Impact of 401(k) on Financial Assets

This notebook presents the 401k case and the core analysis workflow.

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/ioann/miniconda3/envs/causalis/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='str')

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

png

Result

png

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
outcome	net_tfa
estimand	ATE
model	IRM
value	12461.3189 (ci_abs: 9740.2705, 15182.3673)
value_relative	92.8793 (ci_rel: 62.6145, 123.1440)
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	2026-07-19

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	0.070867	GREEN
1	balance_frac_violations	0.000000	GREEN

Sensitivity

Result

	benchmark_confounder	r2_y	r2_d	rho	theta_long	theta_short	delta	cf_y	cf_d	cf_y_raw	...	rho_raw	rho_clipped	cf_y_clipped	cf_d_clipped	rho_fallback	boundary_calibration	strengths_valid	calibration_valid	calibration_issue	calibration_warning
0	inc	0.10311	1.0	0.125838	12461.318916	17050.008442	-4588.689527	0.114964	1.0	0.114964	...	0.125838	False	False	True	False	True	False	False	DoubleML-clipped cf_d=1 is outside the finite ...	cf_d_raw=1.13691 was clipped to 1

1 rows × 25 columns

Result

================== Bias-aware Interval ==================

------------------ Scenario ------------------ Significance Level: alpha=0.05 Null Hypothesis: H0=0.0 Sensitivity parameters: r2_y=3.8e-05; r2_d=9.626565e-08, rho=1.0, use_signed_rr=False

statistics value 0 bias_aware_ci [9739.9914, 15182.6523] 1 theta [12461.0369, 12461.3189, 12461.6009] 2 sampling_ci [9740.2705, 15182.3673] 3 rv 0.077900 4 rva 0.062000 5 se 1388.315500 6 max_bias 0.282000 7 max_bias_base 147443.412300 8 bound_width 0.282000 9 sigma2 3962737020.773400 10 nu2 5.486000

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	psi_p99_over_med	34.659465	RED
1	psi_kurtosis	130.538114	RED
2	max_\|t\|_g1	3.672067	YELLOW
3	max_\|t\|_g0	2.292418	YELLOW
4	max_\|t\|_m	1.287034	GREEN
5	oos_max_abs_t	0.000047	GREEN

Result

png

Result

png

Result

png

Overlap

Result

png

Result

	metric	value	flag
0	edge_0.01_below	0.009077	GREEN
1	edge_0.01_above	0.000000	GREEN
2	edge_0.02_below	0.024710	GREEN
3	edge_0.02_above	0.000000	GREEN
4	KS	0.306276	YELLOW
5	AUC	0.711745	GREEN
6	ESS_treated_ratio	0.343135	GREEN
7	ESS_control_ratio	0.875427	GREEN
8	tails_w1_q99/med	8.021585	YELLOW
9	tails_w0_q99/med	2.465538	YELLOW
10	ATT_identity_relerr	0.063478	YELLOW
11	clip_m_total	0.009077	GREEN
12	calib_ECE	0.020958	GREEN
13	calib_slope	0.789433	YELLOW
14	calib_intercept	-0.172876	GREEN

Result

png

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