Impact of 401(k) on Financial Assets

Data explanation

1991 Survey of Income and Program Participation

net_tfa — Net Total Financial Assets. Calculated as the sum of all liquid and interest-earning assets (IRA balances, 401(k) balances, checking accounts, U.S. savings bonds, other interest‐earning accounts, stocks, mutual funds, etc.) minus non‐mortgage debts.
e401 — 401(k) Eligibility Indicator. Equals 1 if the individual's employer offers a 401(k) plan; otherwise 0.
p401 — 401(k) Participation Indicator. Equals 1 if the individual participate in 401(k) plan; otherwise 0.
age — Age. Age of the individual in years.
inc — Annual Income. Annual income of the individual, measured in U.S. dollars for the year 1990.
educ — Years of Education. Number of completed years of formal education.
fsize — Family Size. Total number of persons living in the household.
marr — Marital Status. Equals 1 if the individual is married; otherwise 0.
twoearn — Two-Earner Household. Equals 1 if there are two wage earners in the household; otherwise 0.
db — Defined-Benefit Pension Plan. Equals 1 if the individual is covered by a defined-benefit pension plan; otherwise 0.
pira — IRA Participation. Equals 1 if the individual contributes to an Individual Retirement Account (IRA); otherwise 0.
hown — Home Ownership. Equals 1 if the household owns its home; 0 if renting.

We download it with fetch_401K function from doubleML.datasets

This dataset has a problem. confounders were measured in the same year as treatment and outcome, like they are demographic factors that do not change over time. So inference might still be biased.

Result

/Users/ioannmartynov/miniconda3/envs/causalkit/lib/python3.14/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html from .autonotebook import tqdm as notebook_tqdm

Result

Index(['net_tfa', 'age', 'inc', 'fsize', 'educ', 'db', 'marr', 'twoearn', 'p401', 'pira', 'hown'], dtype='object')

EDA

Result

	treatment	count	mean	std	min	p10	p25	median	p75	p90	max
0	0	7321	10890.477539	55256.829173	-502302.0	-5427.0	-1184.0	200.0	7399.0	33500.0	1462115.0
1	1	2594	38262.058594	79087.535303	-283356.0	-1300.0	3000.0	15249.0	45985.5	98887.4	1536798.0

Participants’ average net worth is ≈28k higher, but this gap cannot be causally attributed solely to participation. The classes are imbalanced—only 26% are treated.

Result

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Result

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Our outcome has large right tail

Result

	treatment	n	outlier_count	outlier_rate	lower_bound	upper_bound	has_outliers	method	tail
0	0	7321	1292	0.176479	-14058.50	20273.50	True	iqr	both
1	1	2594	212	0.081727	-61478.25	110463.75	True	iqr	both

Result

	confounders	mean_d_0	mean_d_1	abs_diff	smd	ks_pvalue
0	inc	32889.802486	49366.975713	16477.173227	0.662197	0.00000
1	hown	0.589127	0.765227	0.176100	0.383456	0.00000
2	pira	0.200246	0.360447	0.160201	0.362421	0.00000
3	db	0.228248	0.391673	0.163426	0.358968	0.00000
4	twoearn	0.337659	0.502699	0.165040	0.339096	0.00000
5	educ	12.991121	13.813416	0.822294	0.299061	0.00000
6	marr	0.574512	0.690439	0.115928	0.242175	0.00000
7	age	40.900970	41.509638	0.608668	0.060108	0.00000
8	fsize	2.848108	2.915960	0.067852	0.044731	0.00076

Treatment and control are unbalanced on all confounders except age and fsize; nonetheless, we retain age and fsize in the model to gain efficiency

Inference

Result

	value
field
estimand	ATE
model	IRM
value	11027.1737 (ci_abs: 8241.3361, 13813.0113)
value_relative	79.0032 (ci_rel: 53.3308, 104.6757)
alpha	0.0500
p_value	0.0000
is_significant	True
n_treated	2594
n_control	7321
treatment_mean	38262.0605
control_mean	10890.4771
time	2026-02-20

Average Treatment Effect is significant and equals 12486.5221 (ci_abs: 9791.0517, 15181.9924)

Refutation

Unconfoundedness

Result

	metric	value	flag
0	balance_max_smd	0.071103	GREEN
1	balance_frac_violations	0.000000	GREEN

Sensitivity

Result

	r2_y	r2_d	rho	theta_long	theta_short	delta
p401	0.000038	9.626565e-08	1.0	11027.17369	14961.333165	-3934.159474

Result

{'theta': 11027.173690133526, 'se': 1421.3718379696486, 'alpha': 0.05, 'z': 1.959963984540054, 'H0': 0.0, 'sampling_ci': (8241.336079073513, 13813.01130119354), 'theta_bounds_cofounding': (11026.878096998567, 11027.469283268485), 'bias_aware_ci': (8241.052409910035, 13813.318820768469), 'max_bias_base': 154546.29526314724, 'max_bias': 0.29559313495817796, 'bound_width': 0.29559313495817796, 'sigma2': 3792734186.778151, 'nu2': 6.29745091623553, 'rv': 0.06659988318083149, 'rva': 0.05062630379913903, 'params': {'r2_y': 3.8e-05, 'r2_d': 9.626565e-08, 'rho': 1.0, 'use_signed_rr': False}}

SUTVA

Result

1.) Are your clients independent (i). Outcome of ones do not depend on others? 2.) Are all clients have full window to measure metrics? 3.) Do you measure confounders before treatment and outcome after? 4.) Do you have a consistent label of treatment, such as if a person does not receive a treatment, he has a label 0?

Score

Result

	metric	value	flag
0	se_plugin	1.421372e+03	NA
1	psi_p99_over_med	3.625835e+01	RED
2	psi_kurtosis	1.700952e+02	RED
3	max_\|t\|_g1	3.709872e+00	YELLOW
4	max_\|t\|_g0	1.989905e+00	GREEN
5	max_\|t\|_m	2.116322e+00	YELLOW
6	oos_tstat_fold	2.643408e-16	GREEN
7	oos_tstat_strict	1.982299e-16	GREEN

Result

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Result

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Result

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Overlap

Result

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Result

	metric	value	flag
0	edge_0.01_below	0.008472	GREEN
1	edge_0.01_above	0.000000	GREEN
2	edge_0.02_below	0.024307	GREEN
3	edge_0.02_above	0.000000	GREEN
4	KS	0.316022	YELLOW
5	AUC	0.711829	GREEN
6	ESS_treated_ratio	0.383340	GREEN
7	ESS_control_ratio	0.903632	GREEN
8	tails_w1_q99/med	7.777954	YELLOW
9	tails_w0_q99/med	2.375994	GREEN
10	ATT_identity_relerr	0.049028	GREEN
11	clip_m_total	0.008472	GREEN
12	calib_ECE	0.022127	GREEN
13	calib_slope	0.798318	YELLOW
14	calib_intercept	-0.163574	GREEN

Result

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We find no evidence of a violation of the overlap (positivity) assumption.

Conclution

There are problems with design: confounders are measured not before treatment. So treatment affected confounders. However estimate is robust and in real life participation in 401k is increasing net financial assets. To keep in mind real CI bounds may differ from our estimation