## _wp09187

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---

### 7.5 percentage points. A closer look at the effect on enrollment ratios by gender and age

- Transition matrix and simulated impact on schooling choices
  - Table 11: transition from observed occupational choices (rows) to simulated choices after receiving the transfer (columns), eligible individuals only, based on 1000 simulations.
  - Original outcome (rows) and Predicted outcome (columns) counts:
    - Not school → Not school: 3,378
    - Not school → Work and school: 118
    - Not school → School only: 1,165
    - Not school total: 4,661
    - Work and school → Not school: 0
    - Work and school → Work and school: 1,551
    - Work and school → School only: 0
    - Work and school total: 1,551
    - School only → Not school: 0
    - School only → Work and school: 9
    - School only → School only: 10,816
    - School only total: 10,825
    - Total (original outcomes): 3,378, 1,678, 11,981, total 17,037
  - Note: All households in which the transfer would have surpassed the monthly limit were dropped at the outset of the analysis (2.7 percent of households).

- Randomization, pre–program balance, and sample notes
  - PROGRESA was implemented as a randomized experiment dividing households into treatment and control groups.
  - Randomization was generally successful; control and treatment groups do not exhibit large pre-program differences.
  - Pre-program enrollment differences by age and gender:
    - For boys (Table 12), differences between control and treatment in the eligible sample range from -0.6 to 4 percentage points and are generally not significant.
    - For girls (Table 13), one significant pre-program difference is noted where the treatment group exhibits a significantly lower value (-4.5 percent) in one category; another age category (13 years) shows the treatment group higher by 4 percent (not significant). Except for these two cases differences are negligible.
  - The comparison between school attendance before and after the program is confined to cross-section comparison between wave 5 (November 99) and waves 1 and 2.
  - Note: Table reports for each cell school enrolment ratios, the difference and the t-values. First wave only.

- Difference estimation (D) and difference-in-differences (DD) results
  - If randomization is successful, the DD estimator should coincide with the simple difference estimator (D). Given no significant pre-program differences and common shocks, the simple D estimator is sufficient.
  - Table 14 (Boys) — Difference estimator results by age:
    - Difference by age (10,11,12,13,14,15,16 and 10–16 aggregate): 0.017, 0.019, 0.050, 0.045, 0.040, 0.082, 0.041
    - Eligible sample difference (10–16 aggregate): 0.049
    - Reported t-values include: 2.52, 2.36, 3.69, 2.44, 1.79, 3.18, 1.60
    - Not-eligible differences examples: -0.003, 0.010, 0.041, -0.094, -0.041, 0.065, 0.031
  - Table 15 (Girls) — Difference estimator results by age:
    - Difference by age (10,11,12,13,14,15,16 and 10–16 aggregate): 0.001, 0.006, 0.061, 0.084, 0.077, 0.069, 0.058, aggregate 0.053
    - Eligible sample differences by age: -0.001, 0.013, 0.059, 0.081, 0.102, 0.098, 0.062, aggregate 0.061
    - Reported t-values include: 0.14, 0.62, 3.90, 4.16, 3.20, 2.64, 2.11, 6.26
    - Not-eligible differences examples: 0.015, -0.032, 0.079, 0.105, -0.042, -0.048, 0.041, 0.008
  - Comparison of D and DD:
    - The D and DD estimators produce very similar results, especially for girls.
    - A small kink in the DD estimate for 13 years old reflects pre-program differences in that age group.
    - For boys, the D estimate is slightly above the DD estimate but follows the same pattern.

- Magnitude and age pattern of effects
  - For eligible boys (last column reported in the text), the enrollment ratio has risen, on average, by 4.9 percentage points.
    - Increase most pronounced in age groups 13 to 15 years (up 8 points).
    - Lowest among 10 to 11 years old (2 percentage points).
  - For girls, the average effect was higher at 6.1 percentage points.
    - Among the eligible the effect was highest for 13 to 15 years old and lowest in the youngest age group, where it is also insignificant.

- Comparison of ex ante simulation and ex post results
  - The trichotomous choice variable is reduced to a binary indicator of whether a child attends school or not for comparison.
  - The simulation results, the difference estimator, and the difference-in-differences estimator are presented by gender and age in Table 16; Figure 2 shows graphical results with 90 percent confidence intervals.
  - In general:
    - While the difference estimator puts the increase in overall school enrollment ratio at 5.4 percentage points, the simulated effect is estimated to be somewhat higher.

