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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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Experimental and field studies show that investors who own stocks that have lost value hold them longer than they hold `winning’ stocks, before selling (Shefrin and Statman, 1985; Odean, 1996; Weber and Camerer, in press). Purchase of consumer goods like orange juice fall a lot when prices are increased, compared to how much purchases rise when prices are cut (Hardie, Johnson and Fader, 1993). These tendencies can only be explained by investors and consumers isolating single decisions about stocks and products from the more general decision about the contents of their stock portfolio or shopping cart, and being unusually sensitive to losing money on the isolated stock or paying more for the isolated product.

Various psychological processes could cause drivers to use daily income targeting. For example, targeting is a simple decision rule: It requires drivers to keep track only of the income they have earned. This is computationally easier than tracking the ongoing balance of foregone leisure utility and marginal income utility (which depends on expected future wages) which is required for optimal intertemporal substitution. Targeting might just be a heuristic shortcut which makes deciding when to quit easier.

Daily targets can also help mitigate self-control problems (as many mental accounts do, see Shefrin and Thaler, 1992). There are two kinds of self-control problems drivers might face. First, driving a cab is tedious and tiring and, unlike many jobs, work hours are not rigidly set; drivers are free to quit any time they want. A daily income goal, like an author imposing a daily goal of written pages, establishes an output-based guideline of when to quit. A weekly or monthly target would leave open the temptation to quit early today and make up for today's shortfall tomorrow, or next week, and so on, in an endless cycle.

Second, in order to substitute intertemporally, drivers must save the windfall of cash they earn from driving long hours on a high-wage day so they can afford to quit early on low-wage days.

But a drive home through Manhattan with $200-$300 in cash from a good day is an obstacle course of temptations for many drivers, creating a self-control problem that is avoided by daily targeting.

Finally, daily targeting can account for the effect of experience rather naturally: Experienced drivers who have larger elasticities either learn over time to take a longer horizon (and to resist the temptations of quitting early and squandering cash from good days), or to adopt the simple rule of driving a fixed number of hours each day. Alternatively, some drivers may just lack these qualities to begin with and they quit at higher rates, selecting themselves out of the experienced-driver pool because they have less leisure and income. Either way, experienced drivers will have more positive wage elasticities.

–  –  –

Dynamic theories of labor supply predict a positive labor supply response to temporary fluctuations in wages. Previous studies have not been able to measure this elasticity precisely, and the measured sign is often negative, contradicting the theory. These analyses, however, have been plagued by a wide variety of estimation problems.

Most estimation problems are avoided by estimating wage elasticities for taxi drivers.

Drivers have flexible self-determined work hours and face wages that are highly correlated within days, but only weakly correlated between days, (so fluctuations are transitory). The fact that our analyses yield negative wage elasticities suggests that elasticities of intertemporal substitution around zero (or at least, not strongly positive) may represent a real behavioral regularity. Further support for this assertion comes from analyses of labor supply of farmers (Berg, 1961; Orde-Brown,

1946) and self-employed proprietors (Wales, 1973) who, like cab drivers, set their own hours and often have negative measured wage elasticities. These data suggest that it may be worthwhile to search for negative wage elasticities in other jobs in which workers pay a fixed fee to work, earn variable wages and set their own work hours-- such as fishing, some kinds of sales, and panhandling.

Of course, cab drivers, farmers, and small-business proprietors are not representative of the working population. Besides some demographic differences, all three groups have self-selected onto occupations with low variable wages, long hours and (in the case of farmers and cab drivers), relatively high rates of accidents and fatalities. However, there is no reason to think their planning horizons are uniquely short. Indeed, many cab drivers are recent immigrants who, by immigrating, are effectively making long-term investments in economic and educational opportunity for themselves and their children.

Because evidence of negative labor supply responses to transitory wage changes is so much at odds with conventional economic wisdom, these results should be considered a provocation for further theorizing. It may be that the cab drivers’ situation is special. Or it may be that people generally take a short horizon and set income targets, but adjust these targets flexibly in ways which can create positive responses to wage increases,5 so that myopic adjustable targeting can explain both positive elasticities observed in some studies and the negative elasticities observed in drivers.

We have two ideas for further research. A natural way to model a driver’s decision is by using a hazard model which specifies the probability that a driver will quit after driving t hours, as a function of different variables observable at t. Daily targeting predicts that quitting will depend on 5 For example, suppose the target is adjusted depending on the daily wage (e.g., a driver realizes this will be a good day and raises his target for that day). Then his behavior will be very much like that of a rational driver intertemporally substituting over time, even though the psychological basis for it is different (and does not require any foresight).

the total wages cumulated at t in a strongly nonlinear way (when the daily total reaches a target the probability of quitting rises sharply). Intertemporal substitution predicts that quitting will depend only on the average wage earned up to time t.

