metadata: authors: 0: author: Cordella,Tito
count: World
docna: 0: docna: Optimizing finance for development
docty: Policy Research Working Paper
subtopic: Private Sector Economics,Tax Policy,International Trade and Trade Rules,Financial Economics,Finance and Development,Financial Sector Policy
teratopic: Law and Development,Private Sector Development,Industry,Science and Technology Development,Public Sector Development
abstracts: cdata!: The World Bank Group recently adopted
            the "cascade framework" to "maximize finance
            for development." The cascade recommends that reforms
            be tried first, followed by subsidies, and then public
            investments. To understand the economics of the cascade,
            this paper presents a model where reforms, subsidies, and
            public investments can be used to fill the investment gap,
            and computes the welfare associated with their different
            sequencing. The cascade is optimal when reforms increase
            efficiency at no cost. When they are costly, if policies can
            be project specific, their sequencing does not matter; if
            not, the cascade can be optimal if agents are myopic, but
            not if they are forward-looking. Tensions may thus arise
            between maximizing private financing and optimizing
            financing for development.
repnme: repnme: Optimizing finance for development
display_title: Optimizing finance for development
listing_relative_url: /research/2018/01/29543418/optimizing-finance-development
topicv3: Public-Private Partnerships m1326334 2206,Trade m1326924 698,Finance and Growth m1327404 1081,Financial Sector Development m1327681 1920,Tax Incentives m1327701 883
publishtoextweb_dt: 2018-01-29T00:00:00Z
historic_topic: Law and Development,Private Sector Development,Industry,Science and Technology Development,Public Sector Development
no_of_pages: 36
author_keys: 0: author_key: 879396
model_extractions: WPS8320 Policy Research Working Paper 8320 Optimizing Finance for Development _Tito Cordella_ Development Economics Vice Presidency Strategy and Operations Team January 2018
Policy Research Working Paper 8320

# **Abstract**

The World Bank Group recently adopted the “cascade framework” to “maximize finance for development.” The cascade recommends that reforms be tried first, followed by subsidies, and then public investments. To understand the economics of the cascade, this paper presents a model where reforms, subsidies, and public investments can be used to fill the investment gap, and computes the welfare associated with their different sequencing. The cascade is optimal when reforms increase efficiency at no cost. When they are costly, if policies can be project specific, their sequencing does not matter; if not, the cascade can be optimal if agents are myopic, but not if they are forward-looking. Tensions may thus arise between maximizing private financing and optimizing financing for development.

This paper is a product of the Strategy and Operations Team, Development Economics Vice Presidency. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at tcordella@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Optimizing Finance for Development<sup>�</sup>

Tito Cordella The World Bank

> �I started this project with Oliver Masetti. Unfortunately, he got too busy implementing the cascade and had to quit. I thank him for his initial contribution to the paper, and for the many long discussions we have had. I would also like to thank Shanta Devarajan, Marianne Fay, Ana Paula Fialho Lopes, Joaquim Levy, David Rosenblatt, Anushka Thewarapperuma, and Mike Toman for constructive comments and suggestions. Woori Lee provided outstanding research assistance. The usual disclaimers apply.
# 1 Introduction

In September 2015, the UN general assembly adopted a resolution laying out an ambitious agenda for sustainable development (Agenda 2030).<sup>1</sup> Multilateral development banks readily embraced it, but they soon realized that existing o¢ cial resources were not enough for the undertaking.<sup>2</sup> The challenge, to use World Bank President Jim Yong Kim’s words, became that of ...nding ways to “leverage the billions of dollars in o¢ cial development assistance to trillions in investment of all kinds, whether public or private, national or global.”<sup>3</sup> Against this backdrop, in March 2017, the World Bank Group (WBG) adopted<sup>4</sup> the “cascade approach as a concept to guide the WBG’s e¤ort to leverage the private sector for growth and sustainable development,”(World Bank, 2017b, p.1). If such language may sound a bit elusive, the guidelines on how to implement the cascade are very clear: “When a project is presented ask - ‘Is there a sustainable private sector solution that limits public debt and contingent liabilities?’If the answer is ‘Yes’ - promote such private solutions. If the answer is ‘No’ - ask whether it is because of: (i) Policy or regulatory gaps or weakness? If so, provide WBG support for policy and regulatory reforms. (ii) Risks? If so, assess the risks and see whether WBG instruments can address them. If you conclude that the project requires public funding, pursue that option.” (World Bank, 2017b, p.2) The aim of this paper is to provide a simple framework that helps us understand better (i) how the adoption of the cascade may a¤ect the allocation of ...nance across projects, and (ii) the conditions under which maximizing and optimizing ...nance for development are likely to coincide, and those under which they are not.

