The Effects of Birth Epoch on Risk Aversion:

Empirical Approach in the Health Retirment Study

Melika Liporace

May 22, 2014

Abstract

This paper investigates the causal relationship between birth epoch and risk aversion.Using the Health Retirment Survey (HRS) Data, we first reject the assumption of timeinvariance, therefore accounting for both the age and the epoch of birth. We then runboth multinomial and binary models to seize the effects of interest. Finally, we performrobustness checks to verify the legitimacy of our epoch dummy. We find that the birthera has a significant effect on risk aversion, although its magnitude is modest and itsrobustness somewhat restricted.

1 Introduction

Risk aversion is often treated as a black box, or rather a Pandora box, that should not be opened,on pain of endogeneity. Early literature used risk aversion as an explanatory variable - notably1 Barsky et al.(1997), who found a causal effect between risk tolerance and risky behaviors.Recently, 2 Jung (2014) investigated risk aversion as a dependent variable, establishing his linkwith education.

But other determinants of risk aversion are yet to be explored, like the economic frameworkduring childhood, reflected by the birth date. Our aim is especially to quantify the effect ofthe Great Depression on preferences. Quick summary statistics from the database discussedthereafter show that the share in extreme risk aversion of respondents born before 1935 is biggerthan their share in the overall database, as seen in Table 1.

Table 1: Evolution of Conditional Proportion of Risk Aversion in Population

Epoch Dummy

Risk Aversion 0 1 Total

1 79.21 20.79 100.002 78.40 21.60 100.003 82.45 17.55 100.004 75.66 24.34 100.00Total 77.37 22.63 100.00

Observations 27688

More generally, it seems essential to understand how preferences are formed, especiallyto determine whether crisis fathered by risky behaviors can breed a generation of risk averseagents. Far from answering that question, we attempt to lay a first small foundation stone.

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2 Data and Methodology

Our analysis is based on the HRS Data Base, collecting longitudinal information on morethan 30’000 elderly respondents in the United States. We are particularly interested in theRisk Aversion index computed from responses to hypothetical gambles over lifetime income.Although not evaluated for each wave, it ranges from 1 (risk loving) to 4 (extremely risk averse).To account for the change in wording of the related questions, we add a dummy variable thattakes 1 for wave 4 measures and forward.

Although 2 Jung (2014) uses basic demographics, to our knowledge, the literature providesno consensus over the control variables to use here. Some should form risk aversion, namely,our variable of interest, education, parent’s education - as a proxy for parental income (risklessenvironment) and parental own risk aversion (inheritance) - and usual demographics (gender,race, religion) ; other characteristics should transform risk aversion through a worrying atmo-sphere, like low income, responsibility of children or other household residents. Finally, weinclude the self-reported health as a proxy for the perceived probability to die.

Now, to avoid fixing an arbitrary limit between eras, we could directly regress on birth date.However, if age in itself also influences risk aversion, its coefficient would have an ambiguousinterpretation. To test this assumption, we compute for each respondent the change in measuredrisk aversion from one interview to the other, and regress it on the occurred change in age. Weadd the change in time-variants as controls (see Appendix: Table 6 for summary statistics).We perform a pooled OLS regression, clustered at the individual level1 (Appendix: Table 7).The change-in-age coefficient is significant, meaning that risk aversion is not time invariant,not even for small time intervals.

Hence, in addition to age, we have to define a dummy that reflects the risk aversion premiumfrom the economic framework during childhood. As we are particularly interested in the effectsof the Great Depression, our epoch dummy is 1 if the respondent is born prior to 1935 (seeAppendix: Figure 1 for birth date distribution). We then test the robustness of our resultswhen the birth date threshold is changed and when other epoch groupings are included.

We use a multinomial model. Table 2 displays summary statistics for the variables used.We regress both a pooled ordered probit and logit, clustered by respondent. We also run pooledprobit and logit binary models, where the dependent variable reflects whether the respondenthas an extreme risk aversion (outcome 4).

