- Email: [email protected]
The behavioral science of transportation
ARTICLE IN PRESS
Transport Policy 14 (2007) 269–274 www.elsevier.com/locate/tranpol
The behavioral science of transportation Daniel McFadden University of California, Berkeley, USA Available online 7 September 2007
One can think of transportation as a technological behemoth bedeviled by human behavior. Transportation research contributes technological and management innovations that drive this beast forward, and can also offer insights into the limits that human actors and institutions can impose on implementation of an efficient transportation system. Transportation is affected by human behavior through its consumers (drivers, riders, vehicle buyers, and shippers); through its managers and workers; and through the policy-makers and voters who determine transportation infrastructure and policy. In this presentation, I will concentrate on consumers, and add some comments on their influence on policy. However, human behavior impinges on transportation systems at many points. When I was 8 years old, a neighbor was promoted to conductor on the Southern Railroad. I asked him if he would be working on the Southern Crescent, the premier passenger train on that railroad. ‘‘Oh no,’’ he said, ‘‘if I did that, I would have to deal with people. Railroad men would rather work with freight.’’ Today, it is important for transportation workers, and transportation researchers, to recognize that there is no escape from humans and the impact of their behavior on transportation systems. One has to work with people. Transportation researchers have modeled consumer behavior at three levels. First, physical analogies have been used, such as explaining trip volumes by the gravity model for attraction between bodies, or traffic with hydrodynamic models of fluid and turbulent flow. Second, there is extensive use of the economic theory of rational behavior, in which individuals make choices to maximize their preferences. Finally, there is increasing use of models of behavior that is not exactly individually rational, drawing on findings from sociology, anthropology, cognitive psychology, and brain science. A question for Tel.: +1 510 643 8428; fax: +1 510 642 0638.
E-mail address: [email protected] 0967-070X/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.tranpol.2007.07.001
transportation researchers is what level of modeling of behavior is appropriate for their problems. One answer is that it depends on the grain of the problem. Physical analogies may be adequate for aggregate, long-term forecasting, economic optimizing models may be most satisfactory for dealing with issues such as congestion charges and fuel efficiency standards, and the insights of cognitive psychology may be needed to understand driving behavior. A second answer is that economic and behavioral sciences are progressing rapidly, and what works best in transportation research may change as time goes on. I will start with three historical examples of the role of economic models of behavior in transportation. They are the linking of demand and utility by the French bridge engineer, Dupuit (1844); the application by Ravenstein (1885) and Zipf (1946) of Newton’s law of gravitation to explain peoples’ movements; and the development by Domencich and McFadden (1976) of disaggregate travel demand forecasting models based on random utility maximization. Dupuit is one of the founding fathers of both transportation science and economic theory. He recognized that a product will be demanded up to the point where the dollar value of the marginal utility of an additional unit purchased falls to the opportunity cost of that dollar amount. He recognized that as a consequence, the area behind the demand curve, the area A+B in the diagram below, measured the relative utility of two situations expressed in dollars. This was consumer surplus, and when combined with the producer surplus, the area CA in the diagram, obtained from the net increase in revenues generated by selling the product at alternative prices, his analysis allowed a quantification of the benefits and costs of policy changes, such as setting bridge tolls and determining whether investment in a new bridge was desirable. For example, in the diagram, the net benefit of reducing tolls on an existing bridge equal the consumer surplus, areas A+B, plus the net producer surplus, areas
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CA, giving a total net social surplus from the toll reduction equal to the areas B+C. Marshall (1895), Hicks (1939), and Frisch (1926) showed that this calculation is exact if the marginal utility of money is constant and social welfare is judged using a utilitarian calculus in which the marginal value of a dollar is the same for everyone (Fig. 1). The gravity model put forward by Zipf (1946) postulates that the number of trips Tij ¼ kPiPj/Dijb between two zones i and j with populations Pi and Pj and separated by a distance Dij is proportional to the product of the populations divided by some power of the distance. This model was adopted widely for transportation planning in the 1960’s, and is still used for long-range travel forecasts. It fits aggregate trip tables fairly well, and may give reasonable forecasts of response to policies that affect zones in a homogeneous way and can be quantified in the generalized distance Dij, such as a change in the gasoline tax. However, the model lacks sensitivity to policy changes that have a heterogeneous impact within zones or interact with sociodemographics, such as changes in bus routes that affect people differently depending on their location relative to bus stops and the circumstances of their travel needs and car availability. Also, the model is not easy to reconcile with individual transport choice data or decision models. My last historical example is the random utility model of discrete choice, applied by Domencich and McFadden in 1972 to construct a model of urban trip generation, destination, scheduling, and mode choice. The premise of this model is that individuals obtain utility from activities that require travel, and make travel choices to maximize utility. Different people have different tastes, and this is captured by making utility random. Observed discrete choices are then used to estimate the distribution of utility and its dependence on transportation variables. This analysis was implemented with special assumptions on utility structure that produce multinomial logit and nested logit models for trip generation, timing, destination, and
mode. These particular models have been widely used in transportation and many other applied fields, so that transportation researchers encounter them regularly. However, applied researchers may be less aware that the logit models used in everyday practice are quite special cases of a general approach to modeling behavior that can be articulated and adjusted to the grain of policy applications ranging from very detailed analysis of household activities to broad questions of transportation system investment and operation. In their early days, disaggregate behavioral travel demand models were met with skepticism, and in the Urban Travel Demand Forecasting Project that I organized at Berkeley in 1972, I set out to give the approach an acid test. At that time, BART was under construction, and scheduled to open in 1975. I collected data on a sample of 631 commuters in 1973, and based on detailed construction of the attributes of alternative transportation choices, estimated a multinomial logit model of mode choice. I then used this model to predict mode choices in the sample in 1975 following the opening of BART. The columns of the Table 1 below are the choices predicted for 1975, based on 1973 pre-BART behavior, and the rows are the observed choices in 1975. The cell counts are sums of the predicted probabilities for the alternative for those observed in a certain outcome. Thus, 15.2 in the northeast corner is the sum of the predicted probabilities of taking BART for those actually observed to drive alone. The diagonals in the Table 1 are the cases where the forecast was exactly right— 53% successful predictions. The model predicted that 6.3% of commute trips in 1975 would be on BART. This was well below the official prediction at the time, which was a 15% BART share, but it turned out to be a very good prediction of the actual BART share of 6.2%. There was a element of luck in this, as our forecast had a standard error of 72 percentage points, and not all of our detailed forecasts were as accurate, but the test illustrated the power of making efficient use of individual choice data and describing carefully the attributes of the choices that individuals face. By the way, BART did not appreciate our low estimate of ridership, and to this day has never Table 1 Prediction success table, work trips (pre-BART model and post-BART choices) Post-BART actual choices in 1975
Pre-BART predicted choices from 1973 Auto alone
Fig. 1. . Dupuit’s analysis of bridge tolls.
