You can download the data for this chapter by clicking here: https://stats.idre.ucla.edu/wp-content/uploads/2016/02/dee.sas7bdat.
(a) Univariate Statistics from Table 10.1 on page 207.
proc univariate data=dee;
var register college;
run;
The UNIVARIATE Procedure
Variable: register (Is respondent currently registered to vote?)
Moments
N 9227 Sum Weights 9227
Mean 0.67085727 Sum Observations 6190
Std Deviation 0.46992736 Variance 0.22083173
Skewness -0.7273222 Kurtosis -1.4713213
Uncorrected SS 6190 Corrected SS 2037.39352
Coeff Variation 70.048785 Std Error Mean 0.00489216
Basic Statistical Measures
Location Variability
Mean 0.670857 Std Deviation 0.46993
Median 1.000000 Variance 0.22083
Mode 1.000000 Range 1.00000
Interquartile Range 1.00000
Tests for Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 137.1291 Pr > |t| <.0001
Sign M 3095 Pr >= |M| <.0001
Signed Rank S 9580573 Pr >= |S| <.0001
Quantiles (Definition 5)
Quantile Estimate
100% Max 1
99% 1
95% 1
90% 1
75% Q3 1
50% Median 1
25% Q1 0
10% 0
5% 0
1% 0
0% Min 0
The UNIVARIATE Procedure
Variable: register (Is respondent currently registered to vote?)
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
0 9227 1 9221
0 9222 1 9223
0 9220 1 9224
0 9218 1 9225
0 9217 1 9226
The UNIVARIATE Procedure
Variable: college (Attended junior, community or 4year college by 1984?)
Moments
N 9227 Sum Weights 9227
Mean 0.54709006 Sum Observations 5048
Std Deviation 0.49780456 Variance 0.24780938
Skewness -0.189232 Kurtosis -1.9646171
Uncorrected SS 5048 Corrected SS 2286.28937
Coeff Variation 90.9913372 Std Error Mean 0.00518237
Basic Statistical Measures
Location Variability
Mean 0.547090 Std Deviation 0.49780
Median 1.000000 Variance 0.24781
Mode 1.000000 Range 1.00000
Interquartile Range 1.00000
Tests for Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 105.5675 Pr > |t| <.0001
Sign M 2524 Pr >= |M| <.0001
Signed Rank S 6371838 Pr >= |S| <.0001
Quantiles (Definition 5)
Quantile Estimate
100% Max 1
99% 1
95% 1
90% 1
75% Q3 1
50% Median 1
25% Q1 0
10% 0
5% 0
1% 0
0% Min 0
The UNIVARIATE Procedure
Variable: college (Attended junior, community or 4year college by 1984?)
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
0 9226 1 9219
0 9224 1 9221
0 9222 1 9223
0 9220 1 9225
0 9218 1 9227
Cross-tabulation of register and college, with a chi-squared test. (Not shown in the text.)
proc freq data=dee;
table register*college / chisq cellchi2 expected;
run;
The FREQ Procedure
Table of register by college
register(Is respondent currently registered to vote?)
college(Attended junior, community or 4year college
by 1984?)
Frequency
Expected
Cell Chi-Square
Percent
Row Pct
Col Pct 0 1 Total
0 1780 1257 3037
1375.5 1661.5
118.96 98.483
19.29 13.62 32.91
58.61 41.39
42.59 24.90
1 2399 3791 6190
2803.5 3386.5
58.366 48.319
26.00 41.09 67.09
38.76 61.24
57.41 75.10
Total 4179 5048 9227
45.29 54.71 100.00
The FREQ Procedure
Statistics for Table of register by college
Statistic DF Value Prob
Chi-Square 1 324.1293 <.0001
Likelihood Ratio Chi-Square 1 324.2767 <.0001
Continuity Adj. Chi-Square 1 323.3285 <.0001
Mantel-Haenszel Chi-Square 1 324.0942 <.0001
Phi Coefficient 0.1874
Contingency Coefficient 0.1842
Cramer's V 0.1874
Fisher's Exact Test
Cell (1,1) Frequency (F) 1780
Left-sided Pr <= F 1.0000
Right-sided Pr >= F 1.270E-72
Table Probability (P) 1.573E-72
Two-sided Pr <= P 2.092E-72
(b) Sample Bivariate Correlations and Covariances from Table 10.1 on page 207.
proc corr data=dee cov;
var register college;
run;
The CORR Procedure
2 Variables: register college
Covariance Matrix, DF = 9226
register college
register Is respondent currently registered to vote? 0.2208317276 0.0438448426
college Attended junior, community or 4year college by 1984? 0.0438448426 0.2478093831
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
register 9227 0.67086 0.46993 6190 0 1.00000
college 9227 0.54709 0.49780 5048 0 1.00000
Simple Statistics
Variable Label
register Is respondent currently registered to vote?
college Attended junior, community or 4year college by 1984?
