Default Behavior and Risk Aversion in Defined Contribution Retirement Systems: Evidence from Chile

Marcela Parada-Contzen

doi:10.1515/bejeap-2021-0388

Published by De Gruyter July 15, 2022

Default Behavior and Risk Aversion in Defined Contribution Retirement Systems: Evidence from Chile

Marcela Parada-Contzen

From the journal The B.E. Journal of Economic Analysis & Policy

https://doi.org/10.1515/bejeap-2021-0388

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Abstract

This paper studies the design of investment policies in defined contribution retirement systems. I estimate a dynamic system of correlated equations of lifecycle behavior that fully models the individual’s decision-making process to account for estimation biases. In the model, individuals make decisions that impact their retirement wealth within the Chilean retirement system. Behaviors are allowed to depend on risk preferences while modeling other sources of nonlinear unobserved heterogeneity. The estimated decision-making process allows us to simulate the effects of policy experiments (ex ante), such as defaulting individuals into riskier investment strategies or increasing contribution rates. The results indicate that individuals react by opting into safer plans despite their observed inertia and that increases in mandatory contributions generate little crowding out of other behaviors. Not modeling risk aversion and its endogeneity with behavior leads to substantial simulation biases.

Keywords: retirement income policy; default investment; elicited risk aversion

JEL Classification: C30; D91; E21; G11; J26; J32

Corresponding author: Marcela Parada-Contzen, Millennium Nucleus (Intergenerational Mobility: From Modeling to Policy) and Departamento de Ingeniería Industrial, Facultad de Ingenería, Universidad de Concepción, Edmundo Larenas 219, Concepción, Chile, E-mail: mparadacontzen@gmail.com

Funding source: UdeC-VRID

Award Identifier / Grant number: 2021000177INI

Funding source: ANID - Millennium Science Initiative Program

Award Identifier / Grant number: NCS2021_072

Acknowledgement

I thank the Chilean Subsecretary of Social Prevision for providing and authorizing the use of the data. No conflicts of interest need to be declared. This work was funded by ANID - Millennium Science Initiative Program - NCS2021_072 and by UdeC-VRID 2021000177INI.

Appendix A: Figures

Figure 1:

Timing of decisions, subjective assessments, and stochastic realizations.

Appendix B: Data Description

B.1 Construction of Elicited Risk Aversion

The questions asked in waves 2, 3, and 4 of the EPS follow. The first question asks, “Suppose that you are the only income earner in the household. You need to choose between two jobs. Which option do you prefer? (Option A) a job with a lifetime-stable and certain salary or (Option B) a job where you have the same chances of doubling your lifetime income or earning only 1/4 of your lifetime income”. If the answer to the question is “option A”, the interviewer continues. “Now, what do you prefer? (Option A) a job with a lifetime-stable and certain salary or (Option B) a job where you have the same chances of doubling your lifetime income or earning only half of your lifetime income”.

The least risk-averse categories come directly from question 1. Elicited risk aversion equals 3 for individuals who selected “option B” in the first question. If the individual chooses “option A” in the first question, the risk aversion index is constructed using the second question. Individuals who chose “option B” in the second question belong to the second category (elicited risk aversion of 2), and individuals who chose “option A” in the second question belong to the most risk-averse category because individuals assigned to this category exhibited that they are not willing to accept any gamble (elicited risk aversion equals 1).

Wave 1 uses “decreasing up to 75%”. Because the first wave is used to set the initial conditions, observed risk aversion from wave 1 does not enter the model. Only one specification exists in which initial elicited risk aversion is modeled. Although the questions are mathematically equivalent, to prevent loss aversion biases through changes in the wording,^[32] the specification accounts for measurement error, among other potential sources of bias.

B.2 Sample Construction

Table B1:

Construction of research sample.

Sample	# Individuals
Whole sample	21,051
Reference sample
Age between 25 and 59 years old in 2002^I	13,178
And observed in 3 consecutive periods
First three waves	8545
Last three waves	8869
And no attrition no death
Observed in all four waves^II	7238
And information available for key variables
Research sample^III	7168

(a) ^IIndividuals who show up in more than one period. ^IIDeath rates are low for individuals aged between 25 and 59 years in 2002. ^IIINo missing information on health status, optional savings decisions, work experience, marital status, and region of residence.

Table B2:

Summary statistics for demographic variables between reference and research sample (2002).

Variable	Reference sample		Research sample
	Mean	Std. Dev.	Mean	Std. Dev.
Age	40.633	9.461	40.715	9.275
Female	0.497	0.500	0.462	0.499
Education category
Less than high school	0.413	0.492	0.531	0.499
High school	0.259	0.438	0.285	0.452
Technical college	0.104	0.305	0.109	0.311
College or Post-college	0.067	0.250	0.065	0.247
Missing	0.158	0.365	0.010	0.098

B.3 Summary Statistics

Table B3:

Summary statistics of dependent variables for research sample.

Variable	Estimator	Mean	Std. Dev.	Min.	Max.	N
Employment (e_t)	mlogit					21,504
Full-time employed		0.690	0.462	0	1
Part-time employed		0.031	0.174	0	1
Not working		0.278	0.448	0	1
Occupation (o_t) (if working)	mlogit					15,327
Elementary occupations		0.219	0.414	0	1
Legis., prof., tech., other		0.185	0.388	0	1
Clerical support workers		0.107	0.309	0	1
Service and sales workers		0.147	0.354	0	1
Agricultural, craft and trade		0.057	0.231	0	1
Operators and assemblers.		0.286	0.452	0	1
Investment (i_t)	Logit					21,504
Account A (riskier)		0.104	0.305	0	1
Account B		0.231	0.422	0	1
Account C		0.495	0.500	0	1
Account D		0.215	0.411	0	1
Account E (safest)		0.037	0.189	0	1
Savings outcomes (s_t)	Logit					21,490
Any optional savings		0.263	0.441	0	1
Duration of Life T t e	ols	75.780	10.091	30	110	17,287
Elicited Risk Aversion (r_t)	mlogit					20,557
Most risk-averse		0.747	0.435	0	1
Intermediate risk-averse		0.076	0.265	0	1
Least risk-averse		0.177	0.381	0	1
Log of wage (w_t)	Ols	0.657	1.440	−10.219	5.255	14,705
Marital status (m_t+1)	Logit					21,504
Married		0.571	0.495	0	1
Variation in children(n_t+1)	mlogit					21,060
No change		0.788	0.408	0	1
Decrease		0.184	0.387	0	1
Increase		0.028	0.165	0	1
Medical consumption (k_t+1)	Ols					21,438
Number of medical visits		6.697	12.639	0	240
Health status (H_t+1)	mlogit					14,336
Very good		0.147	0.354	0	1
Good		0.519	0.500	0	1
Regular		0.266	0.442	0	1
Poor		0.068	0.252	0	1

