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trop

Triply Robust Panel Estimator for Stata

Stata 17+ License: AGPL-3.0 Version: 1.0.0

trop

Overview

trop implements the Triply RObust Panel (TROP) estimator proposed by Athey, Imbens, Qu, and Viviano (2025) for Stata. The estimator combines three components — unit weights, time weights, and a nuclear-norm-regularized low-rank regression adjustment — to estimate average treatment effects on the treated (ATT) in panel data with potentially complex assignment patterns.

In semi-synthetic simulations calibrated to seven real datasets (Table 1 of the paper), TROP achieves the lowest RMSE in 20 out of 21 specifications, outperforming DID, SC, SDID, MC, and DIFP estimators across diverse data-generating processes:

Data set Outcome Treatment N T TROP SDID SC DID MC DIFP
CPS log-wage min wage 50 40 1.00 1.14 1.44 1.91 1.26 1.22
CPS urate min wage 50 40 1.00 1.05 1.11 1.89 1.10 1.09
PWT log-GDP democracy 111 48 1.00 1.44 1.59 7.85 1.76 1.54
Germany GDP random 17 44 1.00 1.46 2.82 3.58 1.56 2.46
Basque GDP random 18 43 1.00 1.02 4.55 9.11 1.70 2.47
Smoking packs pc random 39 31 1.00 1.22 1.48 2.16 1.14 1.45
Boatlift log-wage random 44 19 1.00 1.34 1.62 1.35 1.04 1.62

Normalized RMSE from Table 1 of Athey et al. (2025). Full results cover 21 specifications across 7 datasets.

Features:

  • Triple Robust Estimation — Asymptotically unbiased if any one of unit weights, time weights, or the regression adjustment removes biases (Theorem 5.1)
  • Two Estimation Methods — Twostep (per-observation, heterogeneous effects; Algorithm 2) and Joint (weighted least squares, homogeneous effect)
  • Leave-One-Out Cross-Validation — Data-driven selection of tuning parameters via coordinate-cycling LOOCV (Algorithm 1)
  • Bootstrap Inference — Stratified unit block bootstrap for variance estimation and confidence intervals (Algorithm 3)
  • General Assignment Patterns — Handles staggered adoption, switching treatments, and arbitrary binary treatment matrices
  • Post-Estimation Diagnostics — 7 estat subcommands and 8 predict types for comprehensive analysis
  • High-Performance Backend — Core computation in Rust via compiled plugin; no external dependencies

Key Concepts

Triple Robustness

The TROP estimator combines three components, each targeting a different source of confounding:

Component Role Controlled by
Unit weights $\omega_j$ Upweight control units similar to treated units $\lambda_{\text{unit}}$
Time weights $\theta_s$ Upweight time periods close to the treatment period $\lambda_{\text{time}}$
Low-rank factor model $\mathbf{L}$ Capture unobserved interactive fixed effects $\lambda_{nn}$

The key insight is that the estimator's bias is bounded by the product of three imbalance terms (Theorem 5.1). If any single component successfully removes bias, the overall bias vanishes — hence triple robustness. This multiplicative bound is strictly tighter than the additive bounds of DID, SC, or SDID.

Special Cases

The TROP framework nests existing estimators:

Setting Recovers
$\lambda_{nn} = \infty$, uniform weights DID / TWFE
Uniform weights, $\lambda_{nn} < \infty$ Matrix Completion
$\lambda_{nn} = \infty$, specific unit/time weights SC / SDID

Requirements

  • Stata 17.0 or later
  • No additional Stata packages required
  • Precompiled plugin included for macOS ARM64 (Apple Silicon); other platforms can be built from the Rust source

Installation

Install the package

net install trop, from("https://raw.githubusercontent.com/gorgeousfish/TROP/main") replace

This automatically installs:

  • All commands and help files
  • Pre-compiled Mata library
  • macOS ARM64 plugin

Verify Installation

trop, version
trop_check

Quick Start with Examples

All examples below use the CPS log-wage dataset — 50 US states × 40 years (1979–2018) of state-level log wages, where d flags state-years in which a minimum wage increase was in effect. This is one of the seven benchmark datasets from Athey et al. (2025).

