Yuqing Hu, Juvenn Woo

GARP, the generalized axiom of revealed preference, is a dichotomous notion. A dataset can either satisfy the theory of a rational consumer or violate it[1]. There are several challenges in testing GARP consistency in an experiment. One challenge comes from the nature of budget sets, as there are more individual-level variations in expenditure than variations in prices. This causes the overlap of two budget sets, upon which the test based could bias towards the satisfaction of GARP, with the extreme case that no violation would occur if the budget sets are nested. Another challenge stems from lack of identities of consumers such that individuals have to be treated as the same for revealed preference tests (Chambers & Echenique, 2016).

 

A few indices have been invented to measure the degree of GARP violations. One is Afriat’s efficiency index (AEI) (Afriat, 1967), which uses the degree of “deflation” of expenditure that is needed to make GARP consistent. Other variations of AEI are Varian’s efficiency index (VEI) (Varian, 1983), and the money pump index (MPI) (Echenique, Lee, & Shum, 2011).

 

There is a modest amount of literature in experimental economics that test GARP consistency, which is summarized below.

 

Battalio et al.(1973) pioneered applying GARP consistency in experimental study. They ran field experiments among psychotic patients to let them exchange tokens for different consumption goods. They induced a variety of different budget sets by changing the value of tokens, and they found that if small measurement errors were allowed, then almost all patients’ behavior was consistent with GARP.

 

Sippel (1997) ran lab experiments in which 42 students were asked to repeatedly choose a bundle of priced entertaining items under different standard budget constraints. Individuals were paid in consumption goods, and were required to actually consume the goods at the experiment. The experiment showed 63% of subjects made choices violating GARP, though the median number of violations over all subjects was only 1 of 45 choices. The number did not change even if the study perturbed demand close to actual demand. Even though the (remarkably) low number of violations for individual indicates the subjects were highly motivated when making choices, a majority of subjects could not be classified as rational in the sense of utility maximization.

 

Harbaugh, Krause and Berry (2001) examined the development of choice behavior for kids. The study conducted simple choice experiments over cohorts of second graders, sixth graders, and undergraduates. They measured and compared number of GARP violations. It found out that for the particular test, about 25% of 7-year-olds, and 60% of 11-year-olds were making choices consistent with GARP respectively, and there is no increase in consistency from 11 to 21-year old. They also found that violations of GARP are not significantly correlated with the results of a test that measures mathematical ability in children.

 

Andreoni and Miller (2002) ran dictator-game experiments to test whether the observed altruistic behavior is utility-maximizing. They found that 98% of subjects make choices that are consistent with utility maximization. Andreoni and Miller went further than most revealed-preference exercises in estimating a parametric function of a utility function accounting for subject’s choices (about half the subjects can be classified as using a linear, CES (constant elasticity of substitution), or Leontief utility).

 

Hammond and Traub (2012) designed a three-stage experiment, where participant advances to next stage of test only if he or she made GARP consistent choices at current one. It had been conducted over 41 (non-economics) undergraduates. The study found that, at the 10% significance level, only 22% of subjects (compared to 6.7% of simulated random choice-maker) passed second-stage tests, and 19.5% passed all three stage tests. The result reinforced Sippel’s study suggesting that human is generally not perfectly rational. It should be noted though conditional on passing second-stage rationality, 62.5% of subjects passed third-stage tests.

 

Choi, Kariv, Müller and Silverman (2014) conducted with CentERpanel survey a comprehensive study on rationality. Measuring GARP consistency by Afriat Critical Cost Efficiency Index (CCEI) and correlation with socio-economic factors, it found that: on average, younger subjects are more consistent than older, men more than women, high-education more than low-education, and high-income subjects more consistent than low-income.

 

Brocas, Carillo, Combs and Kodaverdian (2016) studied choice behaviors in cohorts of young and older adults, varying choice tasks from simple domain to complex domain. They showed that while both young and older adults are about equally well consistent in simple domain, older ones were observed being significantly more inconsistent in complex tasks. Beyond that, by performing working memory and fluid intelligence (IQ) test, further correlation examinations reveal that older adults’ inconsistency in complex domain can be attributed to decline in working memory and fluid intelligence.

[1] One can, however, evaluate the degree of violations.

 

Reference:

 

Afriat, S. N. (1967). The Construction of Utility Functions from Expenditure Data. International Economic Review, 8(1), 67–77.

Andreoni, J., & Miller, J. (2002). Giving According to GARP: An Experimental Test of the Consistency of Preferences for Altruism. Econometrica, 70(2), 737–753.

Battalio, R. C., Kagel, J. H., Winkler, R. C., Edwin B. Fisher, J., Basmann, R. L., & Krasner, L. (1973). A Test of Consumer Demand Theory Using Observations of Individual Consumer Purchases. Western Economic Journal, XI(4), 411–428.

Brocas, I., Carillo, J. D., Combs, T. D., & Kodaverdian, N. (2016). Consistency in Simple vs. Complex Choices over the Life Cycle.

Chambers, C. P., & Echenique, F. (2016). Revealed Preference Theory. Cambridge University Press.

Choi, S., Kariv, S., Müller, W., & Silverman, D. (2014). Who Is (More) Rational? The American Economic Review, 104(6), 1518–1550.

Echenique, F., Lee, S., & Shum, M. (2011). The Money Pump as a Measure of Revealed Preference Violations. Journal of Political Economy, 119(6), 1201–1223.

Grether, D. M., & Plott, C. R. (1979). Economic Theory of Choice and the Preference Reversal Phenomenon. The American Economic Review, 69(4), 623–638.

Hammond, P., & Traub, S. (2012). A Three-Stage Experimental Test of Revealed Preference.

Harbaugh, W. T., Krause, K., & Berry, T. R. (2001). GARP for Kids: On the Development of Rational Choice Behavior. American Economic Review, 91(5), 1539–1545. http://doi.org/10.1257/aer.91.5.1539

Sippel, R. (1997). An Experiment on the Pure Theory of Consumer’s Behaviour. The Economic Journal, 107(444), 1431–1444. http://doi.org/Doi 10.1111/1468-0297.00231

Varian, H. R. (1983). Non-Parametric Tests of Consumer Behaviour. The Review of Economic Studies, 50(1), 99–110. http://doi.org/10.1007/sl0869-007-9037-x