### 8.1 percentage points. The deviations seem to be highest for the age group of 15 and 16

- Simulation performance and overall conclusions
  - The microsimulation correctly predicts that school enrollment ratios among the target population will increase as a result of a cash payment for school attendance.
  - The model is a valuable tool to assess the effects of conditional cash transfer schemes which, by increasing educational attainment, are also likely to reduce poverty in the long run.
  - The discrete model of occupational choice allows for three outcomes: attend school, work, or do both, and explicitly considers actual and potential market earnings of each child.
  - Two main shortcomings identified:
    - The simulation does not perform well when the population is unequally distributed over the three categories of the dependent variable.
    - The model does not capture well the transition to secondary school.

- Age and gender patterns; deviations between simulated and actual effects
  - 8.1 percentage points. The deviations seem to be highest for the age group of 15 and 16 years.
  - In 9 of the 14 gender/age subgroups the actual effect is within a 90 percent confidence interval of the simulation.
  - The simulated and the real effect follow a similar pattern across ages and gender; the model seems to capture the underlying age-gender differences well.
  - Simulation results by age groups:
    - Simulation results are close to the actual for middle age group (ages 12-14); differences for the young age group are also small, but significant.
    - Deviations between simulation and actual effect are largest for the eldest group (ages 15 and 16).
  - Example of misprediction at the transition to secondary school:
    - For 16 years olds that have completed primary school, actual enrollment ratio increased from 9 to 12 percent during PROGRESA, whereas the model would predict an increase to 25 percent.

- Child labor incidence and occupational outcomes
  - The estimated transition matrix (Table 11) indicates the program will also reduce the incidence of child labor.
  - Some 90 percent of the children that are predicted to resume schooling are also predicted not to participate in the labor market, whereas 16 will do both, go to school and work.
  - The poor predictive power of the multinomial choice model for some age/choice combinations negatively affects the overall result of the simulation.
  - Distributional imbalance examples:
    - Among 10 and 11 years, one outcome is clearly dominating and the fraction of children that work but do not go to school is very small.
    - Among 15 to 16 years old, the fraction of those who “work and go to school” is very small.
  - Specific count noted: of the (1,165+118) children that will attend school, 1,165 will not work.

- Sensitivity of simulation to parameter K (Table 16)
  - The simulation is robust to various choices of K. Simulations for smaller K lead to smaller effects, but the impact of K is small relative to the difference between the overall simulation and the actual effect.
  - Selected exact figures reported in Table 16 (enrolment ratios at the beginning and impacts):
    - Boys Before: 0.974 0.953 0.885 0.788 0.646 0.476 0.361 0.726
      - Simulated impact: 0.022 0.044 0.033 0.054 0.062 0.158 0.118 0.070
      - D impact: 0.02 0.02 0.051 0.070 0.054 0.085 0.044 0.049
      - DD impact: 0.024 0.016 0.046 0.028 0.026 0.062 0.015 0.031
    - Girls Before: 0.967 0.953 0.815 0.687 0.538 0.389 0.271 0.660
      - Simulated impact: 0.027 0.046 0.061 0.087 0.103 0.191 0.127 0.092
      - D impact: -0.001 0.013 0.059 0.081 0.102 0.098 0.062 0.059
      - DD impact: -0.016 0.014 0.091 0.063 0.116 0.101 0.021 0.056
    - Total Before: 0.971 0.953 0.85 0.738 0.592 0.433 0.316 0.693
      - Simulated impact: 0.024 0.045 0.047 0.071 0.083 0.174 0.123 0.081
      - D impact: 0.009 0.017 0.055 0.075 0.078 0.091 0.053 0.054
      - DD impact: 0.004 0.015 0.068 0.046 0.071 0.081 0.018 0.043
    - Total Simulated impact (K = 1): 0.024 0.045 0.047 0.071 0.083 0.174 0.123 0.081
    - Total Simulated impact (K = 0.75): 0.025 0.044 0.046 0.075 0.080 0.168 0.124 0.080
    - Total Simulated impact (K = 0.5): 0.024 0.045 0.042 0.078 0.078 0.158 0.123 0.078

- Transition to secondary school (Table 17 observations)
  - Estimation does not capture the transition to secondary school well. Differences between the simulation and actual effect are largest among those who have just completed primary school.
  - Extracted enrollment ratio observations from Table 17 (cross-tabulation of age and education, actual and simulated) include values: 92.6, 63, 9.3, 0.7, 5.6, 98.5 97.1 94.6 91.2 78.2 94.0, 96.5 97.9 96.0 84.5 74.7 93.0, 96.3, 96.1 96.1 92.0 87.2 93.3, 94.9 91.1 79.1 52.3 22.9 89.0, 96.9 93.6 80.3 57.9 31.8 92.8, 96.1 93.1 85.4 69.4 42.0, 73.1 51.7 29.7 19.7 8.9 3.3, 81.8 64.0 38.6 21.4 11.9 5.0, 81.1 64.7 44.8 46.8 25.5, 99.0 98.0 96.5 94.7 87.2, 98.8 96.9 90.9 86.8 93.9, 97.2 98.1 95.3 91.7 96.0
  - Note: Table 17 is a cross tabulation of age and education, indicating for each cell the actual and simulated enrollment ratios.

