Neither of the two meta‐analyses contains a discussion of potential differences in φ between developed and developing countries. However, Calderon, et al. (2015),<sup>24</sup> using a relatively extensive cross‐country sample, find that the long‐run elasticity of infrastructure does not seem to vary with countries’ per capita income levels, infrastructure endowment or population size.

# <u>5.2.2.  Initial capital‐to‐output ratios and depreciation rates</u>

Our default data source for aggregate data on capital stocks and depreciation rates is the PWT 8.1, which is also used in the Standard LTGM. Unfortunately, PWT 8.1 does not include the split into public and private capital so we rely on data from the IMF for the relative shares of public and private capital stocks (see IMF 2015 and <u>http://www.imf.org/external/np/fad/publicinvestment/).</u><sup>25</sup> Given different computation methodologies, aggregate K/Y ratios differ between the PWT 8.1 and the IMF, and are on average lower in the latter case.<sup>26</sup> We assume that public capital is mostly structures, and so apply the 2% structures depreciation rate from PWT 8.1. The private capital depreciation rate is a residual determined by the country‐specific PWT 8.1 depreciation rate for aggregate K: δ�δ<sup>��</sup> �<sup>��</sup> + δ<sup>��</sup> �<sup>�</sup> ~~.~~

# = = <u>5.2.3.  Congestion (ζ 1) vs pure public good (ζ 0) and actual vs measured TFP growth</u>

Users of the LTGM‐PC must choose either a calibration with congestion (ζ=1) or without it (pure public good ζ=0). Unless users strongly feel that public capital in their country is not congested, we recommend using the congestion calibration. We use this ourselves as the default for the results in this paper and in the Excel‐based tool. The reason is that without congestion, _actual_ TFP in the model ( A� in equation 1) tends to depart from _measured_ TFP using standard growth accounting exercises. In any practical application of the LTGM‐PC, the actual TFP growth rate is one of the most important assumptions ‐ and also the most difficult to calibrate. When using the congestion specification, the actual TFP growth rate is similar to what one would get applying a standard growth accounting exercise. In contrast, without congestion the measured TFP growth rate is above the actual TFP growth rate, and so cannot be used to guide the calibration of the actual TFP growth rates without some kind of adjustment.

To see this, for each country we used the LTGM‐PC to generate a growth path by assuming that actual TFP growth A� was the same as that recorded in PWT 8.1 (over a 10‐year average).<sup>27</sup> Then we performed a standard growth accounting exercise on the generated growth rates (given growth rates of other growth fundamentals like human capital and the total capital stock), to generate _measured_ TFP growth. We then compared the measured TFP growth to the inputted actual TFP growth.

> 24 In the study, infrastructure is measured as a composite of several physical infrastructure indicators (as opposed to the monetary value of capital stock). A panel data set is used, comprising 88 countries that cut across different income levels and infrastructure endowments.

> 25 We use the following data from the IMF to calculate the shares: general government capital stock and private capital stock in billions of constant 2011 international dollars.

> 26 Both sources of data use variations of the perpetual inventory method to estimate aggregate capital stocks and do not take account of the destruction/damage of capital from wars/conflicts (which is naturally difficult to measure). Wars/conflicts also reduce output, perhaps faster than they destroy capital, and so the aggregate K/Y ratio may rise as a country enters a war/conflict. In the reconstruction period, it would not be surprising if measured public capital it extremely high because it fails to take account of the public capital destroyed in the conflict.

> 27 To be clear, the exercise is not dependent on the source of assumed actual TFP growth, but just that its distribution across countries is reasonable.

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