tanaka time preferences

Risk and Time Preferences: Linking Experimental and Household

Survey Data from Vietnam

Tomomi Tanaka, Colin F. Camerer, and Quang Nguyen

American Economic Review, 2010.

Roberto Mendoza Serrano

La aversin al riesgo e impaciencia explican el porqu la gente no deja de ser pobre?

Discernir entre preferencias y circunstancias.

Tres parmetros >> un slo parmetro.

Cmo estos parmetros se relacionan con variables demogrficas y econmicas.

1) No linealidad en Probabilidades, 2) Av.

riesgo prdida ganancia, 3)

concavidad de U()

Concavidad de U()

Sentimiento de vulnerabilidad en pobres (aversin al riesgo) Mayor riqueza mayores inversiones riesgosas e ingreso?

Cmo midieron tres parmetros? Hyperbolic Discounting: An Experimental Analysis. (2007) Jess Benhabib, Alberto Bisin, Andrew Schotter.

Literatura de psicologa y sus problemas

0. Vasta literatura sobre inconsistencia. PERO:

1.- Preguntas con temporalidad pero pagos in situ 2.- Manipulacin estratgica

3.- Efectos de encuadre

Hasta ese momento no se haba corroborado la diferencia estadstica de un modelo hiperblico

vs exponencial

La estrategia de identificacin consiste en explotar el SESGO POR EL PRESENTE: hoy es castigo

maana es recompensa. Para esto habr un modelo de costo variable y uno de costo fijo.

D(y,t) = 11+ rt ,r > 0yD(y,t) t D(y,t)D(y,t)

D(y,t) = exp{rt},r > 0

D(y,t) = exp(rt), 0

El modelo c-h tiene implcito un costo variable

Probar especificacin

Intuicin

sup(yDch ()) = y (1 )y

yD(y,t) = exp(rt)(y + bexp(mt)) b

yD(y,t) = exp(rt)y byD(y,t) = yexp(rt) (1 exp(rt))b

Modelo con costo fijo

b es ms pequeo relativamente a medida que y aumenta

Note that in this question instead of asking what amount of money they need todayto make them indierent to a given amount of money in the future, we ask them whatamount of money if given at a specic time in the future would make them indierent toa xed amount today. In this question they were not allowed to state an amount largerthan some pre-determined quantity, yLarge. Here yLarge varied from $10, to $20, to $30,to $50 and nally to $100 while the time horizons varied form 3 days to 1 week, 1 month,to 3 months and nally to 6 months, just as in Session 1. The $x amounts given themwere derived from the answers to questions received in Session 1 and were the minimumof the amounts stated there.4

In summation, we employed a within-subject design using 27 subjects and two treat-ments where the treatments varied according to the type of question asked.

3.2 Estimates of discounting

Kirby, 1997, uses econometric methods to t discount curves.5 In his main experiment,the hyperbolic discount specication ts better that the exponential, in the sense that theR2 is higher, for 19 out of 23 participants. What is missing from his analysis is a formalstatistical test of the hyperbolic specication against the exponential alternative. Thecomparison of R2 across specications, while illustrative, cannot be considered sucientstatistical evidence.

To this end we introduce a two-parameter class of discount factor specications nest-ing hyperbolic and exponential discounting:

D(y; t; 6; r) = (1# (1# 6)rt) 11!! (7)It is immediate to see that:

D(y; t; 6 = 1; r) = expf#rtgD(y; t; 6 = 2; r) =

1

1 + rt;

and hence estimating the parameter 6 from experimental data will possibly allow us todistinguish hyperbolic discounting, that is 6 = 2; from exponential discounting, 6 = 1:

4For example, one question was, "What amount of money, $y, would make you indierent between$14 today and $y 3days from now? (yLarge = 20)". Here the subject was forced to give an answerof$20 or less. Note that in answers for Session 1 we had not observed an amount less than$14 being askedfor $20 in 3 days. In Session 2, seven of the subjects consistently chose the amounts yLarge for thefull set of 30 questions. Compared to Session 1, a strategy of consistently chosing yLarge would favorpresent payments over the future ones. The choices of these seven agents may reect a framing eectthat aects the estimates of the parameters of their discounting curves for Session 2 . However overall,we fail to identify signicant framing eects between the results of Session 1and Session 2; see Section3.3 below.

