1 Outsourcing Tasks Online: Matching Supply and Demand on Peer-to-Peer Internet Platforms Zoë Cullen and Chiara Farronato December 2014 Job Market Paper Latest version at Abstract. We study a central economic problem for peer-to-peer online marketplaces: how to create successful matches when demand and supply are highly variable. To do this, we develop a parsimonious model of a frictional matching market for services, which lets us derive the elasticity of labor demand and supply, the split of surplus between buyers and sellers, and the efficiency with which requests and offers for services are successfully matched. We estimate the model using data from TaskRabbit, a rapidly expanding platform for domestic tasks, and report three main findings. First, supply is highly elastic: in periods when demand doubles, sellers work almost twice as hard, prices hardly increase and the probability of requested tasks being matched only slightly falls. Second, we estimate average gains from each trade to be $37. Because of the matching frictions and search costs needed to find potential matches, the ex-ante gains are more modest, but are maximized by the elastic labor supply: if the number of hours worked were held constant, there would be 15 percent fewer matches in equilibrium. Third, we find that platform success varies greatly across cities. The cities which grow fast in the number of users are also those where the market fundamentals promote efficient matching of buyers and sellers. This heterogeneity in matching efficiency is not attributable to scale economies, but is instead related to two measures of market thickness: geographic density (buyers and sellers living close together), and level of task standardization (buyers requesting homogeneous tasks). We would like to thank Jon Levin, Susan Athey, and Liran Einav for their mentorship and guidance. We are also grateful to Tim Bresnahan, Pascaline Dupas, Brad Larsen, Andrey Fradkin, Michael Dinerstein, Akshaya Jha, and many other seminar participants at Stanford University for their invaluable comments. We appreciate TaskRabbit for providing essential data access. Support for this research was provided through the B.F. Haley and E.S. Shaw Fellowship for Economics through the Stanford Institute for Economic Policy Research. Department of Economics, Stanford University.

2 1 Introduction The Internet has facilitated the growth of peer-to-peer marketplaces for the exchange of underutilized goods and services. Users rent rooms on Airbnb, arrange rides on Uber, and find cleaning and moving help on TaskRabbit. These platforms, which may compete with more traditional service providers, act as marketplaces for decentralized buyers and sellers to meet up and transact. This paper studies a basic economic problem for peer-to-peer marketplaces: how to equilibrate highly variable demand and supply when matches often need to be made locally and rapidly. One obvious answer is that a decentralized market should equilibrate on price. Prices should rise when sellers are in short supply, causing buyers to pull back demand and sellers to expand supply. Of course, this leaves open the question of which side adjusts more: are peer-to-peer markets characterized by elastic demand or elastic labor supply? The theoretical literature (Rochet and Tirole, 2006, Armstrong, 2006, and Weyl, 2010) confirms that these elasticities are critical for platform design, and affect choices such as where to focus advertising or how to structure platform fees. Moreover, recent empirical research emphasizes that peer-to-peer markets are inherently frictional (Fradkin, 2014, and Horton, 2014). Perhaps when sellers are scarce, prices do not adjust and buyers simply fail to find matches, as in theories of frictional labor markets (Diamond, 1982, Mortensen, 1982, and Pissarides, 1985, among many). In this paper, we use an analytical framework to analyze the possible mechanisms contributing to market equilibration when demand and supply fluctuate. We develop a simple but fully specified static model of a frictional matching market for services. Conditional on parameter values, the model lets us derive the elasticity of labor demand and supply, the split of surplus between buyers and sellers, and the efficiency with which requests and offers for services are successfully matched. All these results combined allow us to measure the aggregate value created by the peer-to-peer platform where these exchanges take place. Our framework can easily be applied to a variety of online peer-to-peer platforms for local services. We apply our model to data from TaskRabbit, an online marketplace where buyers (posters) can hire sellers (rabbits) to perform a wide range of domestic tasks and errands. We work with internal data from the company that allows visibility into all posted tasks, offers, and transactions. The setting allows us to think about the efficiency and benefits of online marketplaces because successful matches must happen rapidly and locally, so we can divide the activity on the platform into separate sub-markets by time and geography, and use the large and plausibly exogenous fluctuations in 1

3 buyers and sellers to estimate the demand and supply parameters of our model. 1 We establish that seller effort, or labor supply, is the key equilibrating factor. When demand is high relative to the number of sellers, the latter sharply expand their effort with very little price adjustment and little reduction in the ability of buyers to consummate trades. Our estimates imply that average gains from trade are $37 for each successful match. Because of matching frictions and search costs needed to find potential matches, the ex-ante gains are more modest. But so long as there are a lot of requests for tasks, the market can still be successful if matching frictions can be reduced and labor supply is elastic, as in this case. Specifically, the elastic supply leads to a 15 percent increase in the value of matches created relative to a setting in which seller effort does not adjust to equilibrate the market. Both the platform and the buyers equally benefit from this elastic supply. We discuss our results in light of the recent platform change on TaskRabbit, which reduced both matching and search frictions, while efficiently making use of sellers slack capacity. We also explain why on TaskRabbit some cities are more successful than others using our model estimates. Successful cities attract and retain demand at higher rates, and are more efficient in converting requests and offers for tasks into productive matches. We relate matching efficiency to two measures of market thickness: geographic density (buyers and sellers leaving close together), and level of task standardization (buyers requesting homogeneous tasks). We conclude by combining our results to estimate the aggregate value created by peer-to-peer platforms for domestic tasks. We start in Section 2 by describing TaskRabbit, in particular how buyers post tasks such as cleaning or grocery shopping, and how sellers submit offers to perform those tasks. We then introduce the key economic problem faced by the platform, which is to balance demand and supply to create valuable matches when these matches need to be found quickly and locally. Section 3 provides preliminary evidence that when demand is high relative to supply, sellers adjust the number of offers they submit, without significant adjustments on the buyer side. We also show that price does not adjust very much, and that the fraction of posted tasks that are completed stays relatively constant. We then propose a simple economic model that captures the labor demand and supply decisions 1 The opportunity to observe multiple spot markets where variable numbers of buyers and sellers match while using the same platform technology is empirically relevant. A common challenge that economists face in studies of online platforms is that it can be difficult to define and compare separate markets. In studying ebay, for example, it is hard to divide buyers and sellers into geographically segregated markets given the prevalence of cross-state and cross-country transactions. There also can be a selection problem related to the fact that only platforms which have achieved a certain level of success are in use and can be studied. The fact that TaskRabbit operates essentially separate markets in different cities, and that we can observe these markets as they grow over time creates useful variation for understanding demand and supply decisions and how scale economies might or might not arise. 2

