Using Big Data to Estimate Consumer Surplus:
The Case of Cohen, , , , and 1
August 30, 2016
Estimating consumer surplus is challenging because it requires identification of the entire
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demand curve.
We rely on
Uber’s “surge” pricing algorithm and the richness of its individual
level data to first estimate demand elasticities at several points along the demand curve. We then
use these elasticity estimates to estimate consumer surplus. Using almost 50 million individual-
level observations and a regression discontinuity design, we estimate that in 2015 the UberX
service generated about $2.9 billion in consumer surplus in the four U.S. cities included in our
analysis. For each dollar spent by consumers, about $1.60 of consumer surplus is generated.
Back-of-the-envelope calculations suggest that the overall consumer surplus generated by the
UberX service in the United States in 2015 was $6.8 billion.
Keywords: consumer surplus, demand estimation, discontinuity design, peer-to-peer markets, Uber.
JEL: D1, D2, D4, L1.
1 We are grateful to Josh Angrist, , , , , , , and for helpful comments and discussions. We are also grateful to for excellent research assistance. Affiliations: Cohen: Uber; Hahn: and Institute for Thinking, University of Oxford; Hall: : University of Chicago Department of Economics and National Bureau of Economic Research; Metcalfe: University of Chicago Department of Economics and Institute.
1. Introduction
For over 250 years, economists have recognized the importance of consumer surplus when making welfare calculations.2 Consumer surplus (and the closely related concepts of equivalent variation and compensating variation) is a critical input to many economic policies, such as antitrust analysis, the valuation of non-market goods, and measuring the value of innovation (e.g., Williamson 1968, Willig 1976, Bresnahan 1986).
In practice, however, obtaining convincing empirical estimates of consumer surplus has proven to be extremely challenging. We typically observe only the equilibrium point that balances supply and demand. Variations in that equilibrium across time and space are generally the result of a combination of supply-driven and demand-driven shocks and thus are of little use in this regard. A large body of economic research focuses on demand estimation (see, for instance, Deaton 1986). The key to estimating demand elasticities is to isolate exogenous shifts in the supply curve, holding demand factors constant. In recent years, a great deal of work has focused on the development of new techniques for generating demand estimates in differentiated product markets (Baker and Bresnahan 1988, Berry et al. 1995, Nevo 2000, Petrin 2002).3 This strand of the literature focuses on overcoming the data limitations that are often present in standard economic settings, such as the absence of individual level data, unobservable product characteristics, and unobservable consumer characteristics.
Existing empirical explorations of demand almost always generate local estimates of demand elasticities. These elasticities describe how consumers are likely to respond to small variations around the equilibrium price. Local elasticities, however, are not sufficient for estimating consumer surplus. To compute consumer surplus one needs to integrate the area under the demand curve, which requires knowledge of the quantity demanded for each possible price. Typically, there are no direct estimates of elasticities far from the equilibrium price, necessitating a strong functional form assumption (e.g., iso-elastic demand) to produce consumer surplus estimates.
In this paper we exploit the remarkable richness of the data generated by Uber, and in particular its low-cost product UberX, to generate consumer surplus estimates that require less restrictive identifying assumptions than any other prior research that we are aware of.
2 The concept of consumer surplus, or “utilite relativé,” was first introduced in 1844 by French engineer . later independently reintroduced and named the concept in his 1890 publication Principles of Economics (Houghton, 1958; Svoboda, 2008).
3 In differentiated product markets such as those studied by Berry et al. (1995) and Nevo (2000), one needs not only instruments for price, but also instruments that shift market shares through a channel other than prices (Berry and Haile 2014).
UberX is an app-based service that algorithmically matches drivers to consumers seeking rides (see uber.com).4 A critical feature of Uber is that it uses real-time pricing (“surge” pricing) to equilibrate local, short-term supply and demand. A consumer wishing to take a particular trip can face prices ranging from the base price (what we call the “no surge” or “1.0x” price) to five or more times higher, depending on local market conditions. Importantly, we observe detailed information not only for every trip taken using Uber, but also, critically, when a consumer searches for a ride using Uber without ultimately deciding to make a request. We, thus, observe the price offered to the consumer, and whether she accepts or rejects that offer. This information is crucial in our strategy for estimating demand.
