Slack Time and Innovation

Traditional innovation models assume that ideas are developed as long as their benefit is greater than their cost. So, when the opportunity cost of time is lowered, such as during a holiday from work, more projects are developed, but they have a lower expected benefit. We develop a simple theoretical framework that allows innovators to choose the level of effort they apply towards the development of their idea in a context where the returns to effort are greater for higher quality ideas. We also allow for lower team coordination costs during periods when individuals have overlapping slack time. Under these conditions, slack time may lead to not only lower but also higher quality projects. We test the model's predictions using data on 165,410 projects posted on Kickstarter during college breaks. Consistent with the model's predictions, during university breaks more projects are posted and the increase is largest for projects of either very high or very low quality. Furthermore, projects posted during breaks are more complex, with larger teams and more diverse skills.

Slack Time and Innovation Ajay Agrawal, Christian Catalini, Avi Goldfarb, Hong Luo∗ December 30, 2016 Abstract Traditional innovation models assume that ideas are developed as long as their beneﬁt is greater than their cost. So, when the opportunity cost of time is lowered, such as during a holiday from work, more projects are developed, but they have a lower expected beneﬁt. We develop a simple theoretical framework that allows innovators to choose the level of eﬀort they apply towards the development of their idea in a context where the returns to eﬀort are greater for higher quality ideas. We also allow for lower team coordination costs during periods when individuals have overlapping slack time. Under these conditions, slack time may lead to not only lower but also higher quality projects. We test the model’s predictions using data on 165,410 projects posted on Kickstarter during college breaks. Consistent with the model’s predictions, during university breaks more projects are posted and the increase is largest for projects of either very high or very low quality. Furthermore, projects posted during breaks are more complex, with larger teams and more diverse skills. JEL Classifications: L26, O31, J22. Keywords: crowdfunding, entrepreneurship, slack time, teamwork, low-opportunity cost time, internet. ∗ We thank the review team, Michael Ewens, Lee Fleming, Joshua Gans, Scott Stern, and seminar participants at the NBER Changing Financing Market for Innovation & Entrepreneurship Conference, the 2014 AEA Meetings, the 2014 REER Conference at Georgia Tech, Duke University, Johns Hopkins University, University of Maryland, National University of Singapore, Singapore Management University, Stanford University, Harvard Business School, ZEW Conference 2014, UC Berkeley, the EEI Conference at Queen’s School of Business, World Bank, MIT, and University of Toronto for comments. We thank SSHRC, the Centre for Innovation and Entrepreneurship at the University of Toronto, and the Edward B. Roberts (1957) MIT Fund Grant for Technology-Based Entrepreneurship for financial support. Errors remain our own. Ajay Agrawal (University of Toronto): ajay.agrawal@rotman.utoronto.ca; Christian Catalini (MIT): catalini@mit.edu; Avi Goldfarb (University of Toronto): agoldfarb@rotman.utoronto.ca; Hong Luo (HBS): hluo@hbs.edu. “It’s no coincidence that Microsoft and Facebook both got started in January. At Harvard that is (or was) Reading Period, when students have no classes to attend because they’re supposed to be studying for finals.” - Paul Graham, Y-Combinator Founder, quoted in “How to Get Startup Ideas” 1 Introduction Companies and governments encourage innovation because it enhances productivity and competitiveness. However, innovation is costly. It requires time, eﬀort, and other resources. In equilibrium, under common innovation model assumptions, the marginal beneﬁt of one more innovation would just equal the marginal cost of producing it. As such, when innovators have more slack time, they will innovate more as lowering the opportunity cost of time shifts the supply curve to the right. Traditional models also predict that the additional innovations are marginal ones. This raises a puzzle. Why do ﬁrms, such as Google, LinkedIn, 3M, and Wella, which already provide innovation-oriented work environments, also provide slack time to encourage more innovation if doing so only facilitates the development of marginal ideas? How should such policies be designed? Why do we see a recent shift from spread-out forms of individual slack time (e.g., Google’s 20% time) to more structured programs that provide teams of employees with longer, continuous blocks of time oﬀ from regular commitments (e.g., Google’s “Area 120”)? We develop a simple theoretical framework to capture the diﬀerences between periods of high versus low opportunity cost time (work weeks versus break weeks). Low opportunity cost time may induce: 1) lower quality ideas to be developed (a selection eﬀect); 2) more eﬀort to be applied for any given idea quality (an eﬀort eﬀect); and 3) an increase in the use of teams because scheduling is less constrained and communication is less delayed (a coordination eﬀect). As a result, the eﬀect of breaks on the outcome distribution is ambiguous because on the one hand the selection eﬀect may induce lower quality ideas, but on the other hand the eﬀort and coordination eﬀects may lead to more high-quality, complex ideas. We explore this model using data from Kickstarter, the world’s leading rewards-based crowd- 1 funding platform.1 We leverage variation in the availability of slack time generated by school breaks across locations with top U.S. colleges. Relative to more fragmented, constrained spare time during the semester, breaks provide students with longer blocks of time to work on non-school related projects. Crowdfunding platforms have become increasingly important for entrepreneurial endeavors in a variety of segments, ranging from the arts to technology. Further understanding of the determinants of the creative supply on these platforms is in and of itself interesting. Additionally, our results generate useful implications for the design of “slack time” policies in ﬁrms and other organizations. Our sample includes all projects launched on Kickstarter between April 2009 and April 2015. We combine these data with information on the exact timing of school breaks in locations with top US colleges. Our unit of analysis is the city-week. We compare the number of projects launched in a given city during break weeks versus work weeks. The regressions control for city and week ﬁxed eﬀects to isolate confounding factors such as general time trends, seasonality, and diﬀerent baseline levels of innovative activity across diﬀerent locations. We ﬁrst document the positive impact of breaks on the quantity of projects posted. In particular, the regression results show that the number of crowdfunding campaigns launched increases during school breaks by up to 46%, depending on the speciﬁcation. We provide a series of empirical results in support of the causal interpretation that the additional projects are driven by an increase in the availability of slack time. Speciﬁcally, we show that when top engineering schools are on break, we see a positive eﬀect on technology projects but not art projects, and vice versa when art and design schools are on break. We also examine days when universities are closed for snow, providing an exogenous increase in slack time. Signiﬁcantly more projects are posted on snow days. Furthermore, we report results suggesting that the increase in postings and funding is unlikely to be driven by increased capital availability due to students providing more funds while on break. We also show that relative to work weeks, break weeks are associated with signiﬁcantly more projects at the very low end of the value distribution, fewer projects in the middle, and more 1 Crowdfunding is the practice of funding a project by raising small amounts of money from a large number of people by leveraging a digital platform. It is a form of early-stage capital for many technology companies and has become an important source of funding for the arts (Agrawal, Catalini, and Goldfarb 2013, Mollick and Nanda 2016, Belleflamme, Lambert, and Schwienbacher 2014). 2 projects at the high end of the distribution. In terms of welfare, it is signiﬁcant that a substantial proportion of the latter category of extra projects are relatively large, high-value projects. The empirical patterns also support the model predictions about the diﬀerences in eﬀort levels: when the opportunity cost of time is lower, more eﬀort is allocated to ideas, especially high-value ones. Lower opportunity cost time may also ease coordination among individuals working as a team. In an extension of the baseline model, we explore the consequences of easier coordination on the types of projects being developed, with the premise that complex projects may beneﬁt disproportionately from teams with diﬀerent skills and perspectives. We test and ﬁnd support for this prediction using data on the number of individuals involved in the projects and their skills. Last, we exploit a Kickstarter policy change that increased the posting requirement for projects in the Design and Technology categories (but not in other categories). This diﬀerence-in-diﬀerences empirical strategy allows us to test the robustness of our baseline model to a change in the minimum eﬀort needed to post an idea. Results are consistent with the model prediction: after the change, the relative share of top-valued and team projects in the aﬀected categories increases disproportionately during the breaks. Our paper provides a formal framework for analyzing the relationship between the opportunity cost of time and innovative outputs. Our results highlight that a suﬃcient amount of time (in contiguous blocks, in particular) is critical for implementing high-potential and complex projects, and that “overlapping slack” is important when ideas beneﬁt from team collaboration and diverse skills. At the same time, it cautions that too many marginal, low-potential projects might also be generated when slack is introduced. Therefore, complementary policies mitigating such incentives - such as stricter screening mechanisms - are likely to be valuable in conjunction with slack. The paper proceeds as follows. The rest of this section summarizes the related literature. Section 2 presents a formal model that derives the diﬀerences in the quantity and type of projects developed during break and work periods. Section 3 describes the data and our empirical strategy. Section 4 reports the regression results, and Section 5 concludes. 3 1.1 Related Literature This paper links the nascent but rapidly growing literature on crowdfunding to the more established literature on innovation. Mollick (2014) provides an early study documenting the funding dynamics, and Agrawal, Catalini, and Goldfarb (2013) discuss a broad range of topics from the viewpoints of both entrepreneurs and ﬁnanciers, in particular on information-related frictions. A key ﬁnding of the literature is that funding increases with accumulated capital. The crowd views accumulated capital as a signal of quality, and this may lead to herding (Agrawal, Catalini, and Goldfarb 2015, Zhang and Liu 2012, Kuppuswamy and Bayus 2013). One exception to this ﬁnding is Burtch, Ghose, and Wattal (2013), who show that public-goods concerns can counteract herding eﬀects. Mollick and Nanda (2016) examine the “wisdom of the crowd” and show that overall the crowd appears to select similar projects to experts. Also related to information, Burtch, Ghose, and Wattal (2015) show that privacy concerns play a role in funding decisions. Instead of informational issues given existing projects, our paper focuses on the determinants of the supply of projects and their quality. Whereas the literature in management, economics, and sociology on innovation is extensive, there have only been a few studies focusing explicitly on the impact of the opportunity cost of time on inventive outcomes. Davis, Davis, and Hoisl (2014), using survey data on more than 3,000 inventions in Germany, ﬁnd that leisure-time inventions by employees are more likely to focus on conceptually-based problems, rely on interactions with people outside the organization, and focus on smaller R&D projects. Harhoﬀ and Hoisl (2007) ﬁnd instead that leisure-time patented inventions are more likely to be of higher value. A relevant stream of work in the management literature studies the costs and beneﬁts of organizational slack on innovation, often measuring slack in terms of ﬁnancial resources. In his seminal work on organizational design, Galbraith (1974) highlights the key trade-oﬀs that the creation of slack resources entails for a ﬁrm. Later proponents for slack argue that it fosters a culture of experimentation and supports creativity and innovation (e.g., Bourgeois (1981) and Singh (1986)). The opposing view argues that slack is an unnecessary cost that detracts from the overall value of a company (e.g., Leibenstein (1969)). Using a combined measure derived from two interview questions covering the extent of slack in terms of time and ﬁnancial resources, Nohria and Gulati (1996) show an inverse U-shaped relationship between slack and innovation in 4 a sample of 178 departmental managers from two large multinational corporations.2 Catalini (2016) also studies the role of low-opportunity cost time on invention, in his case from a microgeographic perspective: co-location, by lowering search and execution cost for proximate scientists, inﬂuences both the rate and direction of inventive activity. Additionally, our results broadly resonate with studies on the impact of organizational design on innovation such as the degree of decentralization versus centralization (Argyres and Silverman 2004, Lerner 2007, Arora, Belenzon, and Rios 2013) and the identiﬁcation of constraints preventing individuals from launching entrepreneurial projects (e.g., Chatterji and Bennett (2016)). Finally, our focus on time relates to studies in sociology on time as social input. For example, Perlow (1999) documents the potential negative impact of interactive activities for engineers because they fragment individual concentration. Winship (2009) studies scheduling conﬂicts as barriers to social relations. Young and Lim (2014) argue that time is a network good, the value of which depends on an individual’s ability to coordinate that time with others. 