Tom Mroz

Appendix Table A.1

Large Sample Estimates
Corresponding to Data Generating Processes in Other Tables
(Sample Size = 100,000)


OLS Two Stage Normal MLE 2 pt. Factor 3 pt. Factor 4 pt. Factor
Table 1
E[d] = 0.50 2.248 0.995 0.997 1.401 1.053 0.997
E[d] = 0.75 2.269 1.005 1.054 1.350 1.048 1.047
Table 2
E[d] = 0.50 1.917 1.042 1.047 1.274 1.069 1.054
E[d] = 0.75 1.938 0.954 0.929 1.304 1.037 0.958
Table 3
E[d] = 0.50 1.641 1.007 1.007 1.194 1.024 1.007
E[d] = 0.75 1.589 1.006 0.967 1.150 0.991 0.968
Table 4
E[d] = 0.50 2.942 0.951 0.997 1.859 1.218 1.042
E[d] = 0.75 2.982 0.974 0.895 1.859 1.274 0.970
Table 7(A)
E[d] = 0.50 2.183 1.021 1.102 1.306 1.103 1.069
E[d] = 0.75 1.938 1.019 -0.061 1.307 1.067 0.950
Table 7(B)
E[d] = 0.50 1.919 0.988 1.042 1.251 1.046 1.011
E[d] = 0.75 1.735 1.022 0.864 1.220 1.036 1.033
Table 7(C)
E[d] = 0.50 1.641 0.974 1.028 1.128 1.018 0.996
E[d] = 0.75 1.508 0.998 0.970 1.122 1.017 1.011
Table 7(D)
E[d] = 0.50 2.925 1.054 0.548 1.534 1.325 1.243
E[d] = 0.75 2.503 0.892 -1.686 1.463 1.299 1.239



Appendix Table A.2
Skewed Distributions

Correlation of Regressors: 1.00
Error Correlation: 0.33
R2's: 0.20


----------------- E[d] = 0.50 ------------------------------------ E[d] = 0.75 -----------------
Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

 Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

n = 1,000
OLS 2.362 0.168 1.883 [2.25,2.35,2.48] 2.064 0.188 1.167 [1.93,2.07,2.23]
Two Stage 0.787 6.596 43.12 [-3.2,1.05,4.82] 0.922 2.623 6.819 [-.93,0.80,2.55]
Normal MLE 1.889 1.898 4.356 [0.12,2.17,3.28] 0.005 1.846 4.366 [-1.2,-.64,0.28]
2 pt. Factor 1.328 0.366 0.240 [1.08,1.35,1.60] 1.474 0.593 0.573 [1.22,1.35,1.61]
3 pt. Factor 0.786 0.652 0.467 [0.36,0.87,1.27] 1.068 0.933 0.866 [0.56,0.99,1.25]
4 pt. Factor 0.315 0.811 1.120 [-.24,0.40,0.86] 0.754 0.917 0.892 [0.27,0.65,1.11]
n = 2,000
OLS 2.272 0.110 1.630 [2.20,2.28,2.36] 2.051 0.112 1.117 [1.97,2.05,2.13]
Two Stage 1.028 4.208 17.53 [-1.9,0.97,3.91] 1.052 1.699 2.861 [-.15,0.86,2.16]
Normal MLE 1.797 1.428 2.655 [0.31,2.16,2.89] -.455 1.274 3.723 [-1.1,-.79,-.43]
2 pt. Factor 1.363 0.223 0.181 [1.21,1.32,1.55] 1.320 0.173 0.132 [1.20,1.31,1.44]
3 pt. Factor 0.873 0.463 0.229 [0.56,0.93,1.22] 0.920 0.397 0.162 [0.59,0.99,1.24]
4 pt. Factor 0.500 0.588 0.592 [0.05,0.55,0.89] 0.675 0.503 0.356 [0.36,0.69,1.11]
n = 3,000
OLS 2.366 0.107 1.878 [2.28,2.36,2.43] 2.037 0.115 1.089 [1.96,2.02,2.11]
Two Stage 1.308 3.985 15.81 [-1.3,1.59,3.56] 0.919 1.399 1.943 [0.07,0.99,1.88]
Normal MLE 1.841 1.258 2.274 [0.80,2.03,2.88] -.369 1.396 3.804 [-1.1,-.84,0.50]
2 pt. Factor 1.406 0.199 0.204 [1.27,1.42,1.53] 1.335 0.173 0.142 [1.21,1.32,1.48]
3 pt. Factor 0.977 0.392 0.153 [0.67,1.02,1.26] 0.961 0.369 0.136 [0.72,1.05,1.21]
4 pt. Factor 0.676 0.535 0.389 [0.26,0.70,1.08] 0.698 0.449 0.291 [0.36,0.74,1.04]
n = 5,000
OLS 2.313 0.075 1.730 [2.27,2.31,2.36] 2.079 0.076 1.171 [2.02,2.08,2.14]
Two Stage 1.083 2.821 7.887 [-.71,0.83,2.91] 0.890 1.077 1.160 [0.15,0.92,1.68]
Normal MLE 1.482 1.319 1.955 [0.22,1.76,2.64] -.816 0.601 3.654 [-1.1,-.89,-.65]
2 pt. Factor 1.380 0.154 0.168 [1.28,1.39,1.48] 1.362 0.148 0.153 [1.28,1.35,1.46]
3 pt. Factor 1.032 0.354 0.125 [0.80,1.12,1.28] 0.976 0.339 0.114 [0.71,1.04,1.24]
4 pt. Factor 0.700 0.413 0.259 [0.40,0.71,0.97] 0.775 0.406 0.214 [0.48,0.84,1.11]



