Ride-Hailing Demand Elasticity: a Regression Discontinuity Method

Ride-hailing Demand Elasticity: A Regression discontinuity Method

∗ Hosein Joshaghani , Seyed Ali Madanizadeh†, and Reza Moradi‡

September 16, 2020

Abstract

Using the unique pricing method of Tapsi, the second-largest ride-hailing company in Iran, we estimate the price elasticity of demand for Tapsi rides. Tapsi mechanically divides Tehran, the largest city of Iran, into 256 regions using a 16×16 matrix of straight lines, to implement surge pricing to excess regional demand or supply. Surge multiplier works for all ride requests within each region, independent of supply and demand in neighboring regions or rides characteristics. We exploit this sharp discontinuity in pricing by running a regression discontinuity to estimate the causal effect of the price change on the number of ride requests, i.e., price elasticity of demand. Using information of more than 10 million unique ride requests, we estimate not only average price elasticity, but also price elasticity at different levels of surge multiplier. Moreover, we measure price elasticity for 1-hour and 6-hour horizons and estimate the price elasticity of -0.25 and -0.54 for each horizon, respectively. This can be explained by the fact that in longer horizons, customers can more easily choose alternative modes of transport. This finding supports the very fundamental economic principle of higher elasticities in the long-run than in the short-run.

Keywords: Estimating Demand Elasticity, Regression Discontinuity Design, Ride- hailing Applications, Two-sided Markets

JEL Codes: R41, R40, L90, L91, C55

∗ [email protected] † [email protected] ‡ [email protected] 1 Introduction

As a new entrant, ride-hailing companies have become serious competitors for the incumbent taxi system in the world. For instance, by the end of Jan 2015, Uber provided about 60,000 trips in New York City, while 460,000 trips were taken by regular taxis. However, by the end of Feb

2020, Uber provided about 542,000 trips, compared to around 231,000 trips by regular taxis.1

The same pattern of market penetration is observed around the world. In 2019, Snapp and

Tapsi, the two largest ride-hailing companies in Iran, record more than 2 million rides per day.

In order to measure consumer welfare, and in order to implement a more eﬀicient pricing system, it is necessary to measure demand elasticity with an accurate and low-cost method. In this paper, we use a discontinuity in the pricing of Tapsi, the second-largest ride-hailing company in Iran, to estimate demand elasticity for Tapsi rides.

The fare that Tapsi charges consists of two separate parts: 1) baseline ride price, which is calculated by unique characteristics of each ride such as ride distance, estimated time of the ride, estimated wait time at the destination for the next ride request, and so on, and 2) surge multiplier coeﬀicient, which is independent of the unique characteristics of the ride and is calculated based on the number of ride requests (demand) and the number of online drivers

(supply) in the rides origin. To exploit the surge coeﬀicient, Tapsi divides Tehran into a 16×16 matrix with straight lines into 256 regions with the same areas. Then Tapsi calculates the demand and supply in each of these 256 iso-area regions every 5 minutes to assign a surge multiplier to each of these regions.

The primary identification assumption of this paper is that straight borderlines of these 256 regions, separate customers, are located very close to each other and randomly between regions. Two neighbors with similar socioeconomic characteristics can be assigned to two regions, with an independent surge multiplier, only by chance. Therefore, similar customer observes different fare for a similar ride with an origin at each side of the border. We interpret the difference between the number of ride requests on two sides of the border as the

1 New York City Taxi & Limousine Commission

1 causal effect of price difference between two regions. In this regard, we use Regression Discontinuity Design (RDD) to identify the demand elasticity, i.e., the percentage change in demand due to a 1 percent change in price.

Having access to the information of more than 10 million unique rides, we can use this regression discontinuity to measure not only average price elasticity of demand, but also measure price elasticity at different levels of surge multiplier. In other words, we estimate price elasticity at different points on the demand schedule.

Moreover, we measure price elasticity for a short horizon and longer horizons. For instance, we count the number of ride requests within 1 hour and 6-hour horizons of neighboring regions and estimate the price elasticity of -0.25 and -0.54 for each horizon, respectively. This can be explained by the fact that in longer horizons, customers can easier choose alternative modes of transport. This finding supports the fundamental economic principle of higher elasticities in the long-run than in the short run. Also, we show that there will be an increase in demand if passengers observe more online taxis around themselves.

Furthermore, the demand of Tapsi, as a ride-hailing application, increases for rides, which has long-distance or other characteristics that affect their base price positively.

This paper is continuing the growing literature of studying the impact of ride-hailing companies and their features. The effect of Uber on DUI related death rate of motor vehicle drivers (Greenwood and Wattal (2015)), the relationship between the satisfaction from Uber’s services and lack of taxis in a city (Wallsten (2015)), the opposite effects of Uber on traﬀic

(Alexander and González (2015)), and the empirical study on the effect of Uber on traﬀic and

CO2 emission in a city (Li et al. (2016)) are just some examples of researches that related to the social effects of the ride-hailing market. Moreover, there are works about other aspects of ride- hailing systems, such as pricing and supply-side: the alleviating effect of dynamic pricing on the

”wild goose chase” phenomenon (Castillo et al. (2017)), the effect of dynamic pricing on drivers’ work hours (Chen and Sheldon (2015)), the short-run and long-run effects of sudden fare changes on drivers’ earnings (Hall et al. (2017)) and so forth.

