econometrics question and answer

8/19/2019 Econometrics Question and Answer

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Question 6.

Tennessee's Student Teacher Achievement Ratio (STAR) project was a large-

scale, four-year eperimental study designed to evaluate the e!ect on

learning of reduced class si"es# The study compared three alternative class

si"e arrangements for $indergarten through %rade &• regular class si"e, with to students per class, a single teacher

and no aides

• small class si"e, with *&-*+ students per class and no aide

• regular class si"e plus a teachers aide#

Refer to the documents in folder .uestion / for more information# Read the

data description carefully as you need to understand how di!erent varia0les

are constructed and what di!erent values they ta1e# Some of these varia0les

you are going to use 0elow have missing values that you need to eclude

when you are analy"ing the data#

(A) 2se the dataset star/ and report simple di!erences estimates of the

impact of the two treatments relative to the 0ase case of a regular class si"e

with no teachers aide for students attending project STAR classes# 2se as an

outcome measure the students com0ined score on the math and reading

portions of the Stanford Achievement Test# Show these results for each grade

level (i#e# 1indergarten, grade*, grade, grade&) in a ta0le, together with

standard errors# 3ndicate which estimates are statistically signi4cant at the

*5 and 5 signi4cance levels# Also report the sample si"es in the ta0le#

PartA(1) (2) (3) (4)

Kindergarten Grade1 Grade2 Grade3

Small Class 13.90*** 29.78*** 19.39*** 15.59***

(2.409) (2.807) (2.710) (2.395)eg!lar Class "it# $ea%#er Aide 0.314 11.9&*** 3.479 '0.291

(2.310) (2.&8&) (2.5&&) (2.302)

N 578& &379 &049 59&7

R2 0.007 0.017 0.009 0.010Standard errrs in arent#eses* p 0.10+ ** p 0.05+ *** p 0.01

(6) Add controls for gender, race, 7uarter of 0irth, school type and socio-

economic status in regressions for each grade level, and report in a ta0le the

same set of impact estimates as reported in part (A)# 3nterpret your

estimated coe8cients for these control varia0les# Are there any statistically

signi4cant di!erences 0etween the estimated treatment e!ects without

controls and those with controls for di!erent grades9 :hat do you infer from



the di!erences (or a0sence of di!erences) 0etween these two sets of

estimated impacts9

(1) (2) (3) (4)


Small Class 14.95*** 22.72*** 13.09*** 8.753***

(3.182) (3.5&5) (3.577) (3.324)eg!lar Class , Aide '0.0909 &.589* 2.899 '0.342

(3.117) (3.&74) (3.&52) (3.412)

-emale 9.024*** &.198** &.77&** &.4&5**

(2.578) (2.938) (2.871) (2.&0&)

#ite '83.85* '&&.51 '123.8** '&3.07

(4&.58) (53.84) (52.&&) (47.17)

/la% '103.1**

'89.35*

'158.0***

'89.5&*

(4&.81) (54.10) (52.90) (47.40)

Asian '120.0** '44.&& '82.04 '50.&1

(52.83) (&1.09) (59.73) (53.50)isani% '75.01 24.03 '105.2 '13.32

(&5.80) (7&.07) (74.40) (&&.&4)

1st !arter - /irt# '8.&08** '9.143** '5.251 '&.893*

(3.724) (4.2&2) (4.158) (3.777)

2nd !arter - /irt# '19.8&*** '17.28*** '10.09** '7.481**

(3.742) (4.28&) (4.181) (3.791)3rd !arter - /irt# '29.53*** '2&.24*** '18.43*** '13.21***

(3.757) (4.277) (4.1&7) (3.803)nner Cit S%#l '2.904 '39.94*** '18.05** '9.&&3

(7.499) (8.54&) (8.35&) (7.57&)S!!ran S%#l '8.453 '17.45** '10.29 '5.377

(&.332) (7.2&3) (7.102) (&.41&)

6ran S%#l '14.11** '7.280 1.&98 '4.480(5.813) (&.&9&) (&.558) (5.90&)

ree !n%# '24.9&*** '42.21*** '34.13*** '33.14***

(3.104) (3.528) (3.435) (3.158)

N 2&17 2&97 2&9& 2&29

R2 0.095 0.202 0.171 0.13&

Regarding the e!ect of small class si"e, the estimated coe8cients for

$indergarten students dont change much, 0ut for all other grades they

decrease signi4cantly across the 0oard when we add the controls to the

model# This suggests that part of the 0etter performance of students in

smaller classes has to do with the o0served characteristics that are



correlated with class si"e# 3n other words, students in smaller classes tend to

have 0etter characteristics that eplain part of their 0etter performance#

Regarding the e!ect of regular class si"e with teacher aide, the only

coe8cient that changes signi4cantly is the one for grade*, which suggests

the same thing argued a0ove#

(;) :rite down the regression e7uation you would run to estimate whether

the e!ect of the two treatments is di!erent for 0lac1 versus white students

(<int 1eep in mind that there are races other than 0lac1 and white in the

data# :e want those o0servations to 0e included in the regressions, 0ut we

only want to compare the 0lac1s and whites# =ne way to do this is to lump all

other races into one category (using an indicator) and including them as one

group (e#g# other races) in your regression)#>or each grade level, run this regression (use the same control varia0les as

