The researchers also simulate a city that is otherwise identical to Manhattan, but is one third as dense – that is, the same number of potential passengers is spread over a larger territory covered by the same number of potential taxis. This case predicts dramatic losses in efficiency due to lower density, but these inefficiencies are alleviated by a dispatch platform like Uber whose performance is much better in a less dense environment.

Partial coverage by a dispatcher has two effects compared with a market with no dispatcher: on the one hand, the partial dispatcher is a more effective platform for taxis and passengers that are served by it; on the other hand, segmentation of the market makes both segments thinner, with the consequence of longer average distances between a random taxi and a random passenger.

They then consider what happens in the more realistic case in which the dispatch platform only achieves partial market penetration, with the remainder of the market functioning according to the traditional street-hailing system. The results indicate that market segmentation on different platforms creates an inefficiency that is due to a reduction in the thickness of the market for both platforms.

Specifically, they consider an improved matching technology in line with the dispatch system of the Uber platform and other ride-hailing services. They first consider a polar opposite of the decentralized decision-making model in New York City by introducing a centralized dispatcher for the entire fleet. The results show relatively large gains for both sides of the market due to reductions in wait times for both passengers and taxis.

The researchers build a model of that process and then estimate it using data on every trip of the yellow cab fleet in New York City from 2011 to 2012, including the fare, tip, distance, and duration, as well as the geo-spatial start and end points of the trip. They then consider a series of hypothetical scenarios in this market, including the magnitude of ‘frictions’ in the matching process between passengers and taxis, and possible ways to reduce them.

While in textbook markets, prices serve to balance demand and supply, in the traditional taxi market, this balancing process is performed by passenger wait times and taxi search times. In contrast with prices, these service delays are wasteful. The determination of the matching process between taxis and passengers is a key feature of the analysis in this study.

Traditional taxi services are giving way to ride-hailing companies such as Uber in many cities around the world – partly as a result of new technologies that make it easier to match waiting passengers with searching drivers; and partly because new entrants have been able to avoid local price and entry regulation. A new study uses data from New York City yellow cabs before the arrival of Uber to analyze the matching process, and to simulate the effects of new entry into the market, alternative matching technologies, and different market densities.

Main article

Traditional taxi services are giving way to ride-hailing companies such as Uber and Lyft in many American cities and throughout the world. This development is partly driven by new technologies (GPS tracking through smartphones) that have reduced ‘matching frictions’ in these markets: drivers and passengers no longer need to search physically for trading partners. The new entrants have also been able to avoid local price and entry regulation.

Our study explores the importance of these two factors – technological innovation and regulatory arbitrage – in the New York City taxi market. Our study is part of an emerging body of research in economics that explores the implications of technological change in the transport sector.

Another notable study that complements ours is by Nick Buchholz, who also considers the New York context. In contrast to our work, Buchholz (2019) analyzes the dynamic neighborhood search of New York taxi drivers: he models where drivers are at each point in time, while we model how many drivers there are at each point in time.

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Price inflexibility, limited supply, and search frictions

Before Uber and Lyft were active in the city, all available medallions (licenses to operate a yellow cab) were used at some point during a typical day, indicating that entry regulations were binding. If no other frictions were present, one might therefore expect all taxis to be active at least during the daytime.

But activity is often well below capacity, highlighting the importance of understanding the labor supply decisions of taxi drivers. Labor supply cannot instantaneously adjust to market conditions, because drivers operate on a two-shift system, leading to shift indivisibilities in labor supply.

Because of regulations, this market does not feature any price flexibility. This inflexibility, together with the limited supply of medallions and the presence of matching (search) frictions, implies that regular (and predictable) patterns of variation in demand for rides during the day (for example, rush hours) lead to large fluctuations in costly delays for matches between passengers and taxis.

Drivers’ earnings and the number of active taxis vary during the day depending on how long drivers need to spend searching for their passengers. The average search time for an active taxi between dropping off a passenger and picking up the next one ranges between 5 and 16 minutes depending on the time of day.

