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

Transcription

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

2 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)

3 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?

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

5 Percentage Possible Interpretations (cont.) List (2007) 50% 45% 40% 35% 30% 25% 20% Baseline Take $1 15% 10% 5% 0% Amount Transferred

6 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

7 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

8 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

9 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

10 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.

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

12 Equal Treatments

13 Inequality Treatments

14 Envy Treatments

15 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

16 Average Allocations

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

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

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

20 Percentage Example of Observed Contraction Effects Inequality 70% 60% 50% 40% 30% 20% Give Take Symmetric 10% 0% Final Payoff to Dictator

21 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 o o Let m and y denote maximum feasible payoffs: and o o m ( F) sup{ m ( m, y) F} y ( F) sup{ y ( m, y) F}

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

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

24 Moral Monotonicity Axiom Let R denote not smaller or not larger For every agent i one has: Moral Monotonicity Axiom (MMA): If G F, g R f and g f r r r r i i i i then f F G g R f, g G i i

25 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: M r r Property : if G Fand g f then F G G r r Property : if G F and g f then G M implies F G F

26 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 ] And assume s* [A,B ] j j j j Contrasting implications: Conventional rational choice theory implies: t* = g* = s* Our theory implies: t* northwest g* northwest s*

27 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.

28 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* ** (0.216) (0.326) (0.458) Observations a 46 Means {Take, Give} {6.16, 6.51} {4.60, 5.06} {2.84, 3.38} Nobs {Take, Give} (Kruskal-Wallis) Chi-Squared {50, 53} {25, 33} {25, 21} * 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

29 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.

30 Support for Result 2: Contraction Table 4: Contraction of the Symmetric Set (within treatment) Average marginal effects from the hurdle model (Cragg, 1971). Dependent Variable Dictator Payoff (1) Inequality (2) Equal (3) Envy Give Action [-] *** *** (0.263) (0.532) (0.482) Take Action [-] *** *** *** (0.245) (0.522) (0.440) Observations 143 a 73 a 64 Means (Take, Give, Symm.) (6.16, 6.51, 7.83) (4.60, 5.06, 5.94) (2.84, 3.38, 3.94) Nobs (Take, Give, Symm.) (Kruskal-Wallis test) Chi-Squared (50, 53, 41) (25, 33, 16) (25, 21, 18) 52.07*** 15.51*** 12.25*** Note: MMA predicted sign in square brackets. Standard errors in parentheses. Includes Experimenter fixed effects and children demographics (gender, age, race). The Symmetric action set is the omitted category. Only choices from [A, B] are included. Choice at the highest dictator s payoff is treated as hurdle. ***

31 Implications for Data from other Experiments Korenok, Millner & Razzolini (2014) Their Contraction data are consistent with warm glow model reported in Korenok, Millner & Razzolini (2013) Their Give vs. Take ( framing ) data are inconsistent with their theoretical model and Property alpha We show that their data are consistent with MMA Andreoni & Miller (2002) They ask whether their data are consistent with GARP We show MMA places tighter restrictions on their data than does WARP

32 Give vs. Take Action Sets in Korenok, et al. (2014)

33 Action Sets in Korenok, et al. (cont.) Endowments are at points 1, 3, 6, 8, and 9 Korenok, et al. theory and conventional rational choice theory imply choices invariant to these endowment (and give vs. take action set) changes The moral reference points for our theory are shown at points f for j = 1, 3, 6, 8, and 9 j MMA implies that choice points move northwesterly along with endowments

34 Implications of Data from Korenok, et al. The average recipient payoffs for the five scenarios are: S1($4.05), S3($5.01), S6($5.61), S8($6.59) and S9($6.31). The data are inconsistent with Korenok, et al. theory and with conventional rational choice theory The data support predictions of MMA except for the change from $6.59 to $6.31, which is insignificant