Auto alone Carpool Bus BART
255.1 74.7 12.8 9.8
Total Predicted share Actual share
352.5 55.8% 59.9%
Carpool
79.1 37.7 16.5 11.1 144.5 22.9% 21.7%
Bus
BART
28.5 15.7 42.9 6.9
15.2 8.9 4.7 11.2
94.0 14.9% 12.2%
40.0 6.3% 6.2%
Total
378 137 77 39 631 100% 100%
ARTICLE IN PRESS D. McFadden / Transport Policy 14 (2007) 269–274
adopted or acknowledged disaggregate travel demand modeling as transportation policy tool. One of the current lively topics in transportation policy is the use of congestion pricing, particularly the use of toll rings and high-occupancy toll (HOT) lanes, and the use of taxes on gasoline or carbon to reduce oil dependence and greenhouse gases. I will outline a simple economic analysis of ring tolls that builds on the random utility model. Consider a simple general equilibrium model of an urban area with consumers indexed n ¼ 1, y, N who have riskneutral indirect utility functions of Gorman (1961) polar form: un ¼ V ðyn þ sn ; p; c; n Þ AðpÞ1 fyn þ sn Bn ðpÞ minð0; c þ ðn mÞ=lg,
ð1Þ
where yn is income, sn is a net subsidy, p is a finitedimensional vector of prices of private market goods, Bn(p) is a committed expenditure on private goods that is heterogeneous across consumers, A(p) is a price index, c is the generalized cost of travel across a ring and into a city center, including out-of-pocket costs and tolls and the value of time, en is a standard normal disturbance that reflects individual distaste for travel, and l and m are positive parameters. This consumer will travel into the ring if c+(enm)/l is negative, and an indicator for travel, given by Roys identity, is d n ¼ 1ðlc m þ n o0Þ ¼ ðqV =qcÞ=ðqV =qyn Þ. The share of the population that travels into the ring is then given by a cumulative normal, or probit, evaluated at an argument that is decreasing in the generalized travel cost c: S ¼ Probðlc m þ n o0Þ ¼ Fðm lcÞ.
(2)
To complete the model, assume that generalized cost rises with the ring toll t, declines with infrastructure investment k, and through the effects of congestion, rises with the share S traveling into the ring. For simplicity, assume generalized cost is linear in these factors: c ¼ t þ a þ bS gk ¼ t þ a þ bFðm lcÞ gk,
ð3Þ
where a, b, g are non-negative parameters. Balance in equilibrium requires that the average net subsidy equal toll collections less investment: s ¼ Esn ¼ tS k ¼ tFðm lcÞ k.
(4)
Use the property of the standard normal that j0 (e) ¼ ej(e), and hence that E minð0; c þ ðn mÞ=lÞ Z ¼ ðlc m þ ÞjðÞd=l omlc
¼ ½ðm lcÞFðm lcÞ þ jðm lcÞ=l. A related result is q½ðm lcÞFðm lcÞ þ jðm lcÞ=qc ¼ lFðm lcÞ.
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A consequence of the model of individual preferences is an exact expression for utilitarian expected welfare per capita, depending on net tax x and on generalized cost c: w ¼ AðpÞ1 fy þ s B ðpÞ þ ½ðm lcÞFðm lcÞ þ jðm lcÞ=lg, ¼ AðpÞ1 fy B ðpÞ k þ tFðm lcÞ þ ½ðm lcÞFðm lcÞ þ jðm lcÞ=lg,
ð5Þ
where y* is per capita income, and B* ¼ EBn. The optimal toll and optimal level of investment in infrastructure are obtained by maximizing (5) in t and k, taking into account from (3) of the impact t and k on c: qc=qt ¼ ½1 þ lbjðm lcÞ1 and qc=qk ¼ g½1 þ lbjðm lcÞ1 . Then, qw=qt ¼ AðpÞ1 fFðm lcÞ ltjðm lcÞ ½1 þ lbjðm lcÞ1 Fðm lcÞ ½1 þ lbjðm lcÞ1 g, ¼ AðpÞ1 ½1 þ lbjðm lcÞ1 ljðm lcÞ fbFðm lcÞ tg. The optimal toll satisfies t ¼ bF(mlc) ¼ bS. It is zero when congestion externalities are zero (b ¼ 0), and in general, it charges each traveler the incremental cost imposed on others due to this traveler’s contribution to congestion. Similarly, qw=qk ¼ AðpÞ1 f1 þ gltjðm lcÞ½1 þ lbjðm lcÞ1 þ gFðm lcÞ½1 þ lbjðm lcÞ1 g, ¼ AðpÞ1 ½1 þ lbjðm lcÞ1 f1 lðb gtÞjðm lcÞ þ gFðm lcÞg. When the toll is set optimally to t ¼ bF(mlc), this reduces to qw=qk ¼ AðpÞ1 ½1 þ lbjðm lcÞ1 ð1 þ lbjðm lcÞÞðgFðm lcÞ 1Þg. Then, optimal infrastructure investment satisfies gF(mlc) ¼ 1, so that the dollar value of the reduction in generalized cost for travelers equals the unit cost of the incremental investment. If the toll is above optimal, equaling t ¼ bF(mlc)+D with D40, then qw=qk ¼ AðpÞ1 ½1 þ lbjðm lcÞ1 ð1 þ lbjðm lcÞÞðgFðm lcÞ 1Þ þ lgDjðm lcÞg, and investment higher than the jointly optimal level results. The reverse is true when the toll is below the optimal level. These are the textbook results that an optimal congestion charge equals the added cost that a traveler imposes on other travelers due to his contribution to congestion, and
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infrastructure investment should rise to the point that a dollar of investment reduces aggregate generalized cost to travelers by a dollar, with an additional adjustment if congestion tolls are not set optimally and investment is also used for second-best mitigation. For further review of this theory, see Diamond and Mirrlees (1971), Atkinson and Stern (1974), Small (1983), Dixit (1985), King (1986), Mayeres and Proost (1997), McFadden (1999, 2004). My reason for going through this simple toll ring model is that it demonstrates how the economic tools of random utility, and general equilibrium welfare and balance, can be used to carry through a standard congesting pricing exercise, and obtain the optimal toll in a model that can be fitted using data on individual trips. Here is a numerical example based on stylized data in which generalized cost absent a toll is $15 per day under uncongested conditions, and $45 per day with maximum congestion. In the absence of a toll, 30% of people travel into the ring, and their elasticity of demand for trips with respect to generalized cost is 0.2. The optimal ring toll, calculated by maximizing the previous formula for per capita welfare, is $8.42, leading to a 6% reduction of trips into the ring. Of course, this toy calculation does not account for heterogeneity in tastes and circumstances. A realistic calculation for, say, Manhattan, would require a lot more detail. Nevertheless, the example illustrates several points. First, it implements Dupuit’s (1844) program for benefit–cost analysis of transportation policy, and corresponds precisely to the case where exact, unambiguous measurement of consumer welfare is possible. Second, it builds on individual random utility foundations, and facilitates efficient fitting from individual travel data. Third, it is a template that can be expanded to analyze a wide variety of transportation policy alternatives. Ring tolls and other congestion charges should be ubiquitous. Economic efficiency requires that resources be priced at their marginal cost, including marginal congestion cost. The cost burden of collecting tolls is a problem historically, but current technology, using transponders, GPS, cell technology, and satellites, can meter vehicle location on specific roadways and lanes at specific times, and communicate and charge articulated tolls inexpensively and practically. Tolls can be revenue-neutral, or net revenues can underwrite worthwhile public transit and infrastructure projects. Because congestion is a frictional loss of economic efficiency, pricing it correctly frees resources that can in principle be reallocated so that everyone gains, a ‘‘win-win’’ situation. Finally, where congestion charges have been implemented, the Bergen, London, and Stockholm ring tolls, and HOT lanes in various locations, they seem to work well. Further, gasoline and carbon taxes can work to lower vehicle use, can be combined with redistribution to be equitable, and are more efficient economically than CAFE´ standards. Given that pricing transportation services makes so much economic sense, why is consumer resistance to pricing so strong? In the UK in 2007, a BBC poll found
