The Psychometric and Empirical Properties of Measures of ... · Job B will give you a 50-50 chance...

The Psychometric and Empirical Properties of Measures of

Risk Preferences

ONLINE APPENDIX

Jonathan Beauchamp, David Cesarini, Magnus Johannesson

Jonathan Beauchamp (To whom correspondence should be addressed)

Department of Economics, Harvard University,

Littauer Center 1805 Cambridge Street Cambridge, MA 02138

[email protected]

David Cesarini,

Department of Economics and Center for Experimental Social Science, New York University,

19 W. 4th Street, 6FL New York, NY 10012

[email protected].

Magnus Johannesson,

Department of Economics, Stockholm School of Economics,

P.O.Box 6501, Sveavagen 65 SE-113 83 Stockholm

[email protected].

1

ONLINE APPENDIX I - Variables Construction

This appendix provides additional details on the variables used in the paper. It is organized by

the di↵erent sources from which our data was obtained.

SALTY Survey

Survey Timeline

Beginning in early 2009, SALTY was sent to a total of 24,914 Swedish twins in several waves.

The final reminders were sent out during the spring of 2010 to those who did not initially respond

to the survey. The test-retest surveys were sent out in August and September 2010.

Zygosity

Zygosity was resolved either by questionnaire items with high reliability or, when available, by

analysis of biosamples (Lichtenstein et al., 2006).

Risk Attitudes

Risk General and Risk Financial. Our Risk General and Risk Financial questions measure

risk attitudes on a scale from one to ten, where one denotes complete unwillingness to take risks

and ten denotes complete willingness to take risks. Risk General asks about general risk attitudes

and Risk Financial asks about risk attitudes in the domain of financial risk. These questions are

available in several waves of the German Socioeconomic Panel. Dohmen et al. (2011, 2012) establish

the behavioral validity of the Risk General question and use it to study the transmission of risk

attitudes from parent to child. The Risk General question asks the following:

How do you see yourself: are you generally a person that is fully prepared to take risks

or do you try to avoid taking risks? Please tick on the scale below, where the value 1

means ”unwilling to take risks” and the value 10 means ”fully prepared to take risks”.

The Risk Financial question asks the following:

Are you a person that is fully prepared to take financial risks or do you try to avoid

taking financial risks? Please tick on the scale below, where the value 1 means ”unwilling

to take risks” and the value 10 means ”fully prepared to take risks”.

Risk HRS. Risk HRS Barsky et al. (1997) asks people to make three hypothetical comparisons

between a job which pays SEK 25,000 for the rest of the respondent’s life and a job with a 50-50

chance of SEK 50,000 or a lower amount. The lower amount varies by question. We use responses to

these questions to categorize respondents into one of four distinct categories, with a higher category

corresponding to higher risk tolerance. More than 97.8% of the respondents gave consistent answers

2

across the three questions; the respondents who gave inconsistent answers were coded as missing

for this variable. Question 1 is reproduced below:

Imagine the following hypothetical situation. You are the sole provider of your house-

hold and you have the choice between two equally good jobs:

Job A will with certainty give you SEK 25,000 per month after taxes for the rest of

your life.

Job B will give you a 50-50 chance of SEK 50,000 per month after taxes for the rest of

your life, and a 50-50 chance of SEK 20,000 per month after taxes for the rest of your

life.

Which job do you choose?

Question 2 and Question 3 are identical to Question 1, but with the second leg of the gamble in

Job B o↵ering 50-50 chances of SEK 22,000 and SEK 17,000 per month after taxes for the rest of

one’s life, respectively.

Risk Gain and Risk Loss. Our final two questions about risk attitudes ask subjects about

their attitudes toward two hypothetical gambles over large stakes. We coded both variables sepa-

rately as one for the respondents who preferred the gamble and as zero for the respondents who

preferred the sure amount. The Risk Gain question asked respondents the following:

Which of the following two alternatives would you chose:

A: To receive SEK 24000 with certainty

B: A 25% chance of winning SEK 100000

The Risk Gain question asked respondents the following:

Which of the following two alternatives would you chose:

A: To lose SEK 24000 with certainty

B: A 25% chance of losing SEK 100000

We adopted these two questions from the series of hypothetical gambles used by Tversky and

Kahneman (1992) to estimate risk attitudes over gains and losses. We used considerably higher

hypothetical stakes than Tversky and Kahneman, and we included a single binary choice question

for each of the two gambles, whereas they used a series of binary choices to estimate the certainty

equivalent of the gambles (our sure outcomes in the two binary questions are close to the me-

dian certainty equivalents in Tversky and Kahneman, scaled up proportionally to the hypothetical

stakes).