Download the dataset first:

net get trop                 /* downloads datasets to the current directory */
use cps_logwage.dta, clear

Or load directly from GitHub:

use "https://raw.githubusercontent.com/gorgeousfish/TROP/main/data/cps_logwage.dta", clear

Dataset: N = 50, T = 40, 2,000 observations. y = log state-level wage; d = minimum wage treatment (8 treated state-year cells, 0.4%); id = state identifier; t = year.

Example 1: Fixed Hyperparameters (Twostep)

Using the paper's recommended values for CPS log-wage (Table S.1 of Athey et al. 2025):

use "https://raw.githubusercontent.com/gorgeousfish/TROP/main/data/cps_logwage.dta", clear
trop y d, panelvar(id) timevar(t) fixedlambda(0.1 0 0.9)

Output:

------------------------------------------------------------------------------
TROP Estimation Results
------------------------------------------------------------------------------
Method:            twostep
Grid style:        default (17 grid points/cycle, coordinate descent)

Panel dimensions:  N = 50, T = 40
Observations:      2000
Treated:           8 ( 0.4%)

Fixed hyperparameters (LOOCV skipped):
  lambda_time =   0.1000
  lambda_unit =   0.0000
  lambda_nn   =   0.9000

Treatment Effect (ATT):
  tau     =     0.031406

Example 2: LOOCV-Selected Hyperparameters

use "https://raw.githubusercontent.com/gorgeousfish/TROP/main/data/cps_logwage.dta", clear
trop y d, panelvar(id) timevar(t)

Output:

------------------------------------------------------------------------------
TROP Estimation Results
------------------------------------------------------------------------------
Method:            twostep
Grid style:        default (17 grid points/cycle, coordinate descent)

Panel dimensions:  N = 50, T = 40
Observations:      2000
Treated:           8 ( 0.4%)

Selected hyperparameters (via LOOCV):
  lambda_time =   0.5000
  lambda_unit =   5.0000
  lambda_nn   =   1.0000
  Q(lambda_hat) =   3.471727

Treatment Effect (ATT):
  tau     =     0.034188

Note: LOOCV on N = 50, T = 40 sums over every D = 0 cell (paper Eq. 5) and can take 20–40 minutes. Use fixedlambda() when a full grid search is not needed.

Example 3: Bootstrap Inference

use "https://raw.githubusercontent.com/gorgeousfish/TROP/main/data/cps_logwage.dta", clear
trop y d, panelvar(id) timevar(t) ///
    fixedlambda(0.1 0 0.9) bootstrap(200) seed(42)

Output:

Treatment Effect (ATT):
  tau     =     0.031406
  SE     =     0.015716
  t      =       1.9984
  p-value=       0.0858
  95% CI = [   -0.005756,     0.068568]

Example 4: Joint Method

use "https://raw.githubusercontent.com/gorgeousfish/TROP/main/data/cps_logwage.dta", clear
trop y d, panelvar(id) timevar(t) ///
    method(joint) fixedlambda(0.1 0 0.9)

Output:

Treatment Effect (ATT):
  tau     =     0.031406

Global intercept:
  mu     =     5.154320

Example 5: Post-Estimation Workflow

use "https://raw.githubusercontent.com/gorgeousfish/TROP/main/data/cps_logwage.dta", clear
trop y d, panelvar(id) timevar(t) fixedlambda(0.1 0 0.9)

* Predict counterfactual outcomes and treatment effects
predict y0_hat, y0
predict te_hat, te

* Diagnostics
estat summarize
estat weights
estat factors

estat summarize output:

-----------------------------------------------------------------
Estimation sample summary
-----------------------------------------------------------------
  Number of observations:        2000    (balanced panel)
  Number of units (N):             50
  Number of periods (T):           40
  Missing rate:                   0.0%

Treatment structure:
  Treated observations:             8    (  0.4%)
  Control observations:          1992    ( 99.6%)
  Treated units:                    8    ( 16.0%)
  Treated periods:                  1    (  2.5%)
  Pattern:                   multiple_treated_simultaneous
-----------------------------------------------------------------

