Hevia and Loayza 2012), which we refer to as the Standard LTGM. However, in the Solow‐Swan model (and Standard LTGM), capital is simply an aggregate, and so those models cannot simulate the specific effect of an increase in public investment. In contrast, in the LTGM‐PC, total capital is split into public and private portions. The LTGM‐PC retains many other realistic growth drivers and features of the Standard LTGM, including other growth fundamentals (human capital, TFP, demographics, labor market participation by gender), and also implications for poverty rates. Section 2 presents the model and Section 3 describes how it is implemented in the Excel‐based tool.

Despite being theoretical, the paper draws extensively on the empirical literature to guide the choice of parameters. The most important parameter is the elasticity of output to public capital, φ , which we call the _usefulness_ of public capital. In Section 5 we review the evidence from two meta‐analyses and other literature, which suggests an elasticity of φ =0.17 for essential infrastructure and φ =0.10 for generic public capital like buildings (though users can also specify its value). We also calculate the country‐specific scarcity of public capital using a new public capital database from the IMF’s Fiscal Affairs Department.

However, we could not find a suitable measure of the fraction of public capital that is of high quality (we use “efficiency” and “quality” interchangeably).<sup>4</sup> So in Section 4 we develop a new cardinal Infrastructure Efficiency Index (IEI) to quantify the extent to which public capital is of high quality in different countries. The IEI is based on estimates of the fraction of roads that are in poor condition, water that never reaches its final customers, and electricity that is lost through transmission and distribution.

Our second contribution is to document how the quantity and quality of public capital vary across countries with different levels of development, and how this affects the impact of new public and private investment on growth (Section 6). This analysis is conducted through the lens of the LTGM‐PC and utilizes the cross‐country data on the IEI and public capital stocks collected for the Excel‐based tool.

Surprisingly, we find that the effect of an extra 1ppt of GDP of public investment on growth is roughly constant across different levels of development.<sup>5</sup> This puts us at odds with optimistic commentators claiming that sizable “infrastructure gaps” mean a larger growth dividend from public investment in low‐income countries. But it also puts us at odds with pessimistic commentators who claim that the low efficiency of public investment in developing countries ‐ due to corruption and mismanagement for example ‐ means that such projects have little effect on growth.<sup>6</sup> Overall a 1ppt increase in public investment as a share of GDP increases growth by 0.1‐0.2ppts in our model, depending on the calibration. As public investment is typically around 5% of GDP and usually less than 10% of GDP, higher public investment alone cannot turn a slow‐growing country into a tiger economy.

Instead, developing countries are short of _private_ capital, both relative to GDP and in absolute terms. Private capital as a share of GDP in low‐income countries is only 2/3 of that in middle‐income countries, and almost half that in high‐income countries. By our calculations, this means the return to

> 4 Other indices like the World Economic Forum’s infrastructure quality index or the IMF Public Investment Efficiency Index (PIE‐ X) include survey‐based scores or distance to the frontier analysis, which means that a quality or efficiency score does not reflect the cardinal or absolute fraction of public capital operating as it should (see Section 4). The literature uses the terms quality and efficiency interchangeably as well.

> 5 This result follows from measured public capital as a share of GDP being roughly constant across countries with different levels of development (which is possibly overstated in low‐income countries with weak governance; Keefer and Knack 2007).

> 6 As in Berg et al. (2015), the level of efficiency in the LTGM‐PC has no effect on the return to new public investment because the low quality of new public investment is exactly offset by greater need for public capital due to the poor quality of past public investment. See Sections 2 and 6.5.

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