- Methodological notes
  - Confidence intervals obtained using the bootstrap mechanism outlined in Appendix D.
  - Bootstrap algorithm summary:
    - Step 1: Compute the original sample estimates: estimation of equations (4) and simulation of the program.
    - Step 2: Draw with replacement a new sample containing as many observations as the original sample and compute all estimates described in step 1.
    - Step 3: Repeat step 2 for 1000 times collecting the predicted values of the age/gender specific impact. Drop the upper and lower five percentile of this distribution.
    - Step 4: Use the distribution of values obtained in step 3 to obtain confidence intervals around the estimates obtained in step 1.
  - For drawing choice-consistent residuals the inverse of the conditional c.d.f. (derived from the double exponential distribution assumption) is used; random numbers are drawn from [0,1] and transformed as specified in Appendix C.

- Suggested model improvements (concluding remarks)
  - Consider a microsimulation method for a dichotomous framework (binary choice) as an extension to improve forecasting abilities with respect to school enrollment ratios; this may come at the cost of losing features such as the effect of the program on the amount worked.
  - Improve modeling of the transition to secondary school to better match observed increases in enrollment among those who have just completed primary school.

*Source: _wp09187 - 7.5 percentage points. A closer look at the effect on enrollment ratios by gender and age; _wp09187 - 8.1 percentage points. The deviations seem to be highest for the age group of 15 and 16*

### 7.5 percentage points. A closer look at the effect on enrollment ratios by gender and age

### 7.5 percentage points. A closer look at the effect on enrollment ratios by gender and age

### Transition matrix and simulated impact on schooling choices
- Table 11 shows the transition from observed occupational choices (rows) to simulated choices after receiving the transfer (columns), eligible individuals only, based on 1000 simulations.
- Original outcome (rows) and Predicted outcome (columns) counts:
  - Not school → Not school: 3,378
  - Not school → Work and school: 118
  - Not school → School only: 1,165
  - Not school total: 4,661
  - Work and school → Not school: 0
  - Work and school → Work and school: 1,551
  - Work and school → School only: 0
  - Work and school total: 1,551
  - School only → Not school: 0
  - School only → Work and school: 9
  - School only → School only: 10,816
  - School only total: 10,825
  - Total (original outcomes): 3,378, 1,678, 11,981, total 17,037
- Note: All households in which the transfer would have surpassed the monthly limit were dropped at the outset of the analysis (2.7 percent of households).

### Randomization, pre–program balance, and sample notes
- PROGRESA was implemented as a randomized experiment dividing households into treatment and control groups.
- Randomization was generally successful; control and treatment groups do not exhibit large pre-program differences.
- Pre-program enrollment differences by age and gender:
  - For boys (Table 12), differences between control and treatment in the eligible sample range from -0.6 to 4 percentage points and are generally not significant.
  - For girls (Table 13), one significant pre-program difference is noted where the treatment group exhibits a significantly lower value (-4.5 percent) in one category; another age category (13 years) shows the treatment group higher by 4 percent (not significant). Except for these two cases differences are negligible.
- The comparison between school attendance before and after the program is confined to cross-section comparison between wave 5 (November 99) and waves 1 and 2.
- Note: Table reports for each cell school enrolment ratios, the difference and the t-values. First wave only.

