Learning through Crowdfunding Gilles Chemla and Katrin Tinn August 25, 2016

Abstract This paper examines the role of reward-based crowdfunding in learning about demand and improving investment decisions. The information gathered while raising funds from consumers provides …rms with a real option to invest if demand is su¢ ciently high. Despite moral hazard problems stemming from the …rms’ability to divert the funds raised, all-or-nothing schemes are nearly as e¢ cient as frictionless surveys and full money-back guarantees. Dominant platforms adopt features such as limited campaign length and transparency between backers, which are essential to overcome moral hazard. Our results are consistent with stylized facts and provide new testable implications. JEL codes: D80, G30, L14, L26, O30 Keywords: Reward-based crowdfunding, moral hazard, real options, learning, uncertainty, Kickstarter

Both authors are with Imperial College Business School. Chemla is also a research fellow at DRM/CNRS and at CEPR. Correspondance to Imperial College Business School, South Kensington campus, London SW7 2AZ, UK. E-mail: [email protected] and [email protected]. We thank Bruno Biais, Raj Iyer, Lubos Pastor, Jean-Charles Rochet, Wilfried Sand-Zantmann, Antoinette Schoar, and seminar participants at the CEPR 2015 European Summer Symposium in Financial Markets, the ESRC 2015 "Crowd-funding and other alternative forms of entrepreneurial …nance" conference, the Bank of Estonia’s 2015 Winter conference, the Imperial College FinTech Showcase 2016, the Paris-Dauphine 2016 Corporate Finance conference, SKEMA, Toulouse, and Imperial College for helpful discussions.

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1

Introduction

Raising external funds is hampered by moral hazard and informational frictions, in particular for new, innovative projects (Bussgang 2014, Tirole 2006). Both corporate …nance and monetary economics emphasize these issues as realistic and essential departures from the frictionless Arrow-Debreu setting, either through optimal contracting between …rms and outside investors (Innes 1990, Bolton and Scharfstein 1990), or when studying frictions that complicate the interactions between …rms and consumers (that Wicksell 1934, Townsend and Wallace 1987, Kiyotaki and Moore 2002). With these frictions in mind, the success of reward-based crowdfunding platforms, which enable …rms to raise funds from consumers without any …nancial reward, may seem surprising.1 The funds raised through reward-based crowdfunding have been substantial. The Kickstarter platform alone has enabled over 100,000 projects to raise over $2.4 billion in the past 6 years. Many projects have raised amounts comparable to funds raised during an angel or venture capital investment round.2 For example, in 2015, Pebble Technology raised over $20.3 million by pre-selling their product to over 78 000 backers after raising $10.3 million in its previous 2012 campaign. In 2014, estimations on global funds raised through reward-based crowdfunding range from $4 billion to $7.2 billion, i.e., around 10-15% of new venture capital investments, and practitioner reports have highlighted the rapid expansion and expected growth of the crowdfunding market. Crowdfunding, and in particular reward-based crowdfunding, is widely expected to become an essential component of early stage entrepreneurial …nance.3 In this paper, we develop a framework that provides a rationale for the existence 1

In contrast to other forms of crowdfunding (debt, equity), reward-based crowdfunding only allows rewards that are not …nancial, e.g., the Kickstarter rules state: "Projects can’t promise to /.../ o¤ er …nancial incentives like equity or repayment." (https://www.kickstarter.com/rules). 2 Business angels and venture capitalists have traditionally been considerd to be the best sources of …nancing risky and innovative projects. Typically, a venture capital investment exceeds $1 million, while a angel investment ranges from $20; 000 to $100; 000 (Bussgang 2014). As of February 9, 2016 around 150 projects have raised over $1 million and 2; 800 projects have raised over $100 000 though Kickstarter alone. The average successful US-based technology project on Kickstarter raised nearly $100; 000, from around 200 backers, between January 1, 2015 to September 17, 2015, 3 Funds raised through crowdfunding, among which reward-based crowdfunding is one of the largest components, grew from $530 million in 2009 to $16.2 billion in 2014, and has been estimated to amount to $34.4 billion in 2015 and $93 billion by 2025 (see Massolution 2015 and World Bank 2013). Forbes (Jun 9 2015) forecasts that crowdfunding industry will surpass VC industry in 2016. See also EY (2015), Massolution (2015), Crowdfunder (2015), and NVCA, 2015, "Annual Venture Capital Investment Tops $48 Billion in 2014, Reaching Highest Level in Over a Decade", January 16, http://nvca.org/pressreleases/.

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and success of these platforms in an environment where asymmetric information and moral hazard remain the prime sources of trading and contracting frictions. To raise funds, …rms promise backers rewards that typically take the form of an opportunity to pre-order the product being developed (Mollick 2014). Hence, these platforms function as a market place between producers and consumers, rather than a means to raise funds from benevolent or charitable backers. In our rational setting, pre-orders enable …rms to credibly learn about the preferences of a subset of consumers as well as to update their beliefs about overall future demand. As learning takes place before the …rm makes sunk investments, it provides …rms with a real option to develop projects if consumer demand is high enough, and to not invest if demand is low. We show that the option value of learning is maximized when investment costs are intermediate, i.e. when projects have zero or close to zero NPV based on prior beliefs, and that the overall relationship between the value of learning and investment costs is inverted U-shaped. We …nd that, ceteris paribus, the value of learning increases with the level of uncertainty about future demand. Such learning is valuable whether or not the …rm is …nancially constrained, and we do not impose credit constraints. Our model incorporates moral hazard, which arises because the …rm, after receiving the funds, may fail to do its best to deliver the product pre-ordered by its backers. Such moral hazard can be illustrated by the reported case of Erik Chevalier, who successfully crowdfunded a boardgame project on Kickstarter but was subsequently convicted and …ned $122,000 for spending the funds for his personal use instead of developing the project.4 As pointed out in Tirole (2006), there are many ways for …rms to divert funds, e.g., by claiming that a project failed despite the provision of best e¤ort. Although reward-based crowdfunding platforms are not legally responsible for guaranteeing the delivery of rewards, the vast majority of the projects do deliver them (Mollick 2014). One might expect the severity of moral hazard to increase with the amounts raised. Instead, we show that raising more funds alleviates moral hazard. When the number of consumers who reveal that they value the product is higher, the …rm also expects higher future demand from the consumers who did not have the chance to pre-order the product. Such Bayesian learning increases the …rm’s incentives to invest. For this learning e¤ect to overcome moral hazard, it is 4

