Exercise 1

Exercise 1.1

The major question of this study examines if accelerated investment in the human capital of women can expedite their empowerment and dramatically alter their life course, or if deep-rooted cultural values and lower aspirations hinder such progress despite the intentions of public policy programs.

To explore this question, the study evaluates a broad-based intervention targeting adolescent girls in Uganda. This program offers these women vocational training designed to create economic empowerment, alongside life skills that enable prudent decision-making regarding sexual health, reproductive issues, and marriage. It seeks to break the cycle of intergenerational transmission of being involved in low-skilled work and high fertility through a prioritization of early investments in economic and social capital.

The randomized control trial (RCT) was conducted across 10 BRAC branch offices, where 15 communities per branch were selected: 10 assigned to treatment and 5 to control, totaling 100 treatment and 50 control communities. The program was delivered via adolescent development clubs, designed to be accessible to both in-school and out-of-school girls.

Data were collected at three different timepoints: baseline (2008), midline (2010), and endline (2012), among a sample of 5,966 adolescent girls. Longitudinal individual outcomes are assessed based on three specific indices of empowerment: economic empowerment, bodily autonomy, and aspirations. These indices are computed from relevant variables that are standardized to z-scores.

To estimate program impact, the authors use OLS analysis of covariance, controlling for baseline characteristics and branch-level stratification. They address sample attrition with Lee bounds.

Additional analyses examine spillovers, assess cost-effectiveness, and utilize Marginal Treatment Effects (MTEs) for examining the selection mechanisms that affect participation, alongside mediation analysis to address the questions of how strongly various program components affect outcomes.


Exercise 1.2

The study adopts a randomized control trial design to evaluate the Empowerment and Livelihood for Adolescents (ELA) program, implemented by BRAC Uganda. In each of the 10 branches, 15 communities were selected: 10 randomly assigned to treatment and 5 to control, ensuring balance through branch-level stratification.

A community census was conducted, and around 40 adolescent girls per community were surveyed at three time points: baseline, midline, and endline. This panel structure allowed tracking changes in individual outcomes across 5,966 girls.

The intervention combined three main components:

  • Vocational training: Skills in trades such as tailoring, hairdressing, and poultry farming.
  • Life skills education: Topics included sexual and reproductive health, legal rights, and negotiation.
  • Adolescent development clubs: Safe, community-based spaces for peer interaction, facilitated by trained female mentors, held five afternoons per week.

The study estimates Intent-to-Treat (ITT) effects on three empowerment indices (economic, bodily autonomy, and aspirations) using standardized z-scores. To account for attrition, the authors apply Lee bounds.


Exercise 1.3

The empirical strategy is built around a randomized control trial, ensuring causal identification of the treatment effect.

The unit of randomization is the community, stratified across ten BRAC branches. Each branch has 15 communities, with 10 treated and 5 control. Surveys were conducted at three time points: baseline, midline, and endline. The panel data structure allows for tracking changes over time.

Since participation in the program is voluntary, the authors estimate Intent-to-Treat (ITT) effects, which capture the average impact of being in a treated community, regardless of individual take-up.

They construct three outcome indices: economic empowerment, control over the body, and aspirations. Each index is built by combining z-scores of multiple relevant variables and averaging them.

To address potential bias from attrition, the authors apply Lee bounds, which provide a range for the estimated effect under monotonicity assumptions.

Further, they investigate spillovers, use Marginal Treatment Effects (MTEs) to understand heterogeneous effects and selection into participation, and apply mediation analysis to explore how specific components influence the overall impact.

The core regression equation used is:

\[y_{ijt} = \alpha + \gamma_t \cdot \text{Treatment}_{ij} + \beta \cdot X_{ij0} + \delta \cdot y_{ij0} + \varepsilon_{ijt}\]

Here:

  • \(y_{ijt}\): Dependent variable – the outcome of interest (e.g., an empowerment index) for individual \(i\) in community \(j\) at time \(t\)
  • \(\text{Treatment}_{ij}\): Independent variable of interest – a binary indicator equal to 1 if community \(j\) was assigned to treatment
  • \(X_{ij0}\): Vector of baseline control variables, such as age, a factor for the corresponding branch, etc.
  • \(y_{ij0}\): Baseline value of the dependent variable, used to improve precision
  • \(\varepsilon_{ijt}\): Error term, capturing unobserved influences
  • \(\gamma_t\): Treatment effect at time t, which is the main coefficient of interest

This setup enables the authors to isolate the causal impact of the ELA program by controlling for pre-treatment characteristics and accounting for community-level stratification. The analysis is conducted separately at midline and endline to observe both short- and long-term effects of the intervention.