Other Variables from the SALTY Survey

Behavioral Inhibition and Rotter Locus of Control Scale. SALTY respondents filled out

two personality scales, one measuring behavioral inhibition and one measuring locus of control. To

3

measure beliefs of personal control, we used the Locus of Control (LOC) scale (Rotter, 1966). This

scale is made up of 13 questions, one of which asked about student testing and was not included on

the survey due to the age of the sample; our LOC score is thus based on twelve questions and ranges

from zero to twelve. External control is also strongly related to neuroticism and internal control

with self-e�cacy (Judge et al., 2002). To measure behavioral inhibition, the survey included the 16-

item Adult Measure of Behavioral Inhibition (AMBI) battery (Gladstone and Parker, 2005). Each

item is measured on a three-point scale and the scores on all items are summed to obtain a variable

ranging from zero to 32. The AMBI is a subjective measure of general long-standing inhibition

designed to capture how an individual responds to social novelty and risk stimuli (Gladstone and

Parker, 2005). Higher scores on the AMBI reflect a proneness for social avoidance and introversion.

Equity Share. To measure wealth, we ask invidivuals in the SALTY survey to list the value

of their assets in each of six categories. The equity share is then estimated as the share of stocks

out of total wealth (the sum of the assets in the six categories). The question reads as follows:

Below, please state the value of your assets in each of the categories. By value we

mean the value at which you could sell the assets tomorrow, if the need were to arise.

State the value in SEK. If the assets are jointly owned with someone else, for example

a spouse, only state your share of the assets.

· Property, including summer cottage, forest and farmland

· Stocks· Bonds· Bank· Boat, car and other vehicles.

· Other assets, for example jewelry, antiques and art.

Own Business. To measure of entrepreneurship, we used responses to the question “Have you

ever been running your own business?”. Individuals who answered in the a�rmative were coded as

having an own business.

SALT Survey

Alcohol Consumption. To measure alcohol consumption, we utilize a set of questions in

SALT. Our main question reads:

Have you drunk, wine or liquor more than twice during the last month? By beer we

mean beer which is stronger than light beer.

Respondents who answered no to this question were asked the following question:

How often do you usually drink beer? By beer I mean beer stronger than light beer.

How often do you usually wine?

How often do you usually liquor?

4

Each of these three questions had the same eight response categories, ranging from never to every

day. We classify an individuals as alcohol consumers if they answered the first question, about

drinking habits in the last month, in the a�rmative. We also classified individuals as alcohol

consumer if their answers to the follow-up questions indicated that they usually drinks either beeer,

wine or liquor at least twice a month (twice per month was one of the eight response categories).

Birthweight. The main source of our data on birthweight is the SALT survey, which contained

the question “What was your birth weight?” For twins in the SALT cohort, we also have information

on birth weight collected from delivery archives throughout Sweden (Lichtenstein et al., 2006). The

birth records contain detailed information on the characteristics of each child. The archival data

are preferrable to the self-report data, and thus we used them when both were available. Our

birthweight variable is scaled in kilograms.

Smoking. To measure smoking, we utilized the SALT question:

Have you ever smoked or used snu↵?

The response categories were

·No, I have not even tried it

·Yes, but I have only tried it

·I used to smoke on and o↵

·I used to smoke regularly

·I used to smoke at parties

·I used to use snu↵ on and o↵

·I used to snu↵ regularly

·I presently smoke on and o↵

·I presently smoke regularly

·I presently smoke at parties

·I presently use snu↵ on and o↵

·I presently snu↵ regularly

·Don’t know

·Refuse

Individuals whose answers indicated that they smoke regularly, that they used to smoke regularly,

that they smoke on and o↵, or that they used to smoke on and o↵ were all classified as smokers.

All other respondents were classified as non-smokers.

Statistics Sweden

Income. The income measure used in this is paper (sammanraknad forvarvsinkomst) is defined

as the sum of income earned from wage labor, income from own business, pension income and

unemployment compensation. Capital income is not included and the variables are not censored.

Since administrative records only contain information on legally earned, taxed income, annual

income is only an imperfect proxy for actual income earned. We use the natural logarithm of

5

income in 2005. We code the log income variable as missing for individuals with zero income or

with very low income (this applied to fewer than 1.2% of individuals in the sample).

Marital Status. This is a binary variable taking the value one if the individual was married

in the year 2005.

