斯托克计量经济学课后习题实证答案
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(b) Bob’s predicted years of completed education 13.96 0.073 u 2 13.81 Bob’s predicted years of completed education if he was 10 miles from college 13.96 0.073 u 1 13.89
Predicted growth 0.64 2.31 u 1 2.95 (d) G·rowth 0.96 1.68 u Tradeshare
Predicted growth 0.96 1.68 u 1 2.74
(e) Malta is an island nation in the Mediterranean Sea, south of Sicily. Malta is a freight transport site, which explains its large “trade share”. Many goods coming into Malta (imports into Malta) and immediately transported to other countries (as exports from Malta). Thus, Malta’s imports and exports and unlike the imports and exports of most other countries. Malta should not be included in the analysis.
0.188
6.136.87
Solutions to Empirical Exercises in Chapter 3 109
(e)
Average Hourly Earnings in 1992 (in $2004)
Mean
SE(Mean) 95% Confidence Interval
High School
13.48
0.091
13.3013.65
College
19.07
0.148
18.7819.36
Difference SE(Difference) 95% Confidence Interval
CollegeHigh School
5.59
0.173
5.255.93
(f)
AHEHS,2004 AHEHS,1992
(c) The standard deviation of Beauty is 0.789. Thus Professor Watson’s predicted course evaluations 4.00 0.133 u 0 u 0.789 4.00 Professor Stock’s predicted course evaluations 4.00 0.133 u 1 u 0.789 4.105
0
-5 0
.5
1
1.5
2
Trade Share
Yes, there appears to be a weak positive relationship.
(b) Malta is the “outlying” observation with a trade share of 2. (c) G·rowth 0.64 2.31 u Tradeshare
AHE2004 AHE1992
Average Hourly Earnings, Real $2004
Mean
SE(Mean) 95% Confidence Interval
15.66
0.086
15.4915.82
16.77
0.098
16.5816.96
Difference SE(Difference) 95% Confidence Interval
Mean
SE(Mean) 95% Confidence Interval
11.63
0.064
11.5011.75
16.77
0.098
16.5816.96
Difference SE(Difference) 95% Confidence Interval
5.14
0.117
4.915.37
(b)
AHE1992 AHE2004
PART TWO
Solutions to Empirical Exercises
Chapter 3
ReBiblioteka Baiduiew of Statistics
Solutions to Empirical Exercises
1. (a)
AHE1992 AHE2004
AHE2004 AHE1992
Average Hourly Earnings, Nominal $’s
14.57 6.55 2770 11.86 5.21 1870 2.71
0.173
2.373.05
14.88 7.16 2772 11.92 5.39 1574 2.96
0.192
2.593.34
There is a large and statistically significant gender gap in earnings for high school graduates. In 2004 the estimated gap was $2.96 per hour; in 1992 the estimated gap was $2.71 per hour (in $2004). The increase in the gender gap is somewhat smaller for high school graduates than it is for college graduates.
Gap2004 Gap1992
5.59 6.50 Difference 0.91
0.173 0.188 SE(Difference) 0.256
5.255.93 6.136.87 95% Confidence Interval 0.411.41
Wages of high school graduates increased by an estimated 0.33 dollars per hour (with a 95% confidence interval of 0.06 0.60); Wages of college graduates increased by an estimated 1.24 dollars per hour (with a 95% confidence interval of 0.82 1.66). The College High School gap
2. (a)
5
Course Evaluation
4
3
2
-2
-1
0
1
2
Beauty Index
There appears to be a weak positive relationship between course evaluation and the beauty index.
(b) C·ourse _ Eval 4.00 0.133 u Beauty. The variable Beauty has a mean that is equal to 0; the
AHECol,2004 AHECol,1992
Average Hourly Earnings in 2004
Mean
SE(Mean) 95% Confidence Interval
0.33
0.137
0.060.60
1.24
0.217
0.821.66
Col–HS Gap (1992) Col–HS Gap (2004)
estimated intercept is the mean of the dependent variable (Course_Eval) minus the estimated slope (0.133) times the mean of the regressor (Beauty). Thus, the estimated intercept is equal to the mean of Course_Eval.