5See also Green-Marakovic, 1995, Myerson-Green, 1995, Rachlin-Raineri-Cross, 1991.

7

More generally, it is straightforward to extend the two-parameter specication (7) toa four-parameter specication which also nests quasi-hyperbolic discounting and xedcosts:

yD(y; t; 6; r; (; b) =

!y if t = 0

( (1# (1# 6)rt) 11!! y # b if t > 0 ; ( < 1 (8)

Our data consists, for each subject h = 1; 2; ::::, of answers to a battery of questionssuch as [Q # present] and [Q # future], for dierent values of x and t. We presentrst our analysis of data regarding [Q # future]. Qualitative results are the same for[Q# present]; we discuss framing in Section 3.3.

Let yh(x; t) denote the answer given by subject h to question [Q # future] foramount x and delay t. We start by estimating (7), to statistically document decliningsubjective discount rates. We then estimate (8) to better characterize the functionalform of discounting, and the present bias.

To estimate (7) we assume that yh(x; t); the data is generated by

yh(x; t) = x"1# (1# 6h)rht# 11!!h "h(x; t)

where the error "h(x; t) is i.i.d. with respect to subjects h and questions (x; t): Moreover,we assume "h(x; t) is lognormally distributed. Note that we allow the parameters of thediscount curve, (6h; rh); to be indexed by the subject. We estimate individual discountcurves, independently across subjects, (6h; rh)h=1;:::;25, by non-linear least squares.

Results are collected in Table 16 and are somewhat consistent with Kirbys, 1997,conclusions.In fact, for 23 of the 27 agents the exponential specication, 6 = 1, is rejectedby the data. Nonetheless the estimates do not appear particularly appealing, essentiallybecause the point estimates for r are extremely high, in 17 cases of the order of thousandsof percentage points. Even though when discounting is not exponential r does notrepresent the discount rate, it is still the case that one dollar with no delay is worthmore than 5 in a year, for more than half of the agents in the sample at the pointestimates. The point estimates of r are in only 1 case less than 100%.7

We turn then to a second specication. In this formulation discounting is allowed tobe hyperbolic, as in the previous specication. But we include a xed cost component tothe preference for the present, that is we estimate (8) under the restriction that ( = 1.Results are reported in Table 2. The xed cost b is estimated to be signicantly dierentthan 0 for all the subjects (except subject 19 for which the estimate does not converge).It is, on average, about $4 (with a minimum value of $:31 and a maximum value of$5:38). The estimates of r are also more reasonable when we include xed costs. For

6In this and in the following tables estimates for individual subjects are not reported when thenon-linear least square algorithm did not converge.

7This is by no means only a property of our data. Similar discount rates have been generally imputedfrom experimental data; see Frederick-Loewenstein-ODonoghue, 2002, Table 1.1.

8


yD(y; t; 6; r; (; b) =

!y if t = 0

( (1# (1# 6)rt) 11!! y # b if t > 0 ; ( < 1 (8)




yh(x; t) = x"1# (1# 6h)rht# 11!!h "h(x; t)






8


yD(y; t; 6; r; (; b) =

!y if t = 0

( (1# (1# 6)rt) 11!! y # b if t > 0 ; ( < 1 (8)




yh(x; t) = x"1# (1# 6h)rht# 11!!h "h(x; t)






8

Para descuento temporal

Experimento

27 estudiantes de NYU - 2 tratamientos

En promedio la ganancia fue de $28

$10 3 d$20 1 s $30 2 s $50 m$100 3 m

6 m

Variante de Becker-DeGroot-Marschak (aleatorio en 30 preg) Cunto hoy o en un mes $50,

ejemplo $40, $0 hoy o $50 mes

Variante de Becker-DeGroot-Marschak (aleatorio en 30 preg) Cunto en un mes si hoy $50,

hubo lmite inf y sup

Los resultados favorecen a la especificacin de costos fijos con $4 para las cantidades usadas. Se rechaza un modelo

exponencial < cuasi-hiperblico. La curvatura no se obtiene de manera concluyente

25h en 137v -> 4v

25h en 142v -> 5v

Encuesta 2002

Experimento 2005

Media del experimento: 11 dlares (6 a 9 das de trabajo eventual y no calificado)