Years of Education. Educational data is drawn from administrative records which include

a set of dummy variables for highest degree attained. These dummies are converted into years of

schooling using population averages estimated by Isacsson (2004). We use data for the year 2005.

Swedish National Service Administration

Cognitive Ability. We used social security numbers to match the men in the SALTY sample

to conscription data provided by the Swedish National Service Administration. All men in our

sample were required by law to participate in military conscription around the age of 18 (SFS

1941:967). They enlisted at a point in time when exemptions from military duty were rare and

typically only granted to men who could document a serious handicap that would make it impossible

to complete training. Indeed, in our sample, we were able to successfully match 95% of the male

twins to the information in the military archives. The actual drafting procedure could take several

days, during which recruits underwent medical and psychological examinations, including an IQ

test. For the men born after 1950, approximately half of our sample, the military data has been

digitalized. For the remaining twins, we manually retrieved the information from the Military

Archives. The first test of cognitive ability used by the Swedish Military was developed in 1943,

and it has subsequently been revised and improved on a few occasions. Its basic structure has,

however, remained unchanged during the study period considered in this paper. Carlstedt (2000)

discusses the history of psychometric testing in the Swedish military and provides evidence that the

measure of cognitive ability is a good measure of general intelligence Spearman (1904). The male

SALTY respondents studied in this paper took four subtests (logical, verbal, spatial and technical)

which, for most of the study period, were graded on a scale from 0 to 40. Because there were

minor changes to the test during our study period, we do not use the raw scores as our measure of

cognitive ability. Instead, we first transformed the subjects’ test scores to percentile ranks and then

to a normally distributed z-score with mean zero and variance one, separately by birthyear, using a

standardization sample of all twins for whom data was available (not just the SALTY respondents).

For a more comprehensive discussion, see Lindqvist and Vestman (2011).

Swedish National Insurance Board

Portfolio Risk. Our Portfolio Risk variable is the average risk level of the funds invested in

by an individual, with the risk of each fund measured as the (annualized) standard deviation of the

fund’s monthly rate of return over the previous years. This was the definition of risk used by the

Premium Pension Authority. For additional information, see Cesarini et al. (2010).

6

ONLINE APPENDIX II - The Asymptotic Distribution of the KSS

Estimator with Clustering

KSS’s GMM estimator is

� =

"�

⇢

�

z

#⌘ A �1

N

·DN

,(1)

where AN

⌘ 1

N

NX

i=1

"h

2i

h

i

zi

�h

i

zi

z0i

zi

#, D

N

=1

N

NX

i=1

"h

i

y

i

z0i

y

i

#,

and where we use h

i

to denote the posterior score ⇢

EB

i

, for notational simplicity and to follow the

KSS notation. It follow that

� = A �1N

·

1

N

NX

i=1

"h

i

(hi

�

⇢

+ zi

�

z

+ ⌘

i

)

z0i

(�hi

�

⇢

+ zi

�

z

+ !

i

)

#!

= A �1N

· A

N

"�

⇢

�

z

#+

1

N

NX

i=1

"h

i

⌘

i

z0i

!

i

#!

=)pN

⇣� � �

⌘= A �1

N

·

1pN

NX

i=1

"h

i

⌘

i

z0i

!

i

#!.(2)

To find the asymptotic distribution of (2), we separate the sum in a part for the twin pairs,

whose error terms ⌘i

and !

i

are correlated, and a part for the singletons:

1pN

NX

i=1

"h

i

⌘

i

z0i

!

i

#=

rT

N

1pT

TX

t=1

(mt1 +m

t2) +

rS

N

1pS

SX

s=1

ms

,

where mi

⌘ [hi

⌘

i

, zi

!

i

]0and where t = 1...T indexes the twin pairs and s = 1...S indexes the

singletons (so N = 2T + S). By the Central Limit Theorem,

1pT

TX

t=1

(mt1 +m

t2) �!d

Normal�0, E

⇥(m

t1 +mt2) (mt1 +m

t2)0⇤� and

1pS

SX

s=1

ms

�!d

Normal�0, E

⇥m

s

m0s

⇤�.

It follows from the independence of the sum of twin pairs from the sum of singletons that

1pN

NX

i=1

"h

i

⌘

i

z0i

!

i

#�!

d

Normal (0, Bclus

) ,(3)

where Bclus

=T

N

E

⇥(m

t1 +mt2) (mt1 +m

t2)0⇤+ S

N

E

⇥m

s

m0s

⇤.