If the degree of surge pricing faced by a consumer on a given trip were generated at random, then all that would be required to trace out a demand curve would be to compute the share of Uber searches culminating in a ride at each level of surge pricing. With randomization, if 70 percent of searches lead to a transaction at the base price, but only 63 percent of searches lead to trips when the price is ten percent higher (1.1x surge), then we could assume that people who received surge 1.0x would also have requested trips at a rate of 63 percent, had they been quoted the 1.1x price. This would imply that the elasticity of demand would be one on this part of the demand curve (i.e. a 10 percent reduction in the share of people who accept the offer–from a 70% purchase rate to a 63% purchase rate–is associated with a 10 percent increase in price).5 Similar comparisons of ride completion rates at higher prices would trace out demand over whatever range of prices consumers faced. Combining these elasticity estimates with the actual quantity purchased at 1.0x surge yields the demand curve for customers offered 1.0x surge, as well as an associated consumer surplus.
In practice, the surge price that consumers face is not random; it reflects local demand and supply conditions. There is, however, a component of Uber pricing that is largely random from a consumer’s perspective. Uber calculates each surge price to an arbitrary number of decimal places, but consumers are presented with discrete price increments (e.g., the lowest surge price is 1.2x, or 20 percent higher than the base price) to facilitate a simple, easy user experience.6 Market conditions are nearly identical when the algorithm suggests a surge of 1.249x and when it
4 The rampant growth of “peer-to-peer” transactions and the “sharing” economy have had a profound impact on many industries in recent years. A burgeoning economic literature is devoted to this topic (e.g. Cramer (2016), Cullen and Farronato (2014), Einav et al. (2015), Fraiberger and Sundararajan (2015), Hall and Krueger (2015)).
5 In this example, the 63 percent of consumers who demonstrated a willingness to pay of 1.1x, reveal that had they only been asked to pay the base price, they would have received a consumer surplus of at least 10 percent of that base price. The 7 percent of customers who refuse to transact at 1.1x, by this same logic, reveal a consumer surplus when transacting at the base price that is less than 10 percent of the base price.
6 For example, Uber might estimate that the appropriate multiplier is 1.61809, but for easy interpretation, they would charge the customer 1.6x.
suggests a surge of 1.251x, but in one case consumers face a 1.2x surge and in the other case they face a 1.3x surge. This provides the opportunity for regression discontinuity (RD) analysis, which allows us to estimate local elasticities of demand across the full range of surge prices.7 A complicating factor in our analysis is that the expected wait time a consumer faces systematically changes at the price discontinuity. We observe the expected wait time of the customer in our data, so we can control for this factor in our analysis. Additionally, the expected wait time algorithm used by Uber is continuous, but is rounded to whole minutes when presented to customers. This allows us to use an RD design for identifying the causal impact of expected wait time on purchases and thus to more convincingly purge any impact of wait time differences from our price elasticity estimates.
Using a sample of nearly 50 million UberX consumer sessions, which represents the first 24 weeks in 2015 from Uber’s four biggest U.S. markets, we estimate demand elasticities for Uber’s most used service (“UberX”).8 Empirically, three basic facts emerge. First, our estimated demand elasticities are similar regardless of the sources of variation that we use in the estimation or the set of included controls, suggesting that our results are robust. Second, demand is quite inelastic. Our methodology estimates a set of price elasticities, most of which are between -.4 and -.6. Third, the elasticity of demand varies somewhat (but perhaps less than expected) as a function of observable characteristics such as time of day, user experience with Uber, or the presence of close substitutes.