Exercise 2

Exercise 2.1

For the sake of brevity, we decided to omit the code to perform data cleaning prior to generating the desired table. In general, this is how we addressed the problem:

  • Defined variable groups for different panels

  • Initialized an empty data frame summary_stats for summary statistics

  • Filled values of summary_stats using for loops through each variable to calculate N, Mean, SD, Min, Max, and Missing values.

  • Assigned descriptive labels to variables

  • Displayed results as a clean HTML table stored as formatted_table

See the accompanying .Rmd file for implementation details.

formatted_table <- kable(
  summary_stats,
  col.names = c("Variable", "N", "Mean", "SD", "Min", "Max", "Missing"),
  digits = 3,
  caption = "**Table 1 - Summary Statistics of Selected Variables**",
  format = "html"
) %>%
  add_header_above(
    header = c(" " = 1, "Summary Statistics (Total N=4,167)" = 6)
  ) %>%
  pack_rows("Panel A. Characteristics", 1, 4) %>%
  pack_rows("Panel B. Economic Empowerment", 5, 8) %>%
  pack_rows("Panel C. Control Over the Body", 9, 13) %>%
  pack_rows("Panel D. Beliefs and Aspirations", 14, 15) %>%
  kable_classic(full_width = FALSE, html_font = "Times New Roman") %>%
  footnote(
    general = "Binary variables show proportion of 1s. Missing values indicate non-response or non-applicable cases.",
    general_title = "Note:",
    footnote_as_chunk = TRUE
  )
## Warning in attr(x, "align"): 'xfun::attr()' is deprecated.
## Use 'xfun::attr2()' instead.
## See help("Deprecated")
formatted_table
Table 1 - Summary Statistics of Selected Variables
Summary Statistics (Total N=4,167)
Variable N Mean SD Min Max Missing
Panel A. Characteristics
Age 4122 16.36 2.86 10 28 45
Back to school 1110 0.54 0.50 0 1 3057
Has children 4038 0.10 0.30 0 1 129
Has partner 4091 0.10 0.30 0 1 76
Panel B. Economic Empowerment
Entrepreneurship index 4133 70.41 24.93 0 100 34
Self-employed 4167 0.06 0.24 0 1 0
Wage employed 4167 0.05 0.21 0 1 0
Worry about job 4064 0.42 0.49 0 1 103
Panel C. Control Over the Body
Unwilling sex 1519 0.18 0.38 0 1 2648
Pregnancy knowledge 3984 0.74 0.44 0 1 183
HIV knowledge 4167 3.79 1.23 0 6 0
Always condom 1285 0.52 0.50 0 1 2882
Other contraceptive 1285 0.16 0.37 0 1 2882
Panel D. Beliefs and Aspirations
Empowerment index 4167 29.64 24.53 0 100 0
Ideal marriage age 2461 28.88 7.07 16 50 1706
Note: Binary variables show proportion of 1s. Missing values indicate non-response or non-applicable cases.

Interpretations from the summary statistics:

Panel A – Characteristics

  • Age ranges from 10 to 28 years (mean: 16.36).
  • “Back to school” has high missingness (3,057 missing values), suggesting it was likely asked only to specific subgroups.
  • Around 10% of respondents have children or partners.

Panel B – Economic Empowerment

  • Entrepreneurship index spans the full 0–100 range (mean: 70.4).
  • Employment rates are low: 6.4% are self-employed, and 4.7% are wage employed.
  • There is complete data for employment-related variables (no missing values).

Panel C – Control Over the Body

  • High missingness in sexual behavior variables, indicating they apply only to sexually active respondents.
  • HIV knowledge ranges from 0 to 6 (mean: 3.79).

Panel D – Beliefs and Aspirations

  • Empowerment index spans 0–100 (mean: 29.6).
  • Ideal marriage age varies widely, from 15 to 50 years (mean: 28.9).