4 of buyers and sellers. In the model of Section 4, buyers choose how many tasks to post, sellers choose how intensively to search for possible jobs, and these choices determine the number of matches and the price at which trade occurs. In the model, matching frictions prevent some offers from being accepted and some tasks from being filled. We allow for scale effects, both in the matching technology and in the seller cost of search. We use comparative statics to discuss the response of buyers and sellers individual choices to changes in the aggregate number of buyers and sellers, and discuss how the size of this response depends on the model parameters. In Section 5, we take our model to the data. The model offers a set of moment conditions: matching and pricing technologies, individual choices to post tasks and submit offers. Estimation is carried out in two steps by method of moments. First, price and number of matches are estimated as a function of the total number of offers and tasks. We allow for city heterogeneity in the efficiency with which each city is able to match tasks and offers. Second, the utility parameters of buyers and sellers are estimated from their choices to post tasks and submit offers as functions of expected match rates and prices. Our estimates rely on variation across cities and over time in the number of buyers, both in absolute levels and relative to the number of sellers. Our key assumption is that the decision to join or leave the platform is not affected by the anticipation of unobserved match effectiveness or price shocks, nor by the expectation on others adoption or attrition decisions. Roughly, we assume that prospective buyers and sellers have access to the same historical data on the market that we have. In Section 5 we discuss this assumption and provide supporting evidence. Section 6 answers our first two questions. First, we quantify the high labor supply elasticity that allows the market to equilibrate in response to supply and demand shocks. We find that seller search costs are low in general ($7 for each accepted offer in the median market) and that sellers, paid $48.5 for each completed task, work at close to their opportunity cost, $33. The highly elastic supply curve, together with an average cost of listing tasks equal to 50c, implies that buyers do not need to adjust their rate of posting tasks when they are abundant relative to sellers. Buyers are neither rationed – i.e. they still match with similar probability – nor are they charged considerably higher prices. Second, we estimate the gains from trade and the surplus created by TaskRabbit. Gains from each successful match, excluding seller search costs, are equal to $37, and are shared similarly among the buyer, the seller, and the platform. However, matching frictions and seller search costs considerably affect the aggregate surplus generated by the platform. We also find that the surplus does not increase considerably with market scale: the matching technology does 3

5 not display increasing returns to scale, although a larger market size moderately lowers sellers search costs. The existence of an elastic supply curve, however, allows the market to efficiently accommodate variable demand and to create 15 percent higher value from aggregate matches. In the conclusion, we come back to this feature and our estimates of search and matching frictions to support the recent platform change. Section 7 focuses on our third question, related to city heterogeneity. The biggest reason why some cities are more successful than others on TaskRabbit seems to be that in those cities demand is higher and the matching of buyers and sellers is more efficient. We find that buyers are somewhat sensitive to recent outcomes: the higher the probability that their task is completed today, the higher their probability to post again in the future. The general matching efficiency of the city s platform thus affects buyer retention, which together with adoption is the crucial ingredient to growth given the elasticity of existing sellers labor supply. The geography of the city seems to be an important determinant of matching efficiency, as well as the level of task standardization. There is little evidence for economies of scale leading to increasingly larger heterogeneity across cities after small initial differences in platform success, but it is possible that more experienced buyers learn to post tasks better, i.e. in homogeneous categories, and that makes matching more efficient. We conclude our work by discussing some implications of our findings for platform design, and for other peer-to-peer markets in Section 8. Our research contributes to a growing literature studying the economics of online marketplaces and especially peer-to-peer platforms. Recent work in this area has focused on the micro-structure of specific marketplaces, estimating search inefficiencies (Fradkin, 2014), heterogeneity in the matching process and problems of congestion (Horton, 2014), the consequences of search frictions and platform design for price competition (Dinerstein et al., 2014), the differences between distinct types of pricing mechanisms (Einav et al., 2014). There is also a large literature on trust and reputation systems (e.g. Nosko and Tadelis, 2014, and Pallais, 2014), which dates back to early work by Resnick and Zeckhauser (2002) and Bajari and Hortaçsu (2003). Our work is complementary to this literature in that we present an explicit model of market equilibrium and use it to study the effects of platform design and how market efficiency depends on fundamentals at the city level. Our approach abstracts from many forms of individual heterogeneity and asymmetric information that are emphasized in other papers, and from issues of strategic pricing and reputation. Instead, we offer a framework that enables us to examine in detail the particular problem, which we view as both important and common, of balancing highly variable 4

6 demand and supply, and the process of market equilibration. The model we propose is in principle applicable to other peer-to-peer marketplaces that match buyers and sellers of local and timesensitive services. In studying the balancing of demand and supply on TaskRabbit, our modeling approach draws on the literature on frictional search and matching in labor markets (Petrongolo and Pissarides, 2001). In particular, Pissarides (2000, ch.5) most closely resembles our model. Workers submit applications to posted vacancies, at a cost, and employers select among applications received. In equilibrium, the number of applications submitted reflects the expectation of matching. Most theoretical work assumes constant returns to scale in the functional form of the matching technology, supported in part by results in the empirical literature – for example, in Anderson and Burgess (2000). The are two differences in our setup. First, ours is a market for services in the spirit of Michaillat and Saez (2013), where each buyer (resp. seller) can be matched to multiple sellers (buyers). Second, we allow for economies of scale in the costly search process. Our analysis of scale economies and platform growth and success touches on two additional areas of research. First, papers such as Ellison and Fudenberg (2003) have emphasized that an important issue when marketplaces compete for buyers and sellers is whether increasing scale makes a marketplace more efficient. We find that scale economies per se are not a major determinant of market efficiency, for instance compared to basic fixed features such as the geography of a given city. In modeling platform growth, through adoption and attrition decisions, we also connect to a large literature on innovation diffusion and how the speed of growth of new technologies can depend on information flows, technology improvements, and network effects (Young, 2009 ). We mention other related papers in Section 7. 2 Setting and Data This section describes the TaskRabbit platform, the data, and some salient facts that are important for our analysis. We first describe how the platform operates, how tasks are posted, and how offers are made and accepted. We then show that matches are either made quickly and locally, or not at all. As a result, a central problem for the platform is to balance supply and demand, which are highly variable, on a local high-frequency basis. In the next section we provide some initial evidence that the market equilibrates mainly through variation in seller effort, with only minimal price responsiveness. We tailor our model in Section 4 to capture this feature. Finally, we provide 5