=

p=prob(X), Q=prob(Y)

, : Curvatura (AR) SS

UE

Intuicin del experimento

= 1, = 1 1 : Aversin a prdida

( , )Experimento

Alfa es distinto de 1 con sig de .01. Sigma=0.59, alfa=0.74

La curva tiene forma de S

Resultados similares a granjeros chinos

Resultados de experimento

Ahora el anlisis ser la AR como variable explicada por covariantes de localidades

IV: lluvia y habilidad para trabajo del jefe del hogar

Table 5?IV-2SLS Regressions for Risk Aversion (

Descuento Temporal, recordar a Benhabib, et al.

566 THE AMERICAN ECONOMIC REVIEW MARCH 2010

Table 6?Comparison of Exponential, Hyperbolic, and Quasi-Hyperbolic Discounting Models

Exponential Hyperbolic Quasi-hyperbolic Equation (1) /i (xlO"6) 6.26*** 7.60*** 8.58*** 8.70 ***

(0.319) (0.408) (0.544) (0.553) r 0.021*** 0.046*** 0.008*** 0.078

(0.001) (0.004) (0.001) (0.074) ? 0.644*** 0.820***

(0.019) (0.070) 0 5.070***

(0.659)

Observations 5,340 5,340 5,340 5,340 Adjusted/?2 0.515 0.519 0.522 0.523

Notes: Robust standard errors are in parentheses. Standard errors are adjusted for within-subject correlations. *** Significant at the 1 percent level.

assigns a value to reward y at time ofy?(1 ?

(1 ?

6)rt) for t > 0 (or simply y for immediate reward at t = 0).13

The three factors r, ?, and 6 separate conventional time discounting (r), present-bias (/?), and hyperbolicity (0) of the discount function. When ? = 1, as 6 approaches one the discounted value reduces to exponential discounting (e~rt) in the limit. When 0 = 2 and ? = 1, it reduces to true hyperbolic discounting (1/(1+7?)). When 6 = 1 (in the limit) and ? is free, it reduces to quasi-hyperbolic discounting (?e~rt). The three-parameter form enables a way to compare three familiar models at once.

In our experiments, subjects make 75 choices between smaller rewards delivered today and larger rewards delivered at specified times in the future as follows: Option A: receive x dong today; or Option B: receive y dong in t days.

The reward x varies between 30,000 to 300,000 and the time delay t varies between three days and three months (see Table A2 in the Web Appendix).14

Before conducting the experiment, we chose and announced a trusted agent who would keep the money until delayed delivery date to ensure subjects believed the money would be delivered. The selected trusted persons were usually village heads or presidents of women's associations. In five villages, the trusted agents were also experimental subjects. Agreement letters of money delivery were signed between the trusted agents and the first author. Agents were instructed to deliver the money to the houses of experimental subjects, which tries to equalize the pure trans action costs of receiving money immediately (i.e., at the end of the experiment) or in the future.15

After subjects completed all 75 questions, we put 75 numbered balls in the bingo cage and drew one ball to determine a pairwise choice. The option chosen for that pair (i.e., A or B) deter mined how much money was to be delivered, and when.

13 The original Benhabib-Bisin-Schotter model includes the present bias in the form of a fixed cost. Zafer Akin and Abdullah Yavas (2007) estimate the model and find the present bias parameter in the form of a fixed cost is not well supported by the data. 14 The largest amount of y, 300,000 dong (about 19 dollars), is 15 days' wages in the rural north. 15 A referee suggested appropriately cautious wording: "There are many risks involved with leaving the money with the village head; one is that the village head will give out the money early, another is that the village head will keep the

money for himself, another is that the village head will encourage those players who will be receiving a lot of money in the future to redistribute it within the village as earnings are no longer anonymous. These issues may affect the values of r, ?, and 9 in different ways. Given the difficulties in experimental design we did the best we can, and these are interesting issues for future research."

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Qu indican beta, theta?

