library(qte)
library(ggplot2)
set.seed(42)
data(lalonde)
xf <- ~ age + I(age^2) + education + black + hispanic + married + nodegreeautoplot(res_exp, ylab = "QTE (earnings, 1978)")
2026-07-22
The Average Treatment Effect (ATE) or Average Treatment Effect on the Treated (ATT) summarizes the causal effect of a treatment by a single number: the mean difference in outcomes between treated and untreated units. This is often a natural quantity, but it can miss important heterogeneity. If a job training program substantially raises earnings at the bottom of the distribution while having little effect at the top, the ATE obscures this. If a minimum wage increase compresses the wage distribution, an average effect conceals the compression.
The Quantile Treatment Effect at level τ is QTE(τ) = QY(1)(τ) − QY(0)(τ), where QY(d)(τ) is the τ-th quantile of the potential outcome distribution under treatment status d. Mapping QTE(τ) across τ ∈ (0, 1) traces how the treatment shifts the entire outcome distribution. The Quantile Treatment Effect on the Treated (QTT) conditions on the treated group.
This vignette demonstrates unc_qte(), the qte package’s estimator for cross-sectional settings (no panel data required). For DiD-based estimators and staggered treatment adoption, see vignette("panel-estimators") and vignette("staggered-adoption").
library(qte)
library(ggplot2)
set.seed(42)
data(lalonde)
xf <- ~ age + I(age^2) + education + black + hispanic + married + nodegreeUnder random assignment, no covariate adjustment is needed: the unconditional quantiles of the treated and control outcome distributions identify the QTE directly. unc_qte() implements the semiparametrically efficient estimator of Firpo (2007). We use the experimental Lalonde data (lalonde.exp), where treatment was randomly assigned.
res_exp <- unc_qte(
yname = "re78",
dname = "treat",
data = lalonde.exp,
target = "qte",
probs = seq(0.1, 0.9, 0.1),
biters = 100
)
summary(res_exp)#>
#> Overall ATE:
#> ATE Std. Error [ 95% Conf. Int.]
#> 1794.343 614.3984 590.1444 2998.542 *
#>
#>
#> QTE:
#> Tau QTE Std. Error [ 95% Simult. Conf. Band]
#> 0.1 0.000 0.0000 0.0000 0.0000
#> 0.2 0.000 158.4803 -310.6157 310.6157
#> 0.3 929.884 400.0082 145.8823 1713.8856 *
#> 0.4 1176.944 943.3150 -671.9198 3025.8070
#> 0.5 1091.468 831.0748 -537.4088 2720.3446
#> 0.6 1466.690 842.6293 -184.8326 3118.2136
#> 0.7 1810.696 1032.9801 -213.9081 3835.2995
#> 0.8 2300.454 1054.5595 233.5552 4367.3524 *
#> 0.9 2856.068 1795.8551 -663.7429 6375.8796
#> ---
#> Signif. codes: `*' confidence band does not cover 0autoplot(res_exp, ylab = "QTE (earnings, 1978)")
The confidence band indicates that the QTE is positive across much of the distribution, with the effect somewhat larger in the lower quantiles.
When treatment is not randomly assigned, the unconfoundedness assumption (conditional independence of potential outcomes given covariates) provides identification (Firpo 2007). We use the observational Lalonde data (lalonde.psid), which combines the treated group from the experiment with a comparison group from the PSID.
unc_qte() supports three estimation methods:
"ipw" — inverse probability weighting (propensity score re-weighting)"or" — outcome regression (conditional quantile regression)"aipw" — augmented IPW (doubly robust; recommended)xf <- ~ age + I(age^2) + education + black + hispanic + married + nodegree
res_psid <- unc_qte(
yname = "re78",
dname = "treat",
data = lalonde.psid,
xformla = xf,
est_method = "aipw",
target = "qte",
probs = seq(0.1, 0.9, 0.1),
biters = 100
)
summary(res_psid)#>
#> Overall ATE:
#> ATE Std. Error [ 95% Conf. Int.]
#> -13194.78 1669.31 -16466.57 -9922.995 *
#>
#>
#> QTE:
#> Tau QTE Std. Error [ 95% Simult. Conf. Band]
#> 0.1 0.000 636.5657 -1247.646 1247.646
#> 0.2 -6404.679 1637.5230 -9614.165 -3195.193 *
#> 0.3 -8523.773 2123.4289 -12685.617 -4361.929 *
#> 0.4 -11114.085 2398.9413 -15815.924 -6412.247 *
#> 0.5 -12684.516 2756.7181 -18087.584 -7281.448 *
#> 0.6 -13532.837 2739.1129 -18901.399 -8164.274 *
#> 0.7 -14181.889 2214.9031 -18523.019 -9840.759 *
#> 0.8 -18285.313 2239.9340 -22675.503 -13895.123 *
#> 0.9 -22580.785 3682.3739 -29798.105 -15363.464 *
#> ---
#> Signif. codes: `*' confidence band does not cover 0autoplot(res_psid, ylab = "QTE (earnings, 1978)")
Setting target = "qtt" estimates the Quantile Treatment Effect on the Treated — the distributional effect for the subpopulation that actually received treatment.
res_qtt <- unc_qte(
yname = "re78",
dname = "treat",
data = lalonde.psid,
xformla = xf,
est_method = "aipw",
target = "qtt",
probs = seq(0.1, 0.9, 0.1),
biters = 100
)
summary(res_qtt)#>
#> Overall ATT:
#> ATT Std. Error [ 95% Conf. Int.]
#> -4685.583 835.1563 -6322.459 -3048.707 *
#>
#>
#> QTT:
#> Tau QTT Std. Error [ 95% Simult. Conf. Band]
#> 0.1 0.0001 9.4440 -18.5099 18.5100
#> 0.2 -1002.7420 705.1096 -2384.7314 379.2474
#> 0.3 -3400.5673 1505.4521 -6351.1992 -449.9354 *
#> 0.4 -5009.2491 1072.6921 -7111.6870 -2906.8111 *
#> 0.5 -4602.4652 936.3507 -6437.6789 -2767.2516 *
#> 0.6 -5229.1454 1282.4542 -7742.7095 -2715.5814 *
#> 0.7 -5507.4720 1268.5601 -7993.8040 -3021.1399 *
#> 0.8 -6885.7529 1501.3663 -9828.3768 -3943.1290 *
#> 0.9 -10517.0625 2368.3837 -15159.0092 -5875.1159 *
#> ---
#> Signif. codes: `*' confidence band does not cover 0autoplot(res_qtt, ylab = "QTT (earnings, 1978)")
summary() prints the overall ATT, the QTE/QTT at each quantile, and standard errors with confidence intervals. autoplot() returns a ggplot object so you can add layers:
autoplot(res_qtt) +
ggplot2::labs(title = "QTT — Lalonde (observational)",
subtitle = "AIPW with pre-treatment covariates")By default autoplot() shows a uniform confidence band (cband = TRUE), which provides simultaneous coverage over all quantile levels — a stronger guarantee than pointwise intervals. Pass cband = FALSE for pointwise intervals instead.
Standard errors are computed via the empirical bootstrap. The biters argument controls the number of iterations (default 100). Parallel computation is available via the cl argument.