Theft, Gift-Giving, and Trustworthiness: Honesty is Its Own Reward in Rural Paraguay Laura Schechter

Transcription

1 Theft, Gift-Giving, and Trustworthiness: Honesty is Its Own Reward in Rural Paraguay Laura Schechter 1

2 Outline of the Presentation Motivation Previous literature Model Data Empirics 2

3 Motivation 50% of farmers in survey conducted in 2002 in Paraguay experienced theft in the past year (median theft-loss of 2% of annual income) 42% didn t plant a crop because of fear of theft 42% gave gifts to a person believed to be a thief Main Question Do farmers in rural Paraguay contract with one another to limit theft? Lack of e ective legal enforcement + non-anonymous and repeated interactions===> use of implicit contracts to minimize crime Agent cannot credibly commit to refrain from stealing from another agent so must be induced to limit his theft by the promise of future gifts 3

4 Previous literature One period model with anonymous utility maximizer thief. Becker(1968), Levitt(2004), Gould et al. (2002) Main prediction: more theft when the potential gains are greater and the probability of punishment is smaller *Dynamic limited commitment model: interactions of thief and victim in a context of ine ective judicial system. Gifts: fairness grounds reward actors with good intentions Rabin(1993), taste for equality Fehr & Schmidt(1999), form of mutual insurance Coate & Ravallion (1993), signalling as willingness to enter into a relationship Camerer (1988) * Gift as theft prevention- villagers are forced into relationships with one another due to geographic proximity. *Main result contradicts predictions of models in which the higher the trust the more likely transfers will occur 4

5 Stylized Facts about theft 1. People who steal smaller items have a di erent relationship with their victims than do people who steal larger items. 70% of smaller items were stolen by a neighbor or a relative while only 18% of larger items were stolen by a neighbor (and none by relatives). 66% of the known thieves of small items were given gifts, lent money, or hired by the victim before the theft while only 36% of the known thieves of large items were given these transfers. 4% of known thieves of small items were reported to the police, 64% of thieves of large items were reported. 2. Theft is common and economically important. Median value stolen -$17(1% of median household income) 3. Victims know who is stealing from them. 4. It is believed that some people receive less psychic disutility from thieving than others. 5. Victims do not report thieves to the police or punish them physically. 6. Some plots of land are more vulnerable to theft than others. 7. Households give transfers to thieving households to avoid being stolen from. If you know someone is a thief, do you give him gifts to avoid getting stolen from? 42% answered yes. 5

6 8. Investment decisions are distorted due to the potential of theft. The stylized facts above suggest that both gift-giving and theft occur in equilibrium while current gift-giving and the promise of future gift-giving is used to limit theft. 6

7 Model two types of transfers: gifts (!) and prescribed theft (r p s) y 1 farmer sure income y 2 thief sure income v(y 1! r p s) farmer s momentary utility u(y 2 +! + r p s) thief s momentary utility c(s; r s ) cost of stealing c0(s; :) > 0 and c 00 (s; :) > 0 t(r d s) psychic trustworthiness disutility from stealing r d s> r p s; t 0 () > 0; t 00 () > 0 Inada conditions lim y!0 u0(y) =1; lim y!1 u0(y) = 0 u 0 (:) > 0; u 00 (:) < 0(and likewise for v(:)) Both prefer transfer as gift. Theft would be eliminated in equilibrium if the farmer could give a larger gift when the cost of stealing was lower Given that we see theft in equilibrium assumption that gifts not be state contingent is necessary. The timing of the model is as follows : 1)farmer sets rs p and! 2) s is realized and the thief decides r s 3) farmer observes r s and decides whether or not to give him the gift. One-shot version of this game: farmer will never give the gift. 7