In spite of numerous studies on social effects, pricing, and supply side of ride-hailing companies, there are fewer papers about the demand side of these markets. This paper is in the trend of ride-hailing demand studies, using geographical Regression Discontinuity

Design on different rich data from Tapsi. Lam and Liu (2017) identify the demand elasticity of Uber by the discrete choice model used in the literature before (Berry et al. (1995), Nevo

(2000), Petrin (2002), and so on). Cohen et al. (2016) use Regression Discontinuity in other surge coeﬀicient levels to estimate the demand elasticity of Uber. Compare to the Cohen et al. (2016), our identification considers the location that ride request sent, which is a proxy of the place customers live, work, and even their income, as unobservable characteristics to make the identification more precise. Moreover, the flexibility of our identification leads us to use one regression to estimate all demand elasticities. Therefore, we can use all records in the data to exploit the fixed effects of our estimation effectively.

In Section 2, we briefly explain the system of Tapsi and facts about the data, especially the discontinuity between the ride requests of customers on two sides of the border of regions with different surge coeﬀicients. In Section 3, we explain our identification method and how we apply the Regression Discontinuity Design on our data. In Section 4, we show the results and explain them, and in Section 5, we conclude our findings.

2 Data

Tapsi, founded in April 2016, is one of the most important ride-hailing firms in Iran. The company provides service in 15 cities in Iran.2 Due to its CEO, in 2018, 600 people were working for Tapsi directly. Moreover, 250,000 drivers signed up which 150,000 of them were active drivers. The CEO also claimed that they have 40% of the market share in 2018.3

2 https://tapsi.ir 3 https://virgool.io

3 At first, a passenger launches Tapsi mobile application and determines her destination after observing near online taxis. Tapsi calculates the price based on the unique characteristics of the ride request along with the demand (number of requests) and supply

(number of online taxis) in the initial location. Tapsi divides Tehran into 256 hypothetical regions to apply the demand and supply in those regions to the price. ”Surge coefficient” is calculated by considering the number of ride requests and taxis. If the surge coefficient is more than 1 in a region, there will be a significant excess demand, and surge coefficient less than 1 illustrates excess supply of taxis. The price calculated by the unique characteristics of each ride is multiplied by the surge coefficient to obtain the price that is observed by the customer.

The customer decides to send a ride request after observing the price and nearby taxis on a map. This request is received by the two nearest drivers who observe the location, destination, approximate distance to the passenger, and the price. Drivers have 15 seconds to accept or reject the request, and if they do nothing during this time, the application will assume that the request is rejected. If both drivers reject the request, the next two nearest drivers will observe the request. In a period of time, if none of the drivers accepts the request, the application informs the customer that no driver is found.

Data used in this paper are Tapsi ride proposals from January to June 2018 in Tehran.

We use the variables related to riding requests, such as the price, the surge coeﬀicient, the time of the requests, the number of online taxis, and the location of the passengers. We also use the Tapsi formula to convert longitudes and latitudes to the integer numbers in the range of 0 and 255, in which each one of them represents each region. Observations in which their ride requests and destination are out of 256 regions of Tehran were deleted.

Tapsi calculates the surge coefficient based on the ride requests and the number of taxis in each region. These continuous numbers round to some discrete levels: 0.8, 0.9, 1, 1.2, 1.4, 1.6, 1.8 and 2. Surge coefficients less than one are set due to excess supply of taxis, and the surge coefficients more than one are set due to excess demand.

Table 1 shows the mean, standard deviation, median, minimum, and maximum of important

4 variables in the data set. First of all, ride request generated to use for demand elasticity estimation seems a skewed variable. Also, because the average surge coeﬀicient is almost 1, it can be inferred that on average, demand and supply meet each other in

Tehran. The average of Ride Estimated Time and Ride Distance is about 21 minutes and 11 kilometers, which are reasonable for a metropolis like Tehran.

Table 1: Summary Statistics of Some Variables

Mean S.D. Median Min Max Average of Base Prices (1000 Toman per 6 hours in a section) 10.74 3.32 10.50 1.50 31.88 Average of Base P rices (1000 Toman per 1 hour in a section) 10.75 3.63 10.50 1.00 31.88 P rice (1000 Toman) 11.06 4.27 10.50 1.00 25.50 Surge Coef f icient 1.03 0.21 1 .8 2 Ride Estimated T ime (minutes) 20.99 10.06 19.92 0.00 104.75 Ride Distance (kilometers) 10.74 6.38 9.99 0 66.94 P ickup Estimated T ime (minutes) 2.76 1.81 2.37 0 10.67 P ickup Distance (kilometers) 0.56 0.38 0.50 0 3.00 P ickup Actual T ime (minutes) 5.30 4.57 4.37 0 59.88 Ride Actual T ime (minutes) 27.49 12.41 26.21 0.03 59.91

Note: Sections are determined by the division of 4 triangles, which are separated by the cross of diagonals in a region, into 50 parts with some areas (Figure 4). The time periods are 1 hour or 6 hours of a day, which may be workdays, Thursdays, or Fridays, in a week. Average of Base Prices are the average of prices customers face divided by surge coeﬀicients in a section into mentioned time periods. Ride Estimated Time and Pickup Estimated Time are respectively the estimation of ride and pickup by Tapsi. Ride Actual Time and Pickup Actual Time are respectively the ride and pick up time by reported by drivers. Due to the privacy policy, the number of observations is not determined.

Figure 1 shows the average number of ride requests in different surge coefficient levels. For the surge coefficient of more than 1, the trend shows the negative relationship between the number of ride requests and the surge coefficient. However, the trend seems to have a positive slope for surge coefficients less than 1. So, it seems that the excess supply of the drivers may cause a decline in surge coefficient below 1. The same pattern can be observed on Weekends in Figure 7.

