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\title{\LARGE{Double/Debiased Machine Learning (DDML) for 
\\
Conditional Average Treatment Effects (CATE)  Estimation}}
\author{Luiza Antonie, University of Guelph \\
Miana Plesca, University of Guelph \\
Mohammad Havaledar, University of Guelph
\\
}
%\date{\today}
\date{}

\begin{document}
\begin{frame}
  \titlepage
  \vspace{-0.4cm}
  \begin{center}
  %\footnotesize 
  Carpathian Stata Conference

  July 28, 2026 Cluj-Napoca
  \end{center}
\end{frame}

\begin{frame}{What is CATE? Conditional Average Treatment Effect}
Athey and Imbens (2016), Wager and Athey (2018)


\begin{itemize}
\medskip
\item Allows for \textbf{heterogeneity} in the impact of treatment %(policy), which can differ across observed characteristics.

\vspace{0.15cm}
\[
\tau_0(z)=E[Y(1)-Y(0)\mid Z=z]
\]


  \medskip
  \item $Y$ is outcome and $Z$ are the variables used to describe heterogeneity in treatment effects.

  \medskip
For example,  $Y$ is income and $Z$ can include age, education, race, earnings history, occupation, employer, region, etc.

\medskip  
\item \textbf{Causal}  in the sense that focus shifts away from predicting outcome to comparing potential outcomes under treatment and no treatment.

Needs CIA to hold for identification:
$(Y(1),Y(0)) \perp D \mid X$
and $0 < P(D=1\mid X) < 1$.


  \medskip
  \item A good ATE is not enough if the research question is about who gains, who loses, and where effects are concentrated.
\end{itemize}


%\footnotesize Related motivation: Bitler, Gelbach, and Hoynes (2006); Carneiro, Heckman, and Vytlacil (2011); Davis and Heller (2020).
\end{frame}

\begin{frame}{What is DDML? Double/Debiased Machine Learning}
Chernozhukov, Chetverikov, Demirer, Duflo, Hansen,  Newey, and Robins (2018)

Chernozhukov, Escanciano, Ichimura, Newey, and Robins (2022)

\begin{itemize}

\medskip
\item
ML can introduce regularization and overfitting  bias.

   
  \item \textbf{Orthogonalization} is used to reduce regularization bias from the ML first stages.
  \item \textbf{Cross-fitting} estimates nuisance models on one part of the data and evaluates the causal score on another part.
  \end{itemize}


\medskip
Ahrens, Hansen, Schaffer, Wiemann (2024) ``ddml''

\vspace{0.2cm}
\begin{center}
{\Large\bf What is the effect of choice of Machine Learner and Hyper Parameter Optimization (HPO) when the target is CATE?}
\end{center}
\begin{itemize}
 \item A machine learner can predict the outcome well but still give a poor treatment-effect estimate.
  \item A learner can recover the average effect while missing treatment-effect heterogeneity.
  \item Tuning choices that look reasonable for prediction can create unstable participation probabilities or unstable estimated CATEs.
%  \item The main applied question is therefore not only ``which learner predicts best?'' but:
  \end{itemize}
  
  \end{frame}





\begin{frame}{Partially Linear and Interactive CATE Regression Models}
%PLRM and IRM: two CATE-DDML structures

\medskip
\textbf{PLRM / partialing-out} %is useful when the treatment effect is represented through a selected set of effect modifiers $Z$.
``\code{cate po}''  

\[
Y=\ell(X)+D(X)\tau(Z)+U,
\qquad
D=m(X)+V.
\]

\begin{itemize}
  \item $m(X)$ is the participation model.
  \item $\ell(X)$ is the PLRM outcome nuisance.
  \item $CATE=\tau(Z)$ varies with $Z$.
  \item orthorgonalization is through residuals on residuals regression.
\end{itemize}

\bigskip
\textbf{IRM / AIPW } %is more flexible 
``\code{cate aipw}''
\[
Y=g(X, D)+U,
\qquad
D=m(X)+V.
\]
\[
g_1(X)=E[Y\mid D=1,X],
\qquad
g_0(X)=E[Y\mid D=0,X],
\qquad
m(X)=P(D=1\mid X).
\]

\begin{itemize}
\item $g(X)$ is the IRM/AIPW outcome nuisance.
\item $CATE=g_1(Z)-g_0(Z)$ where $Z$ is a subset of $X$.
\item orthogonalization is through AIPW. 
%  \item IRM is useful when the treated and untreated outcome relationships are very different.
\end{itemize}


\end{frame}

\begin{frame}{Experiment map: what is being compared?}
\small
\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{p{0.20\textwidth}p{0.43\textwidth}p{0.28\textwidth}}
\toprule
Experiment block & Purpose & Main comparison \\
\midrule
Synthetic DGPs & Known truth. Lets us directly evaluate CATE accuracy. & \textbf{Linear vs nonlinear} outcome and participation designs. \\
\\
LaLonde/NSW-PSID & Experimental benchmark plus observational stress test. & \textbf{RCT}, \textbf{PSID controls}, all controls, placebo controls. \\
\bottomrule
\end{tabular}
\end{adjustbox}

\medskip Do conclusions change when we move from known-truth simulations to a real observational benchmark?