Conor, Ga¤ey, 2015, "$122,000 Kickstarter Fraud Case Highlights Dangerous Lack of Regulation, Newsweek,12 June

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essential that the number of backers that did not have access to the campaign be su¢ ciently high. The …rm’s incentives to invest are enhanced by two contractual features of existing third-party platforms that facilitate direct trade between backers and the …rm: a …xed and limited campaign length, and transparency. We argue that these two contractual features enable reward-based crowdfunding platforms to bring value by externalizing commitment.5 A …xed campaign length implies that a …rm can, de facto, only pre-sell the product to a limited subset of backers. Transparency ensures that backers observe each other’s pledges during the campaign and can coordinate not to back a …rm that they expect will have insu¢ cient incentives to invest. Beyond alleviating moral hazard, transparency bene…ts the …rm, which can then pre-sell the product at a minimal discount. We explore two prominent types of schemes: All-or-Nothing (AoN) and Keepit-All (KiA). AoN schemes prevail on Kickstarter while Indiegogo allows …rms to choose between AoN or KiA. With both schemes the …rm sets a target before the campaign starts. During the campaign, backers can observe the overall contributions and choose whether or not to participate. They can also withdraw their contributions during the campaign. When the campaign ends, the funds raised are passed on to the …rm. With AoN the funds are returned to backers if the target is not met, while with KiA all the funds raised are passed on to the …rm. We show that AoN weakly dominates KiA. While our model identi…es parameters under which both schemes coexist, it suggests that the AoN scheme is more likely to prevail. We show that when moral hazard is su¢ ciently severe, the …rm must set a target that is higher than the …rst best investment threshold as rational backers would not participate otherwise. Despite this ine¢ ciency, the expected payo¤ to the …rm from an AoN campaign is nearly as high as under the …rst best. Indeed, learning about demand is also valuable to a …rm that does not meet the target. Since the equilibrium target is higher than the optimal investment threshold, this …rm may still choose to invest and to complete the project. If the failure to meet the target is associated with a reputation cost, the …rm obtains the …rst best payo¤ minus the expected value of this cost and platform fees. Our model delivers empirical predictions that are consistent with a number of existing …ndings. For example, we provide a rationale for frequently oversubscribed 5

Dewatripont (1988) examines the constraints that renegotiation imposes on …rms’ability to commit to contracts with third parties. Third-party platforms would …nd it di¢ cult to renegotiate previous contracts as their reputation would su¤er from this.

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successful campaigns, the higher success rate associated with shorter campaigns, and the investment made by a number of …rms after failed AoN crowdfunding campaigns. We suggest additional testable empirical predictions regarding the relationships between …rm characteristics, prior beliefs, targets, success rates and prices. We discuss the robustness of our main …ndings to variable costs and uncertainty about the …rm’s ability to develop their product idea. Earlier theoretical explanations of reward-based crowdfunding have focused on backer preferences rather than learning and moral hazard. For example, Belle‡amme, Lambert, and Schwienbacher (2014) assume that participation in crowdfunding provides backers with an additional utility compared to their valuation for the product, which enables …rms to raise funds and to price-discriminate. Varian (2013) endogenizes this additional utility by deriving an equilibrium in which the seemingly altruistic preferences of backers are due to each of them having a pivotal role in ensuring that the …rm has enough funds to invest and to produce the good that the backer values. Yet, these important consumer side e¤ects cannot explain some important patterns of successful crowdfunding campaigns. Namely, at odds with the prediction of price-discrimination, many products are pre-sold at par or at a discount, and numerous projects are over-funded to a degree that cannot be explained by the pivotal role of any individual backer. We emphasize the importance of learning about demand as an essential reason why …rms engage in reward-based crowdfunding. While news articles and research on this topic often consider …nancial constraints to be the main reason for crowdfunding, recent empirical evidence suggests otherwise (Xu 2016). Further, in their survey to …rms that had both successful and unsuccessful crowdfunding campaigns on Kickstarter, Mollick and Kuppuswamy (2014) show that the respondents reported learning about demand to be the single most important motive for crowdfunding while funding was only the fourth. In addition, they report that 30% of the …rms that failed to meet their funding target still completed their project.6 Strausz (2016) also considers a setting in which pre-selling through crowdfunding enables …rms to learn about consumer preferences. While it elegantly highlights some important di¢ culties of raising funds from backers, it does not explain why …rms would choose crowdfunding over alternative forms of external …nance. His 6

Cumming, Leboeuf, and Schwienbacher (2014) provide evidence consistent with the idea that All-or-Nothing schemes dominate Keep-it-All schemes. Both Mollick (2014), and Agrawal, Catalini and Goldfarb (2015) analyze the determinants of the success probability of crowdfunding, including the importance of geography. These papers have also found a negative correlation between campaign duration and success probability, which is consistent with our model.

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paper assumes that all …rms that participate are unable to raise funds otherwise. In contrast, we allow …rms to have frictionless access to other forms of …nancing (e.g., angel, venture capital, banks), and allow …rms to update their beliefs. Even though credit constraints could be an important motive for participation, it is unlikely to be the main motive: this is suggested by empirical evidence regarding numerous …rms completing their project in spite of failing to meet their crowdfunding target and the fact that large, …nancially unconstrained corporations such as Sony have crowdfunded projects. Without the real option value of demand, moral hazard implies that …rms that are most likely to participate and raise funds are those with low investment costs. This seems at odds with the fact that Kickstarter has attracted most of its projects from categories likely to involve substantial …xed costs such as technology, design, and games. As of June 2016, these three categories have crowdfunded about 10 times more Kickstarter projects and raised 45 times more funds than projects from categories such as Dance, Journalism, Crafts likely to involve low …xed costs. More generally, our paper relates to the strands of corporate …nance and monetary economics, which view asymmetric information and moral hazard as the sources of …nancial constraints (Myers 1977, Stiglitz and Weiss 1981, Hart 1995, Tirole 2006). As we consider similar frictions, crowdfunding and more traditional forms of …nancing appear to be complements. Whether or not the …rm is credit constrained only matters at the investment stage. The campaign itself may either provide actual funding or alleviate the root causes of …nancial constraints. For example, if …nancial constraints are driven by asymmetric information about demand, then the crowdfunding campaign that generates public information about demand alleviates these constraints.7 If a …rm and its future consumers can overcome moral hazard, then the …rm’s participation in crowdfunding may also alleviate the same moral hazard problem faced by traditional outside …nanciers. There are reported cases where …rms, after succeeding in reward-based crowdfunding, obtain further …nancial resources from angels, venture capitalists or investor-based crowdfunding.8 Relatedly, 7