En el experimento la espera puede ser de 3 das a 3 meses, el dinero sera entregado en sus casas, 75 preguntas

la Benhabib. La aleatorizacin para pagar una preferencia fue con tmbola.VOL. WO NO. 1 TANAKA ETAL.: RISK AND TIME PREFERENCES 567

We denote the probability of choosing immediate reward of x over the delayed reward of y in t days by P(x > (y\t)), and use a logistic function to describe this relation as follows:

(1) P(x > {y,t)) l + exp(-M(^ - y?{\ - (l - eytyi^)) We estimate the parameters /i, ?, 6, and r in the logistic equation above. The variable p is a

response sensitivity or noise parameter.

C. Empirical Results

Estimation results comparing specific functions are given in Table 6. We fitted the logistic function (1) by using a nonlinear least-squares regression procedure.16 The estimated values of (r, ;3, 6) are (0.078, 0.82, 5.07).17 This implies subjects should trade 6,151 dong today for 10,000 dong in a week, and 4,971 dong today for 10,000 dong in three weeks.

In addition to the general model (1) (shown in the far right column), we estimated exponen tial, hyperbolic, and quasi-hyperbolic discounting models. Estimating the full model (1) with unrestricted 0 does not improve R2 much compared with the estimation of the quasi-hyperbolic model, so we focus attention only on the quasi-hyperbolic discounting.

Next, we estimate the following logistic function (2) to see whether demographic variables correlate with individual difference in present bias (/?) and discount rates (r):

(2) P{X > Cv'r)) = l+exp(-Mx-^exp[-rt])) '

where ? = ?0 -h Ti?iXh r = r0 + Tjr-tXh and demographic variables and associated coefficients are represented by X,- and ?t or r-v

Table 7 shows the results from regressing estimates of the quasi-hyperbolic discounting model, allowing ? and r to depend on demographic variables. We conducted nonlinear estima tions of the logistic function (2), using household income as an independent variable for the first regression (reported in column (1)), and relative and mean village income as independent variables for the second regression (reported in column (2)).18 The variable "trusted agent" is a dummy variable, taking the value 1 if the subject is a trusted agent for money delivery. The variable "risk payment" corresponds to the amount of money the subject received in the risk experiment.

The largest effects are on discount rates r. Household income and mean village income are

positively related with patience (lower r). None of the income variables explains individual difference in present bias (?) while the estimated coefficient of ? in Table 6 (0.644) indicates subjects are present biased. This implies people are present biased regardless of their wealth, and the degree of present bias is comparable to estimates from a variety of other studies.19

16 We excluded data from three subjects who made alternating responses across consecutive rows. 17 r-tests of 9 = 1 (quasi-hyperbolic discounting) and each of the restrictions ? ? 9 = 1 (exponential discounting)

and ? = 1 and 9 = 2 (hyperbolic discounting) reject all restrictions at p > 0.0001. 18 The coefficients of explanatory variables for r (discount rates) are multiplied by 100. 19 See Alexander L. Brown, Camerer, and Zhikang Eric Chua (2009) for a review of quasi-hyperbolic model estimates.


Preferencia por el presente (logstico), recordar Pi

Mu es una parmetro de sensibilidad o simplemente ruido


Table 6?Comparison of Exponential, Hyperbolic, and Quasi-Hyperbolic Discounting Models

Exponential Hyperbolic Quasi-hyperbolic Equation (1) /i (xlO"6) 6.26*** 7.60*** 8.58*** 8.70 ***

(0.319) (0.408) (0.544) (0.553) r 0.021*** 0.046*** 0.008*** 0.078

(0.001) (0.004) (0.001) (0.074) ? 0.644*** 0.820***

(0.019) (0.070) 0 5.070***

(0.659)

Observations 5,340 5,340 5,340 5,340 Adjusted/?2 0.515 0.519 0.522 0.523

Notes: Robust standard errors are in parentheses. Standard errors are adjusted for within-subject correlations. *** Significant at the 1 percent level.

assigns a value to reward y at time ofy?(1 ?

(1 ?

6)rt) for t > 0 (or simply y for immediate reward at t = 0).13

The three factors r, ?, and 6 separate conventional time discounting (r), present-bias (/?), and hyperbolicity (0) of the discount function. When ? = 1, as 6 approaches one the discounted value reduces to exponential discounting (e~rt) in the limit. When 0 = 2 and ? = 1, it reduces to true hyperbolic discounting (1/(1+7?)). When 6 = 1 (in the limit) and ? is free, it reduces to quasi-hyperbolic discounting (?e~rt). The three-parameter form enables a way to compare three familiar models at once.