Exercise 2.2

In causal inference, especially in analyzing randomized controlled trials (RCTs), “balancedness” denotes the initial similarity of baseline characteristics between control and treatment groups before implementing the intervention.

Balanced allocation ensures these groups are statistically comparable in observed covariates, allowing post-treatment outcome differences to be attributed to the treatment instead of pre-existing differences. Balancedness is crucial in well-run randomized experiments; successful randomization makes treatment assignment independent of outcomes and other characteristics.

However, perfect balance isn’t always assured, especially with smaller samples or cluster randomization, necessitating empirical balance assessments. This usually involves comparing baseline variable distributions across treatment groups, with several common methods used for this purpose:

  • Mean Comparison Tests: Independent samples t-tests are widely applied to examine whether the average value of a continuous baseline variable differs significantly between the treatment and control groups. A non-significant p-value suggests that the variable is balanced across groups.

  • Standardized Mean Differences (SMDs): Researchers frequently calculate SMDs to assess balance. Unlike p-values, SMDs are not affected by sample size, making them a preferred method in many settings. An SMD below 0.1 is typically considered indicative of good balance.


Exercise 2.3

As in Exercise 2.1, we merely display the code needed to generate the desired table. These were the steps required beforehand:

  • Filtered the dataset to baseline observations and created control/treatment groups.

  • Organized outcome variables into 4 panels.

  • Used loops to compute group means, differences, standard errors, and p-values for each variable.

  • Created a merged data frame combining all panels and formatted significant differences with stars.

  • Displayed results as a clean HTML table stored as balancedness_table

See the accompanying .Rmd file for implementation details.

balancedness_table <- kable(
  final_table,
  digits = 3,
  caption = "**Table 2 - Balancedness Check: Baseline Characteristics by Treatment Status**",
  format = "html",
  escape = FALSE
) %>%
  add_header_above(
    header = c(" " = 1, "Group Means" = 2, "Difference Test" = 3)
  ) %>%
  pack_rows("Panel A. Characteristics", 1, 4) %>%
  pack_rows("Panel B. Economic Empowerment", 5, 8) %>%
  pack_rows("Panel C. Control Over the Body", 9, 13) %>%
  pack_rows("Panel D. Beliefs and Aspirations", 14, 15) %>%
  kable_classic(full_width = FALSE, html_font = "Times New Roman") %>%
  footnote(
    general = c(
      paste("Control group N =", nrow(control), "; Treatment group N =", nrow(treatment)),
      "Standard errors from two-sample t-tests assuming equal variances.",
      "*** p<0.01, ** p<0.05, * p<0.1"
    ),
    general_title = "Notes:",
    footnote_as_chunk = TRUE
  )
## Warning in attr(x, "align"): 'xfun::attr()' is deprecated.
## Use 'xfun::attr2()' instead.
## See help("Deprecated")
balancedness_table
Table 2 - Balancedness Check: Baseline Characteristics by Treatment Status
Group Means
Difference Test
Variable Control Mean Treatment Mean Difference SE P-value
Panel A. Characteristics
Age 16.440 16.320 -0.12 0.090 0.190
Currently enrolled in school 0.520 0.540 0.02 0.030 0.550
Has child(ren) 0.100 0.100 0 0.010 1.000
Married or cohabiting 0.120 0.090 -0.03*** 0.010 0.000
Panel B. Economic Empowerment
Entrepreneurship index 72.492 69.367 -3.125*** 0.822 0.000
Self-employed 0.057 0.067 0.01 0.008 0.200
Wage employed 0.034 0.053 0.019*** 0.007 0.005
Worry about job 0.400 0.425 0.025 0.016 0.121
Panel C. Control Over the Body
Unwilling sex 0.130 0.200 0.07*** 0.020 0.000
Pregnancy knowledge 0.750 0.740 -0.01 0.010 0.520
HIV knowledge 3.740 3.810 0.07* 0.040 0.090
Always condom 0.520 0.510 -0.01 0.030 0.760
Other contraceptive 0.170 0.160 -0.01 0.020 0.740
Panel D. Beliefs and Aspirations
Gender empowerment index [0–100 score] 31.620 28.659 -2.961*** 0.805 0.000
Suitable age at marriage for a woman 27.957 29.338 1.381*** 0.302 0.000
Notes: Control group N = 1387 ; Treatment group N = 2780 Standard errors from two-sample t-tests assuming equal variances. *** p<0.01, ** p<0.05, * p<0.1

Why This Matters:

Balancedness testing serves two critical purposes:

  1. Randomization Verification: Ensures observable characteristics do not predict treatment assignment, verifying successful randomization.
  2. Baseline Equivalence: Confirms statistical similarity between treatment and control groups before the intervention through t-tests.