7

For the asymptotics to be meaningful, we thus need to fix the fractions T

N

and S

N

= 1 � 2TN

as

N �! 1. Combining (3) with the fact that

plim AN

= A ⌘E

"h

2i

h

i

zi

�h

i

zi

z0i

zi

#,

it follows from the asymptotic equivalence lemma (Wooldridge, 2002, p. 39) that the asymptotic

distribution of the estimator (1) in the presence of cluster samples is

pN

⇣� � �

⌘!

d

Normal�0,A�1B

clus

A�1�.

8

ONLINE APPENDIX III - Estimating Pairwise Correlations

It follows from the paper’s equation (12) that the correlation between any two measurement-

error-adjusted risk variables in the model is given by

(4) corr(&⇤j

, &

⇤j

0) =�

j

�

j

0q(�

j

2 + �

2"j)(�

j

02 + �

2"j0

).

We again focus our attention on &

⇤, rather than ⇢

⇤, because doing so allows us to estimate the

correlations with the covariates sex and birth year partialled out from the permanent component

of risk attitudes.

The �j

parameters (j = 1...J) are identified from the�J

2

�empirical pairwise covariances between

the J risk variables. When J = 2, there is only one pairwise covariance and two �

j

parameters,

so the model is underidentified and we make the identifying assumption that �

2"1

= 0. (When

J = 3, there are as many pairwise covariances as �

j

parameters, and when J � 4 there are more

covariances than parameters; in both cases, no such identifying assumption is needed.) Notably,

when J = 2 or J = 3, the �

j

(and �

2"j) parameters su�ce to fully describe all pairwise covariances

(and correlations) without loss of information, and (4) is the measurement-error-adjusted polychoric

correlation between &

⇤j

and &

⇤j

0 . Below, we obtain consistent estimates of all pairwise correlations

between the five risk variables by estimating bivariate (J = 2) versions of the paper’s equation (13)

(with covariates age and sex) for all possible pairwise combinations of risk variables and substituting

the resulting estimates in (4).

In the absence of measurement error (�2m

= 0) and when only data from the first measurement

is used, we make the usual identifying assumption that �2"j

= 1 (j = 1..J). When J = 2, there is

only one pairwise covariance and two �

j

parameters, so the model is underidentified and we make

the additional identifying assumption that �1 = 11. (This assumption is not needed when J � 3.)

Expression (4) still applies and is now the unadjusted polychoric correlation between &

⇤j

and &

⇤j

0

when J = 2 or J = 3. As above, we substitute estimates from bivariate (J = 2) versions of the

paper’s equation (13) in (4).

Online Appendix III Table I reports estimates of the pairwise correlations between the risk-

attitude variables. The lower and upper diagonal entries are the estimates from the models with

and without adjustment for measurement error. The adjusted estimates are noticeably higher than

the unadjusted estimates, once again underscoring the importance of correcting for measurement

error. The correlations – especially those between the three most reliably measured variables

(Risk General, Risk Financial, and Risk HRS) – are sizeable and highly significant, suggesting the

1This assumption implies the following constraint:��corr(&⇤j , &

⇤j0)

�� =��

1·�2p(1+1)

p�2

2+1)

�� 1p2⇡ 0.707. However,

this constraint cannot be binding, as our test-retest reliability estimates (with sex and birthyear partialled out) are allsmaller than 0.64 and the correlation between two variables cannot exceed the geometric mean of their signal-to-noiseratios. (Setting �

2"1 = 0 instead of �2

"1 = 1, as for the model with measurement error, would circumvent this issue, butthe GLLAMM program we use for this estimation does not allow such a specification in the absence of measurementerror.)

9

variables share much of their variance. At the same time, the correlations are all far from unity,

thus also suggesting an important part of the variance is specific to each variable.

Online Appendix III Table I. Pairwise Correlations Between the Risk Variables

Risk General Risk Financial Risk HRS Risk Gain Risk Loss

Risk General 0.581 (0.004) 0.312 (0.011) 0.167 (0.017) 0.132 (0.013)

Risk Financial 0.912 (0.022) 0.434 (0.010) 0.236 (0.016) 0.135 (0.013)

Risk HRS 0.506 (0.023) 0.670 (0.026) 0.263 (0.018) 0.136 (0.014)

Risk Gain 0.310 (0.045) 0.420 (0.049) 0.486 (0.058) 0.129 (0.021)

Risk Loss 0.238 (0.027) 0.236 (0.027) 0.261 (0.031) 0.242 (0.050)

NOTES: Entries above the diagonal are unadjusted for measurement error and entries below the diagonal

are adjusted. All estimates are significant at the 1% level.