\bigskip
\bigskip

\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{p{0.20\textwidth}p{0.43\textwidth}p{0.28\textwidth}}
\toprule
Estimator  & Purpose & Main comparison \\
\midrule
Native Stata \code{cate} & Main DDML-style implementation.  & \code{cate po} vs \code{cate aipw}\\
& Built-in orthogonalization and cross-fitting. & Lasso vs RF-HPO. \\
\\
Manual orthogonal& Diagnostics for cross-fitting. & PLR vs IRM\\
learners & &cross-fitted vs not cross-fitted. \\
\\
Non-DDML baselines & Non-orthogonal CATE reference points. & S-learner, T-learner. \\
\bottomrule
\end{tabular}
\end{adjustbox}

\medskip When do orthogonalization and cross-validation matter in practice? 
\end{frame}
\begin{frame}{Five common CATE meta-learner families}
\small
\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{p{0.14\textwidth}p{0.52\textwidth}p{0.26\textwidth}}
\toprule
Learner & Basic idea & Role in this deck \\
\midrule
S-learner & Estimate one outcome model using treatment plus covariates, then compare predicted outcomes with treatment switched on/off. & non-DDML baseline \\
T-learner & Estimate separate outcome models for treated and untreated groups, then difference the predictions. & non-DDML baseline \\
X-learner & Impute treatment effects within treated and untreated groups, then combine them using a weighting rule. & taxonomy/reference, not central in code \\
R-learner & Residualize outcome and treatment, then learn treatment-effect heterogeneity from the residualized relationship. & close to PLR/manual orthogonal logic \\
DR-learner & Build a doubly robust pseudo-outcome and regress it on heterogeneity variables. & close to IRM/AIPW logic \\
\bottomrule
\end{tabular}
\end{adjustbox}

\vspace{0.15cm}
The native \code{cate po} and \code{cate aipw} routines are the main DDML-style estimators here. The S/T/IPW learners are included as simpler benchmarks.
\end{frame}

\begin{frame}{Experiment map: Limitations}
\small

\begin{itemize}
    \item DGP has only $n = 4,000$. LaLonde NSW is also small $n$ small $p$.
    \item No evaluation for $p$/$n$.
    \item Not sufficiently investigated: high-dimensional categorical $X$ (e.g. occupation fixed effects).
    \item Only learners evaluated are: OLS, Lasso, RF. Other learners (gradient boosting, neural nets, etc.) can be more effective with large data.
    \item Combinations of different learners for outcome, participation.
    \item Choice of $Z$ as subset of $X$.

    \bigskip
    \item Loss functions in evaluating results: recent work on ``grounded truth'' DGP.
\end{itemize}


\end{frame}




\begin{frame}{Synthetic DGPs:  outcome, treatment-effect and participation equations}
\scriptsize
%\medskip
Four scenarios LL, LN, NL, NN: outcome(treatment) and participation   

\medskip
Common setup: $x_1,\ldots,x_8$ are standard normal variables, $z_1=1[x_5>0]$, and $z_2=1[x_6>0]$. Each simulated dataset has \textbf{$N=4{,}000$}.

\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{p{0.06\textwidth}p{0.48\textwidth}p{0.40\textwidth}}
\toprule
DGP & Baseline outcome $\mu_0(X)$ & Treatment effect $\tau(X)$ \\
\midrule
LL & $1+.70x_1-.60x_2+.35x_3+.25x_4+.40x_5-.30x_6+.35z_1-.25z_2$ & $1+.70x_1-.40x_2+.30x_3-.20x_4$ \\
LN & same linear $\mu_0(X)$ as LL & same linear $\tau(X)$ as LL \\
NL & $1+\sin(x_1)+.60(x_2^2-1)+.50x_3x_4+.30x_5-.25x_6+.70z_1-.50z_2$ & $1+.80\sin(x_1)-.45(x_2^2-1)+.65x_3x_4+.50z_1-.35z_2$ \\
NN & same nonlinear $\mu_0(X)$ as NL & same nonlinear $\tau(X)$ as NL \\
\bottomrule
\end{tabular}
\end{adjustbox}

%\end{frame}

%\begin{frame}{Synthetic DGPs: actual participation equations}

\bigskip
\scriptsize
Treatment is drawn from a logistic participation model. The true propensity is clipped to avoid a completely deterministic treatment rule.