that 74% of the adult population oppose road pricing. An anti-pricing petition sponsored by Peter Roberts was signed by 6% of all the drivers in the UK Why? Three common arguments are that the toll revenues will be used inefficiently, that tolls are regressive and inequitable, and that the individual consumer is more likely to lose than to gain by obtaining transportation services in a market. The first of these, inefficient use of toll revenues, is a real problem that can be addressed either by making the toll system revenue-neutral, or by earmarking the revenues for projects that voters want. Issues of regressivity need to be addressed by adjusting other taxes and subsidies to avoid shifting the standard of living distribution. However, some equity realignments are necessary because existing uncompensated congestion costs are inequitable, and heavy contributors to congestion need to see the stick in order to get the adjustments in behavior needed. I will now turn my attention to the third source of consumer resistance. I will expand on fear of markets as an explanation for the difficulty of getting consumers to understand and accept market pricing of transportation services. We are challenged by market choices. In the words of a Dutch proverb, ‘‘He who has choice has trouble’’. Psychologists use the term ‘‘agoraphobia’’ for a psychosis that means, literally, fear of the marketplace, and is characterized by fear of leaving a safe place, fear of being in situations from which escape might be difficult or embarrassing; fear of losing control in a public place such as a restaurant or shopping mall. Most consumers display some degree of agoraphobia in their attitudes toward markets and market solutions to problems of resource allocation, distrusting markets and their own decisionmaking ability. Markets present risks, of three types. Market risks are shifts in product attributes, uncertainty about prices and supply, and ambiguity surrounding products and information that the market provides. Personal risks are the mistakes an individual can make in choices, due to memory lapses, errors of perception and calculation, and mistaking one’s own tastes. Social risks are the stresses of interactions between people under the contentious conditions of market transactions, including the stress of information gathering and search, bargaining, pressures from social norms, accountability for choices, and possible social sanctions, including the potential embarrassment of performing less well than one’s peers. Markets punish consumer inconsistencies. However, markets are inconsistent teachers, and provide no road map to success. They thrive on consumer failures, and are quick to exploit them. As a result, consumers learn to be defensive, refusing trading opportunities that are of uncertain merit or are ambiguous. The result is a conservative bias toward the status quo: ‘‘The devil you know is better than the devil you don’t’’. Critically, market punishment of poor decision-making breeds paranoia and agoraphobia—I perceive my losses as outweighing my
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gains, and blame this on everyone but myself: the greed of corporations, conspiracy, fraud, corrupt politicians, inside information. I vote against market solutions that require me to make choices, even if rationally I concede that they are actuarially fair on paper, and instead vote for the status quo, or alternatives that restrict choice. To understand how market and personal risks affect consumers’ attitudes toward choice and toward markets, turn to cognitive psychology and brain science. Consumers show asymmetries, with losses from their reference points looming larger than gains, and future, uncertain, or ambiguous events heavily discounted relative to the present. For example, a majority of drivers queued on a congested highway have the perception that other lanes move more quickly than their own. This is caused by loss aversion, the fact that falling behind the truck one lane over is more noticeable and more painful than the satisfaction from gaining equivalent ground. This leads drivers, and consumers more generally, to mistrust proposed changes from their status quo, and to fear markets that confront them with these choices. Brain science establishes that these phenomena are substantially a result of how our brains are wired, how we parse and process information, and how we experience pleasure and pain. We are products of an evolutionary history that leads us to handle threats at a more primitive level than we handle most rewards. Communication and reconciliation between different brain levels is incomplete. Trade arose early in our evolution, and perhaps because of the trust and communication skills it requires, it may be substantially responsible for making us what we are. One result is that trade stimulates the brain at a surprisingly primitive level, and involves a significant emotional component. A picturesque but true characterization is that shopping and sex share the same neurotransmitters and receptors. Trade is a contest, involving its own stresses, pleasures, and pains. Trust is an essential element in commercial transactions, and again there is a long evolutionary history linking trade and trust. Ernst Fehr and his colleagues in Zurich find that giving subjects the peptide oxytocin that is associated with maternal bonding leads them to be more trusting in economic transactions. Humans are on a hedonic treadmill, quickly habituating to homeostasis and forming reference points, and experiencing particularly acute pain from losses relative to these reference points. Personal and social risks are additional reasons to mistrust markets. Consumers may legitimately fear that lapses in memory, reasoning, or understanding of the choice process and their own goals will put them at a disadvantage relative to skilled traders. Further, trade involves dealing with adversaries, and for trading outcomes, facing comparisons with peers, accountability, and approval. Herb Simon said that a wealth of information creates a poverty of attention. Douglas and Wildavsky point out that humans internalize social pressures and delegate their decision-making processes.