To also inspect LOOCV diagnostics, run without fixedlambda():

use "https://raw.githubusercontent.com/gorgeousfish/TROP/main/data/cps_logwage.dta", clear
trop y d, panelvar(id) timevar(t)
estat loocv

Example 6: Standalone Bootstrap (Post-Estimation)

use "https://raw.githubusercontent.com/gorgeousfish/TROP/main/data/cps_logwage.dta", clear

* Estimate without bootstrap first (faster iteration)
trop y d, panelvar(id) timevar(t) fixedlambda(0.1 0 0.9)

* Then add bootstrap inference separately
trop_bootstrap, nreps(200) seed(42)

Output:

------------------------------------------------------------
TROP Bootstrap Inference Results
------------------------------------------------------------
ATT estimate:       0.031406
Bootstrap SE:       0.015716
95% CI:       [   -0.005756,     0.068568]
p-value:              0.0858

Bootstrap reps:        200
Valid reps:            200
------------------------------------------------------------

Example 7: PWT Log-GDP Panel (111 Countries × 48 Years)

For a large panel, use the Penn World Tables democracy dataset:

use "https://raw.githubusercontent.com/gorgeousfish/TROP/main/data/pwt_loggdp.dta", clear

* Paper's hyperparameters for PWT. Large panels with very small lambda_nn
* may require many iterations; use maxiter(1000) for tighter convergence.
trop y d, panelvar(id) timevar(t) fixedlambda(0.4 0.3 0.006) maxiter(1000)

Output:

------------------------------------------------------------------------------
TROP Estimation Results
------------------------------------------------------------------------------
Method:            twostep
Grid style:        default (17 grid points/cycle, coordinate descent)

Panel dimensions:  N = 111, T = 48
Observations:      5328
Treated:           29 ( 0.5%)

Fixed hyperparameters (LOOCV skipped):
  lambda_time =   0.4000
  lambda_unit =   0.3000
  lambda_nn   =   0.0060

Treatment Effect (ATT):
  tau     =    -0.014818

Convergence note. With a very small lambda_nn (e.g. 0.006), the low-rank factor matrix L can have many nonzero singular values, and the alternating minimization progresses slowly on large panels. The strict tol(1e-6) default may not be reached within maxiter(1000); the point estimate is nevertheless stable to the third decimal place. For faster and fully-converged estimates, either (i) increase lambda_nn (e.g. fixedlambda(0.4 0.3 0.1) converges in about 110 iterations to τ = -0.006672) or (ii) relax the tolerance via tol(1e-4). Verified end-to-end against diff_diff==3.1.1 (|Δτ| < 4e-7).

Available datasets (download via net get trop):

File Description N T
cps_logwage.dta CPS state-level log wage (min wage treatment) 50 40
cps_urate.dta CPS state-level unemployment rate (min wage treatment) 50 40
pwt_loggdp.dta Penn World Tables log GDP (democracy transition) 111 48
germany_gdp.dta Abadie & Gardeazabal (2003) West Germany GDP 17 44
basque_gdp.dta Abadie (2003) Basque Country GDP 18 43
smoking_packs.dta California Prop 99 cigarette consumption 39 31

germany_gdp, basque_gdp, and smoking_packs have d = 0 throughout — they are raw outcome panels designed for semi-synthetic simulation (as in Table 1 of Athey et al. 2025). Assign a treatment indicator before running trop.

Recommended Workflow

Step 1: Validate     →  trop_validate depvar treatvar, panelvar() timevar()
Step 2: Estimate     →  trop depvar treatvar, panelvar() timevar()
Step 3: Diagnose     →  estat summarize / estat weights / estat loocv / estat factors
Step 4: Inference    →  trop_bootstrap, nreps(1000)    — or —    bootstrap() in Step 2

Step 1 — Validate data structure. trop_validate checks panel balance, treatment patterns, missing data, and minimum sample requirements before estimation. This step is also performed automatically inside trop.

trop_validate y d, panelvar(id) timevar(t)

Step 2 — Estimate ATT. Choose method(twostep) (default) for heterogeneous effects, or method(joint) for faster homogeneous estimation. LOOCV selects hyperparameters automatically.