The significant imbalances found (particularly in economic empowerment and gender attitudes) suggest either:

  • Randomization was not perfectly executed
  • Random chance led to some baseline differences

BALANCEDNESS FINDINGS REPORT

Executive Summary

The balancedness analysis reveals mixed results regarding the success of randomization in this study. While most baseline characteristics show good balance between treatment (N=2,780) and control (N=1,387) groups, several significant imbalances raise concerns about the randomization process and have important implications for subsequent analyses.

Key Findings by Domain

Panel A: Demographics and Basic Characteristics

  • Age: Well balanced (16.32 vs 16.44 years, p = 0.188)
  • School enrollment: Well balanced (54.4% vs 52.5%, p = 0.547)
  • Having children: Perfectly balanced (10.4% vs 10.3%, p = 0.998)
  • Marriage/cohabitation: SIGNIFICANT IMBALANCE (8.8% vs 11.7%, p = 0.003***)

Panel B: Economic Empowerment

  • Entrepreneurship index: SIGNIFICANT IMBALANCE (69.37 vs 72.49, p < 0.001***)
  • Self-employment: Well balanced (6.7% vs 5.7%, p = 0.200)
  • Wage employment: SIGNIFICANT IMBALANCE (5.3% vs 3.4%, p = 0.005***)
  • Job worry: Well balanced (42.5% vs 40.0%, p = 0.121)

Panel C: Control Over the Body

  • Unwilling sex: SIGNIFICANT IMBALANCE (20.0% vs 13.3%, p = 0.001***)
  • Pregnancy knowledge: Well balanced (73.6% vs 74.6%, p = 0.516)
  • HIV knowledge: Marginally balanced (3.81 vs 3.74, p = 0.088)
  • Condom use: Well balanced (51.3% vs 52.2%, p = 0.760)
  • Other contraceptives: Well balanced (16.2% vs 16.9%, p = 0.737)

Panel D: Beliefs and Aspirations

  • Gender empowerment index: SIGNIFICANT IMBALANCE (28.66 vs 31.62, p < 0.001***)
  • Ideal marriage age: SIGNIFICANT IMBALANCE (29.34 vs 27.96 years, p < 0.001***)

Critical Implications

  1. Randomization Concerns

The presence of multiple significant baseline differences (5 out of 15 variables) suggests potential issues with the randomization process. This is concerning because:

  • True randomization should produce balanced groups on observable characteristics
  • The pattern of imbalances is not random but appears systematic
  • Some imbalances are in key outcome-related domains
  1. Threats to Internal Validity

The observed imbalances pose several threats:

  • Selection bias: Differences in outcomes may reflect pre-existing group differences rather than treatment effects
  • Confounding: Baseline differences in empowerment and attitudes could confound treatment effect estimates
  • Generalizability: Questions about whether randomization failure affects external validity

Exercise 3

Exercise 3.1

Economic empowerment:

  • By four (two) years post-intervention, treated communities were 4.9 (6.8) [compare Table 2: Row 2, Column 4 and 3, respectively] percentage points more likely to engage in income-generating activities constituting a 48% (67%) increase over baseline level.

  • Increase in income-generating activities primarily results from a rise in self-employment activities: At endline (midline), self-employment rates are approximately 50% (nearly double) higher than those in control communities at baseline, rising from 6.3 percentage points to 9.5 pp (12.2 pp) [compare Table 2: Row 3, Column 4 and 3, respectively].

Control Over the Body:

  • Early childbearing decreased by 3.8 percentage points in treated communities being a 34% reduction from the baseline mean.

  • Likelihood of marriage/cohabiting dropped by 6.9 pp at midline and 8 pp at endline.