Pearson Correlation Coefficients, N = 9227
Prob > |r| under H0: Rho=0
register college
register 1.00000 0.18743
Is respondent currently registered to vote? <.0001
college 0.18743 1.00000
Attended junior, community or 4year college by 1984? <.0001
(c) OLS Regression Analysis: Outcome=register from Table 10.1 on page 207.
proc glm data=dee;
model register = college;
run;
The GLM Procedure
Number of Observations Read 9227
Number of Observations Used 9227
The GLM Procedure
Dependent Variable: register Is respondent currently registered to vote?
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 1 71.570283 71.570283 335.86 <.0001
Error 9225 1965.823236 0.213097
Corrected Total 9226 2037.393519
R-Square Coeff Var Root MSE register Mean
0.035128 68.81117 0.461625 0.670857
Source DF Type I SS Mean Square F Value Pr > F
college 1 71.57028291 71.57028291 335.86 <.0001
Source DF Type III SS Mean Square F Value Pr > F
college 1 71.57028291 71.57028291 335.86 <.0001
Standard
Parameter Estimate Error t Value Pr > |t|
Intercept 0.5740607801 0.00714090 80.39 <.0001
college 0.1769297112 0.00965436 18.33 <.0001
(a) Univariate Statistics from Table 10.2 on page 219. Note that only the variable distance has been added from panel a of Table 10.1.
proc univariate data=dee;
var distance;
run;
The UNIVARIATE Procedure
Variable: distance (Miles from respondents HS to nearest 2yr college)
Moments
N 9227 Sum Weights 9227
Mean 9.73599232 Sum Observations 89834.0011
Std Deviation 8.70228565 Variance 75.7297756
Skewness 1.18127321 Kurtosis 0.60086158
Uncorrected SS 1573306.05 Corrected SS 698682.909
Coeff Variation 89.3826265 Std Error Mean 0.09059476
Basic Statistical Measures
Location Variability
Mean 9.735992 Std Deviation 8.70229
Median 7.000000 Variance 75.72978
Mode 5.000000 Range 35.00000
Interquartile Range 12.00000
Tests for Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 107.4675 Pr > |t| <.0001
Sign M 4443.5 Pr >= |M| <.0001
Signed Rank S 19746914 Pr >= |S| <.0001
Quantiles (Definition 5)
Quantile Estimate
100% Max 35
99% 35
95% 30
90% 25
75% Q3 15
50% Median 7
25% Q1 3
10% 1
5% 1
1% 0
0% Min 0
The UNIVARIATE Procedure
Variable: distance (Miles from respondents HS to nearest 2yr college)
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
0 9048 35 9081
0 9047 35 9082
0 9046 35 9083
0 9045 35 9084
0 9044 35 9085
(b) Sample Bivariate Correlations and Covariances from Table 10.2 on page 219.
proc corr data=dee cov;
var register college distance;
run;
The CORR Procedure
3 Variables: register college distance
Covariance Matrix, DF = 9226
register college
register Is respondent currently registered to vote? 0.22083173 0.04384484
college Attended junior, community or 4year college by 1984? 0.04384484 0.24780938
distance Miles from respondents HS to nearest 2yr college -0.13687315 -0.48247222
Covariance Matrix, DF = 9226
distance
register Is respondent currently registered to vote? -0.13687315
college Attended junior, community or 4year college by 1984? -0.48247222
distance Miles from respondents HS to nearest 2yr college 75.72977557
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
register 9227 0.67086 0.46993 6190 0 1.00000
college 9227 0.54709 0.49780 5048 0 1.00000
distance 9227 9.73599 8.70229 89834 0 35.00000
Simple Statistics
Variable Label
register Is respondent currently registered to vote?
college Attended junior, community or 4year college by 1984?
distance Miles from respondents HS to nearest 2yr college
Pearson Correlation Coefficients, N = 9227
Prob > |r| under H0: Rho=0
register college distance
register 1.00000 0.18743 -0.03347
Is respondent currently registered to vote? <.0001 0.0013
college 0.18743 1.00000 -0.11137
Attended junior, community or 4year college by 1984? <.0001 <.0001
distance -0.03347 -0.11137 1.00000
Miles from respondents HS to nearest 2yr college 0.0013 <.0001
(c) Method-of-Moments IVE Estimate from Table 10.2 on page 219 can be done as a hand calculation: -.136873/-.482472 = .28369107
Table 10.3 on page 228.
