# _6. 5 The efficiency of public investment_

# <u>6.5.1  Stylized facts</u>

One of the reasons that public capital might have less effect on growth in developing countries is that it is inefficient. However, as already noted in Section 2, the _level_ of efficiency θ does not affect the marginal product of measured public capital and the effect of additional public investment on growth. For low efficiency countries, only a fraction of new investment might become productive capital, but this is offset by the greater need for public capital given that past investment was also inefficient.<sup>39</sup> However this does not mean that _increasing_ public investment efficiency cannot have a large effect on growth.

The potential for higher growth through greater efficiency of public investment depends on current efficiency being low. In the first row of Table 6 we calculate the median of the Infrastructure Efficiency Index (IEI) for each income group (see Section 4 for details on the construction of the IEI). As expected, based on the full set of computed IEI, HI countries have the highest median efficiency, with around 87% of roads being paved or water/electricity reaching their final destination. For middle‐income countries, efficiency is about 74%, or 1/7<sup>th</sup> lower. Efficiency is the lowest for LI countries, where only 59% of roads are paved or water/electricity reach their final destination; which is about 1/3 lower than efficiency in HI countries.

**<u>Table 6:</u> Efficiency – Income Group Medians (with φ=0.17; ζ=1)**

|**Parameter/Variable**|**HI**|<br>**UMI**|**LMI**|**LI**|
|---|---|---|---|---|
|Efficient public capital stockθ|0.870|0.753|0.730|0.590|
|_No. of countries**_|_21_|_25_|_27_|_10_|
|Efficient public capital‐to‐output ratioG�/Y��θK�<br>��/Y�|0.751|0.726|0.656|0.574|
|Marginal product of e_fficient_public capital_MP_K�<br>G= ~~�~~<br>�<br>����<br>����<br>�<br>�|0.226|0.234|0.259|0.296|
|Marginal product of efficiencyMPe�φ�<br>��<br>���<br>�<br>����<br>����<br>⁄<br>~~�~~|0.009|0.011|0.015|0.022|
|μ=I<sup>�</sup>/Y/θ � pptsincrease inI<sup>�</sup>/Yequivalent to 1pptsincrease<br>inθ<sup>�</sup>after oneyear(also equivalent by2040)|0.045|0.065|0.079|0.125|
|For a general description of the sources of data, see Table 3.<br>Countries are classified according to the 2018 World Bank classification of countries<br>* Multiply by 100 (except values in ppts) to obtain parameter/variable values in per<br>** Number of countries for efficiencyθis based on IEI data.<br>Calculations forθK�<br>��/Y�,_MP_K�<br>�,MPeandμ, are formed by combining the data in<br>(not on a constantgroupof countries).|by income fo<br>centage shar<br>Table 5 with|r the 2017 ca<br>e or growth te<br>the efficiency|lendar year.<br>rms (%).<br> θfor each inco|me group|

One can also use the IEI to calculate the _efficient public capital‐to‐output ratio_ θK���/Y� . Because the public capital‐to‐output ratio ( KGm0 /Y0 ) is roughly constant across levels of development, but efficiency θ increases with development, the combined efficient public capital‐to‐output ratio also increases with development. Specifically, the efficient public capital‐to‐output ratio is around 0.75 in HI countries, 0.73 in UMI countries, 0.66 in LMI countries and 0.57 in LI countries. This suggests that LI countries do not have a shortage of measured public capital (as argued above), but rather a shortage of _efficient_ public capital.

> 39 Berg et al. (2015) show that for the Cobb‐Douglas production function (as used here), these two are exactly offsetting. However, even with the CES production function the two factors are mostly offsetting unless public and private capital are extremely complementary (their Figure 3).

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