Method Use when Speed
twostep Heterogeneous effects; general assignment Slower
joint Homogeneous effect; simultaneous adoption only Faster

Step 3 — Diagnose results.

Subcommand What to check
estat summarize Panel dimensions, treatment pattern, balance
estat weights Whether weights concentrate on few units/periods
estat loocv Convergence, failure rate, selected lambdas
estat factors Effective rank, explained variance by top singular values

Step 4 — Conduct inference. Use bootstrap() inline or trop_bootstrap post-estimation. The bootstrap resamples units within treatment strata (Algorithm 3).

* Inline (re-runs estimation + bootstrap together)
trop y d, panelvar(id) timevar(t) bootstrap(1000) seed(42)

* Post-estimation (uses stored estimation results)
trop_bootstrap, nreps(1000) seed(42)

Tutorial

An interactive Jupyter notebook tutorial is included as ancillary material:

net get trop

The downloaded file 10_trop_stata.ipynb covers data generation, estimation with both methods, all estat diagnostics, prediction, and a real-data CPS example.

Commands

Command Description
trop Main estimation command (twostep or joint method)
trop_bootstrap Standalone bootstrap inference (post-estimation)
trop_validate Panel data structure validation
trop_check Environment and installation check

Post-estimation (available after trop):

Command Description
estat Diagnostics dispatcher (7 subcommands; see below)
predict Prediction dispatcher (8 types; see below)

Options

trop Options

Required:

Option Description
panelvar(varname) Unit (panel) identifier variable
timevar(varname) Time identifier variable

Optional:

Option Description Default
method(string) Estimation method: twostep / joint (or aliases local / global) twostep
grid_style(string) Lambda grid style: default or extended default
lambda_time_grid(numlist) User-specified grid for lambda_time auto
lambda_unit_grid(numlist) User-specified grid for lambda_unit auto
lambda_nn_grid(numlist) User-specified grid for lambda_nn auto
fixedlambda(numlist) Fix (lambda_time lambda_unit lambda_nn); skip LOOCV —
tol(real) Convergence tolerance for iterative estimation 1e-6
maxiter(integer) Maximum number of iterations 100
bootstrap(integer) Number of bootstrap replications (0 = skip inference) 200
seed(integer) Random number generator seed 42
level(cilevel) Confidence level for intervals c(level)
verbose Display detailed diagnostic output off

Grid styles:

  • default — 6 × 6 × 5 = 180 grid combinations, 17 evaluations per coordinate-descent cycle
  • extended — 14 × 16 × 18 = 4,032 combinations, 48 evaluations per cycle (finer search, slower)

Grid notes:

  • lambda_time_grid() and lambda_unit_grid() must be finite, non-negative numlists; Stata missing (.) is rejected at parse time.
  • lambda_nn_grid() and the third slot of fixedlambda() accept . as +infinity, mirroring the diff-diff 3.1.1 Python reference. The default grid includes this corner so LOOCV can select the "no factor structure" regime (classical DID / synthetic control) when it minimises Q(λ).

trop_bootstrap Options

Option Description Default
nreps(integer) Number of bootstrap replications 1000
level(real) Confidence level in percent (10–99.99) c(level)
seed(integer) Random number generator seed 42
maxiter(integer) Maximum iterations per replication 100
tol(real) Convergence tolerance per replication 1e-6
verbose Display progress information off

Stored Results

Scalars

Core estimates:

Scalar Description
e(att) ATT point estimate
e(se) Bootstrap standard error
e(t) t statistic (att/se)
e(pvalue) Two-sided p-value
e(ci_lower) Lower bound of confidence interval
e(ci_upper) Upper bound of confidence interval
e(mu) Global intercept (joint only; missing for twostep)

Tuning parameters:

Scalar Description
e(lambda_time) Selected lambda_time
e(lambda_unit) Selected lambda_unit
e(lambda_nn) Selected lambda_nn
e(loocv_score) Optimal LOOCV score Q(lambda_hat)

