The SAS System 09:24 Tuesday, November 2, 1999 8 Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------- QB 17 112.8705882 13.4242674 85.4000000 131.6000000 Y 17 394.5882353 35.1035234 353.0000000 469.0000000 PB 17 33.4558824 4.4386316 25.6800000 39.8400000 PL 17 19.9194118 2.1998337 17.8600000 27.1100000 PP 17 53.2923529 2.9836252 45.7400000 57.9000000 LPB 17 3.5017838 0.1347220 3.2457125 3.6848714 LY 17 5.9742393 0.0868179 5.8664681 6.1506028 LQB 17 4.7191894 0.1242633 4.4473461 4.8797670 LPL 17 2.9866445 0.1004617 2.8825636 3.2999027 LPP 17 3.9742657 0.0574858 3.8229732 4.0587174 -------------------------------------------------------------------- The SAS System 09:24 Tuesday, November 2, 1999 9 MODEL Procedure Model Summary Model Variables 1 Parameters 5 Equations 1 Number of Statements 1 Model Variables: LQB Parameters: B1 B2 B3 B4 B5 Equations: LQB The SAS System 09:24 Tuesday, November 2, 1999 10 MODEL Procedure The Equation to Estimate is: LQB = F( B1(1), B2(LPB), B3(LPL), B4(LPP), B5(LY) ) Instruments: 1 LPB LPL LPP LY The SAS System 09:24 Tuesday, November 2, 1999 11 MODEL Procedure GMM Estimation NOTE: At GMM Iteration 1 convergence assumed because OBJECTIVE=1.234208E-28 is almost zero (< 1E-12). GMM Estimation Summary Dataset Option Dataset DATA= ONE Parameters Estimated 5 Kernel Used PARZEN l(n) 1.76234035 Minimization Summary Method GAUSS Iterations 1 Final Convergence Criteria Criterion 1.2342E-28 R 1 PPC 0 RPC . Object 4.7516E-23 Trace(S) 0.00492312 Objective Value 1.2342E-28 Observations Processed Read 17 Solved 17 The SAS System 09:24 Tuesday, November 2, 1999 12 MODEL Procedure GMM Estimation Nonlinear GMM Summary of Residual Errors DF DF Equation Model Error SSE MSE Root MSE R-Square Adj R-Sq LQB 5 12 0.05908 0.0049231 0.07016 0.7609 0.6812 Nonlinear GMM Parameter Estimates Approx. 'T' Approx. Parameter Estimate Std Err Ratio Prob>|T| B1 4.672576 1.31441 3.55 0.0040 B2 -0.826572 0.20675 -4.00 0.0018 B3 0.199681 0.15513 1.29 0.2223 B4 0.437138 0.32846 1.33 0.2080 B5 0.101672 0.22835 0.45 0.6641 Number of Observations Statistics for System Used 17 Objective 1.234E-28 Missing 0 Objective*N 2.098E-27 The SAS System 09:24 Tuesday, November 2, 1999 13 MODEL Procedure Model Summary Model Variables 1 Parameters 5 Equations 1 Number of Statements 1 Model Variables: LQB Parameters: B1 B2 B3 B4 B5 Equations: LQB The SAS System 09:24 Tuesday, November 2, 1999 14 MODEL Procedure The Equation to Estimate is: LQB = F( B1(1), B2(LPB), B3(LPL), B4(LPP), B5(LY) ) The SAS System 09:24 Tuesday, November 2, 1999 15 MODEL Procedure OLS Estimation OLS Estimation Summary Dataset Option Dataset DATA= ONE Parameters Estimated 5 Minimization Summary Method GAUSS Iterations 1 Final Convergence Criteria R 2.5264E-12 PPC 1.83E-11 RPC(B1) 46262.14 Object 0.9998439 Trace(S) 0.00492312 Objective Value 0.00347515 Observations Processed Read 17 Solved 17 The SAS System 09:24 Tuesday, November 2, 1999 16 MODEL Procedure OLS Estimation Nonlinear OLS Summary of Residual Errors DF DF Equation Model Error SSE MSE Root MSE R-Square Adj R-Sq LQB 5 12 0.05908 0.0049231 0.07016 0.7609 0.6812 Nonlinear OLS Parameter Estimates Approx. 