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People make interpersonal comparisons, judging the desirability of options from the apparent satisfaction and advice of others. While personal experience determines the utility of familiar objects, our primary sources of information on novel objects comes from observations on others, and their advice. The consequence is that discussions and votes on transportation projects may be shaped by a great deal of imitative behavior. Then, a small but loud core of opponents of congestion pricing or other transportation market solutions may have impacts well beyond their numbers. Affiliation with social networks, limiting choice by accountability to network norms, can be an efficient decision-making strategy for individuals. An example is the pellaton, a tightly packed groups of riders in bicycle racing that creates an energy-saving, choice-limiting environment. I consider the pellaton an instructive model of consumer choice behavior more generally, with most consumers associating voluntarily with groups that guide and limit their choices, a device that conserves scarce attention time and provides, through a sort of ‘‘hive intelligence’’, outcomes that are usually satisfactory and certainly socially acceptable. There will be occasional break-aways, with new pellatons forming, when some participants see a clearly preferred alternative to the old pellaton’s choices, but most of the time staying with the pellaton is defensive and protective. I suggest as a research problem that understanding the behavior of pellaton members and the effectiveness of the pellaton as a collective decision-making group would be useful for understanding of how social welfare is influenced by voluntary affiliations, and how consumers pack together when they drive, ride transit, or vote on transportation projects. Perhaps by understanding the formation and stability of anti-tax, anti-road-pricing pellatons, one might see how to encourage pellatons that support efficient market solutions to congestion in transportation. Summarizing, economic and behavioral science provides insights and models that are useful at the many points of human interaction in transportation systems. The behavioral science useful for transportation research depends on the grain of transportation policies studied, and needs to be updated regularly with the progress of economic and behavioral science. Consumers are likely to resist market solutions for transportation problems, and careful education and framing may be needed to overcome agoraphobia. Finally, transportation research can benefit from continuing close connections to economic and behavioral science, and active pursuit of new ideas and findings from the behavioral sciences that can improve your ability to understand and predict the effects of human behavior in transportation systems. References Atkinson, A., Stern, N., 1974. Pigou, taxation and public goods. Review of Economic Studies 41 (1), 119–128.
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Diamond, P., Mirrlees, J., 1971. Optimal taxation and public production. American Economic Review 61, 8–27, 261–278. Dixit, A., 1985. Tax policy in open economies. In: Auerbach, A., Feldstein, M. (Eds.), Handbook of Public Economics, vol. 1. NorthHolland, New York and Oxford, pp. 313–374. Domencich, T., McFadden, D., 1976. Urban Travel Demand: A Behavioral Analysis. North-Holland, Amsterdam. Dupuit, J., 1844. On the measurement of the utility of public works. Annales des ponts et chausse´es. (English translation, International Economic Review, 1952). Frisch, R., 1926. Sur un Probleme of Economie Pure. Norsk Matematisk Forenings SSkrifter, 16, 1–40; Translation in J. Chipman, L. Hurwicz, M. Richter, H. Sonnenschein (Eds.), Preferences, Utility, and Demand, Harcourt, New York. Gorman, W., 1961. On a class of preference fields. Metroeconomica 13, 53–56. Hicks, J., 1939. Value and Capital. Clarendon Press, Oxford. King, M., 1986. A Pigovian rule for the optimum provision of public goods. Journal of Public Economics 30 (3), 273–291.
Marshall, A., 1895. Principles of Economics. Macmillan, London, New York. Mayeres, I., Proost, S., 1997. Optimal tax and public investment rules for congestion type of externalities. Scandinavian Journal of Economics 99 (2), 261–279. McFadden, D., 1999. Computing willingness-to-pay in random utility models. In: Moore, J., Riezman, R., Melvin, J. (Eds.), Trade, Theory and Econometrics: Essays in Honour of John S. Chipman. Routledge, London. McFadden, D., 2004. Welfare economics at the extensive margin: giving Gorman Polar consumers some latitude. Working Paper, June 2004. Ravenstein, E., 1885. The laws of migration. Journal of the Royal Statistical Society 48, 167–227 and 52, 241–301. Small, K.A., 1983. The incidence of congestion tolls on urban highways. Journal of Urban Economics 13, 90–111. Zipf, G., 1946. The P1P2/D hypothesis: on the intercity movement of persons. American Sociological Review 11, 677–686.