Sample information:

Scalar Description
e(N_units) Number of units
e(N_periods) Number of time periods
e(N_obs) Total observations
e(N_treat) Number of treated observations
e(N_control) Number of control observations
e(N_treated_units) Number of treated units
e(N_control_units) Number of control units
e(T_treat_periods) Number of treatment periods
e(bootstrap_reps) Number of bootstrap replications

Convergence:

Scalar Description
e(n_iterations) Number of iterations
e(converged) Convergence indicator (1/0)
e(n_obs_estimated) Successfully estimated observations (twostep only)
e(n_obs_failed) Failed observations (twostep, if > 0)

LOOCV diagnostics:

Scalar Description
e(loocv_n_valid) Number of valid LOOCV evaluations
e(loocv_n_attempted) Number of attempted LOOCV evaluations (= every D=0 cell, paper Eq. 5)
e(loocv_fail_rate) LOOCV failure rate
e(loocv_used) Whether LOOCV was performed (1/0)
e(seed) RNG seed used

Grid information:

Scalar Description
e(n_lambda_time) Number of lambda_time grid values
e(n_lambda_unit) Number of lambda_unit grid values
e(n_lambda_nn) Number of lambda_nn grid values
e(n_grid_combinations) Total Cartesian grid combinations
e(n_grid_per_cycle) Grid evaluations per coordinate-descent cycle

Other:

Scalar Description
e(balanced) Balanced panel indicator (1/0)
e(miss_rate) Missing data rate
e(alpha_level) Significance level for CI
e(effective_rank) Effective rank of factor matrix
e(n_bootstrap_valid) Number of valid bootstrap replications
e(data_validated) Data validation indicator (1/0)

Macros

Macro Description
e(cmd) "trop"
e(cmdline) Full command line as issued
e(method) "twostep" or "joint"
e(grid_style) "default", "extended", or "custom"
e(depvar) Dependent variable name
e(treatvar) Treatment variable name
e(panelvar) Panel variable name
e(timevar) Time variable name
e(vcetype) "Bootstrap" or ""
e(estat_cmd) "trop_estat"
e(treatment_pattern) Treatment assignment pattern description

Matrices

Matrix Description
e(b) Coefficient vector (1×1, ATT)
e(V) Variance-covariance matrix (1×1; requires bootstrap)
e(alpha) Unit fixed effects (N×1)
e(beta) Time fixed effects (T×1)
e(factor_matrix) Low-rank factor matrix L (T×N)
e(tau) Per-cell treatment effects (N_treated×1); populated for both methods. For joint the vector carries the scalar tau replicated, so mean(e(tau)) == e(att) holds to machine precision for either method.
e(tau_matrix) Treatment effects arranged as a T×N panel-shaped matrix with . in untreated cells (when panel metadata is available)
e(converged_by_obs) Convergence flag per treated cell (1 converged, 0 hit maxiter(), -1 solver error); twostep only
e(n_iters_by_obs) Iteration count per treated cell; twostep only
e(bootstrap_estimates) Bootstrap distribution (B×1; requires bootstrap)
e(theta) Time weights (twostep only)
e(omega) Unit weights (twostep only)
e(delta_time) Time weights (joint only)
e(delta_unit) Unit weights (joint only)
e(lambda_time_grid) Lambda time grid values
e(lambda_unit_grid) Lambda unit grid values
e(lambda_nn_grid) Lambda nuclear norm grid values

Post-Estimation

estat Subcommands

Subcommand Abbreviation Description
estat summarize sum Sample structure and treatment allocation
estat vce Variance-covariance matrix display
estat sensitivity sens Hyperparameter sensitivity analysis
estat weights weight Unit and time weight diagnostics
estat bootstrap boot Bootstrap distribution diagnostics
estat loocv LOOCV hyperparameter selection diagnostics
estat factors Factor matrix (L) SVD analysis

predict Types

After trop, use predict newvar, type to generate predictions:

Type Description
y0 Counterfactual outcome Y(0) [default]
y1 Counterfactual outcome Y(1)
te Treatment effect (treated obs only)
residuals Residuals Y - Y(0)
alpha Unit fixed effects
beta Time fixed effects
mu Global intercept (joint only)
xb Linear prediction (equivalent to y0)

Methodology

The TROP Estimator

The TROP estimator models the potential control outcome as $Y_{it}(0) = \alpha_i + \beta_t + L_{it} + \epsilon_{it}$, where $\alpha_i$ are unit fixed effects, $\beta_t$ are time fixed effects, $L_{it}$ is a low-rank factor component, and $\epsilon_{it}$ is idiosyncratic noise.