\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{p{0.20\textwidth}p{0.57\textwidth}p{0.17\textwidth}}
\toprule
Participation design & Index used inside the logit participation model & DGPs \\
\midrule
Linear participation & $-.15+.65x_1-.55x_2+.35x_3+.20x_4+.30z_1-.20z_2$ & LL, NL \\
Nonlinear participation & $-.15+.85\sin(x_1)-.70(x_2^2-1)+.55x_3x_4+.35x_5-.25x_6+.45z_1-.30z_2$ & LN, NN \\
\bottomrule
\end{tabular}
\end{adjustbox}

\bigskip
LL/LN are friendly to linear CATE models. NL/NN require learners to recover nonlinear heterogeneity.


\end{frame}


\begin{frame}[fragile]{Actual Stata commands behind the native CATE estimates}
\small
The generic native specification is:

\begin{verbatim}
cate po   ($Y $CATEVARS) ($D), controls($CONTROLS)  ///
    omethod(...) tmethod(...) cmethod(...)          ///
    xfolds(5) rseed(90210) nolog

cate aipw ($Y $CATEVARS) ($D), controls($CONTROLS) ///
    omethod(...) tmethod(...) cmethod(...)          ///
    xfolds(5) rseed(90210) nolog
\end{verbatim}

Examples of learner choices:

\begin{verbatim}
omethod(lasso, selection(plugin))
tmethod(lasso, selection(plugin))
cmethod(rforest, ntrees(600) splitminobs(10)
        splitmeanvars(4) samprate(.50))
\end{verbatim}

\begin{itemize}
  \item \code{omethod}: outcome nuisance learner.
  \item \code{tmethod}: treatment/participation learner.
  \item \code{cmethod}: CATE learner.
  \item Native \code{cate} always uses five-fold cross-fitting here.
\end{itemize}
\end{frame}

\begin{frame}{Machine learners and parametrization}
\small
\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{p{0.20\textwidth}p{0.30\textwidth}p{0.40\textwidth}}
\toprule
Learner family & Where used & Parametrization \\
\midrule
Parametric & Native and manual baseline & OLS regression for outcome; logit for participation; OLS regression for CATE. \\
Lasso plug-in & Native and manual nuisance & \code{selection(plugin)}. Penalty chosen by theory-driven plug-in rule. \\
Lasso CV & Native and manual nuisance & \code{selection(cv, folds(5))}. Penalty chosen by five-fold CV. \\
Random forest HPO & Native CATE and nuisance  & Five RF candidates over trees, split size, split variables, sampling rate, and honesty. \\
Non-DDML baselines & S/T/IPW-style comparisons & OLS, lasso, logit, and lasso-logit variants without orthogonal DDML structure. \\
\bottomrule
\end{tabular}
\end{adjustbox}

\vspace{0.1cm}
Learner selection is part of the experiment: the same DGP can look different under parametric, lasso, and RF-HPO choices.
\end{frame}



\begin{frame}{Specification \code{spec} and cross-fit \code{xfit} models}
\scriptsize
\begin{adjustbox}{max width=\textwidth,max totalheight=.78\textheight}
\begin{tabular}{p{0.22\textwidth}p{0.29\textwidth}p{0.41\textwidth}}
\toprule
Label & Meaning & Important interpretation \\
\midrule
\code{family = native\_cate\_hpo} & Stata native \code{cate}. & These are the blue rows/points. A row such as \code{lasso\_cv\_rfHPO\_rf3\_mid} is still native \code{cate}. \\
\code{family = manual\_orth} & Hand-coded orthogonal PLR/IRM diagnostics. & These are orange. They are not Stata native \code{cate}. \\
\code{family = nonddml} & Non-orthogonal S/T/IPW baselines. & These are gray and are included as benchmarks. \\
\code{xfit = xfold5} & Five-fold cross-fitting. & This is DDML sample-splitting, not lasso HPO. Native \code{cate} uses \code{xfolds(5)}. \\
\code{xfit = noxfit} & No cross-fitting. & Used only for non-DDML and manual diagnostics. \\
\code{lasso\_cv} & Lasso penalty selected by inner cross-validation. & This is lasso HPO. \\
\code{rfHPO\_rf*} & Random forest candidate selected from the RF grid. & This is RF HPO; the final estimate is still native \code{cate} if \code{family = native\_cate\_hpo}. \\
\bottomrule
\end{tabular}
\end{adjustbox}
\vspace{0.1cm}
\footnotesize Reading rule: \code{spec} describes learner/HPO choices. \code{xfit} describes cross-fitting. They are related but not the same.
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Lasso tuning and Random forest HPO grid}
\small

