Multiple price list design

There are four common methods of measuring risk aversion in the field, all of which have

been applied to some extent in a developing country context: Ordered Lottery Selection

(OLS), Multiple Price List (MPL), Titration Procedure, simple investment games. 1 The point

of each method is to elicit the deviance of the respondents’ utility function from that which

would be expected by Expected Utility Theory. Respondents who are risk-averse will have a

certainty equivalent value (CEV) below the expected monetary value (EMV) of an option and

conversely, those that are risk-loving will have a CEV above the EMV. As an example, if the

choice is between having a fixed amount of money or a 50% chance at £10: someone who is

risk neutral would demand exactly £5 to take the fixed amount option (CEV=EMV=£5),

someone who is risk-averse would demand less than £5 (CEV<EMV) to forgo the chance at

£10, and someone who is risk-loving would only accept more than £5 (CEV>EMV) to take

that fixed amount over the chance at £10.

The Multiple Price List (MPL) design is promising because it allows for a more accurate

measure of Constant Relative Risk Aversion (CRRA) than OLS, is more robust than

Titration, might be less perceived as gambling as compared to simple investment games, and

has been successfully piloted in field trials in Uganda (Tanaka & Munro, 2014). The original

design of the MPL is given in the seminal paper of Holt & Laury (2002) which has been cited

by over 2,000 subsequent experiments in the literature. All of these subsequent experiments

are similar in nature to the original design of Holt & Laury (2002) with modifications to

allow for time-variance, loss-aversion, and other modified characteristics of the utility

function that may be relevant for the given research question. For simplicity and in order to

make the survey results more comparable to the literature, a version of the design of Tanaka

& Munro (2014) was used and is based on the original MPL design of Holt & Laury (2002).

As shown in Figure 1, Respondents chose between option A or option B. Option A is the safe

option with a 4/4 (100% probability) of yielding 4,000 UGX. Option B is the chance option

with ¾ (75% probability) of the left hand value and ¼ (25% probability) of the right hand

value. The respondent starts at the top and chooses each time between A or B. A should be

chosen in row #1, while B in row #8 and the switching point—where the respondent 1 Methods informed by conversation with Ben D’Exelle of University of East Anglia (UEA) at a Methods in the Field Course conducted by UEA London, 18 May, 2013.

“switches” from only answering A to only answering B—will allow the researcher to elicit

the respondent’s risk aversion as measured by the Constant Relative Risk Aversion (CRRA)

parameter.

#

Bag A Bag B4 red

marbles

3 red marbles

1 white marble

Pick a marble from

A or B?1 4,000 4,000 2,000

2 4,000 4,500 2,000

3 4,000 5,000 2,000

4 4,000 5,500 2,000

5 4,000 6,000 2,000

6 4,000 7,000 2,000

7 4,000 7,000 3,000

8 4,000 7,000 4,000

NB: pay-outs are in Ugandan Shillings (conversion rate at the time of survey: 4,000UGX £1 GBP)

Figure 1: Example MPL design used for farmer survey in Buikwe, Mukono, and Kayunga districts based on Tanaka & Munro (2014).

In measuring the degree of a respondent’s level of risk-aversion or risk-loving, a popular

choice is the Constant Relative Risk Aversion (CRRA) measure. This is the value r in the

utility function U ( x )= x1−r

1−r for which the probability-weighted sum of utility outcomes is

maximized (i.e.max ¿); where x i is the pay-out to the individual (i) with probabilitypi. Based

on the researchers’ experimental design, they can elicit different ranges of the CRRA for

which the respondent’s choice in the experiment was optimal—assuming expected utility

theory is true. It is easiest to demonstrate the methodology and results in column 2 of Table 1

below with an example calculation.

Assume a given participant answers A for all choices until row 6, where she switches to B for

that row through the rest of the game (rows 6, 7, 8 see Figure 1). For row 5, she chose the

safe option of a guaranteed (i.e. 100% probability of) 4,000 UGX, which by revealed

preference she must have preferred more than the 75% chance of 6,000 UGX. However, for

row 6 she took the probabilistic option of 75% likelihood of 7,000 UGX and 25% likelihood

of 2,000 UGX. Her risk preference can then be calculated as interval between the solutions

for r given the two equations (1) and (2) shown below:

40001−r

1−r> 0.75∗60001−r

1−r+ 0.25∗20001−r

1−r(1)

40001−r

1−r≤ 0.75∗70001−r

1−r+ 0.25∗20001−r

1−r(2)

Solving (1) yields r>2 and solving (2) yields r ≤2.391. As such, the interval for the actual

risk aversion parameter is given by 2.00<r ≤2.39 (as shown in Table 1). It is also easy to

calculate the expected value difference between choice A and choice B at her switching point

of row 6 (see equation (3) below). The expected value of choosing the safe option of 4,000

UGX is 1,750 UGX less than what would be expected by taking the probabilistic option in B

(as shown in Table 1 as well).

E ( A )−E (B )=[1.00∗( 4,000 ) ]−[ 0.75∗7,000+0.25∗2,000 ]=−1,750 (3)

To enhance understanding of the experimental design, Tanaka & Munro (2014) had each row

of the game (like Figure 1) presented at a different table in the experiment room. Thus, when

a participant came in, she would physically sit at a different location to make each choice.

She was also making each choice in isolation, although, the order of the choices was

preserved. Tanaka & Munro (2014) argue this allows the participant—who might be illiterate,

elderly, and with no formal education—to focus on the decision and not get confused by the

structure of the game. Given the low levels of education in impoverished, rural areas, even a

simple game like this requires a great degree of attention and thought to understand fully.

Likely, this simplified and focused setup allowed them to get relatively low irrational

response rates in their experiments.

Table 1: Risk aversion classification based on lottery choices for design in

above

Row of first B(switching

point)

Range of relative risk aversion

for U ( x )= x1−r

1−r

Expected value difference at switch point

(E [A]−E[B])Risk preference classification*

ALL B - 500 Irrational

2 −∞<r ≤−0.82 125 Very risk-loving

3 −0.82<r ≤0.92 -250 Risk-loving to risk neutral

4 0.92<r ≤1.62 -625 Slightly risk-averse

5 1.62<r ≤2.00 -1,000 Moderately risk-averse

6 2.00<r ≤2.39 -1,750 Intermediate risk-averse

7 2.39<r ≤3.79 -2,000 Highly risk-averse

8 3.79<r ≤∞ -2,250 Very risk-averse

ALL A - - Irrational

MULTIPLE - - Irrational

* Terminology based on Tanaka & Munro (2014)

The third column of Table 1 shows the expected pay-off difference between choosing option

A compared to option B. From the first 2 choices, option A has a higher expected pay out

than option B. Most respondents will choice option A in the first instance and switch to

option B at some point before the final round (8 th row). Variations of this basic setup abound

in the literature, mostly to fit the research context or simplify the setup; the original risk-

aversion classification from Holt & Laury (2002) is reprinted as a further example in Table 2.

Table 2: Risk-aversion classification based on lottery choices from Holt & Laury (2002)

Works Cited

Holt, C.A. & Laury, S.K. (2002) Risk aversion and incentive effects. The American Economic Review. 92 (5), 1644–1655.Tanaka, Y. & Munro, A. (2014) Regional Variation in Risk and Time Preferences: Evidence from a Large-scale Field Experiment in Rural Uganda. Journal of African Economies. 23 (1), 151–187.