Finally, we conducted no particular strategy to drop outliers. We dropped observationswhere some used variables were missing.

3 Results

Table 3 displays similar results for the pooled multinomial probit and logit models Both the ageand the economic framework of childhood matter. Neither variables should suffer from reversecausality. Although a possible sample selection could arise from the relationship between risky(lethal) behavior and risk aversion, we assume it is negligible and do not correct for it.

Only a few control variables are significant. Particularly, both gender and Christian religionsinfluence positively risk aversion; while the first effect is exogenous, the second one could beendogenous. The strongly significant negative (possibly endogenous) effect of education is inaccordance with 1 Jung (2014), which reinforces our faith in the legitimacy of risk aversionmeasures. Overall, predictions fit the real data well (see Appendix: Table 8 for summarystatistics).

Concerning the size of the effects, the average partial effects and partial effects at the means

1some respondents change their risk aversion several times

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Table 2: Variable Used: Summary Statistics

Mean Min Max

Variable of interest:

Risk Aversion 3.27 1 4

Epoch Dummy 0.23 0 1

Age at the Interview 56.74 23 95

Interview design:

Reformulation of Questions 0.64 0 1

Controls:

Female 0.58 0 1

Race:

Black 0.13 0 1

Hispanic 0.09 0 1

Other Race 0.02 0 1

Religion:

Protestant 0.63 0 1

Catholic 0.27 0 1

Jewish 0.02 0 1

Other Religion 0.01 0 1

Education:

Years of Education 12.94 0 17

Mother’s Education 9.96 0 17

Father’s Education 9.60 0 17

HH characteristics:

Log total HH income 10.69 1 17

Self-reported Health 2.54 1 5

# of Children 3.10 0 21

# of Residents in HH 2.56 1 19

Observations 27688

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Table 3: Regression of Risk Aversion

OPROBIT OLOGIT

(1) (2) (3) (4)Basic with Controls Basic with Controls

Variable of interest:Epoch Dummy 0.0814∗∗∗ 0.0838∗∗∗ 0.141∗∗∗ 0.143∗∗∗

(0.0262) (0.0265) (0.0439) (0.0447)Age at the Interview 0.00485∗∗∗ 0.00554∗∗∗ 0.00892∗∗∗ 0.0100∗∗∗

(0.00157) (0.00166) (0.00261) (0.00278)Controls:

Female 0.197∗∗∗ 0.318∗∗∗

(0.0166) (0.0279)Race:

Black -0.0301 -0.0358(0.0249) (0.0420)

Hispanic -0.0100 -0.00278(0.0334) (0.0565)

Other Race 0.0363 0.0908(0.0631) (0.107)

Religion:Protestant 0.135∗∗∗ 0.210∗∗∗

(0.0326) (0.0541)Catholic 0.0810∗∗ 0.137∗∗

(0.0350) (0.0581)Jewish -0.0742 -0.122

(0.0628) (0.104)Other Religion 0.0149 0.00601

(0.0892) (0.147)Education:

Years of Education -0.0215∗∗∗ -0.0384∗∗∗

(0.00356) (0.00609)Mother’s Education -0.00739∗∗ -0.0123∗∗

(0.00321) (0.00537)Father’s Education -0.00547∗ -0.00884∗

(0.00280) (0.00468)HH characteristics:

Log total HH income 0.0188∗∗ 0.0226(0.00895) (0.0152)

Self-reported Health 0.0124 0.0182(0.00756) (0.0128)

# of Children -0.00700∗ -0.0111(0.00418) (0.00702)

# of Residents in HH 0.00284 0.00624(0.00720) (0.0121)

Reformulation Dummy Yes Yes Yes Yes

Observations 27688 27417 27688 27417

Notes: Columns (1) and (2) result from a ordered probit. (1) is the baseline model withessential controls. (2) includes the whole set of controls. Columns (3) and (4) follow to thesame distinction, but from an ordered logit.Standard errors clustered by respondent in parentheses. (∗p < 0.10 ∗∗p < 0.05 ∗∗∗p < 0.01).

