------------------------------------------------------------------------------- name: log: /Users/carlosmendez/Documents/GitHub/starter-academic-v501/content > /post/stata_cate/analysis.log log type: text opened on: 2 May 2026, 21:43:39 . . . *================================================================ . * Section 0: Stata 19 version gate . *================================================================ . * . * The -cate- command is brand-new in Stata 19. There is NO . * equivalent in Stata 18 or earlier. We refuse to run on older . * Stata so that the user gets a clear error rather than a stream . * of "command cate is unrecognized" messages. . *---------------------------------------------------------------- . . if c(stata_version) < 19 { . di as error "" . di as error "============================================================ > " . di as error " ERROR: this script requires Stata 19 or later." . di as error " Detected Stata version: " c(stata_version) . di as error " The -cate- command was introduced in Stata 19." . di as error "============================================================ > " . log close . exit 198 . } . . di as text "Stata version detected: " c(stata_version) " -- OK." Stata version detected: 19 -- OK. . . . *================================================================ . * Section 1: Setup -- globals and reproducibility . *================================================================ . * . * Two macros control the analysis: . * . * $catecovars: the variables for which we want to know how the . * effect varies. These are the inputs to tau(x). . * . * $controls: variables used by the nuisance functions (the . * outcome model g(x,w) and the treatment model . * f(x,w)). Often the same as catecovars, but you . * can pass a richer set with interactions to soak . * up confounding without overcomplicating tau(x). . * . * The seed makes cross-fitting and the random-forest internals . * reproducible. We use the same seed throughout. . *---------------------------------------------------------------- . . global catecovars age educ i.incomecat i.pension i.married i.twoearn i.ira i. > ownhome . global controls age educ i.incomecat i.pension i.married i.twoearn i.ira i. > ownhome . global rseed 12345671 . . . *================================================================ . * Section 2: Data loading and exploration . *================================================================ . * . * assets3 is shipped with Stata's example data. Each row is one . * household. e401k = 1 if the household is eligible for a 401(k) . * through their employer; 0 otherwise. asset is total net . * financial assets in dollars. . *---------------------------------------------------------------- . . webuse assets3, clear (Excerpt from Chernozhukov and Hansen (2004)) . . * Quick variable description and sample size . describe asset e401k age educ income incomecat pension married twoearn ira ow > nhome Variable Storage Display Value name type format label Variable label ------------------------------------------------------------------------------- assets float %9.0g Net total financial assets e401k byte %12.0g lbe401 401(k) eligibility age byte %9.0g Age educ byte %9.0g Years of education income float %9.0g Household income incomecat byte %9.0g Income category pension byte %16.0g lbpen Pension benefits married byte %11.0g lbmar Marital status twoearn byte %9.0g lbyes Two-earner household ira byte %9.0g lbyes IRA participation ownhome byte %9.0g lbyes Homeowner . . * Summary statistics . summarize asset e401k age educ income, detail Net total financial assets ------------------------------------------------------------- Percentiles Smallest 1% -23500 -502302 5% -9000 -409000 10% -4757 -336789 Obs 9,913 25% -500 -315701 Sum of wgt. 9,913 50% 1499 Mean 18054.17 Largest Std. dev. 63528.63 75% 16549 1317947 90% 54860 1324445 Variance 4.04e+09 95% 91999 1462115 Skewness 10.63739 99% 219948 1536798 Kurtosis 186.7368 401(k) eligibility ------------------------------------------------------------- Percentiles Smallest 1% 0 0 5% 0 0 10% 0 0 Obs 9,913 25% 0 0 Sum of wgt. 9,913 50% 0 Mean .3714315 Largest Std. dev. .4832118 75% 1 1 90% 1 1 Variance .2334937 95% 1 1 Skewness .5321684 99% 