# **4** . **Evidence on the efficiency/quality of the public capital stock,** θ

This section develops a new Infrastructure Efficiency Index (IEI) to measure the proportion of public capital spending that delivers useful public capital/infrastructure services. For example, power lines and power plants might not deliver electricity to households and businesses, dams and pipelines might not be able to deliver water due to leaks, and roads may be in poor condition (such as being unpaved) (World Bank 1994). The IEI combines these measures into a single index for all countries.

# _4.1 A new Infrastructure Efficiency Index (IEI)_

An infrastructure efficiency index for measuring θ� in the model above should have several key features: (i) informative about many countries; (ii) simple and transparent in its construction; and (iii) cardinal rather than conveying a relative rank/score. A cardinal index is needed because a doubling of θ� in our model _doubles_ the efficient public infrastructure stock, whereas a doubling in score or rank could mean the increase in the efficient public infrastructure stock is smaller or greater than double. While there are other infrastructure efficiency indices in the literature (surveyed below in Section 5.2), none of them have all three features. Our new Infrastructure Efficiency Index (IEI) does, following a similar methodology as Rioja (2003)<sup>15</sup> but for as many countries as possible subject to data availability.

Specifically, we construct the index using more recent data for three indicators – (i) electricity transmission and distribution losses (% of output); (ii) water losses (% of provision); and (iii) paved roads (% of total roads). Ideally, we would like to have used the percentage of paved roads in good condition as a subcomponent of the IEI. However, this statistic is no longer available. As such, we follow Calderon and Serven (2010) who use paved roads (% of total roads) as an indicator of the quality of road networks in their analysis of the quantity and quality of infrastructure services in Latin America. We nevertheless recognize that unpaved roads are not always undesirable or inefficient and may depend on country‐ specific geographic features. Electricity losses reflect inefficiency at the transmission and distribution stages ‐ which is what our index intends to measure ‐ but also electricity delivered but not paid for which can be attributable to theft and unmetered supply. For some countries the second type of non‐technical losses can be large – however, this can still to some extent be seen as related to dysfunctional infrastructure in terms of construction and management (or operational inefficiency) (Jimenez et al. 2014). We also do not include telecommunications in the composite index since fixed‐telephone line faults may no longer be relevant due to the rising importance of mobile telephony, and data on the quality of mobile phone service are not as extensive.

In calculating the IEI, we want to include the latest data, but also recognize that infrastructure losses for a single year can be very noisy. As such we take the average of the index for the latest available year and the post 2000 average, using a weighted average of water losses, power losses and paved roads:

> 15 Rioja (2003) uses the physical infrastructure losses reported in World Bank (1994), weighted by corresponding infrastructure stock shares (from Ingram and Fay (1994)), to proxy the efficiency parameter for public capital stock in seven Latin American countries and five industrialized countries. The infrastructure loss indicators comprise electricity power transmission and distribution losses (% of output), faults per 100 main telephone lines per year, percentage of paved roads not in good condition, and water losses (% of total provision).  Calderon and Serven (2004, 2010) construct an infrastructure quality index based on the first principal component of electricity losses, the share of paved roads, and the waiting time for telephone line installation.

13