### Difference estimation (D) and difference-in-differences (DD) results
- If randomization is successful, the DD estimator should coincide with the simple difference estimator (D). Given no significant pre-program differences and common shocks, the simple D estimator is sufficient.
- Table 14 (Boys) — Difference estimator results by age:
  - Difference by age (10,11,12,13,14,15,16 and 10–16 aggregate): 0.017, 0.019, 0.050, 0.045, 0.040, 0.082, 0.041
  - Eligible sample difference (10–16 aggregate): 0.049
  - Reported t-values include: 2.52, 2.36, 3.69, 2.44, 1.79, 3.18, 1.60 (cell-by-cell t-values corresponding to differences)
  - Full sample and not-eligible cells reported; not-eligible differences are generally small and often insignificant (e.g., -0.003, 0.010, 0.041, -0.094, -0.041, 0.065, 0.031)
- Table 15 (Girls) — Difference estimator results by age:
  - Difference by age (10,11,12,13,14,15,16 and 10–16 aggregate): 0.001, 0.006, 0.061, 0.084, 0.077, 0.069, 0.058, aggregate 0.053
  - Eligible sample differences by age: -0.001, 0.013, 0.059, 0.081, 0.102, 0.098, 0.062, aggregate 0.061
  - Reported t-values include: 0.14, 0.62, 3.90, 4.16, 3.20, 2.64, 2.11, 6.26 (cell-by-cell t-values corresponding to differences)
  - Not-eligible differences are generally small and often insignificant (e.g., 0.015, -0.032, 0.079, 0.105, -0.042, -0.048, 0.041, 0.008 with corresponding t-values)
- Comparison of D and DD:
  - The D and DD estimators produce very similar results, especially for girls.
  - A small kink in the DD estimate for 13 years old reflects pre-program differences in that age group.
  - For boys, the D estimate is slightly above the DD estimate but follows the same pattern.

### Magnitude and age pattern of effects
- For eligible boys (last column reported in the text), the enrollment ratio has risen, on average, by 4.9 percentage points.
  - Increase most pronounced in age groups 13 to 15 years (up 8 points).
  - Lowest among 10 to 11 years old (2 percentage points).
- For girls, the average effect was higher at 6.1 percentage points.
  - Among the eligible the effect was highest for 13 to 15 years old and lowest in the youngest age group, where it is also insignificant.

### Comparison of ex ante simulation and ex post results
- The trichotomous choice variable is reduced to a binary indicator of whether a child attends school or not for comparison.
- The simulation results, the difference estimator, and the difference-in-differences estimator are presented by gender and age in Table 16; Figure 2 shows graphical results with 90 percent confidence intervals.
- In general:
  - While the difference estimator puts the increase in overall school enrollment ratio at 5.4 percentage points, the simulated effect is estimated to be somewhat higher.

*Source: _wp09187 - 7.5 percentage points. A closer look at the effect on enrollment ratios by gender and age*

### 8.1 percentage points. The deviations seem to be highest for the age group of 15 and 16

### _wp09187 - 8.1 percentage points. The deviations seem to be highest for the age group of 15 and 16

### Simulation performance and overall conclusions
- The microsimulation correctly predicts that school enrollment ratios among the target population will increase as a result of a cash payment for school attendance.
- The model is a valuable tool to assess the effects of conditional cash transfer schemes which, by increasing educational attainment, are also likely to reduce poverty in the long run.
- The discrete model of occupational choice allows for three outcomes: attend school, work, or do both, and explicitly considers actual and potential market earnings of each child.
- Two main shortcomings identified:
  - The simulation does not perform well when the population is unequally distributed over the three categories of the dependent variable.
  - The model does not capture well the transition to secondary school.

### Age and gender patterns; deviations between simulated and actual effects
- 8.1 percentage points. The deviations seem to be highest for the age group of 15 and 16 years.
- In 9 of the 14 gender/age subgroups the actual effect is within a 90 percent confidence interval of the simulation.
- The simulated and the real effect follow a similar pattern across ages and gender; the model seems to capture the underlying age-gender differences well.
- The simulation results by age groups:
  - The simulation results are close to the actual for middle age group (ages 12-14), the differences for the young age group are also small, but significant.
  - The deviations between simulation and actual effect are largest for the eldest group (ages 15 and 16).
- Example of misprediction at the transition to secondary school:
  - For 16 years olds that have completed primary school, actual enrollment ratio increased from 9 to 12 percent during PROGRESA, whereas the model would predict an increase to 25 percent.

### Child labor incidence and occupational outcomes
- The estimated transition matrix (Table 11) indicates the program will also reduce the incidence of child labor.
- Some 90 percent of the children that are predicted to resume schooling are also predicted not to participate in the labor market, whereas 16 will do both, go to school and work.
- The poor predictive power of the multinomial choice model for some age/choice combinations negatively affects the overall result of the simulation.
- Distributional imbalance example:
  - Among 10 and 11 years, one outcome is clearly dominating and the fraction of children that work but do not go to school is very small.
  - Among 15 to 16 years old, the fraction of those who “work and go to school” is very small.
- Specific count noted: of the (1,165+118) children that will attend school, 1,165 will not work.