Table B4:

Summary statistics of explanatory variables entering period t for research sample.

Variable	Mean	Std. Dev.	Min.	Max.
Work experience (years)	15.646	8.111	0	30
Employment status in period t
Full-time worker	0.691	0.462	0	1
Part-time worker	0.032	0.177	0	1
Not employed	0.277	0.447	0	1
Occupation category in period t
Elementary occupations	0.117	0.322	0	1
Legis., Prof., Tech., other	0.099	0.298	0	1
Clerical support workers	0.057	0.232	0	1
Service and sales workers	0.078	0.269	0	1
Agricultural, craft and trade, other	0.030	0.172	0	1
Operators and assemblers	0.153	0.360	0	1
Lagged investment decision
Account A (riskiest)	0.059	0.235	0	1
Account B	0.135	0.341	0	1
Account C	0.495	0.500	0	1
Account D	0.095	0.293	0	1
Account E (safest)	0.021	0.144	0	1
Value of assets	5.906	12.487	0	241
Any optional savings	0.218	0.413	0	1
Married	0.569	0.495	0	1
Duration of marriage (years)	11.444	12.626	0	56
Number of children	1.009	1.083	0	8
Number of medical visits in period t	5.007	11.31	0	240
Health status
Very good	0.139	0.346	0	1
Good	0.536	0.499	0	1
Fair	0.266	0.442	0	1
Poor	0.059	0.236	0	1
Age	43.965	9.628	25	66
Female	0.462	0.499	0	1
Education category
Less than high school	0.536	0.499	0	1
High school	0.334	0.472	0	1
Technical college	0.097	0.296	0	1
College and post-graduate	0.025	0.156	0	1
Exclusion restrictions
Unemployment rate	9.226	2.261	4.200	15
Number of hospital beds (# per 1000 population)	2.345	0.373	1.300	3.900
Number of doctors (# per 1000 population)	0.978	0.220	0.580	1.870
Number of marriages (# year per 1000 population)	3.486	0.437	2.500	5.100
Inches of rainfall (thousand inches per year)	17.501	13.705	0.000	65.450
College tuition (thousand dollars)	3.240	0.641	0.000	4.300
Missing indicators
Missing: number of children	0.021	0.142	0	1
Missing: education	0.007	0.082	0	1
Missing: occupation	0.261	0.439	0	1
Missing: marriage duration	0.005	0.069	0	1
Missing: number of medical visits	0.252	0.434	0	1

Appendix C: Estimation Results (Preferred Model)

C.1 Likelihood Function

The likelihood function conditional and unconditional to the unobserved heterogeneity is given by Eqs. (12) and (13), respectively.

(12) L c t ( μ , ν t ) = f w ϵ t W | μ , ν t f k ϵ t K | μ , ν t ∏ j J × Pr I d t j = d j | μ , ν t f j ϵ t j | μ , ν t I d t j = d j

where d t j represents a choice, j = {E, O, I^A, I^B, I^C, I^D, I^E, S, T^e, R, M, N, H}, f(⋅) represents the density function of the error term of each equation, Pr(⋅) is the cumulative distribution function for each choice, and I d t j = d j is an indicator of a particular choice.

(13) L t = ∑ q = 1 Q P W μ q ∑ r = 1 R P W ν r ∏ t = 1 T L c t ( μ , ν t )

where PW_μq is the probability of observing q mass points for the permanent component μ, and PW_νr is the probability of observing r mass points for the time-varying component ν_t. These approximate the true distributions of μ and ν_t.

C.2 Empirical Specification and Identification

Table C1:

Specification of set of equations in preferred empirical model.