  • Incidence of non-consensual intercourse decreased by 5.3 pp in treatment areas by endline.

  • Mindset change: ideal age at marriage and preferred age to begin childbearing increased.


Exercise 3.2

Just as in 2.1 and 2.3, we omit the code before generating the desired table. In general, we addressed the problem in the following way:

  • Used original variable names for baseline, and applied prefixes R and Q for midline and endline variables, respectively.

  • For each outcome, we reported: the control group baseline mean (with SD), midline and endline sample sizes, and four ITT estimates (midline/endline × with/without covariates).

  • Trimmed top 1% of values for the expenditure outcome to reduce outlier bias, consistent with the original study.

  • Included exogenous variables: age and branch fixed effects; clustered standard errors at the village (villid) level.

  • Wrapped the logic into a reusable custom function summarize_ITT_table_df().

See the accompanying .Rmd file for implementation details.

kable(full_table, digits = 1, escape = FALSE,
      caption = "**Table 3: ITT Estimates Across Outcomes**") %>%
  add_header_above(
    c(" " = 1, 
      "Baseline" = 1, 
      "Sample Size" = 2,
      "Midline" = 2,
      "Endline" = 2)
  ) %>%
  pack_rows("Panel A. Economic Empowerment", 1, n_econ) %>%
  pack_rows("Panel B. Control Over the Body", n_econ + 1, n_econ + n_control) %>%
  pack_rows("Panel C. Aspirations", n_econ + n_control + 1, n_econ + n_control + n_asp) %>%
  kable_classic(full_width = FALSE, html_font = "Times New Roman") %>%
  footnote(
    general = c(
      "Standard errors in square brackets, standard deviations in parentheses.",
      "Standard errors are clustered by community (villid).",
      "*** p<0.01, ** p<0.05, * p<0.1"
    ),
    general_title = "Notes:",
    footnote_as_chunk = TRUE
  )
## Warning in attr(x, "align"): 'xfun::attr()' is deprecated.
## Use 'xfun::attr2()' instead.
## See help("Deprecated")
## Warning in attr(x, "align"): 'xfun::attr()' is deprecated.
## Use 'xfun::attr2()' instead.
## See help("Deprecated")
Table 3: ITT Estimates Across Outcomes
Baseline
Sample Size
Midline
Endline
Outcome Baseline Mean (SD) N Midline N Endline ITT Midline (ctrl) ITT Endline (ctrl) ITT Midline (uncond) ITT Endline (uncond)
Panel A. Economic Empowerment
Entrepreneurial ability index 72.49 (24.86) 3387 2669 5.57*** [1.12] 1.73* [1.03] 5.69** [2.30] 1.34 [1.84]
Any income-generating activity 0.09 (0.29) 3414 2682 0.08*** [0.02] 0.05** [0.02] 0.08*** [0.02] 0.05** [0.03]
Self-employed 0.06 (0.23) 3414 2682 0.07*** [0.01] 0.04* [0.02] 0.07*** [0.01] 0.04* [0.02]
Wage employed 0.03 (0.18) 3414 2682 0.02** [0.01] 0.02 [0.01] 0.02* [0.01] 0.02 [0.01]
Expenditure on goods in the last month (UGX) 13171.39 (68204.30) 3374 2649 15483.35* [8539.62] 69079.82** [34331.86] 14143.56 [9957.06] 73247.08* [42337.11]
Economic empowerment index 31.62 (25.03) 3414 2682 2.93*** [1.03] -1.11 [1.66] 2.46** [1.23] -0.94 [1.98]
Panel B. Control Over the Body
Has child(ren) 0.10 (0.30) 3396 2638 -0.03*** [0.01] -0.04** [0.01] -0.04* [0.02] -0.04* [0.02]
Married or cohabiting 0.12 (0.32) 3322 2511 -0.07*** [0.02] -0.07*** [0.02] -0.08*** [0.02] -0.07** [0.03]
Had sex unwillingly in the past year 0.75 (0.44) 3356 2616 0.05** [0.02] 0.04** [0.02] 0.06** [0.03] 0.04 [0.03]
Pregnancy knowledge index [0–1] -0.01 (1.01) 3414 2682 0.54*** [0.05] 0.29*** [0.04] 0.55*** [0.06] 0.25*** [0.07]
HIV knowledge index [0–6] 3.74 (1.24) 3414 2682 0.49*** [0.05] 0.09* [0.05] 0.52*** [0.08] 0.08 [0.08]
Always uses condom if sexually active 0.52 (0.50) 1265 1234 0.13*** [0.05] -0.01 [0.04] 0.19*** [0.03] 0.05 [0.04]
Uses other contraceptives if sexually active 0.17 (0.38) 1265 1234 0.02 [0.04] 0.00 [0.05] 0.04 [0.03] -0.00 [0.04]
Control over the body index -0.01 (1.01) 3414 2682 0.54*** [0.05] 0.29*** [0.04] 0.55*** [0.06] 0.25*** [0.07]
Panel C. Aspirations
Gender empowerment index [0–100] -0.02 (0.99) 3414 2682 0.27*** [0.05] 0.08* [0.05] 0.29*** [0.06] 0.05 [0.09]
Suitable age at marriage for a woman 23.90 (3.17) 3383 2671 0.78*** [0.14] 0.29** [0.13] 0.83*** [0.16] 0.23 [0.24]
Suitable age at marriage for a man 27.99 (3.71) 3385 2667 0.73*** [0.15] 0.31** [0.13] 0.78*** [0.21] 0.20 [0.36]
Suitable age for women to have first child 23.72 (3.27) 3377 2661 0.57*** [0.13] 0.32* [0.16] 0.65*** [0.19] 0.27 [0.21]
Preferred age daughters marry 24.81 (2.84) 3359 2617 0.67*** [0.15] 0.10 [0.13] 0.70*** [0.15] 0.06 [0.21]
Preferred age sons marry 28.30 (3.30) 3359 2611 0.11 [0.14] 0.12 [0.12] 0.17 [0.19] 0.06 [0.31]
Aspirations index -0.02 (0.99) 3414 2682 0.27*** [0.05] 0.08* [0.05] 0.29*** [0.06] 0.05 [0.09]
Notes: Standard errors in square brackets, standard deviations in parentheses. Standard errors are clustered by community (villid). *** p<0.01, ** p<0.05, * p<0.1