proc syslin data=dee 2sls;
endogenous college;
instruments distance;
model college = distance;
model register = college;
run;
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model college
Dependent Variable college
Label Attended junior, community or 4year college by 1984?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 28.35903 28.35903 115.86 <.0001
Error 9225 2257.930 0.244762
Corrected Total 9226 2286.289
Root MSE 0.49473 R-Square 0.01240
Dependent Mean 0.54709 Adj R-Sq 0.01230
Coeff Var 90.43015
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.609118 0.007729 78.81 <.0001 Intercept
distance 1 -0.00637 0.000592 -10.76 <.0001 Miles from
respondents HS to
nearest 2yr college
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model register
Dependent Variable register
Label Is respondent currently registered to vote?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 2.282356 2.282356 10.57 0.0012
Error 9225 1991.882 0.215922
Corrected Total 9226 2037.394
Root MSE 0.46467 R-Square 0.00114
Dependent Mean 0.67086 Adj R-Sq 0.00104
Coeff Var 69.26575
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.515653 0.047982 10.75 <.0001 Intercept
college 1 0.283691 0.087258 3.25 0.0012 Attended junior,
community or 4year
college by 1984?
Table 10.4 on page 235.
proc syslin data=dee 3sls;
endogenous college;
instruments distance;
model college = distance;
model register = college;
run;
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model college
Dependent Variable college
Label Attended junior, community or 4year college by 1984?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 28.35903 28.35903 115.86 <.0001
Error 9225 2257.930 0.244762
Corrected Total 9226 2286.289
Root MSE 0.49473 R-Square 0.01240
Dependent Mean 0.54709 Adj R-Sq 0.01230
Coeff Var 90.43015
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.609118 0.007729 78.81 <.0001 Intercept
distance 1 -0.00637 0.000592 -10.76 <.0001 Miles from
respondents HS to
nearest 2yr college
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model register
Dependent Variable register
Label Is respondent currently registered to vote?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 2.282356 2.282356 10.57 0.0012
Error 9225 1991.882 0.215922
Corrected Total 9226 2037.394
Root MSE 0.46467 R-Square 0.00114
Dependent Mean 0.67086 Adj R-Sq 0.00104
Coeff Var 69.26575
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.515653 0.047982 10.75 <.0001 Intercept
college 1 0.283691 0.087258 3.25 0.0012 Attended junior,
community or 4year
college by 1984?
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Cross Model Covariance
college register
college 0.244762 -.026459
register -.026459 0.215922
Cross Model Correlation
college register
college 1.00000 -0.11510
register -0.11510 1.00000
Cross Model Inverse Correlation
college register
college 1.01342 0.11664
register 0.11664 1.01342
Cross Model Inverse Covariance
college register
college 4.14045 0.50738
register 0.50738 4.69347
System Weighted MSE 1.0462
Degrees of freedom 18450
System Weighted R-Square 0.007011
Model college
Dependent Variable college
Label Attended junior, community or 4year college by 1984?
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.609118 0.007729 78.81 <.0001 Intercept
distance 1 -0.00637 0.000592 -10.76 <.0001 Miles from
respondents HS to
nearest 2yr college
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Model register
Dependent Variable register
Label Is respondent currently registered to vote?
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.515653 0.047982 10.75 <.0001 Intercept
college 1 0.283691 0.087258 3.25 0.0012 Attended junior,
community or 4year
college by 1984?
Table 10.5 on page 240.
proc syslin data=dee 2sls;
endogenous college;
instruments distance black hispanic otherrace;
model college = distance black hispanic otherrace ;
model register = college black hispanic otherrace ;
run;
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model college
Dependent Variable college
Label Attended junior, community or 4year college by 1984?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 4 49.70516 12.42629 51.24 <.0001
Error 9222 2236.584 0.242527
Corrected Total 9226 2286.289
Root MSE 0.49247 R-Square 0.02174
Dependent Mean 0.54709 Adj R-Sq 0.02132
Coeff Var 90.01632
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.643146 0.009053 71.04 <.0001 Intercept
distance 1 -0.00692 0.000595 -11.64 <.0001 Miles from
respondents HS to
nearest 2yr college
black 1 -0.05766 0.015959 -3.61 0.0003 Is respondent black?
hispanic 1 -0.11621 0.013257 -8.77 <.0001 Is respondent
hispanic?
otherrace 1 0.033708 0.024010 1.40 0.1604 Is respondent of
another race?
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model register
Dependent Variable register
Label Is respondent currently registered to vote?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 4 9.261561 2.315390 10.85 <.0001
Error 9222 1967.204 0.213316
Corrected Total 9226 2037.394
Root MSE 0.46186 R-Square 0.00469
Dependent Mean 0.67086 Adj R-Sq 0.00425
Coeff Var 68.84653
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.526600 0.046306 11.37 <.0001 Intercept
college 1 0.248862 0.080601 3.09 0.0020 Attended junior,
community or 4year
college by 1984?
black 1 0.061733 0.015174 4.07 <.0001 Is respondent black?
hispanic 1 0.028293 0.014832 1.91 0.0565 Is respondent
hispanic?
otherrace 1 -0.10667 0.022819 -4.67 <.0001 Is respondent of
another race?