Equation	Explanatory variables
	Predetermined	Exogenous	Unobserved
	variables	variables	heterogeneity
Employment (e_t)	i_t−1, s_t−1, A t r , E_t, M_t, N_t, H_t	X_t, Z t E , Z t M , Z t N , Z t K , Z t H	μ^E, ν t E , ε t E
Occupation (o_t)	i_t−1, s_t−1, A t r , E_t, M_t, N_t, H_t	X_t, Z t E , Z t M , Z t N , Z t K , Z t H	μ^O, ν t O , ε t O
Savings (s_t)	i_t−1, s t − 1 , A t r , E_t, M_t, N_t, H_t	X_t, Z t E , Z t M , Z t N , Z t K , Z t H	μ^S, ν t S , ε t S
Investment in A i t A	i_t−1, s_t−1, A t r , E_t, M_t, N_t, H_t	X_t, Z t E , Z t M , Z t N , Z t K , Z t H	μ I A , ν t I A , ε t I A
Investment in B i t B	i_t−1, s_t−1, A t r , E_t, M_t, N_t, H_t	X_t, Z t E , Z t M , Z t N , Z t K , Z t H	μ I B , ν t I B , ε t I B
Investment in C i t C	i_t−1, s_t−1, A t r , E_t, M_t, N_t, H_t	X_t, Z t E , Z t M , Z t N , Z t K , Z t H	μ I C , ν t I C , ε t I C
Investment in D i t D	i_t−1, s_t−1, A t r , E_t, M_t, N_t, H_t	X_t, Z t E , Z t M , Z t N , Z t K , Z t H	μ I D , ν t I D , ε t I D
Investment in E i t E	i_t−1, s_t−1, A t r , E_t, M_t, N_t, H_t	X_t, Z t E , Z t M , Z t N , Z t K , Z t H	μ I E , ν t I E , ε t I E
Duration of life T t E	i_t−1, s_t−1, A t r , E_t, M_t, N_t, H_t	X_t, Z t E , Z t M , Z t N , Z t K , Z t H	μ T e , ν t T e , ε t T e
Elicited risk aversion (r_t)	i_t−1, s_t−1, A t r , E_t, M_t, N_t, H_t	X_t, Z t E , Z t M , Z t N , Z t K , Z t H	μ^R, ν t R , ε t R
Log wage (w_t\|e_t, o_t)	E_t, H_t	X_t, Z t E	μ^W, ν t W , ε t W
Medical consumption (k_t)	H _t	X_t, Z t K	μ^K, ν t K , ε t K
Marital status (m_t+1)	e_t, M_t, N_t	X_t, Z t M	μ^M, ν t M , ε t M
Change in children (n_t+1)	e_t, M_t, N_t	X_t, Z t N	μ^N, ν t N , ε t N
Health status (H_t+1)	e_t, o_t, k_t, E_t, H_t	X_t, Z t H	μ^H, ν t H , ε t H
Initial conditions
Employment (e₁)		X₁, Z 1 E , Z 1 M , Z 1 N , Z 1 K , Z 1 H	μ E I , ε E I
Work experience (E₁)		X₁, Z 1 E , Z 1 M , Z 1 N , Z 1 K , Z 1 H	μ E X I , ε E X I
Occupation (o₁)		X₁, Z 1 E , Z 1 M , Z 1 N , Z 1 K , Z 1 H	μ O I , ε O I
Savings (s₁)		X₁, Z 1 E , Z 1 M , Z 1 N , Z 1 K , Z 1 H	μ S I , ε S I
Marital status (m₁)		X₁, Z 1 M	μ M I , ε M I
Number of children (n₁)		X₁, Z 1 N	μ N I , ε N I
Health status (H₁)		X₁, Z 1 K , Z 1 H	μ H I , ε H I

Table C2:

Joint significance test for all market-level exogenous characteristics.

Equation		Market-level characteristics
Employment at t	c	p-value = 0.000
Occupation at t	c	p-value = 0.000
Investment in A at t	c	p-value = 0.000
Investment in B at t		p-value = 0.120
Investment in C at t	c	p-value = 0.000
Investment in D at t	a	p-value = 0.054
Investment in E at t	c	p-value = 0.000
Savings at t	c	p-value = 0.000
Duration of Life at t	c	p-value = 0.000
Elicited risk aversion at t	c	p-value = 0.000

^{a, b, c}significant at the 10%, 5%, and 1% levels.

Table C3:

Significance test for lagged market-level exogenous characteristics.

Behavior at t	Lagged market-level characteristics (at t − 1)
	Unemployment	Hospital	Number of	Number of	Rainfall	College
	rate	beds	doctors	marriages		tuition
Employment	b	Not sig	c	c	a	Not sig
Occupation	c	Not sig	c	c	c	c
Investment in A	Not sig	Not sig	b	c	c	Not sig
Investment in B	Not sig	Not sig	Not sig	Not sig	Not sig	c
Investment in C	Not sig	Not sig	b	c	c	Not sig
Investment in D	Not sig	Not sig	Not sig	Not sig	Not sig	Not sig
Investment in E	Not sig	Not sig	c	Not sig	Not sig	Not sig
Savings at t	b	Not sig	Not sig	Not sig	Not sig	c
Duration of Life	b	Not sig	Not sig	Not sig	Not sig	Not sig
Elicited risk aversion	b	b	c	b	Not sig	b

^{a, b, c}significant at the 10%, 5%, and 1% levels.

C.3 Parameter Estimates

Table C4:

Multinomial logit on employment status (relative to working full-time).

Variable	Part-time		Not working
	Coeff.	St.Er.	Coeff.	St.Er.
Work experience	−0.065	0.021^c	−0.078	0.011^c
Experience squared	0.001	0.001	−0.001	0.000^c
Lagged investment in A	−0.164	0.340	−0.077	0.098
Lagged investment in B	−0.089	0.293	−0.100	0.081
Lagged investment in C	−0.093	0.311	−0.100	0.079
Lagged investment in D	−0.043	0.325	0.051	0.094
Lagged investment in E	0.265	0.483	−0.047	0.139
Lagged assets	−0.042	0.006^c	−0.002	0.002
Lagged optional savings	−0.148	0.097	−0.143	0.049^c
Lagged marital status	−0.399	0.138^c	−0.249	0.069^c
Number of children	−0.052	0.075	−0.078	0.035^b
Interaction Female-married	0.519	0.174^c	0.698	0.092^c
Interaction Female-children	0.140	0.085^a	0.233	0.043^c
Health: Very good	−0.007	0.126	0.003	0.066
Health: Fair	0.083	0.099	0.328	0.050^c
Health: Poor	0.455	0.172^c	1.005	0.088^c
Age	0.126	0.064^b	0.162	0.029^c
Age squared	−0.044	0.033	−0.072	0.015^c
Age cubic	0.006	0.005	0.014	0.002^c
Female	0.619	0.147^c	0.602	0.077^c
High school	−0.276	0.107^c	−0.486	0.052^c
Technical college	−0.221	0.168	−1.031	0.093^c
College	−0.106	0.849	−1.581	0.347^c
Unemployment rate	−0.017	0.025	0.033	0.012^c
Number of hospital beds	0.201	0.201	−0.087	0.092
Number of doctors	1.174	0.512^b	0.191	0.213
Number of marriages	0.166	0.212	0.272	0.082^c
Inches of rainfall	0.010	0.004^b	0.006	0.002^c
College tuition	0.093	0.091	−0.063	0.045
Missing: number of children	0.189	0.871	−0.317	0.194
Missing: education	−0.261	0.785	−0.176	0.317
Time trend	0.086	0.066	0.065	0.019^c
Constant	−6.321	0.916^c	−2.654	0.406^c
Permanent Unob. Het.	−0.543	0.258^b	−1.229	0.124^c
Permanent Unob. Het.	0.395	0.154^b	0.883	0.091^c
Permanent Unob. Het.	−0.499	0.176^c	−1.399	0.120^c
Time-varying Unob. Het.	0.297	0.140^b	0.028	0.064
Time-varying Unob. Het.	0.678	0.310^b	1.637	0.409^c
Time-varying Unob. Het.	0.312	0.177^a	−0.146	0.095

^{a, b, c}significant at the 10%, 5%, and 1% level.