2 Theoretical Framework This section develops a simple model to explore the impact of breaks on innovation. Relative to work periods, break periods are diﬀerent in two important ways: 1) the opportunity cost of time is lower, and 2) the coordination cost among collaborators is lower because people have more open schedules and communication is less delayed. In the following, we ﬁrst develop a baseline model that considers only the ﬁrst diﬀerence in the opportunity cost of time. We later extend the model to allow for the use of teams and incorporate the second diﬀerence in coordination costs.3 2.1 Basic setup One idea arrives in each period. The realized value of a project, v, depends on two factors: the idea’s intrinsic quality, q, and the amount of eﬀort (or, equivalently, time in our context) devoted 2 A number of studies in the product development literature highlight the impact of deadlines and scheduling on new product development (Richtner and Ahlstrom 2006, Richtner, Ahlstrom, and Goffin 2014). 3 In the Appendix, we also provide an extension to a two period model in which projects arriving during the work period can be “shelved” to the break. This model does not generate new predictions, but it proves useful in interpreting the empirical results. 5 to developing the project, e. We assume that v = q · e. Thus, the realized value of a project increases with both the idea’s intrinsic quality and the amount of eﬀort. The innovator’s payoﬀ from developing an idea at a certain eﬀort level is assumed to be: πw = qe − c(e; w), (1) where c(e; w) is the cost of eﬀort, with w ∈ {0 = break; 1 = work} indicating the time period. Because the time cost is higher during work weeks, c′ (e; 0) < c′ (e; 1). To obtain analytical results, we assume that idea quality q follows an exponential distribution 2 and that the cost function is convex in eﬀort: c(e; w) = cw e2 , with c0 < c1 .4 The payoﬀ in equation (1) can be re-written as: πw = qe − cw e2 . 2 (2) The ﬁrst-order condition yields the optimal eﬀort level as e∗w = q/cw . Thus, given any quality level, less eﬀort is spent when time is more precious; while given the same time cost, more eﬀort is spent when the idea is better. Inserting e∗w back into equation (2), we obtain the innovator’s payoﬀ at ∗ (q) = the optimal level as πw q2 2cw . The innovator needs to exert a minimum amount of eﬀort, denoted as ē, to pass the posting requirement of the funding platform. Denote the innovator’s payoﬀ at the minimum required eﬀort 2 level as π̄w (q) = qē − cw ē2 . Taking into account the minimum eﬀort requirement, the innovator’s payoﬀ can be written as: π̃w (q) = where    ✶{q≥cw ē} 2cq w + ✶{q<cw ē} (qē − cw ē2 ) if develop the project 2 2   0 , (3) if drop the project ✶{·} is an indicator function. If the innovator develops a project, she obtains πw∗ (q) = q2 2cw when the quality of the idea is suﬃciently high (when q ≥ cw ē). In this quality range, the optimal amount of eﬀort is above the minimum requirement. For ideas of relatively low quality (when 4 We use an exponential distribution because it captures two features of our context: the support is positive, and the distribution is skewed to the low end (that is, lower-quality ideas are more likely than higher-quality ones). 6 2 q < cw ē), the innovator’s payoﬀ is π̄w (q) = qē − cw ē2 , because the optimal eﬀort is below the required level. In this range, the innovator over-develops the project (relative to the desired amount of eﬀort given the quality of the idea) to meet the minimum requirement and obtains a payoﬀ that is below the desired level. Despite this, the innovator still develops the project if π̄w (q) > 0, which is the normalized outside option. Figure 1a illustrates the innovator’s payoﬀs separately for break and work periods using a numerical example. Given any idea quality q, the innovator’s payoﬀ for a break is higher than a work period. This is because the time cost is lower during breaks and, at the same time, the project’s value is higher as more time is spent on it. It is straightforward to show that the innovator develops an idea only if its quality is above a certain threshold and that the threshold for breaks is less stringent.5 Thus, we have Prediction 1 (see Appendix A for the proof of this and other results):6 Prediction 1 (Diﬀerence in quantity). More ideas are developed during a break period than a work period. The value of a developed project is: ṽw (q) = ✶{q≥cw ē} Notice that ideas with qualities q < cw ē 2 q2 + ✶{ cw ē <q<cw ē} qē. 2 cw (4) are dropped. Figure 1b illustrates the value of developed projects as a function of idea quality. It highlights two consequences of a lower time cost on the overall value of projects. First, because time is less costly, the innovator is less selective about screening out marginal ideas. Thus, the value of some projects developed during breaks is lower than any project developed during a work period. We call this the “selection eﬀect.” Second, also because time is less costly, the innovator works more on any given idea. This “eﬀort eﬀect” increases a project’s value v, given the same intrinsic quality q. 2 5 The thresholds are determined by π̄w (q) = 0 ⇔ qē − cw ē2 = 0 ⇔ q̄w = cw2 ē . Thus, q̄0 < q̄1 as c0 < c1 . Because it is empirically impossible to identify different arrival rates, we normalize them to be the same for the two periods in the model. Allowing for different arrival rates affects only the first prediction because the other predictions are normalized statements. Intuitively, the arrival rate is likely to be higher during the break because there is more time to think about ideas. This would make the quantity of ideas developed during the break even higher. 6 7 The comparison of the expected value of projects between a work and a break period is ambiguous because the two eﬀects discussed above push it in opposite directions. We therefore compare the distributions directly. Figure 1c plots the conditional densities of developed projects by their value v using the same numerical example in Figure 1, with q following an exponential distribution. Compared to a work period, there are disproportionately more projects at the low end of the distribution during a break because the innovator is less selective about screening out marginal projects. At the same time, there are also more projects at the high end of the distribution because the required idea quality to achieve the same project value is lower during a break due to the eﬀort eﬀect. Prediction 2 (Diﬀerence in distribution of project value, conditional on development). Relative to a work period, projects developed during the break are both more likely to be at the low end of the c1 ē2 2 ) distribution (v < and at the high end (v ≥ c1 ē2 ). The above result hinges on the assumption that more eﬀort makes projects better. As illustrated in Figure 1b, the innovator can achieve the same value v with a lower-quality idea during the break because she can devote more time to the project. Prediction 3 builds on this observation. Prediction 3 (Diﬀerence in eﬀort). For projects with the same value v, the amount of effort spent on projects developed during a break is greater than (or equal) to the amount of effort spent on projects developed during a work period. Furthermore, the difference in effort is greater for projects of higher value v. During our sample period, Kickstarter increased the posting requirements for projects in certain categories. We will explain the policy change in detail in Section 4.4, but in the context of our model, this policy translates into an increase in the minimum eﬀort requirement ē. Overall, a more stringent posting requirement should increase the quality thresholds for both break and work periods and, as a result, fewer projects should be developed. The relative size of the reductions, however, is ambiguous. On the one hand, the increase in the threshold per se is greater for a work period (i.e., ∂ q̄1 ∂ē = c1 2 > ∂ q̄0 ∂ē = c0 2 ), which is intuitive because increasing the eﬀort requirement is more taxing when time is more precious. On the other hand, because the distribution of idea 8 quality q is likely to be skewed to the left, the number of projects dropped may be greater during breaks if these periods are disproportionately characterized by lower quality projects. The following result shows that if the distribution of q is not too skewed to the left, the reduction in quantity is smaller for breaks. Prediction 4 (Eﬀect of increasing minimum eﬀort requirement ē on relative quantities). When the distribution of idea quality, q, is not too skewed to the left (when the mean of the exponential distribution is greater than c1 ē 2 ), the reduction in quantity due to an increase in the minimum effort requirement is smaller for a break than for a work period. For both break and work periods, the expected value of projects developed should be higher after an increase in the posting requirement. The relative size of the increases is again ambiguous, depending on the parameter values and the distribution of q. However, because this policy shock does not aﬀect projects of high quality, the share of top-valued projects developed during a break (relative to the total number of projects developed during both periods) should increase. That is: Prediction 5 (Eﬀect of increasing minimum eﬀort requirement ē on relative project value). The share of top-valued projects developed during breaks (relative to the total number of projects developed for both periods) increases after an increase in the minimum effort requirement. 2.2 An Extension: Team and Project Complexity Projects may be carried out by teams for at least two reasons: 1) with multiple people sharing the workload, a team may relax the capacity constraint of a single person, and 2) a complex project may require people with diﬀerent, complementary skills (or perspectives on a problem). The downside of a team, however, is that it requires coordination, and this coordination requirement may be especially high for complex projects. In this section, we extend the baseline model to allow for the use of teams and incorporate a second diﬀerence between break and work periods: coordination costs among team members are lower during breaks. In addition to the baseline setup, this extended model assumes the following. First, a project can be developed solo, by a team of two, or dropped. Second, in team projects, each individual’s 9 payoﬀ consists of half of the value of the project, minus the individual time cost and a coordination cost. For simplicity, the coordination cost is normalized to be zero for simple projects regardless of the time period. Complex projects involve a positive coordination cost, and this cost is greater for work periods. Third, whereas in simple projects teaming up does not bring any direct beneﬁt to the project’s value, in complex projects there is a positive eﬀect (e.g., from complementary skills and perspectives), and this beneﬁt is more likely to be pronounced as idea quality increases. Appendix A2 provides details on the extended model and the decision rules separately for simple and complex projects. The basic trade-oﬀs are as follows. For simple projects, there are no coordination costs, and the beneﬁt from using a team is limited to the ability to share the workload. In our model, this beneﬁt matters only for ideas of relatively low quality (for which the minimum eﬀort requirement is too high given the idea’s quality). For complex projects, while teaming up incurs non-trivial coordination costs, it also introduces two