With these goals in mind, we present a very simple model where investment projects, which create positive externalities, can be ...nanced by the private or by the public sector. We then identify the set of worthy projects that the private sector should ...nance (because of its e¢ ciency advantage vis-à-vis the public sector), but that it does not (because they are not commercially viable). To ...ll such an investment gap, following the cascade, we consider three di¤erent government interventions: the ...rst is an upstream policy reform that allows private investors to extract (part of) the externalities; the second is a public subsidy (for instance in the form of public sector co...nancing of projects or of subsidized guarantees/insurance instruments) that induces the private sector to invest; the third intervention is the direct funding of the entire project by the government.

If upstream reforms are able to crowd private investments in at no cost for the society then, by themselves, they can address the investment gap. In such a case, the cascade is clearly optimal. When instead, there are costs associated with reforms (e.g., higher private returns are the outcome

> 1 Available at http://www.un.org/ga/search/view_doc.asp?symbol=A/RES/70/1&Lang=E

> 2 See https://sustainabledevelopment.un.org/

> 3 Address at the Third International Conference on Financing for Development Addis Ababa, Ethiopia, June 13, 2015. Available at http://documents.worldbank.org/curated/en/144851468190446079/pdf/101985-WPBox393267B-PUBLIC-2015-07-13-JK-Billions-To-Trillions-Ideas-to-Actions.pdf

> 4 World Bank (2017a).

1
of e¢ ciency gains but also of higher fees that restrict access) trade-o¤s between the three di¤erent policy instruments arise. To get a better understanding of such trade-o¤s, we consider ...rst the case in which government interventions can be perfectly targeted to speci...c projects. When this is the case, the government has the ability to o¤er subsidies that are project speci...c and to decide the set of projects to which a particular reform applies or not. We then consider the case in which the subsidy should be the same for all projects and, if reforms are implemented, they a¤ect all (un...nanced) projects. In both cases, we compute the allocation and the welfare levels associated with any of the possible sequences of policies: reforms ...rst, subsidy second, public project third; subsidy ...rst, reforms second, public project third, and so forth.

Our main ...ndings are the following: (i) when reforms and subsidies can be perfectly targeted to projects, the sequencing of policies does not matter; (ii) when they cannot, the sequencing does matter. If the agents/agencies in charge of a speci...c policy are “myopic,” that is, they do not anticipate the policies implemented by other agencies, there are situations in which the cascade sequencing can be optimal; (iii) when agencies are forward-looking and anticipate the e¤ects of their own policies on downstream policy interventions (and reforms are part of the optimal solution) then the cascade is never optimal and the optimal sequencing requires subsidies/guarantees to be o¤ered ...rst.

While the paper focuses on a very speci...c problem: the economic underpinnings of the cascade framework recently adopted by the WBG, the issues it touches relate to a wide body of literature. With respect to the Agenda 2030, Schmidt-Traub and Sachs (2015) provide an assessment of public and private investment needs to achieve the SDGs, while Samans (2016) analyzes the investment barriers that the private sector faces in emerging markets and looks at the role that blended ...nance can play in overcoming them.

Of course, the discussion on the role that public and private investment play in the process of economic development predates the Agenda 2030. Khan and Reinhart (1990), and Khan and Kumar (1997) study the contribution of investments, public and private, on long term growth in developing countries and conclude that the contribution of private investments is larger. The problem is that, in such countries, private investments often fail to take o¤. The reasons can be many, ranging from property rights and institutional quality (Banerjee et al., 2006) to political uncertainty (Rodrik, 1991).