Appendix Table A.3
Skewed Distributions

Correlation of Regressors: 0.80
Error Correlation: 0.33
R2's: 0.20

----------------- E[d] = 0.50 ------------------------------------ E[d] = 0.75 -----------------
Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

 Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

n = 1,000
OLS 2.214 0.186 1.509 [2.07,2.23,2.35] 2.028 0.158 1.080 [1.92,2.02,2.13]
Two Stage 0.873 0.766 0.597 [0.28,0.88,1.45] 1.110 0.908 0.828 [0.53,1.03,1.83]
Normal MLE 0.968 0.726 0.523 [0.47,0.93,1.46] 0.284 1.228 2.005 [-.68,0.07,1.17]
2 pt. Factor 1.254 0.351 0.186 [1.04,1.25,1.47] 1.329 0.268 0.179 [1.14,1.34,1.54]
3 pt. Factor 0.831 0.487 0.264 [0.48,0.83,1.13] 0.941 0.450 0.204 [0.70,0.93,1.30]
4 pt. Factor 0.636 0.621 0.515 [0.20,0.62,1.04] 0.762 0.502 0.306 [0.41,0.82,1.17]
n = 2,000
OLS 2.264 0.109 1.609 [2.20,2.25,2.34] 1.990 0.119 0.994 [1.92,1.98,2.08]
Two Stage 1.022 0.589 0.343 [0.62,1.13,1.42] 0.927 0.582 0.340 [0.51,0.90,1.36]
Normal MLE 1.067 0.570 0.326 [0.72,1.09,1.49] 0.112 0.846 1.497 [-.53,-.06,0.43]
2 pt. Factor 1.301 0.220 0.138 [1.19,1.30,1.46] 1.305 0.207 0.136 [1.15,1.34,1.44]
3 pt. Factor 0.906 0.399 0.166 [0.66,0.93,1.20] 0.928 0.357 0.131 [0.66,0.97,1.21]
4 pt. Factor 0.798 0.437 0.230 [0.53,0.82,1.14] 0.749 0.414 0.232 [0.48,0.78,1.06]
n = 3,000
OLS 2.234 0.090 1.532 [2.19,2.25,2.30] 1.953 0.092 0.917 [1.88,1.96,2.02]
Two Stage 1.004 0.474 0.223 [0.70,1.01,1.31] 1.016 0.518 0.266 [0.67,1.01,1.43]
Normal MLE 1.064 0.420 0.179 [0.77,1.07,1.35] 0.148 0.812 1.380 [-.48,-.02,0.39]
2 pt. Factor 1.309 0.180 0.128 [1.20,1.33,1.43] 1.279 0.144 0.098 [1.19,1.28,1.37]
3 pt. Factor 1.018 0.287 0.082 [0.80,1.04,1.26] 0.994 0.275 0.075 [0.82,1.02,1.18]
4 pt. Factor 0.855 0.352 0.144 [0.58,0.92,1.13] 0.882 0.311 0.110 [0.68,0.89,1.10]
n = 5,000
OLS 2.221 0.069 1.495 [2.17,2.22,2.27] 2.019 0.073 1.044 [1.97,2.02,2.06]
Two Stage 0.996 0.302 0.090 [0.78,1.02,1.21] 1.034 0.367 0.135 [0.74,1.02,1.30]
Normal MLE 1.109 0.264 0.081 [0.97,1.11,1.30] 0.077 0.585 1.191 [-.32,-.06,0.34]
2 pt. Factor 1.283 0.116 0.093 [1.21,1.29,1.37] 1.311 0.113 0.110 [1.22,1.32,1.40]
3 pt. Factor 0.992 0.209 0.043 [0.85,1.02,1.16] 1.007 0.257 0.066 [0.86,1.01,1.21]
4 pt. Factor 0.884 0.222 0.062 [0.72,0.89,1.05] 0.892 0.285 0.092 [0.69,0.91,1.13]