The analyses in Tables 10.6 and 10.7 include a variable that is restricted, so these analyses cannot be reproduced using the available dataset.
Table 10.8 from page 249. Note that many of the coefficients in the first stage models are equal to 0.
* Form interaction terms;
* Then form interactions between instruments and exog race variables as instruments;
data dee;
set dee;
distxblack = distance*black;
distxhispanic = distance*hispanic;
distxotherrace = distance*otherrace;
collegexblack = college*black;
collegexhispanic = college*hispanic;
collegexotherrace = college*otherrace;
run;
proc syslin data=dee 2sls;
endogenous college collegexblack collegexhispanic collegexotherrace;
instruments distance black hispanic otherrace distxblack distxhispanic distxotherrace;
model college = distance black hispanic otherrace distxblack distxhispanic distxotherrace;
model collegexblack = distance black hispanic otherrace distxblack distxhispanic distxotherrace;
model collegexhispanic = distance black hispanic otherrace distxblack distxhispanic distxotherrace;
model collegexotherrace = distance black hispanic otherrace distxblack distxhispanic distxotherrace;
model register = college black hispanic otherrace collegexblack collegexhispanic collegexotherrace;
run;
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model college
Dependent Variable college
Label Attended junior, community or 4year college by 1984?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 7 50.20795 7.172564 29.57 <.0001
Error 9219 2236.081 0.242551
Corrected Total 9226 2286.289
Root MSE 0.49250 R-Square 0.02196
Dependent Mean 0.54709 Adj R-Sq 0.02122
Coeff Var 90.02084
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.645183 0.010058 64.15 <.0001 Intercept
distance 1 -0.00711 0.000723 -9.83 <.0001 Miles from
respondents HS to
nearest 2yr college
black 1 -0.06506 0.022762 -2.86 0.0043 Is respondent black?
hispanic 1 -0.12759 0.019368 -6.59 <.0001 Is respondent
hispanic?
otherrace 1 0.058954 0.035074 1.68 0.0928 Is respondent of
another race?
distxblack 1 0.000890 0.002012 0.44 0.6583
distxhispanic 1 0.001291 0.001577 0.82 0.4131
distxotherrace 1 -0.00299 0.002941 -1.02 0.3086
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model collegexblack
Dependent Variable collegexblack
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 7 289.5044 41.35777 1336.08 <.0001
Error 9219 285.3711 0.030955
Corrected Total 9226 574.8755
Root MSE 0.17594 R-Square 0.50359
Dependent Mean 0.06676 Adj R-Sq 0.50322
Coeff Var 263.53779
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 1.94E-17 0.003593 0.00 1.0000 Intercept
distance 1 -202E-20 0.000258 -0.00 1.0000 Miles from
respondents HS to
nearest 2yr college
black 1 0.580126 0.008132 71.34 <.0001 Is respondent black?
hispanic 1 -216E-19 0.006919 -0.00 1.0000 Is respondent
hispanic?
otherrace 1 -328E-19 0.012530 -0.00 1.0000 Is respondent of
another race?
distxblack 1 -0.00622 0.000719 -8.66 <.0001
distxhispanic 1 1.43E-18 0.000563 0.00 1.0000
distxotherrace 1 2.51E-18 0.001051 0.00 1.0000
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model collegexhispanic
Dependent Variable collegexhispanic
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 7 326.3327 46.61895 949.38 <.0001
Error 9219 452.6976 0.049105
Corrected Total 9226 779.0302
Root MSE 0.22160 R-Square 0.41890
Dependent Mean 0.09310 Adj R-Sq 0.41845
Coeff Var 238.02882
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 1.88E-17 0.004525 0.00 1.0000 Intercept
distance 1 -406E-21 0.000326 -0.00 1.0000 Miles from
respondents HS to
nearest 2yr college
black 1 -266E-19 0.010242 -0.00 1.0000 Is respondent black?
hispanic 1 0.517593 0.008714 59.39 <.0001 Is respondent
hispanic?
otherrace 1 -297E-20 0.015781 -0.00 1.0000 Is respondent of
another race?
distxblack 1 1.31E-18 0.000905 0.00 1.0000
distxhispanic 1 -0.00582 0.000709 -8.21 <.0001
distxotherrace 1 -241E-21 0.001323 -0.00 1.0000
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model collegexotherrace
Dependent Variable collegexotherrace
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 7 168.0322 24.00460 2119.51 <.0001
Error 9219 104.4102 0.011326
Corrected Total 9226 272.4424
Root MSE 0.10642 R-Square 0.61676
Dependent Mean 0.03045 Adj R-Sq 0.61647
Coeff Var 349.44899
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 1.22E-17 0.002173 0.00 1.0000 Intercept
distance 1 -713E-21 0.000156 -0.00 1.0000 Miles from
respondents HS to
nearest 2yr college
black 1 -109E-19 0.004919 -0.00 1.0000 Is respondent black?