10

ONLINE APPENDIX IV - The ACE and the ADE Models and our

Empirical Framework

The A, C, D, E factors

Additive genetic factors (A) capture the variation due to the sum of the individual e↵ects of all

individual alleles in the genome (alleles are the alternative forms of the DNA sequences that may

occupy a given locus, and a locus is the location of a DNA sequence on a chromosome). Dominant

genetic factors (D) capture the variation attributable to cases in which the combined e↵ect of the

two alleles at a locus is di↵erent from the sum of the individual e↵ects of each allele. Common

environment (C) captures the environmental influences that vary exogenously between the homes or

families but that are shared by twins (or siblings). Finally, individual environment (E) encompasses

everything that is not captured by the other factors; to the econometrician, this is simply an error

term.

Estimating the ACE and the ADE Models with our Empirical Framework

It follows from the assumptions of the ACE model that

corr

ACE

dz

(yi

, y

i

0) =1

2�

2A

⇤ + �

2C

⇤ and(5)

corr

ACE

mz

(yi

, y

i

0) = �

2A

⇤ + �

2C

⇤ .(6)

For the ADEmodel, we assume further, as is implied by biometrical genetic theory, that corrdz

�D

⇤i

, D

⇤i

0�=

1/4. It follows that

corr

ADE

dz

(yi

, y

i

0) =1

2�

2A

⇤ +1

4�

2D

⇤ and(7)

corr

ADE

mz

(yi

, y

i

0) = �

2A

⇤ + �

2D

⇤ .(8)

and that the ADE model predicts that corrmz

(yi

, y

i

0) � 2 · corrdz

(yi

, y

i

0), whereas the ACE model

predicts the opposite.

Model With Measurement Error

To model the correlation between MZ twins and between DZ twins in our framework, let &⇤ in

the paper’s equation (1) satisfy&

⇤imd

�

&

⇤= T

⇤d

+M

⇤md

+ U

⇤imd

,

where d indexes all same-sex twins (both DZ and MZ), m indexes all MZ twins, and i indexes the

individual respondents (we still assign unique indices d and m to the subjects without twins or

without MZ twins). T

⇤d

, M⇤md

, and U

⇤imd

are assumed to be normally distributed with mean zero

11

and mutually independent. It follows that �2T

⇤ + �

2M

⇤ + �

2U

⇤ = 1 and that

corr

dz

(&⇤imd

, &

⇤i

0m

0d

) = �

2T

⇤ and(9)

corr

mz

(&⇤imd

, &

⇤i

0md

) = �

2T

⇤ + �

2M

⇤ .(10)

We focus our attention on &

⇤ rather than ⇢

⇤ here, as this will allow us to estimate the heritability

of risk attitudes residualized on the covariates sex and birthyear. Letting y = &

⇤/�

⇢

⇤ be the trait

of interest in the ACE model and combining (9), (10), (5), and (6) yields

�

2A

⇤ = 2�2M

⇤ ; �

2C

⇤ = �

2T

⇤ � �

2M

⇤ ; and �

2E

⇤ = �

2U

⇤ .

Combining (9), (10), (7), and (8) yields the corresponding results for the ADE model:

�

2A

⇤ = 3�2T

⇤ � �

2M

⇤ ; �

2D

⇤ = 2��

2M

⇤ � �

2T

⇤�; and �

2E

⇤ = �

2U

⇤ .

Model Without Measurement Error

In the absence of measurement error (�2m

= 0) and using only the data from the first measure-

ment, the model is once again unidentified, so we make the identifying assumption that �2&

⇤ ·�2U

⇤ = 1.

12

ONLINE APPENDIX V - Additional Results

13

Online Appendix V Table I. Predictive Validity of the Risk Variables: Entire Sample

Portfolio Risk Equity Share Own Business Alcohol Smoking

�

p

R

2 �R

2�

p

R

2 �R

2�

p

R

2 �R

2�

p

R

2 �R

2�

p

R

2 �R

2

Risk General

�

2m

= 0 0.289*** 0.026 0.002 0.006*** 0.022 0.003 0.061*** - - 0.022*** - - 0.028*** - -

(0.091) (0.002) (0.005) (0.004) (0.005)

�

2m

> 0 0.373*** 0.027 0.003 0.007*** 0.024 0.004 0.080*** - - 0.028*** - - 0.037*** - -

(0.117) (0.002) (0.006) (0.005) (0.007)