Whatever the structural reasons that deter private investments in developing countries are, public policies can be part of the solution. OECD (2004) provides an overview of the existing sources of ...nance for developing countries and discusses how to mobilize new ones, including for the provision of global public goods. OECD (2015) looks at the di¤erent ...nancing instruments that can support infrastructure investments in the sectors or regions that need them the most. Klemm, (2010) provides a comprehensive overview of existing tax incentives for business investments,<sup>5</sup> while

> 5 The fact that tax incentives are very common instruments used to attract investments does not mean that they are uncontroversial. According to Pennings (2000) and Yu et al. (2007) investment subsidies are a better instrument than tax cuts to foster private investments. However, Danielova and Sarkar (2011) show that when debt ...nancing is possible, a combination of tax reduction and investment subsidy is optimal.

2
Engel et al. (2014) analyze the economics and ...nance of public-private partnerships. Finally, ADB (2015) discusses how public and private sources should coexist and reinforce each other in the new sustainable development agenda. While this paper builds on the ...nancial incentives literature, the model we present is designed with the cascade framework in mind. This explains some of its non-standard features.

The paper is organized as follows: Section 2 describes the basic model and explains why a ...nancing gap arises; Section 3 discusses the di¤erent instruments that can be used to ...ll such a gap, and how they should be allocated when they can perfectly target the di¤erent projects. Section 4 deals with the more realistic case in which subsidies and reforms cannot be project speci...c, so that the sequencing of policy actions matters; it then solves for the allocations and the welfare levels associated with di¤erent policy sequencing. It also distinguishes between the case in which agents/agencies are myopic and forward looking. Finally, Section 5 discusses the critical assumptions of the model and concludes.

# 2 The Basic Model

We assume that there is a continuum of investment projects, k = fxi ; �jg 2 K. All projects are of the same size, which we normalize to 1, they are indivisible, and they can be undertaken either by the private, P , or by the public sector, G. Investment projects di¤er with respect to the returns they generate. The returns associated with project k, are Rk<sup>l=r</sup> ka<sup>l+ r</sup> ke<sup>l,wherer</sup> ka<sup>l</sup> denotes appropriable returns (e.g., pro...ts), and rke<sup>lnon-appropriablereturns(e.g.,externalities).</sup> Superscript l, l 2 [P; G], denotes whether a project is undertaken by the private or by the public sector.

The existence of a di¤erence in the returns associated with privately and publicly ...nanced investment projects is what motivates the cascade approach. The private sector’s appropriable returns are denoted by ria<sup>P=1 + xi,andthepublicsector’sbyr</sup> ia<sup>G=1.Tofocusonthepolicy</sup> relevant trade-o¤s, most of the analysis features the case in which the private sector has an e¢ ciency advantage vis-à-vis the public sector, that is, when xi � 0.

We further assume that the private sector’s e¢ ciency advantage is project speci...c, and that it does not extend to externalities. Non-appropriable returns are thus the same, independently of whether the project is undertaken by the public or the private sector. We thus set rje<sup>G=r</sup> je<sup>P=</sup> �j, with �j � 0. Hence, a project k is characterized by an xi and a �j that we assume to be independently and uniformly distributed on the interval [0; 1], so that K = [0; 1]<sup>2</sup> . As per the costs associated with the di¤erent projects, we assume that one unit of capital is needed to ...nance a project. The cost of such unit of capital, c � 1, the cost of funding hereinafter, is the same for the public and the private sector;<sup>6</sup> therefore, the total cost of the project, c, is also the same. Without great loss of generality, we assume that c 2 (1; 2).

> 6 Of course, the private sector’s cost of borrowing can di¤er from the public sector’s. However, in our simple framework, this would be equivalent to a horizontal shift in the support of xi, towards the left when the public sector has a cost advantage, towards the right when the private sector has it.