In Figure 2, we can observe that the sum of ride requests decreases sharply because of a change in surge coeﬀicient from 1 to 1.2. As we assume the same unobservable characteristics for passengers near the border, the sharp decline in ride requests is mere because of change in surge coeﬀicient.

Figure 1: Ride Request of Workdays in Different Surge Coeﬀicient Level

Note: The vertical axis is the normalized sum of ride requests for a level of surge coeﬀicient in the workdays. Workdays are from Saturday to Wednesday. We are called the 6 a.m. to 12 p.m. morning, from 12 p.m. to 6 p.m. afternoon, 6 p.m to 12 a.m night, from 12 a.m. to 6 a.m after midnight. Due to privacy policy, the sum of ride requests normalized by the highest amount in the figure.

Figure 2: Sum of Ride Requests in Each Section of Adjacent Regions with Surge Coeﬀicient 1 and 1.2

Note: The vertical axis is the normalized sum of ride requests in a section. In this figure, just adjacent regions, which one of them has surge coefficient one and the other one has surge coefficient 1.2, are considered. Sections are determined by the division of the closest triangle to the borders of adjacent regions into 50 parts with some areas (Figure 4). Distance to Border is the distance of the furthest point of a section normalized by the width of a region. Sections in the regions with lower surge coefficient have negative distances, and sections in the regions with higher surge coefficient have positive distances. Due to privacy policy, the sum of ride requests normalized by the highest amount in the figure.

7 We can observe the same gap in other levels of surge coeﬀicient except for changes from

1.8 to 2 in Figure 8. This can be occurred due to the lack of data in these surge coefficient levels. Although the same gap can be observed in adjacent regions with surge coefficient 0.9 and 1 and also adjacent regions with surge coefficients 0.8 and 0.9, the ride requests are decreasing due to the distance to the border. We observe this pattern in Figure 3. Compared to the regions with surge coefficients equal to 1, it can be inferred that regions with surge coefficients less than one usually face excess supply of taxis rather than lack of ride requests.

This can also be supported by the sharp decrease in the average number of online taxis when surge coeﬀicient increases to 1, shown in Figure 9 in the Appendix. However, a different trend in

Figure 8 is an interesting question to investigate in further studies.

3 Identification

As in any demand estimation question, this research faces the same simultaneity problem too; The price changes affect the demand, and simultaneously, the demand changes affect the price. That is why we cannot use a simple OLS regression to estimate the demand elasticity. Therefore, we must use an identification method which isolates supply shocks from demand shifts.

The Tapsi method in dividing Tehran into 256 regions is a chance to use Regression Discontinuity Design (RDD) for estimating demand elasticity. In each region, Tapsi offers consumers different surge coefficient based on different situations of demand and supply. People who are near the border of the two regions are the same in their unobservable features, such as income, traffic, and so forth. A comparison of their response to different surge coefficients can help us estimate and identify the demand elasticity.

Figure 4 is an example of the method we used. Suppose that we want to estimate the demand elasticity between surge 1 and 1.2. For this purpose, we must select adjacent regions which one of them faces surge coeﬀicient 1 (green regions) and another one faces a surge

Figure 3: Sum of Ride Requests in Each Section of Adjacent Regions with Surge Coeﬀicient 0.9 and 1

Note: The vertical axis is the normalized sum of ride requests in a section. In this figure, just adjacent regions, which one of them has surge coefficient 0.9 and the other one has surge coefficient 1, are considered. Sections are determined by the division of the closest triangle to the borders of adjacent regions into 50 parts with some areas (Figure 4). Distance to Border is the distance of the furthest point of a section normalized by the width of a region. Sections in the regions with lower surge coefficient have negative distances, and sections in the regions with higher surge coefficient have positive distances. Due to privacy policy, the sum of ride requests normalized by the highest amount in the figure.

9 coefficient 1.2 (red regions). We may have separate regions with desirable surge coefficients, like the region in the second row from the bottom and second column from the left in Figure 4; however, we need to pick neighbor regions with surge coefficients equal to both 1 and 1.2.

Figure 4: Example of Tapsi regions in Tehran

Note: This figure is an example of regions in a time period. Surge coeﬀicient in white regions is 0.9, in green regions is 1, in red regions is 1.2 and in yellow regions is 1.4. In each triangle, sections are divided by dashed lines. The dependent variable is the sum of ride requests in a section in a period of time.

The closest triangles to the border of adjacent regions, which is made by the intersection of diagonals in a region, are considered to compare ride requests in two regions with different surge coeﬀicient. Figure 5 is an example of two regions with surge equal to 1 (green region) and surge equal to 1.2 (red region) and the closest triangle to the border in each region. Each triangle is divided into sections with the same areas to sum ride requests in a time period. In

Figure 5, the sections are the areas between dotted lines in each triangle. For instance, the first section in the red region is between the first dotted line in the triangle (it is the dotted line associated to the point 1 in the top horizontal axis in the red region) and the border of the adjacent green and red regions (line associated to the point 0). The last section in a region is between the last dotted line in the triangle and the vertex of the triangle (it is associated with

10 point 5 in the top horizontal axis in the red region).

Figure 5: Example of Adjacent Regions and Their Sections

Note: This figure is an example of two adjacent regions in a time period. Surge coeﬀicient in the green region is one, and in the red region is 1.2. In each triangle, sections are divided by dotted lines. All sections have equal areas. Each number on the top horizontal axis shows the number of each section from the border, n, and each number on the bottom horizontal axis shows the normalized distance of each section from the border, d.