Further, making information about consumer preferences public can alleviate information asymmetry in an unbiased manner. In contrast, when information is revealed publicly through the actions of privately informed entrepreneurs, it may distort both the market value of the …rm and investment decisions. For example, Myers and Majluf (1984) argue that equity issuance decisions convey negative information to investors, and Tinn (2010) and Angeletos, Lorenzoni and Pavan (2010) show that technology investments can be perceived as a positive public signal. 8 Brunstein, Joshua, 2014, "How Kickstarter turned into the Venture Capitalist’s Best Friend?", Bloomberg Business, August 11, http://www.bloomberg.com/bw/articles/2014-08-11/kickstartersuccesses-pivot-from-crowdfunding-to-venture-capital

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investor-based crowdfunding highlights the bene…ts of learning public information from the "crowd" in terms of screening creditworthiness (see Iyer et al 2015).9 Our paper also contributes to the literature that points out that investing in entrepreneurial projects enables …rms to experiment new technologies (Hellmann 2002, Bettignies and Chemla 2008, Kerr, Nanda, and Rhodes-Kropf 2014). We show that crowdfunding is an e¢ cient mechanism to learn about demand without experimentation costs. We argue that the real option to invest only if demand is high enough is su¢ cient for an entrepreneur to learn about demand, leading to products better attuned to backer preferences. Crowdfunding further appears to improve accessibility to entrepreneurship. Finally, our paper also relates to the industrial organization literature on preselling (Tirole, 1988, Rob, 1991, Crawford and Shum, 2005, Chu and Zhang, 2011), which primarily focuses on the …rm’s opportunity to price-discriminate. While this literature focuses on pre-selling existing products, we focus on the value of preselling at an earlier stage of the product cycle, while the product is still being developed and the …rm’s major …xed investment decisions can still be altered. Section 2 presents the model. Section 3 examines the …rst-best investment decision and the value of learning. Section 4 examines pre-selling through rewardbased crowdfunding platforms. Section 5 discusses extensions, Section 6 highlights testable implications, and Section 7 concludes.

2

The Model

We consider a three-date rational model in which a …rm has a new product idea, and can learn about demand after observing consumer decisions at date 0. At date 1, the …rm updates its beliefs and decides whether or not to invest I

0. At date

2 it produces and sets price p2 at which it sells the product to consumers. For now, the …rm’s marginal cost of production is zero. We do not impose exogenous …nancial constraints. We assume that all agents are risk neutral and discount future cash ‡ows at rate

< 1.

The …rm can sell 1 unit of the product to each of N potential consumers. Each consumer i 2 f1; :::; N g has private valuation vi = f0; 1g for one unit of the product and 0 for any additional unit. The fraction

of consumers with valuation vi = 1

(resp. vi = 0), which we refer to as 1-consumers (resp. 0-consumers), is initially 9

Hildendbrand, Puri, and Rocholl (2015) examine the incentives of borrower group leaders on Prosper.com, a debt-based crowdfunding platform.

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unknown to the …rm. Private valuations are i.i.d, which implies that consumer i’s valuation is a Bernoulli trial drawn from the true distribution, i.e., Pr (vi = 1j ) = . The fraction

follows a beta distribution, the p.d.f. of which is 1

(1 ) B( ; )

f( )= where

1

(1)

;

are positive parameters and B ( ; ) is the beta function. Beta dis-

;

tributions enable us to capture di¤erent distributions of prior beliefs, be they Ushaped, hump-shaped, or uniform.10 For the sake of clarity, we write = (1

0)

, where

0

2 [0; 1] and

E[ ] = V ar [ ] = That is,

0

+

=

0

and

> 0, such that =

0

2

( + ) ( +

is the prior mean and a higher

+ 1)

=

(1 0) . ( + 1)

0

implies a lower level of uncertainty

based on prior beliefs. All agents know the prior distribution. Consumer i knows his own valuation for the product.11 We start by exploring a benchmark setting where the …rm can frictionlessly learn the preferences of a subset M

N backers at date 0, e.g., by asking them to respond

to a survey. Frictionless consumer surveys re‡ect the …rst best, but rely on an unrealistic assumption that consumers would truthfully reveal their preferences.12 We argue that reward-based crowdfunding provides consumers with credible incentives to truthfully reveal their preferences. This is because 0-consumers never pre-order the product at a positive price (p0 > 0), while 1-consumers pre-order it as long as p0 is not strictly higher than the opportunity cost of waiting and of not receiving the product. We keep M …xed to compare the benchmark setting and the crowdfunding model. Figure 1 summarizes the timing of events under the main crowdfunding model and the appropriate benchmark. 10

If parameters

;

1 are positive integers, the beta function is given by B (x; y) =

(x 1)!(y 1)! (y) . More generally, the beta function can be expressed as B (x; y) = (x) (x+y 1)! (x+y) , where R1 x 1 t (x) = 0 t e dt is the gamma function. For example, the prior distribution is uniform when

=

= 1, and hump-shaped if ; > 1. Consumers and …rms are assumed to have the same prior beliefs, but our main results would obtain if we relaxed this assumption. 12 For example, consumers may have lexicographic preferences, with primary preferences for the product itself (which depends on vi ), and secondary preferences for telling the …rm that they like the product when asked directly. Then a 0-consumer would only reveal his type if it is costly to for him to deviate and claim to be a 1-consumer. 11

