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The Dependent Variable: Performance and School Progression in Urugua^y and Chile

The average results of PISA 2009 scores show statistically significant better results for Chilean students in science and reading tests. Mean results in science are 26 points higher in Chile than in Uruguay (0.3 standard deviations), while the same difference in reading scores is 30 points (0.35 standard deviations).On the other hand, the results in mathematics do not significantly differ, on average, between Chile and Uruguay. These results persist when comparing students of the same percentiles of individual socioeconomic status in both countries.[1] That is, at the same percentile of socioeconomic status, Chilean students perform better than Uruguayan students in science and reading, while no significant differences are found in mathematics test scores (see Table 5.5).

Moreover, Uruguay shows greater variance in test scores. The difference in test scores between the lowest and highest quartile of students ranked by socioeconomic status is much higher in Uruguay (107 points on average) than in Chile (84 points on average).

In addition, Chile shows a significantly higher degree of school progression at age 15 than does Uruguay. In Chile, 77 percent of students are enrolled in fourth grade or higher at the time they are tested by PISA, compared to 61 percent in Uruguay. Moreover, differences in school progression by individual socioeconomic status are dramatically higher in

Table 5.5 PISA 2009 tests scores in Uruguay and Chile, by quartile of index of socioeconomic status

PISA index of socioeconomic status

Test scores

Uruguay

Chile

Science

Maths

Reading

Science

Maths

Reading

1st quartile

Mean

375

375

372

417

385

412

S.D.

78

72

82

68

63

71

2nd quartile

Mean

404

405

403

434

409

438

S.D.

78

73

84

67

64

68

3rd quartile

Mean

437

437

435

457

430

462

S.D.

82

79

87

70

68

72

4th quartile

Mean

483

479

481

495

474

498

S.D.

87

84

93

78

78

78

Total

Mean

425

424

423

451

425

453

S.D.

91

87

96

77

76

79

Difference 4th-1st

108

105

109

78

89

86

Source: Elaborated by authors

Uruguay than in Chile. On the one hand, if we compare students from the highest quartile of socioeconomic status in both countries, we do not find significant differences in school progression, as the percentage of students in fourth grade or above is similar in Uruguay than in Chile (85 percent and 82 percent, respectively). But if we look at students in the lowest quartile of socioeconomic status, we find dramatic differences in school progression between both countries. While 70 percent of Chilean students are enrolled in fourth grade or above, only 39 percent of Uruguayan students are enrolled (see Table 5.6).

Also, nearly one-third of students in the lowest quartile of socioeconomic status show a lag of two grades or more (are in grade 2 or below at the time of the PISA test), while that percentage is only 6 percent for Chilean students. These features indicate much higher repetition rates among Uruguayan students across all levels of socioeconomic status, but particularly dramatic in the lowest two quartiles (see Table 5.6).

This aspect is very important since school progression is likely to have an impact on acquired cognitive skills. What follows attempts to discern how much of the observed differences in test results (particularly in reading and science) between Chile and Uruguay are due to students having

Table 5.6 Percentage of students in each grade by quartile of the index of socioeconomic status in Chile and Uruguay

PISA 2009

Grade attended by student

Uruguay

Chile

PISA index of

socioeconomic

status

Grade 2 or below

Grade

3

Grade 4 or upper

Total

Grade 2 or below

Grade

3

Grade 4 or upper

Total

1st quartile

Mean

32%

30%

39%

100%

6%

24%

70%

100%

2nd quartile

Mean

21%

29%

50%

100%

3%

20%

77%

100%

3rd quartile

Mean

12%

19%

69%

100%

3%

17%

80%

100%

4th quartile

Mean

5%

10%

85%

100%

1%

17%

82%

100%

Total

Mean

17%

22%

61%

100%

3%

20%

77%

100%

Difference 4th-1st

-26

-19

46

-5

-7

12

Source: Elaborated by authors based on data from PISA 2009

completed one or more school grades, and how much to other factors, including institutional features. But we have to note that the final interpretation of the results is not straightforward, as school progression is likely to be affected by the same features that affect test scores. For example, if a type of institutional framework has a positive impact on school performance (test scores), it is also likely to influence student school progression. Therefore, if we find an association between school progression and test results, it may reflect both a direct impact of school progression on achievement (greater exposure to class time and educational resources should have an impact on cognitive skills) and an indirect effect (the effect of unobserved school or institutional factors affecting both school progression and learning).