In this paper, we separate each week into three periods: workdays (from Saturday to

Wednesday), Thursday and Friday. The sum of ride requests in a section of a region is calculated in 6 hours (12 a.m.-6 a.m, 6 a.m.-12 p.m, 12 p.m-6 p.m. and 6 p.m.-12 a.m.)

Of these three time periods for a surge coeﬀicient. We also use 1 hour period in a separate

Regression to estimate the demand elasticity for a shorter period of time. This approach allows us to compare relatively short-run and long-run demand elasticity.

To identify demand elasticity, we assume:

• There is no systematic migration of customers between regions due to different

surge coeﬀicients.

• In adjacent regions, there are the same number of potential customers in the first sections

11 (as we defined before) of both regions.

The first assumption means that people do not know about borders, or if they do, the cost of displacement would be too much to make the incentive of migration. Therefore, there should be no endogenous change in the number of requests due to the different surge coeﬀicients of adjacent regions. It seems that this assumption is reasonable because Tapsi has not published its formula for determining regions. The second assumption means that the potential customers (number of people on two sides of the border, which are online) do not differ significantly. As a result, the percentage difference of ride requests between both sides of the border would be equivalent to the difference between the share of requesting customers in all available customers. This eventuates to the estimation of elasticity, instead of semi-elasticity.

Therefore, our specification is as following:

log(RideRequest)st = constst+θW indows×P ostst+β2W indows+β3(1−W indows)P ostst+

β4(1 − P ostst) × dst + β5P ostst × dst + Ctrlst + F E + ϵst (1)

RideRequest is the sum of the ride requests in a section (s) of a region in 1-hour/6-hour time periods (t). W window is a dummy variable, which is 1 for the first sections in both regions. P ost is a dummy variable, which is 1 for the region, which has a higher surge coeﬀicient.

D is a variable that shows the normalized distance of a section from the border. In the region with a lower surge coefficient, d is negative, and in the region with a higher surge coefficient, d is positive. |d|, the absolute distance, is the distance between the furthest point of a section, the upper edge of a section, and the border of the regions. This variable is normalized by the width of a region. So, the highest values of d are 0.5 (the distance between the triangle’s vertex and the border in the region with higher surge coefficient), and the lowest value is -0.5 (the distance between the triangle’s vertex and the border in the region with a lower surge coefficient).

12 We define d as follows:

√

1− N−n N if P ost = 1 2 d = (2)

− − 2 N 1 √ N−n if P ost = 0

Where N is the number of sections generated, and n is the number of the section from the border. For example, Post = 0 because of the lower surge in the green region, and P ost

= 1 because of the higher surge in the red region. Moreover, the number of sections from the border, n, is on the top horizontal axis. In this figure, the number of sections generated,

N, is 5, as it can be observed as the highest n on the top. Therefore, we generate the normalized distance of a section from the border, d, for this presumptive case on the bottom horizontal axis based on Equation 2. As we noticed, the areas of all sections are equal.

Ctrl is the symbol of three control variables. The first one is the average number of online taxis in two adjacent regions. We use this control variable because each customer observes the number of online taxis around herself before requesting a ride. As a result, more online taxis may encourage customers to place their order in Tapsi, rather than another ride-hailing application. The next one is the average base price of ride requests in a section for a time period. Including this variable allows us to capture any systematic heterogeneity related to the different types of requests in different locations. Base price is defined as the price customers that face, divided by surge coeﬀicient. The last control variable is oﬀicial holidays in the Iranian calendar, so we capture different behavior of customers on holidays. The F E is the fixed effect of region and time effect or their interaction. In the end, after estimating θ by Equation1, demand elasticity is determined as follows:

θ Elasticity : ε = %∆Surge (3)

Our second approach is estimating all elasticities of different surge levels in merely one regression. In this regard, we define dummy variables for each pair of surge coeﬀicients.

13 Therefore, the regression captures fixed effects more eﬀicient because of using all records in the data. Out specification is as follows:

∑ log(RideRequest)cst = λc[constcst+θcW indows×P ostcst+βc2W indows+βc3(1−W indows)P ostcst+ c

βc4(1 − P ostcst) × dcst + βc5P ostcst × dcst + Ctrlcst] + F E + ϵcst (4)

Where λc is a dummy variable defined to a separate pair of surge coefficients from each other; therefore, the λc is 1 for the pair of surge coefficients c (e.g., 1 and 1.2) and 0 for other pairs. So, θc is the average percentage change of ride requests between two surge coefficient levels of pair c. We obtain the demand elasticity of each pair using equation 3. The advantage of equation 4 is that fixed effects are calculated for larger data than equation 1.

At last, the average of demand elasticity for a time period can be calculated by pooling all observations and use RDD as follows:

log(RideRequest)cst = constcst + εpoolW indows × P ostcst × (%∆Surgec) + β2W indows+ β3(1

− W indows)P ostcst + β4(1 − P ostcst) × dcst + β5P ostcst × dcst + Ctrlcst + F E + ϵcst

(5)

Where %∆Surgec is the percentage of change for each pair of surge coeﬀicients. In this specification, εpool is the average demand elasticity in the whole data set.

4 Results

The first step is running Equation 1 for each pair of surge coeﬀicients separately. The results of this regression are shown in Table 2 and Table 3. The dependent variable is the logarithm of

14 Ride requests in a section for a period of time. The sections are 0.02 of the closest triangles to the borders in the adjacent regions (N = 50) with surge coeﬀicients in the left column of tables.