7 a first look at differences in market success across cities, an issue we return to in Section The TaskRabbit Platform TaskRabbit is an online platform that allows posters to outsource domestic tasks to rabbits. Between 2009 and mid-2014, it operated in 20 major cities in the United States. 2 Posters post a description of the requested task in a flexible manner. Rabbits can search through posted tasks on city-specific lists and respond with offers (Fig. 1). We will refer to posters as buyers and rabbits as sellers of services. 3 Buyers on TaskRabbit can post virtually any sort of domestic tasks or errand (e.g. babysitting for a goldfish), but the majority of tasks are relatively standard and generic. The five largest categories are shopping and delivery (24%), moving help (12%), cleaning (9%), home repairs (6%), and furniture assembly (4%). These tasks typically do not require sellers with highly specialized skills. The nature of the tasks implies that services generally are provided locally and on relatively short notice. Almost all users (93.6 percent of them) participate in just one city. At the same time, of the 48.5 percent of tasks that are matched, 97 percent are filled within one or two days. 4 The matching process can work in two ways. A buyer can post a task-specific price and then accept the first offer, or ask for bids and review the prices offered by sellers. Fixed price tasks are slightly more standardized (65 percent of them are in the top 5 categories versus 48 percent of auctions), and prices are lower ($49 versus $63), but their share on the platform, at 41 percent, has not changed considerably over time or across cities. About 77 percent of tasks receive an offer, and of them 63 percent result in a match. Matches can fail because the buyer finds a better alternative and does not select any of the bids received, or because the buyer and seller cannot coordinate on specific task details. Platform users tend to be either buyers or sellers, but not both. Indeed, 80.3 percent of users have only ever posted task requests, and 16.3 percent have only ever submitted offers. The buyers 2 The active cities in the US are, in order of entry: Boston (2008), San Francisco (June 2010), Los Angeles (June 2011), New York (July 2011), Chicago (September 2011), Seattle (December 2011), Portland (January 2012), Austin (February 2012), San Antonio (August 2012), Philadelphia and Washington DC (July 2012), Atlanta, Dallas and Houston (August 2013), Miami and San Diego (October 2010) Phoenix and Denver (November 2011). 3 Leah Busque first formulated her idea for TaskRabbit when one evening she realized she had ran out of dog food. With her husband she started contemplating the idea of a place online where we could say we needed dog food, name the price we d be willing to pay, and see if there was someone in our neighborhood who would be willing to help us out ( 4 To add to the local and urgent nature of tasks, the platform s ranking algorithm prioritizes newly posted tasks within each city. Indeed, to every seller searching through posted tasks, the platform shows a list of local tasks, ranked according to their posting time (most recent at the top). 6

8 on the site are predominantly female (55 percent of buyers) and relatively affluent. The modal buyer is a woman between the age of 35 and 44 with a household income between $150,000 and $175,000. The sellers are younger and not surprisingly have lower income. The modal seller is years old and has a household income between $50,000 and $75,000. Buyers go through a basic verification process that checks their identity on social networks and their payment method. There is a more rigorous screening process for sellers. Until March 2013, applicants received a background check, a digitized survey of their motivations, skills, and availability, and were interviewed by TaskRabbit employees to determine their fit. Acceptance rates of sellers applications varied widely. They ranged between 7 and 49 percent in different months, and on average they were very low – only 13.6 percent. In the spring of 2013 TaskRabbit reduced the amount of screening in a successful attempt to add more sellers. The current process involves simpler background checks and social controls – Facebook or Linkedin verification – paired with a system of users reviews. 2.2 Data Our study uses internal data from TaskRabbit. We focus on the period from June 2010 to May During this period, TaskRabbit operated in 18 cities, although entry in these cities was staggered over time. Since we have no record of the actual entry date, we define the month of entry into a city as the first calendar month in which 20 or more local tasks were posted. 5 The data include all posted tasks, offers, and matches that occurred on the platform during the study period. We exclude virtual tasks 6 (10.4%) and tasks posted in not yet active cities (0.23%). We also drop 10.3 percent of tasks that use other assignment mechanisms and keep only auction and posted price tasks. We merge the tasks with the corresponding offers, and we drop extreme price outliers (top and bottom 1 percent in bids or charged prices). To deal with the fact that posted price tasks occasionally receive multiple offers (6.04 percent of them did), we only keep the matched offer in case of success, or select one of the received offers at random. This simplification restricts posted price tasks to receive either one or no offers. Finally, for much of the paper we will aggregate activity at the city-month level, and drop city-months with less than 50 buyers posting tasks or less than 20 sellers making offers. 5 We verified the accuracy of our definition through media coverage of the platform and by talking with TaskRabbit employees. 6 A task is classified as virtual if the service does not require the seller to be at a specific location. Examples include writing and editing, or usability testing of mobile applications. 7

9 Table 1 shows summary statistics for the data. In the first panel, an observation is a posted task. Out of all posted tasks 78 percent receive offers, and those tasks receive 2.8 offers on average. Of the tasks receiving offers, 63 percent are successfully completed at an average price of $57. The platform charges a 20% commission fee on successful tasks. 7 In the second panel of Table 1, an observation is a city-month. We define a buyer to be active in a city-month if she posts at least one task in that city-month. Analogously, a seller is active if he submits an offer to a task posted within the city-month. On average, there are 708 active buyers and 255 sellers in a city-month, but there is large variation across cities and months. Each buyer posts 1.6 tasks, and each seller submits 6.4 offers. The task success rate is 46 percent and the average price paid is $56. Of these four variables (tasks per buyer, offers per seller, task match rate, and prices), the number of offers per sellers varies the most across city-month observations, with limited variation in tasks per buyer, matches, and prices. During the 4-year period we study, the platform was growing in all cities, and quite rapidly in some. Figure 2 plots the number of successful matches for the 10 oldest cities. 8 Over the period considered, some cities grew from a few monthly matches to thousands of exchanges, like San Francisco and New York, while some others grew at a reduced pace, like Portland and Seattle. We will use the cross-city and over time variation in market size in our empirical section to study the effect of scale. We will also examine the dynamic forces underlying the platform growth in Section 7. 3 Descriptive Evidence A key feature of the platform is that there are large fluctuations in demand and supply. Since matches must be made quickly and locally, this raises the question of what happens when demand is especially high or low relative to the number of sellers. Here we provide some initial evidence. In the next section we develop a theoretical model of market equilibration which allows us to analyze labor demand, labor supply, and market clearing in more detail. Figure 3 shows the variability of demand relative to supply in the 10 oldest cities at a monthly level. Specifically the figure plots the number of active buyers in the city-month divided by the number of active sellers. As before, activity is defined as posting at least one task (for buyers) or 7 The commission fee can sometimes depart from 20 percent, for example in the case of coupons, referral bonuses, or other credits that reduce the price paid by buyers without affecting the price received by sellers. 8 Similar patterns to those in Figure 2 are found in the 8 youngest cities. 8