(c) The regression R2 is 0.0074, so that distance explains only a very small fraction of years of completed education.
(d) SER 1.8074 years.
4. (a)
10
5 Growth
1.11
0.130
0.851.37
(c) The results from part (b) adjust for changes in purchasing power. These results should be used. (d)
Average Hourly Earnings in 2004
(b) Bob’s predicted earnings 3.32 0.45 u 26 $11.70 Alexis’s predicted earnings 3.32 0.45 u 30 $13.70
(c) The R2 is 0.02.This mean that age explains a small fraction of the variability in earnings across individuals.
Mean
SE(Mean) 95% Confidence Interval
High School
13.81
0.102
13.6114.01
College
20.31
0.158
20.0020.62
Difference SE(Difference) 95% Confidence Interval
CollegeHigh School 6.50
(e) The regression R2 is 0.036, so that Beauty explains only 3.6% of the variance in course evaluations.
3. (a) E¶d 13.96 0.073 u Dist. The regression predicts that if colleges are built 10 miles closer to where students go to high school, average years of college will increase by 0.073 years.
increased by an estimated 0.91 dollars per hour.
(g) Gender Gap in Earnings for High School Graduates
Year 1992 2004
Ym
sm
nm
Yw
sw
nw Ym Yw SE( Ym Yw ) 95% CI
Solutions to Empirical Exercises in Chapter 4 111
(d) The standard deviation of course evaluations is 0.55 and the standard deviation of beauty is 0.789. A one standard deviation increase in beauty is expected to increase course evaluation by 0.133 u 0.789 0.105, or 1/5 of a standard deviation of course evaluations. The effect is small.
Chapter 4
Linear Regression with One Regressor
Solutions to Empirical Exercises
1. (a) ·AHE 3.32 0.45 u Age Earnings increase, on average, by 0.45 dollars per hour when workers age by 1 year.
Predicted growth 0.64 2.31 u 1 2.95 (d) G·rowth 0.96 1.68 u Tradeshare
Predicted growth 0.96 1.68 u 1 2.74
(e) Malta is an island nation in the Mediterranean Sea, south of Sicily. Malta is a freight transport site, which explains its large “trade share”. Many goods coming into Malta (imports into Malta) and immediately transported to other countries (as exports from Malta). Thus, Malta’s imports and exports and unlike the imports and exports of most other countries. Malta should not be included in the analysis.
0.188
6.136.87
Solutions to Empirical Exercises in Chapter 3 109
(e)
Average Hourly Earnings in 1992 (in $2004)
Mean
SE(Mean) 95% Confidence Interval
High School
13.48
0.091
13.3013.65
College
19.07
0.148
18.7819.36
Difference SE(Difference) 95% Confidence Interval
CollegeHigh School
5.59
0.173
5.255.93
(f)
AHEHS,2004 AHEHS,1992
(c) The standard deviation of Beauty is 0.789. Thus Professor Watson’s predicted course evaluations 4.00 0.133 u 0 u 0.789 4.00 Professor Stock’s predicted course evaluations 4.00 0.133 u 1 u 0.789 4.105
0
-5 0
.5
1
1.5
2
Trade Share
Yes, there appears to be a weak positive relationship.