For each treated unit–time pair $(i,t)$, the estimator predicts the counterfactual outcome by solving a weighted nuclear-norm penalized regression (Eq. 2 of the paper):

$$(\hat{\alpha}, \hat{\beta}, \hat{\mathbf{L}}) = \arg\min_{\alpha, \beta, \mathbf{L}} \sum_{j=1}^{N} \sum_{s=1}^{T} \theta_s^{i,t} \omega_j^{i,t} (1-W_{js})(Y_{js} - \alpha_j - \beta_s - L_{js})^2 + \lambda_{nn} |\mathbf{L}|_*$$

where the weights exhibit exponential decay (Eq. 3):

$$\theta_s^{i,t} = \exp(-\lambda_{\text{time}} \cdot |t - s|), \qquad \omega_j^{i,t} = \exp(-\lambda_{\text{unit}} \cdot \text{dist}_{-t}^{\text{unit}}(j, i))$$

The unit distance measures RMSE of outcome differences over shared control periods:

$$\text{dist}_{-t}^{\text{unit}}(j,i) = \left(\frac{\sum_{u} \mathbf{1}{u \neq t}(1-W_{iu})(1-W_{ju})(Y_{iu}-Y_{ju})^2}{\sum_{u} \mathbf{1}{u \neq t}(1-W_{iu})(1-W_{ju})}\right)^{1/2}$$

The treatment effect is then $\hat{\tau}{it} = Y{it} - \hat{\alpha}_i - \hat{\beta}t - \hat{L}{it}$.

This formulation encompasses DID, SC, MC, and SDID all as special cases. For $\lambda_{nn} = \infty$ and $\omega_j = \theta_s = 1$, we recover the DID/TWFE estimator. For $\omega_j = \theta_s = 1$ and $\lambda_{nn} &lt; \infty$, we recover the MC estimator. For $\lambda_{nn} = \infty$ with specific unit and time weights, we recover SC and SDID.

Triple Robustness Property

The bias satisfies a multiplicative bound (Theorem 5.1):

$$\left|\mathbb{E}[\hat{\tau} - \tau \mid \mathbf{L}]\right| \leq |\Delta^{\mathbf{u}}(\omega, \Gamma)|_2 \times |\Delta^{\mathbf{t}}(\theta, \Lambda)|_2 \times |B|_*$$

where $\Delta^{\mathbf{u}}$ is unit imbalance, $\Delta^{\mathbf{t}}$ is time imbalance, and $B$ captures regression adjustment misspecification. The estimator is consistent if any one of the three terms is negligible (Corollary 1):

  1. Balance over unit factor loadings ($|\Delta^{\mathbf{u}}|_2 \approx 0$)
  2. Balance over time factor loadings ($|\Delta^{\mathbf{t}}|_2 \approx 0$)
  3. Correct regression adjustment specification ($|B|_* \approx 0$)

This multiplicative bias bound is strictly tighter than the additive bounds that govern DID, SC, and SDID, giving TROP stronger robustness properties.

Tuning Parameter Selection

The triplet $(\lambda_{\text{time}}, \lambda_{\text{unit}}, \lambda_{nn})$ is selected via leave-one-out cross-validation minimizing (Eq. 5):

$$Q(\lambda) = \sum_{i=1}^{N} \sum_{t=1}^{T} (1 - W_{it})(\hat{\tau}_{it}(\lambda))^2$$

This is equivalent to choosing the tuning parameters with the smallest out-of-sample squared error for predicting the potential outcome under control on the control observations. The grid search uses coordinate descent (Algorithm 1): each parameter is optimized in turn while holding the other two at their most recently selected values, then the cycle repeats until convergence.