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Figure 1: Timing of main events. Comparison of reward-based crowdfunding and the appropriate benchmark. Our model of crowdfunding captures the main real world features of crowdfunding. There are two common types of schemes. The most common scheme is all-or-nothing (AoN) where the …rm sets a target p0 m0 and the funds are passed on to the …rm if, and only if, the …rm meets its funding target p0 m0

p0 m; where

m 2 f0; 1; ::; M g is the number of consumers who pre-order the product is m. The keep-it-all (KiA) scheme is similar, with the exception that p0 m is passed on to the …rm regardless of the target. We denote S 2 fY; N g the outcome of the crowdfund-

ing campaign, where when S = Y , the …rm’s campaign is successful and meets the target (i.e, p0 m0

p0 m); and when S = N , the campaign is unsuccessful. We allow

the fees 'S (m) set by the platform to depend on S and m. We assume that the platform market is competitive, and that providing intermediation services costs Z > 0. When analyzing reward-based crowdfunding, we make the following assumptions: 9

Schemes are transparent: during the campaign (afternoon of date 0), participants observe each other’s decisions and can withdraw their funds any time before the end of the campaign. This is akin to a simultaneous move game with perfect information. More formally, when consumer i decides whether or not to pre-order, he observes fm i ; p0 ; m0g, where m

i

denotes the number of

other consumers who back the project. Provided all 1-consumers participate in equilibrium, it is clear that m = m i + 1 if i is a 1-consumer (and m = m

i

if i is a 0-consumer). Whereas the e¤ect of i on m enables us to capture Varian’s (2013) argument about pivotal consumers, being pivotal need not drive consumer decisions. Firms obtain funds before they decide whether or not to invest (evening of date 0). This timing discrepancy in the source of moral hazard: …rms have a choice between investing and producing or diverting p0 m. While not necessary, we allow for potential realistic reputation costs Speci…cally,

Y,

S

0:

the cost of not delivering the product in spite of a successful

campaign, may be interpreted as a mere reputation cost, e.g. through being shamed on social media, and/or as an expected cost of litigation. In turn, N

captures the cost of a failed campaign if the …rm pursues the project:

it re‡ects either the risk that some initially interested consumers lose their interest, or the greater di¢ culty for a …rm that failed its campaign to obtain funding from other sources. These assumptions re‡ect the common features adopted by prominent rewardbased crowdfunding platforms such as Kickstarter and Indiegogo.

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Benchmark and value of learning

3.1

Demand

In this benchmark setting, we assume that at date 0 the …rm directly learns the preferences of a sample M of potential consumers. We denote m 2 f0; 1; :::; M g the number of 1-consumers within the sample M .

After the …rm observes m, it updates its expectations about the overall share of 1-consumers in the population, N . Since vi j is a Bernoulli trial, mj follows the binomial distribution

Pr (mj ) =

M m 10

m

(1

)M

m

.

(2)

Bayes’rule implies 0 +m

f ( jm) / Pr (mj ) f ( ) /

1

(1

)

(1

m 1

0 )+M

and the posterior distribution is also Beta, i.e., jm

Be (

0

+ m; (1

0)

+M

m) :

Therefore, the posterior expectations are E [ jm] =

+m . +M

0

(3)

To determine the expected value of learning at date 0, we also specify the distribution of m. As shown in (2) m is conditionally binomial, with drawn from

Be (

0;

qm

(1

From (1) we obtain

0 )) :

Pr (m) =

Z

unknown and

1

(4)

Pr (mj ) f ( ) d

0

=

M B( m

0

+ m; (1 0) + M B ( 0 ; (1 0 ))

m)

.

The shape of the beta-binomial distribution replicates the shape of the underlying prior beta distribution.13 Unconditional central moments of the beta-binomial variable can be written E [m] = M

0

and V ar [m] = M ( + M ) V ar [ ] =

M ( + M ) 0 (1 ( + 1)

0)

:

The expected m is proportional to the prior mean of the share of 1-consumers, and a higher

implies a lower level of uncertainty about both

(5) 0,

and m for any

M > 1.

3.2

First best investment decision

At date 2, the …rm can sell its product at price p2 > 0 to 1-consumers only. The surplus for each of these consumers is then 1

p2 , and the expected …rm value at

date 1 is p2 (m + (N

M ) E [ jm])

I,

where m consumers are known to value the product and (N

M ) E [ jm] other

future consumers are expected to be 1-consumers. It follows immediately that both For example, when the prior is uniform, i.e., = 2 and 0 = 12 , Pr (m) = M1+1 , i.e. the distribution of m is discrete uniform. If …rms prior beliefs are U-shaped (hump-shaped), then the distribution of m, is also U-shaped (hump-shaped). 13

11

the …rm value and the joint surplus, i.e. the sum of the payo¤ to the …rm and of the consumer surplus, are maximized when p2 = 1. The …rm extracts all consumer surplus and invests in all projects that are non-negative NPV based on updated beliefs. Denoting dxe the ceiling function, i.e. the nearest integer rounded up, we obtain

the following proposition:

Proposition 1 The …rst best investment decision is as follows: If I < I0 M) , +M

0 (N

then the …rm invests regardless of the realization of m. If I

the …rm invests at date 1 if, and only if, & ( + N) m m ~ = +M

1

(I

'

I0 ) .

I0 ,

(6)

The …rm’s date 1 NPV is D (m) = =

m + (N M ) E [ jm] +N m + I0 I, +M

(7)

I

Proof. Follows from (3), the NPV being non-negative at date 1, i.e., (m + (N

M ) E [ jm])

I

0, and m being an integer.

It will be useful to notice that the unconditional date 1 NPV of the project is E [ 1] =

I + p2 N E [ ] =

(8)

I + N 0;

the value of which at date 0 is E [ 0 ] = E [ 1 ]. This implies that if the …rm cannot learn about demand, it invests if, and only if, I

N

(9)

0

We will refer to this benchmark …rm as the reference …rm.

