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«*This paper is a revised and shortened version of a paper with the same title, published in the Quarterly Journal of Economics, May 1997, 407-441. It ...»

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Colin Camerer, Caltech

Linda Babcock, CMU

George Loewenstein, CMU

Richard Thaler, U of Chicago

*This paper is a revised and shortened version of a paper with the same title, published in the

Quarterly Journal of Economics, May 1997, 407-441. It is published in Choices, Values, and Frames,

D.Kahneman and A. Tversky (Eds.), 2000, Cambridge: Cambridge University Press, pp. 356-370.


Theories of labor supply predict how the number of hours people work will change when their hourly wages or income change. The standard economic prediction is that a temporary increase in wages should cause people to work longer hours. This prediction is based on the assumption that workers substitute labor and leisure intertemporally, working more when wages are high and consuming more leisure when its price-- the foregone wage-- is low (e.g., Lucas and Rapping, 1969). This straightforward prediction has proven difficult to verify. Studies of many types often find little evidence of intertemporal substitution (e.g., Laisney, Pohlmeier, and Staat, 1992). However, the studies are ambiguous because when wages change, the changes are usually not clearly temporary (as the theory requires). The studies also test intertemporal substitution jointly along with auxiliary assumptions about persistence of wage shocks, formation of wage expectations, separability of utility in different time periods, etc.

An ideal test of labor supply responses to temporary wage increases requires a setting in which wages are relatively constant within a day but uncorrelated across days, and hours vary every day. In such a situation, all dynamic optimization models predict a positive relationship between wages and hours (e.g., MaCurdy [1981] p. 1074).

Such data are available for at least one group of workers-- New York City cab drivers. Drivers face wages which fluctuate on a daily basis due to demand shocks caused by weather, subway breakdowns, day-of-the-week effects, holidays, conventions, etc. Although rates per mile are set by law, on busy days drivers spend less time searching for customers and thus earn a higher hourly wage.

These wages tend to be correlated within days and uncorrelated across days (i.e., transitory).

Another advantage of studying cab drivers is that, unlike most workers, they choose the number of hours they work each day because drivers lease their cabs from a fleet for a fixed fee (or own them) and can drive as long as they like during a continuous 12-hour shift. Furthermore, most analyses of labor supply measure hours (and sometimes income) by self-reports. For cab drivers, better measures of hours and income are available from "trip sheets" the drivers fill out and from meters installed in cabs, which automatically record the fares.

Because drivers face wages which fluctuate from day to day, and can work flexible hours, the intertemporal substitution hypothesis makes a clear prediction: Drivers will work longer hours on highwage days. Behavioral economics suggests an alternative prediction (which is what motivated our research in the first place): Many drivers told us they set a target for the amount of money they wanted to earn that day, and quit when they reached the target. (The target might be a certain amount beyond the lease fee, or twice the fee.) Daily targeting makes exactly the opposite prediction of the intertemporal substitution hypothesis: When wages are high, drivers will reach their target more quickly and quit early; on low-wage days they will drive longer hours to reach the target. To test the standard intertemporal substitution hypothesis against the daily targeting alternative, we collected three samples of data on the hours and wages of drivers.

We find little evidence for positive intertemporal substitution because most of the wage elasticities-- the ratio of percentage change in hours to percentage change in wages-- are estimated to be negative. This means that drivers tend to quit earlier on high wage days drive longer on low wage days.

Elasticities for inexperienced drivers are around -1 for two of the three samples of cab drivers we used in our study. The results are robust to outliers and many different specifications. (And since our paper was originally published, in 1997, one replication using survey data from Singapore also found negative elasticities; see Chou, 2000.) There are several possible explanations for these negative elasticities, other than the daily targeting hypothesis, but most can be comfortably ruled out.

–  –  –

In this section, we use data on trip sheets of New York City cab drivers to explore the relationship between hours that drivers choose to work each day and the average daily wage. Many details are omitted here but are included in Camerer et al (1997).

A trip sheet is a sequential list of trips that a driver took on a given day. For each trip, the driver lists the time the fare was picked up and dropped off and the amount of the fare (excluding tip). Fares are set by the Taxi and Limousine Commission (TLC). For the first period we study (1988), the fares were $1.15 per trip plus $.15 for each 1/5 of a mile or 60 seconds of waiting time. For the second period we study (1990 and 1994) fares were $1.50 per trip plus $.25 each 1/5 of a mile or 75 seconds of waiting time. In both periods, a $.50 per-trip surcharge is added between 8 PM and 6 AM.

Our data consist of three samples of trip sheets. We describe each data set briefly. The first data set, TRIP, came from a set of 192 trip sheets from the spring of 1994. We borrowed and copied these from a fleet company. Fleet companies are organizations that own many cabs (each affixed with a medallion which is required to operate it legally). They rent these cabs for 12 hour shifts to drivers who, in our sample period, typically paid $76 for a day shift and $86 for a night shift. The driver also has to fill the cab up with gas at the end of the shift (costing about $15). Drivers get most of their fares by "cruising" and looking for passengers. (Unlike many cities, trips to the airport are relatively rare--around one trip per day on average). Drivers keep all the fares including tips. The driver is free to keep the cab out as long as he wants, up to the 12 hour limit. Drivers who return the cab late are fined. When a driver returns the cab the trip sheet is stamped with the number of trips that have been recorded on the cab's meter. This can then be used to determine how carefully the driver has filled in the trip sheet.

The measure of hours worked is obtained directly from the trip sheet. It is the difference between the time that the first passenger is picked up and the time that the last passenger is dropped off.

Total revenue was calculated by adding up the fares listed on the trip sheet. The average hourly wage is total revenue divided by hours worked.