Table C5:

Multinomial logit on occupation category (relative to elementary occupation).

Variable	Prof and tech		Clerical support		Service and sales		Agricul and craft		Plant and machine
	Coeff.	St.Er.	Coeff.	St.Er.	Coeff.	St.Er.	Coeff.	St.Er.	Coeff.	St.Er.
Work experience	−0.072	0.029^b	−0.013	0.031	−0.058	0.024^b	−0.003	0.029	−0.014	0.029
Experience squared	0.001	0.001	0.000	0.001	0.001	0.001^a	0.002	0.001^b	0.000	0.001
Lagged investment in A	−0.108	0.205	−0.078	0.200	0.000	0.209	−0.134	0.251	−0.161	0.191
Lagged investment in B	−0.118	0.157	0.174	0.155	0.334	0.156^b	−0.001	0.204	−0.083	0.150
Lagged investment in C	−0.401	0.160^b	−0.016	0.157	0.063	0.158	−0.347	0.206^a	−0.245	0.147^a
Lagged investment in D	−0.241	0.220	−0.124	0.218	−0.149	0.215	−0.026	0.232	−0.196	0.196
Lagged investment in E	−0.568	0.373	−0.310	0.386	0.348	0.316	−0.404	0.379	−0.237	0.275
Lagged assets	0.051	0.004^c	0.054	0.004^c	0.041	0.004^c	−0.004	0.006	0.028	0.004^c
Lagged optional savings	0.317	0.085^c	0.135	0.089	−0.007	0.089	0.118	0.104	−0.191	0.085^b
Lagged marital status	0.401	0.174^b	0.591	0.171^c	0.137	0.177	0.068	0.120	0.192	0.133
Number of children	−0.077	0.063	−0.162	0.068^b	0.012	0.065	−0.111	0.053^b	0.104	0.049^b
Interaction Female-married	0.134	0.259	−0.390	0.245	0.098	0.258	0.471	0.249^a	−0.210	0.243
Interaction Female-children	−0.030	0.086	0.083	0.089	−0.133	0.088	0.226	0.102^b	−0.239	0.089^c
Health: Very good	0.236	0.115^b	0.042	0.119	0.121	0.119	0.077	0.135	−0.092	0.111
Health: Fair	−0.265	0.115^b	−0.072	0.114	−0.078	0.110	0.079	0.102	−0.067	0.098
Health: Poor	−0.151	0.446	0.042	0.406	0.121	0.372	0.076	0.227	−0.171	0.305
Age	0.010	0.025	−0.080	0.026^c	−0.054	0.023^b	−0.046	0.026^a	0.013	0.025
Age squared	0.002	0.006	0.010	0.006	0.011	0.005^b	0.006	0.006	−0.003	0.006
Female	−0.227	0.180	0.324	0.174^a	0.752	0.184^c	−1.039	0.202^c	−2.275	0.175^c
High school	2.656	0.115^c	2.778	0.118^c	1.558	0.109^c	−0.503	0.121^c	1.075	0.105^c
Technical college	6.471	0.275^c	4.494	0.291^c	2.771	0.269^c	−0.271	0.477	1.523	0.285^c
College	8.027	0.602^c	5.560	0.710^c	3.578	0.732^c	1.209	1.048	1.302	0.867
Unemployment rate	0.027	0.025	0.021	0.027	−0.025	0.024	0.018	0.026	0.061	0.025^b
Number of hospital beds	−0.136	0.206	−0.199	0.223	−0.275	0.202	−0.217	0.212	−0.058	0.195
Number of doctors	0.743	0.392^a	0.446	0.467	1.156	0.412^c	−1.558	0.536^c	0.418	0.417
Number of marriages	0.063	0.173	0.423	0.183^b	0.323	0.164^b	−0.620	0.195^c	0.253	0.161
Inches of rainfall	0.001	0.005	0.004	0.005	−0.003	0.004	0.027	0.005^c	0.005	0.004
College tuition	0.204	0.089^b	0.439	0.094^c	0.006	0.089	−0.765	0.102^c	0.164	0.090^a
Missing: number of children	−0.084	0.308	−0.235	0.356	−0.586	0.356^a	0.081	0.523	0.181	0.332
Missing: education	4.686	0.538^c	3.454	0.633^c	2.151	0.613^c	−11.427	1.186^c	1.692	0.642^c
Time trend	0.023	0.038	−0.041	0.038	−0.026	0.037	−0.006	0.048	0.038	0.035
Constant	−2.650	0.696^c	−5.162	0.770^c	−2.541	0.696^c	4.692	0.814^c	0.597	0.660
Permanent Unob. Het.	−1.440	0.193^c	1.370	0.232^c	−1.106	0.222^c	−1.406	0.339^c	−4.461	0.168^c
Permanent Unob. Het.	−3.777	0.259^c	−1.824	0.269^c	−0.729	0.209^c	0.755	0.248^c	−4.240	0.144^c
Permanent Unob. Het.	1.585	0.228^c	1.103	0.307^c	3.710	0.217^c	−1.595	0.547^c	−3.281	0.253^c
Time-varying Unob. Het.	0.005	0.117	−0.037	0.118	−0.034	0.117	−0.004	0.131	−0.163	0.109
Time-varying Unob. Het.	1.171	0.330^c	0.358	0.361	0.887	0.344^c	0.453	0.501	0.311	0.327
Time-varying Unob. Het.	0.709	0.176^c	0.477	0.180^c	0.211	0.183	−0.294	0.227	−0.068	0.175

^{a, b, c}Significant at the 10%, 5%, and 1% level.

