Dependent Variable: Log monthly hours of PT

1 Tobit

Variables OLS

Characteristics Gender

school ranking 1 st quintile

School ranking 2 nd quintile

School ranking 4 th quintile

School ranking 5 th quintile

Family Log monthly income

Average years of

parents’ schooling

Number of children

School Private (=1)

Student-teacher ratio

School size: 300-500 rd

School size: 500 or more rd

High school under

Equalization Policy (=1)

Special Purpose

High school (=1)

Contextual effect Proportion of classmates

receiving PT service

Price Log hourly price of PT

Metropolitan cities

Constant 4.6137*** -5.8062*** 2.6856***

Lambda( λ )

Rho ( ρ )

-- 0.7429

Observations 2,515 3,562 3,601 2 R 2 / Pseudo R

Note. 1. Standard error in parentheses are adjusted for clustering on schools. 2. Standard errors in parentheses are adjusted for clustering on schools.

***p<.01 , **p<.05, * p<.1

TABLE 5. Conditional Moments Tests Results Dependent Variable: Log monthly expenditure on PT

Test Moment Restrictions t-statistics Omitted Variables 2 E( PRED ) = 0 44.37

3 E( PRED ) = 0 45.46

2 Heteroscedasticity 2 E ( Z

1 ( E ( u | y ) − σ ˆ )) = 0 30.19

2 ( E ( u | y ) − σ ˆ )) = 0 22.36

3 ( E ( u | y ) − σ ˆ 2 )) = 0 16.78

4 y ) − σ ˆ )) = 0 10.74

5 ( E ( u | y ) − σ ˆ )) = 0 7.69 E ( Z 6 ( E ( u 2 | y ) − 2 σ ˆ )) = 0 52.06

E ( Z 7 ( E ( u 2 | y ) − σ ˆ 2 )) = 0 51.45

8 ( E ( u | y ) − σ ˆ 2 )) = 0 47.63

9 ( E ( u | y ) − σ ˆ )) = 0 25.60 E ( Z 10 ( E ( u 2 | y ) − σ ˆ 2 )) = 0 35.00

11 ( E ( u | y ) − σ ˆ )) = 0 23.23 E ( Z 12 ( E ( u 2 | y ) − ˆ 2 σ )) = 0 51.36 E ( Z 13 ( E ( u 2 | y ) − ˆ 2 σ )) = 0 47.47

14 ( E ( u | y ) − σ ˆ )) = 0 10.25 E ( Z ( E ( u 2 | y ) − 15 2 σ ˆ )) = 0 53.36

16 ( E ( u | y ) − σ ˆ )) = 0 35.79 E ( Z 17 ( E ( u 2 | y ) − ˆ 2 σ )) = 0 18.07

Non-normality 3 E ( E ( u | y )) = 0 7.39 4 4 E ( E ( u | y ) − 3 σ ) = 0 5.58

i β ) × η ˆ ), PRED = ( x i β ˆ ) × η ˆ ), η is the gener ized residuals. al Note 2. Absolute values

2 ' ˆ 2 3 ' Note 3 1. PR ED = ( x

Note 3. Z

1 =Gende r, Z 2 = school ranking 1 quintile, Z 3 = School ranking 2 quintile, Z 4 =Sch ool ranking 4 quintile, Z

5 = School ranking 5 quintile, Z 6 =Log monthly income, Z 7 =Average years of parents’ schooling, Z 8 =Number of children, Z 9 =Private school, Z =School size:300 -500 3 rd 10 grade, Z 11 = School size:500 or more 3 rd grade, Z 12 = Teacher-student ra o, Z ti 13 =High scho ol unde r Equalization Policy, Z 14 =Special Purpose High School, Z 15 =Proportion of classmates recei ving PT service, Z 16 = Seoul, Z 17 = Metropolitan cities

TABLE 6. Conditional Moments Tests Results Dependent Variable: Log monthly hours of PT

Test Moment Restrictions t-statistics

2 Omitted Variables E( PRED ) = 0 0.01 3 E( PRED ) = 0 5.81

Heteroscedasticity E ( Z ( E ( u 1 2 | y ) − 2 σ ˆ )) = 0 10.19 E ( Z ( E ( u 2 | y ) − ˆ 2 2 σ )) = 0 10.48

E ( Z 3 ( E ( u 2 | y ) − ˆ 2 σ )) = 0 9.87

4 ( E ( u | y ) − σ ˆ )) = 0 5.99

5 ( E ( u | y ) − σ )) = 0 1.35

6 ( E ( u | y ) − σ ˆ )) = 0 19.39

7 ( E ( u | y ) − σ ˆ )) = 0 20.09 E ( Z ( E ( u 8 2 | y ) − σ ˆ 2 )) = 0 18.11

E ( Z 9 ( E ( u 2 | y ) − ˆ 2 σ )) = 0 10.34

10 ( E ( u | y ) − σ ˆ )) = 0 14.40 E ( Z E 11 2 ( ( u | y ) − ˆ 2 σ )) = 0 10.51

12 ( E ( u | y ) − σ ˆ )) = 0 19.15

13 ( E ( u | y ) − σ ˆ )) = 0 19.31

E ( Z 14 ( E ( u 2 | y ) − ˆ 2 σ )) = 0 2.83

15 ( E ( u | y ) − σ ˆ 2 )) = 0 22.20 E ( Z 16 ( E ( u 2 | y ) − σ ˆ 2 )) = 0 18.63

17 ( E ( u | y ) − σ ˆ 2 )) = 0 4.05

18 ( E ( u | y ) − σ ˆ )) = 0 18.05

Non-normality 3 E ( E ( u | y )) = 0 9.15 4 4 E ( E ( u | y ) − 3 σ ) = 0 13.14

i β ) × η ), PRED = ( x i β ˆ ) × η ˆ ), η is the generalized residuals. Note 2. Absolute values

Note 3 1. PR ED = ( x

Note3. Z =

1 Gender, Z 2 =school ranking 1 th quintile, Z 3 = School ran ing 2 k nd quintile, Z 4 =Scho ol ranking 4 th quintile, Z 5 =School ranking 5 quintile, Z 6 =Log monthly income, Z 7 =Aver age yea rs of parents’

rd grade, Z 11 = School size:500 or more 3 rd

schooling, Z 8 =Number of children, Z 9 =Private school, Z =School size:300

10 -500 3 grade, Z 12 =Student-teacher ra tio, Z 13 =High school u nde r Equalization Policy, Z 14 =Special Purpose High School, Z 15 =Proportion of classmates receiving PT service, Z 16 =

Seoul, Z 17 =Metropolitan cities, Z 18 =Price of PT

Dependent Variable: Log monthly hours of PT