Further details on the sources of data, IEI summary statistics as well as discussion on robustness checks for the index are provided in Appendix 2.

- _4.2 IEI versus other measures of public investment efficiency_

In this section, we briefly discuss some of the other measures of public investment efficiency that are available. These serve as useful checks against the IEI, but do also face some limitations for use in our model – primarily that they indicate relative performance rather than being a cardinal measure.

Afonso, Schuknecht and Tanzi (2005, 2010) and various IMF papers, starting with Albino‐War et al. (2014) take the approach of distance to frontier, where inefficiency is measured relative to best performing peer countries. In the case of the papers by Afonso, Schuknecht and Tanzi (2005, 2010) which respectively cover 23 industrial countries (2005 paper), and 23 emerging and new EU member states (2010 paper), the output measure is a composite of public sector performance based on a series of quantitative and qualitative socio‐economic indicators, while the input measure is public sector spending (i.e. more than just public investment).<sup>16</sup> For our model analysis purposes, we find that the results from these two papers may not be suitable because: one, the outcome variable encompasses broad, indirect macroeconomic outcomes; and two, efficiency is compared within a small group of countries – this may be particularly worrisome in the case of the emerging market/new EU member sample.<sup>17</sup> On the other hand, the IMF public investment efficiency indicator (PIE‐X) covers more than 100 countries. The output variables are directly related to infrastructure ‐ a quantity index (physical infrastructure coverage and provision of social services<sup>18</sup> ) and a survey‐based quality index<sup>19</sup> respectively, as well as a hybrid of the two; while the input variable is public capital stock per capita.<sup>20</sup> While individual country efficiency scores have not been published, group averages of the quantity indicator suggest that advanced economies are 70% efficient (infrastructure output could be increased by 30% for the same amount of public capital input), emerging markets are 60% efficient, while low‐income developing countries are at about 45% efficiency. Nevertheless, these are still _relative_ performance indicators rather than cardinal indicators of quality: a score of 70% does not mean that 30% of infrastructure stock is not productive but rather the economy is operating 30% below the best performer in its peer group.

Aside from the above measures of inefficiency, there is also the IMF Public Investment Management Index (PIMI) (see Dabla‐Norris et al. 2012), a purely qualitative indicator based on scores for individual country performance in terms of the investment process (project appraisal, selection, implementation and evaluation). While it provides information on relative performance across 71 developing countries and shows positive correlation with GDP per capita and indicators of governance quality, it is not a cardinal indicator of the proportion of public capital that is productive, and only

> 16 Qualitative indicators of corruption, red tape, judiciary efficiency, public infrastructure quality; and quantitative indicators ‐ shadow economy size, secondary school enrollment, education achievement, infant mortality, life expectancy, as well as broad macroeconomic outcomes – income distribution, growth performance and stability, inflation and unemployment.

> 17 Sinha (2017) uses the emerging market/new EU member state average efficiency as a reference point for public investment efficiency in Bangladesh.

> 18 Length of road network, electricity production, access to water, number of secondary teachers and number of hospital beds.

> 19 Based on the World Economic Forum Global Competitiveness Report survey responses on the quality of key infrastructure services.

> 20 With GDP per capita as an auxiliary input variable.

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