Table C6:

Wage equation.

Variable	Wage (log)
	Coeff.	St.Er.
Work experience	0.006	0.003^a
Experience squared	0.000	0.000
Legislators	0.561	0.022^c
Clerical	0.339	0.022^c
Service and sales	0.118	0.023^c
Agricultural	−0.079	0.023^c
Plant operators	−0.042	0.021^b
Health: very good	0.060	0.013^c
Health: fair	−0.107	0.013^c
Health: poor	−0.196	0.026^c
Number of children	0.003	0.007
Lagged marital status	0.092	0.011^c
Age	0.001	0.001
Female	−0.196	0.013^c
High school	0.257	0.012^c
Technical college	0.686	0.021^c
College	0.875	0.040^c
Missing: occupation	0.139	0.044^c
Unemployment rate	−0.003	0.003
Missing: education	0.365	0.059^c
Missing: number of children	0.000	0.031
Constant	0.572	0.039^c
Permanent Unob. Het.	−0.263	0.028^c
Permanent Unob. Het.	−0.411	0.024^c
Permanent Unob. Het.	−0.314	0.029^c
Time-varying Unob. Het.	0.039	0.014^c
Time-varying Unob. Het.	−10.294	0.039^c
Time-varying Unob. Het.	0.180	0.019^c

^{a, b, c}significant at the 10%, 5%, and 1% levels.

Table C7:

Estimation results: marital status and variation in number of children.

Variable	Marital status		Children variation
	(relative to married)		(relative to no change)
			Decrease		Increase
	Coeff.	St.Er.	Coeff.	St.Er.	Coeff.	St.Er.
Duration of marriage	−0.025	0.004^c	0.066	0.004^c	−0.098	0.014^c
Lagged marital status	−4.382	0.106^c	−1.133	0.115^c	0.798	0.195^c
Number of children	−0.258	0.035^c	1.161	0.032^c	0.691	0.065^c
Interaction Female-married	−0.097	0.106	−0.316	0.095^c	−0.076	0.213
Interaction Female-children	0.100	0.048^b	0.177	0.041^c	−0.035	0.098
Full-time employed	−0.047	0.071	0.297	0.060^c	0.554	0.194^c
Part-time employed	−0.029	0.153	0.254	0.127^b	0.148	0.463
Age	0.063	0.028^b	0.515	0.017^c	−0.153	0.025^c
Age squared	−0.037	0.017^b	−0.113	0.004^c	0.006	0.009
Age cubic	0.006	0.003^b
Female	0.357	0.090^c	0.263	0.098^c	0.005	0.211
High school	0.016	0.060	−0.078	0.049	0.202	0.118^a
Technical college	−0.079	0.092	−0.131	0.080^a	0.068	0.187
College	−0.452	0.159^c	−0.075	0.127	0.037	0.583
Number of marriages	−0.317	0.085^c
College tuition			−0.001	0.039	−0.217	0.087^c
Missing: Marriage Duration	−0.082	0.441	1.595	0.443^c	−0.026	0.988
Missing: Number of children	−0.641	0.158^c
Missing: Education	−0.374	0.553	0.114	0.426	0.941	0.893
Constant	3.257	0.388^c	−8.618	0.261^c	−2.371	0.463^c
Permanent Unob. Het.	0.184	0.093^b	−0.107	0.079	−0.053	0.200
Permanent Unob. Het.	0.016	0.078	0.041	0.064	−0.112	0.206
Permanent Unob. Het.	0.045	0.093	−0.099	0.076	−0.183	0.198
Time-varying Unob. Het.	0.015	0.089	−0.011	0.079	−0.199	0.212
Time-varying Unob. Het.	−1.795	0.352^c	0.866	0.319^c	3.972	0.439^c
Time-varying Unob. Het.	−0.043	0.130	0.254	0.105^b	−0.072	0.271

^{a, b, c}Significant at the 10%, 5%, and 1% levels.

Table C8:

Health status and medical care consumption.

Variable	Health status						Medical
	(relative to very good)						Consumption
	Good		Regular		Poor
	Coeff.	St.Er.	Coeff.	St.Er.	Coeff.	St.Er.	Coeff.	St.Er.
Health: Very good	−0.528	0.060^c	−0.789	0.084^c	−0.889	0.203^c	−1.047	0.246^c
Health: Fair	0.289	0.081^c	1.526	0.084^c	1.845	0.122^c	4.887	0.207^c
Health: Poor	0.678	0.329^b	2.353	0.322^c	4.108	0.333^c	15.679	0.424^c
Number of medical visits	0.010	0.003^c	0.022	0.004^c	0.027	0.004^c
Work experience	0.003	0.005	−0.004	0.006	−0.005	0.008
Legislators	−0.296	0.142^b	−0.442	0.175^b	−0.288	0.330
Clerical	−0.025	0.143	0.007	0.172	0.282	0.352
Service and sales	0.011	0.156	−0.090	0.187	0.084	0.322
Agricultural	−0.165	0.178	−0.244	0.204	−0.191	0.342
Plant operators	0.062	0.141	−0.018	0.163	0.208	0.264
Age	0.034	0.014^b	0.084	0.017^c	0.163	0.032^c	−0.048	0.040
Age squared	−0.004	0.003	−0.009	0.004^b	−0.021	0.007^c	0.019	0.009^b
Female	0.170	0.064^c	0.379	0.075^c	0.618	0.115^c	4.149	0.177^c
High school	−0.098	0.066	−0.537	0.077^c	−0.693	0.121^c	1.370	0.198^c
Technical college	−0.214	0.105^b	−0.924	0.139^c	−1.301	0.274^c	2.881	0.378^c
College	−0.489	0.253^a	−1.445	0.520^c	−1.873	0.826^b	3.974	0.943^c
Inches of rainfall	0.001	0.002	0.006	0.002^b	0.003	0.004
Number of hospital beds							−0.038	0.299
Number of doctors							0.550	0.671
Missing: Occupation	−0.096	0.327	−0.341	0.438	−0.405	0.691
Missing: Education	−0.201	0.492	−0.657	0.712	−0.766	0.922	2.248	1.000^b
Not employed	0.123	0.333	0.254	0.448	0.713	0.686
Constant	0.869	0.200^c	−0.946	0.244^c	−4.435	0.508^c	1.537	0.882^a
Permanent Unob. Het.	−0.079	0.139	−0.130	0.168	−0.220	0.294	−0.302	0.413
Permanent Unob. Het.	0.072	0.118	0.409	0.136^c	0.749	0.206^c	−0.201	0.480
Permanent Unob. Het.	0.075	0.137	0.093	0.169	0.296	0.288	−0.657	0.434
Time-varying Unob. Het.	−0.068	0.075	−0.055	0.090	0.009	0.150	0.215	0.340
Time-varying Unob. Het.	1.084	1.442	1.105	1.442	1.624	1.670	−1.633	0.699^b
Time-varying Unob. Het.	−0.095	0.103	−0.273	0.126^b	−0.325	0.210	0.947	0.598