3.3

The real option value of learning under the …rst best scheme

The (…rm-level) value of learning is the expected value at date 0 of a …rm that does have an opportunity to learn about demand minus the expected value of the reference …rm. Recall that the expected …rm pro…t D (m) at date 1 is (7) and the investment threshold is (6). From (5) the unconditional expectation of the date 1 pro…t is E [D (m)] =

+N E [m] + I0 +M 12

I=N

0

I;

which is equal to the expected pro…t of the reference …rm. Therefore, the expected value of learning about demand is UI

E [D (m) jm =

U NI

m] ~ Pr (m

m) ~

(N

0

I)

E [D (m) jm < m] ~ Pr (m < m) ~ for I < N E [D (m) jm

m] ~ Pr (m

m) ~ for I

N 0,

(10)

0

(11)

where the superscripts "I" and "N I" denote whether or not the reference …rm invests. Since D (m) < (>) 0 for any m < (>) m ~ and D (m)

0 if m = m, ~ both

U I and U N I are positive. Further, U I and U N I represent both the value of learning and the joint surplus from learning. From (6), the value of learning is positive if, and only if, the …rm’s investment cost satis…es

+N . +M This guarantees that the investment threshold, m, ~ is above 0 and can be met with I0 < I < I0 + M

a positive probability, i.e., m ~ 2 f1; 2; :::; M g. Proposition 2 The value of learning is maximized when I = N 0 . Further, U I is increasing in I and U N I is decreasing in I. Proof. See Appendix A.2. Proposition 2 shows that a …rm that expects to break even based on prior beliefs has most to gain from learning, while the overall relationship between I and the value of learning is hump-shaped. Indeed, the …rst best investment threshold is (weakly) increasing in I. If I < N 0 , the …rm bene…ts from avoiding a sub-optimal investment. This bene…t increases with the investment cost that it expects to save. If I > N 0 , the …rm bene…ts mostly because it can learn that investment is worth undertaking, and thus the higher I the lower the returns from the investment. An opportunity to learn is essentially a real option. It is worth noticing that if I = N 0 , from (6), the optimal threshold is m ~ = dM 0 e. Since we know from (5) that M

0

= E [m], the threshold for …rms that have

most to gain from learning equals the unconditional expected value of 1-consumers, i.e. m ~ = dE [m]e : This observation will be useful when we discuss the empirical relevance and testable predictions of our model.

Our setting also enables us to examine the e¤ect of prior uncertainty on the value of learning. With a beta prior, the …rm beliefs are fully characterized by the prior mean

0

and by ; which is inversely related to dispersion. 13

Figure 2: First-best value of learning Proposition 3 Ceteris paribus, the value of learning increases with the degree of prior uncertainty about demand, i.e., it decreases with . Proof. See Appendix A.3. Proposition 3 shows that …rms with U-shaped prior beliefs, i.e., …rms that expect their product to be desirable either by many consumers or by few consumers, have most to gain from learning. Since one expects more novel and creative consumer products (e.g., new technology gadgets) to be more likely to be characterized by such belief structures than existing products, we expect innovative …rms to bene…t most from learning. Note that

a¤ects the date 0 …rm value through three channels. First, an

increase in uncertainty increases the di¤erence between the …rm prior and updated beliefs about the share of 1-consumers, i.e., jE [ jm]

E [ ]j =

jm M M+

0j

. Hence, from

(7); the expected value of the …rm at date 1 is all the higher (resp. lower) as the

realized m exceeds (resp. is lower than) E [m] = M 0 . Second, from equation (6), higher uncertainty may a¤ect the threshold, m, ~ at which the …rm …nds it optimal to invest. Third, the distribution of m with a higher

second order stochastically

dominates the one with a lower . Overall, the second order stochastic dominance, which implies that the probability of extreme realizations of m decreases with ; ensures that the e¤ect of an increase in uncertainty is positive. Both the value of learning and its embedded real option increase with the realization of m. Finally, the e¤ect of

on the …rst best investment threshold further enhances the bene…t

of learning when there is higher uncertainty. Figure 2 illustrates these comparative statics by plotting the value of learning about demand as a function of

and I. We consider two possible prior distributions 14

with the same mean (

0

= 21 ) and di¤erent values of . We chose

so that the distribution with

1

is U-shaped and the one with

as illustrated on Panel 1. The …gure assumes

=

0

M=N = 0:1. Firms break even if I = 8000 for both of learning is positive if I 2 (6:7; 15993) for =

both

4

2. 1

=

1 , 2

= 1,

1

= 1:5
0. We focus on informative equilibria, where all 1-consumers that observe the product description do pre-order it.14 It is optimal for the …rm to set p0 =

2

.

That is, it o¤ers

consumers a minimal discount, only compensating them for the time value of money. Indeed, transparency enables consumers to coordinate and to avoid backing a …rm that would not have su¢ cient incentives to invest. While the …rm can extract all consumer surplus at date 0, it has to set the target to m0 such that consumers expect that it will actually invest at date 1. Otherwise, consumers do not back the project, i.e., m = 0. We provide formal proofs for this in Online Appendix B. Since crowdfunding platforms are perfectly competitive, the expected fee income must equal the cost Z of running the platform, i.e., Pr (m < m0) E ['N (m) jm < m] + Pr (m

4.1

m0) E ['Y (m) jm

m] = Z.

(12)

All-or-Nothing scheme

At mid-day at date 0, the …rm announces a target m0 . If m consumers participate, the date 1 investment is worth p0 m

+ (N

M ) E [ jm]

14

I,

There is always an uninformative equilibrium where 1-consumers expect other 1-consumers not to participate and the …rm does not learn about demand. In this case, the …rm relies on its prior when deciding whether or not to invest.

15

2

which is equal to D (m) when p0 =

. The payo¤s to the …rm can then be written:

invests D (m) 'Y (m) D (m) 'N (m)

S = Y , i.e., m m0 S = N , i.e., m < m0

N

does not invest m 'Y (m) Y 'N (m)

The …rm invests if, and only if D (m)

m

D (m)

if S = Y

(13)

0 if S = N

(14)

Y

N

Using the expression for D (m) shown in (7), the incentive compatibility constraint can be written m

mY A =

+M N M

I

I0

Y

if S = Y

(15)

+ M I + N I0 if S = N: (16) +N It appears that the fee structure a¤ects payo¤s, but not the …rm’s incentive m

mN A =

compatibility constraints. Recall that from (6), m ~ is the …rst best investment threshold. The …rm’s equilibrium target and investment threshold need not be the same. This is because a …nancially unconstrained …rm may also invest if it fails to raise m

m0 . Denoting m0A the equilibrium target and mA the investment threshold, we

obtain the following Proposition. Proposition 4 With AoN: 1) if both reputation costs are small, i.e., Y

then m ~ m

+

N N

M < +N

+M (I +N

(17)

I0 ) ;

mY A . The …rm sets its target to m0A = mY A , but invests whenever

mN A

mA = mN A .