1 1 Kurtosis 1.283203 Age ------------------------------------------------------------- Percentiles Smallest 1% 25 25 5% 26 25 10% 28 25 Obs 9,913 25% 32 25 Sum of wgt. 9,913 50% 40 Mean 41.05891 Largest Std. dev. 10.3446 75% 48 64 90% 57 64 Variance 107.0107 95% 60 64 Skewness .4023391 99% 63 64 Kurtosis 2.196163 Years of education ------------------------------------------------------------- Percentiles Smallest 1% 4 1 5% 9 1 10% 11 1 Obs 9,913 25% 12 1 Sum of wgt. 9,913 50% 12 Mean 13.20629 Largest Std. dev. 2.810628 75% 16 18 90% 17 18 Variance 7.899629 95% 18 18 Skewness -.6430457 99% 18 18 Kurtosis 4.969568 Household income ------------------------------------------------------------- Percentiles Smallest 1% 4107 0 5% 8916 0 10% 12240 0 Obs 9,913 25% 19413 27 Sum of wgt. 9,913 50% 31488 Mean 37208.4 Largest Std. dev. 24770.73 75% 48585 192990 90% 69612 199041 Variance 6.14e+08 95% 86400 200997 Skewness 1.565042 99% 119133 242124 Kurtosis 6.898131 . . * Treatment-group sizes (raw counts and proportions) . tab e401k, missing 401(k) | eligibility | Freq. Percent Cum. -------------+----------------------------------- Not eligible | 6,231 62.86 62.86 Eligible | 3,682 37.14 100.00 -------------+----------------------------------- Total | 9,913 100.00 . . * Naive mean-difference (NOT a causal estimate -- groups differ . * in age, income, education, etc.). This is the "before doing . * anything sensible" benchmark. . tabstat asset, by(e401k) statistics(mean sd n) Summary for variables: assets Group variable: e401k (401(k) eligibility) e401k | Mean SD N -------------+------------------------------ Not eligible | 10789.9 54527.02 6231 Eligible | 30347.39 74800.21 3682 -------------+------------------------------ Total | 18054.17 63528.63 9913 -------------------------------------------- . . * Export the raw dataset so the blog post / report skill can . * reference exact numbers without rerunning Stata. . export delimited asset e401k age educ income incomecat pension married /// > twoearn ira ownhome using "assets3_raw.csv", replace (file assets3_raw.csv not found) file assets3_raw.csv saved . . . *================================================================ . * Section 3: Baseline ATE -- the "single number" view . *================================================================ . * . * Estimand: ATE = E{y(1) - y(0)} . * . * Before estimating *heterogeneous* effects, we anchor with a . * good *average* effect. We use AIPW (doubly robust) so the ATE . * is consistent if EITHER the outcome model OR the propensity . * score model is correct. . * . * This is exactly the workhorse you might already know from . * Stata's -teffects- suite. It returns ONE number: the average . * effect across the whole sample. . * . * Why this isn't enough: the ATE could be $8,000 on average and . * still hide huge variation -- maybe high-income households gain . * $20,000 and low-income households gain almost nothing. . * Sections 4 onward open the hood. . *---------------------------------------------------------------- . . teffects aipw > /// > (asset c.age c.educ i.incomecat i.pension i.married i.twoearn i.ira i.own > home) /// > (e401k c.age c.educ i.incomecat i.pension i.married i.twoearn i.ira i.own > home) Iteration 0: EE criterion = 1.363e-21 Iteration 1: EE criterion = 1.368e-23 Treatment-effects estimation Number of obs = 9,913 Estimator : augmented IPW Outcome model : linear by ML Treatment model: logit ------------------------------------------------------------------------------ | Robust assets | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- ATE | e401k | (Eligible | vs | Not elig..) | 8019.463 1152.038 6.96 0.000 5761.51 10277.42 -------------+---------------------------------------------------------------- POmean | e401k | Not eligi.. | 13930.46 817.613 17.04 0.000 12327.97 15532.96 ------------------------------------------------------------------------------ . . * Quick "naive" subgroup table to motivate the rest of the . * tutorial: do raw mean differences look uniform across income . * categories? (Spoiler: no.) . table incomecat e401k, statistic(mean asset) nformat(%10.0f) -------------------------------------------------- | 401(k) eligibility | Not eligible Eligible Total ----------------+--------------------------------- Income category | 0 | 889 5900 1562 1 | 4249 6015 4717 2 | 7944 12797 9800 3 | 14753 23774 19138 4 | 42690 63639 55040 Total | 10790 30347 18054 -------------------------------------------------- . . . *================================================================ . * Section 4: PO estimator on the partial-linear model . *================================================================ . * . * Estimand: CATE tau(x) = E{y(1) - y(0) | x = x} . * . * The partial-linear (PO = Partialing-Out) model assumes: . * . * y = d * tau(x) + g(x,w) + epsilon . * d = f(x,w) + u . * . * where g and f are flexible nuisance functions estimated by . * machine learning (lasso by default), and tau(x) is the object . * of interest. . * . * PO partials out g and f using cross-fitting (Robinson 1988; . * Chernozhukov et al. 2018), then fits a causal forest on the . * residuals. The output: . * - "Average treatment effect" line (this is the ATE) . * - And, behind the scenes, a function tau(x) we will probe . * in the next sections. . * . * Why PO first: it is robust and uses the default settings the . * manual recommends. We compare with AIPW in Section 8. . *---------------------------------------------------------------- . . cate po (asset $catecovars) (e401k), rseed($rseed) Cross-fit fold 1 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Cross-fit fold 2 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Cross-fit fold 3 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Cross-fit fold 4 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Cross-fit fold 5 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Cross-fit fold 6 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Cross-fit fold 7 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Cross-fit fold 8 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Cross-fit fold 9 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Cross-fit fold 10 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Performing random forest for IATE ... Estimating AIPW scores ... Estimating ATE ... Conditional average treatment effects Number of observations = 9,913 Estimator: Partialing out Number of folds in cross-fit = 10 Outcome model: Linear lasso Number of outcome controls = 17 Treatment model: Logit lasso Number of treatment controls = 17 CATE model: Random forest Number of CATE variables = 17 ------------------------------------------------------------------------------ | Robust assets | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- ATE | e401k | (Eligible | vs | Not elig..) | 7937.182 1153.017 6.88 0.000 5677.309 10197.05 -------------+---------------------------------------------------------------- POmean | e401k | Not eligi.. | 14016.38 833.4423 16.82 0.000 12382.87 15649.9 ------------------------------------------------------------------------------ . . * Formal test of treatment-effect homogeneity . * H0: tau(x) is constant -- i.e., there is NO heterogeneity. . * If we reject H0, the rest of this script is justified. . estat heterogeneity Treatment-effects heterogeneity test H0: Treatment effects are homogeneous chi2(1) = 4.11 Prob > chi2 = 0.0427 . . * Linear projection: regress the (latent) tau_i on the catecovars. . * This gives an interpretable summary of WHICH covariates drive . * heterogeneity -- think of it as "an OLS view of the function . * tau(x)". Big positive coefficients = the variable raises the . * effect. . estat projection $catecovars Treatment-effects linear projection Number of obs = 9,913 F(11, 9901) = 4.90 Prob > F = 0.0000 R-squared = 0.0045 Adj R-squared = 0.0034 Root MSE = 1.146e+05 ------------------------------------------------------------------------------ | Robust | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- age | 205.1206 117.9809 1.74 0.082 -26.14605 436.3873 educ | -442.4583 488.4721 -0.91 0.365 -1399.963 515.0466 | incomecat | 1 | -2439.222 2013.522 -1.21 0.226 -6386.136 1507.692 2 | 1874.817 2295.155 0.82 0.414 -2624.154 6373.788 3 | 5707.689 3298.341 1.73 0.084 -757.7313 12173.11 4 | 18194.6 5398.391 3.37 0.001 7612.651 28776.54 | pension | Receives .. | 3817.355 2454.437 1.56 0.120 -993.8419 8628.553 | married | Married | -2399.333 