^{a, b, c}Significant at the 10%, 5%, and 1% level.

Table C9:

Pearson’s correlation coefficient for unobserved heterogeneity between subjective assessments and outcomes.

Outcome	Risk aversion				Expected
	Intermediate		Least		Duration of life
	Perm.	Time-var.	Perm.	Time-var.	Perm.	Time-var.
Employment (relative to full-time worker)
Part-time worker	−0.021	0.681	−0.558	−0.014	−0.689	0.765
Not working	−0.092	−0.236	−0.597	0.027	−0.643	0.867
Occupation (relative to elementary occupation)
Legis., prof., tech., other	0.626	0.435	0.967	0.794	0.022	0.815
Clerical support workers	0.058	0.527	0.623	0.948	0.626	0.543
Service and sales workers	0.842	0.081	0.829	0.587	−0.244	0.903
Agricultural, craft and trade	−0.069	−0.638	−0.558	−0.505	−0.664	0.425
Operators and assemblers	0.506	−0.589	0.612	0.479	−0.474	0.339
Investment decision
Account A (riskier)	0.114	0.917	0.682	0.680	0.526	0.407
Account B	−0.389	0.610	0.225	−0.465	0.728	0.321
Account C	0.343	−0.984	−0.210	−0.465	−0.909	−0.399
Account D	0.269	−0.067	−0.285	−0.912	−0.492	0.069
Account E (safest)	−0.238	0.838	−0.749	−0.169	−0.279	0.351
Saving outcomes
Optional savings	0.222	0.884	0.726	0.432	0.255	−0.151
Elicited Risk Aversion (relative to most risk averse)
Intermediate risk-averse	1.000	1.000	0.804	0.342	−0.699	0.268
Least risk-averse	0.804	0.342	1.000	1.000	−0.213	0.300
Marital status
Married	−0.675	0.134	−0.209	−0.254	0.997	−0.915
Variation in number of children (relative to no change)
Decrease	0.038	0.177	−0.467	0.609	−0.740	0.920
Increase	−0.263	−0.240	0.012	0.268	0.041	0.859
Health status (relative to very good)
Good	0.587	−0.336	0.013	0.188	−0.762	0.812
Regular	0.071	−0.478	−0.529	−0.064	−0.564	0.713
Poor	0.139	−0.369	−0.459	−0.111	−0.561	0.776
Expected duration of life	−0.699	0.268	−0.213	0.300	1.000	1.000
Log wage	0.270	0.179	0.573	−0.181	−0.146	−0.899
Medical consumption	−0.236	0.729	−0.277	0.278	−0.314	−0.440

(a) Permanent unobserved heterogeneity also enters the initial condition equations.

Appendix D: Simulation Results

Table D1:

[Preferred model] share of individuals that stay in the default at the end of each period (%) – all individuals are treated.

Period	Baseline			Default + 1			Riskier default
	Total	Women	Men	Total	Women	Men	Total	Women	Men
All individuals are treated
t = 3	72.99^c	72.02^c	73.84^c	37.33^c	37.24^c	37.42^c	35.15^c	32.83^b	37.18^c
	(6.02)	(6.00)	(6.07)	(8.96)	(8.67)	(9.28)	(13.24)	(13.12)	(13.45)
t = 4	66.72^c	65.24^c	68.01^c	27.64^c	28.21^c	27.15^c	24.90^b	22.55^a	26.95^b
	(5.87)	(5.75)	(6.06)	(9.38)	(8.80)	(9.98)	(12.18)	(11.90)	(12.55)
t = 5	63.86^c	61.90^c	65.59^c	23.86^c	24.79^c	23.05^b	21.55^b	19.38^a	23.44^b
	(5.66)	(5.42)	(6.02)	(8.92)	(8.27)	(9.59)	(10.68)	(10.36)	(11.07)
t = 6	63.15^c	60.89^c	65.13^c	21.67^b	23.17^b	20.36^b	20.53^b	18.54^b	22.28^b
	(5.63)	(5.31)	(6.14)	(8.50)	(7.77)	(9.24)	(9.43)	(9.10)	(9.81)
t = 7	63.09^c	60.57^c	65.31^c	19.31^b	21.11^b	17.73^b	20.37^b	18.61^b	21.92^b
	(5.63)	(5.30)	(6.26)	(8.05)	(7.40)	(8.73)	(8.30)	(7.96)	(8.68)
t = 8	64.86^c	62.03^c	67.34^c	18.00^b	20.27^b	16.01^b	20.42^c	18.57^c	22.04^c
	(5.68)	(5.47)	(6.25)	(7.44)	(6.86)	(8.06)	(7.04)	(6.69)	(7.43)

(a) Individuals start period t = 1 with their observed initial conditions. Individuals observed to be in the default in period t = 2 are treated. After the treatment, the simulated outcomes are used to update the next period’s endogenous explanatory variables. (b) Baseline simulation corresponds to the evolution of the model without policy intervention. (c) Bootstrapped standard errors are in parentheses using 100 draws.