These estimated Marshallian price elasticities form the basis of our consumer surplus calculations, but further assumptions are required. To compute consumer surplus, one needs to know how consumers would have responded had they faced a higher price. We do not directly observe this in the data. Instead, what we observe is how price responsive consumers are when market conditions dictated a higher price. The set of sessions with high surge prices may, however, differ systematically in their price responsiveness from those who see low surge.9 We deal with this complication in two ways. First, we use propensity score methods to identify a subset of sessions that saw high surge prices, but whose observable characteristics (e.g., location, time of day, day of the week, and past usage of Uber) match the pool of sessions that face no surge. Second, we redo our estimates eliminating from the sample all observations where there is a positive local demand shock. The prices charged depend on the interplay of supply and
7 Additionally, there are Uber business rules that sometimes cause prices to be far below what the surge algorithm recommends, allowing us also to analyze consumer behavior when the differences between the surge level and the surge generator are larger.
8 The data were chosen in conjunction with Uber to be large enough to be representative, while not revealing information that may have more business sensitivity.
9 Note that the same consumer opening the app under different circumstances may have different likelihoods of making a purchase and different sensitivities to price. Thus, we focus on sessions as our unit of analysis, not individuals.
demand. If the supply of drivers is low, prices can be high even though the number of requests in a given time and place are not out of the ordinary. Price spikes driven by idiosyncratically low supply are likely to provide a better counterfactual than those triggered by unusually high demand. Neither the propensity-score methods nor eliminating positive demand shocks materially affects the consumer surplus results.
We obtain large estimates of the consumer surplus generated by UberX. We compute the dollar value of consumer surplus from UberX rides taken in Uber’s four biggest U.S. markets in 2015 (Chicago, Los Angeles, , and San Francisco) to be roughly $2.88 billion (SE=$122 million) annually. This is more than six times Uber’s revenues from UberX in those cities.10 In 2015, these cities accounted for around 42.6% of UberX US gross bookings. If we assume that consumer surplus is proportional to gross bookings, we can extrapolate to an estimate of $6.76 billion in consumer surplus from UberX in the U.S. The estimated consumer surplus is approximately 1.57 times as large as consumer expenditures on rides taken at base pricing. That is, for each $1 spent on an UberX ride at 1.0x, we estimate the consumer receives $1.57 in extra surplus. These estimates of consumer surplus are large relative to the likely gains or losses experienced by taxi drivers as a consequence of Uber’s entrance into the market (Cramer 2016).
From a public policy perspective, our consumer surplus estimates have two shortcomings. First, they are derived from short-run demand elasticities, but any policy decision is likely to be interested in long-run consequences.11 Second, our estimates miss the consumer surplus associated with other ride-sharing products (both those offered by Uber and by other ride-sharing companies), as well as consumer benefit or harm resulting from responses of the taxi cab industry to Uber’s entry. We discuss in the concluding section what economic theory tells us about mapping from the numbers we are able to credibly estimate to the numbers that are of greatest economic interest.
Although very different methodologically from our paper, Buchholz (2016) is the most similar prior work in terms of goals. Buchholz (2016) estimates a dynamic spatial equilibrium model of City taxi cabs to assess the efficiency cost of existing regulations. He concludes that efficient two-part tariff pricing and a directed matching technology would deliver welfare gains of over $2 billion annually in .12 Also in the basic spirit of our work in estimating
10 This assumes a 25% commission of gross fares reserved for Uber. This percentage likely overstates Uber’s actual average commission rate on the trips represented.
11 The price variation we exploit is highly transient, and the set of competitors is fixed. Thus, the appropriate interpretation of our estimate is roughly, if Uber’s system malfunctioned and Uber were therefore unavailable for a day, how much would consumers suffer? (The answer would be 1/365th of our annual consumer surplus number, or about $18 million.)
12 More specific to the literature on taxis, there are a very rich set of papers that have attempted to understand the supply side of the taxi market (see Camerer et al., 1997; Farber, 2005, 2008, 2015; Crawford and Meng, 2011).
welfare impacts on consumers are Petrin (1999), Nevo (2000), Brynjolfsson et al. (2003), Goolsbee and Petrin (2004), Mortimer (2007), Crawford and Yurukoglu (2012), Quan and Williams (2014), and Crawford et al. (2015).