After controlling by individual characteristics, grade attended by student, and school inputs, how does Uruguay compare to Chile? Estimations indicate that the observed gross average difference in PISA 2009 science scores for Chile can be accounted for partly by differences in socioeconomic status of students in both countries and partly by differences in school progression of students. On average, students’ socioeconomic status is slightly higher in Chile than in Uruguay, while school progression is significantly better in Chile than in Uruguay. They also show that the observed difference in reading scores (for Chile) can be accounted for partly by differences in socioeconomic status, partly by differences in school progression, and partly by differences in characteristics of schools. If we compare students with the same individual characteristics, grade, and school characteristics, we observe better performance of Uruguayan students in mathematics.

Table 5.7 summarizes these findings. Individual controls include gender and the PISA index of socioeconomic status. Grade is a set of dummies indicating the grade attended by the student (2 or below, 3, 4, or above). School controls include the PISA index of quality of school resources, school size, a set of dummies describing school admission policies, school socioeconomic status, a set of dummies indicating private/public provision and private/public financing. The second set of columns in Table 5.7 shows the estimated coefficients for Uruguay after controlling for individual characteristics and grade attended by the student. Note that after controlling for these factors, there is no difference between Uruguayan and Chilean students in science. Finally, the last three columns of Table 5.7 report the estimated coefficients for Uruguay after controlling for individual characteristics, grade, and school characteristics.

The Oaxaca decomposition of the mean difference in test scores between Chile and Uruguay indicates that about nearly half the difference in results can be accounted for by greater internal efficiency (school progression at age 15) in Chile over Uruguay. In all cases, estimates indicate that if the ratio of students per grade in Uruguay resembled that of Chilean students, the difference in scores between Chile and Uruguay would be reduced by between 12 and 13.5 points, according to the test. This represents between 45 percent and 50 percent of the differences in science and reading.

Another important factor accounting for differences in mean scores is the difference in socioeconomic status. The decomposition shows that between about 7 and 10 point difference in average results can be accounted for by differences in socioeconomic status of students and schools, which constitutes approximately 30 percent of the observed differences in science and reading (Table 5.8).

In the case of mathematics, there is a large unexplained difference in test scores, which corresponds to the difference in favor of Uruguay if Uruguay had Chilean values of socioeconomic status, school progression, school characteristics, and assessed governance factors. However, this difference cannot be attributed to variables that can be assessed with the PISA data.

Table 5.7 Linear regression coefficients of test scores (LTruguay vs Chile)

Variables

Science

Maths

Reading

Science

Maths

Reading

Science

Maths

Reading

Uruguay

-15.94***

10.87***

-20.19***

-3.630

22.26***

-7.056**

-2.380

21.72***

-4.487

Individual

controls

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Grade

No

No

No

Yes

Yes

Yes

Yes

Yes

Yes

School

controls

No

No

No

No

No

No

Yes

Yes

Yes

Private-

public

No

No

No

No

No

No

Yes

Yes

Yes

Source: Elaborated by authors based on data from PISA 2009

Table 5.8 Decomposition of the mean difference in test score between Chile and Uruguay

Group variables

Science

endowment effect

Maths

(%)

Reading endowment effect

Endowment

effect

%

Male

0.53

2

0.96

-0.57

-2

Grade

12.94

50

11.64

13.66

46

Individual

socioeconomic status

1.91

7

1.82

2.02

7

School socioeconomic status

5.84

22

8.05

6.99

23

Other school characteristics

3.15

12

1.14

4.75

16

Unexplained

1.62

6

-22.61

3.16

11

Total difference in scores (Ch-Ury)

26

100

1

30

100

Source: Elaborated by authors

In sum:

  • • Chile shows levels of internal efficiency higher than Uruguay.
  • • Average results of PISA 2009 scores show statistically significant better results for Chilean students in science and reading tests.
  • • Results in mathematics do not significantly differ, on average, between Chilean and Uruguayan students. When controlling for student and school characteristics and grade, it is possible to observe better performance of Uruguay.
  • • The difference in test scores between the lowest and highest quar- tile of students ranked by socioeconomic status is much higher in Uruguay (107 points on average) than in Chile (84 points on average).
  • • Chile shows a degree of school progression at age 15 significantly higher than in Uruguay. In Chile, 77 percent of students are enrolled in fourth grade or higher at the time they are tested by PISA, compared to 61 percent in Uruguay.
  • • Differences in school progression by individual socioeconomic status are dramatically higher in Uruguay than in Chile. While 70 percent of Chilean students in the lowest quartile by socioeconomic status are enrolled in fourth grade or above, only 39 percent of Uruguayan students are enrolled.

  • [1] We ranked the students relative to the distribution of their own country.
 
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