3403.066 -0.71 0.481 -9070.035 4271.37 | twoearn | Yes | -1428.041 4347.025 -0.33 0.743 -9949.094 7093.013 | ira | Yes | -2438.404 3619.217 -0.67 0.500 -9532.807 4656 | ownhome | Yes | 3162.649 1669.587 1.89 0.058 -110.081 6435.379 _cons | 232.7251 8072.023 0.03 0.977 -15590.08 16055.53 ------------------------------------------------------------------------------ . . * Predict the individual treatment effects (IATEs) for use in . * CSV export below. -iate- is the default option; we name it . * explicitly so the code reads pedagogically. . predict double iate_po, iate . . * Export IATE predictions (one row per household). Wrapped in . * -capture- so a missing-variable issue does not derail the rest . * of the script. . capture { . . * Figure 1: distribution of individual effects (PO). . * A wide spread = strong heterogeneity. A spike at one value = . * near-homogeneity. Look for a fat right tail in this dataset. . categraph histogram, /// > title("Distribution of individual treatment effects (PO)") /// > xtitle("Estimated tau_hat_i (dollars)") /// > note("Source: assets3, Stata 19 cate po") (bin=39, start=-40204.13, width=2975.4332) . graph export "stata_cate_iate_histogram_po.png", replace width(1200) (file stata_cate_iate_histogram_po.png not found) file stata_cate_iate_histogram_po.png written in PNG format . . . *================================================================ . * Section 5: How does the effect vary with one variable? . *================================================================ . * . * IATE plots show tau(x_j) varying ONE covariate at a time, with . * the other covariates fixed at their reference values. This is . * the most intuitive way to see "where does the effect peak?". . * . * Each plot includes confidence bands (from honest random-forest . * inference, the bootstrap-of-little-bags procedure). . *---------------------------------------------------------------- . . * Figure 2: effect as a function of age . categraph iateplot age, /// > title("Estimated CATE by age") /// > ytitle("tau_hat (dollars)") xtitle("Age (years)") Note: IATE estimated at fixed values of covariates other than age. -------------------------------------------------- Variable | Statistic Value Type ------------+------------------------------------- educ | mean 13.20629 continuous incomecat | base 0 factor ira | base 0 factor married | base 0 factor ownhome | base 0 factor pension | base 0 factor twoearn | base 0 factor -------------------------------------------------- . graph export "stata_cate_iateplot_age.png", replace width(1200) (file stata_cate_iateplot_age.png not found) file stata_cate_iateplot_age.png written in PNG format . . * Figure 3: effect as a function of education . categraph iateplot educ, /// > title("Estimated CATE by years of education") /// > ytitle("tau_hat (dollars)") xtitle("Education (years)") Note: IATE estimated at fixed values of covariates other than educ. -------------------------------------------------- Variable | Statistic Value Type ------------+------------------------------------- age | mean 41.05891 continuous incomecat | base 0 factor ira | base 0 factor married | base 0 factor ownhome | base 0 factor pension | base 0 factor twoearn | base 0 factor -------------------------------------------------- . graph export "stata_cate_iateplot_educ.png", replace width(1200) (file stata_cate_iateplot_educ.png not found) file stata_cate_iateplot_educ.png written in PNG format . . . *================================================================ . * Section 6: GATE on prespecified groups . *================================================================ . * . * Estimand: GATE tau(g) = E{Gamma_i | G_i = g} . * . * where Gamma_i is the AIPW orthogonal score for unit i. A GATE . * averages the individual effect within a prespecified group -- . * here, the 5 income categories (incomecat). . * . * The trick: -reestimate- recycles the IATE function fitted in . * Section 4. We do NOT refit the (slow) causal forest. We just . * recompute group means. . *---------------------------------------------------------------- . . cate, group(incomecat) reestimate Estimating GATE ... Conditional average treatment effects Number of observations = 9,913 Estimator: Partialing out Number of folds in cross-fit = 10 Outcome model: Linear lasso Number of outcome controls = 17 Treatment model: Logit lasso Number of treatment controls = 17 CATE model: Random forest Number of CATE variables = 17 ------------------------------------------------------------------------------ | Robust assets | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- GATE | incomecat | 0 | 4087.014 987.7124 4.14 0.000 2151.133 6022.895 1 | 1399.398 1663.193 0.84 0.400 -1860.4 4659.196 2 | 5154.329 1349.842 3.82 0.000 2508.688 7799.97 3 | 8532.238 2287.664 3.73 0.000 4048.499 13015.98 4 | 20510.94 4723.741 4.34 0.000 11252.58 29769.3 -------------+---------------------------------------------------------------- ATE | e401k | (Eligible | vs | Not elig..) | 7937.182 1153.017 6.88 0.000 5677.309 10197.05 -------------+---------------------------------------------------------------- POmean | e401k | Not eligi.. | 14016.38 833.4423 16.82 0.000 12382.87 15649.9 ------------------------------------------------------------------------------ . . * Joint test: are the GATEs equal across the 5 income groups? . * Reject H0 = effect is heterogeneous across income. . estat gatetest Group treatment-effects heterogeneity test H0: Group average treatment effects are homogeneous ( 1) [GATE]0bn.incomecat - [GATE]1.incomecat = 0 ( 2) [GATE]0bn.incomecat - [GATE]2.incomecat = 0 ( 3) [GATE]0bn.incomecat - [GATE]3.incomecat = 0 ( 4) [GATE]0bn.incomecat - [GATE]4.incomecat = 0 chi2(4) = 18.44 Prob > chi2 = 0.0010 . . * Figure 4: GATE bar chart with 95% CIs . categraph gateplot, /// > title("GATE by income category") /// > ytitle("tau_hat (dollars)") xtitle("Income category (1 = low, 5 = high)") . graph export "stata_cate_gate_incomecat.png", replace width(1200) (file stata_cate_gate_incomecat.png not found) file stata_cate_gate_incomecat.png written in PNG format . . * Save group-level results to CSV (estimate, SE, CI bounds). . * Wrapped in -capture- because the column-naming convention from . * r(table) is sensitive to factor levels. . capture noisily { . matrix gate_table = r(table)' . preserve . clear . svmat double gate_table, names(col) number of observations will be reset to 1 Press any key to continue, or Break to abort Number of observations (_N) was 0, now 1. . export delimited using "gate_results.csv", replace (file gate_results.csv not found) file gate_results.csv saved . restore . } . . . *================================================================ . * Section 7: GATES on data-driven quartiles . *================================================================ . * . * GATES = "Group Average Treatment Effect Sorted". Stata sorts . * households by their *predicted* effect tau_hat_i and bins them . * into quartiles (or any quantile via group(#)). Then it reports . * the mean effect within each bin. . * . * This is the cleanest single picture of heterogeneity: . * - Bin 1 = the top 25% of predicted effects . * - Bin 4 = the bottom 25% . * If the bars look almost the same, there is little . * heterogeneity. If they fan out, there is a lot. . * . * Cross-fitting protects against p-hacking: the binning uses . * out-of-sample predictions, so a unit's bin is not informed by . * its own outcome. . *---------------------------------------------------------------- . . cate po (asset $catecovars) (e401k), rseed($rseed) group(4) Cross-fit fold 1 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Estimating IATE rankings ... Estimating AIPW scores ... Cross-fit fold 2 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Estimating IATE rankings ... Estimating AIPW scores ... Cross-fit fold 3 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Estimating IATE rankings ... Estimating AIPW scores ... Cross-fit fold 4 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Estimating IATE rankings ... Estimating AIPW scores ... Cross-fit fold 5 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Estimating IATE rankings ... Estimating AIPW scores ... Cross-fit fold 6 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Estimating IATE rankings ... Estimating AIPW scores ... Cross-fit fold 7 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Estimating IATE rankings ... Estimating AIPW