\textbf{Lasso tuning} 

 \code{lasso linear y x1 x2 ..., selection(plugin)}
 
 \code{lasso linear y x1 x2 ..., selection(cv, folds(5))}

\begin{itemize}
  \item Cross-validated lasso chooses the penalty that predicts well in held-out folds.
  \item Plug-in lasso chooses the penalty using a theory-driven rule intended to control noise-variable selection.
  \item In practice, plug-in lasso is often more conservative than CV lasso. That can matter for DDML: nuisance prediction is not the same as causal accuracy!%, and overly aggressive selection can change the residualized causal score.
\end{itemize}

\textbf{RF tuning} 

\begin{itemize}
    \item External to \code{cate}: a tuning subsample is used to select a candidate RF specification, then the selected RF is run on the full sample.% with five-fold cross-fitting.
\end{itemize}
\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{p{0.16\textwidth}rrrrp{0.32\textwidth}}
\toprule
Candidate & trees & {\scriptsize split min} & {\scriptsize split vars} & {\scriptsize samp rate} & interpretation \\
\midrule
RF1-cons & 400 & 20 & 2 & .50 & conservative forest \\
RF2-small & 600 & 10 & 4 & .50 & moderate forest \\
RF3-mid & 800 & 6 & 5 & .60 & larger middle option \\
RF4-deep & 1000 & 3 & 6 & .70 & deeper/aggressive option \\
RF5-aggr & 1200 & 3 & 6 & .75 & aggressive, no-honesty option \\
\bottomrule
\end{tabular}
\end{adjustbox}

\vspace{0.15cm}
Some RF candidates may fail in Stata because \code{cate} imposes restrictions on combinations such as \code{samprate()} %and inference-tree settings. Failed candidates are skipped.

\end{frame}



\begin{frame}{HPO design}
\small
\begin{itemize}
  \item A 30 percent tuning subsample is created for RF HPO.
  \item In simulations, HPO can use the true CATE because the DGP is known.
  \item In LaLonde, HPO can use distance from the RCT benchmark only as a retrospective research exercise.
  \item In an ordinary observational application, this benchmark-guided tuning would not be available.
\end{itemize}

\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{p{0.25\textwidth}p{0.30\textwidth}p{0.34\textwidth}}
\toprule
Data block & HPO criterion used in this run & Interpretation \\
\midrule
Synthetic simulations & PEHE & Selects RF specification closest to true heterogeneity. \\
RCT LaLonde & distance from experimental benchmark & Ex-post benchmark exercise. \\
Observational LaLonde & distance from RCT benchmark & Method-evaluation exercise, not ordinary applied tuning. \\
Placebo controls & distance from zero & Selection diagnostic. \\
\bottomrule
\end{tabular}
\end{adjustbox}
\end{frame}









\begin{frame}{Evaluation metrics and where they are used}
\scriptsize
\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{p{0.18\textwidth}p{0.38\textwidth}cccc}
\toprule
Measure & What it tells us & Simulation & RCT & Observational & Placebo \\
\midrule
\code{atehat} & Estimated average effect from the CATE estimator. & \checkmark & \checkmark & \checkmark & \checkmark \\
\\
\code{trueate} & True average effect from the DGP. & \checkmark & -- & -- & -- \\
\code{bias\_true} & Difference between estimated and true ATE. & \checkmark & -- & -- & -- \\
\code{pehe} & Precision in Estimation of Heterogeneous Effect: CATE/IATE RMSE against true individual effects. & \checkmark & -- & -- & -- \\
\code{corr} & Correlation between estimated and true CATE. & \checkmark & -- & -- & -- \\
\\
\code{benchate} & Experimental RCT benchmark. & -- & \checkmark & \checkmark & \checkmark \\
\code{bias\_bench} & Difference between estimate and benchmark. & -- & \checkmark & \checkmark & \checkmark \\
\\
\code{tau\_sd} & Spread of estimated individual effects. & \checkmark & \checkmark & \checkmark & \checkmark \\
\code{tau p10/p50/p90} & Distribution of estimated individual effects. & \checkmark & \checkmark & \checkmark & \checkmark \\
\\
\code{rc} & Stata return code; nonzero means did not run. & \checkmark & \checkmark & \checkmark & \checkmark \\
\bottomrule
\end{tabular}
\end{adjustbox}