10 submitting at least one offer (for sellers). There are sizable fluctuations in the ratio of active buyers to active sellers, both within a city over time, and across cities within a month. In San Francisco, for example, certain months have two buyers per seller, while other months have six buyers. During the same calendar month, some cities may have only one buyer per seller, while other cities have five. The variability is not due to a single time trend. Month-to-month changes in the buyer to seller ratio are both positive and negative in no particular order. Finally, we emphasize some persistent heterogeneity across cities and across months. For instance, San Francisco has many more buyers per seller than Los Angeles. In principle, there are several ways in which the market might function given this variability. One possibility is that with fewer sellers, buyers may not be able to have tasks performed, either because of higher prices which deter them, or because a smaller fraction of posted tasks receive offers. Another possibility is that seller labor supply expands. We show that the latter occurs, and that labor supply is sufficiently elastic that the level of price increase needed to generate a supply response is small. Figure 4 first shows that the number of posts per buyer does not adjust when sellers are in short supply. Here, we divide the 336 city-months into four groups, corresponding to the four quartiles of the distribution of the buyer to seller ratio. For each group we compute the average number of tasks per buyer and offers per seller. The figure shows that regardless of the number of buyers per seller, buyers always post 1.6 tasks each. In contrast, Figure 4 shows that sellers submit many more offers when they are scarce relative to demand. For the city-months in the lowest quartile of the buyer to seller ratio (1.5 buyers per seller on average) sellers submit 4.4 offers on average. For the city-months at the other extreme (3.8 buyers per seller) sellers each submit twice as many offers, 9.1. Offers do not fully double as buyers double relative to sellers, so the match rate of tasks slightly declines (Figure 5). However, the sellers intensive margin response, together with buyers constant rate of task posting, translate into a large expansion in the number of trades as the number of buyers per seller increases. Perhaps surprisingly, transacted prices move very little when sellers are scarce or abundant. Figure 5 shows the average price of completed tasks for the city-months sorted by the buyer to seller quartiles. Average transacted price is always between $52 and $59, even if the number of buyers per seller doubles and each seller chooses to work harder. Putting aside possible issues of task composition and seller heterogeneity, an apparent implication is that not much price increase is needed to generate a large intensive margin increase in labor supply. 9

11 So far we have not ruled out the possibility that there might be something special about certain cities or certain months that leads to sellers making more offers when they are scarce for reasons that are not causal. For example, San Francisco tends to have a higher number of buyers per seller than other cities, so San Francisco city-months are disproportionately represented in the upper quartiles of the buyer to seller ratio distribution in Figure 4. If sellers in San Francisco submit more offers for reasons unrelated to the number of buyers per seller – for example because they can find tasks that are closer to them – from Figure 4 we might wrongly conclude that a higher number of buyers per seller leads sellers to work harder. A first step towards establishing causality is to consider a simple difference in differences specification that includes city and time fixed effects, and therefore controls for factors leading certain cities or months to have more buyers to focus instead on idiosyncratic time variation in demand conditions within cities and within months. Specifically, we estimate OLS regressions of the following type: log(y tc ) = θ 1 log ( Btc S tc where c, t denote city c and calendar month t, ) ( ) + θ 2 log Stc B tc + η c + η t + ν tc, (1) B tc S tc is the buyer to seller ratio, S tc B tc is the geometric average of buyers and sellers, and y tc is one of the four relevant variables: users choices (tasks per buyer, offers per seller), and outcomes (task match rate, prices). η c controls for cityspecific propensities to use TaskRabbit which are time invariant. Similarly, η m captures timespecific adjustments to usage intensities that are common across all active cities. Standard errors are clustered at the city level. 9 The results are shown in Table 2. The top panel shows the regression results without fixed effects, the bottom panel shows those with fixed effects. We first call attention to the comparison of the coefficients between the two panels: adding fixed effects does not change the response of 9 Given the log-specification, we can transform the right-hand side to be a function of the number of buyers and sellers: log(y tc) = ˆθ 1 log B tc + ˆθ 2 log S tc + η c + η m + ν tc, where ˆθ 1 = θ θ 2 and ˆθ 2 = θ θ 2. The results in Table 2 imply that buyers post the same number of tasks, regardless of how many users are active. Each seller submits more offers when there are more buyers, holding constant the number of sellers, but submits fewer offers when there are more sellers. The task match rate goes down as more buyers post tasks, but goes up when there are more sellers. Finally the price stays relatively constant as a function of buyers and sellers. The specification of the regression in terms of number of buyers and sellers helps interpret the effects of the number and composition of users in terms of network externalities: the utility a user derives from participating in a city-month depends on the number and type of other active users. We do still prefer the specification from equation 1 because of the particular nature of network externalities on TaskRabbit: users benefit from the platform insofar as it allows them to trade services, and users participation affects the terms of trade. A seller benefits from a market with relatively more buyers, where his services are highly demanded, but is hurt in a market with relatively more sellers, where his services face fierce competition. At the same time, holding the relative number of buyers and sellers constant, a seller can like a large market more or less than a small market. A preference for larger markets can arise because of scale economies, while one for smaller markets may be due to congestion. 10

12 sellers to fluctuations in the buyer to seller ratio, not in sign, size, or significance. The same can be said for the task match rate. While the coefficients on price and tasks per buyers are one or two orders of magnitude smaller when controlling for city and time characteristics, they are in both cases quantitatively small and statistically insignificant. This provides some confidence that the platform is used by buyers and sellers in a similar way both over time and across cities. The size of the coefficients confirm what was shown in the plots. We discuss those from the bottom panel of Table 2, obtained controlling for potential city and month differences. An increase in the number of buyers per seller has virtually no effect on how many tasks each buyer posts. On the other hand, doubling the number of buyers per seller of the median city-month, where the median is selected according to the distribution in the buyer to seller ratio and holding everything else constant, increases the number of offers submitted by each seller from 5.6 to 7.5. The effect on the task match rate is negative, but smaller in percentage terms: doubling the median number of buyers per seller decreases the match rate of tasks from 65.6 to 56.2 percent. Finally, buyers pay just a few cents more for completed tasks when they are twice as prevalent relative to sellers. The regressions also estimate the effect of market size, previewing possible mechanisms for economies of scale. A city-month with more active participants significantly increases the number of offers submitted by sellers, holding constant the relative number of active buyers and sellers. In particular, holding the ratio of buyers to sellers fixed and doubling the number of participants of the median sized city-month increases the number of offers submitted from 5.5 to 6.5. More active participants also seem to raise buyers rate of task posting and the task match rate, but the effect is not statistically significant when including city and month fixed effects. Finally, the price appears invariant to the number of participants, consistently across the two panels. We will capture each of these features in our model. 4 Model of a Market for Services We now propose a model of how the TaskRabbit marketplace matches tasks and offers, and how buyers and sellers make decisions about whether to post tasks and how much effort to put into making offers. We then use the model to explain what happens when there is variation in the number of active buyers and sellers, and explain how this variation can be used to identify the elasticity of labor demand and supply, the division of surplus in the market, the effects of increased market size, and the efficiency of matching in different cities and different market conditions. 11