Risk Financial

�

2m

= 0 0.754*** 0.035 0.011 0.016*** 0.039 0.019 0.061*** - - 0.022*** - - 0.006 - -

(0.088) (0.002) (0.005) (0.004) (0.005)

�

2m

> 0 0.937*** 0.041 0.018 0.020*** 0.053 0.032 0.079*** - - 0.029*** - - 0.007 - -

(0.116) (0.003) (0.006) (0.005) (0.007)

Risk HRS

�

2m

= 0 0.685*** 0.031 0.008 0.006*** 0.023 0.002 0.066*** - - 0.020*** - - -0.005 - -

(0.097) (0.002) (0.005) (0.004) (0.006)

�

2m

> 0 1.005*** 0.043 0.020 0.009*** 0.027 0.006 0.101*** - - 0.030*** - - -0.006 - -

(0.150) (0.003) (0.008) (0.007) (0.009)

NOTES: This table reports the KSS estimates of the e↵ect of risk attitudes on the five outcome variables given in the column headings

and the KSS R

2 for the model with measurement error adjustment (�2m

> 0), as well as the OLS estimates and R

2 for the model

without adjustment (�2m

= 0). 30 regressions were run to generate these results (3 risk variables ⇥ 5 outcomes ⇥ 2). Results are for

the entire sample. �R

2 is the incremental R2 from including the risk variable in the regression. All specifications include a constant

and controls for sex, birthyear, birth weight, log income, marital status, and education.

* Significant at 10% level; ** significant at 5% level; *** significant at 1% level.

14

Online Appendix V Table II. Predictive Validity of the Risk Variables: Complete Results for Risk HRS, Males Only

Portfolio Risk Equity Share Own Business Alcohol Smoking�

2m

= 0 �

2m

> 0 �

2m

= 0 �

2m

> 0 �

2m

> 0 �

2m

= 0 �

2m

= 0 �

2m

> 0 �

2m

= 0 �

2m

> 0Risk HRS 0.697*** 1.070*** 0.010*** 0.016** 0.145*** 0.091*** 0.007 0.013 -0.009 -0.009

(0.152) (0.242) (0.005) (0.008) (0.015) (0.009) (0.006) (0.010) (0.010) (0.016)Birth Year 0.138*** 0.117*** -0.003*** -0.003*** -0.005** -0.002 0.001 0.001 -0.014*** -0.014***

(0.028) (0.029) (0.001) (0.001) (0.015) (0.002) (0.001) (0.001) (0.002) (0.002)Education 0.075 0.044 0.004** 0.004** -0.007* -0.004 0.005** 0.005** -0.011*** -0.011***

(0.056) (0.058) (0.002) (0.002) (0.004) (0.004) (0.002) (0.002) (0.004) (0.004)Log Income -0.550* -0.865*** -0.001 -0.004 -0.161*** -0.130*** 0.039*** 0.033** -0.034 -0.040*

(0.303) (0.333) (0.013) (0.014) (0.023) (0.021) (0.013) (0.013) (0.021) (0.022)Birth Weight -0.222 -0.217 -0.0018 -0.003 0.044*** 0.049*** 0.006 0.006 0.033*** 0.028

(0.254) (0.258) (0.007) (0.007) (0.017) (0.016) (0.010) (0.010) (0.017) (0.018)1 if Married -0.010 -0.039 -0.012 -0.015* 0.046** 0.051*** 0.053*** 0.053*** -0.026 -0.021

(0.273) (0.275) (0.008) (0.008) (0.018) (0.017) (0.012) (0.012) (0.019) (0.019)Cognitive 0.422** 0.314* 0.002 -0.001 0.000 0.027** 0.005 0.002 -0.044*** -0.043***

Ability (0.177) (0.189) (0.005) (0.005) (0.012) (0.011) (0.008) (0.008) (0.011) (0.012)R

2 0.029 0.042 0.024 0.034 0.088 0.045 0.023 0.023 0.042 0.043�R

2 0.009 0.021 0.004 0.013 0.072 0.027 0.000 0.002 0.000 0.000N 2,558 2,498 1,462 1,426 3,305 3,388 3,167 3,093 3,312 3,228NOTES: This table reports complete regression results for each of the five outcome variables given in the column headings, with covariates Risk HRS and

control variables (including cognitive ability). Results are for the male sample. The KSS estimates and R

2 are reported for the model with measurement

error adjustment (�2m

> 0) and the OLS estimates and R

2 are reported for the model without adjustment (�2m

= 0). �R

2 is the.incremental R2 from

including the Risk HRS variable in the regression. All specifications include a constant.