Transport Policy 14 (2007) 269–274 www.elsevier.com/locate/tranpol
The behavioral science of transportation Daniel McFadden University of California, Berkeley, USA Available online 7 September 2007
One can think of transportation as a technological behemoth bedeviled by human behavior. Transportation research contributes technological and management innovations that drive this beast forward, and can also offer insights into the limits that human actors and institutions can impose on implementation of an efficient transportation system. Transportation is affected by human behavior through its consumers (drivers, riders, vehicle buyers, and shippers); through its managers and workers; and through the policy-makers and voters who determine transportation infrastructure and policy. In this presentation, I will concentrate on consumers, and add some comments on their influence on policy. However, human behavior impinges on transportation systems at many points. When I was 8 years old, a neighbor was promoted to conductor on the Southern Railroad. I asked him if he would be working on the Southern Crescent, the premier passenger train on that railroad. ‘‘Oh no,’’ he said, ‘‘if I did that, I would have to deal with people. Railroad men would rather work with freight.’’ Today, it is important for transportation workers, and transportation researchers, to recognize that there is no escape from humans and the impact of their behavior on transportation systems. One has to work with people. Transportation researchers have modeled consumer behavior at three levels. First, physical analogies have been used, such as explaining trip volumes by the gravity model for attraction between bodies, or traffic with hydrodynamic models of fluid and turbulent flow. Second, there is extensive use of the economic theory of rational behavior, in which individuals make choices to maximize their preferences. Finally, there is increasing use of models of behavior that is not exactly individually rational, drawing on findings from sociology, anthropology, cognitive psychology, and brain science. A question for Tel.: +1 510 643 8428; fax: +1 510 642 0638.
E-mail address: [email protected] 0967-070X/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.tranpol.2007.07.001
transportation researchers is what level of modeling of behavior is appropriate for their problems. One answer is that it depends on the grain of the problem. Physical analogies may be adequate for aggregate, long-term forecasting, economic optimizing models may be most satisfactory for dealing with issues such as congestion charges and fuel efficiency standards, and the insights of cognitive psychology may be needed to understand driving behavior. A second answer is that economic and behavioral sciences are progressing rapidly, and what works best in transportation research may change as time goes on. I will start with three historical examples of the role of economic models of behavior in transportation. They are the linking of demand and utility by the French bridge engineer, Dupuit (1844); the application by Ravenstein (1885) and Zipf (1946) of Newton’s law of gravitation to explain peoples’ movements; and the development by Domencich and McFadden (1976) of disaggregate travel demand forecasting models based on random utility maximization. Dupuit is one of the founding fathers of both transportation science and economic theory. He recognized that a product will be demanded up to the point where the dollar value of the marginal utility of an additional unit purchased falls to the opportunity cost of that dollar amount. He recognized that as a consequence, the area behind the demand curve, the area A+B in the diagram below, measured the relative utility of two situations expressed in dollars. This was consumer surplus, and when combined with the producer surplus, the area CA in the diagram, obtained from the net increase in revenues generated by selling the product at alternative prices, his analysis allowed a quantification of the benefits and costs of policy changes, such as setting bridge tolls and determining whether investment in a new bridge was desirable. For example, in the diagram, the net benefit of reducing tolls on an existing bridge equal the consumer surplus, areas A+B, plus the net producer surplus, areas
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CA, giving a total net social surplus from the toll reduction equal to the areas B+C. Marshall (1895), Hicks (1939), and Frisch (1926) showed that this calculation is exact if the marginal utility of money is constant and social welfare is judged using a utilitarian calculus in which the marginal value of a dollar is the same for everyone (Fig. 1). The gravity model put forward by Zipf (1946) postulates that the number of trips Tij ¼ kPiPj/Dijb between two zones i and j with populations Pi and Pj and separated by a distance Dij is proportional to the product of the populations divided by some power of the distance. This model was adopted widely for transportation planning in the 1960’s, and is still used for long-range travel forecasts. It fits aggregate trip tables fairly well, and may give reasonable forecasts of response to policies that affect zones in a homogeneous way and can be quantified in the generalized distance Dij, such as a change in the gasoline tax. However, the model lacks sensitivity to policy changes that have a heterogeneous impact within zones or interact with sociodemographics, such as changes in bus routes that affect people differently depending on their location relative to bus stops and the circumstances of their travel needs and car availability. Also, the model is not easy to reconcile with individual transport choice data or decision models. My last historical example is the random utility model of discrete choice, applied by Domencich and McFadden in 1972 to construct a model of urban trip generation, destination, scheduling, and mode choice. The premise of this model is that individuals obtain utility from activities that require travel, and make travel choices to maximize utility. Different people have different tastes, and this is captured by making utility random. Observed discrete choices are then used to estimate the distribution of utility and its dependence on transportation variables. This analysis was implemented with special assumptions on utility structure that produce multinomial logit and nested logit models for trip generation, timing, destination, and
mode. These particular models have been widely used in transportation and many other applied fields, so that transportation researchers encounter them regularly. However, applied researchers may be less aware that the logit models used in everyday practice are quite special cases of a general approach to modeling behavior that can be articulated and adjusted to the grain of policy applications ranging from very detailed analysis of household activities to broad questions of transportation system investment and operation. In their early days, disaggregate behavioral travel demand models were met with skepticism, and in the Urban Travel Demand Forecasting Project that I organized at Berkeley in 1972, I set out to give the approach an acid test. At that time, BART was under construction, and scheduled to open in 1975. I collected data on a sample of 631 commuters in 1973, and based on detailed construction of the attributes of alternative transportation choices, estimated a multinomial logit model of mode choice. I then used this model to predict mode choices in the sample in 1975 following the opening of BART. The columns of the Table 1 below are the choices predicted for 1975, based on 1973 pre-BART behavior, and the rows are the observed choices in 1975. The cell counts are sums of the predicted probabilities for the alternative for those observed in a certain outcome. Thus, 15.2 in the northeast corner is the sum of the predicted probabilities of taking BART for those actually observed to drive alone. The diagonals in the Table 1 are the cases where the forecast was exactly right— 53% successful predictions. The model predicted that 6.3% of commute trips in 1975 would be on BART. This was well below the official prediction at the time, which was a 15% BART share, but it turned out to be a very good prediction of the actual BART share of 6.2%. There was a element of luck in this, as our forecast had a standard error of 72 percentage points, and not all of our detailed forecasts were as accurate, but the test illustrated the power of making efficient use of individual choice data and describing carefully the attributes of the choices that individuals face. By the way, BART did not appreciate our low estimate of ridership, and to this day has never Table 1 Prediction success table, work trips (pre-BART model and post-BART choices) Post-BART actual choices in 1975
Pre-BART predicted choices from 1973 Auto alone
Fig. 1. . Dupuit’s analysis of bridge tolls.