Exercise 3.3

The replicated results show both alignment and divergence with the original paper’s findings. The key observations are:

  1. Sample Sizes: Our replication has smaller sample sizes (~3,400 midline vs ~4,800 in original).

  2. Effect Sizes: While direction and significance generally match (e.g., 5.57*** vs 5.63*** for entrepreneurial index), some estimates differ substantially. Expenditure impacts are notably larger in our replication (15,483 UGX* vs 4,676 UGX).

  3. Imbalanced Covariates: Baseline differences (like +0.019*** in wage employment from Exercise 2.3) could influence results despite our controls.

  4. Implementation Differences: Variations in variable construction (indices, trimming thresholds) and missing data handling likely contribute to discrepancies, particularly for continuous outcomes like expenditures.


Exercise 4

Exercise 4.1

  1. Heterogeneity Analysis: The authors check whether specific subsamples of adolescent girls are primarily responsible for the results, specifically all three indices as well as education-related outcomes. The following dimensions are considered: (i) rural versus urban households; (ii) rich versus poor households, as defined by whether the household’s asset values at baseline are above or below the median for all households; and (iii) girls aged above/below 16 at baseline. The study shows that impacts are mainly homogenous across these dimensions.

  2. Cost Effectiveness: The authors conduct a cost-benefit analysis of the ELA program, examining both program expenditures and measured outcomes. The analysis considers: (i) fixed versus variable costs; (ii) first-year versus subsequent-year expenditures and (iii) costs per eligible adolescent girl. Program costs totaled $365,690 in the first year and $232,240 in subsequent years, with a fourth-year cost of $17.9 per eligible girl.

    The authors begin by stressing that quantifying the monetary effect of the ELA program is very challenging, as gains will mainly materialize over the life cycle. The study monetizes benefits through the intent-to-treat impact on annual earnings, finding a $50 increase per participant. Additional unquantified benefits include delayed marriage, improved vocational skills, and enhanced social empowerment.

