The Trade-off between money and time: A test of the theory of reference-dependent preferences

De Borger, Bruno and Fosgerau, Mogens (2007): The Trade-off between money and time: A test of the theory of reference-dependent preferences.

Abstract

We formulate a model of reference-dependent preferences based on the marginal rate of substitution at the reference-point of a reference-free utility function. Using binary choices on the trade-off between money and travel time, reference-dependence is captured by value functions that are centered at the reference. The model predicts a directly testable relationship among four commonly used valuation measures (willingness to pay (WTP), willingness to accept (WTA), equivalent gain (EG) and equivalent loss (EL)). Moreover, we show that the model allows recovering the underlying ‘reference-free’ value of time. Based on a large survey data set, we estimate an econometric version of the model, allowing for both observed and unobserved heterogeneity. In a series of tests of high statistical power, we find that the relationship among the four valuation measures conforms to our model and that the constraints on the parameters implied by the model are met. The gap between WTP and WTA is found to be a factor of four. Loss aversion plays an important role in explaining responses; moreover, participants are more loss averse in the time dimension than the cost dimension. We further find evidence of asymmetrically diminishing sensitivity. Finally, we show that the fraction of ´mistakes` (in the sense that participants are observed to sometimes select dominated options), varies systematically in a way consistent with the model of reference-dependence. The results of the paper have important implications for the evaluation of infrastructure investment and pricing reforms in the transport sector.

• Item Type: MPRA Paper
• Institution: Technical University of Denmark
• Language: English
• Keywords: Reference-dependence; loss aversion; WTP-WTA gap; value of time
• Subjects: D - Microeconomics > D0 - General > D01 - Microeconomic Behavior: Underlying Principles; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities

References

Andreoni, J. 1995, "Warm-glow versus cold-prickle: The effects of positive and negative framing on cooperation in experiments", Quarterly Journal of Economics, vol. 110, pp. 1-21.

Bateman, I., Kahneman, D., Munro, A., Starmer, C., & Sugden, R. 2005, "Testing competing models of loss aversion: an adversarial collaboration", Journal of Public Economics, vol. 89, no. 8, pp. 1561-1580.

Bateman, I., Munro, A., Rhodes, B., Starmer, C., & Sugden, R. 1997, "A Test of the Theory of Reference-Dependent Preferences", The Quarterly Journal of Economics, vol. 112, no. 2, pp. 479-505.

Bates, J. & Whelan, G. 2001, "Size and sign of Time Savings", ITS Working Paper no. 561. Beesley, M. E. 1965, "The Value of Time Spent in Travelling: Some New Evidence", Economica, vol. 32, no. 126, pp. 174-185.

Benartzi, S. & Thaler, R. H. 1995, "Myopic Loss Aversion and the Equity Premium Puzzle", Quarterly Journal of Economics, vol. 110, no. 1, pp. 73-92.

Bernheim, B. D. & Rangel, A. 2007, "Behavioral Public Economics: Welfare and Policy Analysis with Nonstandard Decision-Makers," in Behavioral Economics and Its Applications, P. Diamond & H. Vartiainen, eds., Princeton University Press, pp. 7-84.

Bierlaire, M. 2003, BIOGEME: a free package for the estimation of discrete choice models, Proceedings of the 3rd Swiss Transport Research Conference, Monte Verità, Ascona, Switzerland.

Bierlaire, M. 2005, "An introduction to Biogeme", www.epfl.ch/biogeme.

Brueckner, J. 2005, "Transport Subsidies, System Choice and Urban Sprawl", Regional Science and Urban Economics, vol. 35, pp. 715-733.

Calfee, J. & Winston, C. 1998, "The value of automobile travel time: implications for congestion policy", Journal of Public Economics, vol. 69, pp. 83-102.

Cameron, T. A. & James, M. D. 1987, "Efficient Estimation Methods for "Closed-Ended" Contingent Valuation Surveys", Review of Economics and Statistics, vol. 69, no. 2, pp. 269-276.

Cantillo, V., Heydecker, B., & de Dios Ortuzar, J. 2006, "A discrete choice model incorporating thresholds for perception in attribute values", Transportation Research Part B: Methodological, vol. 40, no. 9, pp. 807-825.

Cummings, R. G., Brookshire, D., & Schulze, W. D. 1986, Valuing environmental goods Rowman and Allanheld, Totowa, NJ.

De Borger, B. & Proost, S. 2001, Reforming Transport Pricing in the European Union - A Modelling Approach Edward Elgar, Cheltenham, UK.

Diamond, P. A. & Hausman, J. A. 1994, "Contingent Valuation: Is Some Number Better than No Number?", Journal of Economic Perspectives, vol. 8, no. 4, pp. 45-64.

Fosgerau, M. 2006, "Investigating the distribution of the value of travel time savings", Transportation Research Part B: Methodological, vol. 40, no. 8, pp. 688-707.