beneﬁts: workload sharing and a direct increase in project value. The second, direct beneﬁt of teaming up is more relevant for ideas of relatively high quality because for these ideas such a beneﬁt is likely to outweigh coordination costs. As in simple projects, teams also help share the workload when the minimum eﬀort requirement is too high relative to the idea’s quality. However, for complex projects we may not see the use of teams for this range of ideas if coordination costs are too high. A key observation is that, relative to work periods, breaks oﬀer a relative advantage for developing complex projects because teamwork is easier. Such an advantage becomes more salient as the discrepancy between coordination costs becomes larger. In contrast, this relative advantage of breaks is much less relevant for simple projects as they require little coordination. Thus, we have the following prediction: Prediction 6 (Diﬀerence in project complexity, conditional on development). When the coordination cost for complex projects is sufficiently low during breaks but sufficiently high during work periods, the probability of complex projects, conditional on development, is higher during a break than a work period. An important variable observable in the data is whether a project is developed by a team rather than a single person. In general, it is ambiguous whether the conditional probability of using a team 10 should be higher during breaks, in part because teaming up also helps share the workload, and this is particularly useful for work periods when time is more constrained. Since breaks are particularly useful for developing complex projects, the comparison is clearer when separating simple from complex projects: Prediction 7 (Diﬀerence in probability of team projects, conditional on development). When the coordination cost for complex projects is sufficiently low during breaks but sufficiently high during work periods compared to simple projects that require little coordination, complex projects are relatively more likely to be developed by a team during a break than a work period. 3 Data and Empirical Strategy Our empirical setting is Kickstarter, the world-leading reward-based crowdfunding platform. We collect data for the 165,410 US-based projects that attempted to raise money on the platform between April 2009 and April 2015. Project-level information that is publicly available includes the time each project was posted, total funds raised, descriptive information of the project, and the background of the entrepreneur(s). We do not have comprehensive data on the timing of individual contributions within a project nor the location of the funders.7 Kickstarter requires projects to state a funding goal in advance. If a project fails to achieve its funding goal, then the capital is returned to funders and the entrepreneur does not receive any money. We label projects that achieve their funding goal as “successful” and ones that do not as “failed.” Our sample projects collectively raised $1.4B by both successful projects (44% of the projects, 89% of the raised capital) and failed projects (56% of the projects, 11% of the raised capital, though it is eventually returned). As previously documented (Agrawal, Catalini, and Goldfarb 2013), the distribution of capital is highly skewed: the top 1% (10%) of projects accounts for $590M ($1B), or 42% (76%) of the capital. Kickstarter identiﬁes a city for each project, based on the location reported by the entrepreneurs. It provides a smaller geographic measure than a core-based statistical area (CBSA) and a larger 7 The campaign data are obtained from Kickspy, one of the top websites that monitors live Kickstarter activity over time. This data source is often used in papers studying crowdfunding because it is comprehensive in terms of the variables it captures. 11 one than a Census Place. We use city as the location measure in our analysis because it does not involve further aggregation or disaggregation of the core dependent variables. Our sample projects span 10,091 US cities, taken from Kickstarter’s list on its website. Kickstarter is widely used in many college towns. For example, Boulder Colorado, Provo Utah, and Ann Arbor Michigan are among the top 10 places for technology projects per capita. In light of the prominence of locations with colleges on Kickstarter, our empirical analysis exploits the week-by-week variation in the extent of slack time in these places. We manually collect data on school breaks between 2009 and 2015 for the top 200 US colleges as deﬁned by US News & World Report.8 This information is publicly available through posted academic calendars. We consider a location to have a school break in a given week if there is a top 200 college within ﬁve miles of the city center and the college has a break that week. In addition to scheduled breaks, we also manually collect data on snow days from school websites, Twitter, and online news reports. Table 1 presents descriptive statistics at the city-week level for our sample. Approximately 3.3% of our observations are city-weeks where at least one of the top 200 colleges is on break, and Table 2 compares key outcome variables between break weeks and work weeks, providing model-free evidence for some of the basic predictions of our model. During our study period, the average city-week had 0.052 projects launched, with slightly more than half (0.029) failing to reach their goal and the remainder (0.023) successfully reaching it. In most city-weeks, no projects are launched. Relative to work weeks, the number of projects per week is signiﬁcantly higher for breaks (0.39 versus 0.04).9 We use three diﬀerent proxies for eﬀort in our analysis: the length of the text (in words) used to describe a project, the number of frequently asked questions (FAQs) the entrepreneur lists on the page, and the number of project updates posted. Relative to work weeks, the descriptive statistics show that projects posted during the breaks have longer descriptions, more FAQs, and more updates. 8 Source: http://colleges.usnews.rankingsandreviews.com/best-colleges/rankings/national-universities/data (accessed September 2013). 9 In addition, the descriptive statistics show that the maximum number of successful projects for any US city in a single week is 45 (Los Angeles, CA), whereas the maximum number of failed projects is 79 (also Los Angeles). In a single week, cities are able to attract as much as $21.8M in successful funds, with an average per city-week of $445 and a standard deviation of $23,633. 12 We capture team projects by identifying the number of team members listed on a project’s biography pages. Overall, 3% of the projects are posted by teams (usually consisting of two people). Relative to work weeks, a signiﬁcantly greater percentage of projects posted during the breaks use teams (12.8% versus 2.7%). Using biographies, we also identify the skills mentioned by creators in their proﬁles (e.g., programming, photography, etc.). We use this measure to build two proxies for project complexity: the number of unique skills listed, and the number of unique skills divided by the size of the team (to avoid a mechanical relationship between team size and the total number of unique skills). Among projects posted, the mean number of skills is 1.5 and the mean number of skills per team member is 1.2. These values are higher for projects posted during breaks. Overall, the raw data are consistent with the basic predictions of our model: break weeks are characterized by signiﬁcantly more projects, more eﬀort being devoted to the posted projects, an increase in project complexity and the use of teams. However, because these diﬀerences might be driven by a number of confounding factors such as time trends, seasonality, and diﬀerences in the baseline level of crowdfunding activity across cities, we control for these diﬀerences using the empirical strategy described below. 3.1 Empirical Strategy Our econometric framework is straightforward: we exploit variation across cities in the timing of breaks at local colleges and universities to estimate how an increase in slack time inﬂuences the number and type of projects posted. The unit of analysis is a city-week. City ﬁxed eﬀects are included to control for underlying diﬀerences across cities that are constant over time, and week ﬁxed eﬀects are added to control for changes in the Kickstarter environment over time. We focus on a linear model with ﬁxed eﬀects to document the underlying relationships in a direct and easily interpretable manner: Yct = γAllBreaksct + µc + ψt + ǫct , 13 where Yct is the outcome variable such as the number of projects posted on the platform in city c during week t,10 AllBreakct is a dummy that equals one if there is a top 200 college in the focal city on break in the focal week, µc and ψt are city and week ﬁxed eﬀects, and ǫct is an idiosyncratic error term. There are few city-level measures that change at the week level. Unsurprisingly, given city and week ﬁxed eﬀects, results do not change when including controls such as weekly temperature and annual CBSA-level demographics. Thus, we focus on the more parsimonious speciﬁcation and do not include additional covariates. Because the ﬁxed eﬀects completely capture cities in which we never see any crowdfunding activity, we remove these cities from the analysis without any empirical consequences. Robust standard errors are clustered at the city level for all regressions. 4 Results We ﬁrst present the regression results on the quantity of projects posted. The result, consistent with the raw data, shows that a substantially greater number of projects are posted during break weeks. We follow this main result with evidence supporting a casual interpretation. We then report results on the impact of breaks on the distribution of project value because the welfare implications are diﬀerent depending on whether these extra projects are mostly marginal ones with limited potential or if they include large, high-value projects. Third, we examine the diﬀerences in project complexity and the likelihood of team projects during break weeks versus work weeks. The results are informative about the role breaks play in reducing coordination costs. Finally, we exploit a Kickstarter policy change that increased the posting requirement in some but not all project categories to further test our interpretation of data and mechanisms. 4.1 Quantity of Ideas Developed (Prediction 1) Column 1 of Table 3 shows that, controlling for week and city ﬁxed eﬀects, the number of crowdfunding campaigns launched increases during school breaks by 0.024 (signiﬁcant at the 1% level). The 10 Other dependent variables include the total amount raised by the projects posted in city c during week t, the average values of certain characteristics over all projects posted in city c during week t, such as the amount of effort invested into a project (description length, number of FAQs, number of updates), the number of unique skills, and team size. 14 magnitude of the increase is substantial relative to the average number of campaigns per city-week of 0.052 (ﬁrst row in Table 1), implying an increase of 46%. In the Appendix, we show robustness to focusing on cities with more Kickstarter activity, yielding larger coeﬃcients but smaller percentage increases (20-30%). In terms of the total amount of funds raised, we use funding (not logged) as the dependent variable in Column 2 of Table 3. The estimated coeﬃcient on school breaks is also positive but not signiﬁcantly diﬀerent from zero. This is likely because the distribution of funding is highly skewed. Thus, we use log(Funding+1) as the dependent variable in Column 3. The result shows a positive and signiﬁcant correlation between total funding and college breaks, with an increase of about 1.5%.11 Evidence for a causal interpretation The mechanism behind Prediction 1 of our model suggests that the positive correlation between the quantity of projects and breaks is causal: Breaks enable more projects to be developed because the opportunity cost of time is lower. By including city and week ﬁxed eﬀects, our basic empirical strategy helps isolate potential spurious correlation due to general time trends, seasonality, or timeconstant diﬀerences in innovative activity across cities. In the rest of this subsection, we provide additional evidence in support of a causal interpretation of this relationship. In later subsections, our results on outcome variables other than quantity provide further support for the mechanisms introduced in the model. First, we exploit variation across types of universities and Kickstarter categories to examine whether the spike in activity is consistent with the type of human capital involved. We do this because, although we obtain variation in breaks using university-level data, we measure activity at the city level. Thus, demonstrating that the city-level eﬀect (e.g., more technical projects posted on Kickstarter) is consistent with local university-level human capital (e.g., break week for an 11 As with many other quasi-experimental regression papers (e.g., Athey and Stern (2002) and Simcoe and Waguespack (2011)), the R-squared in the analysis in this table is low. This is not surprising given that city fixed effects are differenced out rather than estimated and that there are many reasons why people post projects on Kickstarter besides having time during college breaks. Key for our conclusions is that our coefficient estimates have statistical power and magnitudes of economic importance. 