2) if the cost of no-delivery is intermediate and the cost of a failed campaign is su¢ ciently high, i.e., +M (I +N then m ~

mY A

N

I0 )

N

M +N

Y

+M (I +N

I0 ) ;

(18)

mN A . The …rm sets both the target and the investment threshold

to m0A = mA = mY A : 3) If the cost of no-delivery is su¢ ciently high, i.e., Y

+M (I +M 16

I0 ) ;

(19)

then mY A

m ~

mN A . The …rst best is achieved and the …rm sets the target and

the investment threshold to m0A = mA = m: ~ Proof. See Appendix A.4. Proposition 4 describes the …rm’s decisions under di¤erent ranges of reputation costs. Part 3 shows that if the reputation cost of no-delivery,

Y,

is high, AoN can

achieve the …rst best. The results of Part 1 and 2 with smaller reputation costs, which probably re‡ect better the current crowdfunding industry, indicate that the …rm sets the target higher than the optimal level (6) in order to convince consumers to back the project. Indeed, consumers are aware that the funds the …rm receives before it decides whether or not to invest alter its incentives to invest. Hence, they will only back the project if the announced target is high enough. In addition, from (15), an increase in

Y

alleviates the moral hazard problem.

Further, the target decreases with N

M , and it tends to in…nity when M ! N .

This highlights that in low reputation cost (or weak legal enforcement) environments, pre-selling to all future consumers cannot be achieved though reward-based crowdfunding. This highlights an important feature of third-party reward-based crowdfunding platforms: by keeping the campaigns short, they guarantee that only a subset of consumers can pre-order the product because a limited number of potential consumers can participate on time. From (7) and expanding (13), it appears that M must be su¢ ciently low relative to N : (N Even if

Y

M ) E [ jm]

I+

Y

0:

! 0, the …rm chooses to invest as long as the updated beliefs about

demand for the remaining N

M potential consumers is su¢ ciently high. We

argue that updating beliefs is the key driver that makes reward-based crowdfunding incentive compatible and successful.15 As E [ jm] is increasing in m, campaigns that raise more funds become more likely to deliver.

In contrast, if we did not consider the possibility of updating beliefs, it is clear that with

Y

! 0, the target would not be set strategically and the …rm would invest

if, and only if, (N

M)

0

I: From (8), it appears that this would reduce the

…rm’s incentives to invest after participating in reward-based crowdfunding relative to before the campaign. Hence, no …rm would participate unless crowdfunding were 15

In our setting, the sample M is respresentative. However, a qualitatively similar result would hold if the share of 1-consumers were larger in M than in the overall population. One would only have to adjust expectations relative to this bias.

17

the only possible source of funding.16 Part 1 of Proposition 4 shows that the …rm can also bene…t from learning about demand when it does not meet the target. This is consistent with empirical observations that many …rms complete the project after an unsuccessful campaign. Investing in state S = N comes at a potential reputation cost

N

in the case of a

failed campaign. From Proposition 4, it appears that both …rms and crowdfunding platforms bene…t from increasing the reputation costs associated with no-delivery, Y,

and from reducing the reputation costs due to the failure to meet the target,

N.

This is again consistent with the recent practice of platforms like Kickstarter,

which keeps information about past successful campaigns, but not on failed ones, on its website.17 Overall, AoN crowdfunding is made possible by the platform’s ability to keep M low enough and by the …rm’s ability to update its beliefs about demand. AoN crowdfunding can also achieve the …rst best when

4.2

Y

is su¢ ciently high.

Keep-it-All scheme

The distinct feature of KiA campaigns is that the …rm keeps all the funds raised whether or not it meets the target. However, as in AoN, observing each other’s decisions enables consumers to coordinate in order to avoid backing a …rm that will not invest at date 1. From (7), we can write the date 1 payo¤ to the …rm as follows: invests D (m) 'Y (m) D (m) 'N (m)

S = Y , i.e., m m0 S = N , i.e., m < m0

does not invest m 'Y (m) Y m 'N (m) Y

N

: N

Unlike AoN, we have assumed that the …rm’s failure to deliver the product always entails a reputation cost

Y

whether or not it meets the target. Indeed, under KiA

consumers have paid for the product regardless of the target being met. For any S, the …rm invests at date 1 if, and only if D (m)

Y,

m

(20)

which implies that the …rm invests if, and only if, m

mK =

+M N M

I

Y

I0

.

16 This is an essential di¤erence with Strausz (2016), who does not consider the updating of beliefs, and con…rms that in the absence of the real option feature of crowdfunding, …rms would only choose crowdfunding when faced with extreme …nancial constraints. 17 See e.g., "Kickstarter explains why it hides failures" by Chase Ho¤berger (May 31 in The Daily Dot).

18

where mK = mY A is as in (15). Unlike the AoN scheme where there is a moral hazard problem only if the …rm meets the target, the KiA scheme always entails a moral hazard problem. The …rm’s incentive compatibility constraints are exactly the same condition in both states. Denoting the target and investment threshold with m0K and mK , respectively, we obtain Proposition 5 With a KiA scheme, 1) if the reputation cost of no-delivery is low, i.e., +M (I +N

Y

then m ~

I0 ) ,

(21)

mK . The …rm obtains funds and invests if, and only if, m

The …rm’s best response is to set the target to m0K

mK = mK .

mK

2) if the reputation cost of no-delivery is high, i.e., Y

>

+M (I +N

(22)

I0 )

then m ~ > mK . The …rm obtains funds and invests if, and only if, m The …rm’s best response is to set the target to m0K

mK = mK .

mK

Proof. See Appendix A.5. Proposition 5 highlights that the KiA scheme can also lead to incentive compatible reward-based crowdfunding. However, the KiA scheme fails to achieve the …rst best even with very high reputation costs, with the sole exception that it satis…es (21) with an equality. Comparing Proposition 5 and Part 2 of Proposition 4, both schemes lead to the same outcome only if

Y

is intermediate and

N

is high. This suggests that under

some parameter values both schemes may indeed coexist. In general, KiA leads to strictly worse outcomes than AoN. When

Y

is low,

KiA and AoN yield the same outcome after a successful crowdfunding campaign. However, under AoN, the …rm may bene…t from investing even though its campaign fails because of the value of learning and the absence of moral hazard. If

Y

is high,

then KiA creates another distortion. The …rm may be forced to (over-)invest at date 1, simply to avoid high reputation costs. Hence, the …rm cannot be worse o¤ by choosing AoN. Interestingly, the target set in a KiA scheme carries little meaning. If

N

= 0,

the …rm can set any target. As long as the failure to meet the target is associated 19

with

N

> 0, the …rm sets any target m0K

mK to minimize this cost. KiA also

requires more active monitoring to avoid distributing funds to …rms that do not have at least mK 1-consumers.

