Theory and Experimental Evidence James C. Cox, John A. List, Michael - PowerPoint PPT Presentation

Moral Costs and Rational Choice: Theory and Experimental Evidence James C. Cox, John A. List, Michael Price, Vjollca Sadiraj, and Anya Samek

Dictator Games • Hundreds of dictator games in the past 30 years provide evidence for altruism or warm glow • In standard dictator games  ~60% of subjects pass positive amounts of money;  allocating ~20% of endowment (Camerer, 2003) • Changing the give vs. take action set produces some different results:  Allowing taking significantly decreased transfers (List, 2007; Bardsley, 2008)  Take option effect is robust to heterogeneous adult subjects with earned endowments (Cappelen, et al., 2013)  Take vs. give option effect is robust to charitable contributions (Grossman & Eckel, 2015)  Recipients earn more in a take game than in a payoff equivalent give game (Korenok, Millner & Razzolini, 2014)

Possible Interpretations • Not a “real behavioral phenomenon”; an effect of an artificial environment such as:  “Hawthorn effect”?  “Experimenter demand effect”?  “Framing effect”?  Other artificial environment effect? • Or maybe a Kitty Genovese effect?

Possible Interpretations (cont.) • A “real behavioral phenomenon” that is:  Inconsistent with convex preference theory?  Inconsistent with rational choice theory?

Possible Interpretations (cont.) List (2007) 50% 45% 40% 35% 30% Percentage 25% Baseline Take $1 20% 15% 10% 5% 0% −1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Amount Transferred

Theoretical Interpretation of List (2007) Data • In order for the data to be consistent with convex preference theory:  The height of the blue bar at 0 must equal the sum of the heights of the red bars at -1 and 0  The heights of the blue and red bars must be the same at all other transfer numbers • In order for the data to be consistent with extant rational choice theory:  No red bar to the right of -1 can be taller than the corresponding blue bar

List (2007), Bardsley (2008), Cappelen, et al. (2013) • Data from these experiments are: – Inconsistent with convex preference theory (including “social preferences” models) – Almost completely consistent with extant rational choice theory • These experiments: – Stress-test convex preference theory – Endowments and action sets are not well suited to stress-test rational choice theory

Outline of Contents • Report an experimental design to stress-test rational choice theory • Report an experiment with children • Review properties of conventional theory – Convex preference theory (including “social preferences”) – Rational choice theory • Develop a modified form of rational choice theory, with moral reference points, that explains: – Dependence on irrelevant alternatives (“contraction effects”) – Dependence on give vs. take action sets (“framing effects”) • Use child experiment data and data from college student experiments to test alternative theories

Our Experiment • 329 children, ages 3-7 (Average age: 5, min. 3.5; max. 7.4) • Treatments include variations in: – Action sets: Give, Take, Symmetric – Initial endowments: Inequality, Equal, Envy

Treatments: Varying Endowments and Action Sets • Compare Give, Take, Symmetric to investigate the effect of the action set on final outcomes. • Across Inequality, Equal, Envy: compare the final allocation within action sets.

Feasible Budget Sets • Give and Symmetric start at B • Take starts at A

Equal Treatments

Inequality Treatments

Envy Treatments

Randomization to Treatment • Between subjects : 3 – 4 year olds randomized to Inequality, Equal, or Envy • Within subjects : Plays each of Give, Take, Symmetric in random order  Payoff accumulates after each decision (PAS)  In the main text we report only the decision from the dictator game o when it is played first o and the existence of the second and third choices is unknown to the child  Appendix D reports tests with all of the data

Average Allocations

Extant Rational Choice Theory • The Chernoff (1954) contraction axiom (also known as Property α from Sen ( 1971) states:      Property α: if then G F F G G  • In words, a most-preferred allocation from f feasible set is also a most-preferred allocation F in any contraction of the set that contains G F  the allocation f

* Q j Explanation for Dictator Games Q  • For singleton choice sets: If , that is chosen j from opportunity set , belongs to the [A ,C ] j j Q  subset then is chosen when the [A ,B ] j j j the opportunity set is [A ,B ] j j • This means that no striped bar should be taller than corresponding bars in the intersection of feasible sets in the following figure