in part 6)# Report your results in a new ta0le# 3nterpret your results#

test score=α + β0small+ β

1aide+ β

2(¿∗regular )+ β

3(¿∗small )+ β

4(¿∗aide )+ β

5 (other∗regular )+ β

6 (other

• white in regular class ? α

• white in small class ? α + β0

• white in class with aide ? α + β1

• 6lac1 in regular class ? α + β2

• 6lac1 in small class ? α + β0+ β

3

• 6lac1 in class with aide ? α + β1+ β

4

(1) (2) (3) (4)Kindergarten Grade1 Grade2 Grade3

Small Class 1&.47*** 21.35*** 12.25*** 8.09&**

(3.&9&) (4.245) (4.2&2) (3.942)

eg!lar "it# Aide 1.403 10.02** 4.7&1 0.479

(3.&35) (4.257) (4.279) (4.005)/la% * eg!lar '15.&7** '20.75*** '33.50*** '2&.83***

(&.235) (&.81&) (7.102) (&.7&3)

/la% * Small '20.77*** '15.74** '29.&7*** '23.85***

(&.2&3) (&.733) (&.423) (5.759)/la% * Aide '20.77*** '35.97*** '40.18*** '29.51***

(&.095) (7.577) (&.9&9) (&.319)

t#er * eg!lar '3.885 23.40 88.3&** 40.7&



(33.0&) (34.1&) (43.10) (38.&4)

t#er * Small '3.&&0 43.21 35.40 2&.9&

(33.10) (38.18) (33.42) (29.93)t#er * Aide '12.45 91.7&* 45.74 18.97

(38.13) (53.90) (43.09) (38.&0)

-emale 9.033***

5.934**

&.829**

&.423**

(2.582) (2.939) (2.872) (2.&08)

1st !arter - /irt# '8.809** '9.24&** '5.420 '7.032*

(3.729) (4.2&4) (4.1&1) (3.780)2nd !arter - /irt# '20.13*** '17.38*** '10.33** '7.&51**

(3.748) (4.291) (4.184) (3.795)

3rd !arter - /irt# '29.49*** '2&.30*** '18.45*** '13.21***

(3.7&2) (4.278) (4.172) (3.80&)nner Cit S%#l '2.&11 '39.50*** '18.17** '9.534

(7.513) (8.551) (8.3&1) (7.583)

S!!ran S%#l '8.409 '17.23** '10.40 '5.29&

(&.347) (7.2&7) (7.108) (&.421)6ran S%#l '13.75** '7.0&1 1.&30 '4.3&1

(5.822) (&.&91) (&.5&5) (5.911)ree !n%# '25.12*** '41.99*** '34.28*** '33.1&***

(3.110) (3.528) (3.438) (3.1&0)

N 2&17 2&97 2&9& 2&29 R2 0.094 0.204 0.171 0.13&

(@) :rite down the regression e7uation you would run to estimate whether

the e!ect of the two treatments is di!erent for male versus female students#

>or each grade level, run this regression (use the same control varia0les as

in part 6)# Report your results in a new ta0le# 3nterpret your results#

test score=α + β0small+ β

1aide+ β

2(female∗regular )+ β

3 (female∗small )+ β

4 (female∗aide )+γX +ϵ

• ale in regular class ? α

• ale in small class ? α + β0

• ale in class with aide ? α + β1

• >emale in regular class ? α + β2

• >emale in small class ? α + β0+ β3

• >emale in class with aide ? α + β1+ β

4

(1) (2) (3) (4)


Small Class 22.3&*** 2&.44*** 14.24*** 11.29**

(4.580) (5.175) (5.128) (4.854)



eg!lar , Aide 2.&10 1.717 '1.029 '4.443

(4.4&9) (5.2&5) (5.230) (4.953)

emale * eg!lar 15.25*** 5.&57 5.047 5.&27(4.397) (5.130) (5.337) (5.201)

emale * Small 0.932 '1.&34 2.750 0.&77

(4.595) (4.91&) (4.&81) (4.108)emale * Aide 10.21** 15.&2*** 12.80** 13.77***

(4.415) (5.234) (4.9&7) (4.421)

#ite '81.54* '&2.30 '121.4** '59.89(4&.58) (53.83) (52.&8) (47.17)

/la% '100.3** '85.00 '155.5*** '8&.27*

(4&.81) (54.10) (52.93) (47.40)

Asian '117.&** '39.12 '79.24 '4&.&9(52.85) (&1.09) (59.77) (53.51)

isani% '7&.77 24.45 '104.7 '12.98

(&5.7&) (7&.02) (74.40) (&&.&1)

