Created via SAS program <estimate-LES-on-MPH-ER.sas>

The MODEL Procedure

Model Summary
Model Variables 3
Parameters 36
Equations 3
Number of Statements 13


The parameter a1 is shared by all 3 of the equations to be estimated.


The parameter a2 is shared by all 3 of the equations to be estimated.


The parameter a3 is shared by all 3 of the equations to be estimated.


The parameter a4 is shared by all 3 of the equations to be estimated.

The 3 Equations to Estimate
r1 = F(a1, a2, a3, a4, b1, c10(1), c11(t1), c12(t2), c13(lnkids), c14(lnmds), c15(lncaiddrugs), c16(lnmcaidenrollees))
r2 = F(a1, a2, a3, a4, b2, c20(1), c21(t1), c22(t2), c23(lnkids), c24(lnmds), c25(lncaiddrugs), c26(lnmcaidenrollees))
r3 = F(a1, a2, a3, a4, b3, c30(1), c31(t1), c32(t2), c33(lnkids), c34(lnmds), c35(lncaiddrugs), c36(lnmcaidenrollees))
Instruments 1 poz4 poz5 poz6 poz7 t1 t2 lnkids lnmds lncaiddrugs lnmcaidenrollees y

NOTE: At SUR Iteration 2 CONVERGE=0.001 Criteria Met.


Created via SAS program <estimate-LES-on-MPH-ER.sas>

The MODEL Procedure
SUR Estimation Summary

Data Set Options
DATA= SEGMENT122

Minimization Summary
Parameters Estimated 28
Method Gauss
Iterations 2

Final Convergence Criteria
R 0.000046
PPC(a3) 0.000076
RPC(c36) 0.023732
Object 0.008347
Trace(S) 73171071
Objective Value 2.988842

Observations Processed
Read 3112
Solved 3112
Used 3107
Missing 5


Created via SAS program <estimate-LES-on-MPH-ER.sas>

The MODEL Procedure

Nonlinear SUR Summary of Residual Errors 
Equation DF Model DF Error SSE MSE Root MSE R-Square Adj R-Sq
r1 9.333 3098 8.653E10 27934684 5285.3 0.9937 0.9936
r2 9.333 3098 9.512E10 30706158 5541.3 0.9880 0.9880
r3 9.333 3098 4.501E10 14530230 3811.9 0.9501 0.9500

Nonlinear SUR Parameter Estimates
Parameter Estimate Approx Std Err t Value Approx
Pr > |t|
a1 1059.726 47.7525 22.19 <.0001
a2 1553.206 46.5150 33.39 <.0001
a3 872.5003 15.9482 54.71 <.0001
a4 1493.04 40.8663 36.53 <.0001
b1 0.369944 0.000780 474.14 <.0001
b2 0.261771 0.000820 319.33 <.0001
b3 0.091784 0.000565 162.50 <.0001
c10 141069 3403.3 41.45 <.0001
c11 -776.468 6.7454 -115.11 <.0001
c12 117.7145 0.9587 122.78 <.0001
c13 -3580.69 235.6 -15.20 <.0001
c14 2142.902 144.4 14.84 <.0001
c15 1119.509 160.0 7.00 <.0001
c16 -376.87 198.0 -1.90 0.0571
c20 -178170 3525.8 -50.53 <.0001
c21 758.6982 7.0890 107.03 <.0001
c22 -85.8118 1.0076 -85.16 <.0001
c23 4398.696 247.6 17.77 <.0001
c24 -2725.44 151.7 -17.97 <.0001
c25 -857.163 168.2 -5.10 <.0001
c26 688.166 208.2 3.31 0.0010
c30 -64721.9 2083.8 -31.06 <.0001
c31 294.3886 4.8838 60.28 <.0001
c32 -39.3417 0.6942 -56.67 <.0001
c33 1197.972 170.7 7.02 <.0001
c34 -845.081 104.6 -8.08 <.0001
c35 -738.39 115.9 -6.37 <.0001
c36 29.8613 143.4 0.21 0.8350

Nonlinear SUR Estimates
Term Estimate Approx Std Err t Value Approx
Pr > |t|
Label
a1 1059.726 47.7525 22.19 <.0001  
a2 1553.206 46.5150 33.39 <.0001  
a3 872.5003 15.9482 54.71 <.0001  
a4 1493.04 40.8663 36.53 <.0001  
b1 0.369944 0.000780 474.14 <.0001  
b2 0.261771 0.000820 319.33 <.0001  
b3 0.091784 0.000565 162.50 <.0001  
b4 0.276501 0.000649 425.72 <.0001 1 - (b1 + b2 + b3)

Number of Observations Statistics for System
Used 3107 Objective 2.9888
Missing 5 Objective*N 9286

NOTE: At 3SLS Iteration 2 CONVERGE=0.001 Criteria Met.