Fosgerau, M. 2007, "Using nonparametrics to specify a model to measure the value of travel time", Transportation Research Part A: Policy and Practice, vol. 41, no. 9, pp. 842-856.

Fosgerau, M. & Bierlaire, M. 2007, "A practical test for the choice of mixing distribution in discrete choice models", Transportation Research Part B: Methodological, vol. 41, no. 7, pp. 784-794.

Fosgerau, M., Hjort, K., & Vincent Lyk-Jensen, S. 2006, The Danish Value of Time Study - Results for Experiment 1 www.dtf.dk.

Fosgerau, M. & Nielsen, S. F. 2006, "Deconvoluting preferences and errors: a semi-nonparametric model for binomial data", Econometric Society European Meeting 2006.

Hensher, D. 2001, "The Valuation of Commuter Travel Time Savings for Car Drivers: Evaluating Alternative Model Specifications", Transportation, vol. 28, pp. 101-118.

Honoré, B. E. & Lewbel, A. 2002, "Semiparametric binary choice panel data models without strictly exogenous regressors", Econometrica, vol. 70, no. 5, pp. 2053-2063.

Horowitz, J. K. & McConnell, K. E. 2003, "Willingness to accept, willingness to pay and the income effect", Journal of Economic Behavior \& Organization, vol. 51, no. 4, pp. 537-545.

Hultkrantz, L. & Mortazavi, R. 2001, "Anomalies in the Value of Travel-Time Changes", Journal of Transport Economics and Policy, vol. 35, no. 2, pp. 285-300.

Jiang, M. & Morikawa, T. 2004, "Theoretical analysis on the variation of value of travel time savings", Transportation Research Part A: Policy and Practice, vol. 38, no. 8, pp. 551-571.

Johnson, E. J., Gächter, S., & Herrman, A. 2006, "Exploring the Nature of Loss Aversion", IZA DP, vol. 2015.

Kahneman, D., Knetsch, J. L., & Thaler, R. 1990, "Experimental Tests of the Endowment Effect and the Coase Theorem", Journal of Political Economy, vol. 98, no. 6, pp. 1325-1348.

Kahneman, D. & Tversky, A. 1979, "Prospect Theory: An Analysis of Decision under Risk", Econometrica, vol. 47, no. 2, pp. 263-292.

Kidokoro, Y. 2006, "Benefit estimation of transport projects--a representative consumer approach", Transportation Research Part B: Methodological, vol. 40, no. 7, pp. 521-542.

Köszegi, B. & Rabin, M. 2006, "A model of reference-dependent preferences", The Quarterly Journal of Economics, vol. Forthcoming.

List, J. A. 2004, "Neoclassical Theory Versus Prospect Theory: Evidence from the Marketplace", Econometrica, vol. 72, no. 2, pp. 615-625.

Munro, A. & Sugden, R. 2003, "On the theory of reference-dependent preferences", Journal of Economic Behavior \& Organization, vol. 50, pp. 407-428.

Pilegaard, N. & Fosgerau, M. 2007, "Cost-benefit analysis of a transport improvement in the case of search unemployment", Journal of Transport Economics and Policy, vol. Forthcoming.

Plott, C. R. & Zeiler, K. 2005, "The Willingness to Pay–Willingness to Accept Gap, the "Endowment Effect," Subject Misconceptions, and Experimental Procedures for Eliciting Valuations", The American Economic Review, vol. 95, no. 3, pp. 530-545.

Randall, A. & Stoll, J. R. 1980, "Consumer's Surplus in Commodity Space", American Economic Review, vol. 70, no. 3, pp. 449-455.

Small, K. 2005, "Fundamentals of Economic Demand Modeling: Lessons from Travel Demand Analysis," in Decision-Based Design: Making Effective Decisions in Product and Systems Design, forthcoming edn, Kemper Lewis & Linda C.Schmidt, eds., ASME Press.

Small, K. A., Winston, C., & Yan, J. 2005, "Uncovering the Distribution of Motorists' Preferences for Travel Time and Reliability", Econometrica, vol. 73, no. 4, pp. 1367-1382.

Stott, H. P. 2006, "Cumulative prospect theory's functional menagerie", Journal of Risk and Uncertainty, vol. 32, no. 2, pp. 101-130.

Tversky, A. & Kahneman, D. 1991, "Loss Aversion in Riskless Choice: A Reference-Dependent Model", The Quarterly Journal of Economics, vol. 106, no. 4, pp. 1039-1061.

Venables, A. J. 2007, "Evaluating urban transport improvements: cost-benefit analysis in the presence of agglomeration and income taxation", Journal of Transport Economics and Policy no. Forthcoming.

Wardman, M. 2001, "A review of British evidence on time and service quality valuations", Transportation Research Part E: Logistics and Transportation Review, vol. 37, no. 2-3, pp. 107-128.