In Table 2, Column (1) is a simple OLS regression of the dependent variable on surge coeffi-client. This regression is biased due to reverse causality between demand and surge coefficient. For instance, the demand elasticity is estimated -12.5 between surge coefficients 0.8 and 0.9. Column (2) shows the results of separate RD regressions, which were discussed in Section ??. It is evident that the RD method changed the demand elasticity in all surge levels significantly. Moreover, all results are now negative, which is reasonable for a demand curve. Adding Regional Fixed Effect and Time Effect in Column

(3) and Region-Time Interaction in Column (4) change results significantly. For instance, demand elasticity between surge 1.6 and 1.8 becomes significant at the 95% level. The demand elasticity between surge coeﬀi-client 1.8 and 2 is not statistically significant in all columns due to the lack of data (less than %0.01 of the records). Consequently, we simply remove the results of this estimation from our tables. Control variables are used in Column

(5). As customers observe some of the online taxis near their location, the first control variable is the average of online taxis in two adjacent regions in a 6-hour period of time used in calculating the dependent variable. In addition, we also control the average base prices of ride requests and oﬀicial holidays in the Iranian calendar. The results in the last column of Table 2 illustrates that the estimation of demand elasticity with the RD method is almost robust.

The Column (5) in the table shows that by 10 percent increase in the price level, the ride request decreases 3.3 percent in surge level 0.8, 7 percent in surge level 0.9, 6.6 percent in surge level 1 and 1.2, 9.6 percent in surge level 1.4, 6.4 percent in surge level 1.6. It is noteworthy to consider that the demand elasticities obtained for different surge levels do not differ significantly from each other except for surge level 0.8.

In Table 3, we estimate the specification in 1 for a 1-hour time period. All the points mentioned in the previous paragraph, such as the bias of OLS estimation, correctness by fixed

Table 2: Demand Elasticity in 6-hour Periods by Separate Regressions

Surge Coef f icient (1) (2) (3) (4) (5) 0.8-0.9 -12.50∗∗∗ -0.85∗∗∗ -0.35∗∗∗ -0.25∗∗ -0.33∗∗∗ (0.23) (0.16) (0.13) (0.12) (0.12) 0.9-1 -13.80∗∗∗ -1.04∗∗∗ -0.55∗∗∗ -0.72∗∗∗ -0.70∗∗∗ (0.15) (0.1) (0.08) (0.08) (0.08) 1-1.2 0.27∗∗∗ -0.32∗∗∗ -0.50∗∗∗ -0.64∗∗∗ -0.66∗∗∗ (0.05) (0.07) (0.06) (0.06) (0.06) 1.2-1.4 -1.04∗∗∗ -0.19 -0.49∗∗∗ -0.64∗∗∗ -0.66∗∗∗ (0.09) (0.12) (0.11) (0.10) (0.10) 1.4-1.6 0.19 -0.41∗∗ -0.73∗∗∗ -0.93∗∗∗ -0.96∗∗∗ (0.14) (0.20) (0.16) (0.16) (0.16) 1.6-1.8 1.43∗∗∗ -0.03 -0.37 -0.58∗∗ -0.64∗∗ (0.23) (0.31) (0.27) (0.27) (0.27)

Identification OLS RD RD RD RD Regional Fixed Effect No No Yes Yes Yes Time Effect No No Yes Yes Yes Region Time Interaction No No No Yes Yes Control Variables No No No No Yes

Standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Note: Equation 1 is run for adjacent regions with surge coefficient levels shown on the left side of the table separately. Each week is separated into workdays (from Saturday to Wednesday), Thursday and Friday. The dependent variable is calculated in every 6 hours (12 a.m to 6 a.m., 6 a.m. to 12 p.m., 12 p.m. to 6 p.m., and 6 p.m. to 12 a.m.) of each three parts of a week in each section. Sections are determined by the division of the closest triangle to the borders of adjacent regions into 50 parts with some areas (Figure 4). Column (1) is a simple OLS regression of the dependent variable on the surge coefficient. Column (2) is RD regression explained in Section 3. Column (3) is RD regression with fixed effects of region and effect of time. Column (4) is RD regression, which is controlled with the interaction of region and time. Column (5) has control variables such as average online taxis in two adjacent regions in the mentioned period of time, the average of the base price of ride requests in a section in the mentioned period of time, and official holidays in the Iranian calendar.

16 effects, and robustness is true about this table too. In the last column of this table, we can observe that by 10 percent increase in the price level, the ride request decreases 3 percent in surge level 0.8, 3.1 percent in surge level 0.9, 3.5 percent in surge level 1, 2.6 percent in surge level 1.2, and 5.4 percent in surge level 1.4. Therefore, the demand elasticities in

Table 3 seem generally lower than demand elasticities in Table 2. This can be due to the customers’ access to more and better substitutions rather than Tapsi taxis in the long-run.

Regression results from the specification in Equation 4, which show estimations of demand elasticities with merely one regression in a 6-hour time period, are reported in Table 4. In this regression, dummy variables are defined to separate each pair of surge coeﬀicients from others.

This method enhances the estimation of fixed effects by using all observations together. This improvement is shown in the estimation of demand elasticities in Table 4. The demand elasticity between surge coeﬀicient 0.8 and 0.9 in this table is more than twice of what was in Table 2.