Auto alone Carpool Bus BART
255.1 74.7 12.8 9.8
Total Predicted share Actual share
352.5 55.8% 59.9%
Carpool
79.1 37.7 16.5 11.1 144.5 22.9% 21.7%
Bus
BART
28.5 15.7 42.9 6.9
15.2 8.9 4.7 11.2
94.0 14.9% 12.2%
40.0 6.3% 6.2%
Total
378 137 77 39 631 100% 100%
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adopted or acknowledged disaggregate travel demand modeling as transportation policy tool. One of the current lively topics in transportation policy is the use of congestion pricing, particularly the use of toll rings and high-occupancy toll (HOT) lanes, and the use of taxes on gasoline or carbon to reduce oil dependence and greenhouse gases. I will outline a simple economic analysis of ring tolls that builds on the random utility model. Consider a simple general equilibrium model of an urban area with consumers indexed n ¼ 1, y, N who have riskneutral indirect utility functions of Gorman (1961) polar form: un ¼ V ðyn þ sn ; p; c; n Þ AðpÞ1 fyn þ sn Bn ðpÞ minð0; c þ ðn mÞ=lg,
ð1Þ
where yn is income, sn is a net subsidy, p is a finitedimensional vector of prices of private market goods, Bn(p) is a committed expenditure on private goods that is heterogeneous across consumers, A(p) is a price index, c is the generalized cost of travel across a ring and into a city center, including out-of-pocket costs and tolls and the value of time, en is a standard normal disturbance that reflects individual distaste for travel, and l and m are positive parameters. This consumer will travel into the ring if c+(enm)/l is negative, and an indicator for travel, given by Roys identity, is d n ¼ 1ðlc m þ n o0Þ ¼ ðqV =qcÞ=ðqV =qyn Þ. The share of the population that travels into the ring is then given by a cumulative normal, or probit, evaluated at an argument that is decreasing in the generalized travel cost c: S ¼ Probðlc m þ n o0Þ ¼ Fðm lcÞ.
(2)
To complete the model, assume that generalized cost rises with the ring toll t, declines with infrastructure investment k, and through the effects of congestion, rises with the share S traveling into the ring. For simplicity, assume generalized cost is linear in these factors: c ¼ t þ a þ bS gk ¼ t þ a þ bFðm lcÞ gk,
ð3Þ
where a, b, g are non-negative parameters. Balance in equilibrium requires that the average net subsidy equal toll collections less investment: s ¼ Esn ¼ tS k ¼ tFðm lcÞ k.
(4)
Use the property of the standard normal that j0 (e) ¼ ej(e), and hence that E minð0; c þ ðn mÞ=lÞ Z ¼ ðlc m þ ÞjðÞd=l omlc
¼ ½ðm lcÞFðm lcÞ þ jðm lcÞ=l. A related result is q½ðm lcÞFðm lcÞ þ jðm lcÞ=qc ¼ lFðm lcÞ.
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A consequence of the model of individual preferences is an exact expression for utilitarian expected welfare per capita, depending on net tax x and on generalized cost c: w ¼ AðpÞ1 fy þ s B ðpÞ þ ½ðm lcÞFðm lcÞ þ jðm lcÞ=lg, ¼ AðpÞ1 fy B ðpÞ k þ tFðm lcÞ þ ½ðm lcÞFðm lcÞ þ jðm lcÞ=lg,
ð5Þ
where y* is per capita income, and B* ¼ EBn. The optimal toll and optimal level of investment in infrastructure are obtained by maximizing (5) in t and k, taking into account from (3) of the impact t and k on c: qc=qt ¼ ½1 þ lbjðm lcÞ1 and qc=qk ¼ g½1 þ lbjðm lcÞ1 . Then, qw=qt ¼ AðpÞ1 fFðm lcÞ ltjðm lcÞ ½1 þ lbjðm lcÞ1 Fðm lcÞ ½1 þ lbjðm lcÞ1 g, ¼ AðpÞ1 ½1 þ lbjðm lcÞ1 ljðm lcÞ fbFðm lcÞ tg. The optimal toll satisfies t ¼ bF(mlc) ¼ bS. It is zero when congestion externalities are zero (b ¼ 0), and in general, it charges each traveler the incremental cost imposed on others due to this traveler’s contribution to congestion. Similarly, qw=qk ¼ AðpÞ1 f1 þ gltjðm lcÞ½1 þ lbjðm lcÞ1 þ gFðm lcÞ½1 þ lbjðm lcÞ1 g, ¼ AðpÞ1 ½1 þ lbjðm lcÞ1 f1 lðb gtÞjðm lcÞ þ gFðm lcÞg. When the toll is set optimally to t ¼ bF(mlc), this reduces to qw=qk ¼ AðpÞ1 ½1 þ lbjðm lcÞ1 ð1 þ lbjðm lcÞÞðgFðm lcÞ 1Þg. Then, optimal infrastructure investment satisfies gF(mlc) ¼ 1, so that the dollar value of the reduction in generalized cost for travelers equals the unit cost of the incremental investment. If the toll is above optimal, equaling t ¼ bF(mlc)+D with D40, then qw=qk ¼ AðpÞ1 ½1 þ lbjðm lcÞ1 ð1 þ lbjðm lcÞÞðgFðm lcÞ 1Þ þ lgDjðm lcÞg, and investment higher than the jointly optimal level results. The reverse is true when the toll is below the optimal level. These are the textbook results that an optimal congestion charge equals the added cost that a traveler imposes on other travelers due to his contribution to congestion, and
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infrastructure investment should rise to the point that a dollar of investment reduces aggregate generalized cost to travelers by a dollar, with an additional adjustment if congestion tolls are not set optimally and investment is also used for second-best mitigation. For further review of this theory, see Diamond and Mirrlees (1971), Atkinson and Stern (1974), Small (1983), Dixit (1985), King (1986), Mayeres and Proost (1997), McFadden (1999, 2004). My reason for going through this simple toll ring model is that it demonstrates how the economic tools of random utility, and general equilibrium welfare and balance, can be used to carry through a standard congesting pricing exercise, and obtain the optimal toll in a model that can be fitted using data on individual trips. Here is a numerical example based on stylized data in which generalized cost absent a toll is $15 per day under uncongested conditions, and $45 per day with maximum congestion. In the absence of a toll, 30% of people travel into the ring, and their elasticity of demand for trips with respect to generalized cost is 0.2. The optimal ring toll, calculated by maximizing the previous formula for per capita welfare, is $8.42, leading to a 6% reduction of trips into the ring. Of course, this toy calculation does not account for heterogeneity in tastes and circumstances. A realistic calculation for, say, Manhattan, would require a lot more detail. Nevertheless, the example illustrates several points. First, it implements Dupuit’s (1844) program for benefit–cost analysis of transportation policy, and corresponds precisely to the case where exact, unambiguous measurement of consumer welfare is possible. Second, it builds on individual random utility foundations, and facilitates efficient fitting from individual travel data. Third, it is a template that can be expanded to analyze a wide variety of transportation policy alternatives. Ring tolls and other congestion charges should be ubiquitous. Economic efficiency requires that resources be priced at their marginal cost, including marginal congestion cost. The cost burden of collecting tolls is a problem historically, but current technology, using transponders, GPS, cell technology, and satellites, can meter vehicle location on specific roadways and lanes at specific times, and communicate and charge articulated tolls inexpensively and practically. Tolls can be revenue-neutral, or net revenues can underwrite worthwhile public transit and infrastructure projects. Because congestion is a frictional loss of economic efficiency, pricing it correctly frees resources that can in principle be reallocated so that everyone gains, a ‘‘win-win’’ situation. Finally, where congestion charges have been implemented, the Bergen, London, and Stockholm ring tolls, and HOT lanes in various locations, they seem to work well. Further, gasoline and carbon taxes can work to lower vehicle use, can be combined with redistribution to be equitable, and are more efficient economically than CAFE´ standards. Given that pricing transportation services makes so much economic sense, why is consumer resistance to pricing so strong? In the UK in 2007, a BBC poll found