    Cost-effectiveness is assessed through comparison with prior studies in development economics: (i) the Latin American Jovenes programs ($600-$2,000 per participant); and (ii) unconditional cash transfers ($374 per recipient). The ELA program demonstrates superior cost-effectiveness at $17.9 per eligible girl ($85 per participating girl given 21% take-up).

    The analysis shows the program’s benefits outweigh costs when considering both immediate earnings impacts and long-term empowerment effects.


Exercise 4.2

Idea:

  • To extend the original analysis, it is possible to examine whether the ELA program’s effect on aspirations differs depending on whether a girl continues to attend the club.
  • The motivation for this analysis stems from a desire to understand not just whether the ELA program improves girls’ aspirations, but how continuous engagement influences its effectiveness.
  • By examining this, it is possible to tailor interventions better to encourage ongoing participation, ensuring that resources are used efficiently and that girls receive the full benefits of the program.

\[ \text{Aspiration}_{ijt} = \alpha + \gamma_t \cdot \text{Treatment}_{ij} + \delta \cdot y_{ij0} + \beta \cdot X_{ij0} + \psi_1 \cdot \text{StillGoing}_{it} + \psi_2 \cdot (\text{Treatment}_{ij} \times \text{StillGoing}_{it}) + \varepsilon_{ijt} \]

Aspiration:

  • Aspiration is the dependent variable in this analysis because it represents the main outcome we want to understand - how girls’ self-belief changes.

Treatment:

  • The treatment variable indicates whether a girl comes from a community that received the ELA program.
  • This allows us to estimate the overall effect of the program on aspirations by comparing those exposed to the program with those who were not.

Treatment * StillGoing (Interaction Term):

  • Including the interaction between treatment and continued attendance lets us test if the impact of the program differs depending on whether the girl kept attending the club.
  • This interaction helps reveal whether continued attendance amplifies or changes the program’s effect on aspirations.

StillGoing:

  • This captures whether a girl continued to attend the ELA club meetings after initially joining.
  • This variable is important as it helps us understand if sustained participation influences the program’s effectiveness, under the idea that girls who stay engaged may benefit more.

Heterogeneity Analysis Using Interactions in Mathematical Terms:

We can illustrate how the interaction term captures treatment heterogeneity using partial derivatives:

  • Conditional Effect When StillGoing = 1 (i.e., participants who are still enrolled):

    \[ \left. \frac{\partial \text{Aspiration}_{ijt}}{\partial \text{Treatment}_{ij}} \right|_{\text{StillGoing}_{it} = 1} = \gamma_t + \psi_2 \]

    The treatment effect equals the main effect \(\gamma_t\) plus the interaction effect \(\psi_2\).

  • Conditional Effect When StillGoing = 0 (i.e., participants who dropped out):

    \[ \left. \frac{\partial \text{Aspiration}_{ijt}}{\partial \text{Treatment}_{ij}} \right|_{\text{StillGoing}_{it} = 0} = \gamma_t \]

    The interaction term drops out, and the treatment effect equals the main effect \(\gamma_t\) only.

These expressions confirm that \(\psi_2\) captures how the treatment effect differs between girls who are still enrolled in the program vs. those who are not.


Exercise 4.3

We estimate the following linear regression model to test the effect of the ELA program and continued attendance on girls’ aspirations:

\[ \text{Aspiration}_{ijt} = \alpha + \gamma_t \cdot \text{Treatment}_{ij} + \delta \cdot y_{ij0} + \beta \cdot X_{ij0} + \psi_1 \cdot \text{StillGoing}_{it} + \psi_2 \cdot (\text{Treatment}_i \times \text{StillGoing}_{it}) + \varepsilon_{ijt} \]

Our logic behind coding the extended regression model. For the sake of brevity, it was left out in the output file:

  • Estimated midline and endline regressions of the aspirations index, both with and without an interaction term between treatment status and school continuation (StillGoing).

  • Defined a coefficient map linking model terms to corresponding Greek letters following out notation (e.g., \(\psi_1\) and \(\psi_2\)).

  • Built a table using the custom create_custom_table() function to organize and display regression results side by side.

  • For each model, extracted relevant coefficients and formatted them with stars (based on significance) and standard errors in parentheses.

  • Appended model fit statistics (\(R²\), Adjusted \(R²\), \(N\)) and styled the output using kableExtra with grouped headers and footnotes for clarity.