hispanic 1 -809E-20 0.004185 -0.00 1.0000 Is respondent
hispanic?
otherrace 1 0.704137 0.007579 92.91 <.0001 Is respondent of
another race?
distxblack 1 6.34E-19 0.000435 0.00 1.0000
distxhispanic 1 6.34E-19 0.000341 0.00 1.0000
distxotherrace 1 -0.01011 0.000635 -15.90 <.0001
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model register
Dependent Variable register
Label Is respondent currently registered to vote?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 7 10.29933 1.471333 6.74 <.0001
Error 9219 2011.839 0.218228
Corrected Total 9226 2037.394
Root MSE 0.46715 R-Square 0.00509
Dependent Mean 0.67086 Adj R-Sq 0.00434
Coeff Var 69.63453
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.464046 0.055299 8.39 <.0001 Intercept
college 1 0.358693 0.096492 3.72 0.0002 Attended junior,
community or 4year
college by 1984?
black 1 0.278024 0.162701 1.71 0.0875 Is respondent black?
hispanic 1 0.176548 0.120819 1.46 0.1440 Is respondent
hispanic?
otherrace 1 0.174217 0.175600 0.99 0.3212 Is respondent of
another race?
collegexblack 1 -0.39859 0.302067 -1.32 0.1870
collegexhispanic 1 -0.29291 0.247842 -1.18 0.2373
collegexotherrace 1 -0.46335 0.284396 -1.63 0.1033
Reproduce last model (Table 10.8 page 249), dropping the irrelevant terms. Note that the results are identical. (Not shown in the text.)
proc syslin data=dee 3sls;
endogenous college collegexblack collegexhispanic collegexotherrace;
instruments distance black hispanic otherrace distxblack distxhispanic distxotherrace;
model college = distance black hispanic otherrace distxblack distxhispanic distxotherrace;
model collegexblack = black distxblack ;
model collegexhispanic = hispanic distxhispanic ;
model collegexotherrace = otherrace distxotherrace;
model register = college black hispanic otherrace collegexblack collegexhispanic collegexotherrace;
run;
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model college
Dependent Variable college
Label Attended junior, community or 4year college by 1984?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 7 50.20795 7.172564 29.57 <.0001
Error 9219 2236.081 0.242551
Corrected Total 9226 2286.289
Root MSE 0.49250 R-Square 0.02196
Dependent Mean 0.54709 Adj R-Sq 0.02122
Coeff Var 90.02084
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.645183 0.010058 64.15 <.0001 Intercept
distance 1 -0.00711 0.000723 -9.83 <.0001 Miles from
respondents HS to
nearest 2yr college
black 1 -0.06506 0.022762 -2.86 0.0043 Is respondent black?
hispanic 1 -0.12759 0.019368 -6.59 <.0001 Is respondent
hispanic?
otherrace 1 0.058954 0.035074 1.68 0.0928 Is respondent of
another race?
distxblack 1 0.000890 0.002012 0.44 0.6583
distxhispanic 1 0.001291 0.001577 0.82 0.4131
distxotherrace 1 -0.00299 0.002941 -1.02 0.3086
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model collegexblack
Dependent Variable collegexblack
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 289.5044 144.7522 4678.80 <.0001
Error 9224 285.3711 0.030938
Corrected Total 9226 574.8755
Root MSE 0.17589 R-Square 0.50359
Dependent Mean 0.06676 Adj R-Sq 0.50349
Coeff Var 263.46635
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 -916E-20 0.001958 -0.00 1.0000 Intercept
black 1 0.580126 0.007551 76.83 <.0001 Is respondent black?
distxblack 1 -0.00622 0.000671 -9.28 <.0001
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model collegexhispanic
Dependent Variable collegexhispanic
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 326.3327 163.1663 3324.62 <.0001
Error 9224 452.6976 0.049078
Corrected Total 9226 779.0302
Root MSE 0.22154 R-Square 0.41890
Dependent Mean 0.09310 Adj R-Sq 0.41877
Coeff Var 237.96429
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 -643E-20 0.002577 -0.00 1.0000 Intercept
hispanic 1 0.517593 0.007879 65.70 <.0001 Is respondent
hispanic?
distxhispanic 1 -0.00582 0.000630 -9.24 <.0001
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model collegexotherrace
Dependent Variable collegexotherrace
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 168.0322 84.01609 7422.30 <.0001
Error 9224 104.4102 0.011319
Corrected Total 9226 272.4424
Root MSE 0.10639 R-Square 0.61676
Dependent Mean 0.03045 Adj R-Sq 0.61668
Coeff Var 349.35427
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 -123E-20 0.001136 -0.00 1.0000 Intercept
otherrace 1 0.704137 0.007347 95.84 <.0001 Is respondent of
another race?