8 Finding the Constrained-E cient Frontier Farmer s max problem s.t. X V (U) = Max!;Us;r s p s [v(y 1! rs) p + V (U s )] s X s [u(y 2 +! + rs) p + V (U s )] U (1) s u(y 2 +!+r p s) c(s; r p s)+v (U s ) u(y 2 +r d s) c(s; r d s) t(r d s)+d 2 8s; r d s s s (2) v(y 1! r p s) + V (U s ) v(y 1 r p s) + D 1 8s s s (3) r p s 0 8s s s (4)! 0 (5) One equilibrium: r s rs p is enforceable with threat of punishment in an in nitely repeated game. Abreu(1988) if u0(y 2 ) < c0(s; 0) + t0(0) =) r s rs p F.O.C. w.r.t. U s : V 0(U s ) = + s 1 + s (6) Envelope T heorem : V 0(U) = (7) r p s : v 0 (y 1! r p s) u 0 (y 2 +! + r p s) c 0 (s; r p s) ( s + s v 0 (y 1 r p s)) (1 + s )(u 0 (y 2 +! + r p s) c 0 (s; r p s) = + s 1 + s (8) 8

9 Proposition 1 Let the history of states h t = (s 1 ; s 2 ; :::; s t ) be given and let s be the state which occurs at time t. Any constrained-e cient contract can be characterized as follows: there exist S state dependent intervals [ s ; s ] such that (h t ) evolves according to the following rule (h t ) = 8 9 < s if (h t 1 ) < s = (h t 1 ) if (h t 1 ) 2 [ : s ; s ] ; s if (h t 1 ) > s where s = V 0(U s ), and s = V 0(U s ). I de ne U s as the lowest sustainable continuation payo that the thief could receive in state s so as to just satisfy his IC constraint (2). Likewise U s is the highest sustainable continuation payo that the thief could receive in state s so as to just satisfy the farmer s IC constraint (3). This completely characterizes the contract once an initial value for h t 1 is given. 9

10 Comparative Statics gift given prescribed theft trust cost of stealing# " " # trustworthiness # " # risk aversion of farmer" " # - trustworthiness: t(r s ) P lack of trust: s s s > 0 ) as t() falls higher consumption and higher continuation utility(u s ) )higher gift since theft is costly Less trustworthy thief causes the farmer to be less trusting (6) Assumption: perfect information about the identity of the thief, amount stolen and the state of nature Conditional on crop choice, comparative statics hold Choice between a more stealable and less stealable crop distorted =)decrease in e ciency due to lack of enforcement- If the thief becomes so untrustworthy that the farmer switches to planting a less stealable crop, then a less trustworthy thief will actually receive a lower value gift 10

11 Data Panel data of over 200 household in 16 villages in 3 states in 1991,1994,1999 and 2002 on self-reported data on gift, theft and experiments measuring trust, risk aversion and trustworthiness 11

12 Empirics Due to nonlinearities in the decision rules derive comparative statics which hold in equilibrium Y=gift given, theft experienced, trust (measured according to a survey- trust/system of rewards and sanctions) X= cost of stealing (HH size, walk past a eld), risk aversion(experiment) and trustworthiness of neighbors ( # relatives close to the HH, level of trustworthiness of the least trustworthy of the household s three closest neighbors) y 1 = x 1 + u 1 y 2 = x 2 + u 2 y 3 = x 3 + u 3 system is just identi ed-ols equation by equation no village FE but clustered sd Biased results because omit crop choice 12

13 Controlling for crop choice: y 1 = x u 1 y 2 = x u 2 y 3 = x u 3 Instrument for crop choice: altitude and potential evapotranspiration 13

14 Households planting more stealable crops give signicantly more gifts,though there is no e ect on theft or trust Households with elds no-one passes and living in the same village with more close family members still give fewer gifts, experience less theft, and trust more. Large households and households with more trustworthy neighbors no longer give signi cantly more gifts than other households. # of relatives capture punishment/cost of stealing 14

15 Estimation by GMM z=[ x ] E[z u g ] = x i1 0 0 X i = 4 0 x i x i3 y i1 Y i = 4y i2 5 y i3 ^^^ = [X 0 Z(Z 0 Z) 1 Z 0 X] 1 X 0 (Z 0 Z) 1 Z 0 Y u i = y i X i ^W = (N 1 P Z 0 ^Z i i ) 1 i ^ = u i u 0 i = [X 0 Z ^W Z 0 X] 1 X 0 Z ^W Z 0 Y 15