3
In the simple set-up we just described, it is easy to identify the set of welfare improving projects that the private sector should, but does not ...nd it pro...table to ...nance. Indeed, the private sector, which maximizes private returns, Ri<sup>P�c,...ndsitpro...tabletoinvestinaprojecti¤ 1 + xi�c,or</sup> However, since the private sector does not internalize the externality, �j, its participation constraint (1) is stricter than the condition that insures that the project is welfare improving. Such a condition can be written as 1 + xi + �j � c, or Our basic set-up is summarized in Figure 1a, where, setting c = 2<sup><u>3</u>,weordertheprojects’space</sup> according to the associated private sector’s e¢ ciency advantage and externalities, that is, in the (xi; �j) space. Region D, is the locus of the projects that are quintessentially private. They are characterized by high private sector e¢ ciency advantage (xi > <u>xP</u><sup>),andtheyalwayssatisfythe</sup> private sector participation constraint (1). We will disregard such projects in the remaining of the paper, as we will disregard the projects in region C, with xi < 0, where the public sector has an e¢ ciency advantage and, thus, it should always undertake them. Hence, the area of interest for policy makers, and the focus of this paper, is Region B, where xi 2 [0; x ~~P~~<sup>],and�</sup> j<sup>�</sup><sup><u>�</u></sup> ~~P~~<sup>.</sup> Projects that belong to such a region should, on welfare grounds, be undertaken by the private sector. Having disregarded regions C and D, the parameter space that is pertinent to the analysis is the one depicted in Figure 1b. In the ...gure, we split region B in two subregions, B<sup>0</sup> and B<sup>00</sup> . In Region B<sup>0</sup> , we have that and hence public investments are welfare improving. However, on e¢ ciency grounds, it would be preferable if projects were undertaken by the private sector. Instead, in region B00, condition (3) does not hold so that the only projects that are welfare improving are those undertaken by the private sector. This being said, since the private sector does not internalize the positive externality, and projects do not generate positive net returns–condition (1) is not met–, the private sector is not willing to invest in region B. Finally, projects in region A are not worth ...nancing by either the private or the public sector. However, we cannot ignore them altogether because, as we will see later, some of them could end up being ...nanced if the government is not able to target subsidies to speci...c projects.

# 3 How to ...ll the investment gap?

Before discussing issues related with the sequencing of interventions, it is useful to introduce the three di¤erent policies that, in our framework, can ...ll the investment gap: reforms, subsidies, and public investments, separately. We then compute the conditions under which each of them is 4
<!-- Start of picture text --> Figure la: Basic set-up Figure 1b: Benchmark<br>11<br>7<br>0c-1 1 0 c-1<br>x x<br><!-- End of picture text --> ay Qa a] -—ay a< as a a]
interval, in all possible scenarios, the welfare associated with reforms increases monotonically with �. Hence, without loss of generality, we only consider the case � = �. That is, denoting the reform scenario by tilde, we assume that if reforms crowd in private investments the associated returns are given by In such a case, the private sector ...nds it pro...table to invest if 1 + xi + �� � c, or Notice that, under assumption (4), private and total welfare<sup>7</sup> associated with reform induced private sector’s investments are exactly the same. This means that the private sector participation constraint, and the condition that insures that the private sector’s projects are welfare improving, coincide. This condition can be written as Notice that, when �= 1, by the sole use of reforms the government is able to induce the private sector to ...nance all welfare improving projects at no cost for the society as a whole. Moreover, if � > 1, reforms increase the set of welfare improving projects B. For smaller values of �, a set of valuable projects (those below <u>�</u> ~~R~~<sup>inFigure2a)thatarenot...nancedbytheprivatesector</sup> remains; in the special case of �= 0, no additional project is ...nanced. Figure 2a illustrates how the introduction of reforms changes the private sector’s incentives to invest for di¤erent values of � .

# 3.2 Public sector intervention: Subsidies and public investments

Let us now consider the situation in which the government is willing to use subsidies (guarantees) or public projects to ...ll the ...nancing gap. We start with the subsidies, si, that the government can o¤er to the private sector at a cost csi. Since the government looks at total welfare, and si is a pure transfer from the government to the private sector, the welfare cost of a subsidy si, is si(c � 1),which is equal to the government’s cost of funding. Under such a policy, the private sector ...nds it pro...table to invest if 1 + xi + si � c, or

> 7 Throughout the paper, we assume that the public sector maximizes total returns, that is, the pro...ts and externalities associated with the projects.