distxotherrace 1 -0.01011 0.000616 -16.41 <.0001
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model register
Dependent Variable register
Label Is respondent currently registered to vote?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 7 10.29933 1.471333 6.74 <.0001
Error 9219 2011.839 0.218228
Corrected Total 9226 2037.394
Root MSE 0.46715 R-Square 0.00509
Dependent Mean 0.67086 Adj R-Sq 0.00434
Coeff Var 69.63453
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.464046 0.055299 8.39 <.0001 Intercept
college 1 0.358693 0.096492 3.72 0.0002 Attended junior,
community or 4year
college by 1984?
black 1 0.278024 0.162701 1.71 0.0875 Is respondent black?
hispanic 1 0.176548 0.120819 1.46 0.1440 Is respondent
hispanic?
otherrace 1 0.174217 0.175600 0.99 0.3212 Is respondent of
another race?
collegexblack 1 -0.39859 0.302067 -1.32 0.1870
collegexhispanic 1 -0.29291 0.247842 -1.18 0.2373
collegexotherrace 1 -0.46335 0.284396 -1.63 0.1033
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Cross Model Covariance
college collegexblack collegexhispanic collegexotherrace register
college 0.242551 0.030946 0.049092 0.011322 -.011576
collegexblack 0.030946 0.030938 0.000000 -.000000 0.006014
collegexhispanic 0.049092 0.000000 0.049078 0.000000 0.005229
collegexotherrace 0.011322 -.000000 0.000000 0.011319 0.002175
register -.011576 0.006014 0.005229 0.002175 0.218228
Cross Model Correlation
college collegexblack collegexhispanic collegexotherrace register
college 1.00000 0.35724 0.44995 0.21609 -0.05031
collegexblack 0.35724 1.00000 0.00000 -0.00000 0.07319
collegexhispanic 0.44995 0.00000 1.00000 0.00000 0.05053
collegexotherrace 0.21609 -0.00000 0.00000 1.00000 0.04376
register -0.05031 0.07319 0.05053 0.04376 1.00000
Cross Model Inverse Correlation
college collegexblack collegexhispanic collegexotherrace register
college 1.63583 -0.59752 -0.74510 -0.36134 0.17950
collegexblack -0.59752 1.22367 0.27590 0.13522 -0.13949
collegexhispanic -0.74510 0.27590 1.34197 0.16682 -0.13279
collegexotherrace -0.36134 0.13522 0.16682 1.08175 -0.08385
register 0.17950 -0.13949 -0.13279 -0.08385 1.02962
Cross Model Inverse Covariance
college collegexblack collegexhispanic collegexotherrace register
college 6.74425 -6.8977 -6.8292 -6.8960 0.78021
collegexblack -6.89775 39.5524 7.0805 7.2258 -1.69760
collegexhispanic -6.82921 7.0805 27.3434 7.0776 -1.28312
collegexotherrace -6.89600 7.2258 7.0776 95.5659 -1.68704
register 0.78021 -1.6976 -1.2831 -1.6870 4.71810
System Weighted MSE 1.0187
Degrees of freedom 46110
System Weighted R-Square 0.4339
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Model college
Dependent Variable college
Label Attended junior, community or 4year college by 1984?
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.645183 0.008650 74.59 <.0001 Intercept
distance 1 -0.00711 0.000571 -12.45 <.0001 Miles from
respondents HS to
nearest 2yr college
black 1 -0.06506 0.019493 -3.34 0.0008 Is respondent black?
hispanic 1 -0.12759 0.017201 -7.42 <.0001 Is respondent
hispanic?
otherrace 1 0.058954 0.028648 2.06 0.0396 Is respondent of
another race?
distxblack 1 0.000890 0.001724 0.52 0.6057
distxhispanic 1 0.001291 0.001395 0.92 0.3550
distxotherrace 1 -0.00299 0.002402 -1.25 0.2126
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Model collegexblack
Dependent Variable collegexblack
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 2.4E-17 0.001958 0.00 1.0000 Intercept
black 1 0.580126 0.007551 76.83 <.0001 Is respondent black?
distxblack 1 -0.00622 0.000671 -9.28 <.0001
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Model collegexhispanic
Dependent Variable collegexhispanic
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 2.64E-17 0.002577 0.00 1.0000 Intercept
hispanic 1 0.517593 0.007879 65.70 <.0001 Is respondent
hispanic?
distxhispanic 1 -0.00582 0.000630 -9.24 <.0001
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Model collegexotherrace
Dependent Variable collegexotherrace
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 1.01E-17 0.001136 0.00 1.0000 Intercept
otherrace 1 0.704137 0.007347 95.84 <.0001 Is respondent of
another race?
distxotherrace 1 -0.01011 0.000616 -16.41 <.0001
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Model register
Dependent Variable register
Label Is respondent currently registered to vote?