13 We assume for simplicity that buyers are all identical and in equilibrium choose the same number of tasks to post. Similarly, sellers are identical and choose the same intensity with which to search and submit offers. We also treat tasks as homogeneous. Obviously, this is a large simplification, but it does correspond to our earlier observations that most tasks on the platform are relatively standard and generic, and that they do not require specialized skills. More importantly, it allows us to focus on the problem of widely fluctuating supply and demand, without being bogged down by a complicated heterogeneous matching framework. Market Technology. There is a measure B of identical buyers and a measure S of identical sellers. Each buyer will choose a number of tasks, β, to post. Each seller chooses a number of offers, σ, to make. The total number of services requested in a market is b Bβ, while the total number of offers submitted is s Sσ. The number of trades between buyers and sellers is given by the matching function: m = M(s, b). (2) M(s, b) is continuous and differentiable, and increasing in both its arguments. Each request is matched with probability q b = m b and each offer is successful with probability qs = m s. We assume that M(s, b) b and M(s, b) s to guarantee that matches are never larger than total requests or offers. In each match, the buyer pays price p = P (s, b), the seller receives (1 τ)p, and the platform keeps τ p as commission fee. In particular, price is determined as a function of services requested and offered, and is assumed to be a continuous and differentiable function, increasing in b and decreasing in s. 10 Later we will estimate the matching and price functions from the data, but we will not provide a more micro-level model of price determination – e.g. by modeling the posted pricing decision or the bidding game between sellers. Buyers and sellers choose how many requests to post and how many offers to submit with full knowledge of the matching and price determination processes, but without the possibility to affect either of those with their individual choices because each participant is small relative to the market. Buyer s Choice to Post Requests for Services. Each buyer randomly receives a number 10 In fact, several matching models of the labor market assume that the wage is either a parameter altogether or pinned down by other parameters. See, for example, Montgomery (1991), Hall (2005), Blanchard and Gali (2010), Michaillat (2012), and Michaillat and Saez (2013). 12

14 of potential needs to outsource. We assume that the number of service needs is a random draw from a Poisson distribution, iid across buyers, with mean arrival µ. 11 Each service is worth v p to its buyer, where v is the fixed value of having the task completed and p is the price paid. There is a cost ξ of posting each task, drawn from an exponential distribution, iid across needs and buyers: ξ exp(η). The average cost of posting a task is therefore equal to 1 η. The buyer s problem is to choose whether to post each needed service. The decision is separable across service needs. If a buyer makes a request for need t, she pays cost ξ t and expects payoff q b (v p). She optimally chooses to submit a request whenever the listing cost is small enough: ξ t q b (v p). The expected number of requests posted by a representative buyer is: ( ) ( ) β = µp r ξ q b (v p) = µ 1 e ηqb (v p). (3) Seller s Choice to Submit Offers for Services. Each seller chooses a level of effort σ spent searching through buyers requests. An effort level σ corresponds to a discovery process of profitable requests, to which the seller submits offers. Higher effort σ makes it more likely to find a higher number of profitable submissions. 12 Specifically, we assume that the number of suitable tasks identified and offers submitted is a random draw from a Poisson distribution P oi(σ), with mean equal to the chosen effort level and independent across sellers. Given this assumption, we will interchangeably refer to σ as the level of search effort or the expected number of offers submitted by a representative seller. Search effort is costly, and its cost rises at an increasing rate. In particular, we assume that the cost of search effort is equal to 1 2γ(b) σ2, with γ(b) being a continuous and increasing function of the total number of tasks posted. 13 Conditional on matching a submitted offer, the seller s profit is (1 τ)p c, where τ is the platform commission fee and c is the fixed cost of completing the task. The problem of a representative seller is to choose the optimal level of search intensity subject 11 For the conditions under which a continuum of independent and identically distributed random variables sum to a nonrandom quantity in large economies, see Judd (1985), and Duffie and Sun (2012). 12 Specifically, we assume that the distribution of application arrivals for a given σ first order stochastically dominates the distribution for any σ σ. 13 We model sellers search costs as increasing in the intensity of search at an increasing rate. This assumption can be better understood in terms of time needed before finding a new task to which a seller chooses to make an offer. Conditional on a level of effort, it is likely that the first profitable task is easier to find than the second, the second is easier than the third, and so on. If a seller wanted to double the number of profitable tasks found, his level of effort would then be more than twice as costly. In addition, search costs are decreasing in the number of total tasks posted. In a market with many posted tasks, a seller is likely to spend less time finding the same number of profitable applications as in a smaller market. If a seller wanted to send the same expected number of offers in a large market his level of effort would then be less costly. 13

15 to expectations on matching and prices: Max ˆσ The optimal level of search effort satisfies: 14 ˆσq s [(1 τ)p c] 1 2γ(b) ˆσ2, σ = γ(b)q s [(1 τ)p c]. (4) Equilibrium. Equilibrium in the market is defined as a state in which buyers and sellers maximize their objective functions subject to the matching and pricing technologies and correct expectations of other agents behavior. The equilibrium requires consistency of individual optimal choices (β and σ) with expectations on average behavior in the market (β and σ). Given the size of buyers B and sellers S present in the market, we define the competitive equilibrium as a vector (β, σ, p, m) such that: The transacted price is determined according to p = P (s, b), and the number of matches is determined according to m = M(s, b), where b = Bβ and s = Sσ. Taking q b = m b and p as given, buyers list the number of service requests to maximize utility. The number of requests β of the representative buyer is given by equation (3). Taking q s = m s and p as given, sellers choose the level of search intensity to maximize utility. The level of search intensity σ (i.e. of offers submitted) of the representative seller is given by equation (4). The actual average number of requests posted is β = β and offers submitted is σ = σ. In equilibrium, all buyers choose the same strategy in terms of the decision to post tasks, which in turn is consistent with the expected posting rate. The model explains differences in the actual number of requests across buyers as arising from the Poisson arrival rate of needs and from different draws of listing costs. Analogously, in equilibrium, all sellers choose the same level of search intensity, which in turn is consistent with the market average intensity. Differences in the rate of offer 14 Buyers choice to post tasks and sellers choice of search effort are not symmetric. On the buy side, there is an exogenous arrival of tasks, and a decision to post each of them separately conditional on arrival. A buyer in need of moving help selects whether to post it or find an alternative solution – another service provider or informal help – as a function of the expected value from each option. On the sell side, the setup is truly a choice of platform usage intensity. A seller selects his optimal level of search effort, and if he finds profitable tasks he submits offers for sure. In this case, a seller chooses his time allocation between leisure and searching for services to sell as a function of the expected benefits from the two activities. 14