The remainder of the paper is structured as follows. Section 2 provides background on Uber. Section 3 describes the data and identification approaches underlying our estimates of demand elasticities. Section 4 presents the estimation results along with a series of sensitivity analyses. Section 5 explores the set of assumptions necessary to translate the demand estimates into consumer surplus and the conclusions we reach based on these calculations. Section 6 concludes with a discussion of the economic implications and interpretations of our findings.
2. Background on is a technology company founded in 2009, which created a smart phone application that matches and handles payments between consumers seeking rides and Uber’s “driver-partners.” Uber’s service has proven extremely popular, growing dramatically in terms of both geography and volume.13
To use Uber, a consumer downloads the app onto her smartphone for free. When seeking a ride, the consumer opens the Uber app and sees something akin to the screenshot in Figure 1. There is a map of the local area, a display of driver-partners in the area available to provide rides, and an estimate of how many minutes it will take the nearest vehicle to reach the consumer’s location. Uber offers a number of different products, as shown near the bottom of the screen in Figure 1. The user is able to scroll between those products. If a consumer places an order, driver-partners are sequentially given the opportunity to accept that order until one does so. That driver-partner then picks up the rider and drops her off at her desired location. Uber defines a user product- session in which the user opens the app, culminating either in the user ordering a ride or electing not to order a ride.14 Throughout this interaction, Uber records all actions taken on the app as well as certain background information relevant to the transaction. These data are collected and stored regardless of whether or not the session ends with a purchase.
13 City governments have had varying reactions to Uber’s operations, which dramatically alter the status-quo of transportation. Historically, for-hire transportation has been heavily regulated, usually via a taxi medallion system (see Frankena and Pautler, 1984). The incumbent taxi cab providers, not surprisingly, have been hostile to Uber’s presence.
14 A session is Uber’s best attempt to identify a consumer’s decision as to whether or not to make a purchase. For simplicity with our focus on UberX, we use “session” to refer to a product-session of UberX interaction unless otherwise specified. Technically, if the rider interacts with another Uber product at a similar time, this creates a separate product-session. A session is defined as a period of, not necessarily continuous, use between opening the app to UberX and either requesting a ride or ceasing to use the app for a period of 30mins. Thus, multiple closings and openings of the app in a short period of time do not generate many sessions. The median elapsed time of a session is 31 seconds.
Uber offers several products, which differ in terms of the types and size of cars, whether the ride is shared with other passengers, and the price. Our focus is on UberX, the core product that represented almost 80 percent of all Uber rides during the time period of our sample. With UberX, a rider summons a driver-partner who drives her own private vehicle and delivers the rider to the desired location without stops.15
Uber’s base pricing system has components similar to standard cab pricing systems in which each city and product has a fare defined by price per mile, price per minute, a fixed fee, and a minimum total fare.16 In contrast to regulated cabs, Uber also utilizes a dynamic pricing system, called surge pricing, on many of its products.17 Uber’s surge algorithm monitors rider demand and available driver supply and institutes a multiplier on the base price when demand outstrips supply at the base price.18 This pricing system helps increase supply at times of high demand, and allocate rides to riders who value them most highly (Hall et al. 2015).
Around 21% of UberX sessions in our dataset have some surge price exceeding 1.0x. Figure 2 presents the observed distribution of UberX sessions in our data for surge prices greater than 1.0x. The number of sessions between 1.2x (the lowest surge) and 1.5x are roughly equally common. 1.5x is somewhat overrepresented due to less than perfect accuracy in excluding sessions where the surge price was altered by Uber business rules. Beyond that point, the number of sessions decreases monotonically with the level of surge. Roughly 4.1 percent of surge sessions involve surge levels at or above 3.0x; 0.65 percent involve a surge greater than or equal to 4.0x.
Although consumers are only shown a limited number of discretized surge levels, the algorithm generates a continuous measure of surge (which we call the “s
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