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Table 4: Ordered Probit with Controls: Average Partial Effects

Outcome 1 Outcome 2 Outcome 3 Outcome 4Epoch Dummy -0.0172∗∗∗ -0.0078∗∗∗ -0.0064∗∗∗ 0.0313∗∗∗

Age at the Interview -0.0011∗∗∗ -0.0005∗∗∗ -0.0004∗∗∗ 0.0021∗∗∗

Notes: Average partial effects of the variable of interest, computed from the the orderedprobit model with the whole set of control variables. The significance levels correspond tothe significance of the corresponding coefficient (∗p < 0.10 ∗∗p < 0.05 ∗∗∗p < 0.01).

Table 5: Ordered Probit with Controls: Partial Effects at Means

Outcome 1 Outcome 2 Outcome 3 Outcome 4Epoch Dummy -0.0171∗∗ -0.0080∗∗ -0.0066∗∗ 0.0317∗∗

Age at the Interview -0.0011∗∗∗ -0.0005∗∗∗ -0.0004∗∗∗ 0.0021∗∗∗

Notes: Partial effects of the variable of interest at the mean value of every explanatoryvariable, computed from the the ordered probit model with the whole set of control variables.The significance levels correspond to the significance of the corresponding coefficient (∗p <0.10 ∗∗p < 0.05 ∗∗∗p < 0.01).

are displayed in Table 4 and 5. APE and PEM are of similar magnitude. Roughly, beingborn before 1935 increases risk aversion: on average, the probability of having an extremerisk aversion increases by 3 percentage points. Aging in itself also tends to increase (with alesser magnitude) the risk aversion: one more year increases the mentioned probability by 0.2percentage point.

To properly analyze the extreme risk aversion in opposition to other risk aversion levels,we set a binary model, whose dependent variable is 1 if risk aversion is 4, 0 otherwise. Othermotivations for this procedure are the overlapping of the cutoff points’ confidence intervalsand the prediction intervals (Appendix: Table 8 and Table 9) illustrated by the cross of thecorresponding curves (Appendix: Figure 2). The results for the binary model (Appendix:Table 10) show similar significance and magnitude of the epoch dummy. The effect of the ageis somewhat bigger. In brief, the results from the binary model are consistent with our previousanalysis.

Then, we test the legitimacy of our epoch dummy by changing its definition. We let the birthdate threshold vary between 1925 and 1964, run the baseline model with the new definition andanalyze the significance and sign of its coefficient (see Appendix: Table 11 and 12 for results).For the dummy to be significantly positive, the threshold can only variate for about ±1 year;however, the coefficient is significantly positive only during the early thirties, which correspondsto the expected effect of the Great Depression on the formation of the youth’s risk aversion.Thresholds before 1933 are not significant. The smaller size of this group could not balance theimportance of the 1933-1935 group included in the basegroup. Forties thresholds also yield tosignificant negative results: optimistic forties children’s weight in the interest group overcomesthe thirties children’s lesser risk aversion.

We conduct a second robustness check where we define four mostly 10-year long generationalgroups (see Appendix: Table 13 for summary statistics) and run regressions with different setsamong the corresponding dummies. The findings (Appendix: Table 14) correspond to theinterpretation developed above: 1935-1945 children have a significantly lower risk aversionthan respondents born after 1955 (column (1)). However, when the 1935-1945 children are

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included in the base group (column (5) and (6)), being born between 1925 and 1935 has againa significantly positive effect on risk aversion.

4 Conclusion

Birth date does matter in the formation of preferences. Its effects are significant and somewhatrobust. We find that being born before 1935, therefore, having known the Great Depression,increases the probability of extreme risk aversion by 3 percentage point. The effect is modest butstrongly significant. Furthermore, the 1935-1945 children have a lower risk aversion, reflectingan optimistic post-crisis era.