1

st

!arter - /irt# '8.3&0

**

'8.745

**

'5.0&4 '&.&05

*

(3.724) (4.2&2) (4.1&0) (3.778)

2nd !arter - /irt# '19.80*** '17.12*** '9.979** '7.328*

(3.742) (4.284) (4.182) (3.790)

3rd !arter - /irt# '29.20*** '25.91*** '18.29*** '12.99***

(3.759) (4.27&) (4.1&8) (3.802)

nner Cit S%#l '3.&40 '39.9&*** '18.24** '9.893(7.502) (8.540) (8.35&) (7.573)

S!!ran S%#l '8.854 '17.04** '10.10 '5.321

(&.332) (7.2&2) (7.103) (&.413)6ran S%#l '14.32** '7.077 1.718 '4.5&4

(5.811) (&.&92) (&.557) (5.903)

ree !n%# '24.8&*** '41.98*** '33.92*** '33.03***

(3.107) (3.52&) (3.437) (3.157)

N 2&17 2&97 2&9& 2&29 R2 0.097 0.204 0.172 0.137

(B) Cow suppose you wish to eamine the e!ect of teacher eperience on

student achievement, using the same outcome measure as in previous parts#

Teachers were randomly assigned to the three alternative class si"e

arrangements within schools, 0ut not across schools# Add teacher

eperience as an additional control varia0le to the regressions estimated inpart 6, and report the estimates in a ta0le (for each grade level)# :ill the

estimated coe8cients associated with the teacher eperience varia0le

provide un0iased estimates of the impact of teacher eperience on student

achievement9 Bplain#

(1) (2) (3) (4)




Small Class 15.41*** 22.2&*** 13.19*** 8.990***

(3.171) (3.5&8) (3.594) (3.340)

eg!lar , Aide '0.838 5.871 3.71& '0.723

(3.109) (3.&84) (3.&80) (3.433)

$ea%#er :;erien%e 1.051***

0.391**

'0.039& 0.384**

(0.231) (0.170) (0.1&8) (0.154)

-emale 8.&80*** &.23&** &.8&4** &.722**

(2.5&9) (2.93&) (2.88&) (2.&17)

#ite '80.5&* '&5.&0 '123.7** '59.49

(4&.41) (53.80) (52.71) (47.24)

/la% '99.27** '87.55 '158.1*** '8&.18*

(4&.&4) (54.07) (52.9&) (47.48)

Asian '11&.1** '44.02 '81.85 '45.81

(52.&4) (&1.04) (59.80) (53.&0)isani% '70.00 2&.08 '104.7 '5.422

(&5.5&) (7&.01) (74.48) (&&.79)1st !arter - /irt# '8.52&** '9.10&** '5.53& '&.309*

(3.709) (4.258) (4.17&) (3.794)

2nd !arter - /irt# '19.73*** '17.14*** '9.935** '&.939*

(3.728) (4.283) (4.205) (3.808)

3rd !arter - /irt# '29.40*** '2&.10*** '18.54*** '13.12***

(3.743) (4.274) (4.18&) (3.81&)

nner Cit S%#l '1.758 '40.91*** '17.27** '9.575

(7.475) (8.549) (8.413) (7.&23)S!!ran S%#l '9.901 '17.00** '10.37 '5.143

(&.31&) (7.2&0) (7.123) (&.432)

6ran S%#l '14.9&

***

'&.78& 1.&52 '3.32&(5.794) (&.&94) (&.5&7) (5.930)

ree !n%# '25.0&*** '42.19*** '33.77*** '33.18***

(3.093) (3.525) (3.449) (3.178)

N 2&17 2&97 2&74 2&13

R2 0.102 0.204 0.1&7 0.137

(>) 3f the teacher eperience estimates in part % are not necessarily

un0iased, are there covariates that could 0e included as additional controls

that would yield un0iased estimates of the e!ect of teacher eperience on

student achievement9 Bplain your reasoning#

Des, we can include teachers highest degree, teachers career ladder level,

and teachers race as other control varia0les#

(%) Add the additional covariates recommended in part <, and interpret the

results#

See the do4le and the document part%-$indergarden =nly/#



(<) >inally, for each grade level, run a regression to eamine whether having

a teacher that has the same race as the student has any impact on the

student achievement (include any control varia0les you deem appropriate for

this regression)# Report your results in a ta0le# 3nterpret your results#

See the do4le and the document part<-$indergarden =nly/#(3) E0onus 7uestion adds 5 to your midtermF

3t occurs to you that similarity of race 0etween students and teachers might

have di!erent impacts for di!erent races# >or eample, while 0lac1 students

might 0ene4t from having a 0lac1 teacher, white students might not 0ene4t

to the same etent (or at all) from having a white teacher# odify your

regression in part (G) to eamine this new hypothesis# >or each grade level,

run this new regression and report your results in a ta0le# 3nterpret your

results#

See the do4le and the document part3-$indergarden =nly/#

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