\begin{algorithmic}
\State 1. Considering the dataset of all applicants to both programs, randomly split the dataset into train and test with equal probability at the applicant level, denote the resulting sets as $I^{train} = \left\{1,..,\mathcal{I}^{train}\right\}$ and $I^{test}= \left\{1,..,\mathcal{I}^{test}\right\}$.
\State 2. In the training dataset, estimate outcome model using cross-validation: $\mu_{train}$
\State 3. In the test set, construct predicted treatment effects using predictions from model $\mu_{train}$. Obtain $\tau^{Op,train}_{i,t} = E[\hat{Y}(p)_{train} - \hat{Y}(O)_{train}|X=x_{i,t} , i \in I^{test}]$, where $\hat{Y}(p)_{train}$ is the predicted outcome under program $p$ constructed using $\mu_{train}$ and $\hat{Y}(O)_{train}$ is the predicted outcome under \emph{Out of Dare IT} and $t \in \left\{1,...,15\right\}$ denotes months. Compute mean treatment effects per user as: $\tau^{Op,train}_{i} = 1/t \times \sum_{t=1}^{15}\tau^{Op,train}_{i,t}$,

\State 4. Assign treatment to maximize treatment effects subject to capacity constraint. Let $Q^{p}$ be the capacity limit of program $p$ and $z_{ip}$ an indicator variable taking the value of one when applicant $i$ is assigned to program $p$ and zero otherwise. We solve the following constrained optimization problem:
\[
\max_{z_{ip}}\sum_{i=1}^{I}\sum_{p=1}^{P}z_{ip}\tau_{i}^{Op,train} \text{ s.t. }\sum_{i=1}^{I}z_{ip} \leq Q^{p} \forall_{p} \text{ \& }\sum_{i=p}^{P}z_{ip} = 1\forall_{i \in I^{test}}.
\]  The first constraint ensures that the capacity constraints are not violated. The second one is that every applicant is assigned to one program. There is no capacity limit on being \emph{Out of Dare IT}. We use \emph{LP Solve} algorithm to solve the problem. We obtain optimal allocation $\mathcal{A}_{X,Q}^{*} = \left\{a_{i}^{*},...,a_{\mathcal{I}^{test}}^{*}\right\}$,

\State 5. Using the test set, estimate new outcome and propensity models using cross-fitting and obtain predictions: $\hat{\mu}_{i,k}$ and $\hat{e}_{i,k}$ for all $i \in I^{test}$. See Appendix \ref{cross_fit_appendix} for details of the cross-fitting procedure. Obtain $\hat{Y}_{i,k}(a^{*})$ the AIPW estimates of the predicted outcomes using cross-fitted models trained in the test set,
    
\State 6. Obtain $\hat{V}_{X,Q}^{*} = \frac{1}{|I^{test}|}\times \sum_{i=1}^{\mathcal{I}^{test}}\hat{Y}_{i,k}(a^{*})$ as the mean of predicted outcomes under the allocation $\mathcal{A}_{X,Q}^{*}$. Estimate standard errors clustered at the applicant level: $\sigma_{X,Q}^{*}$. \Comment \\
\Return{} $(\mathcal{A}_{X,Q}^{*},\hat{V}_{X,Q}^{*},\sigma_{X,Q}^{*},\hat{Y}_{1,k}(a^{*}),...,\hat{Y}_{\mathcal{I}^{test},k}(a^{*}) )$
\end{algorithmic}