Table D2:

[Preferred model] crowding-out effect of increasing contribution rates of 5 and 10 percent (% change).

Period	Investment					Savings	Employment
	A	B	C	D	E		Full-time	Part-time	Not Emp
Contribution rate = 15%
t = 3	0.18^c	0.11^c	0.01	−0.06^c	0.10	0.10^c	0.03	−0.89^c	0.00
	(0.05)	(0.04)	(0.01)	(0.02)	(0.07)	(0.04)	(0.12)	(0.25)	(0.09)
t = 4	0.38^c	0.28^c	0.01	−0.14^c	0.32^b	0.23^c	0.06	−1.58^c	0.00
	(0.11)	(0.10)	(0.02)	(0.04)	(0.14)	(0.08)	(0.27)	(0.57)	(0.20)
t = 5	0.60^c	0.56^c	0.01	−0.22^c	0.50^b	0.38^c	0.10	−2.46^c	0.01
	(0.18)	(0.17)	(0.03)	(0.06)	(0.21)	(0.13)	(0.43)	(0.82)	(0.33)
t = 6	0.82^c	0.80^c	0.00	−0.27^c	0.74^b	0.54^c	0.15	−3.38^c	0.00
	(0.26)	(0.27)	(0.05)	(0.07)	(0.31)	(0.18)	(0.62)	(1.03)	(0.46)
t = 7	1.08^c	1.27^c	0.02	−0.32^c	0.99^b	0.73^c	0.20	−4.28^c	0.01
	(0.35)	(0.40)	(0.06)	(0.09)	(0.41)	(0.24)	(0.84)	(1.37)	(0.61)
t = 8	1.25^c	1.78^c	0.02	−0.38^c	1.37^b	0.93^c	0.24	−5.29^c	0.01
	(0.44)	(0.53)	(0.07)	(0.10)	(0.52)	(0.30)	(1.04)	(1.76)	(0.76)
Contribution rate = 20%
t = 3	0.35^c	0.23^c	0.02	−0.13^c	0.21	0.20^c	0.07	−1.72^c	0.00
	(0.09)	(0.08)	(0.02)	(0.04)	(0.13)	(0.07)	(0.25)	(0.46)	(0.19)
t = 4	0.78^c	0.57^c	0.02	−0.27^c	0.68^b	0.49^c	0.12	−3.10^c	0.00
	(0.22)	(0.19)	(0.04)	(0.07)	(0.27)	(0.16)	(0.53)	(1.01)	(0.40)
t = 5	1.20^c	1.08^c	0.01	−0.41^c	0.96^b	0.75^c	0.20	−4.89^c	0.02
	(0.37)	(0.34)	(0.07)	(0.11)	(0.44)	(0.26)	(0.86)	(1.46)	(0.65)
t = 6	1.66^c	1.69^c	0.02	−0.52^c	1.36^b	1.09	0.30	−6.49	−0.01
	(0.53)	(0.55)	(0.09)	(0.14)	(0.65)	(0.36)	(1.25)	(1.97)	(0.92)
t = 7	2.19^c	2.56^c	0.04	−0.66^c	1.96^b	1.46^c	0.41	−8.39^c	0.01
	(0.72)	(0.80)	(0.12)	(0.17)	(0.83)	(0.48)	(1.68)	(2.48)	(1.22)
t = 8	2.50^c	3.58^c	0.04	−0.81^c	2.65^b	1.85^c	0.47	−10.27^c	0.01
	(0.91)	(1.09)	(0.15)	(0.19)	(1.06)	(0.62)	(2.07)	(3.20)	(1.54)

(a) Percentage change in accumulated assets with respect to the baseline simulation (α = 0.1) (b) Individuals start period t = 1 with their observed initial conditions. All individuals are treated in period t = 2. (c) Bootstrapped standard errors are in parentheses using 100 draws. ^{a, b, c}Significant at the 10%, 5%, and 1% levels.

Table D3:

[Alternative specifications] percentage change in accumulated assets at the end of seven years for different mandatory contribution rates under alternative specifications of the model.

	Alternative a)				Alternative b)
	No subjective assessments – no CUH				Exogenous subjective assessments – CUH
	α = 11%	α = 13%	α = 15%	α = 20%	α = 11%	α = 13%	α = 15%	α = 20%
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Mean	4.54	13.63	22.76	45.77	4.32^a	13.00^a	21.71^a	43.64^a
	(2.87)	(8.66)	(14.52)	(29.36)	(2.34)	(7.09)	(11.94)	(24.49)
Percentile
1%	6.17^b	18.07^b	29.50^b	54.38^b	5.06^a	15.32^a	25.43^a	46.02
	(2.46)	(7.56)	(12.78)	(26.31)	(2.95)	(8.97)	(15.09)	(30.57)
5%	7.23^c	20.73^c	33.43^c	63.93^c	6.45^c	19.06^c	31.07^b	58.56^b
	(1.78)	(5.49)	(9.35)	(19.79)	(2.37)	(7.23)	(12.18)	(24.93)
10%	7.48^c	21.93^c	35.98^c	69.68^c	7.06^c	20.65^c	33.70^c	64.96^c
	(1.46)	(4.56)	(7.89)	(16.91)	(2.07)	(6.27)	(10.64)	(21.99)
25%	7.04^c	20.95^c	34.41^c	67.20^c	6.97^c	20.43^c	33.47^c	64.86^c
	(1.50)	(4.65)	(8.01)	(17.24)	(1.63)	(4.93)	(8.29)	(16.97)
50%	5.83^b	17.28^b	28.45^b	55.77^b	5.67^c	16.69^c	27.58^c	53.83^c
	(2.36)	(7.15)	(12.05)	(24.69)	(1.63)	(4.91)	(8.20)	(16.52)
75%	4.71^a	14.18^a	23.56^a	46.72^a	4.62^b	13.75^b	22.83^b	45.25^b
	(2.77)	(8.33)	(13.97)	(28.32)	(1.98)	(5.97)	(10.02)	(20.41)
90%	3.99	12.23	20.55	41.58	3.83	11.74	19.69	39.81
	(3.03)	(9.15)	(15.33)	(30.94)	(2.47)	(7.48)	(12.66)	(26.22)
95%	3.58	10.71	18.11	37.65	3.32	10.22	17.34	36.10
	(3.16)	(9.54)	(15.99)	(32.31)	(2.73)	(8.36)	(14.16)	(29.45)
99%	3.29	9.80	16.67	35.89	2.77	8.70	14.90	32.71
	(3.39)	(10.27)	(17.24)	(34.85)	(3.13)	(9.55)	(16.10)	(33.08)