Moreover, demand elasticities in other surge coeﬀicient levels are generally lower than the previous method. This method is also used for a 1-hour time span in Table 7 in Appendix. Same as Table 4, in Table 7, the estimation of demand elasticity between surge 0.8 and 0.9 increases, and other estimations decrease compared to Table 3.

Table 5 and Table 6 show the average demand elasticity of the whole data set in a 1-hour/6- hour time span using Equation 5. The interpretation of these results is that in 6-hour periods, as long-run in this context, a 10 percent increase in price leads to a 5.4 percent decrease in demand on average (average demand elasticity is -0.54). On the other hand, in 1-hour periods as short-run, a 10 percent increase in price eventuates in a 2.5 percent decrease in demand on average (average demand elasticity is -0.25). So, the average demand elasticity in the long-run is more than twice the demand elasticity estimated for the short-run. It can be inferred that the long-run elasticity is more than the short-run, which makes sense from Economics principles.

The Wald Test accepts this hypothesis at a 99% significance level.

Moreover, the number of online taxis has a positive effect on demand. However, it seems that this effect is not economically significant: if ten taxis add to the average of online taxis

Table 3: Demand Elasticity in 1-hour Periods by Separate Regressions

Surge Coef f icient (1) (2) (3) (4) (5) 0.8-0.9 -8.98∗∗∗ -0.72∗∗∗ -0.34∗∗∗ -0.25∗∗∗ -0.30∗∗∗ (0.11) (0.07) (0.07) (0.07) (0.07) 0.9-1 -5.26∗∗∗ -0.40∗∗∗ -0.23∗∗∗ -0.33∗∗∗ -0.31∗∗∗ (0.07) (0.05) (0.04) (0.05) (0.05) 1-1.2 0.01 -0.20∗∗∗ -0.26∗∗∗ -0.34∗∗∗ -0.35∗∗∗ (0.03) (0.03) (0.03) (0.04) (0.04) 1.2-1.4 -0.43∗∗∗ -0.06 -0.16∗∗ -0.25∗∗∗ -0.26∗∗∗ (0.05) (0.07) (0.06) (0.07) (0.07) 1.4-1.6 0.22∗∗∗ -0.21∗ -0.37∗∗∗ -0.52∗∗∗ -0.54∗∗∗ (0.09) (0.12) (0.11) (0.11) (0.11) 1.6-1.8 1.03∗∗∗ 0.06 -0.15 -0.21 -0.27 (0.15) (0.20) (0.19) (0.20) (0.20)

Identification OLS RD RD RD RD Regional Fixed Effect No No Yes Yes Yes Time Effect No No Yes Yes Yes Region Time Interaction No No No Yes Yes Control Variables No No No No Yes

Standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Note: Equation 1 is run for adjacent regions with surge coefficient levels shown on the left side of the table separately. Each week is separated into workdays (from Saturday to Wednesday), Thursday and Friday. The dependent variable is calculated in each hour of each three parts of a week in each section. Sections are determined by the division of the closest triangle to the borders of adjacent regions into 50 parts with some areas (Figure 4). Column (1) is a simple OLS regression of the dependent variable on the surge coefficient. Column (2) is RD regression explained in Section 3. Column (3) is RD regression with fixed effects of region and effect of time. Column (4) is RD regression, which is controlled with the interaction of region and time. Column (5) has control variables such as average online taxis in two adjacent regions in the mentioned period of time, the average of the base price of ride requests in a section in the mentioned period of time, and official holidays in the Iranian calendar.

Table 4: Demand Elasticity in 6-hour Periods by One Regression

Surge Coefficient (1) (2) (3) (4) 0.8-0.9 -.82∗∗∗ -.69∗∗∗ -.56∗∗∗ -.71∗∗∗ (0.16) (0.14) (0.14) (0.14) 0.9-1 -1.02∗∗∗ -0.66∗∗∗ -0.67∗∗∗ -0.68∗∗∗ (0.10) (0.09) (0.09) (0.09) 1-1.2 -0.32∗∗∗ -0.45∗∗∗ -0.50∗∗∗ -0.50∗∗∗ (0.07) (0.06) (0.06) (0.06) 1.2-1.4 -0.20 -0.36∗∗∗ -0.39∗∗∗ -0.41∗∗∗ (0.12) (0.11) (0.11) (0.11) 1.4-1.6 -0.42∗∗ -0.51∗∗∗ -0.59∗∗∗ -0.63∗∗∗ (0.20) (0.18) (0.18) (0.18) 1.6-1.8 -0.06 -0.31 -0.40 -0.53∗ (0.31) (0.30) (0.29) (0.29)

Regional Fixed Effect No Yes Yes Yes Time Effect No Yes Yes Yes Region-Time Interaction No No Yes Yes

Standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Note: Equation 4 is run for adjacent regions with surge coefficient levels shown on the left side of the table by just one regression. This regression has a categorical variable that separates each pair of surge coefficients from others. Each week is separated into workdays (from Saturday to Wednesday), Thursday and Friday. The dependent variable is calculated every 6 hours (12 a.m to 6 a.m., 6 a.m. to 12 p.m., 12 p.m. to 6 p.m., and 6 p.m. to 12 a.m.) of each three parts of a week in each section. Sections are determined by the division of the closest triangle to the borders of adjacent regions into 50 parts with some areas (Figure 4). Column (1) is RD regression explained in Section 3. Column (2) is RD regression with fixed effects of region and effect of time. Column (3) is RD regression, which is controlled with the interaction of region and time. Column (4) has control variables such as average online taxis in two adjacent regions in the mentioned period of time, the average of the base price of ride requests in a section in the mentioned period of time, and official holidays in the Iranian calendar.