To appreciate the magnitude of these numbers, note that the average duration of a trip is 12 minutes. We report that the fraction of time taxis drive empty ranges between 30% and 70% depending on the hour of day. Passengers also wait to obtain a taxi, and this wait time varies during the day.

While in textbook markets, prices serve to balance demand and supply, in the taxi market, this balancing process is performed by passenger wait times and taxi search times. In contrast with prices, these service delays are wasteful. Part of the idle time spent by taxis is due to the drivers’ uncertainty about where they might find a waiting passenger. The determination of the matching process between taxis and passengers is, therefore, a key feature of the analysis.

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Matching taxis and passengers in New York City

We build a model of the supply side of this market as well as the demand side, and the matching process between passengers and taxis in order to capture the key characteristics of the market described above. We then estimate the model using rich data on the New York City taxi market from 2011 and 2012. These data include every trip of the yellow cab fleet in this time span. The data entry of a trip includes the fare, tip, distance, and duration, as well as the geo-spatial start and end points of the trip.

In our model, drivers make daily entry and hourly stopping decisions. Licenses to operate a taxi (medallions for the yellow cab fleet) are scarce, so entry is only possible for inactive medallions. Hourly profits are determined by the number of matches between searching taxis and waiting passengers. Ceteris paribus, increasing the number of taxis increases the search time for a driver to encounter the next passenger and reduces expected hourly earnings.

The number of taxis is determined endogenously as part of the competitive equilibrium in this market. Stopping (exit) decisions are determined by comparing a random, terminal outside option with continuation values determined by expected hourly earnings net of a marginal cost of driving. Starting (entry) decisions result from comparing an outside option and the expected value of a shift (given expected optimal stopping behavior).

Prior studies have used the taxi market as a useful environment to study labor supply decisions because drivers have more flexibility in deciding when to stop than workers employed in firms. But we show that important rigidities are tied to the two-shift structure of operation. Our model delivers responses to earnings shocks that strongly depend on their timing during the day.

Specifically, we contrast the response to a uniform shock throughout the day to an hour-specific shock for each hour. The former results in an elasticity estimate of 1.8, which, interestingly, is not too far from the number (1.2) reported by Angrist et al (2017) from an experiment on Uber data. The latter results in estimates that vary from 0.9 to 2.6 depending on the hour, with beginning- and end-of-shift elasticities that are lower than those for the middle of the shift.

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Estimating numbers and wait times of passengers

On the demand side, we face a challenge. Although we observe the number of matches, neither the passengers’ wait time nor the number of hailing passengers are directly observable in the data. But we are able to recover these variables by using information about other observables as well as the nature of the matching process.

A crucial piece of the machinery that we use to model the matching process is a matching function. Such functions have been developed in macroeconomics research to study environments in which there are matching frictions. The matching function is a simple way to capture the difficulty that trading partners have in consuming beneficial trades, and it has been used extensively to study unemployment and the use of money.

An innovation of our study is to develop an explicit micro-founded model of the matching process. In our environment, the matching function maps the number of taxis and passengers (in addition to other observables, such as traffic speed) into the number of matches, as well as values for search time for taxis and wait time for passengers. We develop an explicit description of the geographical nature of the matching process, and we then recover, via simulation, a numerical representation of the matching function.

We can then use the information to deduce both the number of passengers as well as the wait time. In contrast to our study, empirical research on search and matching typically uses known inputs, such as the number of job vacancies and unemployed workers, as well as the observed number of matches, to estimate the parameters of an assumed matching function.

The approach of this study is to proceed in the other direction by using a specific matching process that defines a matching function. We then use the observed matches and the number of active taxis to infer the other key inputs to the matching function – that is, the number of waiting passengers and their wait time. Interestingly, the matching process that we derive displays increasing returns to scale: if the number of passengers and the number of taxis double, the number of matches more than doubles, and search time and wait time both drop.

We also find that frictions depend on the level of activity. At low levels of activity, such as during the night time, returns to scale are substantial. But for daytime levels of activity, returns to scale become essentially constant. This feature of the matching process is important for understanding the consequences of entry by rival platforms such as Uber.