6
<!-- Start of picture text --> Figure 2a: Reforms Figure 2b: Subsidies Figure 2c: Public Investments<br>1 :1 Y 2<br>‘ ses yp(@=0.25) .<br>\ --+ yy9(a=0.5) Cl Subsidies Non Investment<br>‘ — ya(@=1.25) O No financ i ng o financing<br>0 SS NS<br>c-l 0 X cl 5 5 =<br><!-- End of picture text --> y>_ Y2> - = = ~~7~~ Y2 - = ~~y~~
# 3.3 Optimal sequencing of interventions

From the previous analysis, it is clear that a government can rely on di¤erent instruments to ...ll the investment gap. The question that follows is which instrument has to be preferred and under what circumstances. This is what we analyze next, under the assumption that the government can perfectly tailor policies according to the characteristics fxi; �jg of any speci...c project k. In other words, the government can implement reforms that only apply to projects with given values of xi and �j, and the same is true for subsidies and public investments.<sup>8</sup> In what follows, we characterize the allocation of instruments that maximizes total welfare. We denote such allocation as the optimal policy allocation, OPA. Lemma 1 below fully characterizes such an allocation as a function of the the degree of private sector advantage (xi) and the externalities (�j) associated with each speci...c project.

Lemma 1 (1):If reforms are not e¢ cient enough (� <<sup><u>1</u></sup> c<sup>):(i)if�jissu¢cientlylow,noinvest-</sup> ment inducing policy is welfare improving; (ii) for su¢ ciently high values of �j, and low values of xi, it is optimal for the government to implement public projects; (iii) for su¢ ciently high values of �j and xi, subsidies are instead optimal.

(2): If reforms are e¢ cient enough (� �<sup><u>1</u></sup> c<sup>):(i)if�jissu¢cientlylow,noinvestmentinducingpol-</sup> icy is welfare improving; (ii) for high �j and low xi, it is optimal for the government to implement public projects; (iii) for projects with intermediate �j and su¢ ciently high xi, reforms are optimal; while (iv) for su¢ ciently large values of �j and xi, subsidies are optimal.

## Proof: See Appendix.

� Figure 3a summarizes our results for di¤erent values of .<sup>9</sup> The ...rst, easy, takeaway from the ...gure is that, no matter how e¢ cient reforms are, when dealing with high externalities/low private sector advantage-type of projects, the best option is public ...nancing. When private sector advantage is high, instead, the best option is a subsidy. The reason for the optimality of a subsidy is that, when xi is large, a very small subsidy is su¢ cient to crowd in private investors. Hence, b the costs of the subsidy are of second order (si tends to zero when xi tends to c � 1), while those associated with public investments and reforms are always of ...rst order (except in the limit cases in which xi = 0, or �= 1). Thus, while there are always situations in which public investments or subsidies are optimal, for reforms to have a place in an OPA, they should be e¢ cient enough, that is, we need that � ><sup><u>1</u></sup> c<sup>.E¢ciencyhereismeasuredagainstthecostscassociatedwiththe</sup> subsidy. In addition, the appeal of reforms weakens in the presence of large externalities because of the deadweight loss associated.

A pretty trivial, but important point, often forgotten in the cascade debate, is that

> 8 For public investments this is always the case since the government decides which projects to ...nance.

> 9 Also in this ...gure, we set c = 3=2. Hence, in the ...rst two panels of Figure 3a, we have that � < <u>1c</u><sup>,and��</sup><sup><u>1</u></sup> c in the last one.

8
Remark 1 If the government is able to perfectly target the policy instruments, the sequencing of interventions does not matter.

Indeed, if the government can associate an instrument to any fxi, �jg, it will perfectly de...ne the scope of each policy so that the sequencing of the interventions does not matter. In other words, the fact that, in order to ...ll the investment gap, the government starts with reforms, subsidies, or public investments, is irrelevant; what is done ...rst does not pose limits to what can be done next. In such a world, there is no need for a cascade, or for any other sequencing algorithm.

# 4 Imperfect targeting

Let us now remove the assumption that the government can o¤er subsidies or reforms that are project speci...c. Consequently, we assume that xi, and �j are observable but not contractible. This implies that the government can decide which speci...c projects to ...nance directly, but it can only o¤er one subsidy, the same one to all investors. With respect to reforms, they apply to all projects that have not yet been ...nanced, and only to those ones. This means that reforms do not a¤ect the returns of the projects that they are unable to crowd in and that are later ...nanced through a subsidy.<sup>10</sup> We also assume that, once a project is ...nanced, the source of ...nancing cannot be modi...ed. This means that if an investor decides to ...nance a project applying for particular subsidy, it cannot later on renounce the subsidy and take advantage of a reform; similarly, if an investor decides to ...nance a project taking advantage of a particular reform, then it cannot “renounce the reform” and apply for a subsidy.