These results are criticizable. Obviously, the population of interest is limited to the UnitedStates. The large variation of individual risk aversion challenges its legitimacy. The limitedquantity of respondents born before the thirties could confirm a sample selection and limitgeneralizations. Finally, the rareness of significant control variables could indicate a wrongset of controls and, therefore, a possible omitted variable bias. Overall, we are aware that amore complicated analysis would be required, but our first approach leads to results interestingenough for us to hope for further investigation.

A Appendix

A.1 Time Variance of Risk Aversion

• Table 6: Change between Interviews: Summary Statistics , page 7

• Table 7: Regression of Change in Risk Aversion , page 7

A.2 Baseline Models

• Figure 1: Distribution of the birth dates, page 9

• Table 8: Predictions: Summary Statistics , page 8

• Table 9: Cutoff point from Table 3 , page 8

• Figure 2: Representation of the probability of belonging to outcome x as a function ofthe predicted values , page 9

A.3 Robustness checks

• Table 10: Regression on Risk Aversion Dummy , page 10

• Table 11: Evolution of Epoch Dummy significance throughout time (probit) , page 11

• Table 12: Evolution of Epoch Dummy significance throughout time (logit) , page 11

• Table 13: Generation Grouping: Summary Statistics , page 11

• Table 14: Significance of Generation Groups: Different Groupings , page 12

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Table 6: Change between Interviews: Summary Statistics

Mean Min Max

Variables of interest:

Change in Risk Aversion -0.08 -3 3

Change in Age 6.22 2 14

Interview design:

Reformulation of Questions 0.37 0 1

Controls:

Change in # Children -0.08 -15 12

Change in # Resident in HH 0.39 -11 8

Change in Self-Reported Health -0.18 -4 4

Change in Income (in 1′000$) -8.20 -24640 7321

Change in the Log of Income -0.03 -9 10

Table 7: Regression of Change in Risk Aversion

(1) (2) (3)Basic OLS with Controls A with Controls B

Variable of interest:Change in Age -0.0253∗∗∗ -0.0271∗∗∗ -0.0274∗∗∗

(0.0046) (0.0049) (0.0050)Interview design:

Reformulation of Questions 0.1600∗∗∗ 0.1643∗∗∗ 0.1650∗∗∗

(0.0349) (0.0385) (0.0387)Controls:

Change in # Children -0.0064 -0.0087(0.0130) (0.0129)

Change in # Resident in HH 0.0057 0.0063(0.0096) (0.0097)

Change in Self-Reported Health -0.0248∗∗ -0.0277∗∗

(0.0117) (0.0119)Change in Income (in 1′000$) 0.0000

(0.0000)Change in the Log of Income 0.0066

(0.0123)

Observations 18129 17719 17430

Notes: Columns (1) display results of the basic pooled OLS. Column (2) and (3) includesthe whole set of time-variant controls. (2) uses the change in income as a raw difference ofincome. (3) uses change in income as the difference of already log-transformed income.Standard errors clustered by respondent in parentheses. (∗p < 0.10 ∗∗p < 0.05 ∗∗∗p < 0.01).

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Table 8: Predictions: Summary Statistics

Mean Min Max

Type 1 0.1264 0 1

Type 2 0.1011 0 1

Type 3 0.1455 0 1

Type 4 0.6270 0 1

OPROBIT:

Predicted 1 0.1265 0.036 0.265

Predicted 2 0.1009 0.045 0.145

Predicted 3 0.1454 0.085 0.169

Predicted 4 0.6271 0.420 0.835

OLOGIT:

Predicted 1 0.1264 0.045 0.257

Predicted 2 0.1010 0.043 0.158

Predicted 3 0.1454 0.076 0.176

Predicted 4 0.6272 0.409 0.836

Table 9: Cutoff point from Table 3

OPROBIT OLOGIT

(1) (2) (3) (4)Basic with Controls Basic with Controls

Cutoff point 1 [-1.01 ; -0.70] [-1.07 ; -0.51] [-1.68 ; -1.15] [-1.93 ; -0.97]