* Q j Explanation for Dictator Games Q  • For singleton choice sets : If , that is chosen j from opportunity set , belongs to the [A ,C ] j j Q  subset then is chosen when the [A ,B ] j j j the opportunity set is [A ,B ] j j • This means that no striped bar should be taller than corresponding bars in the intersection of feasible sets in the following figure

Example of Observed Contraction Effects Inequality 70% 60% 50% 40% Percentage Give 30% Take Symmetric 20% 10% 0% 0 1 2 3 4 5 6 7 8 9 10 11 12 Final Payoff to Dictator

Introduction of Moral Reference Points • We extend rational choice theory to include objectively-defined moral reference points. • We here consider the N = 2 case needed for dictator games in the give vs. take literature: – Let ( m,y ) denote an ordered pair of money payoffs for the dictator m = “my payoff” and the recipient y = “your payoff” – Let denote the dictator’s compact feasible set F – Let and denote maximum feasible payoffs: o o y m     o and o ( ) sup{ | ( , ) } ( ) sup{ | ( , ) } m F m m y F y F y m y F

Theory Generalization (cont.) • The minimal expectations point M is:     and o o ( ) sup{ | ( , ( )) } ( ) sup{ | ( ( ), ) } m F m m y F F y F y m F y F o o • The moral reference point depends on M and the dictator's endowment:      r ( ( ) (1 ) , ( )) f m F e y f o m o   • Any is consistent with contraction and action (0,1)   set effects. In the paper, we use the value 1/ 2

Graphical Depiction of Examples y A Q = Take Endowment 10 B Q = Give Endowment 6 = Symmetric Endowment C Q 2 m 10 2 4 6

Moral Monotonicity Axiom • Let R denote “not smaller” or “not larger” • For every agent i one has: Moral Monotonicity Axiom (MMA):   r r r r , and g G F g R f f If then   i i i i            , g f F G g R f G i i

Implications of MMA • MMA is a sufficient condition for the choice set to satisfy contraction and expansion axioms (analogs   of Sen’s properties and ) if opportunity sets preserve a moral reference point:   • Property  r r : if and then g f G F M     F G G  • Property   : if and then r r g f G F M         implies G F G F

Testable Implications Within I, Q & E Treatments • Let the choice point be t* when the action set is Take and the opportunity set is [A ,B ] j j • Let the choice point be g* when the action set is Give and the opportunity set is [A ,B ] j j • Let the choice point be s* when the action set is Symmetric and the opportunity set is [A ,C ] j j  – And assume s* [A ,B ] j j • Contrasting implications:  Conventional rational choice theory implies: t* = g* = s*  Our theory implies: t* northwest g* northwest s*

Within Treatments Take vs. Give Effects • Result 1: Effects on choices of within-treatment change from Give to Take action sets are weakly inconsistent with conventional rational choice theory but consistent with our model based on MMA.

Support for Result 1: Take vs. Give Table 3: Comparisons of Give vs. Take Action Sets Average marginal effects from the Hurdle model (Cragg, 1971). Dependent Variable (1) (2) (3) Dictator Payoff Inequality Equal Envy Conditional mean estimates of Give Action [+] 0.400* 0.246 1.174** (0.216) (0.326) (0.458) 57 a Observations 103 46 Means {Take, Give} {6.16, 6.51} {4.60, 5.06} {2.84, 3.38} Nobs {Take, Give} {50, 53} {25, 33} {25, 21} (Kruskal-Wallis) Chi-Squared 2.51 3.26* 2.88* Note: a demographics missing for one child. Predicted sign by MMA in square brackets. Standard errors in parentheses. Choice at the highest dictator’s payoff is treated as hurdle. Includes Experimenter fixed effects and demographics (child age, race and gender). Take action set is the omitted category, and childrens ’ choices in the Symmetric action set are excluded from the analysis. ***p<0.01, ** p<0.05, * p<0.1

Within Treatments Contraction Effects • Result 2: Effects on choices from within-treatment contractions of feasible sets are inconsistent with conventional rational choice theory but consistent with our model based on MMA.