from the Bank of Italy’s 1995 Survey of Household Income and Wealth (SHIW). The survey
collects data on income, consumption and wealth and several demographic variables for a
representative sample of about 8,000 Italian households. The 1995 wave of the survey elicits
attitudes towards risk. The household head is offered a hypothetical lottery and asked to
report the highest price he would be willing to pay to participate.36 Following Guiso and
Paiella (2001), we use the answers to obtain a measure of the Arrow-Pratt index of relative
risk aversion for each consumer.37 Next, we construct a SHIW sample that is comparable
to the INPS sample (people aged 18 to 65, neither self-employed nor working in the public
sector), and run a regression of the coefficient of relative risk aversion on attributes that are
observed in both data sets: a cubic in age, net real earnings, dummies for firm size, industry,
region of residence, occupational status and gender. The K2 of the regression is about 0.2.
We retrieve the estimated coefficients and use them to impute the relative risk aversion of
all the workers present in the INPS∕CAD matched data set. The resulting measure is very
reasonable and conforms to prior expectations: average relative risk aversion is 5.03 and
the median 4.86. The index ranges from 1.79 to 20.64.38 We construct an indicator for high
risk aversion (an imputed coefficient above the cross-sectional median). Using an indicator
30Specifically, respondents are asked the following question:
“We would like to ask you a hypothetical question that we would like you to answer as if the situation were
a real one. You are offered the opportunity of acquiring a security permitting you, with the same probability
of 1∕2, either to gain 10 million lire or to lose all the capital invested. What is the most that you are
prepared to pay for this security?”. Ten million lire corresponds to about Euro 5,000 (or $5,000). Interviews
are conducted personally at home by professional interviewers, who to help respondents understand the
question show an illustrative card and are ready to provide explanations. The respondent can answer in one
of following three ways: a) declare the maximum amount he or she is willing to pay to participate; b) don’t
know; c) unwilling to answer.
3'Let Zi be the maximum amount consumer i is willing to pay to enter the lottery; cι the endowment and
ui the utility function. The maximum price for participating in the lottery is then defined by:
(30)
Eui (cι ) — 2 u ʃ (c Y x) Y 2 u,; (c'’ Z‘ )
where E is the expectations operator and x what the agent gains in the favorable state (i..e, x — 10 million
lire). Taking a second order Taylor expansion and solving for the Arrow-Pratt measure of absolute risk
aversion Ai (c⅛) gives
a ,ʌ _ U (ci ) _ 2(10 - Zi )
a ( ) U (ci) (100 + Z)
(31)
Given that Zi is known, this expression can be recovered for all those who answer the survey question on
the lottery. Relative risk aversion % (c⅛) is obtained by multiplying Ai by individual i’s consumption c⅛.
38Our SHIW sample includes 1,919 workers with valid answers to the risk aversion question. The sample
distribution of the degree of relative risk aversion is right-skewed with a median of 5.35; its value ranges
from 0.005 to 36.26 but 90 percent of the cross-sectional distribution is comprised between 1.5 and 12.6.
29