16 submission across sellers arise from the Poisson process with which they discover profitable requests. Assumptions on Matching and Price. The matching technology displays constant returns to scale if a doubling of the number of tasks b and offers s doubles the number of matches m. Analogously, the price function is invariant to scale if doubling tasks and offers does not affect the price p. If the matching technology displays constant returns to scale, the total number of matches (equation 2) can be rewritten as m = M ( 1, s) b s, where b s is the task to offer ratio, the offer match rate is equal to q s = M ( 1, b ) s and the task match rate is q b = M(1, s) b b. If the price function is invariant to scale, it can also be rewritten just in terms of the task to offer ratio: p = P ( 1, s) b. s With a slight abuse of notation, we let m = M ( b s) s and p = P ( b s). This reformulation implies that the match probabilities of tasks and offers, as well as the price, are just a function of demand relative to supply, and not on the overall level of demand or supply. If, in addition to these two conditions, seller search costs γ(b) do not decrease much with market scale, the equilibrium is unique. Section 6 we test that these conditions hold on TaskRabbit. Anticipating this, we maintain them for the rest of our discussion. In Optimal Choices. Figure 6 illustrates the optimal individual choice of a seller. We discuss the seller side, noting that for buyers the reasoning is analogous. The figure plots the individual level marginal benefit (solid red line) and marginal cost curves (solid blue line) as a function of search effort σ. The marginal cost curve σ γ(b) is increasing in effort, while the marginal benefit curve q s [(1 τ)p c] is independent on the single seller s choice. This is because in a large market the offer match rate and price depend on the market average effort level σ and posting rate β, which cannot be affected by any single participant alone. The shaded area in the picture between the marginal benefit and marginal cost curve is the seller surplus at equilibrium, and can be inferred knowing the matching and pricing functions, as well as seller costs. The flatter the marginal cost curve, in the case of low search costs, the smaller is the seller surplus. In equilibrium, a seller optimal choice of σ must be consistent with the market-average search effort: σ = σ. We can therefore also draw the market level marginal benefit curve, where every seller in the market chooses effort level σ, and the buyers posting rate is held constant at β (red dotted line in Figure 6). In this case, both the offer match rate and the price will be affected by σ: if every seller in the market were to increase his search intensity, each offer would be less likely to be matched, and sellers would receive a lower price for every trade. Thus the market level marginal 15

17 benefit is decreasing in σ. Consistency of σ with σ requires that the market level and the individual level marginal benefit curves must cross the marginal cost curve at the same point (Eq1 in Figure 6): each individual seller takes as given the flat marginal benefit curve generated by every other seller in the market choosing the same effort level as his own. Changes in the match probabilities and prices affect the best response functions. Holding price constant, an increase in the offer match rate q s increases search effort. The increase in q s corresponds to an upward shift of the marginal benefit curve (upper red dotted line in Figure 7). The size of the increase in search – i.e. the horizontal difference between Eq1 and Eq2 – depends on the function γ(b) and on the cost of completing the task c. The lower the cost of search, corresponding to higher γ(b), the flatter is the marginal cost curve in the figure. With an almost flat marginal cost curve even a small change in q s can lead to a large change in search effort. At the same time, the smaller the seller profit (1 τ)p c for each task, the smaller is the upward shift of the marginal benefit curve, thus the smaller the increase in effort. Holding the offer match rate constant, an increase in price will raise a seller s search effort since each task will pay more. As before, the flatter the marginal cost curve (high γ(b)) the larger the change in σ. Moreover, in percentage terms, the smaller the seller profit (1 τ)p c, the higher the change in search effort. Comparative Statics. The model generates predictions about the effects of both market size and market composition. We capture these by thinking about changes in B holding B S fixed, and changes in B S holding B fixed. First consider an increase in B holding B S fixed. This lowers the cost to sellers of finding tasks, and raises their search effort. This in turn makes it more attractive to post tasks, raising buyers posting rates. The result is an increase in β and σ, with sellers responding more. Proposition 1 states it formally (proofs are in Appendix A). Proposition 1. (Effect of scale) An increase in B, holding B S fixed, leads to an increase in β and σ, and a decrease in β σ. This in turn implies lower prices and seller match rates, and higher buyer match rates. Now consider an increase in B S, holding market size B fixed. The direct effect is to make the market more attractive to sellers, thus raising σ, and less attractive to buyers, lowering β. There is an indirect effect because once buyers lower β the market contracts, which raises sellers costs. We show that at equilibrium this effect cannot dominate, so that the new equilibrium involves more seller effort and less buyer posting. However, the endogenous response of buyers and sellers does not fully compensate for seller scarcity, and the task to offer ratio is still higher at the new 16

18 equilibrium. Proposition 2. (Effect of user composition) An increase in B S, holding B fixed, leads to a decrease in β, an increase in σ, a decrease in β σ and an increase in b s. This in turn implies higher prices and seller match rates, and lower buyer match rates. These comparative statics predictions are consistent with our empirical results from the previous section, and will form the basis for our identification strategy. To see how this works, consider the supply side where the unknown parameters will be (c, δ, γ). The demand side is similar. If the search cost parameters (γ, δ) were known and given that p and q s are observable, the choice of σ in a single market would directly pin down the marginal cost c of performing each task, regardless of the number and composition of participating users. A low number of offers σ would imply a low c, holding everything else constant. Next consider adding variation in market size (left-hand side panel of Figure 7). We discuss the intuition holding constant buyers β, although by increasing their posting rate, buyers response actually amplifies the direct effect. An increase in B pivots the marginal cost curve downward. If we knew the other parameters affecting seller utility (c, γ), the magnitude of this shift would only depend on δ, the extent of scale economies in search effort: when δ is large, search costs decrease considerably with market scale, and this directly translates into a large increase in offer submission. So roughly speaking the response of seller offers σ to changes in B identifies δ. Finally, we add variation in the number of buyers relative to sellers B S (right-hand side panel of Figure 7). Again we discuss the intuition holding constant buyers β. An increase in B S shifts and pivots the marginal benefit curve upward by increasing the match rate and the price of each additional offer. If c and δ were known, the magnitude of this shift would only depend on γ, the slope of the marginal cost curve: when γ is large, the marginal cost curve is flat and an increase in the relative number of buyers translates into a large increase in offer submission. So effectively changes in B S and the response of σ allows us to identify γ. 5 Econometric Model In this section, we describe how we move from the theoretical model to an econometric model, and how we apply the model of the TaskRabbit data. We then describe our estimation strategy and discuss our identification assumptions. Our main assumption is that the number of buyers and sellers who consider using the platform in any citymonth does not depend on contemporaneous unobserved characteristics that affect the efficiency 17