scores ... Cross-fit fold 8 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Estimating IATE rankings ... Estimating AIPW scores ... Cross-fit fold 9 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Estimating IATE rankings ... Estimating AIPW scores ... Cross-fit fold 10 of 10 ... Performing lasso for outcome assets ... Performing lasso for treatment e401k ... Estimating IATE rankings ... Estimating AIPW scores ... Performing random forest for IATE ... Estimating AIPW scores ... Estimating sorted GATE ... Conditional average treatment effects Number of observations = 9,913 Estimator: Partialing out Number of folds in cross-fit = 10 Outcome model: Linear lasso Number of outcome controls = 17 Treatment model: Logit lasso Number of treatment controls = 17 CATE model: Random forest Number of CATE variables = 17 ------------------------------------------------------------------------------ | Robust assets | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- GATES | rank | 1 | 17278.94 3440.125 5.02 0.000 10536.42 24021.46 2 | 8121.04 1691.008 4.80 0.000 4806.725 11435.35 3 | 3443.834 1437.64 2.40 0.017 626.112 6261.556 4 | 2919.197 2110.32 1.38 0.167 -1216.955 7055.349 -------------+---------------------------------------------------------------- ATE | e401k | (Eligible | vs | Not elig..) | 7938.209 1152.994 6.88 0.000 5678.382 10198.04 -------------+---------------------------------------------------------------- POmean | e401k | Not eligi.. | 14010.83 833.4653 16.81 0.000 12377.27 15644.39 ------------------------------------------------------------------------------ . . * Figure 5: GATES bar chart (Q1 vs Q4) . categraph gateplot, /// > title("GATES by data-driven quartile of estimated effect") /// > ytitle("tau_hat (dollars)") xtitle("Quartile (1 = highest tau_hat, 4 = lo > west)") . graph export "stata_cate_gates_quartiles.png", replace width(1200) (file stata_cate_gates_quartiles.png not found) file stata_cate_gates_quartiles.png written in PNG format . . * Profile of who's in each bin: -estat classification- runs a . * two-sample t-test comparing the mean of ONE variable between . * the highest-effect and lowest-effect rank groups. Only one . * variable per call; we sweep three. . estat classification age Classification t test with equal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- 1 | 2,480 45.14677 .1822933 9.078133 44.78931 45.50424 4 | 2,471 34.98017 .21922 10.89724 34.5503 35.41004 ---------+-------------------------------------------------------------------- Combined | 4,951 40.07271 .1597646 11.24157 39.7595 40.38592 ---------+-------------------------------------------------------------------- diff | 10.1666 .2850173 9.607844 10.72536 ------------------------------------------------------------------------------ diff = mean(1) - mean(4) t = 35.6701 H0: diff = 0 Degrees of freedom = 4949 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000 . estat classification educ Classification t test with equal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- 1 | 2,480 14.02177 .0520357 2.591358 13.91974 14.12381 4 | 2,471 12.65439 .0518032 2.575095 12.55281 12.75597 ---------+-------------------------------------------------------------------- Combined | 4,951 13.33933 .0379738 2.671962 13.26488 13.41377 ---------+-------------------------------------------------------------------- diff | 1.367383 .0734263 1.223435 1.511331 ------------------------------------------------------------------------------ diff = mean(1) - mean(4) t = 18.6225 H0: diff = 0 Degrees of freedom = 4949 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000 . estat classification income Classification t test with equal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. err. Std. dev. [95% conf. interval] ---------+-------------------------------------------------------------------- 1 | 2,480 62739.02 512.083 25501.53 61734.86 63743.17 4 | 2,471 26860.95 380.2588 18902.34 26115.29 27606.6 ---------+-------------------------------------------------------------------- Combined | 4,951 44832.59 408.4175 28737.62 44031.91 45633.27 ---------+-------------------------------------------------------------------- diff | 35878.07 638.1663 34626.98 37129.16 ------------------------------------------------------------------------------ diff = mean(1) - mean(4) t = 56.2206 H0: diff = 0 Degrees of freedom = 4949 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000 . . . *================================================================ . * Section 8: AIPW estimator -- a doubly-robust contrast . *================================================================ . * . * The fully-interactive (AIPW) model fits separate outcome models . * for treated and untreated: . * y(1) = g_1(x,w) + epsilon_1 . * y(0) = g_0(x,w) + epsilon_0 . * . * The CATE then comes from the AIPW score: . * Gamma_i = [y_hat(1) + d*(y - y_hat(1))/f] . * - [y_hat(0) + (1-d)*(y - y_hat(0))/(1-f)] . * . * This is "doubly robust": consistent if EITHER the outcome . * models OR the propensity score is correct. It is more . * efficient (narrower CIs) than PO when both are well-specified, . * but more sensitive to propensity scores near 0 or 1 (the . * "overlap" issue). . * . * If PO and AIPW give similar pictures, you can trust the . * heterogeneity story. If they disagree wildly, dig into . * overlap and model specification. . *---------------------------------------------------------------- . . cate aipw (asset $catecovars) (e401k), rseed($rseed) Cross-fit fold 1 of 10 ... Estimating lasso for outcome assets if e401k = 0 ... Estimating lasso for outcome assets if e401k = 1 ... Performing lasso for treatment e401k ... Cross-fit fold 2 of 10 ... Estimating lasso for outcome assets if e401k = 0 ... Estimating lasso for outcome assets if e401k = 1 ... Performing lasso for treatment e401k ... Cross-fit fold 3 of 10 ... Estimating lasso for outcome assets if e401k = 0 ... Estimating lasso for outcome assets if e401k = 1 ... Performing lasso for treatment e401k ... Cross-fit fold 4 of 10 ... Estimating lasso for outcome assets if e401k = 0 ... Estimating lasso for outcome assets if e401k = 1 ... Performing lasso for treatment e401k ... Cross-fit fold 5 of 10 ... Estimating lasso for outcome assets if e401k = 0 ... Estimating lasso for outcome assets if e401k = 1 ... Performing lasso for treatment e401k ... Cross-fit fold 6 of 10 ... Estimating lasso for outcome assets if e401k = 0 ... Estimating lasso for outcome assets if e401k = 1 ... Performing lasso for treatment e401k ... Cross-fit fold 7 of 10 ... Estimating lasso for outcome assets if e401k = 0 ... Estimating lasso for outcome assets if e401k = 1 ... Performing lasso for treatment e401k ... Cross-fit fold 8 of 10 ... Estimating lasso for outcome assets if e401k = 0 ... Estimating lasso for outcome assets if e401k = 1 ... Performing lasso for treatment e401k ... Cross-fit fold 9 of 10 ... Estimating lasso for outcome assets if e401k = 0 ... Estimating lasso for outcome assets if e401k = 1 ... Performing lasso for treatment e401k ... Cross-fit fold 10 of 10 ... Estimating lasso for outcome assets if e401k = 0 ... Estimating lasso for outcome assets if e401k = 1 ... Performing lasso for treatment e401k ... Estimating AIPW scores ... Estimating random forest for IATE ... Estimating ATE ... Conditional average treatment effects Number of observations = 9,913 Estimator: Augmented IPW Number of folds in cross-fit = 10 Outcome model: Linear lasso Number of outcome controls = 17 Treatment model: Logit lasso Number of treatment controls = 17 CATE model: Random forest Number of CATE variables = 17 ------------------------------------------------------------------------------ | Robust assets | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- ATE | e401k | (Eligible | vs | Not elig..) | 8120.264 1160.538 7.00 0.000 5845.652 10394.88 -------------+---------------------------------------------------------------- POmean | e401k | Not eligi.. | 13978.94 836.9925 16.70 0.000 12338.47 15619.42 ------------------------------------------------------------------------------ . . * Heterogeneity test under the AIPW spec . estat heterogeneity Treatment-effects heterogeneity test H0: Treatment effects are homogeneous chi2(1) = 5.54 Prob > chi2 = 0.0186 . . * Figure 6: IATE distribution (AIPW). Compare with Figure 1. . categraph histogram, /// > title("Distribution of individual treatment effects (AIPW)") /// > xtitle("Estimated tau_hat_i (dollars)") /// > note("Source: assets3, Stata 19 cate aipw") (bin=39, start=-196082.43, width=10162.687) . graph export "stata_cate_iate_histogram_aipw.png", replace width(1200) (file stata_cate_iate_histogram_aipw.png not found) file stata_cate_iate_histogram_aipw.png written in PNG format . . * Figure 7: AIPW effect by education (compare with PO Figure 3) . categraph iateplot educ, /// > title("Estimated CATE by education (AIPW)") /// > ytitle("tau_hat (dollars)") xtitle("Education (years)") Note: IATE estimated at fixed values of covariates other than educ. -------------------------------------------------- Variable | Statistic Value Type ------------+------------------------------------- age | mean 41.05891 continuous incomecat | base 0 factor ira | base 0 factor married | base 0 factor ownhome | base 0 factor pension | base 0 factor twoearn | base 0 factor -------------------------------------------------- . graph export "stata_cate_iateplot_educ_aipw.png", replace width(1200) (file stata_cate_iateplot_educ_aipw.png not found) file stata_cate_iateplot_educ_aipw.png written in PNG format . . . *================================================================ . * Section 9: Nonparametric series -- a smooth view of tau(x_j) . *================================================================ . * . * -estat series- fits a B-spline (or polynomial) of the IATE . * against one continuous covariate. Unlike -categraph iateplot- . * (which holds other covariates at reference values), this is . * a marginal smoother: it averages over the joint distribution . * of x. . * . * Practical use: tells you whether the relationship between . * tau(x) and x_j is monotone, U-shaped, etc. With knots(5) we . * let the spline have 5 internal knots -- enough flexibility for . * a single covariate. . *---------------------------------------------------------------- . . * Figure 8: nonparametric series of tau against income . estat series income if income <= 150000, graph knots(5) Computing approximating function Computing average derivatives Nonparametric series regression for IATE Cubic B-spline estimation Number of obs = 9,884 Number of knots = 5 ------------------------------------------------------------------------------ | Robust | Effect std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- income | .2131162 .0502993 4.24 0.000 .1145313 .311701 ------------------------------------------------------------------------------ Note: Effect estimates are averages of derivatives. . graph export "stata_cate_series_income.png", replace width(1200) (file stata_cate_series_income.png not found) file stata_cate_series_income.png written in PNG format . . . *================================================================ . * Closing summary . *================================================================ . . di _newline(2) . di "============================================================" ============================================================ . di " CATE analysis complete." CATE analysis complete. . di "" . di " Section 3: ATE estimated by AIPW (single number)." Section 3: ATE estimated by AIPW (single number). . di " Sections 4-5: PO + IATE plots reveal who responds most." Sections 4-5: PO + IATE plots reveal who responds most. . di " Sections 6-7: GATE / GATES quantify the spread." Sections 6-7: GATE / GATES quantify the spread. . di " Section 8: AIPW serves as a doubly-robust check." Section 8: AIPW serves as a doubly-robust check. . di " Section 9: nonparametric series shows how tau varies" Section 9: nonparametric series shows how tau varies . di " smoothly with income." smoothly with income. . di "" . di " Figures saved: 8 PNGs (stata_cate_*.png)." Figures saved: 8 PNGs (stata_cate_*.png). . di " CSVs saved: assets3_raw.csv, iate_predictions.csv," CSVs saved: assets3_raw.csv, iate_predictions.csv, . di " gate_results.csv." gate_results.csv. . di "============================================================" ============================================================ . . log close name: log: /Users/carlosmendez/Documents/GitHub/starter-academic-v501/content > /post/stata_cate/analysis.log log type: text closed on: 2 May 2026, 21:52:28 -------------------------------------------------------------------------------