Another prediction derived from daily targeting is that drivers who receive an unusually big tip will go home early. Experimenters posing as passengers could actually hand out big tips (say, $50) to some drivers and measure, unobstrusively, whether those drivers quit early compared to a suitable control group. Standard theory predicts that a single large tip produces a tiny wealth effect which should not make any difference to current behavior6, so a perceptible effect of a big tip would be more evidence in favor of daily targeting and against intertemporal substitution.

Final comments As part of a broader project in behavioral economics, work like ours strives to draw discipline and inspiration for economic theorizing from other social sciences, particularly

psychology, while respecting the twin aesthetic criteria that characterize post-war economics:

models should be formal and make field-testable predictions. The goal is to demonstrate that economic models with better roots in psychology can create interesting challenges for formal modelling, and make better predictions.

6 A crucial assumption is that the tip is seen by the driver as a temporary wage increase, rather than an indicator that more large tips may come in the hours ahead (which would cause them to drive longer). Controlling for drivers’ beliefs, and observing their hours, are challenges for experimental design.

The ingredients of our project suggest a recipe for doing convincing behavioral economics “in the wild”. We derived a simple hypothesis from behavioral economics-- daily targeting-- which predicts that the sign of a regression coefficient would be the opposite of the sign predicted by standard theory, so we have a dramatic difference in two theories. We got lucky and found good data. We had an excellent proxy variable (or instrument) for a driver’s daily wage, the wage of other drivers working at the same time, which eliminated the bias caused by measuring hours with error. We also obtained variables which enabled us to rule out some alternative explanations (such as liquidity constraint and effects of breaks). And we found an effect of experience which is consistent with the hypothesis that targeting is a costly heuristic which drivers move away from with experience, in the direction of intertemporal substitution. Critics who think our findings of negative elastiticities are an econometric fluke must explain why we did not find negative elasticities for experience drivers.

Finally, a growing number of economists have begun to question the benefits of increasing sophistication in mathematical models. In game theory, theorists and experimenters have shown that simple evolutionary and adaptive models of behavior can often explain behavior better than sophisticated equilibrium concepts (e.g., John Gale, Kenneth Binmore, and Larry Samuelson, 1995;

Camerer, Ho and Chong, 2001). Experimental economists have noted how "zero intelligence" programmed agents can approximate the surprising allocative efficiency of human subjects in double auctions (Dan Gode and Shyam Sunder, 1993), and how demand and choice behavior of animals duplicates patterns seen in empirical studies of humans (John Kagel, Raymond Battalio, and Leonard Green, 1995). Our research, too, shows that relatively simple principles and models can often go a long way toward explaining and predicting economic behavior, and even outperform more sophisticated models of economic agents.

–  –  –

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Berg, Elliot J., "Backward-Sloping Labor Supply Functions in Dual Economies-- The Africa Case," Quarterly Journal of Economics, LXXV (3) (1961), 468-492.

Bowman, David, Debby Minehart, and Matthew Rabin. "Loss Aversion in a Savings Model," Journal of Economic Behavior and Organization, 38, February 1999, 155-178.

Browning, Martin, Angus Deaton, and Margaret Irish, "A Profitable Approach to Labor Supply and Commodity Demands Over the Life-Cycle," Econometrica, LIII (1995), 503-43.

Camerer, Colin F., Babcock, Linda; Loewenstein, George; and Thaler, Richard. “Labor supply of New York City cabdrivers: One day at a time,” Quarterly Journal of Economics, May 1997, 407Camerer, Colin F., Teck-Hua Ho, and Juin Kuan Chong, “Behavioral game theory: Thinking, learning and teaching", Caltech working paper. http://www.hss.caltech.edu/~camerer/camerer.html Chou, Yuan K. Testing Alternative Models of Labor Supply: Evidence from Taxi Drivers in Singapore, 2000. University of Melbourne Department of Economics, http://www.economics.unimelb.edu.au/research/768.htm Colin F. Camerer, Eric Johnson, Talia Rymon, and Sankar Sen. `Cognition and sequential bargaining over gains and losses,’ in K. Binmore, A. Kirman, and P. Tani (eds.), Frontiers of Game Theory, MIT Press, 1993.

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Gneezy, Uri and Potters, Jan, “An Experiment on Risk Taking and Evaluation Periods,” Quarterly Journal of Economics, 112, May 1997, 631-646.

Hardie, Bruce G. S., Eric J. Johnson and Peter S. Fader, "Modeling Loss Aversion and ReferenceDependence Effects on Brand Choice," Marketing Science, 12, 1993, 378-394.

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Kahneman, Daniel, Jack Knetsch, and Richard Thaler, "Experimental Tests of the Endowment Effect and the Coase Theorem," Journal of Political Economy, XCVIII (1990), 1325-1348.

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