19 In two adjacent regions, the demand in a 6-hour time span would increase by 0.06 percent on average. This is even worse for 1 hour, which is shown in Table 6: by adding ten taxis to the average of online taxis in two adjacent regions, the demand in 1-hour periods would increase

0.01 percent on average. Furthermore, the effect of base price seems economically insignificant, although it is statistically significant. The effect of oﬀicial holidays on demand is mixed. In Table 5, the demand in 6 hours time span increase in holidays. However, Table 6 estimates the negative effect of oﬀicial holidays on demand in a 1-hour time span. Thus, it can be for further works to estimate the effect of this variable on the demand curve.

To summarize the findings, we can observe that demand elasticities of different levels of surges are generally higher in the long-run than short-run. This result, which is consistent with the literature in Economics, is also true for average demand elasticity in all surge coeﬀicients. We depict the long-run and short-run demand curves in 6. As we can observe, the long-run demand curve shows higher elasticity than the short-run one. Furthermore, by drawing the upper bound of %90 confidence interval of the long-run curve and lower bound of %90 confidence interval of the short-run curve, we can observe that the long-run demand curve still has higher elasticity between surge coeﬀicients 0.8 and 1.2.

In addition, non-price determinants also have interesting effects on demand. For instance, more taxis in a region and longer drives, as we can observe variables Online

Taxis and Base Price in Tables 5 and 6, lead to more demand. In the end, although using dummy variables to estimate the demand elasticities by merely one regression may affect the power of estimation by increasing the number of variables, using more records in estimation and exploiting fixed effects more eﬀicient enhance the specification.

5 Conclusion

Nowadays, access to big data can help us study the behaviors of economic agents more accurately. This will lead economists to observe theories in practice more than before.

Table 5: Average Demand Elasticity in 6-hour Periods

Surge Coef f icient (1) (2) (3) (4) Demand Elasticity -0.461∗∗∗ -0.574∗∗∗ -0.568∗∗∗ -0.540∗∗∗ (0.013) (0.013) (0.013) (0.013) W indow 0.012∗∗∗ 0.030∗∗∗ 0.030∗∗∗ 0.030∗∗∗ (0.003) (0.003) (0.003) (0.003) (1 − W indow) × P ost -0.070∗∗∗ -0.051∗∗∗ -0.051∗∗∗ -0.055∗∗∗ (0.001) (0.001) (0.001) (0.001) P ost × d 0.206∗∗∗ 0.172∗∗∗ 0.171∗∗∗ 0.182∗∗∗ (0.005) (0.004) (0.004) (0.004) (1 − P ost) × d -0.111∗∗∗ -0.108∗∗∗ -0.108∗∗∗ -0.115∗∗∗ (0.004) (0.004) (0.004) (0.004) ∗∗∗ Online T axis 0.006 (3.23e-05) ∗∗∗ Base P rice 5.35e-06 (1.00e-07) ∗∗∗ Official Holidays 0.022 (0.003)

Regional Fixed Effect No Yes Yes Yes Time Effect No Yes Yes Yes Region-Time Interaction No No Yes Yes

Standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Note: The equation five is run by all pairs of surge coeﬀicients in one regression. Each week is separated into workdays (from Saturday to Wednesday), Thursday and Friday. The dependent variable is calculated in every 6 hours (12 a.m to 6 a.m., 6 a.m. to 12 p.m., 12 p.m. to 6 p.m., and 6 p.m. to 12 a.m.) of each three parts of a week in each section. Sections are determined by the division of the closest triangle to the borders of adjacent regions into 50 parts with the same areas (Figure 4). Column (1) is RD regression explained in Section ??. Column (2) is RD regression with fixed effects of region and effect of time. Column (3) is RD regression, which is controlled with the interaction of region and time. Column (4) has control variables such as average online taxis in two adjacent regions in the mentioned period of time, the average of the base price of ride requests in a section in the mentioned period of time, and oﬀicial holidays in the Iranian calendar.

Table 6: Average Demand Elasticity in 1-hour Periods

Surge Coef f icient (1) (2) (3) (4) Demand Elasticity -0.225∗∗∗ -0.263∗∗∗ -0.248∗∗∗ -0.246∗∗∗ (0.008) (0.008) (0.008) (0.008) W indow -0.002 0.003∗ 0.005∗∗∗ 0.003∗ (0.002) (0.002) (0.002) (0.002) (1 − W indow) × P ost -0.0473∗∗∗ -0.0402∗∗∗ -0.0374∗∗∗ -0.0397∗∗∗ (0.0007) (0.0007) (0.0007) (0.0007) P ost × d 0.151∗∗∗ 0.129∗∗∗ 0.130∗∗∗ 0.132∗∗∗ (0.003) (0.002) (0.002) (0.002) (1 − P ost) × d -0.085∗∗∗ -0.080∗∗∗ -0.083∗∗∗ -0.087∗∗∗ (0.002) (0.002) (0.002) (0.002) ∗∗∗ Online T axis 0.00154 (0.00002) ∗∗∗ Base P rice 2.50e-06 (4.86e-08) ∗∗∗ Official Holidays -0.017 (0.001)

Regional Fixed Effect No Yes Yes Yes Time Effect No Yes Yes Yes Region-Time Interaction No No Yes Yes Control Variables No No No Yes

Figure 6: Long-run and Short-run Demand Curves

Note: This figure is long-run and short-run demand curves. The blue line and red line show the long-run and short-run demand curves, respectively. Moreover, we show the upper bound of %90 confidence interval of the long-run demand curve by the green dashed line and the lower bound of %90 confidence interval of the short-run demand curve by the orange dashed line. The numbers in the horizontal axis are hypothetical. The number of ride requests for surge coefficient equal to 1, which is 100, is fixed, and we calculate other numbers based on elasticities in Table 4 and Table 7.

