# Peer Effects, Teacher Incentives, and the Impact of Tracking

1. Read the introduction (first 4 pages) of Peer Effects, Teacher Incentives, and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya by Duflo, Dupas and Kremer (DDK).
a) Provide one theoretical reason that student ability tracking could hurt low ability students [1-2 sentences].
b) Provide one theoretical reason that student ability tracking could help low ability students.[1-2 sentences].
Now look at the theoretical test score production function in section 1 that we discussed in class. [1-2 sentences each].
c) What is f(X-ij)?
d) What is g(e)?
e) What is h(x*-xi)?
2. Comparing Group Means: For parts a-d, report both the appropriate subgroup averages and the difference(s) between the treatment (tracking=1) and control (tracking=0) group averages. NOTE: this homework uses data from only students of regular, civil service teachers, and does not use any data from students of “contract” teachers, so you can ignore that part of the paper.
For a-c, also fill in Table 1 (provided below)
a) What was the average effect of ability tracking on test scores for the full sample? On average, did tracking improve test scores? [1-2 sentences]
b) Given your results in Table 1, did High or Low track students as a group do best under tracking? Why could that be? To answer, write 3-4 sentences on how some part of theoretical test score production function can help explain why this group did well.
c) Given your answer in (b), why might the other ability group have done worse? To answer, write 3-4 sentences on how some part of theoretical test score production function can help explain why this group did poorly.
2. Effects Across Pre-score
a) Generate two scatter plots, one for “low track” (Figure 1) and one for “high track” (Figure 2), with pre-score on the X-axis and test-score on the Y-axis, using different colored symbols for the treatment and control group students in each graph. Add 2 “best fit lines” to each graph, one for treatment group and one for control – excel has an option to do this automatically.
b) At each ability level, as defined by pre-score, what is the vertical difference between the treatment and control group best-fit lines telling you about the effects of tracking? Within each track, is the treatment effect the same across pre-score (meaning do the best and worst kids within the low track experience different treatment effects? In the high track?)
4. Quantile Treatment Effects in the Low Track: Estimate the 10th, 20th, 30th…90thand 99thpercentiles of the test score distribution separately for the treatment and control groups of onlyLOW TRACK students or low track eligible students (low_ability=1).
a) For each of the 10 deciles, of the test-score distribution,fill in Table 2 with the treatment and control group scores for that decile.
Display your estimates in Table 2 (provided below).
b) The “difference” column in this table is an estimate of the “quantile treatment effect” – how much the 30th or 80th percentile of the treatment group is relative the corresponding percentile of the control group distribution.Make a “line graph” (connecting the dots from 10th to 20th to 30th…) of the quantile treatment effects (the “difference” column in Table 2) with quantile on the X-axis and difference on the Y-axis and label it Figure 3. The graph will have 9 points on it, one for each row of Table 2.
c) Write 4-5 sentences interpreting Figure 3(effect across test-score) relative to Figure 2 (effect across pre-score). Is Figure 3 just representing the difference between the two lines in Figure 2? Or is it representing something else? What does Figure 3suggest about the effects of ability tracking?
5. Conclude:
Given all of your results, is tracking overall good or bad? Or is it good for some students and bad for others?Are Figure 2 and Figure 3 telling you the same thing? Write 2 Paragraphs discussing the impact of school tracking in Kenya on students’ test scores and learning. In each paragraph, refer to at least one of the results you have calculated in this exercise.
Data Codebook:
test_score: outcome test score (41 points possible, given in total points)
pre_score: pre-intervention score (0-100; given in percentiles)
low_ability: 1 if student was below median in pre_score (low ability), 0 if student above median (high ability). This determines if a student was eligible for the low track or the high track, regardless of whether their school implemented tracking.
tracking: 1 if student in treatment group (tracking school), 0 if student in control group (non-tracking school).
Table 1: Sub-Group Treatment Effects
Sub-Group Control Treatment Difference
(1) Full Sample
(2) High Ability
(3) Low Ability
Table 2: Quantile Treatment Effects in Low Track
Test-Score Percentile Control Group Treatment Group Difference
10th Percentile
20th Percentile
30th Percentile
40th Percentile
50th Percentile
60th Percentile
70th Percentile
80th Percentile
90th Percentile
99th Percentile