\vspace{0.1cm}
One key distinction: PEHE evaluates heterogeneity directly, while ATE bias evaluates only the average effect.
\end{frame}


\begin{frame}{Simulation results: all estimators ranked by PEHE}
\includegraphics[width=\textwidth,height=.78\textheight,keepaspectratio]{figures/sim_pehe_rank_all_xfitcolor_v2.png}
%{figures/sim_pehe_rank_all.png}

\vspace{0.1cm}
\small This figure uses every valid simulated result. The best methods differ sharply across DGPs: linear-friendly designs favor simple/orthogonal approaches, while nonlinear designs reward richer final CATE models.
\end{frame}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Simulation: best eight specifications by DGP, Linear outcome}
\scriptsize
\begin{adjustbox}{max width=\textwidth,max totalheight=.78\textheight}
\begin{tabular}{llllllllll}
\toprule
DGP & family & est & spec & xfit & ATE & bias & PEHE & corr & tau sd \\
\midrule
LL & manual orth & irm & irm param reg-base & noxfit & 1.005 & 0.007 & 0.051 & 1.00 & 0.887 \\
LL & \sout{manual orth} & irm & irm param reg-base & xfold5 & 1.001 & 0.003 & 0.051 & 1.00 & 0.882 \\
LL & manual orth & irm & irm cv-lasso reg-base & noxfit & 1.010 & 0.012 & 0.053 & 1.00 & 0.877 \\
LL & manual orth & plr & plr param reg-base & noxfit & 1.010 & 0.012 & 0.054 & 1.00 & 0.864 \\
LL & manual orth & plr & plr cv-lasso reg-base & noxfit & 1.010 & 0.012 & 0.054 & 1.00 & 0.866 \\
LL & \sout{manual orth} & plr & plr cv-lasso reg-base & xfold5 & 1.009 & 0.011 & 0.055 & 1.00 & 0.865 \\
LL & \sout{manual orth} & plr & plr param reg-base & xfold5 & 1.013 & 0.015 & 0.056 & 1.00 & 0.865 \\
LL & \sout{manual orth} & irm & irm cv-lasso reg-base & xfold5 & 1.018 & 0.020 & 0.059 & 1.00 & 0.874 \\
LN & native cate & aipw & param reg/logit/reg & xfold5 & 0.982 & -0.027 & 0.055 & 1.00 & 0.912 \\
LN & non-DDML & plain & S-OLS base & noxfit & 0.998 & -0.004 & 0.061 & 1.00 & 0.886 \\
LN & non-DDML & plain & t cv-lasso & noxfit & 1.025 & 0.023 & 0.116 & 0.99 & 0.868 \\
LN & non-DDML & plain & T-OLS rich & noxfit & 1.010 & 0.008 & 0.125 & 0.99 & 0.891 \\
LN & \sout{manual orth} & plr & plr param reg-base & xfold5 & 0.968 & -0.003 & 0.128 & 0.99 & 0.927 \\
LN & \sout{manual orth} & plr & plr cv-lasso reg-base & xfold5 & 0.970 & -0.002 & 0.128 & 0.99 & 0.940 \\
LN & manual orth & plr & plr cv-lasso reg-base & noxfit & 0.973 & 0.001 & 0.132 & 0.99 & 0.943 \\
LN & manual orth & plr & plr param reg-base & noxfit & 0.972 & 0.000 & 0.132 & 0.99 & 0.937 \\
\bottomrule
\end{tabular}
\end{adjustbox}

