# _5.2 Calibration of select parameters_

# <u>5.2.1.  The usefulness of public capital φ (elasticity of output with respect to public capital)</u>

The effect of public investment on growth is most sensitive to the elasticity of output to public capital, φ , which we calibrate carefully in this subsection based on two meta‐analysis studies ‐‐ Bom and Ligthart (2014) and Nunez‐Serrano and Velazquez (2016), and a recent paper by Calderon et al. (2015). Meta‐analyses are necessary due to the controversy in the literature on this parameter with a range of studies with different samples, definitions and methodologies. Our default value is φ�0.17 , which is the upper bound across the two meta‐analyses and should be applied to “essential infrastructure” or “productive capital” only and is the same as in the IMF’s DIG model (Buffie et al. 2012). As such, our default calibration should be viewed as being relatively optimistic about the growth effects of public capital. An alternative value (which could be viewed as a lower bound) is φ�0.10 for all public capital. This latter value is slightly larger than the estimates in Calderon et al. (2015) of φ�0.07 �0.10 .

Bom and Ligthart (2014) look at 68 empirical studies<sup>22</sup> which cover the period 1983 – 2008. These studies are based on the production function approach and measure public capital in monetary and stock terms. Bom and Ligthart’s meta‐analysis indicates an average elasticity of output to public capital of 0.106 (not reported), which is higher in the long run and for core public capital, but lower for aggregate public capital/national government level (compared to the regional/local government level).

Nunez‐Serrano and Velazquez (2016) consider 145 papers<sup>23</sup> which cover the period 1983 – 2011. The empirical studies scrutinized are predominantly those that take a production function approach (85% of the sample) and include studies that use non‐monetary (17%) and flow (7%) measures of public capital. They find an average elasticity of output to public capital of 0.132, which is higher in the long run, 0.161. Though with less statistical significance, there is also indication that the elasticity value is higher with productive public capital. The distinction between monetary and non‐monetary measures of public capital does not have a discernible effect. A summary of select results from the respective meta‐analyses of Bom and Ligthart (2014) and Nunez‐Serrano and Velazquez (2016) is presented in Table 4.

**<u>Table 4: Elasticity of Output to Public Capital,</u>** φ **(“Usefulness”)**

|Bom and Ligthart(2014):*||
|---|---|
|Core infrastructure<sup>a</sup>|0.170|
|Totalpublic capital|0.122|
|Nunez‐Serrano and Velazquez(2016):*||
|Productive capital<sup>b</sup>|0.175|
|Totalpublic capital|0.161|
|Calderon et al. (2015) (infrastructure):*|0.070 to<br>0.100|
|aRefers to roads, railways, airports and utilities.<br>bRefers to capital aimed at health, education, housing and community se<br>installations, communication and transport infrastructure. Values are comp<br>results reported in Table 3, Section B.a. of Nunez‐Serrano and Velazquez (201<br>*Longrun estimates. Note that most studies control for the total orprivate capi|rvices, energy<br>uted based on<br>6).<br>tal stock.|

> 22 Of the 68 studies, 5 cover country groups (of which one is exclusively developing countries) and 63 are country‐specific (all advanced economies).

> 23 Of the 145 studies, 26 cover country groups (of which five are exclusively developing countries) and 119 are country‐specific (of which five are developing countries).

18