It is clear that, now, the order of interventions does matter. If the government starts with reforms, all projects that have been ...nanced through reforms cannot later be ...nanced by subsidies or public investment. The same argument applies to public investment and subsidies. Of course, the optimal allocation of policies is not the same under perfect or imperfect targeting. The constrained optimal policy allocation (COPA)–that is, the policy allocation that is optimal when the government is not able to target policies according to the characteristics of the speci...c projects–should equalize the marginal returns associated with each policy (at least when all policy instruments are utilized in equilibrium). Asking the reader to be patient, and to wait until Section 4.4 for a characterization of the COPA, we illustrate such an allocation in Figure 3b. Unsurprisingly, given that subsidies cannot be properly targeted, and that they end up ...nancing a number of projects that are not worth ...nancing (those under the 45 degree <u>�</u> ~~P~~<sup>line),thegovernmentwill...nditoptimalto</sup> o¤er smaller subsidies under the COPA than under the OPA.

> 10 This is the case when, for instance, a reform allows the private sector to invest in an infrastructure project with a cost plus fee contract. If there is no interest for the private sector to invest under such conditions, but there is with a subsidy, then the fact that the reform occurred does not a¤ect the returns when the subsidy is o¤ered. In the concluding section, we discuss how the relaxation of such assumption may a¤ect our results.

9
<!-- Start of picture text --> Figure 3a: OPA<br>OPA a=1/6 OPA @=1/2 ODA a=5/6<br>|K1 -lIq -1Ni<br>0 c-l 0 c-l 0 c-l<br>x Figure. 3b:x COPA x<br>CORA s=1/6 COPA a=1/2 COBRA #=4/6<br>1 l 1<br>|-|<br>HaI<br>0t-1 0 c-1 0 c-l<br>O No Financinga<br>* * x © Public Inv.<br>Figure; 3c: RSG (Cascade) © Reforms<br>RSG, e=1/6 RSG, g=1/2 RSG, g=sjg «(1 Subsidies<br>1 1 1<br>||-|<br>|\K<br>0c-l 0 c-1 Li) cl<br>x x x<br>Figure 3d: RGS<br>RGS, e=1/6 RGS, e=1/2 RGS, e=5/6<br>41 iN1 aN1<br>0 t=] i] t<1 a] <1<br>x x x<br><!-- End of picture text -->
<!-- Start of picture text --> Figure 3e: SRG<br>SEG, onl /6 SRG, onl /2 SRG, and/é<br>al1 a1 aN1<br>Li c-l 0 c-l 0 c-l<br>x x z<br>Figure 3f: SGR<br>SGR, @=1/6 SGR, g=1/2 SGR, a==5/6<br>1 1 1<br>=» c-] * co] = c-l<br>O No Financing<br>o c-l o c-1 0 c-1 © Pubbe Inv.<br>O Reforms<br>: : :<br>Figure 32: GSR © Subsidies<br>GSR, oul /é GSR, aul/2 GSR, amd /6<br>|-1 -1y |yy1<br>o c=1 o c= 0 c=1<br>x x x<br>Figure 3h: GRS<br>GRS, a=1/6 ORS, gel/2 GRS, a5 /6<br>.A1 -1: -1KY<br>0 c=] o c=] i] c=1<br>z x x<br><!-- End of picture text -->
# 4.1 Myopic beliefs

Having set the optimal benchmark as a yardstick to compare di¤erent policies, we now assume that, when implementing a policy, whatever it be (reform, subsidies, public investments), the agent, or better the governmental agency in charge, does not anticipate that other agencies will adopt other policies at a later stage. When this is the case, each agency maximizes social returns assuming no other policy will ever be put in place.

The reason we focus on such myopic beliefs is that, in our reading, these are the ones implicitly assumed by the cascade approach. Indeed, the algorithm we discussed in the introduction requires that upstream policy reforms be tried ...rst, public coinvestment or risk-sharing next, and ...nally, only if both reforms and subsidies are insu¢ cient to close the ...nancing gap, public investments should be pursued. The assumption of myopic beliefs will be removed in Section 4.5, where we allow the di¤erent agencies to be forward looking and implement each single policy anticipating how it will a¤ect the policies that will be put in place at a later stage by other agencies.

