Crowdfunding campaigns display their funding progress in real-time, but is that wise? And how does this affect entrepreneurs’ pricing and goal choices and the welfare that results? In the BSE Working Paper 1349, “A Theory of Crowdfunding Dynamics,” Matthew Ellman and Michele Fabi develop a dynamic model of crowdfunding to predict funding success and welfare. Their results explain salient dynamic patterns of bidding, shed light on platform design and provide guiding principles for entrepreneurs.
The Anatomy of a Crowdfunding Campaign
In a typical crowdfunding campaign, an entrepreneur makes an open call for funds to cover the costs of producing a new good. A distinctive feature compared to other forms of early-stage financing is that the entrepreneur sets a funding goal, or threshold, and launches production only if crowdfunding bidders pledge enough funds to reach this threshold before a specified deadline. Reaching the threshold provides a credible signal of demand for the entrepreneur’s product. Entrepreneurs avoid sinking production costs when the threshold is not reached, so crowdfunding reduces their exposure to demand uncertainty.
In reward-based variants such as Kickstarter and Verkami, each pledge commits a bidder to buy the entrepreneur’s good if the campaign’s threshold is reached. The amount pledged or bid is held in escrow until the campaign deadline at which date, the crowdfunding platform transfers all bids to the entrepreneur if and only if the campaign succeeds in reaching its threshold. In that success event, the entrepreneur has to produce and deliver the product to all active bidders. If instead accrued funds remain below the threshold, the campaign fails and all money pledged is returned to the bidders.
The evolution of bidding
Projects that start out with weak funding progress usually freeze up and never reach their threshold. Meanwhile, most successful projects have strong starts, then slow down after the first few days, before picking up momentum again as the deadline approaches. As a result, the bidding pattern for successful projects is U-shaped whereas bidding on unsuccessful projects is closer to an L-shape.
Real-Time Disclosure of Funding Progress Underlies these Dynamics
Since crowdfunding platforms display the evolving level of funding on each campaign in real-time, a prospective bidder can estimate a campaign’s (interim) success probability by computing the gap between funds collected so far and the funding threshold, and the time left to fill this gap before the campaign’s deadline. This success estimate plays a central role in determining participation because, while bidders get their money back when a campaign fails to reach its threshold, other costs associated with bidding are not reimbursed. Bidders are only willing to sink these costs on campaigns with sufficiently high success prospects. So success rates encourage bidding and bidding of course raises success rates. The co-evolution of bidding and success rates determine campaign dynamics.
Bidding Costs
Some costs, like the hassle of filling in payment details and the opportunity cost of having one’s money held in escrow, are often small but as crowdfunding products do not yet exist, it is often costly for bidders to find out if they value them. These inspection costs include the time and effort spent reading a project description or watching a video describing the intended product. Except for very cheap products, inspection is an effective prerequisite for bidding, making inspection costs equivalent to direct, sunk costs of bidding. These costs are highly heterogenous. Bidders close to the entrepreneur often find out about the product very easily and costs are effectively zero or negative for friends, family and fans of the entrepreneur who may be curious to find out about the project or to express their loyalty and support. Meanwhile, for socially distant bidders, costs often outweigh the expected gains so that inspection only makes sense for campaigns with very high success rates.
Two Forces Shape the Dynamics and Ultimate Success of a Campaign
The authors identify two novel effects. The Pivotality Effect and the News Effect. Pivotality measures a bidder’s impact: how much a bid raises the probability of campaign success given the date at which the bidder arrives and the gap remaining between the threshold and funds collected by that date. This pivotality tends to decrease over time because, by raising the chance of reaching the threshold, each bid encourages all later arrivals or followers to also bid and an earlier bidder can expect to have more followers. That is, an earlier bid exerts positive influence or strategic complementarity over a longer time period.
This decreasing pivotality pushes later bidding downwards since the reduced influence of later bidders reduces their motivation. Pivotality Effect refers to this negative force on the slope of average bidding. It accounts for the average impact of time on bidders’ success prospects but success rate variance also matters: variance raises average future bidding if there are increasing returns to good news about success prospects and variance lowers it if there are decreasing returns. Technically, a locally increasing density of bidder costs implies that good news shocks raise bidding by more than bad news lowers it; the mass of higher cost bidders who respond to good news by starting to bid then exceeds that of lower cost bidders who respond to bad news by stopping bidding. This is the News Effect. The News Effect is trivial for the uniform and homogenous cost distributions but is positive and can be large for convex cumulative distribution functions (CDFs), as arise when distant bidders have a single-peaked cost density with a peak that precludes bidding. A strong enough, positive News Effect can dominate the, always negative, Pivotality Effect to create an upward-sloping average bidding profile.
These two effects determine the slope of the bidding profile (averaged across campaigns) for any cost distribution. Since crowdfunding campaigns typically involve a mix of close and distant bidders and success is initially uncertain, the distant or high-cost bidders are generally inactive until the late stages of a campaign. Close bidders drive early-stage dynamics and for them, News Effects are negative, complementing the negative Pivotality Effect. In later stages, positive News Effects from activating distant bidders come into play. Especially when averaging conditional on campaign success, these News Effects can dominate to create an increasing bid profile. This provides a succinct explanation of the U-shaped pattern of funding that has been observed in empirical data (as in Fig.1). More importantly, cost heterogeneity may explain why platforms have transparent designs that fully disclose the temporal evolution of bidding.
Can the crowdfunding paradigm be improved?
The authors ask whether an alternative platform design where funding is not disclosed (until after the deadline) would fare better or worse than the current practice of continuous, full disclosure. The answer depends on the two key forces. When the Pivotality Effect is dominant or the News Effect is negative, disclosure is detrimental because falling pivotality reduces success rates and inhibits positive externalities. When the News Effect is positive and dominant, disclosure has the benefit of allowing early arrivals with low costs to activate higher cost bidders who arrive later.
The distribution of costs determines which force dominates. When bidders are relatively homogenous, the Pivotality Effect dominates. Non-disclosure then allows maximal bidding and welfare by precluding bad news. Conversely, polarized cost distributions associated with a mix of close and distant bidders favour full disclosure.
Lessons for Entrepreneurs
Entrepreneurs need to take into account these dynamic interactions among bidders when planning their campaigns. Starting from the basic tradeoff between raising prices and thresholds on the number of bidders to achieve a given funding goal, Ellman and Fabi investigate how entrepreneurs’ pricing choices should depend on the expected abundance or scarcity of bidders in regular settings.When entrepreneurs set a single price, bidder scarcity calls for a high price so as to have a chance of success from few bidder arrivals. When entrepreneurs can set a menu of prices, with limited units at each price, letting early arrivals buy at a discount may be optimal but not always. If bidders are abundant, early discounts do optimally exploit the higher pivotality of early bidders. However, if bidders are scarce, later bidders often face low success rates. Compensating that adversity with a late discount helps to convert early bidding into successes. Since early bidders anticipate these late discounts, late discounts actually encourage early bidders as well.
The analysis raises many questions. So far, Ellman and Fabi found that allowing menus of rewards with limited quantities at different prices raises welfare but future research is needed to establish whether this may harm consumers when entrepreneurs are profit-motivated.