that 74% of the adult population oppose road pricing. An anti-pricing petition sponsored by Peter Roberts was signed by 6% of all the drivers in the UK Why? Three common arguments are that the toll revenues will be used inefficiently, that tolls are regressive and inequitable, and that the individual consumer is more likely to lose than to gain by obtaining transportation services in a market. The first of these, inefficient use of toll revenues, is a real problem that can be addressed either by making the toll system revenue-neutral, or by earmarking the revenues for projects that voters want. Issues of regressivity need to be addressed by adjusting other taxes and subsidies to avoid shifting the standard of living distribution. However, some equity realignments are necessary because existing uncompensated congestion costs are inequitable, and heavy contributors to congestion need to see the stick in order to get the adjustments in behavior needed. I will now turn my attention to the third source of consumer resistance. I will expand on fear of markets as an explanation for the difficulty of getting consumers to understand and accept market pricing of transportation services. We are challenged by market choices. In the words of a Dutch proverb, ‘‘He who has choice has trouble’’. Psychologists use the term ‘‘agoraphobia’’ for a psychosis that means, literally, fear of the marketplace, and is characterized by fear of leaving a safe place, fear of being in situations from which escape might be difficult or embarrassing; fear of losing control in a public place such as a restaurant or shopping mall. Most consumers display some degree of agoraphobia in their attitudes toward markets and market solutions to problems of resource allocation, distrusting markets and their own decisionmaking ability. Markets present risks, of three types. Market risks are shifts in product attributes, uncertainty about prices and supply, and ambiguity surrounding products and information that the market provides. Personal risks are the mistakes an individual can make in choices, due to memory lapses, errors of perception and calculation, and mistaking one’s own tastes. Social risks are the stresses of interactions between people under the contentious conditions of market transactions, including the stress of information gathering and search, bargaining, pressures from social norms, accountability for choices, and possible social sanctions, including the potential embarrassment of performing less well than one’s peers. Markets punish consumer inconsistencies. However, markets are inconsistent teachers, and provide no road map to success. They thrive on consumer failures, and are quick to exploit them. As a result, consumers learn to be defensive, refusing trading opportunities that are of uncertain merit or are ambiguous. The result is a conservative bias toward the status quo: ‘‘The devil you know is better than the devil you don’t’’. Critically, market punishment of poor decision-making breeds paranoia and agoraphobia—I perceive my losses as outweighing my
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gains, and blame this on everyone but myself: the greed of corporations, conspiracy, fraud, corrupt politicians, inside information. I vote against market solutions that require me to make choices, even if rationally I concede that they are actuarially fair on paper, and instead vote for the status quo, or alternatives that restrict choice. To understand how market and personal risks affect consumers’ attitudes toward choice and toward markets, turn to cognitive psychology and brain science. Consumers show asymmetries, with losses from their reference points looming larger than gains, and future, uncertain, or ambiguous events heavily discounted relative to the present. For example, a majority of drivers queued on a congested highway have the perception that other lanes move more quickly than their own. This is caused by loss aversion, the fact that falling behind the truck one lane over is more noticeable and more painful than the satisfaction from gaining equivalent ground. This leads drivers, and consumers more generally, to mistrust proposed changes from their status quo, and to fear markets that confront them with these choices. Brain science establishes that these phenomena are substantially a result of how our brains are wired, how we parse and process information, and how we experience pleasure and pain. We are products of an evolutionary history that leads us to handle threats at a more primitive level than we handle most rewards. Communication and reconciliation between different brain levels is incomplete. Trade arose early in our evolution, and perhaps because of the trust and communication skills it requires, it may be substantially responsible for making us what we are. One result is that trade stimulates the brain at a surprisingly primitive level, and involves a significant emotional component. A picturesque but true characterization is that shopping and sex share the same neurotransmitters and receptors. Trade is a contest, involving its own stresses, pleasures, and pains. Trust is an essential element in commercial transactions, and again there is a long evolutionary history linking trade and trust. Ernst Fehr and his colleagues in Zurich find that giving subjects the peptide oxytocin that is associated with maternal bonding leads them to be more trusting in economic transactions. Humans are on a hedonic treadmill, quickly habituating to homeostasis and forming reference points, and experiencing particularly acute pain from losses relative to these reference points. Personal and social risks are additional reasons to mistrust markets. Consumers may legitimately fear that lapses in memory, reasoning, or understanding of the choice process and their own goals will put them at a disadvantage relative to skilled traders. Further, trade involves dealing with adversaries, and for trading outcomes, facing comparisons with peers, accountability, and approval. Herb Simon said that a wealth of information creates a poverty of attention. Douglas and Wildavsky point out that humans internalize social pressures and delegate their decision-making processes.
