sustainability if efficiency is not improved enough. Specifically, BRI investment is assumed to be fully realized during the period 2019-2023. For each BRI-recipient country, the annual level of BRI investment, assumed constant in U.S. dollar, is used to estimate annual levels of additional growth. The country specific estimates of additional growth from BRI investment are reported in Annex IV.

# _Empirical estimates_

In addition to model-based growth projections, this paper also estimates growth based on an empirical production function approach. BRI investment is expected to significantly increase the infrastructure stock of BRI-recipient countries. Following Calderon (2009), we built an unbalanced panel for a subset of 31 countries, created an index of different infrastructure assets and dealt with endogeneity and reverse causality issues of the infrastructure stock noted in the literature.<sup>28,29</sup> We also depart from Calderon (2009) as we use annual data and not 5-year averages, as we are interested in medium-term effects of installed capital on growth.<sup>30</sup> To measure the quantity of physical capital we built indices of infrastructure using Principal Components Analysis (PCA). This technique allows to avoid multicollinearity problems and measurement errors associated with single-infrastructure indicators. Using weights generated by PCA, we aggregate individual physical measures of infrastructure in telecommunications, electricity, and roads to compute an index of infrastructure stocks. Annex VII describes in more details the PCA analysis and data sources.

We run a regression of growth in real output per capita on a standard set of growth determinants, and on aggregate indices of infrastructure stock. Our estimation methodology is the generalized method of moments (GMM) for dynamic models of panel data (Arellano and Bond, 1991; Arellano and Bover 1995; Blundell and Bond, 1998), which is suited for dynamic panel data and accounts for some endogeneity in the explanatory variables through instrumentation. Our set of control variables comprises information on the level of trade openness, human capital (as proxied by the human capital indicator of Penn World Table), institutional quality (as proxied by the indicator of government effectiveness of the Worldwide Governance Indicators), lack of price stability, and government burden. More specifically, our dynamic panel regression equation is expressed by: where y denotes the real GDP per capita (in logs), X is a set of control and stock of infrastructure measures. When estimating the above equation, we face the potential problem of endogenous regressors. This affects, in principle, both the standard determinants of matrix X given that we can argue that these variables may be jointly determined. Indeed, this may be subject to reverse causality from labor productivity.

> 28 We restrict our sample to 31 countries due to data availability limitations on human capital index from Penn World Table.

> 29 On these concerns, see Blanchard and Giavazzi (2003) for the case of the European Union, and Easterly and Servén (2003) for that of Latin America.

> 30 Calderon (2009) uses 5 years averages as the main focus of that paper is to estimate long-run growth. This paper instead focuses on the medium term, namely the period 2019-2023 and requires estimates of annual elasticity of output which are obtained using annual data.

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