19 of matching or price determination, the cost of search or posting, or the value of trade. We also present the functional forms of the matching and pricing functions, and make assumptions about how buyers and sellers form beliefs about them when making search intensity and posting decisions. Results are presented in the next section. 5.1 Market Definition Our model envisions a single static market, while trades occur continuously in the data. To create an empirical analogue to the model, we define distinct markets in the data. Given that 94 percent of users post or work in a single city, it is natural to treat cities as separate. The fact that 97 percent of successful tasks are matched to offers within 48 hours of posting suggests segmenting the data in time as well. One option is to treat each city-month (e.g. San Francisco in October 2013) as a separate market. Within a city-month, we treat buyers and sellers, as well as their tasks and offers, as homogeneous, following the model, and discuss this further in Appendix B. This definition allows us to consider each participant as small relative to the size of the market, which is our modeling assumption, and also lets us smooth shorter time variation due to potential task heterogeneity. Other market definitions do not change our qualitative results, as shown in the Appendix. Our market definition is motivated by several additional considerations. First, we do not separate markets along the various task categories – cleaning, furniture assembly, and so on – because sellers do not specialize: of the sellers who submitted 10 offers or more 63.6 percent did so in more than 10 categories, and of the sellers who were successfully matched to more than 10 tasks, 43 percent did so for tasks in more than 10 categories. Second, we follow TaskRabbit business practice and do not separate markets into geographic partitions smaller than the metropolitan boundaries. 15 Third, we choose the calendar month as the relevant time window as a way to balance the short time period over which tasks receive offers with the need to have enough offers and tasks in each market to estimate match probabilities, average prices, and search and posting intensities. There is one further data issue we must address in moving between the model and the data. In the model, all buyers choose the same posting threshold, but the distribution of posted tasks across buyers is Poisson. This means that some participating buyers post zero tasks. Similarly the distribution of seller offers is Poisson and some participating sellers make zero offers. However, in 15 We do not observe any sort of clear neighborhood partitioning in the data, although the platform s setup does not preclude it. We provide additional details in the Appendix. 18

20 the data we cannot distinguish between buyers and sellers who were considering posting tasks and submitting offers but did not, and those who were completely disengaged from TaskRabbit. Our solution is to rely on the Poisson assumption in the model and use it to impute the number of buyers posting zero tasks and sellers submitting zero offers. Specifically, if the number of buyers posting at least one task is B and the average number of posts among these buyers is β, then under the Poisson assumption the average number of posts β among all buyers solves Under the same assumption, the total number of participating buyers B, which is the sum of buyers posting zero tasks and those posting one task or more, is equal to B = B. We perform a parallel 1 e β exercise to impute the total number of participating sellers making zero offers, and to appropriately construct S and σ. 16 β 1 e β = β. 5.2 Econometric Model We now describe the econometric model that we take to the data. It has three components: the aggregate pricing and matching functions that map offers and tasks to market outcomes; the expectations formed by buyers and sellers about their probability of matching and the market price (assumed to be rational); and their optimal search and posting decisions. Throughout, n = (c, t) identifies a market, our unit of observation: c denotes the city, and t denotes the calendar month. We let B n and S n denote the number of participating buyers and sellers, β n and σ n denote the participants average posting and offer intensities, and b n and s n denote the total number of posts and offers in a market. Finally, we let M n denote the number of matches, and P n the average transacted price. Matching and Pricing Functions. We assume that the total number of matches and average prices in a market are Cobb-Douglas functions of the number of tasks posted and offers made. 17 Specifically, M(s n, b n ) = A n s α 1 n b α 2 n (5) P (s n, b n ) = K n s ρ 1 n b ρ 2 n, (6) 16 This solution is somewhat imperfect as it relies on a relatively strong distributional assumption. However, we examine the validity of the Poisson assumption, and check the robustness of our results to alternative imputation strategies in the Appendix, finding that our empirical results are not very sensitive to alternative approaches. 17 Petrongolo and Pissarides (2001) summarize the wide empirical support for a Cobb-Douglas matching function with constant returns to scale. For its micro-foundation, see Stevens (2002). 19

21 The variables A n and K n are market level productivity and pricing shifters. We assume that each has an error component structure. That is, A n = A t A c ɛ a n where A t is a month effect, A c is city-specific match efficiency, and ɛ a n is an idiosyncratic shock to matching, which has expected value 1 and is not anticipated by buyers or sellers. Similarly, we assume that K n = K t K c ɛ k n, and again assume that ɛ k n is not anticipated by market participants. In this specification, we expect that the number of matches will be increasing in both inputs, s and b – i.e. α 1 0 and α 2 0. The market exhibits increasing returns in matching if α 1 + α 2 > 1, and constant returns if α 1 + α 2 = 1. Under increasing returns, doubling the number of tasks and offers more than doubles the number of matches. For pricing, we expect more posted tasks will drive up prices, and more offers will reduce them, so that ρ 1 0 ρ 2. If ρ 1 + ρ 2 = 0 the pricing is not affected by scale: doubling both the number of offers and tasks has no price effect. Participants Expectations. Therefore, the expected matching probabilities are qn b = Qn b n qn s = Qn s n, where and the expected price is and Q n = E [A n s α 1 n b α 2 n s n, b n ] = A t A c s α 1 n b α 2 n, (7) p n = E [K n s ρ 1 n b ρ 2 n s n, b n ] = K t K c s ρ 1 n b ρ 2 n. (8) Buyers expect to pay p n, and sellers to receive (1 τ)p n. Given the constant 20 percent platform commission fee, we fix τ = 0.2. Optimal Decisions. Finally we can write the buyer and seller optimal decisions. From Section 4, buyers choose a posting intensity β n equal to [ β n = ɛ b nµ 1 e ηqb (vn pn)] n. (9) ɛ b n is a task arrival shock, known to participating buyers and sellers but independent of their (prior) decisions to participate in the market. It can be thought of as a city-month specific driver of demand for services among participating buyers. An example might be an increase in requests 20

22 for shopping deliveries due to December snowstorms in Chicago, which does not drive buyers or sellers decision to stay or join TaskRabbit in that particular market, but does increase the posting intensity of participating buyers. 18 On the seller side, we specify search costs as 1 ɛ s nγb δ n σ 2 n – i.e. decreasing in the total number of posted tasks at rate δ. Each seller chooses a search intensity σ n equal to σ n = ɛ s nγb δ nq s n(0.8p n c n ). (10) As for buyers, ɛ s n is a supply shock that reduces the cost of search. It can be interpreted as a city-month specific increase in time availability among participating sellers. Recall from equation 8 that price has a time-specific component K t. In order to homogenize values and costs over time, we assume that the same time parameter multiplicatively changes buyer values and seller costs of performing tasks. Specifically, we assume that v n = K t v and c n = K t c. 5.3 Identification We make two key identification assumptions: i) participating buyers and sellers do not anticipate the idiosyncratic pricing and matching shocks in making their posting and offer decisions, and ii) the number of participating buyers and sellers in a given market does not depend on these shocks, nor on the unobserved components of buyer and seller utility. Lastly, we make the additional and convenient assumption that the unobservable shocks are iid across markets. Formally, we write our assumptions as follows: Assumptions: We assume that: 1. Pricing and matching shocks are not anticipated: the vector (ɛ a n, ɛ k n) is independent of (σ n, β n ). 2. Limited predictability for prospective users: the vector (ɛ b n, ɛ s n, ɛ a n, ɛ k n) is independent of (S n, B n ). 3. IID: the vector (ɛ b n, ɛ s n, ɛ a n, ɛ k n) is independently and identically distributed across markets, with mean (1, 1, 1, 1) and variance covariance matrix Σ. 19 An issue of splitting cities into multiple markets over time is that buyers and sellers might anticipate the future value of exchanges on the platform and base their decision to stay or leave on these rational expectations. Two empirical features of TaskRabbit lead us to think that forwardlooking behavior is not prevailing: the low level of retention and its response to future outcomes. 18 Note that it does increase the number of buyers who actively post at least one tasks. 19 Given Assumption 1, which implies that (ɛ a n, ɛ k n) is independent of (ɛ b n, ɛ s n), Σ is block diagonal. 21