See the accompanying .Rmd file for implementation details.

create_custom_table()
Table 4: Extended Regression Model Results for Aspirations Index
Midline Models
Endline Models
Parameter Midline (Original) Midline (Extended) Endline (Original) Endline (Extended)
α (Intercept) -0.229
(0.141)
0.379
(0.419)
-0.151
(0.135)
-0.139
(0.228)
γ (Treatment) 0.267***
(0.047)
0.314
(0.198)
0.081*
(0.048)
0.098
(0.139)
δ (Baseline Aspiration) 0.041**
(0.018)
0.009
(0.040)
-0.003
(0.018)
-0.111**
(0.045)
ψ₁ (StillGoing) 0.177
(0.286)
-0.157
(0.319)
ψ₂ (Treatment × StillGoing) -0.031
(0.299)
0.290
(0.337)
0.075 0.079 0.185 0.187
Adjusted R² 0.072 0.053 0.181 0.162
N 3380 513 2417 471
Note:
Standard errors in parentheses, clustered by village ID.
* p < 0.1, ** p < 0.05, *** p < 0.01
Age and branch controls included but not shown.

Impact of Extended Regression Model:

  • Sample Size Reduction: The inclusion of the StillGoing variable substantially reduces the sample size (e.g., from 3380 to 513 at midline), indicating the variable was only sparsely collected.

  • Decline in Adjusted \(R^2\): The extended models have lower adjusted \(R^2\) values (e.g., 0.072 → 0.053 at midline), suggesting weaker explanatory power once StillGoing and its interaction are added.

  • Treatment Effect Becomes Statistically Insignificant: In both midline and endline extended models, the treatment effect (\(\gamma\)) loses significance.

  • Interaction Term (\(\psi_2\)): The estimated coefficients for the interaction term are not statistically significant. This implies no strong evidence of different treatment effects based on whether girls are still enrolled.

  • Baseline Control Coefficient Changes: At endline, the coefficient on baseline aspirations (\(\delta\)) becomes larger in magnitude and statistically significant only in the extended model, possibly due to selection into the subsample with complete StillGoing data.


Exercise 5

Exercise 5.1

  1. Internal validity: The study demonstrates solid internal validity, referring to the soundness of causal links between independent and dependent variables, thanks to its robust randomized controlled trial setup. The authors allocated 100 communities to treatment and 50 to control, ensuring comparable characteristics in both groups before the intervention, reducing selection bias and supporting a causal association between the program and outcomes. The study’s sample, nearly 5,000 adolescent girls, further bolsters internal validity, permitting precise estimates and enhancing the detection of statistically significant effects. The researchers bolster this strength by showing baseline balance checks, confirming that variables like age, education, and employment status are comparable between treatment and control groups, validating the randomization. Additionally, they use an intent-to-treat (ITT) approach, incorporating all girls designated to the treatment group, regardless of participation level, thus maintaining random assignment integrity and preventing overstatement of the program’s effects.

  2. External validity: The study’s external validity, the extent to which its findings can be generalized outside the study setting, is quite strong in rural low-income contexts in Sub-Saharan Africa. The ELA program was initiated in Uganda, which has high fertility rates, low female labor force participation, and large gender gaps, features that are typical of most other developing settings. The basic model of the program, integrating life skills training, vocational training, and safe spaces for girls, was initially derived from the experience of BRAC in Bangladesh and has since motivated pilots in countries including Tanzania, South Sudan, Liberia and Afghanistan. This demonstrates that the design of the program is transferable in principle.


Exercise 5.2

  1. Complexity of the program: ELA program does a number of things simultaneously, job training, life skills classes, and safe spaces for girls. It is difficult to tell which component of the program leads to which outcomes. In future research, it may be beneficial to test each component separately with a particular kind of experiment. That way, we can figure out what works most effectively and how the components interact. This would assist governments and organizations in spending their funds more effectively.

  2. The long-term impact: The study demonstrates positive effects four years from baseline, but adolescent transitions, into marriage, motherhood, and the workforce, go well beyond this time. We are not sure whether these advantages persist into adulthood, such as when girls become mothers or enter the workforce. More long-term follow-up, for example following girls for 10 years, could determine whether these changes translate into long-term gains in livelihood.