹jt]²

{_υ,₇}∈R+2 1 t~1

(9)
under the constraints:

^v^{(1 +} 7⁾ [^{(1 +} 7⁾^χj,t+ι ^-⁽¹^-^δj⁾^χj,t] ≤ ¹jt Vt = ¹^,..^, T ⁽¹⁰⁾

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

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