15 engineering school as opposed to an art school) provides further evidence that is consistent with our interpretation. In Column 1 of Table 4, we use only projects in art, and in Column 2 we focus on projects in technology.12 Breaks at top art, design, ﬁlm, and theater schools are positively correlated with art projects but not technology projects. Conversely, breaks at top engineering schools are positively correlated with technology but not art projects, consistent with our expectation that technical orientation plays a key role in these types of projects. Relatedly, in Column 3 of Table 4, we run our main speciﬁcation only for projects where we are able to identify the presence of a student on the team using the biographies posted on Kickstarter. Whereas the eﬀect is smaller in magnitude (possibly because of our inability to capture all student projects), it is positive and statistically signiﬁcant. Second, we examine the impact of an unexpected increase in the amount of slack time using college closings due to heavy snow. Column 4 of Table 4 shows that snow breaks are also associated with a signiﬁcant and positive increase in the quantity of projects. In addition, Column 5 uses the city-year as the unit of observation and regresses the number of projects on the total number of snow days in that city-year, controlling for city and year ﬁxed eﬀects. Given that the number of days that a college cancels classes due to snow varies exogenously from year to year and city to city, the positive and signiﬁcant coeﬃcient is consistent with such random increases in slack time having a positive causal impact on the number of projects produced. Third, if breaks provide college students with more time to browse Kickstarter and fund projects, including those by local entrepreneurs, then our result may be driven by an increase in the supply of local capital. To assess this alternative explanation, we examine the timing of funding associated with projects posted in the week preceding a break. In particular, we measure whether funding for those projects increases during the break. For consistency, we speciﬁcally look at 8-14 days after posting. If the eﬀect we measure is due to increased funding during a break, then we would expect to observe an increase in funding during break weeks for projects posted just prior to the break. However, results reported in Columns 6 and 7 of Table 4 indicate that funding associated with projects started during a work week does not rise during break weeks even though fundraising 12 Our sample projects span the main 13 categories defined by Kickstarter, including Art, Comics, Dance, Design, Fashion, Film & Video, Food, Games, Music, Photography, Publishing, Technology, and Theater. 16 eﬀorts continue during those weeks. It is important to highlight that the breaks we explore in our main analysis are scheduled and expected, and therefore people might shelve ideas and wait until they have more time during breaks.13 While it is empirically diﬃcult to capture shelving, for a subset of projects we are able to collect information on when the creator started working on the idea. Excluding these projects that have been clearly shelved does not aﬀect our results.14 We also do not observe strong evidence for shelving in the data. Figure 2 plots the regression results that include dummies for the weeks before and after a college break period in our main speciﬁcation, and the baseline is any week more than ﬁve weeks away from a college break. The ﬁgure shows no decrease in activity immediately before or after the break relative to the baseline level. In addition, we also do not observe a signiﬁcant decreasing trend prior to the breaks. Even though we cannot fully rule out shelving, the lack of any pre-trend at least provides no evidence for a natural way we would expect shelving to happen; that is, if people shift ideas anticipating breaks, we would expect that there is a greater drop immediately before the breaks (because one does not lose much by delaying just a few days) than semester weeks that are farther ahead of the breaks. It is important to note that shelving per se does not invalidate the causal impact of breaks. The notion that people “need” to delay until breaks to work on certain projects implies that a suﬃcient amount of slack time is critical to materialize these ideas. In other words, without breaks, some of these projects may not be generated at all.15 13 Notice that snow breaks, despite being unexpected, do not provide a good test for the presence of shelving because they take place in the same context, where individuals might shelve projects for anticipated breaks. 14 In Appendix Table B-6, when we run our analysis excluding the subset of projects that were clearly shelved (Column 3), our estimate is identical to the one for the full sample. Furthermore, the effect of breaks on shelved projects (Column 2) is very small in magnitude. Shelved projects also seem to appear across all weeks of the breaks (Column 8) in a fairly homogeneous way, i.e., they do not seem to disproportionally appear at the beginning of a break (as one would expect if they were driving the results). Furthermore, even when looking at heterogeneity across breaks of different length and within weeks of the same break, excluding shelved projects does not alter our results (Columns 7 versus 9). 15 An important caveat is that the exact impact of breaks on the quantity and quality of projects would be different with and without the ability to shelve projects. However, assigning a direction or magnitude to this difference is not obvious. In an extension of the baseline model (see Appendix A3 in the paper for details), we allow projects to be shelved with a discount factor on the project’s value. The tradeoff is that if a project is delayed until a break, the time cost to implement it is eventually smaller but at the same time the project may lose some of its value (e.g., due to competing ideas, lack of patience, forgetfulness, loss of momentum). The only situation in which there is some real tension is when the discount factor is in an intermediate range. In this range, the entrepreneur would choose to immediately develop very good ideas and delay relatively poor ones (as ideas of the lowest value are dropped). This is because when the idea quality is high, the entrepreneur would not want to sacrifice its potential by delaying it, 17 4.2 Project Value Distribution and Effort (Predictions 2 & 3) In the previous section, we show that when college students are on break in a city, there are substantially more projects posted and more funds raised on Kickstarter. The increase in quantity may have diﬀerent welfare implications depending on the quality of these additional projects. Prediction 2 shows that relative to work weeks, during breaks we should observe disproportionately more projects at both the low end and the high end of the value distribution. This prediction arises from the lower opportunity cost time during breaks which induces: 1) more marginal projects to be pursued because time is less precious (a selection eﬀect), and 2) more eﬀort to be allocated to the development of an idea, which in turn increases the project’s value (an eﬀort eﬀect). To examine the impact of breaks on the distribution of project value, we divide projects into 15 bins based on the amount of funds raised. The bins are deﬁned by year to account for the growth of the platform. Table 5 reports the results from a regression in which the dependent variable is the number of projects in a speciﬁc bin, the unit of analysis is a city-week bin, and ﬁxed eﬀects for weeks and cities are included as in previous tables. The results are consistent with Prediction 2: relative to work weeks, breaks are characterized by signiﬁcantly more projects of the lowest value (Bin 1), fewer projects in the middle of the distribution (Bins 2 to 6), and more projects again on the right tail of the distribution (Bins 7 to 15). Furthermore, the eﬀects become increasingly larger and more signiﬁcant as we move away from the middle of the distribution.16 Recall that the model assumes that more eﬀort makes projects better, which explains why we observe a positive eﬀect of breaks on the right tail of the project value distribution. It is therefore important to see whether the data are consistent with this mechanism. In particular, Prediction 3 shows that we should observe more eﬀort during breaks and that the diﬀerence in eﬀort should be larger for projects of higher value. This prediction is conﬁrmed by the results reported in Table 6. First, Columns 1 to 3 show that the average values of the three diﬀerent measures of eﬀort (length of project description, number of FAQs, and number of updates) are all signiﬁcantly higher for and the potential is likely to be large compared to the benefit from the time cost savings. This behavior would push against us finding that a substantial amount of the additional projects posted during breaks are better, high-value projects. In the alternative two scenarios, one choice always dominates the other regardless of the intrinsic quality of ideas. 16 In Appendix Table B-4, we show similar results when segmenting the distribution, further allowing for more bins. 18 projects posted during breaks. Second, when we separate projects into diﬀerent bins of the value distribution, results show that for all measures of eﬀort, the diﬀerence between break and work weeks generally increases as we move from the lowest bins (Columns 4, 7, and 10) to the highest ones (Columns 6, 9, and 12).17 To summarize, the results of this section are consistent with the model’s prediction that we should observe disproportionately more projects on both tails of the value distribution. From a welfare perspective, the right tail is particularly interesting because these projects are more likely to have a disproportionate impact on the economy. The results on eﬀort seem to corroborate the mechanism we hypothesized for the creation of these high-impact projects, i.e., entrepreneurs are able to devote more eﬀort to the execution of their ideas when time is less costly. 4.3 Teams and Project Complexity (Predictions 6 & 7) Lower opportunity cost time may also make it easier for team members to coordinate their schedules and execute on their ideas. This relative advantage of breaks should have a disproportionate impact for complex projects, especially if these projects are more likely to beneﬁt from diﬀerent perspectives and skills. Prediction 6 of our model shows that when the coordination cost for complex projects is sufﬁciently high during work weeks but suﬃciently low during breaks, we should observe an increase in the share of complex projects during breaks.18 As for the likelihood of teams, the theory is ambiguous because teaming up can also help share the workload across multiple people, and this eﬀect could be more valuable when time is more constrained (i.e., during work weeks). However, if we contrast complex projects to simpler ones, we should be more likely to observe a team forming around a complex project during a break than during a work week (Prediction 7). The results in this section are consistent with these predictions. As explained above, we use two proxies for project complexity: the number of unique skills on a project (as captured from entrepreneur biographies), and the number of unique skills divided by team size. Columns 1 and 17 In the Appendix, we further focus on the right tail of the distribution by limiting the analysis to successful projects (Table B-10): again, as project value increases, effort levels during the breaks increase too. 18 We turn to Predictions 4 and 5 in Section 4.4 in examining the impact of an increase in minimum effort. 