15

Online Appendix V Table III. Predictors of Risk Attitudes: Entire Sample

Risk General Risk Financial Risk HRS�

2m

= 0 �

2m

> 0 �

2m

= 0 �

2m

> 0 �

2m

= 0 �

2m

> 0Sex -0.239*** -0.306*** -0.375*** -0.477*** -0.329 -0.406***

(0.020) (0.028) (0.020) (0.030) (0.040) (0.033)Birth Year 0.019*** 0.025*** 0.015*** 0.020*** 0.022 0.027***

(0.002) (0.003) (0.002) (0.002) (0.004) (0.003)Birth Weight 0.077*** 0.104*** 0.042** 0.052** 0.020 0.032

(0.020) (0.025) (0.020) (0.025) (0.022) (0.027)Education 0.054*** 0.070*** 0.070*** 0.087*** 0.089 0.110***

(0.004) (0.005) (0.004) (0.006) (0.005) (0.006)R

2pseudo

0.048 0.080 0.080 0.126 0.100 0.152n1 10,440 10,440 10,472 10,472 9,831 9,831n2 - 463 - 463 - 443ln (L) -21,740.01 -22,594.68 -20,519.594 -21,322.79 -11,762.36 -12,230.31NOTES: The estimates in the left column under each variable name are

unadjusted for measurement error (�2m

= 0); the estimates in the second

column are adjusted (�2m

> 0). Results are for the entire sample. All specifications

include covariates for sex, birthyear, birthweight, and educational attainment.

Standard errors (in parentheses) do not reflect the uncertainty from the estimation

of ⌃ and are thus downward biased.


16

ONLINE APPENDIX VI - Results for Risk Gain and Risk Loss

17

Online Appendix VI Table I. Predictive Validity of the Risk Variables: Controlling for Cognitive Ability, Males Only


�

p

R

2 �R

2�

p

R

2 �R

2�

p

R

2 �R

2�

p

R

2 �R

2�

p

R

2 �R

2

Risk Gain

�

2m

= 0 0.054 0.020 0.000 0.006 0.019 0.001 0.028** - - 0.000 - - 0.012 - -

(0.195) (0.006) (0.013) (0.008) (0.014)

�

2m

> 0 0.077 0.021 0.000 0.009 0.024 0.006 0.044** - - 0.001 - - 0.022 - -

(0.289) (0.009) (0.020) (0.012) (0.020)

Risk Loss

�

2m

= 0 0.375* 0.022 0.002 0.000 0.018 0.000 0.023** - - 0.012* - - 0.032*** - -

(0.162) (0.004) (0.020) (0.007) (0.011)

�

2m

> 0 0.615* 0.030 0.009 0.000 0.018 0.000 0.032** - - 0.019* - - 0.050*** - -

(0.241) (0.006) (0.016) (0.010) (0.016)


and the KSS R

2 for the model with measurement error adjustment (�2m


2 for the model without

adjustment (�2m

= 0). 20 regressions were run to generate these results (2 risk variables ⇥ 5 outcomes ⇥ 2). Results are for males only.

�R

2 is the incremental R2 from including the risk variable in the regression. All specifications include a constant and controls for

birthyear, birth weight, log income, marital status, years of education as well as for cognitive ability.


18

Online Appendix VI Table II. Predictors of Risk Attitudes: Controlling for Cognitive Ability, Males Only

Risk Gain Risk Loss�

2m

= 0 �

2m

> 0 �

2m

= 0 �

2m

> 0Birth Year -0.003 -0.008 -0.025*** -0.035***

(0.006) (0.012) (0.005) (0.010)Birth Weight -0.072 -0.165 -0.022 -0.044

(0.054) (0.125) (0.042) (0.064)Education 0.003 0.010 -0.012 -0.018

(0.011) (0.021) (0.009) (0.014)Cognitive 0.071 0.149* 0.044 0.069

Ability (0.034) (0.091) (0.028) (0.042)R

2pseudo

0.006 0.031 0.015 0.032n1 3,586 3,586 3,555 3,555n2 0 155 0 156ln (L) -1,278.63 -1,333.93 -2,235.65 -2,329.18NOTES: The estimates in the left column under each variable name are




> 0). Results are for males only. All specifications

include covariates for birthyear, birthweight, educational attainment,

and cognitive ability. Standard errors (in parentheses) do not reflect

the uncertainty from the estimation of ⌃ and are thus downward biased.