4.3

Expected value under reward-based crowdfunding

Since the investment decision achieves the …rst best when

Y

is su¢ ciently high,

the …rm bene…ts from the real option value of learning minus Z. Low values of Y

and

N

(Part 1 of Proposition 5) are more interesting and more realistic. We

have shown that the …rm prefers AoN. We can summarize the expected value of participating in AoN: Proposition 6 The date 0 expected value of participation in AoN is UI = U NI =

E [D (m) jm < mN A ] Pr (m < mN A ) Pr (mN A m < mY A ) N Z E [D (m) jm Pr (mN A

mN A ] Pr (m m < mY A )

mN A ) Z N

if I < N if I

0

(23)

N 0,

where mN A and mY A are given by (16) and (15), respectively. If

N

mN A ! m. ~

! 0, then

Proof. See Appendix A.6. Since the …rm does not divert funds in equilibrium,

Y

has no direct e¤ect on

the expected payo¤ to the …rm. Further, the …rst term of U I and U N I is exactly the one we obtained in the …rst best benchmark. In addition, if

N

! 0, then the

second term is also zero and the comparative statics derived in Section 3.1 apply with the di¤erence that the …rm only participates if its real option value of learning is higher than Z. Interestingly, this is true despite the fact that …rms are forced to set a high target m0 = mY A > m ~ as shown in Proposition 4 (see also equations (6) and (15)). The main purpose of a feasible target is to ensure that the platform can cover its cost of running the platform while granting the …rm a positive probability of meeting its target. We have also shown that the fee structure does not a¤ect the …rm’s decisions. Even when

Y

! 0, the crowdfunding platform can ensure that

reward-based crowdfunding is possible by keeping the number of participants, M , limited and by guaranteeing transparency.

4.4

Firm characteristics and AoN project funding.

We have shown that even in a low reputation cost environment, the …rm can learn about demand through incentive compatible AoN crowdfunding and that the real 20

option value of learning through crowdfunding is close to the …rst best. Even though …nancial constraints are irrelevant to the crowdfunding target, comparing ex-ante and ex-post funding relative to the investment cost yields insightful results. For clarity consider a …rm subject to the most severe moral hazard problem, i.e., Y

! 0. First consider the case where the investment cost is I = I BE =

0N ,

i.e.,

the …rm breaks even based on prior beliefs. As we have shown, this investment cost maximizes the real option value of learning given f 0 ; g, and the …rm’s incentive M) , +M

0 (N

to participate in AoN crowdfunding. From I0 =

and (15), this …rm sets

a target mBE YA = M

m

0

N+ N M

M I BE N + . N N M

=

It must be possible for the …rm to meet the target mBE Y A with a positive probability, i.e., we must have mBE YA

M . From (15), this holds when N (1

0)

M

0

A successful campaign raises enough funds to cover investment needs if 1 BE p0 mBE Y A = mY A

I BE .

which is satis…ed when I BE Since

M N+ NN M

I BE ()

N (N 2M ) M

(24)

> 0, if the campaign does not reach out to more that half of the potential

consumers, a successful campaign does indeed cover the investment cost as long as the target is feasible, i.e. mBE YA of campaigns. Further, as

M . This is realistic given the short duration

increases, so does the real option value of learning,

and the …rm may be able to reach more than half of its consumers at the cost of a higher threshold. Hence, AoN funds the …rm’s investment. Furthermore, this …rm would likely have better access to external funding after a failed campaign with mY A > m > mN A . While it was merely breaking even based on prior beliefs, it now has a strictly positive NPV for a wide range of parameters. More generally, now consider an investment cost I = I BE +

21

. The …rm sets

the target m

+M N+ + N M N M BE I N+ +M + N M N M BE I + N+ + N M N

mY A = M = =

M N M N

0

For the …rm to be able to meet the target with a positive probability, (N (1

0)

M When

0

M) M

+

M M 0+

> 0, the …rm would not invest based on prior beliefs, and since the

project has a negative NPV based on prior beliefs, the …rm should not obtain outside …nancing. However, when

Y

= 0 and (24) holds, this …rm can successfully raise

enough funds through crowdfunding in order to cover its investment cost. Hence, among the …rms that should not obtain funding in a frictionless capital market, the …rms that bene…t most from AoN crowdfunding are also most likely to be able to fund their project entirely through successful AoN crowdfunding. Finally, a …rm with a positive NPV project based on prior beliefs (i.e.,


I0 as follows. Lemma 10 (1) If 2

p0

and m

= T R, all 1-consumers pre-order the product if, and only if

m. (2) If

= OP , all 1-consumers pre-order the product if, and

only if p0

2

Pr (m mjm 1) + (1 ) Pr (m mjm

(41)

1)

Proof. See Appendix B.2. Lemma 10 shows that if information about other backer preferences and decisions is public, backers can coordinate and back the project only to …rms that have incentives to invest. Coordination also ensures that there is no uncertainty about the …rm’s decision, and if the …rm meets the target m; all 1-consumers pre-order the product as long as the price compensates for discounting. Hence, with the funds raised at date 0 are p0 m if m Because reward-based crowdfunding implies

m and p0

2

= T R;

, and zero otherwise.

= T R, this also proves our earlier

claims about backer behaviour in Section 4. With

= OP , backers cannot coordinate. Hence, when they decide whether

or not to pre-order the product, they need to form beliefs about the probability that that the …rm will invest and that they will receive the product. When

> 0,

the backers need to be compensated for the risk that the …rm may not deliver the product and generally require a larger discount. also be eliminated if we assume that consumers have lexicographic preferences.