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People make interpersonal comparisons, judging the desirability of options from the apparent satisfaction and advice of others. While personal experience determines the utility of familiar objects, our primary sources of information on novel objects comes from observations on others, and their advice. The consequence is that discussions and votes on transportation projects may be shaped by a great deal of imitative behavior. Then, a small but loud core of opponents of congestion pricing or other transportation market solutions may have impacts well beyond their numbers. Affiliation with social networks, limiting choice by accountability to network norms, can be an efficient decision-making strategy for individuals. An example is the pellaton, a tightly packed groups of riders in bicycle racing that creates an energy-saving, choice-limiting environment. I consider the pellaton an instructive model of consumer choice behavior more generally, with most consumers associating voluntarily with groups that guide and limit their choices, a device that conserves scarce attention time and provides, through a sort of ‘‘hive intelligence’’, outcomes that are usually satisfactory and certainly socially acceptable. There will be occasional break-aways, with new pellatons forming, when some participants see a clearly preferred alternative to the old pellaton’s choices, but most of the time staying with the pellaton is defensive and protective. I suggest as a research problem that understanding the behavior of pellaton members and the effectiveness of the pellaton as a collective decision-making group would be useful for understanding of how social welfare is influenced by voluntary affiliations, and how consumers pack together when they drive, ride transit, or vote on transportation projects. Perhaps by understanding the formation and stability of anti-tax, anti-road-pricing pellatons, one might see how to encourage pellatons that support efficient market solutions to congestion in transportation. Summarizing, economic and behavioral science provides insights and models that are useful at the many points of human interaction in transportation systems. The behavioral science useful for transportation research depends on the grain of transportation policies studied, and needs to be updated regularly with the progress of economic and behavioral science. Consumers are likely to resist market solutions for transportation problems, and careful education and framing may be needed to overcome agoraphobia. Finally, transportation research can benefit from continuing close connections to economic and behavioral science, and active pursuit of new ideas and findings from the behavioral sciences that can improve your ability to understand and predict the effects of human behavior in transportation systems. References Atkinson, A., Stern, N., 1974. Pigou, taxation and public goods. Review of Economic Studies 41 (1), 119–128.
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Diamond, P., Mirrlees, J., 1971. Optimal taxation and public production. American Economic Review 61, 8–27, 261–278. Dixit, A., 1985. Tax policy in open economies. In: Auerbach, A., Feldstein, M. (Eds.), Handbook of Public Economics, vol. 1. NorthHolland, New York and Oxford, pp. 313–374. Domencich, T., McFadden, D., 1976. Urban Travel Demand: A Behavioral Analysis. North-Holland, Amsterdam. Dupuit, J., 1844. On the measurement of the utility of public works. Annales des ponts et chausse´es. (English translation, International Economic Review, 1952). Frisch, R., 1926. Sur un Probleme of Economie Pure. Norsk Matematisk Forenings SSkrifter, 16, 1–40; Translation in J. Chipman, L. Hurwicz, M. Richter, H. Sonnenschein (Eds.), Preferences, Utility, and Demand, Harcourt, New York. Gorman, W., 1961. On a class of preference fields. Metroeconomica 13, 53–56. Hicks, J., 1939. Value and Capital. Clarendon Press, Oxford. King, M., 1986. A Pigovian rule for the optimum provision of public goods. Journal of Public Economics 30 (3), 273–291.
Marshall, A., 1895. Principles of Economics. Macmillan, London, New York. Mayeres, I., Proost, S., 1997. Optimal tax and public investment rules for congestion type of externalities. Scandinavian Journal of Economics 99 (2), 261–279. McFadden, D., 1999. Computing willingness-to-pay in random utility models. In: Moore, J., Riezman, R., Melvin, J. (Eds.), Trade, Theory and Econometrics: Essays in Honour of John S. Chipman. Routledge, London. McFadden, D., 2004. Welfare economics at the extensive margin: giving Gorman Polar consumers some latitude. Working Paper, June 2004. Ravenstein, E., 1885. The laws of migration. Journal of the Royal Statistical Society 48, 167–227 and 52, 241–301. Small, K.A., 1983. The incidence of congestion tolls on urban highways. Journal of Urban Economics 13, 90–111. Zipf, G., 1946. The P1P2/D hypothesis: on the intercity movement of persons. American Sociological Review 11, 677–686.