### Sensitivity of simulation to parameter K (Table 16)
- The simulation is robust to various choices of K. Simulations for smaller K lead to smaller effects, but the impact of K is small relative to the difference between the overall simulation and the actual effect.
- Selected exact figures reported in Table 16 (enrolment ratios at the beginning and impacts):
  - Boys Before: 0.974 0.953 0.885 0.788 0.646 0.476 0.361 0.726
    - Simulated impact: 0.022 0.044 0.033 0.054 0.062 0.158 0.118 0.070
    - D impact: 0.02 0.02 0.051 0.070 0.054 0.085 0.044 0.049
    - DD impact: 0.024 0.016 0.046 0.028 0.026 0.062 0.015 0.031
  - Girls Before: 0.967 0.953 0.815 0.687 0.538 0.389 0.271 0.660
    - Simulated impact: 0.027 0.046 0.061 0.087 0.103 0.191 0.127 0.092
    - D impact: -0.001 0.013 0.059 0.081 0.102 0.098 0.062 0.059
    - DD impact: -0.016 0.014 0.091 0.063 0.116 0.101 0.021 0.056
  - Total Before: 0.971 0.953 0.85 0.738 0.592 0.433 0.316 0.693
    - Simulated impact: 0.024 0.045 0.047 0.071 0.083 0.174 0.123 0.081
    - D impact: 0.009 0.017 0.055 0.075 0.078 0.091 0.053 0.054
    - DD impact: 0.004 0.015 0.068 0.046 0.071 0.081 0.018 0.043
  - Total Simulated impact (K = 1): 0.024 0.045 0.047 0.071 0.083 0.174 0.123 0.081
  - Total Simulated impact (K = 0.75): 0.025 0.044 0.046 0.075 0.080 0.168 0.124 0.080
  - Total Simulated impact (K = 0.5): 0.024 0.045 0.042 0.078 0.078 0.158 0.123 0.078

### Transition to secondary school (Table 17 observations)
- The estimation does not capture the transition to secondary school well. Differences between the simulation and actual effect are largest among those who have just completed primary school.
- Extracted enrollment ratio observations from Table 17 (cross-tabulation of age and education, actual and simulated):
  - Enrollment ratio (wave 1) and (wave 5) and (simulated) shown across age/education cells with values including: 92.6, 63, 9.3, 0.7, 5.6, 98.5 97.1 94.6 91.2 78.2 94.0, 96.5 97.9 96.0 84.5 74.7 93.0, 96.3, 96.1 96.1 92.0 87.2 93.3, 94.9 91.1 79.1 52.3 22.9 89.0, 96.9 93.6 80.3 57.9 31.8 92.8, 96.1 93.1 85.4 69.4 42.0, 73.1 51.7 29.7 19.7 8.9 3.3, 81.8 64.0 38.6 21.4 11.9 5.0, 81.1 64.7 44.8 46.8 25.5, 99.0 98.0 96.5 94.7 87.2, 98.8 96.9 90.9 86.8 93.9, 97.2 98.1 95.3 91.7 96.0
  - Note: Table 17 is a cross tabulation of age and education, indicating for each cell the actual and simulated enrollment ratios.

### Methodological notes
- Confidence intervals were obtained using the bootstrap mechanism outlined in Appendix D.
- Bootstrap algorithm summary:
  - Step 1: Compute the original sample estimates: estimation of equations (4) and simulation of the program.
  - Step 2: Draw with replacement a new sample containing as many observations as the original sample and compute all estimates described in step 1.
  - Step 3: Repeat step 2 for 1000 times collecting the predicted values of the age/gender specific impact. Drop the upper and lower five percentile of this distribution.
  - Step 4: Use the distribution of values obtained in step 3 to obtain confidence intervals around the estimates obtained in step 1.
- For drawing choice-consistent residuals the inverse of the conditional c.d.f. (derived from the double exponential distribution assumption) is used; random numbers are drawn from [0,1] and transformed as specified in Appendix C.

### Suggested model improvements (from concluding remarks)
- Consider a microsimulation method for a dichotomous framework (binary choice) as an extension to improve forecasting abilities with respect to school enrollment ratios; this may come at the cost of losing features such as the effect of the program on the amount worked.
- Improve modeling of the transition to secondary school to better match observed increases in enrollment among those who have just completed primary school.

*Source: _wp09187 - 8.1 percentage points. The deviations seem to be highest for the age group of 15 and 16*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09187.pdf_