Estimation Methods

  • Twostep (Algorithm 2): Per-observation estimation allowing heterogeneous treatment effects. For each treated pair $(i,t)$, the model is fitted as if $(i,t)$ were the only treated observation. The ATT is $\hat{\tau} = \frac{1}{\sum_{i,t} W_{it}} \sum_{i,t} W_{it} \hat{\tau}_{it}$.
  • Joint (Remark 6.1): Weighted least squares with a single scalar treatment effect $\tau$, assuming homogeneous effects across all treated unit–time pairs. Uses global weights shared across all treated observations. Computationally more efficient when the homogeneity assumption holds.

Bootstrap Inference

Variance estimation follows Algorithm 3: stratified unit block bootstrap that separately resamples treated and control units with replacement. For each replication $b = 1, \ldots, B$, the full estimation procedure (including LOOCV if applicable) is repeated to obtain $\hat{\tau}^{(b)}$, and the bootstrap variance is:

$$\hat{V}_{\tau} = \frac{1}{B} \sum_{b=1}^{B} (\hat{\tau}^{(b)} - \bar{\hat{\tau}})^2$$

where $\bar{\hat{\tau}} = \frac{1}{B}\sum_{b=1}^B \hat{\tau}^{(b)}$ is the mean of bootstrap estimates.

Architecture

The package uses a four-layer design for performance and numerical accuracy:

┌─────────────────────────────────────────────────┐
│  Stata User Interface  (trop.ado)               │
│  - Syntax parsing, option handling              │
├─────────────────────────────────────────────────┤
│  Mata Interface Layer                           │
│  - Input validation and data conversion         │
│  - e() result storage                           │
├─────────────────────────────────────────────────┤
│  C Bridge Plugin                                │
│  - Pointer conversion, error code mapping       │
├─────────────────────────────────────────────────┤
│  Rust Core                                      │
│  - Distance matrices, weight computation        │
│  - LOOCV grid search, SVD estimation            │
│  - Stratified unit block bootstrap              │
└─────────────────────────────────────────────────┘

All numerical computation (LOOCV, SVD, bootstrap) is performed in Rust for speed and precision. The Mata layer handles data validation and result storage. Users do not need the Rust toolchain — the pre-compiled plugin is included.

References

Athey, S., Imbens, G., Qu, Z., & Viviano, D. (2025). Triply robust panel estimators. arXiv preprint arXiv:2508.21536.

Authors

Stata Implementation:

Methodology:

  • Susan Athey, Stanford University
  • Guido Imbens, Stanford University
  • Zhaonan Qu, Columbia University
  • Davide Viviano, Harvard University

License

AGPL-3.0. See LICENSE for details.

Citation

If you use this package in your research, please cite both the methodology paper and the Stata implementation:

APA Format:

Cai, X., & Xu, W. (2025). trop: Stata module for Triply Robust Panel estimation [Computer software]. GitHub. https://github.com/gorgeousfish/TROP

Athey, S., Imbens, G., Qu, Z., & Viviano, D. (2025). Triply robust panel estimators. arXiv preprint arXiv:2508.21536.

BibTeX:

@software{trop2025stata,
  title={trop: Stata module for Triply Robust Panel estimation},
  author={Xuanyu Cai and Wenli Xu},
  year={2025},
  version={1.0.0},
  url={https://github.com/gorgeousfish/TROP}
}

@article{athey2025triply,
  title={Triply robust panel estimators},
  author={Athey, Susan and Imbens, Guido and Qu, Zhaonan and Viviano, Davide},
  journal={arXiv preprint arXiv:2508.21536},
  year={2025}
}

See Also

About

Stata implementation of the Triply Robust Panel (TROP) estimator from Athey, Imbens, Qu & Viviano (2025). Combines unit weights, time weights, and nuclear-norm regularized factor models for robust ATT estimation in panel data. High-performance Rust backend.(Public Preview, testing...)

Topics

stata causal-inference panel-data robust-estimation difference-in-differences

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