Starting with the case of myopic beliefs, we analyze the policy allocations and the welfare associated with the di¤erent sequencing of the policies. Having three policies, R; S; G, where R stands for reforms, S for subsidies, and G for public (government funded) investments, we have 3!=6 di¤erent sequences. Following the order of the interventions, we denote the cascade approach by RSG, the “anticascade”scenario (that with the opposite sequencing as the cascade) by GSR, and so forth.

In the main text, we provide a sketch on how to compute policy assignments and welfare under the cascade approach, and we compare the cascade with the other scenarios. We refer the reader to the Appendix for the formal derivation of all the di¤erent cases.

# 4.2 The Cascade Approach (RSG)

If the government follows the cascade approach, it starts by implementing reforms, it then moves to subsidies and, if worthy projects remain un...nanced, it ...lls such a gap with public investments. The welfare gains WC<sup>Rassociatedwithreforms(R)underthecascadeapproach(C)aregivenby:</sup> where x~ �fx : <u>�</u> ~~R~~<sup>= 1g = c �1 ��.</sup> Let us now introduce subsidies and compute the additional associated welfare WC<sup>S.Weshould</sup> distinguish between two cases. In the ...rst, � � c � 1, and thus <u>�</u> ~~R~~<sup><1forallxi2[0; 1].When</sup> this condition is veri...ed, the problem of the government is that of ...nding the optimal subsidy s (it can be zero) that maximizes 12
� When, instead, < c � 1, the problem of the government is that of ...nding the optimal subsidy s that maximizes Finally, the government directly ...nances through public investments all projects in the domain <u>xP</u> 1 ~~R~~ Rc�1<sup>d�jdxithathavenotbeencrowdedinbythereformsand/orthesubsidiesputinplace.</sup> 0 We refer the reader to the Appendix for the full derivation of the results. The ...ndings of our analysis are summarized in Figure 3c. When we compare the allocations obtained using the cascade algorithm with the constrained optimal ones, unsurprisingly, we ...nd that the cascade framework pushes reforms far beyond, and reduces public investments far below, what is optimal from a welfare perspective. Interestingly, since the relative cost of subsidies increases with the degree of e¢ ciency of the reforms,<sup>11</sup> it is when reforms are less e¢ cient that subsidies become increasingly generous and, thus, they are more likely to crowd out more e¢ cient public sector projects.

# 4.3 Alternative sequencing

In the same way as we did for the cascade, we can compute the allocations that are associated with the ...ve other possible sequences of policies (see Appendix). The results are summarized in Figure 3d-h. If we compare the cascade, RSG, with the RGS sequence, reforms necessarily lead to the ...nancing of the same set of projects. This, in turn, implies that results are identical when reforms are so e¢ cient that subsidies are never implemented (high values of �). However, they � di¤er substantially for low values of . When this is the case, public investments replace subsidies.

Let us now consider the SRG sequence. Of course, in this case, subsidies play a substantial role. However, di¤erently from the cascade, they are implemented when they are comparatively more e¢ cient, namely when the private sector e¢ ciency advantage is substantial (high values xi). In addition, while for low values of � subsidies completely crowd out reforms, for intermediate values of � both policies coexist at equilibrium. When we move to the SGR sequencing, the scope for subsidies remains the same. However, now, public investments replace reforms completely, for � intermediate values, and partially for high values of .

When we move to the “anticascade”sequence GSR, public investments are implemented when-

> 11 When reforms cover most of the high-� projects, the share of “bad”projects, that is, those that lie below <u>�</u> ~~P~~<sup>=</sup> c � 1 � x, crowded in by subsidies necessarily increases.

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ever they yield positive returns (including the externality), while subsidies crowd in the remaining projects where the private sector has a substantial e¢ ciency advantage; reforms, when su¢ ciently e¢ cient, play the residual role. Lastly, in the GRS scenario, reforms completely crowd out subsidies for intermediate and high values of �, but not for lower ones.