35 Some Feasible Sets from Andreoni & Miller Recipient s Payoffs B A f a a f b b Dictator s Payoffs

36 MMA and WARP Consider the WARP violation shown by choices A and B Note that the shaded quadrilateral (SQ) is a contraction of each budget set Looking at SQ as a contraction of the steeper set : MMA (see Proposition 1) requires that A also be chosen from SQ because the sets have the same moral reference point Looking at SQ as a contraction of the flatter set: MMA requires that the choice from SQ is northwest of B a b because f is to the left of f But this contradicts the choice of A from SQ Thus, any pair of choices of type A and B violate MMA MMA places tighter restrictions on the data than does WARP (in the figure, WARP implies B must be southeast of the intersection; MMA says it must be east of A)

37 Summary Data from List, Bardsley, and Cappelen, et al. contradict convex preference theory Data from our experiment and Korenok, et al. contradict Conventional rational choice theory Warm glow theory of Korenok, et al. Our theory with MMA is consistent with data From Take vs. Give From ( proper ) Contraction

38 Summary (cont.) Our theory with MMA is clearly testable, e.g.: o It places tighter restrictions on data than does WARP in some dictator experiments o It places restrictions across play in moonlighting and investment games

39

40 Making the Decision First, you and the other boy will get some stickers to start. With the stickers on these plates, you still get to decide -- how many you want to keep, and how many you want the other boy to keep. Daniel s plate (Variable endowment) Here are more stickers they are yours now. Other boy s plate (Variable endowment) Here are even more stickers they are his now. Daniel s box (Fixed endowment) These are the stickers you definitely get to take home. Other boy s box (Fixed endowment) These are the stickers he definitely gets to take home.

41 Fig. 5: Reference Points for Proper Contractions

42 Table 5: Contraction of the Symmetric Set (across treatments) Average marginal effects from the hurdle model (Cragg, 1971). Dependent Variable Dictator Payoff (1) Symmetric Equal Inequality Take/Give (2) Symmetric Envy Inequality Take/Give Give Action *** [+] (0.277) (0.296) Take Action [-] 0.875*** [+] (0.289) (0.320) Observations Means (Take, Give, Symm.) (6.16, 6.51, 6.42) (6.16, 6.51, 5.37) Nobs (Take, Give, Symm.) (50, 53, 24) (50, 53, 30) (Kruskal-Wallis test) Chi-Squared ***

43 Convex Preferences on Discrete Choice Sets

44 Strictly convex preferences on a discrete choice set The most preferred set is either a singleton or a set that contains two adjacent feasible points If Q* not in [Aj, Bj] is chosen from [Aj, Cj] then Bj will be chosen from [Aj, Bj] because: o Bj is a convex combination of Q* (that belongs to [Bj, Cj]) and X, for any given X in [Aj, Bj] o Since Q* is preferred to X in [Aj, Cj], by strict convexity Bj is strictly preferred to X

45 Proof of Proposition 1

46 Proof of Properties M and M Let f belong to both F and G. Consider any g from G. r r As G and F have the same moral reference point, g f, MMA requires that gi fi and fi gi, i. These inequalities can be simultaneously satisfied if and only if g f, i.e. f belongs to G which concludes the proof for property M. Note, though, that any choice g from G must coincide with f, an implication of which is G must be a singleton. So, if the intersection of F and G is not empty then choices satisfy property. M

47 Both Axioms from Conventional Rational Choice Theory

48 Properties and Samuelson (1938), Chernoff (1954), Arrow (1959), Sen (1971, 1986) Property : if G F then F G G A most-preferred allocation * * from feasible set F is also a most-preferred allocation in any contraction G of the set F that contains the * allocation f. f F

49 Properties and (cont.) For non-singleton choice sets one also has Property β: if G F and G F then G F * If the most-preferred set F for feasible set F contains at least one most-preferred point from the contraction set G then it contains all of the mostpreferred points of the contraction set. For finite sets, Properties α and β are necessary and sufficient conditions for a choice function to be rationalizable by a weak (complete & transitive) order (Sen, 1971)