44

Finally, from (38), E [ 1 jm] increases with p0 , and hence so does date 1’s ex-

pected pro…t. Therefore, the …rm sets p0 = When choosing

2

if

= T R, and (41) if

= OP .

at date 0, the …rm faces a trade-o¤ between the bene…t of keeping

some of the funds raised if it chooses to not invest and the discount it needs to o¤er to at date 0 to induce rational backers to participate. Proposition 11 For any , the …rm is weakly better o¤ under transparency. Therefore,

= T R is always an optimal equilibrium strategy for the …rm.23

Proof. See Appendix B.3. Proposition 11 shows that the …rm chooses transparency over opacity at any given . The intuition is as follows. Suppose that the …rm has the same investment threshold under under

= T R and

= OP . Then the discount the …rm needs to o¤er

= OP is su¢ ciently large to compensate for any bene…t of keeping funds

in the case where the number of consumers who pre-order the product is low. In addition, as we show, the optimal investment threshold at date 1 is weakly higher under

= OP than under

of choosing

= T R, which provides the …rm with another bene…t

= T R:

We now turn to the optimal full-commitment scheme. Proposition 12 The …rm optimally sets of money-back guarantee, i.e., Proof. From Proposition 11

= T R and chooses the maximum level

= : = T R (weakly) dominates

proves that the investment threshold (mT R

m) ~ under

with and that the …rm’s expected pro…t at date 0 is Pr (m

= OP . Appendic A.4. = T R (weakly) increases mT R ) E [D (m) jm

mT R ] ;

which from Lemma 8 in Appendix A.1 is maximized at mT R = m ~ and decreases with mT R for any mT R

m. ~

Proposition 12 shows that the …rm that can pre-commit chooses transarency and the highest level of money-back guarantee, i.e., the lowest , that it can commit to. Since transparency dominates opacity for any , backers only back …rms that they expect will have su¢ cient incentives to invest. The threshold for investment must be lower than the …rst best threshold m ~ de…ned in (6) and it decreases with . As the expected …rm payo¤ from pre-selling the product decreases with the threshold, the …rm bene…ts from committing to the highest feasible level of money-back guarantee. 23

While Proposition 11 establishes that the …rm is weakly better o¤, this statement is largely due the potential e¤ect of rounding as m must be an integer. In most cases, the …rm is strictly worse o¤ if it choosing = OP instead of = T R.

45

We obtain the following result for the opposite limit: Corollary 13 If the …rm cannot commit to any money-back guarantee, i.e.,

= 1;

pre-selling the product to all potential consumers is not incentive compatible even though

= T R.

Proof. Settingm = = 1 in (39), the …rm invests if, and only if, m l ( +M ) (I I0 ) . If M ! N , then m ! 1. N M

m =

This echoes the earlier result that it is impossible to pre-sell the product to all

potential consumers if the reputation cost of no-delivery is low. This is because this reputation cost and the money-back guarantee serve exactly the same role.

B.2

Proof of Lemma 10

For a 1-consumer, the opportunity cost of waiting is zero, either because there is no product or because the …rm extracts all consumer surplus at date 2 by setting p2 = 1. Consider

= T R. Consumer i observes the number of other consumers who

pre-order the product, m i . If m

1, then if a 1-consumer backs the project

m

i

at date 0, the …rm will invest at date 1 with probability 1 and the consumer’s utility from pre-ordering the product is 2

p0

If m

i

0. Further, the condition m

2

p0 . Hence he participates as long as

1 m

i

1 is equivalent to m = m i + 1

m.

1, then the …rm will not invest with probability 1 and consumer i may

0.

1) (resp. Pr (m

Then, the …rm will invest with probability mjm

M

1)) if he participates (resp. does

not participate).Hence, 1-consumers make identical decisions to back the project, if, and only if Pr (m

mjm

1)

2

p0

Pr (m < mjm

1) p0

0,

which simpli…es to (41).

B.3

Proof of Proposition 11

The …rm sets p0 as high as possible subject to 1-consumer’s participation constraint (10). We denote m the investment threshold under sponding date 0 expected …rm value. 46

and E [

0;

] ( ) the corre-

From (39) and (40), when

2 T R, the …rm optimally sets price p0 =

invests i¤ m

mT R ( ) =

&

1

+N +M

I

Since the …rm only obtains funds if, and only if, m E[ With

0;T R ] (

) = Pr (m

'

I0

2

and it (42)

:

mT R ; then

mT R ( )) E [D (m) jm

mT R ( )] .

(43)

2

(44)

2 OP , the …rm sets the price to p0 = p0;OP

Pr (m mOP ( ) jm 1) + (1 ) Pr (m mOP ( ) jm

2

and it invests if, and only if & +N m mOP ( ) = +M

(1

p0;OP

) 1

1)

1

I

2

;

I0

'

(45)

Since the …rm can obtain funds irrespectively of whether or not it invests, its expected date 0 pro…t is E[

0;OP ] (

) = Pr (m

2

mOP ( )) D (m)

p0;OP mjm

mOP ( ) (46)

+ Pr (m < mOP ( )) p0;OP E [mjm < mOP ( )] We proceed in two steps. Step 1: Let us …x , with a corresponding mOP ( ). From (42) and (45) there exists

0

such that 0

= + (1

) 1

p0;OP 2

,

(47)

which implies mT R ( 0 ) = mOP ( )

c,

where c 2 f1; :::M g

Comparing ((43) and (46)) we obtain E[

0;T R ] (

0

)

E[

0;OP ] (

),

if and only if 2

p0 Pr (m

c) E [mjm

c]

47

Pr (m < c) p0 E [mjm < c] ,

(48)

i.e., the loss from setting a lower price under

= OP must be higher than the

bene…t of keeping the funds. From the law of total expectations and from (44), (48) simpli…es to Pr (m c) E [mjm c] Pr (m cjm 1) From Bayes’rule, we have Pr (m

cjm

1) =

E [m] :

Pr(m c) . Pr(m 1)

And from the law of total

expectations E [m] = Pr (m

1) E [mjm

1]+Pr (m = 0) E [mjm = 0] = Pr (m

1) E [mjm

1] :

Therefore the condition becomes E [mjm

c]

1] ,

E [mjm

which holds for c = 1, and holds for c > 1 from Lemma 7 in Appendix A.1. Step 2. Equation (47) implies that for any ;

0

. Hence, from (42) the

investment threshold mT R ( ) is non-incresing in , mT R ( 0 ) = mOP ( )

mT R ( ) and mT R ( )

m. ~ From (43) and Lemma 7 in A.1, we have E[

0;T R ] (

)

E[

0;T R ] (

which proves Proposition 11.

48

0

)

E[

0;OP ] (

));