Cutoff point 2 [-0.62 ; -0.30] [-0.67 ; -0.11] [-0.97 ; -0.44] [-1.21 ; -0.25]

Cutoff point 3 [-0.20 ; 0.12] [-0.24 ; 0.32] [-0.27 ; 0.26] [-0.50 ; 0.46]

Observations 27688 27417 27688 27417

Notes: 95% confidence intervals of the cutoff points between each categorical value of riskaversion, computed from regressions in Table 3

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Figure 1: Distribution of the birth dates

050

010

0015

0020

00Fr

eque

ncy

1900 1910 1920 1930 1940 1950 1960 1970 1980Birth Date

Figure 2: Representation of the probability of belonging to outcome x as afunction of the predicted values

0.2

.4.6

.81

0 .2 .4 .6 .8

Type 1 Type 2 Type 3 Type 4

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Table 10: Regression on Risk Aversion Dummy

PROBIT LOGIT

Coeff. APE Coeff. APE

Variable of interest:Epoch Dummy 0.085∗∗∗ 0.032 0.139∗∗∗ 0.032

(0.028) (0.045)Age at the Interview 0.007∗∗∗ 0.003 0.011∗∗∗ 0.003

(0.002) (0.003)Controls:

Female 0.177∗∗∗ 0.066 0.287∗∗∗ 0.066(0.018) (0.029)

Race:Black -0.012 -0.004 -0.017 -0.004

(0.026) (0.043)Hispanic 0.006 0.002 0.014 0.003

(0.035) (0.057)Other Race 0.092 0.034 0.153 0.035

(0.064) (0.105)Religion:

Protestant 0.116∗∗∗ 0.043 0.186∗∗∗ 0.043(0.035) (0.055)

Catholic 0.085∗∗ 0.032 0.136∗∗ 0.031(0.037) (0.059)

Jewish -0.082 -0.031 -0.130 -0.030(0.070) (0.111)

Other Religion -0.029 -0.011 -0.047 -0.011(0.094) (0.151)

Education:Years of Education -0.024∗∗∗ -0.009 -0.040∗∗∗ -0.009

(0.004) (0.006)Mother’s Education -0.008∗∗ -0.003 -0.013∗∗ -0.003

(0.003) (0.005)Father’s Education -0.005∗ -0.002 -0.009∗ -0.002

(0.003) (0.005)HH characteristics:

Log total HH income -0.000 -0.000 -0.001 -0.000(0.009) (0.015)

Self-reported Health 0.008 0.003 0.013 0.003(0.008) (0.013)

# of Children -0.005 -0.002 -0.009 -0.002(0.004) (0.007)

# of Residents in HH 0.001 0.000 0.002 0.000(0.007) (0.012)

Reformulation Dummy Yes Yes

Observations 27417 27417

Notes: Both model are run on the whole set of control variables. The first column ofthe probit model displays the usual estimated coefficient β. Standard errors clustered byrespondent in parentheses. (∗p < 0.10 ∗∗p < 0.05 ∗∗∗p < 0.01). The second column of theprobit model shows the following average partial effect. The same structure is applied tothe logit model.