(a) Alternative a) without subjective assessments or correlated unobserved heterogeneity. Alternative b) Model with subjective assessments as exogenous explanatory variables and no correlated unobserved heterogeneity. (b) Percentage change in accumulated assets with respect to the baseline simulation (α = 10%). (c) Bootstrapped standard errors are in parentheses using 100 draws. ^{a, b, c}Significant at the 10%, 5%, and 1% levels.

Table D4:

[Alternative specifications] percentage change in accumulated assets at the end of seven years for alternative default schemes under alternative specifications of the model.

	Investment paths
	Alternative a)					Alternative b)
	No subjective assessments – no CUH					Exogenous subjective assessments – CUH
	Predicted	Riskier	Riskier	All C	All E	Predicted	Riskier	Riskier	All C	All E
	by model	default	gender-equated			by model	default	gender-equated
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
Mean	−2.05	7.92^c	8.60^c	0.82	−12.71^c	−2.10	8.04^b	8.72^c	0.85	−12.81^a
	(7.17)	(2.25)	(2.27)	(0.81)	(3.21)	(7.19)	(3.17)	(3.10)	(1.31)	(7.40)
Percentile
1%	−0.90	13.66	16.60	4.54	−8.87	−2.46	11.89	13.73	4.28	−9.61
	(12.05)	(13.09)	(13.58)	(10.16)	(23.25)	(18.09)	(17.65)	(16.02)	(14.25)	(38.60)
5%	−2.74	10.32	12.32	1.99	−12.29	−2.77	11.07	13.62	2.18	−12.08
	(8.68)	(8.25)	(9.11)	(5.39)	(12.71)	(12.67)	(12.55)	(12.14)	(7.89)	(25.09)
10%	−2.97	8.94	10.93	1.13	−12.45	−2.93	9.37	11.27	1.35	−12.42
	(7.36)	(6.59)	(7.20)	(4.02)	(9.33)	(10.28)	(9.74)	(9.47)	(5.61)	(19.49)
25%	−3.20	7.70^a	9.20^a	−0.08	−12.79^b	−3.29	7.95	9.53	−0.14	−12.91
	(6.80)	(4.52)	(4.72)	(2.45)	(6.22)	(8.08)	(6.30)	(6.37)	(3.62)	(13.92)
50%	−3.23	7.85^b	9.27^c	−0.57	−13.37^c	−3.32	7.99^a	9.50^b	−0.57	−13.46
	(7.13)	(3.15)	(3.20)	(1.47)	(4.48)	(7.40)	(4.39)	(4.75)	(2.29)	(10.63)
75%	−2.84	7.97^c	9.24^c	0.04	−13.19^c	−2.83	8.09^b	9.36^b	0.10	−13.25
	(7.11)	(2.57)	(2.81)	(0.89)	(3.57)	(7.36)	(3.54)	(3.75)	(1.44)	(8.69)
90%	−2.21	7.89^c	8.49^c	1.17	−12.60^c	−2.39	7.97^b	8.69^c	1.11	−12.80^a
	(7.14)	(2.16)	(2.30)	(0.72)	(3.02)	(7.42)	(3.11)	(3.03)	(1.06)	(7.41)
95%	−2.25	7.77^c	7.68^c	1.83^b	−12.29^c	−2.10	7.89^c	7.88^c	1.93^b	−12.37^a
	(7.48)	(2.02)	(2.07)	(0.88)	(2.80)	(7.51)	(2.91)	(2.72)	(0.98)	(6.54)
99%	−0.11	7.65^c	7.23^c	2.83^b	−11.62^c	−0.20	8.04^c	7.18^c	3.03^b	−11.70^b
	(7.89	(2.09)	(1.86)	(1.25)	(2.71)	(7.44)	(2.56)	(2.30)	(1.24)	(5.13)

(a) Alternative a) without subjective assessments nor correlated unobserved heterogeneity. Alternative b) model with subjective assessments as exogenous explanatory variables and no correlated unobserved heterogeneity. (b) Percentage change in accumulated assets with respect to default investment path. (c) Bootstrapped standard errors are in parentheses using 100 draws. ^{a, b, c}Significant at the 10%, 5%, and 1% levels.

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Received: 2021-10-12

Revised: 2022-06-06

Accepted: 2022-06-21

Published Online: 2022-07-15

Default Behavior and Risk Aversion in Defined Contribution Retirement Systems: Evidence from Chile

Abstract

Acknowledgement

Appendix A: Figures

Appendix B: Data Description

B.1 Construction of Elicited Risk Aversion

B.2 Sample Construction

B.3 Summary Statistics

Appendix C: Estimation Results (Preferred Model)

C.1 Likelihood Function

C.2 Empirical Specification and Identification

C.3 Parameter Estimates

Appendix D: Simulation Results

References

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