Many of the trip sheets were incomplete, since the number of trips listed by the cab driver was much fewer than the number of trips recorded by the meter. Therefore, we exclude trip sheets that listed a number of trips that deviates by more than two from the metered number. This screen leaves us with 70 trip sheets from 13 drivers (eight of whom drive on more than one day in the sample).

The advantage of the TRIP data set is that we can use the trip sheets to measure the within-day autocorrelation in hourly earnings as well as differences in earning across days. Even though taxi fares are fixed by the TLC, earnings differ from day to day because of differences in how "busy" drivers are -that is, whether they spend most of the day with passengers in their cab, or have to spend a lot of time searching for passengers.

The second and third data sets of trip sheets were obtained from the TLC. The TLC periodically samples trip sheets to satisfy various demands for information about drivers and earnings (e.g., when rate increases are proposed). In these two data sets, hours and the number of driver-listed trips are obtained from the trip sheets and number of recorded trips, fares, and miles driven are obtained from the meter.

The TLC developed a screen to discard incomplete trip sheets. Because the TLC provided us with the summary measures, but not the trip sheets themselves, we are unable to create an alternative screening procedure, so we use their screened data for our analyses.

The first of the TLC data sets, TLC1, is a summary of 1723 trip sheets from 1990. This data set includes three types of drivers: Daily fleet drivers, lease drivers who lease their cabs by the week or month, and others who own a medallion-bearing cab and drive it. Most owner-drivers rent their cab out to other drivers for some shifts, imposing constraints on when and how long they can drive. Those who do not rent out their cabs can drive whenever they want.

The screened data contain 1044 trip sheets and 484 drivers (234 of whom drove more than one day in the data). The main advantages of this sample are that it includes several observations for each of many drivers and contains a range of different types of drivers.

The second TLC data set, TLC2, is a summary of 750 trip sheets, mostly from November 1-3,

1988. This data set samples owner-drivers as well as drivers from mini-fleet companies (mini-fleets usually lease cabs to drivers weekly or monthly). We discard 38 trip sheets using the TLC screen, leaving us 712 trip sheets. The main differences between TLC2 and TLC1 are that no drivers appear more than once in the data in TLC2 and the fares in TLC2 are slightly lower.

The analyses reported in the body of the paper use only the screened samples of trip sheets for all three data sets. Including the screened-out data does not make much difference.

To learn about important institutional details we also conducted a phone survey of 14 owners and managers at fleet companies which rent cabs to drivers. The average fleet in New York operates 88 cabs so the responses roughly summarize the behavior of over a thousand drivers. The survey responses help make sense of the results derived from analysis of hours and wages.

Sample Characteristics Table I presents means, medians, and standard deviations of the key variables. Cab drivers work about 9.5 hours per day, take between 28 and 30 trips, and collect almost $17 per hour in revenues (excluding tips). In the TRIP data, the average trip duration was 9.5 minutes and the average fare was $5.13. Average hourly wage is slightly lower in the TLC2 sample because of the lower rates imposed by the TLC during that time period.

In the empirical analyses below, we estimate labor supply functions using the daily number of hours as the dependent variable and the average wage the driver earned during that day as the independent variable (both in logarithmic form). The average wage is calculated by dividing daily total revenue by daily hours. This, however, assumes that the decisions drivers make regarding when to stop driving depend on the average wage during the day, rather than fluctuations of the wage rate during the day.

Fluctuations within- and across-days are important because testing for substitution requires that wages be different and roughly uncorrelated across days (and they were), and that hourly wages be correlated within a day. We used the trip-by-trip data available in the TRIP sample to construct hour-byhour measures of wages. One hour’s median wage had an autocorrelation of.493 with the previous hour’s wage, so there is indeed a strong positive correlation within each day; when a day starts out as a high wage day, it will probably continue to be a high wage day. The fleet managers surveyed weakly agreed1 with these patterns, saying the within-day autocorrelation is positive or zero (none said it was negative). Since wages are different each day, fairly stable within days, but uncorrelated across days, they are ideal for calculating the labor supply response to a temporary changes in wages.

Wage Elasticities The simple correlations between log hours and log wages are all modestly negative, -.503,

-.391, and -.269. The wage elasticity-- the percentage change in hours relative to the percentage change in wage-- can be estimated by simply regressing the logarithm of hours against the logarithm of a worker’s wage, using ordinary least squares. These regressions yield estimates between -.19 and -.62, which are generally highly significantly different from zero.

1 Fleet managers were asked whether "a driver who made more money than average in the first half of a shift" was likely to have a second half which was better than average (3 agreed), worse than average (0) or about the same as average (6). Expressing the target-income hypothesis, two fleet managers spontaneously said the second half earning were irrelevant "because drivers will quit early".

However, this standard technique can be misleading because of a potential bias caused by measurement error. Measurement error is a pervasive concern in studies of labor supply, particularly because most data are self-reports of income and hours which may be subject to memory or recording errors, or self-presentation biases. Though the data on hours come from trip sheets rather than from memory, they may still include recording errors. Unfortunately, even if errors in the measurement of hours are random, they lead to a predictable bias in the wage elasticity: Because the average hourly wage is derived by dividing daily revenue by reported hours, overstated hours will produce hours that are too high and wages that are too low. Understated hours will produce hours that are too low and wages that are too high. Measurement error in hours can therefore create spuriously negative elasticities. This bias can be eliminated if we can find a proxy for the drivers’ wage which is highly correlated with the wage, but uncorrelated with a particular driver’s measurement error in hours. (Such a proxy is called an “instrumental variable” (IV) in econometrics.) Fortunately, an excellent proxy for a driver’s wage is a measure of the wage of other drivers who are working on the same day during the same shift.2 We use these measures of other-driver wages in all the regressions that follow.

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