# 4.4 Optimal myopic sequencing

In the previous section, we illustrated the policy allocations associated with the di¤erent possible policy sequences. The obvious question that remains to be answered is which sequence is superior on welfare grounds, and under which circumstances. By a simple comparison of the di¤erent policy allocations with the COPA, it is evident that the latter coincides with SRG and SGR for low values of � and with SGR alone for intermediate values. Instead, for high values of �, the cascade, or the identical RGS scenario, are the ones that resemble more to the COPA. To ...nd a de...nitive answer to the question we compute, for all values of � and c, the welfare functions derived in the Appendix (integrating over xi and �j), we compare them all and, for each combination of the parameters, we compute the policy allocation(s) that leads to higher welfare levels. We ...nd that: Proposition 1 (i) When reform e¢ ciency is low (low values of � ) the optimal myopic sequencing is SRG or SGR (which are identical). (ii) When reform e¢ ciency is high, the optimal myopic sequencing is RSG (the cascade) or RGS (which are identical). (iii) For intermediate values of �, the optimal myopic sequencing is SRG or SGR (which are identical), when the cost of resources c is low, SGR for intermediate values of c, and SRG when c is large.

## Proof: In Appendix

The ...ndings of our analysis are illustrated in Figure 4, which fully characterizes the optimal myopic policy allocations for any value of the parameters, that is in the (�, c) space. From the discussion in the previous section, and from an even cursory inspection of the ...gure, it is evident that, for low values of �, the optimal (myopic) policy sequencing are SRG and SGR–which in this case coincide, since no reform is undertaken–that mimic the COPA. When reforms are very e¢ cient, the cascade (RSG) or RGS–which coincide since reforms completely crowd out subsidies– are instead the optimal allocations. For intermediate values of �, the optimal allocation depends on the value of c. If c is small, so that subsidy costs are limited, reforms will never be implemented and, again, SRG and SGR will be identical, and constitute the preferred option. For intermediate values of c, reforms are implemented and the larger is c, the more likely it is that reforms are a better instrument to ...ll the ...nancing gap than public investments.

# 4.5 Optimal forward-looking sequencing

To understand the results derived in the previous section, it is useful to think of a government with three agencies dealing with the investment gap, one in charge of reforms, one of subsidies, and one of public investments. Each of the agencies is given the mandate of maximizing total 14
<!-- Start of picture text --> 2<br>O SGR<br>& O SRG<br>O RSGor RGS<br>O SRGor SGR<br>1<br>01<br>a<br><!-- End of picture text -->
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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resource constraint, and we further assume that the marginal cost of public funds is constant. However, such assumptions are not critical. Consider the case in which the government has a hard budget constraint or faces an increasing marginal cost of funding. This does a¤ect the amount of subsidies it can o¤er or the number of projects it can ...nance, but not the optimal sequence of policies, both when agencies are myopic and forward looking.

Third, we assumed that the government cannot perfectly target subsidies and reforms. Such an assumption, as we already mentioned, is critical for the sequencing of policies to matter, and thus should be part of any analysis of the cascade. Our modeling of subsidies is pretty standard and, were the government able to o¤er project speci...c subsidies, this would make the case for “subsidies ...rst”even stronger. As per the reforms, we assumed that if a reform does not attract a particular investment project, it does not a¤ect the returns of the same project if the project is ...nanced through subsidies. This is a reasonable assumption if one thinks of regulatory reforms such as those that allow the private sector to bid for concessions. However, it is a less reasonable one if reforms have a cost in terms of externalities. Think, for instance, of a reform that reduces some environmental standards, or one that strengthens patent rights. Once such reforms are undertaken, they apply to all projects, already, and yet to be ...nanced. When this is the case, and agents are myopic, the appeal of subsidies vis-à-vis reforms decreases and the cascade sequencing is optimal for a larger set of parameters. When, instead, agents are forward-looking, then the sequencing becomes irrelevant; the incentives of both subsidies and reforms coexist in any single project; however, the overall appeal of reforms decreases as the associated costs in term of lost externalities now a¤ect all projects that end up being ...nanced by the private sector.

While the previous discussion suggests that our main conclusions should hold true in a more general framework, we do not claim that the subsidy ...rst policy should replace the cascade algorithm under all possible circumstances. For instance, one could add government failures to the model, and this can tilt the decision tree in di¤erent directions.

There is, however, one general lesson that can be learned from our analysis. The lesson is that the objective of maximizing private ...nance for development may con‡ict with the objective of optimizing ...nance for development; this means that policy-makers should carefully weigh the di¤erent trade-o¤s if they want to use the scarce existing resources, which are vital to achieve the Sustainable Development Goals, in the most e¤ective way.

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