Created via SAS program <estimate-LES-on-MPH-ER.sas>

The MODEL Procedure
3SLS Estimation Summary

Data Set Options
DATA= SEGMENT122

Minimization Summary
Parameters Estimated 28
Method Gauss
Iterations 2

Final Convergence Criteria
R 0.000391
PPC(a2) 0.00074
RPC(a2) 0.035794
Object 0.207309
Trace(S) 1.2378E8
Objective Value 0.048837

Observations Processed
Read 3112
Solved 3112
Used 3107
Missing 5


Created via SAS program <estimate-LES-on-MPH-ER.sas>

The MODEL Procedure

Nonlinear 3SLS Summary of Residual Errors 
Equation DF Model DF Error SSE MSE Root MSE R-Square Adj R-Sq
r1 9.333 3098 1.142E11 36873286 6072.3 0.9916 0.9916
r2 9.333 3098 1.509E11 48712131 6979.4 0.9810 0.9809
r3 9.333 3098 1.183E11 38196833 6180.4 0.8689 0.8686

Nonlinear 3SLS Parameter Estimates
Parameter Estimate Approx Std Err t Value Approx
Pr > |t|
a1 -963.674 77.1075 -12.50 <.0001
a2 -85.441 93.1270 -0.92 0.3590
a3 -267.675 50.2331 -5.33 <.0001
a4 -185.625 79.3070 -2.34 0.0193
b1 0.370444 0.000878 421.83 <.0001
b2 0.260624 0.00100 259.57 <.0001
b3 0.093739 0.000861 108.84 <.0001
c10 130525.2 4874.7 26.78 <.0001
c11 -768.91 7.5747 -101.51 <.0001
c12 116.7151 1.0765 108.42 <.0001
c13 -3582.74 264.5 -13.54 <.0001
c14 2124.781 162.2 13.10 <.0001
c15 1200.89 179.5 6.69 <.0001
c16 -320.093 222.2 -1.44 0.1498
c20 -179512 5640.9 -31.82 <.0001
c21 748.0251 8.6969 86.01 <.0001
c22 -84.3919 1.2361 -68.27 <.0001
c23 4129.7 304.1 13.58 <.0001
c24 -2508.53 186.2 -13.47 <.0001
c25 -749.649 206.3 -3.63 0.0003
c26 528.0399 255.6 2.07 0.0389
c30 -35215.8 3807.1 -9.25 <.0001
c31 300.7708 7.4428 40.41 <.0001
c32 -40.0937 1.0576 -37.91 <.0001
c33 1516.275 260.3 5.83 <.0001
c34 -1222.03 160.2 -7.63 <.0001
c35 -943.686 176.7 -5.34 <.0001
c36 82.51485 218.4 0.38 0.7056

Nonlinear 3SLS Estimates
Term Estimate Approx Std Err t Value Approx
Pr > |t|
Label
a1 -963.674 77.1075 -12.50 <.0001  
a2 -85.441 93.1270 -0.92 0.3590  
a3 -267.675 50.2331 -5.33 <.0001  
a4 -185.625 79.3070 -2.34 0.0193  
b1 0.370444 0.000878 421.83 <.0001  
b2 0.260624 0.00100 259.57 <.0001  
b3 0.093739 0.000861 108.84 <.0001  
b4 0.275193 0.000881 312.45 <.0001 1 - (b1 + b2 + b3)

Number of Observations Statistics for System
Used 3107 Objective 0.0488
Missing 5 Objective*N 151.7362


Created via SAS program <estimate-LES-on-MPH-ER.sas>
Elasticties (NL-3SLS) at Mean Shares

Brand Descriptions
Brand1 Ritalin SR,LA
Brand2 Metadate ER,CD
Brand3 Methylin ER
Brand4 Generic Meth SR

Cournot Aggregation and Hicks Law Check
  Brand1 Brand2 Brand3 Brand4
Elasticities Computed at Shares (S_i) 0.29381 0.29671 0.09805 0.31143
SUM_j[Em_ij*S*j] = -S_i forall i -0.29381 -0.29671 -0.09805 -0.31143
SUM_j[Eh_ij] = 0 forall i -0.00000 -0.00000 -0.00000 0.00000

Elasticities computed at the following Shares
(S_i)
Brand1 Brand2 Brand3 Brand4
0.29381 0.29671 0.09805 0.31143

Expenditure Elasticities (ETA_i) - Per '3SLS'
  Brand1 Brand2 Brand3 Brand4 SUM_i [ETA_i*S_i]
= 1
ETA_i 1.26081 0.87839 0.95607 0.88363 1.00000

Conditional Marshallian Price Elasticities (Em_ij) - Per '3SLS'
  Brand1 Brand2 Brand3 Brand4
Brand1 -1.44642 0.07134 0.03659 0.07767
Brand2 0.18301 -1.14101 0.02549 0.05411
Brand3 0.19919 0.05410 -1.26826 0.05890
Brand4 0.18410 0.05000 0.02565 -1.14338

Conditional Compensated Price Elasticities (Eh_ij) - Per '3SLS'
  Brand1 Brand2 Brand3 Brand4
Brand1 -1.07598 0.44543 0.16021 0.47033
Brand2 0.44109 -0.88038 0.11162 0.32767
Brand3 0.48010 0.33777 -1.17453 0.35665
Brand4 0.44372 0.31218 0.11228 -0.86818

Conditional Hicks-Allen Price Elasticities (Eh_ij/S_j) - Per '3SLS'
  Brand1 Brand2 Brand3 Brand4
Brand1 -3.66211 1.50126 1.63403 1.51022
Brand2 1.50126 -2.96718 1.13840 1.05215
Brand3 1.63403 1.13840 -11.97941 1.14520
Brand4 1.51022 1.05215 1.14520 -2.78769