23 Moreover, this would be a powerful instrument to shape better policies by assessing markets precisely.

In this paper, we identify and estimate the demand elasticity of Tapsi, a ride-hailing company in Iran. The first result is that the demand elasticity is increasing due to the time period we constructed. For instance, the demand elasticity in the long-run time period is about -0.54, and in the short-run time period is about -0.25. This may be the result of access to more various options for travel as a substitute in a more extended period of time. Moreover, the competitors in the ride-hailing market may change their prices due to the demand and supply for a long time. Determining substitutes in this market, along with the parameters related to the competitors that affect the demand of a ride-hailing company, can be topics of future studies.

The effect of non-price determinants is also intuitive in this research. More online taxis lead to more demand in a region in both the long-run and short-run. Also, the base price has a positive effect on demand. Therefore, we can conclude that by an increase in the time and distance of travel, customers prefer to use ride-hailing apps more. Exploiting non-price determinants of demand in this market is an interesting case of study in the future.

Quantitatively, we estimate that by a 10 percent increase in price in the short-run, the demand would decrease about 2.5 percent on average. On the other hand, by a 10 percent increase in price in the long-run, the demand will fall about 5.4 percent. The main shortcoming of this research is the data unavailability of customers who observe the prices and do not send their requests. Access to this data could have relieved us from assuming the same potential customers on both sides of the border.

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27 Appendix A. Placeholder

Figure 7: Ride Request of Weekend in Different Surge Coeﬀicient Level

Note: The vertical axis is the normalized sum of ride requests for a level of surge coeﬀicient at the weekend. The weekend is from Thursday to Friday. We are called from 6 a.m. to 12 p.m. morning, from 12 p.m. to 6 p.m. afternoon, 6 p.m to 12 a.m night, and 12 a.m. to 6 a.m after midnight. Due to privacy policy, the sum of ride requests normalized by the highest amount in the figure.

Figure 8: Sum of Ride Requests in Each Section of Adjacent Regions with Surge Coeﬀicient 1.8 and 2

Note: The vertical axis is the normalized sum of ride requests in a section. In this figure, just adjacent regions, which one of them has surge coefficient 1.8 and the other one has surge coefficient 2, are considered. Sections are determined by the division of the closest triangle to the borders of adjacent regions into 50 parts with the same areas (Figure 4). Distance to Border is the distance of the furthest point of a section normalized by the width of a region. Sections in the regions with lower surge coefficient have negative distances, and sections in the regions with higher surge coefficient have positive distances. Due to privacy policy, the sum of ride requests normalized by the highest amount in the figure.

Figure 9: Normalized Average of Online Taxis in Different Surge Coeﬀicient Levels.

Note: The vertical axis is the normalized average of online taxis in adjacent regions in different surge coeﬀicient levels. Due to privacy policy, the sum of online taxis normalized by the highest amount in the figure.

Table 7: Demand Elasticity in 1-hour Periods by a One Regression

Surge Coef f icient (1) (2) (3) (4) 0.8-0.9 -0.71∗∗∗ -0.56∗∗∗ -0.35∗∗∗ -0.49∗∗∗ (0.07) (0.07) (0.07) (0.07) 0.9-1 -0.40∗∗∗ -0.26∗∗∗ -0.26∗∗∗ -0.31∗∗∗ (0.05) (0.04) (0.05) (0.05) 1-1.2 -0.21∗∗∗ -0.28∗∗∗ -0.32∗∗∗ -0.33∗∗∗ (0.03) (0.03) (0.03) (0.03) 1.2-1.4 -0.06 -0.13∗∗ -0.16∗∗ -0.17∗∗∗ (0.07) (0.06) (0.06) (0.06) 1.4-1.6 -0.21∗ -0.29∗∗ -0.42∗∗∗ -0.42∗∗∗ (0.12) (0.12) (0.11) (0.11) 1.6-1.8 0.05 -0.04 -0.06 -0.13 (0.20) (0.19) (0.19) (0.19) 1.8-2 -0.18 -0.14 -0.29 -0.42 (0.47) (0.47) (0.48) (0.48)

Regional Fixed Effect No Yes Yes Yes Time Effect No Yes Yes Yes Region-Time Interaction No No Yes Yes Control Variables No No No Yes

Standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Note: Equation 4 is run for adjacent regions with surge coefficient levels shown on the left side of the table by just one regression. This regression has a categorical variable that separates each pair of surge coefficients from others. Each week is separated into workdays (from Saturday to Wednesday), Thursday and Friday. The dependent variable is calculated in each hour of each three parts of a week in each section. Sections are determined by the division of the closest triangle to the borders of adjacent regions into 50 parts with the same areas (Figure 4). Column (1) is RD regression explained in Section ??. Column (2) is RD regression with fixed effects of region and effect of time. Column (3) is RD regression, which is controlled with the interaction of region and time. Column (4) has control variables such as average online taxis in two adjacent regions in the mentioned period of time, the average of the base price of ride requests in a section in the mentioned period of time, and official holidays in the Iranian calendar.