In our experiments, subjects make 75 choices between smaller rewards delivered today and larger rewards delivered at specified times in the future as follows: Option A: receive x dong today; or Option B: receive y dong in t days.

The reward x varies between 30,000 to 300,000 and the time delay t varies between three days and three months (see Table A2 in the Web Appendix).14

Before conducting the experiment, we chose and announced a trusted agent who would keep the money until delayed delivery date to ensure subjects believed the money would be delivered. The selected trusted persons were usually village heads or presidents of women's associations. In five villages, the trusted agents were also experimental subjects. Agreement letters of money delivery were signed between the trusted agents and the first author. Agents were instructed to deliver the money to the houses of experimental subjects, which tries to equalize the pure trans action costs of receiving money immediately (i.e., at the end of the experiment) or in the future.15

After subjects completed all 75 questions, we put 75 numbered balls in the bingo cage and drew one ball to determine a pairwise choice. The option chosen for that pair (i.e., A or B) deter mined how much money was to be delivered, and when.

13 The original Benhabib-Bisin-Schotter model includes the present bias in the form of a fixed cost. Zafer Akin and Abdullah Yavas (2007) estimate the model and find the present bias parameter in the form of a fixed cost is not well supported by the data. 14 The largest amount of y, 300,000 dong (about 19 dollars), is 15 days' wages in the rural north. 15 A referee suggested appropriately cautious wording: "There are many risks involved with leaving the money with the village head; one is that the village head will give out the money early, another is that the village head will keep the

money for himself, another is that the village head will encourage those players who will be receiving a lot of money in the future to redistribute it within the village as earnings are no longer anonymous. These issues may affect the values of r, ?, and 9 in different ways. Given the difficulties in experimental design we did the best we can, and these are interesting issues for future research."


Estos resultados indican que deberan cambiar $6,151 hoy por $10,000 en una semana y $4,971 hoy por $10,000 en

tres semanas.

Como el cuasi-hiperblico es el mejor de los tres modelos, lo usaremos para ver cmo las variables sociodemogrficas

pueden explicar sus parmetros.

VOL. WO NO. 1 TANAKA ETAL.: RISK AND TIME PREFERENCES 567
















VOL. WO NO. 1 TANAKA ETAL.: RISK AND TIME PREFERENCES 567
















donde


Table 7?Correlations with Present Bias and Discount Rates (OLS)

? (Present bias) r (Discount rate)

/i(xl(r6)

Constant (?{), r0)

Chinese

Trusted agent

Age

Gender

Education

Income

Relative income

Mean village income

Distance to market

South

Risk payment

Observations Adjusted R2 Davidson and MacKinnon test

(1) (2) (2) 8.93***

(0.59) 0.673***

(0.096) -0.037 (0.086)

-0.043 (0.080) 0.001

(0.002) 0.013

(0.039) -0.009

(0.005) 0.510

(0.658)

0.013

(0.012) -0.053 (0.046)

-0.819 (1.011)

5,340 0.52

F-statistic = 4.58

(p = 0.011)

9.14***

(0.61) 0.676***

(0.098) -0.046 (0.089)

-0.032 (0.080) 0.001

(0.002) 0.015

(0.039) -0.009

(0.006)

0.000

(0.019) 1.196

(2.381) 0.013

(0.012) -0.059 (0.050)

-0.928 (1.015)

5,340 0.52

F-statistic = 3.18

(p = 0.014)

0.021***

(0.004) -0.199 (0.337)

-0.189 (0.265)

-0.013** (0.005)

-0.122 (0.141)

-0.037**

(0.017) -4.530**

(1.782)

-0.010 (0.037)

-0.153 (0.152)

-7.144**

(3.593)

0.023** (0.004)

-0.019 (0.316) 0.085 (0.293)

-0.012** (0.005)

-0.121 (0.130)

-0.023 (0.015)

0.016

(0.065) -29.838**

(7.512) 0.000 (0.034) 0.080 (0.163)

-4.115 (3.602)

Notes: Standard errors are in parentheses. Standard errors are adjusted for within-subject correlations. The estimated coefficients of explanatory variables for r (discount rates) are multiplied by 100. ***

Significant at the 1 percent level. ** Significant at the 5 percent level. * Significant at the 10 percent level.