19 2 of Table 7 show that for both measures, projects during breaks appear to be signiﬁcantly more complex than projects posted during work weeks. Second, consistent with the raw data, the regression results show that, on average, projects posted during breaks are signiﬁcantly more likely to be carried out by teams than projects posted during work weeks (Column 3 of Table 7). Last, we further separate the sample into relatively complex projects versus simpler projects based on whether a project is above or below the median of our measures of complexity. Consistent with Prediction 7, the results show that for relatively complex projects (Columns 5 and 6), the likelihood of teams is signiﬁcantly higher during breaks. In contrast, for simpler projects (Columns 7 and 8), there is no signiﬁcant diﬀerence between break and work periods in the likelihood of using a team. 4.4 Effects of Increasing the Minimum Effort Requirement (Predictions 4 & 5) In May 2012, Kickstarter implemented a policy that disproportionately increased requirements to post projects in the Design and Technology categories (e.g., preparing a manufacturing plan, building a working prototype, describing them clearly on the site). We explain the policy change in greater detail below. In the context of our model, the new policy increases the minimum eﬀort required to develop a project. Whereas it is ambiguous whether the relative share of projects posted during breaks should increase after the policy change (Prediction 4), the model predicts that we should observe an increase in the share of top-valued projects (Prediction 5). In response to a series of high-proﬁle Design and Technology projects that raised a signiﬁcant amount of capital and then failed to deliver the promised products in the anticipated amount of time (some delivered very late and others failed to deliver at all), Kickstarter increased the requirements for posting projects in those two categories. One of the primary criticisms was that in most of these cases the entrepreneur raised capital and promised funders a product without any experience or preparation for production or distribution. Therefore, in May 2012 Kickstarter revised its rules to address accountability concerns, explaining in a note that it now requires project creators to “provide information about their background and experience, a manufacturing plan (for hardware 20 projects), and a functional prototype. [Kickstarter] made this change to ensure that creators have done their research before launching and backers have suﬃcient information when deciding whether to back these projects.”19 The policy was further reinforced in September 2012, when Kickstarter reiterated the need for a prototype and made it clear that product simulations and renderings were not enough for posting.20 The regression results in Table 8 contrast the relative changes in a number of key outcome variables for break weeks versus work weeks before versus after the policy shock for projects in the Design and Technology categories compared to the other 11 categories. First, for the relative changes in the quantity of projects, we use a regression in which the dependent variable is the ratio between the number of projects in Design and Technology and the number of projects in all other categories (Column 2 of Table 8). The coeﬃcient of the interaction term between breaks and the period following the policy change is positive and signiﬁcant. This suggests that when comparing Design and Technology to the other categories, after the shock breaks are associated with an increase in the relative number of projects. Column 4 of Table 8 shows a similar result for the relative amount of funding.21 Second, for project value, Column 6 of Table 8 reports results from a regression in which the dependent variable is the ratio between the share of projects with large target amounts (over $30,000) in Design and Technology and the share of such projects in the other categories. Consistent with Prediction 5, the coeﬃcient of the interaction term shows that, after the policy change, relative to other categories, the share of large-goal projects signiﬁcantly increased during break weeks in the Design and Technology categories. Finally, Column 8 of Table 8 shows that after the policy change, the relative likelihood of using teams during breaks increases disproportionately for Design and Technology projects relative to other projects. Intuitively, this result is consistent with breaks facilitating coordination in teams. A more stringent posting requirement makes teams relatively more desirable because multiple people 19 https://www.kickstarter.com/blog/accountability-on-kickstarter (Accessed on March 12, 2015) https://www.kickstarter.com/blog/kickstarter-is-not-a-store (Accessed on March 12, 2015) 21 Columns 1 and 3 provide a baseline level comparison between break and work periods for the relative number of projects (or the relative amount of total funds) in Design and Technology categories with respect to all the other categories. 20 21 can share the workload. Compared to work weeks, innovators are better able to respond to the requirement change by working in teams during break weeks because coordination costs are lower. 5 Conclusion We explore how the opportunity cost of time inﬂuences the quantity, quality, and type of innovation. We develop a simple theoretical framework to capture the diﬀerences between periods of high versus low opportunity cost of time (work weeks versus break weeks). Lower opportunity cost time during break weeks may induce: 1) lower quality ideas to be developed (a selection eﬀect); 2) more eﬀort to be applied for any given idea quality (an eﬀort eﬀect); and 3) an increase in the use of teams because scheduling is less constrained (a coordination eﬀect). As a result, the eﬀect of an increase in slack time on inventive outcomes is ambiguous because the selection eﬀect may induce more low quality ideas, whereas the eﬀort and coordination eﬀect may lead to more high quality, complex ideas. Our model, together with the empirical support from data on crowdfunding activity and college breaks, generates the following results. First, during breaks, more projects are posted on Kickstarter in the immediate region near to the colleges. Second, not all of these projects are marginal ones. In fact, we observe an increase on both tails of the project value distribution. Higher value projects seem to be linked to the ability of entrepreneurs to dedicate more eﬀort to their ideas when the opportunity cost of time is low. Finally, overlapping slack time appears to ease team coordination, leading to more complex projects and more projects being developed by teams rather than lone innovators during break weeks. A key limitation of our paper is that the results are obtained from an idiosyncratic setting (crowdfunding) and population (college students). Within that setting, our estimated eﬀects are large: 46% more projects are posted during breaks. We are also only able to imperfectly measure project value, complexity, and the shelving of ideas in expectation of a future break. That said, we interpret the empirical results as providing support for the insights of the model. These insights are general and inform policies targeted at encouraging innovation and experimentation within ﬁrms and other organizations. 22 First, low opportunity cost time may help develop high potential ideas. Second, “overlapping slack” might be more valuable for innovating on complex ideas than individual slack because of the way it allows teams to coordinate around their development. Anecdotally, Google, which used to provide 20% slack to its employees to work on novel ideas, recently restructured the policy as “Area 120.”22 According to Google’s CEO, Area 120 “is giving people a chance at 20% time more formally” by giving them longer spells of continuous time (up to multiple months), as well as the possibility to build teams across the organization and work together at the same time on ideas with potential. Third, in the absence of other, complementary incentives, slack time may induce more marginal, low-value projects. This suggests that companies interested in increasing experimentation may need to combine these policies with incentives targeted at avoiding marginal contributions. In the case of LinkedIn’s [in]cubator program, not only are projects screened by top executives before entry, but the company has adopted a milestone-based approach to ensure the quality of the projects at diﬀerent stages in their evolution.23 In this way, the insights from the model, supported by the empirical analysis, can help us understand the opportunities and challenges in company policies around slack time. 22 Source: http://www.forbes.com/sites/miguelhelft/2016/05/19/google-ceo-sundar-pichai-confirms-area-120corporate-incubator/#409a3dc44f73. 23 According to the company, ideas must first be developed into prototypes and clear two rounds of judging, the final round run directly by Founder Reid Hoffman and CEO Jeff Weiner. Given the stakes and visibility of these judging rounds, it is clear that employees have strong incentives to perform. Only projects showing promise at 30 days graduate to become 60-day projects, and only those that have made sufficient additional progress at Day 60 are allowed another 30-day extension. Source: https://blog.linkedin.com/2012/12/07/linkedin-incubator. 23 References Agrawal, A., C. Catalini, and A. Goldfarb (2013): Some Simple Economics of Crowdfunding, in Innovation Policy and the Economy, Volume 14 - Josh Lerner and Scott Stern editors. NBER, University of Chicago Press. (2015): “Crowdfunding: Geography, Social Networks, and the Timing of Investment Decisions -,” Journal of Economics and Management Strategy (forthcoming). Argyres, N., and B. Silverman (2004): “R&D, organization structure, and the development of corporate technological knowledge,” Strategic Management Journal, 25, 929–958. Arora, A., S. Belenzon, and L. A. 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Liu (2012): “Rational Herding in Microloan Markets,” Management Science, 58(5), 892–912. 25 6 Tables and Figures Figure 1: A Numerical Illustration of the Model (a) Innovator’s payoff (b) Value of developed projects 60 120 Break week Work week Break Work 50 100 40 project value, v innovator payoff, : 80 30 20 60 40 10 20 0 -10 0 1 c0 ē 2 2 c1 ē 3 c0 ē 2 4 5 0 6 c1 ē 7 8 9 10 0 1 2 3 4 idea quality, q 5 6 7 8 9 10 idea quality, q (c) Density distribution of project value, conditional on development 2 Break week Work week 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 1 1.5 2 2.5 3 3.5 4 4.5 5 log(project value, v) Notes: (a) plots the innovator’s payoff from developing a project as a function of the idea’s intrinsic quality, q. (b) plots the value of developed projects as a function of the idea’s intrinsic quality, q. (c) plots the probability density distributions of v conditional on development. The parameter values of the numerical example are: c0 = 1; c1 = 2; and ē = 3. In addition, for (c), idea quality q is assumed to follow an exponential distribution with mean 1.5. 26 Figure 2: The Number of Projects per Week is Higher During Breaks Notes: Estimated coefficient for weeks before and after the school breaks. Dependent variable is the number of projects created in the focal city-week. Regression includes city and week fixed effects. Error bars represent 95% confidence intervals based on robust standard errors clustered at the city level. 27 Table 1: Summary Statistics Projects Total Successful Projects Total Failed Projects N 3,178,665 3,178,665 3,178,665 Mean .052 .023 .029 SD .761 .398 .425 Min 0 0 0 Max 114 45 79 Funding Total Successful Funding Total Failed Funding 3,178,665 3,178,665 3,178,665 444.686 393.86 50.821 23633.61 23149.05 1784.375 0 0 0 21.8M 21.8M 62,3041 All Breaks Snow Closing 3,178,665 3,178,665 .033 .001 .178 .034 0 0 1 1 Table 2: Comparing Break and Work Periods Projects Funding Log Funding Diﬀerence .356 3700.27 .613 SE .002 74.33 .004 p-value 0 0 0 28 N Break 104,440 104,440 104,440 Mean Break .396 4023.38 .755 N Work 3,074,225 3,074,225 3,074,225 Mean Work .040 323.11 .141 Table 3: Impact of Breaks on the Quantity of Projects (1) Projects (2) Funding (3) Log Funding All Breaks 0.0238*** (0.0083) 20.9730 (259.5038) 0.0155*** (0.0039) Observations R-squared Number of Cities 3,178,665 0.164 10,091 3,178,665 0.003 10,091 3,178,665 0.787 10,091 VARIABLES Notes: The dependent variables are, respectively, the number of projects in a city-week, the total amount of funding, and log(Funding +1). City and week fixed effects are included in all regressions. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. Table 4: Impact of Breaks on the Quantity of Projects: Robustness Checks (1) Artistic Projects (2) Technology Projects (3) Student Projects (4) All Projects All Breaks 0.0020 (0.0013) 0.0003 (0.0004) 0.0034** (0.0017) 0.0495*** (0.0121) Break at Top Engineering School -0.0007 (0.0032) 0.0053* (0.0028) 0.0024** (0.0011) 0.0003 (0.0009) VARIABLES Break at Top Art, Design, Film, Theatre School Snow Closing Observations R-squared Number of Cities 1,604,469 0.001 10,091 1,604,469 0.000 10,091 3,178,665 0.003 (5) All Projects (Annual Data) 0.0403** (0.0178) 1.2407*** (0.4758) 2,966,754 0.008 10,091 50,455 0.013 10,091 (6) Funding Days 8-14 (7) Log Funding Days 8-14 96.3529 (88.8682) 0.0256 (0.0162) 1,321,921 0.000 10,091 1,321,921 0.002 10,091 Notes: The dependent variable is Column (1) is the number of art-intensive projects, and in Column (2) it is the number of technology-intensive projects (available May 2012 to April 2015). In Column (3) the dependent variable only includes projects where the creators explicitly mention in their biography their student affiliation. Columns (4) and (5) use data on snow closing (available until December 2014). The unit of analysis for Column (5) is the city-year level. Columns (6) and (7) use data on weekly investments (available from October 2012 to April 2015). City and week fixed effects are included in all regressions (with the exception of Column (5), which uses Year Fixed Effects because of the different unit of analysis). Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. 29 Table 5: Impact of Breaks on Project Value Distribution (1) Projects VARIABLES All Breaks * Bin 1 (Lowest Value) All Breaks * Bin 2 All Breaks * Bin 3 All Breaks * Bin 4 All Breaks * Bin 5 All Breaks * Bin 6 All Breaks * Bin 7 All Breaks * Bin 8 All Breaks * Bin 9 All Breaks * Bin 10 All Breaks * Bin 11 All Breaks * Bin 12 All Breaks * Bin 13 All Breaks * Bin 14 All Breaks * Bin 15 (Highest Value) Observations Number of Cities R-squared 0.0091*** (0.0019) -0.0115*** (0.0024) -0.0018 (0.0012) -0.0015 (0.0011) -0.0013 (0.0012) -0.0012 (0.0008) 0.0003 (0.0008) 0.0007 (0.0005) 0.0025*** (0.0008) 0.0024** (0.0010) 0.0028** (0.0014) 0.0050** (0.0020) 0.0053** (0.0024) 0.0061** (0.0029) 0.0063* (0.0034) 47,679,975 10,091 0.031 Notes: The dependent variable is the number of projects in a specific bin of project value, and the unit of analysis is a city-week-bin. We divide projects into 15 bins based on the amount of funds they raise, from the lowest (Bin 1) to the highest (Bin 15). Bins are defined by year to account for the growth of the platform. City and week fixed effects are included the regression. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. 30 Table 6: Diﬀerences between Breaks and Work Periods in (Endogenous) Eﬀort Provision (1) Mean Desc. Length (2) Mean FAQs (3) Mean Updates (4) 0-33 Mean Desc. Length (5) 33-66 Mean Desc. Length (6) 66-100 Mean Desc. Length (7) 0-33 Mean FAQs (8) 33-66 Mean FAQs (9) 66-100 Mean FAQs (10) 0-33 Mean Updates (11) 33-66 Mean Updates (12) 66-100 Mean Updates All Breaks 1.6298*** (0.5042) 0.0093*** (0.0019) 0.0185** (0.0072) 0.8673** (0.4007) 1.2517*** (0.4561) 1.9980*** (0.5826) 0.0054*** (0.0010) 0.0047*** (0.0012) 0.0071*** (0.0022) 0.0075*** (0.0028) 0.0144*** (0.0048) 0.0263*** (0.0089) Observations R-squared Number of Cities 3,178,665 0.466 10,091 3,178,665 0.079 10,091 3,178,665 0.203 10,091 3,178,665 0.158 10,091 3,178,665 0.166 10,091 3,178,665 0.152 10,091 3,178,665 0.016 10,091 3,178,665 0.027 10,091 3,178,665 0.038 10,091 3,178,665 0.042 10,091 3,178,665 0.081 10,091 3,178,665 0.102 10,091 VARIABLES Notes: The dependent variables are proxies for effort on the platform. In Columns (1) and (4)-(6) we use the mean length of the project description; in Columns (2) and (7)-(9) the mean number of FAQs; in Columns (3) and (10)-(12) the mean number of project updates to the crowd. In Columns (4) to (12), we progressively divide the projects into three segments based on the bins defined in Table 5. For example, the “0-33” category includes the bottom five bins containing projects that raised the lowest amount of funds, and “66-100” is the highest. City and week fixed effects are included in all regressions. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. 31 Table 7: Diﬀerences between Breaks and Work Periods in Project Complexity and the Share of Teams (1) Mean Skills (2) Mean Skills PP (3) Mean Team Size (4) Share Team in Complex (Skills) (5) Share Team in Simple (Skills) (6) Share Team in Complex (Skills PP) (7) Share Team in Simple (Skills PP) All Breaks 0.0066*** (0.0018) 0.0046*** (0.0016) 0.0024* (0.0014) 0.0009** (0.0004) 0.0004 (0.0004) 0.0009** (0.0004) 0.0007 (0.0005) Observations R-squared Number of Cities 3,178,665 0.350 10,091 3,178,665 0.322 10,091 3,178,665 0.458 10,091 3,178,665 0.049 10,091 3,178,665 0.065 10,091 3,178,665 0.107 10,091 3,178,665 0.164 10,091 VARIABLES Notes: For Columns (1) and (2), the dependent variables are the mean level of measures of project complexity for all projects in a given city-week. The two measures we use are the unique number of skills (“Skills”) and the unique number of skills per team member (“Skills PP”). For Columns (3)-(7), the dependent variable is the share of team projects among all projects for a given city-week. We define complex projects as those that are above the median in terms of our two complexity measures (and simple projects as those that are below the median). City and week fixed effects are included in all regressions. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. Table 8: Eﬀects of Increasing the Minimum Eﬀort Level VARIABLES All Breaks (1) Projects Ratio (2) Projects Ratio (3) Funding Ratio (4) Funding Ratio (5) Large Projects Ratio (6) Large Projects Ratio (7) Team Size Ratio (8) Team Size Ratio 0.0000 (0.0002) -0.0002 (0.0002) 0.0006** (0.0003) 0.0004 (0.0003) -0.0006** (0.0003) 0.0024*** (0.0006) 0.0002 (0.0002) -0.0008*** (0.0002) 0.0024*** (0.0006) 0.0006 (0.0005) -0.0012* (0.0006) 0.0045*** (0.0013) 3,178,665 0.025 10,091 3,178,665 0.025 10,091 3,178,665 0.014 10,091 3,178,665 0.015 10,091 3,178,665 0.002 10,091 3,178,665 0.002 10,091 3,178,665 0.019 10,091 3,178,665 0.019 10,091 All School Breaks * After the Change Observations R-squared Number of Cities Notes: For Columns (1) and (2), the dependent variable is the ratio between the number of projects in the Design and Technology categories and the number of projects in all the other categories for a given city-week. The dependent variables of the other columns are similarly defined based on the total amount of funds, the share of projects with large target amounts (over $30,000), and the share of team projects. “After the Change” indicates time periods after the May 2012 policy change. City and week fixed effects are included in all regressions. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. 32 Appendix A: Proofs of Theoretical Results A1. The baseline model Proof of Prediction 1. The innovator’s payoﬀ from developing the project (Equation (3)) is an 2 increasing function of q. Because 2cq w > 0 regardless of q, the development decision is determined 2 by π̄w (q) = 0. The quality thresholds are thus qē − cw ē2 = 0 ⇔ q̄w = cw2 ē . The probability of developing a project is then Pr(q ≥ cw2 ē ) = 1 − F ( cw2 ē ), where F is the cumulative probability distribution of idea quality q. This probability is a decreasing function of cw , and therefore the probability of developing a project during the break is higher than that a work period. 2 Proof of Prediction 2. At the low end, no projects are developed in either period if v < c02ē . 2 2 However, when c02ē < v < c12ē , no projects are developed during a work period but they are developed during the break. Thus, Pr(v < v̂|developed; break) ≥ Pr(v ≤ v̂|developed; work) for 2 any v̂ ≤ c12ē , because the latter is always zero in this range while the former is positive or zero. At the high end, ignoring the minimum eﬀort requirement for the moment, the project’s value takes the form q · e∗w (q) = q · cqw . Thus, given project value v̂, the corresponding idea quality is √ √ v̂cw and the corresponding eﬀort level is √cv̂w . The conditional probability of projects with value greater than v̂ is therefore Pr(v ≥ v̂|developed) = above conditional probability can be written as √ c0 v̂ c ē −λ( 0 2 ) e e−λ > √ c1 v̂ c ē −λ( 1 2 ) e e−λ when v̂ ≥ √ ē2 ( c 1+ 4 √ c0 )2 √ 1−F ( cw v̂) ē . ) 1−F ( cw 2 √ cw v̂ ē −λ( cw 2 ) e e−λ With an exponential distribution, the , where 1/λ is the mean of the distribution. . Notice that c1 ē2 is the project value at which the desired eﬀort level for a work week equals ē. So the projects’s value derives from q · cqw when v is greater than this value for both break and work periods (and thus the previous analysis holds even after taking into consideration the minimum √ √ ē2 ( c1 + c0 )2 , c1 ē2 } = c1 ē2 because c0 < c1 . Therefore, we eﬀort requirement). Furthermore, max{ 4 can conclude that Pr(v ≥ v̂|developed; break) ≥ Pr(v ≥ v̂|developed; work) for any v̂ ≥ c1 ē2 . Proof of Prediction 3. We have three scenarios. First, for any v̂ ≥ (c1 ē)ē, the project’s √ value takes the form q · e∗w (q) = q · cqw for both periods. Thus, the corresponding idea quality is v̂cw and √ the corresponding eﬀort level is √cv̂w . Because c1 > c0 , the eﬀort level during the break is higher. √ √c −√c The diﬀerence in eﬀort level is v̂( √1c0 c1 0 ), and it is a positive function of v̂. Second, for c1 ē2 2 ≤ v̂ < (c1 ē)ē, the eﬀort level for projects developed during a work week is ē, √ while that for the break is max{ √cv̂0 , ē}. Thus, eﬀort level during the break is weakly higher, and the diﬀerence in eﬀort level is weakly increasing in v̂. 2 Third, for v̂ < c12ē , we cannot make such a comparison because no projects are developed during a work week. Proof of Prediction 4. The probability of developing an idea is Pr(q ≥ q̄w = cw2 ē ) = 1 − F ( cw2 ē ). The change in this probability due to an increase in ē is −f ( cw2 ē ) c2w , which is negative. In order for the reduction to be smaller for the break, we need to have ∂(−f ( cw2 ē ) c2w )/∂cw < 0. With an A-1 exponential distribution, the secondary derivative is: ∂(−f ( cw ē cw cw ē 1 cw ē cw λcw ē ) )/∂cw = ∂(−λe−λ 2 )/∂cw = −λe−λ 2 ( − ) 2 2 2 2 4 Thus, for the above equation to be negative, we need to have λ < cw2 ē and thus the mean of the exponential distribution (i.e., 1/λ) to be greater than cw2 ē . Given that we have two discrete values of cw , it is suﬃcient (though not necessary) to take the greater of the two (i.e., c12ē ) for the above condition to hold. Proof of Prediction 5. First, consider a generic ratio r = a/c, where 0 < a < c. The diﬀerence ′) results from reducing the denominator from c to c′ is ca′ − ac = a(c−c cc′ . This diﬀerence is positive and increases with the numerator a. From Prediction 2, we know that there are more projects with v ≥ c1 ē2 during the break than a work period. Then, the share of top projects developed during the break relative to the total number of projects (break and work periods combined) is greater than the share of top projects developed during a work period relative to the same total number of projects. Thus, following the relationships derived from a generic ratio stated above, as the denominator (the total number of projects) decreases after the posting requirement becomes more stringent, the relative share of top-value projects developed during the break increases. A2. Extension of the baseline model—allowing teams In this section, we extend the baseline model to allow for team projects. Either one or two people can work on the project. If solo, the individual innovator’s payoﬀ is the same as in the baseline model. If with a team, each team member’s payoﬀ consists of half of the value of the project, minus her own time cost and a coordination cost.24 We separate projects into two types: d ∈ {0 = simple; 1 = complex}, and let the unconditional probability of a complex project be ρ and that for a simple project be 1 − ρ. For simplicity, we assume that project complexity is independent of the the distribution of an idea’s intrinsic quality q. We normalize the coordination cost to be zero for simple projects. For complex projects, teaming up incurs a positive coordination cost and such a cost is smaller during the break than a work period; that is, δ0 < δ1 . Finally, for simple projects, teaming up per se generates no direct beneﬁt to the project’s value, while for complex projects, teaming up brings direct beneﬁt to the project (e.g., from complementary skills and perspectives), and this beneﬁt is more pronounced for ideas with greater quality. Thus, the innovator’s payoﬀ from developing a project at eﬀort level e is: ( 2 qe − cw e2 if solo πw = , 1 e2 2 q(1 + dγ) · 2e − cw 2 − δw d if team where w ∈ {0 = break; 1 = work}, d ∈ {0 = simple; 1 = complex}, and γ indicates the direct beneﬁt to a project’s value. We assume that the direct beneﬁt from using teams is not too high 24 In this simple extension, we abstract away from the scenario in which each individual observes a separate idea and decides whether to develop one of the two ideas jointly or develop the ideas separately. The simple extension is as if assuming that the second team member is unlikely to develop any projects on his own if not asked by the first person. A-2 q ē2 (i.e., γ < cw ēc2w−2δ − 1) to rule out the scenario in which using a team dominates developing the w project solo regardless of idea quality. Taking into account the minimum eﬀort requirement ē, we can write the innovator’s payoﬀ functions as follows (analogous to Equation (3) in the baseline model): if solo ✶{q≥cw ē} 2cq w + ✶{q<cw ē} (qē − cw ē2 ) 2 q 2 (1+dγ)2 ē 1 π̃w (q) = cw ē ✶{q≥ 2(1+dγ) − δw d) + ✶{q< cw ē } ( 2 q(1 + dγ)ē − cw 8 − δw d) if team . }( 2cw  2(1+dγ)     2 2 0 if drop (5) Consider only simple projects for the moment. Using a team does not incur any coordination costs. As there is no direct beneﬁt to the project’s value, the beneﬁt from using a team comes from sharing the workload. In our simple setup, this beneﬁt matters only for ideas of relatively low qualities (for which the minimum eﬀort requirement is too high relative to the idea’s quality). The following result shows that for both break and work periods, a simple project is developed solo if the idea’s quality q is suﬃciently high, by a team if q is in an intermediate range, and dropped if q is suﬃciently low. Notice that allowing a team to share the workload lowers the quality threshold of developing a project relative to that in the baseline model ( cw4 ē versus cw2 ē ). Result 1 (Decision rules on “solo” versus “team” for a simple project). A simple project is developed solo if q ≥ cw ē, by a team if cw4 ē ≤ q < cw ē, and dropped otherwise. Proof. For a simple project, d = 0. Both payoﬀs (solo or team) are monotone increasing functions of q. When q > cw ē, developing the project solo generates the same payoﬀ as that from using a team. We let the innovator choose solo because there may still be a small coordination cost working with a team. When q < cw ē, the innovator is better oﬀ working in a team as multiple people share the workload, resulting in a smaller time cost for each individual member. The payoﬀ from developing a project using a team is greater than zero if and only if q > cw4 ē , which is the 2 solution of ( 21 qē − cw ē8 ) = 0 For complex projects, while coordination costs for teams are non-zero, teaming up introduces two beneﬁts: sharing the workload, and an increase in project value. This second, direct beneﬁt becomes more relevant as the idea quality q increases. Similar to simple projects, teams may also help share the workload when the minimum eﬀort requirement is too high relative to the idea’s quality. However, for complex projects we may not see the use of teams for this range of ideas if coordination costs are too high. Formally, we have the following decision rule for complex projects: Result 2 (Decision rules on “solo” versus “team” for a complex project). For a complex project, 2 (a) when the coordination cost is sufficiently high (i.e., δw > cw8ē (1 + γ)2 ), the project is developed by a team if q ≥ q̂w (all thresholds are defined below), solo if cw2 ē ≤ q < q̂w , and dropped otherwise. 