23 Only a small share of buyers active in a given market (31 percent on average across markets) post again at least once in the subsequent three months. For sellers, this share is 66 percent. Moreover, in Section 7, we will consider the decision of current buyers and sellers to stay on the platform and find that there is very little empirical support for forward-looking anticipation of platform outcomes, although there is evidence that sellers respond to past outcomes. We are not overly concerned with the possibility that marketing and advertising could affect both the number of buyers and sellers and their posting and search decisions. This is because, during the period of our study, the platform did not spend heavily to attract buyers and sellers. Advertising relied on articles mentioning TaskRabbit in newpapers and blogs. 40 percent of these articles were not pitched by the platform, but rather made reference to TaskRabbit while discussing the sharing economy. 20 In addition, more than 70 percent of them were on national media, as opposed to local newspapers. Finally, presence on the media was fairly uniform across months. 21 This media coverage is unlikely to be specifically tied to market conditions affecting posting or search effort. Marketing targeted at the city level occurred only for a few weeks around the time of entry into that city: TaskRabbit would start by acquiring some sellers before opening the platform to buyers, and would train them to perform services by assigning them to a small number of marketing tasks – e.g. flyer distribution. By only keeping markets with more than 50 active buyers and 20 active sellers, we are fairly confident that the TaskRabbit s marketing efforts are not the driving activity within a market. This leaves us to consider the participation decisions of new buyers and sellers. Our basic premise is that prospective new buyers and sellers do not have much information about the specific idiosyncratic conditions on the platform. On the buyer side, there is relatively little cost of joining the platform, and we believe that during our study period adoption may have been driven significantly by people simply becoming aware that the platform existed. Our indication is that buyer sign-ups tended to increase notably after media mention, which we do not believe were tied to specific market conditions. On the seller side, a significant source of month to month variation in new participation was driven by changes in the screening process. For a period, sellers were rigorously screened and interviewed by TaskRabbit employees. Acceptance rates of received applications depended on em- 20 The sharing economy (or collaborative consumption) is the term often used to refer to online peer-to-peer marketplaces like Airbnb, Uber, or TaskRabbit. In the sharing economy, owners rent or share something they are not using (e.g., a car, house) or provide a service themselves to a stranger using peer-to-peer platforms. 21 The numbers rely on TaskRabbit s tracking activity of its media presence in

24 ployees time to conduct interviews, were usually very low (13.6 percent) and varied greatly month to month. Further, they introduced a certain delay between the sign-up decision and the actual participation on the platform.we have no evidence that they varied by city-months in response to expectations of higher demand or of lower time availability of each seller. In the spring of 2013 the platform decided to ease sellers screening, and started to require simpler background checks and social controls (Linkedin, Facebook verification). This resulted in an acceleration of sellers acquisitions. Together, the varying screening policies and acceptance rates led to fluctuations in the relative number of buyers and sellers for reasons arguably unrelated to individuals activity within each city-month. We have also assumed that pricing and matching shocks (ɛ a n, ɛ k n) are not anticipated when buyers and sellers make their posting and search decisions. These shocks can result from unexpected concentration of offers among a small number of tasks, for example due to variation in the time when users access the platform: if all sellers in a market find themselves looking for tasks at the same time within a month, offers will tend to be sent to the same tasks, more so than if sellers search for tasks at different times. This could decrease the rate at which offers and tasks are converted into matches and the price at which matches trade. Our assumption essentially requires that buyers and sellers cannot anticipate these coordination problems. 5.4 Estimation The estimation consists of two steps. First, we estimate the pricing and matching functions by ordinary least squares. To do that, we transform equations 5 and 6 by taking logs to obtain log Q n = log A t + log A c + α 1 log s n + α 2 log b n + log ɛ a n (11) and log P n = log K t + log K c + ρ 1 log s n + ρ 2 log b n + log ɛ k n. (12) Second, we estimate the utility parameters by method of moments using our assumption of equilibrium behavior and the orthogonality of S and B from contemporaneous effort shocks. The moment conditions are ( )] β n E [x n µ ( 1 e ηqb (vn pn)) 1 = 0 n 23

25 and ( )] σ n E [x n γb δ nqn(0.8p s n c n ) 1 where x n = (1, B n /S n, B n ) is the three-element column vector of instruments. The model is exactly identified. = 0, 6 Results This section presents our empirical estimates of the pricing and matching functions, and the demand and supply parameters. We use these to derive estimates of the gains from trade, and the role of labor supply elasticity in promoting efficient matching. 6.1 Matches and Prices We start by discussing our results on the aggregate pricing and matching functions. Table 3 presents results from ordinary least square regressions of equations 11 and 12 above. The coefficients can be interpreted as elasticities, because of the log-log specification. The first column shows that doubling the number of tasks, holding constant the number of offers, increases the number of matches by 41 percent (α 1 ). Similarly, doubling the number of offers, holding fixed the number of tasks, increases the number of matches by 52 percent (α 2 ). The estimates suggest that scaling up either tasks or offers contributes about equally to the creation of successful matches. The sum of the two elasticities provides an estimate of the returns to scale in the matching technology. Work on two-sided platforms has emphasized the importance of increasing returns to scale for market structure (Ellison and Fudenberg (2003)). The hypothesis is that active and thick markets may lead to easier matching. In a platform like TaskRabbit where tasks typically require a buyer and a seller to meet, efficiency can come from matching buyers and sellers who live close to each other. Our estimates, however, show no evidence of increasing returns to scale. Returns are slightly (and significantly) less than constant (α 1 + α 2 < 1) when estimated by ordinary least squares, and slightly over 1 when the number of buyers and sellers are used as instruments for tasks and offers. The absence of increasing returns was perhaps unexpected given the specific nature of the market. But interestingly it does not seem to be the case that distances between matched buyers and sellers shrink as a market grows. Figure 13 plots the median distance within a city-month, 24