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.464046 0.055030 8.43 <.0001 Intercept
college 1 0.358693 0.096017 3.74 0.0002 Attended junior,
community or 4year
college by 1984?
black 1 0.278024 0.162287 1.71 0.0867 Is respondent black?
hispanic 1 0.176548 0.120347 1.47 0.1424 Is respondent
hispanic?
otherrace 1 0.174217 0.174887 1.00 0.3192 Is respondent of
another race?
collegexblack 1 -0.39859 0.301308 -1.32 0.1859
collegexhispanic 1 -0.29291 0.246891 -1.19 0.2355
collegexotherrace 1 -0.46335 0.283238 -1.64 0.1019
A model similar to the last two (both of which replicate Table 10.8 page 249) estimated using simultaneous equations, dropping the irrelevant terms and non-significant variables from the model. Note that the results are very similar, but not identical. (Not shown in the text.)
proc syslin data=dee 3sls;
endogenous college collegexblack collegexhispanic collegexotherrace;
instruments distance black hispanic otherrace distxblack distxhispanic distxotherrace;
model college = distance black hispanic otherrace;
model collegexblack = black distxblack ;
model collegexhispanic = hispanic distxhispanic ;
model collegexotherrace = otherrace distxotherrace;
model register = college black hispanic otherrace collegexblack collegexhispanic collegexotherrace;
run;
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model college
Dependent Variable college
Label Attended junior, community or 4year college by 1984?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 4 49.70516 12.42629 51.24 <.0001
Error 9222 2236.584 0.242527
Corrected Total 9226 2286.289
Root MSE 0.49247 R-Square 0.02174
Dependent Mean 0.54709 Adj R-Sq 0.02132
Coeff Var 90.01632
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.643146 0.009053 71.04 <.0001 Intercept
distance 1 -0.00692 0.000595 -11.64 <.0001 Miles from
respondents HS to
nearest 2yr college
black 1 -0.05766 0.015959 -3.61 0.0003 Is respondent black?
hispanic 1 -0.11621 0.013257 -8.77 <.0001 Is respondent
hispanic?
otherrace 1 0.033708 0.024010 1.40 0.1604 Is respondent of
another race?
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model collegexblack
Dependent Variable collegexblack
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 289.5044 144.7522 4678.80 <.0001
Error 9224 285.3711 0.030938
Corrected Total 9226 574.8755
Root MSE 0.17589 R-Square 0.50359
Dependent Mean 0.06676 Adj R-Sq 0.50349
Coeff Var 263.46635
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 -916E-20 0.001958 -0.00 1.0000 Intercept
black 1 0.580126 0.007551 76.83 <.0001 Is respondent black?
distxblack 1 -0.00622 0.000671 -9.28 <.0001
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model collegexhispanic
Dependent Variable collegexhispanic
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 326.3327 163.1663 3324.62 <.0001
Error 9224 452.6976 0.049078
Corrected Total 9226 779.0302
Root MSE 0.22154 R-Square 0.41890
Dependent Mean 0.09310 Adj R-Sq 0.41877
Coeff Var 237.96429
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 -643E-20 0.002577 -0.00 1.0000 Intercept
hispanic 1 0.517593 0.007879 65.70 <.0001 Is respondent
hispanic?
distxhispanic 1 -0.00582 0.000630 -9.24 <.0001
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model collegexotherrace
Dependent Variable collegexotherrace
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 168.0322 84.01609 7422.30 <.0001
Error 9224 104.4102 0.011319
Corrected Total 9226 272.4424
Root MSE 0.10639 R-Square 0.61676
Dependent Mean 0.03045 Adj R-Sq 0.61668
Coeff Var 349.35427
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 -123E-20 0.001136 -0.00 1.0000 Intercept
otherrace 1 0.704137 0.007347 95.84 <.0001 Is respondent of
another race?
distxotherrace 1 -0.01011 0.000616 -16.41 <.0001
The SYSLIN Procedure
Two-Stage Least Squares Estimation
Model register
Dependent Variable register
Label Is respondent currently registered to vote?