2 (b) when the coordination cost is not too high (i.e., δw < cw8ē (1 + γ)2 ), the project is developed team ≤ q < q̌ , and dropped otherwise. by a team if q ≥ q̂w , solo if q̌w ≤ q < q̂w , team again if q̄w w Proof. For a complex project, d = 1. Again, both payoﬀs (solo or team) are monotone increasing functions of q. First, deﬁne the following thresholds: A-3 • The value of q that makes the innovator indiﬀerent between qusing a team or not at the higher 2δw cw )+✶ end of the quality distribution: q̂w = ✶ (γ 2 +2γ)cw ē2 ( (γ 2 +2γ)cw ē2 (q̃w,1 ), γ 2 +2γ {δw < {δw > } } 2 2 p 1 2 − c2 ē2 (γ 2 + 2γ)) is the greater of the two solutions 2c δ (1 + γ) (c ē+ where q̃w,1 = (1+γ) w w w 2 w 2 2 2 2 2 w ē , the payoﬀ from using a team and −δw . When δw > (γ +2γ)c that make qē−cw ē2 = q (1+γ) 2cw 2 the payoﬀ from developing the project solo intersect when the desired eﬀort levels for both 2 2 w ē are above the minimum requirement (ē). When δw < (γ +2γ)c , the two payoﬀs intersect 2 when the desired eﬀort level when using a team is above ē while that for solo is below ē. • The value of q that makes the innovator indiﬀerent between p using a team or not at the low 1 end of the quality distribution: deﬁne q̌w = (1+γ)2 (cw ē − 2cw δw (1 + γ)2 − c2w ē2 (γ 2 + 2γ)), 2 which is the smaller of the two solutions that equate qē − cw ē2 = q 2 (1+γ)2 2cw − δw . • The value of q that makes the innovator indiﬀerent between developing the √ project using cw ē 2δw team w δw a team and dropping it: q̄w = ✶{δ < cw ē2 } ( (1+γ)4 + (1+γ)ē ) + ✶{δ ≥ cw ē2 } ( 2c 1+γ ). When w cw ē2 8 , 8 w 8 the payoﬀ from using a team equals zero when the desired eﬀort level is below ē; δw < otherwise, the payoﬀ equals zero when the desired eﬀort level is above ē. 2 We have two scenarios. First, when the coordination cost is suﬃciently high (i.e., δw > cw8ē (1 + 2 γ) , see the derivation of this threshold value in the last paragraph of this proof), sharing the workload alone is not suﬃcient to justify the use of teams. The only cases in which teams are worth the high coordination cost are when the direct beneﬁt is high enough, which is when the idea’s quality is suﬃciently high. Thus, the project is developed by a team if q ≥ q̂w , solo if cw ē 2 ≤ q < q̂w , and dropped otherwise (the thresholds are deﬁned as above). 2 Second, when the coordination cost is not too high (i.e., δw < cw8ē (1 + γ)2 ), it may also be worthwhile using a team simply to share workload. Thus, project is developed by a team if q ≥ q̂w ; team ≤ q < q̌ ; and dropped otherwise. solo if q̌w ≤ q < q̂w ; team again if q̄w w Finally, to derive the separating threshold for these two scenarios, note that the value of q at which the desired eﬀort level when using a team equals the minimum required eﬀort level is smaller than the value of q at which the innovator is indiﬀerent between dropping the project and cw ē < cw2 ē ). Thus, the threshold value of coordination cost δw that developing it solo (that is, 2(1+γ) separates the two scenarios of whether a team is used again at the relatively low end of the quality distribution is when the optimal payoﬀ from using a team at q = cw2 ē is equal to zero. This yields 2 the threshold value of cw8ē (1 + γ)2 . A key interesting insight from the above results is that complex projects are likely to beneﬁt more from breaks because coordination is easier than during a work week. In contrast, for simple projects, the relative advantage of breaks is not relevant since no coordination is required. The probability of complex projects conditional on development is however not necessarily higher for breaks because the low opportunity cost of time during breaks alone would also allow a greater number of simple projects to be developed. Prediction 6 in the paper provides a suﬃcient condition under which the likelihood of complex projects is greater during breaks. This suﬃcient condition is satisﬁed when the coordination cost for a complex project is suﬃciently high during a work week but suﬃciently low during breaks. A-4 2 2 Proof of Prediction 6. When δ1 > c18ē (1 + γ)2 and δ0 < c08ē , the probabilities of complex projects (conditional on development) during a work and a break week are (recall that ρ is the unconditional probability that an idea is complex): ρ(1 − F ( c12ē )) , (1 − ρ)(1 − F ( c14ē )) + ρ(1 − F ( c12ē )) Pr(Complex|work; developed) = Pr(Complex|break; developed) = team ) ρ(1 − F (q̄w , c0 ē (1 − ρ)(1 − F ( 4 )) + ρ(1 − F (q̄0team ) 2δ0 c0 ē + (1+γ)ē (deﬁned in Result 2). where q̄0team = (1+γ)4 Pr(Complex|break; developed) > Pr(Complex|work; developed) when the following holds: c0 ē 2δ0 (1 − F ( (1+γ)4 + (1+γ)ē ) (1 − F ( c12ē )) < . c1 ē c0 ē (1 − F ( 4 )) (1 − F ( 4 )) (6) With q following an exponential distribution, Equation (6) holds as long as δ0 < 18 ((1 + γ)ē2 c1 + 2 2 2 γc0 ē2 ). This latter condition is satisﬁed when δ0 < c08ē as c08ē < c18ē < 18 ((1 + γ)c1 ē2 + γc0 ē2 ). An important variable observable in the data is whether a project is carried out by a team. It is ambiguous whether the likelihood of team projects (conditional on development) should be higher during breaks, because teaming up also helps share the workload and that is particularly useful for work periods when the opportunity cost of time is higher. Given that the relative advantage of breaks in easier coordination among multiple people is more salient for complex projects, we should observe that compared to simple projects that require no coordination, complex projects are relatively more likely to be developed by a team during a break than during a work period. Prediction 7 in the paper shows that this statement is true when the coordination cost for a complex project is suﬃciently high during a work week but suﬃciently low during breaks. Proof of Prediction 7. For simple projects, the diﬀerence in the probability of using a team between break and work weeks is: = Pr(Team|break; simple & developed) − Pr(Team|work; simple & developed) c0 ē ) 4 c0 ē 1−F ( 4 ) F (c0 ē)−F ( − c1 ē ) 4 c1 ē 1−F ( 4 ) F (c1 ē)−F ( With q following an exponential distribution, c0 ē ) 4 c0 ē 1−F ( 4 ) F (c0 ē)−F ( c0 ē2 8 . The diﬀerence Pr(Team|break; complex & developed) − Pr(Team|work; complex & developed) 1−F (q̂0 )+(F (q̌0 )−F (q̄0team, 1−F (q̄0team, d=1 ) d=1 ) − 1−F (q̂1 )) c ē 1−F ( 12 ) (7) increases with c. Thus, Equation (7) is negative; i.e., the probability of team projects is smaller during breaks. 2 For complex projects, consider the scenario when δ1 > c18ē (1+γ)2 and δ0 < in the probability of using a team between break and work weeks is: = . , (8) where the thresholds are all deﬁned in Result 2. During work periods, because coordination cost is too high, teams are used only at the high end of the quality distribution to take advantage of the A-5 direct beneﬁt to project value. During break periods, because the coordination cost is suﬃciently small, teams are used both at the high end and at the relatively low end in order to take advantage of workload sharing. We can show that the second term in Equation (8), Pr(Team|work; complex & developed) = 1−F (q̂1 )) c1 ē , is a decreasing function of δ1 . That is, the higher the coordination cost, the likelihood 1−F ( 2 ) of using a team is smaller during a work period. At the limit, this likelihood goes to zero. Thus, given any value of δ0 (thus, ﬁxing Pr(Team|break; complex & developed)), there exists a δ̂1 such that Equation (8) is positive for all δ1 > δ̂1 ; that is, the probability of team projects is greater during breaks than work periods. A3. Extension of the baseline model—allowing for shelving In this section, we extend the basic setup to allow the innovator to shelve an idea and develop it later. For an idea arriving during a work week, the innovator can choose to develop it, to shelve and develop it during the break, or to drop the idea. If developing the idea, the innovator faces the same payoﬀ as in the baseline model. If they wait until the break, then the value of the project is discounted to v = βqe, where 0 < β ≤ 1, perhaps due to obsolescence of ideas, competing ideas that emerge during the waiting period, etc. However, the cost of time during the break is lower. Note that for ideas arriving during a break week, the innovator’s problem stays the same as the baseline model as immediate development dominates shelving. This is because the cost of time is higher later while the value of the project is discounted. Thus, we focus on the innovator’s decision during a work week. The innovator’s payoﬀ from developing a project at eﬀort level e is: ( 2 if develop immediately qe − c1 e2 . π1 = e2 βqe − c0 2 if shelve and develop later during the break Relative to immediate development, the beneﬁt from delaying is that time is less costly during the break, while the downside is that the project may lose some of its value. Taking into account the minimum eﬀort requirement ē, we can write the innovator’s payoﬀ as follows (analogous to Equation (3) in the baseline model): π̃1 (q) =      ✶{q≥c1 ē} 2cq 1 + ✶{q<c1 ē} (qē − c1 ē2 ) if develop immediately β 2 q2 ē2 ✶{q≥ c0 ē } 2c0 + ✶{q< c0 ē } (βqē − c0 2 ) if shelve and develop later during the break 2 β 2 β 0 if drop The following results shows that when the project does not lose too much of its value by waiting (that is, β is suﬃciently large), shelving the project dominates immediate development regardless of the idea’s intrinsic quality q. In contrast, when the project loses too much value from waiting (that is, β is suﬃciently low), immediate development dominates shelving the project. Only when β is in an intermediate range does the innovator face meaningful tradeoﬀs between the two choices. The innovator is better oﬀ with immediately developing the project for very good ideas and better oﬀ with shelving when the idea quality is not too high. This is because when the idea quality is very good, the innovator would not want to sacriﬁce its potential, which is high compared to the A-6 beneﬁt from saving the time cost. When the idea’s quality is at an intermediate range, the beneﬁt from saving the time cost would outweigh the cost of discounting the value of the idea. Result 3 (Decision rules on shelving). For ideas arriving during a work week: q • When β > cc01 , shelving dominates immediate development regardless of the idea’s quality q. 0 ē and drops it otherwise. Thus, the innovator shelves the project if q ≥ c2β q p ē }. The innovator • When cc10 < β < cc01 , define q̃ = min{ βē2 (c0 + c0 (c0 − β 2 c1 )), (c1 −c0 ) 2(1−β) develops the idea immediately if q ≥ q̃, shelves the idea if c0 ē 2β < q < q̃, and drops it otherwise. • When β < cc10 , immediate development dominates shelving for values of q with positive payoffs. Thus, the innovator develops the idea immediately if q ≥ c12ē and drops it otherwise. Proof. When comparing only the innovator’s optimal payoﬀs (without considering the minimum eﬀort requirement), shelving is better than immediate development regardless of q if and only q c0 if β > c1 (i.e., the project does not lose too much of its value by waiting). This is because q 2 2 2 q β q c0 > ⇒ β > 2c0 2c1 c1 . Taking into consideration the requirement ē, we have the following three scenarios: q The ﬁrst scenario is when β > cc01 . From above, we know that the innovator’s optimal payoﬀ from shelving is everywhere higher than that from immediate development. At the same time, in this case, the slope of the innovator’s payoﬀ from shelving and exerting ē is smaller (i.e., ﬂatter) than that from immediately developing the project at ē. This is true because the intersection point 1 −c0 )ē of these two payoﬀs, (c2(1−β) , is to the right of cβ0 ē , which is the value of q at which the optimal level of eﬀort with shelving is the same as ē.25 As a result, shelving is better than immediate 0 ē and drop it development regardless of q, and the decision rule is to shelve the idea if q ≥ c2β otherwise. q The second scenario is when cc10 < β < cc01 . From above, we know that the innovator’s optimal payoﬀ from immediate development is everywhere higher than that from shelving the project. However, in this case, we can show that the slope of the innovator’s payoﬀ from shelving and exerting ē is smaller (i.e., ﬂatter) than that from immediately developing the project at ē, and the value of q at which they intersect generates a positive payoﬀ for shelving. This implies that there is a range of value of q for p which shelving generates a higher payoﬀ than immediate development. ē ē Denote q̃ = min{ β 2 (c0 + c0 (c0 − β 2 c1 )), (c1 − c0 ) 2(1−β) }, where the former is the value of q at which the payoﬀ from shelving and optimal eﬀort level is the same as that from immediately developing the project at ē,26 and the latter is the intersecting point for the innovator’s payoﬀ from shelving and exerting ē and that from immediately developing the project at ē. Therefore, the decision rule in this case is to develop the project immediately if q ≥ q̃, shelve the project if c0 ē 2β < q < q̃, and drop the idea otherwise. 