\begin{algorithmic}
\State 1. Considering the dataset of all applicants to both programs, randomly split the dataset into train and test with equal probability at the applicant level, denote the resulting sets as $I^{train} = \left\{1,..,\mathcal{I}^{train}\right\}$ and $I^{test}= \left\{1,..,\mathcal{I}^{test}\right\}$.
\State 2. In the training dataset, estimate outcome model using cross-validation: $\mu_{train}$
\State 3. In the test set, construct predicted treatment effects using predictions from model $\mu_{train}$. Obtain $\tau^{Op,train}_{i,t} = E[\hat{Y}(p)_{train} - \hat{Y}(O)_{train}|X=x_{i,t} , i \in I^{test}]$, where $\hat{Y}(p)_{train}$ is the predicted outcome under program $p$ constructed using $\mu_{train}$ and $\hat{Y}(O)_{train}$ is the predicted outcome under \emph{Out of Dare IT} and $t \in \left\{1,...,15\right\}$ denotes months. Compute mean treatment effects per user as: $\tau^{Op,train}_{i} = 1/t \times \sum_{t=1}^{15}\tau^{Op,train}_{i,t}$,
\State 4. Assign treatment to maximize treatment effects subject to capacity constraint. Let $Q^{p}$ be the capacity limit of program $p$ and $z_{ip}$ an indicator variable taking the value of one when applicant $i$ is assigned to program $p$ and zero otherwise. We solve the following constrained optimization problem:
\[
\max_{z_{ip}}\sum_{i=1}^{I}\sum_{p=1}^{P}z_{ip}\tau_{i}^{Op,train} \text{ s.t. }\sum_{i=1}^{I}z_{ip} \leq Q^{p} \forall_{p} \text{ \& }\sum_{i=p}^{P}z_{ip} = 1\forall_{i \in I^{test}}.
\] The first constraint ensures that the capacity constraints are not violated. The second one is that every applicant is assigned to one program. There is no capacity limit on being \emph{Out of Dare IT}. We use \emph{LP Solve} algorithm to solve the problem. We obtain optimal allocation $\mathcal{A}_{X,Q}^{*} = \left\{a_{i}^{*},...,a_{\mathcal{I}^{test}}^{*}\right\}$,
\State 5. Using the test set, estimate new outcome and propensity models using cross-fitting and obtain predictions: $\hat{\mu}_{i,k}$ and $\hat{e}_{i,k}$ for all $i \in I^{test}$. See Appendix \ref{cross_fit_appendix} for details of the cross-fitting procedure. Obtain $\hat{Y}_{i,k}(a^{*})$ the AIPW estimates of the predicted outcomes using cross-fitted models trained in the test set,
\State 6. Obtain $\hat{V}_{X,Q}^{*} = \frac{1}{|I^{test}|}\times \sum_{i=1}^{\mathcal{I}^{test}}\hat{Y}_{i,k}(a^{*})$ as the mean of predicted outcomes under the allocation $\mathcal{A}_{X,Q}^{*}$. Estimate standard errors clustered at the applicant level: $\sigma_{X,Q}^{*}$. \Comment \\
\Return{} $(\mathcal{A}_{X,Q}^{*},\hat{V}_{X,Q}^{*},\sigma_{X,Q}^{*},\hat{Y}_{1,k}(a^{*}),...,\hat{Y}_{\mathcal{I}^{test},k}(a^{*}) )$
\end{algorithmic}
{
    "title": "effective and scalable programs to facilitate labor market transitions   for women in technology",
    "id": "2211.09968",
    "abstract": "we describe the design, implementation, and evaluation of a low-cost (approximately $15 per person) and scalable program, called challenges, aimed at aiding women in poland transition to technology-sector jobs. this program helps participants develop portfolios demonstrating job-relevant competencies. we conduct two independent evaluations, one of the challenges program and the other of a traditional mentoring program -- mentoring -- where experienced tech professionals work individually with mentees to support them in their job search. exploiting the fact that both programs were oversubscribed, we randomized admissions and measured their impact on the probability of finding a job in the technology sector. we estimate that mentoring increases the probability of finding a technology job within four months from 29% to 42% and challenges from 20% to 29%, and the treatment effects do not attenuate over 12 months. since both programs are capacity constrained in practice (only 28% of applicants can be accommodated), we evaluate the effectiveness of several alternative prioritization rules based on applicant characteristics. we find that a policy that selects applicants based on their predicted treatment effects increases the average treatment effect across the two programs to 22 percentage points. we further analyze how alternative prioritization rules compare to the selection that mentors used. we find that mentors selected applicants who were more likely to get a tech job even without participating in the program, and the treatment effect for applicants with similar characteristics to those selected by mentors is about half of the effect attainable when participants are prioritized optimally.",
    "categories": "econ.gn q-fin.ec",
    "doi": "",
    "created": "2022-11-17",
    "updated": "2024-01-03",
    "authors": [
        "susan athey",
        "emil palikot"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2211.09968"
}
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