\vspace{0.1cm}
\small Manual orthogonal IRM/PLR specifications dominate the linear DGPs. 
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Simulation: best eight specifications by DGP, Non-linear outcome}
\scriptsize
\begin{adjustbox}{max width=\textwidth,max totalheight=.78\textheight}
\begin{tabular}{llllllllll}
\toprule
DGP & family & est & spec & xfit & ATE & bias & PEHE & corr & tau sd \\
\midrule
NL & manual orth & irm & irm plug-lasso reg-rich & noxfit & 1.092 & -0.014 & 0.235 & 0.98 & 1.031 \\
NL & \sout{manual orth} & irm & irm plug-lasso reg-rich & xfold5 & 1.099 & -0.007 & 0.236 & 0.98 & 1.031 \\
NL & \sout{manual orth} & plr & plr plug-lasso reg-rich & xfold5 & 1.073 & -0.033 & 0.237 & 0.98 & 1.092 \\
NL & manual orth & plr & plr plug-lasso reg-rich & noxfit & 1.061 & -0.045 & 0.239 & 0.98 & 1.089 \\
NL & \sout{manual orth} & irm & irm plug-lasso cv-lasso & xfold5 & 1.099 & -0.007 & 0.242 & 0.98 & 0.972 \\
NL & \sout{manual orth} & plr & plr cv-lasso reg-rich & xfold5 & 1.028 & -0.078 & 0.261 & 0.97 & 1.045 \\
NL & manual orth & irm & irm plug-lasso cv-lasso & noxfit & 1.092 & -0.014 & 0.262 & 0.98 & 0.932 \\
NL & manual orth & plr & plr cv-lasso reg-rich & noxfit & 1.028 & -0.078 & 0.264 & 0.97 & 1.044 \\
NN & non-DDML & plain & T-OLS rich & noxfit & 1.206 & 0.118 & 0.264 & 0.98 & 1.012 \\
NN & non-DDML & plain & t cv-lasso & noxfit & 1.228 & 0.140 & 0.267 & 0.98 & 1.020 \\
NN & manual orth & irm & irm plug-lasso cv-lasso & noxfit & 1.201 & 0.145 & 0.307 & 0.97 & 1.061 \\
NN & \sout{manual orth} & plr & plr plug-lasso reg-rich & xfold5 & 1.177 & 0.120 & 0.307 & 0.97 & 1.097 \\
NN & manual orth & plr & plr plug-lasso reg-rich & noxfit & 1.174 & 0.117 & 0.307 & 0.97 & 1.092 \\
NN & \sout{manual orth} & irm & irm plug-lasso cv-lasso & xfold5 & 1.213 & 0.157 & 0.312 & 0.97 & 1.069 \\
NN & manual orth & irm & irm plug-lasso reg-rich & noxfit & 1.201 & 0.145 & 0.318 & 0.97 & 1.101 \\
NN & \sout{manual orth} & irm & irm plug-lasso reg-rich & xfold5 & 1.212 & 0.156 & 0.321 & 0.97 & 1.104 \\
\bottomrule
\end{tabular}
\end{adjustbox}

\vspace{0.1cm}
\small For nonlinear DGPs, rich final CATE models and lasso-based nuisance adjustment become more competitive.
\end{frame}


\begin{frame}{Simulation: ATE bias is not PEHE}
\includegraphics[width=\textwidth,height=.78\textheight,keepaspectratio]{figures/sim_atebias_vs_pehe.png}

\vspace{0.1cm}
\small A method can have small average-effect bias and still miss heterogeneity. This is the main reason to report CATE-specific metrics in addition to ATE metrics.
\end{frame}

\begin{frame}{Simulation: median PEHE by estimator family}
\includegraphics[width=\textwidth,height=.78\textheight,keepaspectratio]{figures/sim_median_pehe_by_family.png}

\vspace{0.1cm}
\small There is no single universal winner. The relative ranking changes when outcome surfaces and participation surfaces become nonlinear.
\end{frame}

\begin{frame}{Simulation: median PEHE by estimator family}
\includegraphics[width=\textwidth,height=.78\textheight,keepaspectratio]{figures/sim_median_pehe_by_family_manual_xfit_as_native.png}

\vspace{0.1cm}
\small There is no single universal winner. The relative ranking changes when outcome surfaces and participation surfaces become nonlinear.
\end{frame}


\begin{frame}{Simulation: RF-HPO changes across designs}
\includegraphics[width=\textwidth,height=.78\textheight,keepaspectratio]{figures/rf_hpo_selection_heatmap.png}

\vspace{0.1cm}
\small HPO selects different RF candidates across DGPs and LaLonde designs. This makes RF parametrization an object of study rather than a harmless default.
\end{frame}

\begin{frame}{Native CATE: HPO groups in the simulations}
\includegraphics[width=\textwidth,height=.78\textheight,keepaspectratio]{figures/native_hpo_pehe_by_group.png}

\vspace{0.1cm}
\small In linear DGPs, parametric or simpler orthogonal methods often dominate. In nonlinear DGPs, RF-HPO improves over a purely parametric CATE model, but it does not automatically become best overall.
\end{frame}

\begin{frame}{Manual orthogonal learners: effect of cross-fitting}
\includegraphics[width=\textwidth,height=.78\textheight,keepaspectratio]{figures/sim_crossfit_delta_pehe.png}