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Table 11: Evolution of Epoch Dummy significance throughout time (probit)

1925 1926 1927 1928 1929 1930 1931 1932 1933 1934-0.06 -0.03 0.00 -0.02 -0.01 -0.01 0.03 0.05 0.06∗ 0.08∗∗

1935 1936 1937 1938 1939 1940 1941 1942 1943 19440.08∗∗ 0.09∗∗∗ 0.04 0.01 0.00 -0.03 -0.06∗ -0.07∗ -0.05∗ -0.09∗∗∗

1945 1946 1947 1948 1949 1950 1951 1952 1953 1954-0.08∗∗ -0.09∗∗∗ -0.10∗∗∗ -0.09∗∗∗ -0.07∗∗ -0.06∗ -0.05 -0.07∗ -0.07 -0.10∗

1955 1956 1957 1958 1959 1960 1961 1962 1963 1964-0.11∗ -0.11∗ -0.09 -0.11 -0.14 -0.10 -0.09 0.01 -0.07 -0.10

Notes: The default notation applies here (∗p < 0.05 ∗∗p < 0.01 ∗∗∗p < 0.001).

Table 12: Evolution of Epoch Dummy significance throughout time (logit)

1925 1926 1927 1928 1929 1930 1931 1932 1933 1934-0.11 -0.05 0.00 -0.04 -0.03 -0.02 0.04 0.07 0.10∗ 0.14∗∗

1935 1936 1937 1938 1939 1940 1941 1942 1943 19440.14∗∗ 0.16∗∗∗ 0.07 0.02 0.01 -0.04 -0.09∗ -0.10∗ -0.09∗ -0.14∗∗

1945 1946 1947 1948 1949 1950 1951 1952 1953 1954-0.13∗∗ -0.15∗∗∗ -0.15∗∗∗ -0.14∗∗ -0.12∗∗ -0.10∗ -0.08 -0.11 -0.10 -0.17∗

1955 1956 1957 1958 1959 1960 1961 1962 1963 1964-0.20∗ -0.20∗ -0.17 -0.20 -0.26∗ -0.20 -0.17 -0.01 -0.15 -0.18

Notes: The default notation applies here (∗p < 0.05 ∗∗p < 0.01 ∗∗∗p < 0.001).

Table 13: Generation Grouping: Summary Statistics

before 1925 1925-1935 1935-1945 1945-1955 after 1955

0 26937 22173 15298 19660 26684

1 751 5515 12390 8028 1004

Total 27688 27688 27688 27688 27688

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Table 14: Significance of Generation Groups: Different Groupings

(1) (2) (3) (4) (5) (6)before 1925 -0.31∗∗ -0.12 0.01

(0.10) (0.07) (0.06)1925-1935 -0.17∗ -0.01 0.02 0.04 0.09∗∗ 0.08∗∗∗

(0.08) (0.04) (0.04) (0.03) (0.03) (0.02)1935-1945 -0.21∗∗∗ -0.08∗∗ -0.06 -0.05∗

(0.06) (0.03) (0.04) (0.02)1945-1955 -0.12∗ -0.02 0.03

(0.05) (0.04) (0.02)Age at the Interview 0.01∗∗∗ 0.01∗∗∗ 0.01∗∗∗ 0.01∗∗∗ 0.01∗∗∗ 0.01∗∗∗

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00)Observations 27417 27417 27417 27417 27417 27417

Notes: Each columns corresponds to an pooled ordered probit model, run on the whole setof control variables. The second generational groups (respondents born between 1925 and1935) is our group of interest. Other groupings are included, implicitly changing the basegroup. (1) includes all of them. (2) includes only groups 1, 2 and 3. (3) includes G2, G3and G4. (4) includes G2 and G3. (5) includes G1 and G2. (6) includes G2 and G4.Standard errors clustered by respondent in parentheses. (∗p < 0.10 ∗∗p < 0.05 ∗∗∗p < 0.01).

References

[1] Robert B. BARSKY et al., Preference Parameters and Behavioral Heterogeneity: Experi-mental Approach in the Health Retirment Study, the Quarterly Journal of Economics, 1997(112 (2): 537-579)

[2] Seeun JUNG, Does Education Affect Risk Aversion?: Evidence from the 1973 British Edu-cation Reform. Working paper, Paris School of Economics, 2014

[3] Sandy CHIEN et al., RAND HRS Data Documentation, Labor & Population Program,RAND Center for the Study of Aging, 2013

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