With the recovered demand data in hand, we proceed to estimate a demand function in terms of the expected wait time for a taxi (recall that fares are fixed). We find that although not large, the demand elasticity implies responsiveness to wait time that is sufficient to play a significant role in evaluating the consequences of entry.

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Scenarios for market entry

By using the model, we are able to consider several hypothetical scenarios (counterfactuals) in this market.

Our first counterfactual evaluates the effects of additional entry. A 10% increase in the number of medallions leads to an increase of 8.9% in the number of active taxis. The reason for the less than proportionate increase relative to the additional entry is that drivers respond to reduced earnings by choosing shorter shifts, highlighting the importance of modeling the intensive margin on the supply side.

But the increase in activity would be a lot smaller if we did not incorporate into the model the dependence of passenger demand on expected wait times. The increase in the number of taxis leads to a reduction in wait time. This leads to an increase in the number of passengers, which in turn moderates the reduction in earnings caused by the increase in the number of medallions.

Our next set of counterfactuals concerns the magnitude of matching frictions and possible ways to reduce them. Specifically, we consider an improved matching technology in line with the dispatch system of the Uber platform and other ride-hailing services.

We first consider a polar opposite of the decentralized decision-making model in New York City by introducing a centralized dispatcher for the entire fleet. We show relatively large gains for both sides of the market due to reductions in wait times for both passengers and taxis.

Interestingly, the number of active taxis increases by almost the same amount as in the counterfactual with 10% more medallions, despite the fact that the number of medallions is left unchanged. The number of matches increases by 12%, a larger amount than the increase in the number of taxis. The difference is due to the fact that the dispatch system reduces matching frictions.

We then consider what happens in the more realistic case in which the dispatch platform only achieves partial market penetration, with the remainder of the market functioning according to the traditional street-hailing system. We show that market segmentation on different platforms creates an inefficiency that is due to a reduction in the thickness of the market for both platforms.

Partial coverage by a dispatcher has two effects compared with a market with no dispatcher: on the one hand, at the market sizes we consider, the partial dispatcher is a more effective platform for taxis and passengers that are served by it; on the other hand, segmentation of the market makes both segments thinner, with the consequence of longer average distances between a random taxi and a random passenger.

When we consider the case in which there is an equal number of potential taxis divided between dispatch and decentralized platforms, we find the second effect dominates, and therefore aggregate outcomes become worse than in the baseline case. Interestingly, the effects are quite different during the daytime relative to night hours, reflecting the importance of the initial thickness of the baseline market environment.

Finally, we consider the effects of density: we simulate a city that is otherwise identical to Manhattan, but is one third as dense; that is, the same number of potential passengers is spread over a larger territory covered by the same number of potential taxis. We find that our model predicts dramatic losses in efficiency due to lower density. But these inefficiencies are substantially alleviated by a dispatch platform whose performance is (comparatively) much better in a less dense environment.

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Implications beyond the taxi market

The insights that we gain from our counterfactuals are of broader relevance than the taxi market. Entry restrictions are related to the issue of occupational licensing, which affects a large number of workers in the United States. For example, Kleiner and Krueger (2013) report that 29% of workers are subject to licensing regulations.

Our results also speak to the effects of shift indivisibility and are therefore relevant to research on the flexibility of work arrangements. They are directly relevant for thinking about search and matching frictions, which have been greatly emphasized in labor markets and housing markets.

In this respect, our study is the first to offer an explicit simulation of the matching process as deriving from spatial matching frictions. This spatial simulation could be a useful metaphor for other markets in which matching frictions are important.

Finally, our results on competing dispatch platforms speak to the emerging body of research on network externalities and trading platforms.

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This article summarizes ‘Frictions in a Competitive, Regulated Market: Evidence from Taxis’ by Guillaume Frechette, Alessandro Lizzeri, and Tobias Salz, published in the American Economic Review in August 2019.

Guillaume Frechette and Alessandro Lizzeri are at New York University. Tobias Salz is at MIT.