(b) Malta is the “outlying” observation with a trade share of 2. (c) G·rowth 0.64 2.31 u Tradeshare
AHE2004 AHE1992
Average Hourly Earnings, Real $2004
Mean
SE(Mean) 95% Confidence Interval
15.66
0.086
15.4915.82
16.77
0.098
16.5816.96
Difference SE(Difference) 95% Confidence Interval
Mean
SE(Mean) 95% Confidence Interval
11.63
0.064
11.5011.75
16.77
0.098
16.5816.96
Difference SE(Difference) 95% Confidence Interval
5.14
0.117
4.915.37
(b)
AHE1992 AHE2004
PART TWO
Solutions to Empirical Exercises
Chapter 3
ReBiblioteka Baiduiew of Statistics
Solutions to Empirical Exercises
1. (a)
AHE1992 AHE2004
AHE2004 AHE1992
Average Hourly Earnings, Nominal $’s
14.57 6.55 2770 11.86 5.21 1870 2.71
0.173
2.373.05
14.88 7.16 2772 11.92 5.39 1574 2.96
0.192
2.593.34
There is a large and statistically significant gender gap in earnings for high school graduates. In 2004 the estimated gap was $2.96 per hour; in 1992 the estimated gap was $2.71 per hour (in $2004). The increase in the gender gap is somewhat smaller for high school graduates than it is for college graduates.
Gap2004 Gap1992
5.59 6.50 Difference 0.91
0.173 0.188 SE(Difference) 0.256
5.255.93 6.136.87 95% Confidence Interval 0.411.41
Wages of high school graduates increased by an estimated 0.33 dollars per hour (with a 95% confidence interval of 0.06 0.60); Wages of college graduates increased by an estimated 1.24 dollars per hour (with a 95% confidence interval of 0.82 1.66). The College High School gap
2. (a)
5
Course Evaluation
4
3
2
-2
-1
0
1
2
Beauty Index
There appears to be a weak positive relationship between course evaluation and the beauty index.
(b) C·ourse _ Eval 4.00 0.133 u Beauty. The variable Beauty has a mean that is equal to 0; the
AHECol,2004 AHECol,1992
Average Hourly Earnings in 2004
Mean
SE(Mean) 95% Confidence Interval
0.33
0.137
0.060.60
1.24
0.217
0.821.66
Col–HS Gap (1992) Col–HS Gap (2004)
estimated intercept is the mean of the dependent variable (Course_Eval) minus the estimated slope (0.133) times the mean of the regressor (Beauty). Thus, the estimated intercept is equal to the mean of Course_Eval.
(c) The regression R2 is 0.0074, so that distance explains only a very small fraction of years of completed education.
(d) SER 1.8074 years.
4. (a)
10
5 Growth
1.11
0.130
0.851.37
(c) The results from part (b) adjust for changes in purchasing power. These results should be used. (d)
Average Hourly Earnings in 2004
(b) Bob’s predicted earnings 3.32 0.45 u 26 $11.70 Alexis’s predicted earnings 3.32 0.45 u 30 $13.70
(c) The R2 is 0.02.This mean that age explains a small fraction of the variability in earnings across individuals.
Mean
SE(Mean) 95% Confidence Interval
High School
13.81
0.102
13.6114.01
College
20.31
0.158
20.0020.62
Difference SE(Difference) 95% Confidence Interval
CollegeHigh School 6.50
(e) The regression R2 is 0.036, so that Beauty explains only 3.6% of the variance in course evaluations.
3. (a) E¶d 13.96 0.073 u Dist. The regression predicts that if colleges are built 10 miles closer to where students go to high school, average years of college will increase by 0.073 years.
increased by an estimated 0.91 dollars per hour.
(g) Gender Gap in Earnings for High School Graduates
Year 1992 2004
Ym
sm
nm
Yw
sw
nw Ym Yw SE( Ym Yw ) 95% CI
Solutions to Empirical Exercises in Chapter 4 111
(d) The standard deviation of course evaluations is 0.55 and the standard deviation of beauty is 0.789. A one standard deviation increase in beauty is expected to increase course evaluation by 0.133 u 0.789 0.105, or 1/5 of a standard deviation of course evaluations. The effect is small.
Chapter 4
Linear Regression with One Regressor
Solutions to Empirical Exercises
1. (a) ·AHE 3.32 0.45 u Age Earnings increase, on average, by 0.45 dollars per hour when workers age by 1 year.