The amount of money made in the risk game earlier in the experimental session is weakly correlated with patience: individuals who received higher payments in the risk game exhibit lower discount rates r. The choices made by the individuals who were assigned the role of money delivery were not significantly different from those of other subjects.20 We also conducted regressions using instrumental variables (IV) for income variables, because the results of the Davidson-MacKinnon test suggest OLS is an inconsistent estimator. Table 8 shows the regres sion results from the IV estimations. It indicates household income, as well as a mean village income correlate with lower discount rates.

~ We also conducted regressions without the data of the five subjects who were assigned the role of money delivery.

There were few changes in regression results (see Web Appendix Table A3).


VOL. 100 NO. 1 TANAKA ETAL.: RISK AND TIME PREFERENCES 569

Table 8?Correlations with Present Bias and Discount Rates (IV-2SLS)

? (Present bias) r (Discount rate)

p (xl(T6)

Constant (?0, rQ)

Chinese

Trusted agent

Age

Gender

Education

Income (IV)

Relative income (IV)

Mean village income (IV)

Distance to market

South

Risk payment

Observations Adjusted R1

(3) (4) (3) (4) 9 09*** (0.61) 0.664***

(0.098) -0.055

(0.078) -0.039 (0.078) 0.000

(0.001) 0.037

(0.045) -0.012

(0.007) 3.801

(4.497)

0.012

(0.012) -0.081 (0.060)

-1.078 (1.104)

5,340 0.52

9 09*** (048) 0.643***

(0.113) -0.086 (0.106)

-0.065 (0.075) 0.000

(0.001) 0.032

(0.040) -0.010

(0.008)

-0.044

(0.144) 5.994

(4.878) 0.010

(0.012) -0.091 (0.055)

-1.605 (1.417)

5,340 0.52

0.024***

(0.004) -0.023 (0.337)

-0.334

(0.223) -0.015**

(0.006) -0.162

(0.140) -0.002

(0.020) -38.985*** (13.313)

0.034

(0.039) 0.239

(0.213) -5.404 (3.993)

0.023***

(0.004) 0.161 (0.358)

-0.147

(0.239) -0.013**

(0.006) -0.051

(0.140) -0.019

(0.022)

-0.128 (0.437)

-36.264** (14.907) 0.034

(0.040) 0.176 (0.212)

-5.022 (4.4507)

Notes: Standard errors are in parentheses. We adjusted standard errors for correlations within individuals. The esti mated coefficients of explanatory variables for r (discount rates) are multiplied by 100. ***

Significant at the 1 percent level. ** Significant at the 5 percent level. * Significant at the 10 percent level.

IV. Conclusion

We conducted experiments in Vietnamese villages to investigate how income and other demo graphic variables are correlated with risk and time preference.

Our results suggest mean village income is related to risk and time preferences. People liv ing in poor villages are not necessarily afraid of uncertainty, in the sense of income variation; instead, they are averse to loss. When we introduce instrumental variables for income vari

ables, mean village income is also significantly correlated with risk aversion (concavity of the utility function). From the time discounting experiment, we found that mean village income is correlated with lower discount rates, that is, people living in wealthy villages are not only less risk averse but also more patient.

Household income is correlated with patience (lower interest rate) but not with risk preference, which is consistent with the classic result of Binswanger (1980, 1981). Our results also demon strate that people are present biased regardless of their income levels and economic environments.

These results are exploratory and the experimental measures are not perfect. Furthermore, in

a cross-sectional study like this, it is difficult to conclude much about the direction of causality between preferences and economic circumstances because the study was not designed to do so.


Conclusiones

Mayores ingresos aumentan la paciencia, menores ingresos aumentan la aversin a a prdida. Con IV result menor aversin al riesgo para comunidades con mayor ingreso.

En general se mostr sesgo por el presente sin importar sus caractersticas.

Problemas con IV.

tanaka time preferences

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