\vspace{0.1cm}
\small Cross-fitting belongs to the DDML design. It is not HPO. In these finite samples, cross-fitting sometimes improves PEHE and sometimes slightly worsens it, which is why repeated splits may be worth exploring later.
\end{frame}

\begin{frame}{Simulation: median performance by family and estimator}
\scriptsize
\begin{adjustbox}{max width=\textwidth,max totalheight=.78\textheight}
\begin{tabular}{lllllll}
\toprule
DGP & family & est & median PEHE & median |bias| & median corr & N \\
\midrule
LL & manual orth & plr & 0.103 & 0.015 & 0.99 & 12 \\
LL & manual orth & irm & 0.120 & 0.011 & 1.00 & 24 \\
LL & non-DDML & plain & 0.132 & 0.022 & 0.99 & 6 \\
LL & native cate & aipw & 0.307 & 0.042 & 0.94 & 4 \\
LL & native cate & po & 0.416 & 0.054 & 0.93 & 4 \\
LN & non-DDML & plain & 0.157 & 0.019 & 0.99 & 6 \\
LN & manual orth & plr & 0.185 & 0.012 & 0.99 & 12 \\
LN & manual orth & irm & 0.202 & 0.022 & 0.98 & 24 \\
LN & native cate & aipw & 0.314 & 0.025 & 0.94 & 4 \\
LN & native cate & po & 0.377 & 0.047 & 0.93 & 4 \\
NL & manual orth & irm & 0.417 & 0.059 & 0.95 & 24 \\
NL & non-DDML & plain & 0.427 & 0.051 & 0.93 & 6 \\
NL & manual orth & plr & 0.620 & 0.043 & 0.71 & 12 \\
NL & native cate & aipw & 0.658 & 0.064 & 0.81 & 4 \\
NL & native cate & po & 0.741 & 0.061 & 0.75 & 4 \\
NN & non-DDML & plain & 0.405 & 0.129 & 0.94 & 6 \\
NN & manual orth & irm & 0.442 & 0.110 & 0.93 & 24 \\
NN & manual orth & plr & 0.681 & 0.162 & 0.69 & 12 \\
NN & native cate & aipw & 0.698 & 0.056 & 0.76 & 4 \\
NN & native cate & po & 0.845 & 0.031 & 0.68 & 4 \\
\bottomrule
\end{tabular}
\end{adjustbox}

\vspace{0.1cm}
%\small This table summarizes the full simulation result set by DGP, estimator family, and estimator type.
\end{frame}

\begin{frame}{LaLonde/NSW-PSID designs}
\scriptsize
The local file contains the randomized NSW sample and a nonexperimental comparison group.

\begin{adjustbox}{max width=\textwidth}
\begin{tabular}{p{0.20\textwidth}p{0.50\textwidth}p{0.22\textwidth}}
\toprule
Design & Estimation sample & Purpose \\
\midrule
RCT & Randomized treated and randomized controls. & Benchmark. \\
OBS-NONEXP & Randomized treated units vs nonexperimental PSID controls. & Classic observational stress test. \\
OBS-ALLCTRL & Randomized treated units vs randomized plus nonexperimental controls. & Checks whether adding controls changes estimates. \\
PLACEBO-CTRL & Randomized controls vs nonexperimental controls. & Selection/placebo diagnostic. \\
\bottomrule
\end{tabular}
\end{adjustbox}

\vspace{0.15cm}
The RCT benchmark estimate in these results is about 886 dollars. The observational designs ask whether methods recover it without using randomized controls as the comparison group.

\bigskip
\scriptsize
\begin{adjustbox}{max width=\textwidth,max totalheight=.78\textheight}
\begin{tabular}{lllllllllll}
\toprule
sample & N & treated & controls & bench & ps p1 & ps p5 & ps med & ps p95 & ps p99 & extreme \\
\midrule
RCT & 722 & 297 & 425 & 886 & 0.270 & 0.328 & 0.396 & 0.552 & 0.604 & 0.0\% \\
OBS\_NONEXP & 2,787 & 297 & 2,490 & 886 & 0.000 & 0.000 & 0.003 & 0.863 & 0.965 & 80.1\% \\
OBS\_ALLCTRL & 3,212 & 297 & 2,915 & 886 & 0.000 & 0.000 & 0.014 & 0.430 & 0.478 & 67.5\% \\
PLACEBO\_CTRL & 2,915 & 425 & 2,490 & 0 & 0.000 & 0.000 & 0.004 & 0.951 & 0.977 & 78.3\% \\
\bottomrule
\end{tabular}
\end{adjustbox}

\vspace{0.1cm}
\small The observational and placebo designs have severe propensity-score overlap problems. This is the most important explanation for large benchmark failures.
\end{frame}

\begin{frame}{LaLonde overlap: visual diagnostic}
\includegraphics[width=\textwidth,height=.78\textheight,keepaspectratio]{figures/lalonde_overlap.png}

\vspace{0.1cm}
\small The RCT sample has broad overlap. The PSID-based comparisons concentrate many observations near 0 or 1, making causal ML much harder.
\end{frame}

\begin{frame}{LaLonde: benchmark recovery for all valid specifications}
\includegraphics[width=\textwidth,height=.78\textheight,keepaspectratio]{figures/lalonde_bias_distribution.png}