0 to hold, we need β > c02c+c , which is satisfied when β > 1 q 4c2 c0 0 0 > c02c+c ⇔ cc01 > c2 +c2 +2c The last condition holds because ⇔ (c1 − c0 )2 > 0. c1 1 0 c1 0 1 p 2 2 2 2 26 β q = qē − c1 ē2 ⇒ (βq − cβ0 ē )2 = βē 2 c0 (c0 − β 2 c1 ) ⇒ q = βē2 (c0 + c0 (c0 − β 2 c1 )). 2c0 25 ē For (c1 − c0 ) 2(1−β) > c0 ē ) β A-7 q c0 c1 because q c0 c1 > 2c0 . c0 +c1 The ﬁnal scenario is when β < cc01 . In this case, developing the project immediately dominates shelving for all values of q that generate a positive payoﬀ for the former. Thus, the innovator chooses to develop the idea immediately if q ≥ c12ē and drops the idea otherwise. A-8 Appendix B: Additional Tables and Figures Figure B-1: The Number of Projects per Week is Higher During Breaks (Poisson) Notes: Estimated coefficient for weeks before and after the school breaks. Dependent variable is the number of projects created in the focal city-week. Poisson regression includes city and week fixed effects. Error bars represent 95% confidence intervals based on robust standard errors clustered at the city level. B-1 Table B-1: Robustness to Sample Deﬁnition by City Size (1) Projects in All Cities (2) Projects in Top 10% Cities (3) Projects in Top 1% Cities All Breaks 0.0238*** (0.0083) 0.0745*** (0.0282) 0.1811* (0.1084) Observations R-squared Number of Cities 3,178,665 0.164 10,091 402,885 0.150 1,279 34,650 0.265 110 VARIABLES Notes: The dependent variable is the number of projects. Column (1) replicates the baseline estimation in Table 3. Columns (2) and (3) respectively only use top cities in terms of crowdfunding activity (ranking is based on the total number of projects). City and week fixed effects are included in all regressions. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. Table B-2: Robustness to Sample Deﬁnition by Enrollment in Schools with Breaks Data (1) Enrollment 0-100 (2) Enrollment 0-75 (3) Enrollment 0-50 (4) Enrollment 0-25 All Breaks 0.0238*** (0.0083) 0.0240** (0.0102) 0.0092** (0.0038) 0.0088 (0.0054) Observations R-squared Number of Cities 3,178,665 0.164 10,091 3,115,035 0.170 9,889 3,051,405 0.393 9,687 2,987,775 0.408 9,485 VARIABLES Notes: The dependent variable is the number of projects. Column (1) replicates the baseline estimation in Table 3. Columns (2)-(4) gradually exclude cities associated with colleges with the largest number of enrolled students. City and week fixed effects are included in all regressions. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. Table B-3: Robustness to Sample Deﬁnition by County-Level College Enrollment and Population (1) Below Median College Students (2) Above Median College Students (3) Below Median Population (4) Above Median Population All Breaks -0.0084 (0.0069) 0.0257*** (0.0090) -0.0068 (0.0050) 0.0274*** (0.0095) Observations R-squared Number of Cities 1,589,175 0.621 5,045 1,589,490 0.142 5,046 1,589,490 0.622 5,046 1,589,175 0.141 5,045 VARIABLES Notes: The dependent variable is the number of projects. Columns (1) and (2) separate the sample by whether the associated counties have above versus below the median number of college students according to the American Community Survey (ACS). Columns (3) and (4) separate the sample by whether a city’s population is above or below the median. City and week fixed effects are included in all regressions. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. B-2 Table B-4: Impact of Breaks on Project Value Distribution (20 Bins) (1) Projects VARIABLES All Breaks * Bin 1 (Lowest Value) All Breaks * Bin 2 All Breaks * Bin 3 All Breaks * Bin 4 All Breaks * Bin 5 All Breaks * Bin 6 All Breaks * Bin 7 All Breaks * Bin 8 All Breaks * Bin 9 All Breaks * Bin 10 All Breaks * Bin 11 All Breaks * Bin 12 All Breaks * Bin 13 All Breaks * Bin 14 All Breaks * Bin 15 All Breaks * Bin 16 All Breaks * Bin 17 All Breaks * Bin 18 All Breaks * Bin 19 All Breaks * Bin 20 (Highest Value) Observations R-squared Number of Cities 0.0128*** (0.0024) -0.0097*** (0.0020) -0.0055*** (0.0014) -0.0017* (0.0009) -0.0007 (0.0009) -0.0010 (0.0008) -0.0007 (0.0007) -0.0017** (0.0008) 0.0001 (0.0007) 0.0006 (0.0006) 0.0008* (0.0005) 0.0019*** (0.0006) 0.0021*** (0.0008) 0.0017** (0.0008) 0.0023* (0.0013) 0.0042*** (0.0016) 0.0038** (0.0016) 0.0046** (0.0022) 0.0042** (0.0021) 0.0052* (0.0028) 63,573,300 0.024 10,091 Notes: The dependent variable is the number of projects in a specific bin of project value, the unit of analysis is a city-week-bin. We divide projects into 20 bins based on the amount of funds they raise, from the lowest (bin 1) to the highest (bin 20). Bins are defined by year to account for the growth of the platform. City and week fixed effects are included the regression. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. B-3 Table B-5: Length of the Break and Week of the Break VARIABLES All Breaks (1) Projects (2) Projects 0.0238*** (0.0083) 1 Week Break 0.0841 (0.0530) 0.0421** (0.0165) 0.0665* (0.0382) 0.0200** (0.0079) 2 Weeks Break 3 Weeks Break > 4 Weeks Break 1 Week Break 0.0839 (0.0530) 0.0424** (0.0188) 0.0418** (0.0169) 0.0697* (0.0371) 0.0650 (0.0404) 0.0021 (0.0082) 0.0220*** (0.0083) 2 Weeks Break, Week 1 2 Weeks Break, Week 2 3 Weeks Break, Week 1 3 Weeks Break, Week 2+ > 4 Weeks Break, Week 1 > 4 Weeks Break, Week 2+ Observations R-squared Number of Cities (3) Projects 3,178,665 0.164 10,091 3,178,665 0.164 10,091 3,178,665 0.164 10,091 Notes: The dependent variable is the number of projects. Column (1) replicates the baseline estimation in Table 3. Column (2) separates breaks by their length. Column (3) separately investigates the first and the second (or more) week for breaks of different lengths. City and week fixed effects are included in all regressions. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. B-4 Table B-6: Shelving VARIABLES All Breaks (1) All Projects (2) Clearly Shelved (3) Excluding Clearly Shelved 0.0447*** (0.0129) 0.0012** (0.0005) 0.0435*** (0.0126) 1 Week Break 2 Weeks Break 3 Weeks Break > 4 Weeks Break (4) All Projects (5) Clearly Shelved (6) Excluding Clearly Shelved 0.0708 (0.0477) 0.0365* (0.0188) 0.0662* (0.0385) 0.0442*** (0.0128) 0.0021 (0.0026) 0.0012 (0.0010) 0.0013 (0.0022) 0.0012** (0.0005) 0.0688 (0.0462) 0.0353* (0.0184) 0.0650* (0.0370) 0.0430*** (0.0124) 1 Week Break B-5 2 Weeks Break, Week 1 2 Weeks Break, Week 2 3 Weeks Break, Week 1 3 Weeks Break, Week 2+ > 4 Weeks Break, Week 1 > 4 Weeks Break, Week 2+ Observations R-squared Number of Cities 2,754,843 0.164 10,091 2,754,843 0.011 10,091 2,754,843 0.164 10,091 2,754,843 0.164 10,091 2,754,843 0.011 10,091 2,754,843 0.164 10,091 (7) All Projects (8) Clearly Shelved (9) Excluding Clearly Shelved 0.0706 (0.0476) 0.0296 (0.0226) 0.0435** (0.0175) 0.0724 (0.0460) 0.0632* (0.0365) 0.0288*** (0.0112) 0.0459*** (0.0131) 0.0021 (0.0026) -0.0007 (0.0013) 0.0032* (0.0019) 0.0021 (0.0032) 0.0008 (0.0021) 0.0023* (0.0013) 0.0011** (0.0005) 0.0686 (0.0461) 0.0303 (0.0226) 0.0404** (0.0168) 0.0703 (0.0443) 0.0623* (0.0352) 0.0265** (0.0104) 0.0448*** (0.0128) 2,754,843 0.164 10,091 2,754,843 0.011 10,091 2,754,843 0.164 10,091 Notes: The dependent variable in Columns (1), (4), and (7) is all projects. In Columns (2), (5), and (8), the dependent variable only captures projects that we identified as clearly shelved by their creators based on the project page (data is available from the beginning of the sample to July 2014). Columns (3), (6), and (9) remove from all projects the projects that are clearly shelved (i.e., the dependent variable is always the difference between the previous two columns). City and week fixed effects are included in all regressions. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. Table B-7: Prediction 3 (Only Successful Projects) (1) 0-33 Mean Desc. Length (2) 33-66 Mean Desc. Length (3) 66-100 Mean Desc. Length (4) 0-33 Mean FAQs (5) 33-66 Mean FAQs (6) 66-100 Mean FAQs (7) 0-33 Mean Updates (8) 33-66 Mean Updates (9) 66-100 Mean Updates All Breaks 0.6184* (0.3370) 0.7593* (0.4289) 1.6403*** (0.5855) 0.0028*** (0.0009) 0.0023** (0.0010) 0.0057*** (0.0021) 0.0106*** (0.0041) 0.0082 (0.0060) 0.0296*** (0.0094) Observations R-squared Number of Cities 3,178,665 0.064 10,091 3,178,665 0.063 10,091 3,178,665 0.059 10,091 3,178,665 0.011 10,091 3,178,665 0.013 10,091 3,178,665 0.018 10,091 3,178,665 0.045 10,091 3,178,665 0.047 10,091 3,178,665 0.047 10,091 VARIABLES Notes: The dependent variables are the mean level of measures of the amount of effort devoted to a project in a city-week. Only successful projects (funds raised exceeding the target amount) are used in these regressions. For each measure of effort, projects are divided into three segments based on the bins defined in Table 5. For example, “0-33” category includes the bottom five bins containing successful projects that raised the lowest amount of funds and “66-100” the highest. City and week fixed effects are included in all regressions. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. Table B-8: Complexity and Week of the Break VARIABLES (1) Mean Skills per Team Member Week 1 0.0053 (0.0034) 0.0023 (0.0033) -0.0010 (0.0042) 0.0058*** (0.0018) Week 2 Week 3 Week 4+ Observations Number of Cities R-squared 3,178,665 10,091 0.322 Notes: The dependent variable is the mean level of our proxy for project complexity (the number of unique skills per team member). The regression separately investigates the first, second, third, or fourth (or more) week within a break. For example, “week 2” is identified by breaks that are at least two weeks long. City and week fixed effects are included in all regressions. Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. B-6 Table B-9: Snow Breaks and Project Value Distribution (1) Projects VARIABLES Snow Breaks * Bin 1 Snow Breaks * Bin 2 Snow Breaks * Bin 3 Snow Breaks * Bin 4 Snow Breaks * Bin 5 Snow Breaks * Bin 6 Snow Breaks * Bin 7 Snow Breaks * Bin 8 Snow Breaks * Bin 9 Snow Breaks * Bin 10 Snow Breaks * Bin 11 Snow Breaks * Bin 12 Snow Breaks * Bin 13 Snow Breaks * Bin 14 Snow Breaks * Bin 15 Observations Number of Cities R-squared 0.0063 (0.0040) -0.0132*** (0.0045) -0.0055* (0.0031) -0.0088** (0.0040) -0.0016 (0.0024) -0.0033 (0.0028) 0.0022 (0.0027) 0.0012 (0.0021) 0.0049* (0.0028) 0.0086** (0.0039) 0.0097*** (0.0034) 0.0054 (0.0034) 0.0113 (0.0075) 0.0081 (0.0050) 0.0080 (0.0062) 44,501,310 10,091 0.032 Notes: The dependent variable is the number of projects in a specific value bin, the unit of analysis is a city-week-bin, and the fixed effects for weeks and cities are included. The 15 bins are defined in the same way as in Table 5, and the regression controls for the interactions between the other breaks and the bins (not reported for space constraints). Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. B-7 Table B-10: Snow Breaks and Complexity VARIABLES Snow Breaks Other Breaks Observations R-squared Number of Cities (1) Mean Skills (2) Mean Team Size (3) Mean Skills per Team Member -0.0006 (0.0076) 0.0064*** (0.0018) 0.0019 (0.0051) 0.0022 (0.0015) -0.0014 (0.0064) 0.0047*** (0.0016) 2,966,754 0.356 10,091 2,966,754 0.455 10,091 2,966,754 0.326 10,091 Notes: The dependent variable is the mean level of our measures of complexity (Columns 1 and 2), and the mean team size (Column 2). Robust standard errors are clustered at the city level. *** p < 0.01, ** p < 0.05, * p < 0.1. B-8

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