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 7 10.29933 1.471333 6.74 <.0001
Error 9219 2011.839 0.218228
Corrected Total 9226 2037.394
Root MSE 0.46715 R-Square 0.00509
Dependent Mean 0.67086 Adj R-Sq 0.00434
Coeff Var 69.63453
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.464046 0.055299 8.39 <.0001 Intercept
college 1 0.358693 0.096492 3.72 0.0002 Attended junior,
community or 4year
college by 1984?
black 1 0.278024 0.162701 1.71 0.0875 Is respondent black?
hispanic 1 0.176548 0.120819 1.46 0.1440 Is respondent
hispanic?
otherrace 1 0.174217 0.175600 0.99 0.3212 Is respondent of
another race?
collegexblack 1 -0.39859 0.302067 -1.32 0.1870
collegexhispanic 1 -0.29291 0.247842 -1.18 0.2373
collegexotherrace 1 -0.46335 0.284396 -1.63 0.1033
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Cross Model Covariance
college collegexblack collegexhispanic collegexotherrace register
college 0.242527 0.030941 0.049084 0.011321 -.011574
collegexblack 0.030941 0.030938 0.000000 -.000000 0.006014
collegexhispanic 0.049084 0.000000 0.049078 0.000000 0.005229
collegexotherrace 0.011321 -.000000 0.000000 0.011319 0.002175
register -.011574 0.006014 0.005229 0.002175 0.218228
Cross Model Correlation
college collegexblack collegexhispanic collegexotherrace register
college 1.00000 0.35720 0.44990 0.21606 -0.05031
collegexblack 0.35720 1.00000 0.00000 -0.00000 0.07319
collegexhispanic 0.44990 0.00000 1.00000 0.00000 0.05053
collegexotherrace 0.21606 -0.00000 0.00000 1.00000 0.04376
register -0.05031 0.07319 0.05053 0.04376 1.00000
Cross Model Inverse Correlation
college collegexblack collegexhispanic collegexotherrace register
college 1.63559 -0.59737 -0.74491 -0.36124 0.17946
collegexblack -0.59737 1.22359 0.27580 0.13517 -0.13946
collegexhispanic -0.74491 0.27580 1.34184 0.16676 -0.13276
collegexotherrace -0.36124 0.13517 0.16676 1.08172 -0.08383
register 0.17946 -0.13946 -0.13276 -0.08383 1.02961
Cross Model Inverse Covariance
college collegexblack collegexhispanic collegexotherrace register
college 6.74396 -6.8963 -6.8278 -6.8946 0.78005
collegexblack -6.89633 39.5499 7.0779 7.2232 -1.69731
collegexhispanic -6.82781 7.0779 27.3409 7.0751 -1.28283
collegexotherrace -6.89459 7.2232 7.0751 95.5633 -1.68675
register 0.78005 -1.6973 -1.2828 -1.6868 4.71807
System Weighted MSE 1.0187
Degrees of freedom 46113
System Weighted R-Square 0.4338
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Model college
Dependent Variable college
Label Attended junior, community or 4year college by 1984?
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.643723 0.008035 80.11 <.0001 Intercept
distance 1 -0.00697 0.000485 -14.37 <.0001 Miles from
respondents HS to
nearest 2yr college
black 1 -0.05782 0.013765 -4.20 <.0001 Is respondent black?
hispanic 1 -0.11633 0.011958 -9.73 <.0001 Is respondent
hispanic?
otherrace 1 0.033595 0.019636 1.71 0.0871 Is respondent of
another race?
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Model collegexblack
Dependent Variable collegexblack
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 -154E-19 0.001958 -0.00 1.0000 Intercept
black 1 0.581107 0.007275 79.88 <.0001 Is respondent black?
distxblack 1 -0.00635 0.000616 -10.30 <.0001
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Model collegexhispanic
Dependent Variable collegexhispanic
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 1.34E-17 0.002577 0.00 1.0000 Intercept
hispanic 1 0.519995 0.007487 69.45 <.0001 Is respondent
hispanic?
distxhispanic 1 -0.00610 0.000560 -10.89 <.0001
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Model collegexotherrace
Dependent Variable collegexotherrace
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 6.98E-18 0.001136 0.00 1.0000 Intercept
otherrace 1 0.702269 0.007220 97.27 <.0001 Is respondent of
another race?
distxotherrace 1 -0.00989 0.000595 -16.62 <.0001
The SYSLIN Procedure
Three-Stage Least Squares Estimation
Model register
Dependent Variable register
Label Is respondent currently registered to vote?
Parameter Estimates
Parameter Standard Variable
Variable DF Estimate Error t Value Pr > |t| Label
Intercept 1 0.462228 0.054885 8.42 <.0001 Intercept
college 1 0.361883 0.095762 3.78 0.0002 Attended junior,
community or 4year
college by 1984?
black 1 0.286554 0.161474 1.77 0.0760 Is respondent black?
hispanic 1 0.187519 0.119711 1.57 0.1173 Is respondent
hispanic?
otherrace 1 0.149163 0.173587 0.86 0.3902 Is respondent of
another race?
collegexblack 1 -0.41439 0.299796 -1.38 0.1669
collegexhispanic 1 -0.31565 0.245606 -1.29 0.1988
collegexotherrace 1 -0.42303 0.281100 -1.50 0.1324
The analyses in shown in Table 10.9 includes a variable that is restricted, so these analyses cannot be reproduced using the available dataset.