\vspace{0.1cm}
\small In the RCT sample, many methods are close to the benchmark. In observational samples, most methods miss the benchmark by thousands of dollars.
\end{frame}

\begin{frame}{LaLonde: ATE benchmark match versus heterogeneity stability}
\includegraphics[width=\textwidth,height=.78\textheight,keepaspectratio]{figures/lalonde_absbias_vs_tausd.png}

\vspace{0.1cm}
\small A method can match the benchmark while producing very dispersed individual effects. Both ATE recovery and CATE stability should be reported.
\end{frame}

\begin{frame}{LaLonde: ten closest specifications to benchmark in each design}
\includegraphics[width=\textwidth,height=.78\textheight,keepaspectratio]{figures/lalonde_top10_by_absbias.png}

\vspace{0.1cm}
\small The closest specifications differ by sample construction. In OBS-NONEXP, even the best specifications remain far from the RCT benchmark, which points to overlap/selection problems.
\end{frame}

\begin{frame}{What the full results say so far}
\small
\begin{itemize}
  \item \textbf{ATE and CATE are different targets.} Some specifications recover average effects but do poorly on PEHE or produce very dispersed individual effects.
  \item \textbf{Linear designs are forgiving.} In LL and LN, simple/manual orthogonal specifications often perform very well.
  \item \textbf{Nonlinear heterogeneity changes the ranking.} In NL and NN, rich final CATE models and flexible learners become more important.
  \item \textbf{HPO matters, but it is not magic.} RF-HPO can improve native \code{cate} results in nonlinear settings, but aggressive RF choices can also create instability.
  \item \textbf{The LaLonde observational samples are hard because of support.} The PSID comparisons have extreme propensities; most methods miss the RCT benchmark by large amounts.
\end{itemize}
\end{frame}

\begin{frame}{What this means for applications}
\small
%For inequality analysis, the main practical message is:


\begin{center}
\Large Do not report only the average effect.
\end{center}

\vspace{0.15cm}
\begin{itemize}
  \item Report the ATE and the distribution of estimated CATEs.
  \item Check whether the best ATE estimator also gives credible heterogeneity.
  \item Examine support/overlap before interpreting subgroup or individual effects.
  \item Compare parametric, lasso, and RF-HPO versions, especially when there are nonlinearities or many controls.
  \item Treat HPO choices as part of the research design, not an implementation detail.
\end{itemize}

\small
An appendix contains the detailed result tables:
\begin{itemize}
  \item full native \code{cate}, non-DDML, and manual orthogonal simulation tables;
  \item full native \code{cate}, non-DDML, and manual orthogonal LaLonde/NSW-PSID tables;
  \item all slides previously numbered 27--42 and 49--70 in the full diagnostic deck.
\end{itemize}

\end{frame}


\begin{frame}[allowframebreaks]{References}
\footnotesize
\begin{thebibliography}{99}

\bibitem{bach2024}
Bach, Philipp, Daniel Schacht, Victor Chernozhukov, and Stephan Klaassen. 2024.
``Hyperparameter Tuning for Causal Inference with Double Machine Learning.''
Proceedings of Machine Learning Research.


\bibitem{chernozhukov2018}
Chernozhukov, Victor, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whitney Newey, and James Robins. 2018.
``Double/Debiased Machine Learning for Treatment and Structural Parameters.''
\emph{The Econometrics Journal} 21(1): C1--C68.


\bibitem{knaus2021}
Knaus, Michael C., Michael Lechner, and Anthony Strittmatter. 2021.
``Machine Learning Estimation of Heterogeneous Causal Effects: Empirical Monte Carlo Evidence.''
\emph{The Econometrics Journal} 24(1): 134--161.

\bibitem{kunzel2019}
K{\"u}nzel, S{\"o}ren R., Jasjeet S. Sekhon, Peter J. Bickel, and Bin Yu. 2019.
``Metalearners for Estimating Heterogeneous Treatment Effects Using Machine Learning.''
\emph{Proceedings of the National Academy of Sciences} 116(10): 4156--4165.

\bibitem{niewager2021}
Nie, Xinkun, and Stefan Wager. 2021.
``Quasi-Oracle Estimation of Heterogeneous Treatment Effects.''
\emph{Biometrika} 108(2): 299--319.

\bibitem{wagerathey2018}
Wager, Stefan, and Susan Athey. 2018.
``Estimation and Inference of Heterogeneous Treatment Effects using Random Forests.''
\emph{Journal of the American Statistical Association} 113(523): 1228--1242.
doi: 10.1080/01621459.2017.1319839.

\end{thebibliography}
\end{frame}
\end{document}