19

Online Appendix VI Table III. Correlations between Risk Attitudes and Personality

Behavioral Inhibition Rotter Locus of Control�

2m

= 0 �

2m

> 0 �

2m

= 0 �

2m

> 0RiskGain 0.080***(0.017) 0.130*** (0.033) 0.002 (0.018) 0.001 (0.032)RiskLoss 0.068***(0.013) 0.124***(0.031) 0.028** (0.014) 0.048* (0.025)NOTES: The estimates in the left column under each variable name are




> 0).* Significant at 10% level; ** significant at 5% level; *** significant at 1% level.

20

Online Appendix VI Table IV. Twin Correlations and Behavior Genetic Variance Decomposition

Risk Gain Risk Loss�

2m

= 0 �

2m

> 0 �

2m

= 0 �

2m

> 0corr

MZ

0.166* 0.382** 0.164*** 0.353***s.e. (0.086) (0.194) (0.052) (0.115)# pairs 1,107 1,107 1,059 1,059corr

DZ

0.075 0.131 0.036 0.080s.e. (0.074) (0.154) (0.050) (0.102)# pairs 1,187 1,187 1,130 1,130

a

2 0.135 0.144 -0.020 -0.034(0.309) (0.626) (0.205) (0.421)

c

2 - - - -- - - -

d

2 0.031 0.239 0.185 0.387(0.344) (0.692) (0.224) (0.462)

e

2 0.834*** 0.618 0.836*** 0.647***(0.086) (0.194) (0.052) (0.115)

NOTES: The estimates in the left column under each variable name are unadjusted

for measurement error (�2m

= 0); the estimates in the second column are adjusted

(�2m

> 0). The lower panel shows the implied estimates for the ACE variance

components whenever they are all positive; if one variance component estimate

is negative, we report the ADE implied estimates instead.


21

Online Appendix VI Table V. Predictive Validity of the Risk Variables: Entire Sample


�

p

R

2 �R

2�

p

R

2 �R

2�

p

R

2 �R

2�

p

R

2 �R

2�

p

R

2 �R

2

Risk Gain

�

2m

= 0 0.063 0.024 0.000 0.006* 0.020 0.001 0.014* - - 0.001 - - 0.009 - -

(0.137) (0.003) (0.007) (0.006) (0.009)

�

2m

> 0 0.095 0.024 0.000 0.010* 0.028 0.008 0.021* - - 0.003 - - 0.017 - -

(0.202) (0.005) (0.011) (0.009) (0.013)

Risk Loss

�

2m

= 0 0.351*** 0.025 0.002 0.001 0.019 0.000 0.007 - - 0.013*** - - 0.016** - -

(0.108) (0.002) (0.006) (0.005) (0.007)

�

2m

> 0 0.526*** 0.030 0.007 0.002 0.020 0.000 0.009 - - 0.021*** - - 0.023** - -

(0.160) (0.003) (0.008) (0.007) (0.010)


and the KSS R

2 for the model with measurement-error adjustment (�2m


2 for the model

without adjustment (�2m

= 0). Twenty regressions were run to generate these results (2 risk variables ⇥ 5 outcomes ⇥ 2). Results are for

the entire sample. �R

2 is the incremental R2 from including the risk variable in the regression. All specifications include a constant

and controls for sex, birth year, birth weight, log income, marital status, and years of education.


22

Online Appendix VI Table VI. Predictors of Risk Attitudes: Entire Sample

Risk General Risk Financial�

2m

= 0 �

2m

> 0 �

2m

= 0 �

2m

> 0Sex -0.239*** -0.306*** -0.375*** -0.477***

(0.020) (0.028) (0.020) (0.030)Birth Year 0.019*** 0.025*** 0.015*** 0.020***

(0.002) (0.003) (0.002) (0.002)Birth Weight 0.077*** 0.104*** 0.042** 0.052**

(0.020) (0.025) (0.020) (0.025)Education 0.054*** 0.070*** 0.070*** 0.087***

(0.004) (0.005) (0.004) (0.006)R

2pseudo

0.048 0.080 0.080 0.126n1 10,440 10,440 10,472 10,472n2 - 463 - 463ln (L) -21,740.01 -22,594.68 -20,519.594 -21,322.79NOTES: The estimates in the left column under each variable name are




> 0). Results are for the entire sample. All specifications

include covariates for sex, birth year, birth weight, and educational attainment.

Standard errors (in parentheses) do not reflect the uncertainty from the estimation

of ⌃ and are thus downward biased.


23

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