'T' Approx. Parameter Estimate Std Err Ratio Prob>|T| B1 4.672576 1.65958 2.82 0.0156 B2 -0.826572 0.18265 -4.53 0.0007 B3 0.199681 0.21272 0.94 0.3664 B4 0.437138 0.38369 1.14 0.2768 B5 0.101672 0.29397 0.35 0.7354 Number of Observations Statistics for System Used 17 Objective 0.003475 Missing 0 Objective*N 0.0591 Heteroscedasticity Test Equation Test Statistic DF Prob Variables LQB White's Test 14.04 14 0.4468 Cross of all vars The SAS System 09:24 Tuesday, November 2, 1999 17 MODEL Procedure Model Summary Model Variables 1 Parameters 5 Equations 1 Number of Statements 1 Model Variables: LQB Parameters: B1 B2 B3 B4 B5 Equations: LQB The SAS System 09:24 Tuesday, November 2, 1999 18 MODEL Procedure The Equation to Estimate is: LQB = F( B1(1), B2(LPB), B3(LPL), B4(LPP), B5(LY) ) The SAS System 09:24 Tuesday, November 2, 1999 19 MODEL Procedure OLS Estimation OLS Estimation Summary Dataset Option Dataset DATA= ONE Parameters Estimated 5 Minimization Summary Method GAUSS Iterations 1 Final Convergence Criteria R 2.5264E-12 PPC 1.83E-11 RPC(B1) 46262.14 Object 0.9998439 Trace(S) 0.00492312 Objective Value 0.00347515 Observations Processed Read 17 Solved 17 The SAS System 09:24 Tuesday, November 2, 1999 20 MODEL Procedure OLS Estimation Nonlinear OLS Summary of Residual Errors DF DF Equation Model Error SSE MSE Root MSE R-Square Adj R-Sq LQB 5 12 0.05908 0.0049231 0.07016 0.7609 0.6812 Nonlinear OLS Parameter Estimates Approx. 'T' Approx. Parameter Estimate Std Err Ratio Prob>|T| B1 4.672576 1.65958 2.82 0.0156 B2 -0.826572 0.18265 -4.53 0.0007 B3 0.199681 0.21272 0.94 0.3664 B4 0.437138 0.38369 1.14 0.2768 B5 0.101672 0.29397 0.35 0.7354 Number of Observations Statistics for System Used 17 Objective 0.003475 Missing 0 Objective*N 0.0591 Heteroscedasticity Test Equation Test Statistic DF Prob Variables LQB Breusch-Pagan 1.47 2 0.4790 Y, PB, 1 The SAS System 09:24 Tuesday, November 2, 1999 21 Autoreg Procedure Dependent Variable = LQB Ordinary Least Squares Estimates SSE 0.059077 DFE 12 MSE 0.004923 Root MSE 0.070165 SBC -33.846 AIC -38.0121 Reg Rsq 0.7609 Total Rsq 0.7609 Durbin-Watson 1.1501 Variable DF B Value Std Error t Ratio Approx Prob Intercept 1 4.672576 1.6596 2.816 0.0156 LPB 1 -0.826572 0.1826 -4.526 0.0007 LPL 1 0.199681 0.2127 0.939 0.3664 LPP 1 0.437138 0.3837 1.139 0.2768 LY 1 0.101672 0.2940 0.346 0.7354 Multiplicative Heteroscedasticity Estimates SSE 0.146342 OBS 17 MSE 0.008608 Root MSE 0.092781 Log L 29.05986 Total Rsq 0.4077 SBC -35.454 AIC -42.1197 Normality Test 2.7217 Prob>Chi-Sq 0.2564 Variable DF B Value Std Error t Ratio Approx Prob Intercept 1 4.473554 2.8147 1.589 0.1120 LPB 1 -0.371670 0.4992 -0.745 0.4565 LPL 1 0.562660 0.4828 1.165 0.2438 LPP 1 0.691630 0.4985 1.387 0.1653 LY 1 -0.476520 0.6284 -0.758 0.4483 HET0 1 0.178020 1.1233 0.158 0.8741 HET1 1 -0.102034 0.0383 -2.661 0.0078 HET2 1 1.119578 0.2091 5.353 0.0001