which it implements public investments and reforms really does not matter (as the choice will only be based on their relative e¤ectiveness). Using the cascade sequencing, if reforms are part of the policy menu, they will necessarily crowd out more e¢ cient subsidies. Hence, it is only when no reforms are part of the COPA that the cascade is as good as any other sequencing, since, in this case, it does not matter whether to implement reforms or public investments ...rst, since reforms will not be implemented in either case.

# 5 Concluding Remarks

According to a recent McKinsey report (McKinsey Global Institute, 2016), to keep current growth trajectories, the world needs to invest about $3.3 trillion, 3.8 percent of GDP a year, in economic infrastructure, about 60 percent of which in developing and emerging economies. The estimated ...nancing gap for the world as a whole is about $350 billion a year, a ...gure that should be multiplied by three, if one budgets in new global commitments. The available public and o¢ cial resources alone clearly do not su¢ ce, so that the success of the Agenda 2030 critically depends on private sector participation; this is not only because of the ...nancial resources but also because of the expertise the private sector can bring to the table.

The cascade framework, adopted by the WBG, is an attempt to crowd in private resources by using public funds as a last resort. In adopting the framework, the WBG wants to signal that the timing of “using public ...nance till there is money and only then consider private sector options”had to be replaced by that of “trying everything and only if nothing works use public funds.”<sup>12</sup> While the motivations and the political economy behind the cascade framework are easy to understand, the economic underpinnings of the algorithm are less clear. This is what drove us to “write a model.” The model we presented is the simplest one–at least the simplest one we could come up with– that can describe the main trade-o¤s associated with the cascade framework. We like simple models; however, it is important to discuss how reasonable our simplifying assumptions, and more importantly how robust our results, are. This is what we try to do next.

First, discussing the sequencing of policies, we assumed that when investors are o¤ered a subsidy they do not wait for a more pro...table reform (at a later stage) to invest, or if o¤ered a subsidy they do not wait for a more pro...table reform. While such behavior could be seen as a consequence of myopic behavior (similar to the one of the government agencies), it can also be seen as the outcome of a competitive environment: if one investor passes on a pro...table opportunity, another will take advantage of it.

Second, the main rationale behind the cascade framework is that public resources are scarce, and this is why they should be used only as a last resort. In our model, we do not have a public

> 12 Actually, the IBRD article of agreements 1.(ii) already stated that the purpose of the Bank is “To promote private foreign investment by means of guarantees or participations in loans and other investments made by private investors; and when private capital is not available on reasonable terms, to supplement private investment by providing, on suitable conditions, ...nance for productive purposes out of its own capital, funds raised by it and its other resources,”something that echoes the cascade framework. I thank Aart Kraay for pointing this out.

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