Appendix Table A.4
Skewed Distributions

Correlation of Regressors: 0.80
Error Correlation: 0.33
R2's: 0.33

----------------- E[d] = 0.50 ------------------------------------ E[d] = 0.75 -----------------
Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

 Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

n = 1,000
OLS 1.889 0.114 0.803 [1.82,1.90,1.96] 1.688 0.112 0.486 [1.61,1.70,1.77]
Two Stage 1.002 0.405 0.162 [0.70,1.04,1.27] 0.883 0.451 0.215 [0.55,0.86,1.24]
Normal MLE 1.090 0.341 0.123 [0.86,1.09,1.34] 0.715 0.557 0.388 [0.30,0.67,1.05]
2 pt. Factor 1.175 0.213 0.075 [1.00,1.17,1.31] 1.139 0.191 0.055 [1.02,1.14,1.25]
3 pt. Factor 0.972 0.254 0.065 [0.79,0.97,1.14] 0.914 0.272 0.081 [0.77,0.92,1.10]
4 pt. Factor 0.877 0.277 0.091 [0.70,0.88,1.08] 0.803 0.307 0.132 [0.64,0.80,1.02]
n = 2,000
OLS 1.863 0.092 0.753 [1.79,1.87,1.94] 1.704 0.091 0.504 [1.65,1.70,1.75]
Two Stage 0.956 0.270 0.074 [0.75,0.96,1.12] 0.986 0.369 0.135 [0.74,0.95,1.26]
Normal MLE 1.004 0.257 0.065 [0.84,1.03,1.16] 0.847 0.421 0.198 [0.54,0.83,1.14]
2 pt. Factor 1.179 0.148 0.054 [1.08,1.19,1.27] 1.177 0.154 0.055 [1.08,1.17,1.28]
3 pt. Factor 0.956 0.203 0.043 [0.82,0.95,1.11] 0.979 0.207 0.043 [0.83,0.99,1.13]
4 pt. Factor 0.882 0.242 0.072 [0.76,0.90,1.03] 0.890 0.237 0.068 [0.74,0.90,1.06]
n = 3,000
OLS 1.912 0.072 0.837 [1.87,1.92,1.96] 1.723 0.075 0.528 [1.67,1.73,1.78]
Two Stage 0.957 0.227 0.053 [0.81,0.95,1.12] 1.037 0.280 0.079 [0.88,1.06,1.22]
Normal MLE 1.014 0.215 0.046 [0.83,1.01,1.20] 0.822 0.387 0.180 [0.54,0.82,1.06]
2 pt. Factor 1.198 0.117 0.053 [1.11,1.20,1.28] 1.200 0.102 0.050 [1.13,1.20,1.27]
3 pt. Factor 0.978 0.181 0.033 [0.86,1.00,1.10] 1.000 0.165 0.027 [0.89,1.02,1.13]
4 pt. Factor 0.909 0.185 0.042 [0.78,0.91,1.04] 0.939 0.184 0.037 [0.82,0.95,1.08]
n = 5,000
OLS 1.884 0.050 0.784 [1.85,1.88,1.92] 1.741 0.052 0.552 [1.70,1.74,1.78]
Two Stage 0.997 0.182 0.032 [0.89,0.99,1.12] 0.973 0.242 0.059 [0.82,0.94,1.16]
Normal MLE 1.044 0.165 0.029 [0.95,1.03,1.15] 0.804 0.300 0.128 [0.58,0.80,1.04]
2 pt. Factor 1.207 0.091 0.051 [1.15,1.20,1.25] 1.208 0.092 0.052 [1.15,1.21,1.27]
3 pt. Factor 1.025 0.131 0.017 [0.95,1.02,1.11] 1.011 0.141 0.020 [0.93,1.01,1.11]
4 pt. Factor 0.970 0.148 0.023 [0.88,0.96,1.06] 0.942 0.176 0.034 [0.83,0.96,1.05]



Appendix Table A.5
Skewed Distributions

Correlation of Regressors: 0.80
Error Correlation: 0.33
R2's: 0.50

----------------- E[d] = 0.50 ------------------------------------ E[d] = 0.75 -----------------
Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

 Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

n = 1,000
OLS 1.596 0.095 0.364 [1.53,1.60,1.67] 1.522 0.092 0.281 [1.45,1.53,1.59]
Two Stage 1.000 0.244 0.059 [0.84,0.98,1.13] 1.042 0.274 0.076 [0.85,1.03,1.23]
Normal MLE 1.023 0.215 0.046 [0.87,1.03,1.15] 1.032 0.294 0.087 [0.86,1.02,1.23]
2 pt. Factor 1.109 0.169 0.040 [1.01,1.10,1.20] 1.159 0.161 0.051 [1.06,1.17,1.26]
3 pt. Factor 0.981 0.191 0.037 [0.87,0.99,1.12] 1.010 0.203 0.041 [0.87,1.02,1.15]
4 pt. Factor 0.921 0.219 0.054 [0.76,0.91,1.05] 0.964 0.218 0.048 [0.81,0.96,1.12]
n = 2,000
OLS 1.633 0.061 0.405 [1.59,1.64,1.67] 1.479 0.060 0.233 [1.44,1.47,1.53]
Two Stage 1.052 0.185 0.037 [0.92,1.03,1.17] 0.969 0.165 0.028 [0.86,0.96,1.10]
Normal MLE 1.073 0.147 0.027 [0.96,1.06,1.16] 0.943 0.170 0.032 [0.83,0.96,1.07]
2 pt. Factor 1.145 0.105 0.032 [1.07,1.13,1.22] 1.117 0.086 0.021 [1.07,1.11,1.17]
3 pt. Factor 1.023 0.120 0.015 [0.94,1.03,1.11] 0.993 0.123 0.015 [0.91,0.99,1.08]
4 pt. Factor 0.988 0.134 0.018 [0.88,0.98,1.08] 0.955 0.143 0.022 [0.86,0.96,1.07]
n = 3,000
OLS 1.648 0.053 0.423 [1.61,1.65,1.69] 1.526 0.053 0.280 [1.49,1.52,1.57]
Two Stage 1.012 0.133 0.018 [0.93,1.01,1.09] 0.985 0.167 0.028 [0.85,0.98,1.10]
Normal MLE 1.046 0.120 0.016 [0.98,1.04,1.12] 0.966 0.167 0.029 [0.84,0.96,1.08]
2 pt. Factor 1.142 0.079 0.026 [1.09,1.14,1.19] 1.129 0.086 0.024 [1.07,1.12,1.19]
3 pt. Factor 1.026 0.103 0.011 [0.97,1.02,1.10] 0.991 0.125 0.016 [0.90,1.00,1.09]
4 pt. Factor 0.981 0.107 0.012 [0.90,0.98,1.06] 0.954 0.134 0.020 [0.86,0.95,1.04]
n = 5,000
OLS 1.638 0.039 0.408 [1.61,1.64,1.66] 1.505 0.040 0.257 [1.48,1.51,1.53]
Two Stage 0.995 0.107 0.011 [0.92,1.01,1.06] 0.994 0.123 0.015 [0.91,0.98,1.08]
Normal MLE 1.041 0.093 0.010 [0.97,1.05,1.11] 0.961 0.139 0.021 [0.85,0.96,1.06]
2 pt. Factor 1.131 0.062 0.021 [1.09,1.13,1.18] 1.133 0.061 0.021 [1.09,1.13,1.18]
3 pt. Factor 1.019 0.077 0.006 [0.97,1.02,1.07] 1.007 0.098 0.010 [0.93,1.00,1.09]
4 pt. Factor 0.985 0.083 0.007 [0.92,0.99,1.06] 0.976 0.102 0.011 [0.89,0.97,1.05]



Appendix Table A.6
Skewed Distributions

Correlation of Regressors: 0.80
Error Correlation: 0.50
R2's: 0.20

----------------- E[d] = 0.50 ------------------------------------ E[d] = 0.75 -----------------
Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

 Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

n = 1,000
OLS 2.850 0.136 3.441 [2.77,2.84,2.94] 2.616 0.172 2.639 [2.50,2.62,2.74]
Two Stage 1.038 0.717 0.510 [0.60,1.01,1.54] 0.933 1.059 1.114 [0.30,0.93,1.53]
Normal MLE 0.332 0.889 1.228 [-.37,0.28,1.02] -1.86 0.268 8.277 [-2.1,-1.9,-1.6]
2 pt. Factor 1.516 0.138 0.285 [1.41,1.54,1.62] 1.509 0.157 0.284 [1.41,1.53,1.61]
3 pt. Factor 1.289 0.158 0.109 [1.18,1.29,1.41] 1.298 0.171 0.118 [1.16,1.30,1.42]
4 pt. Factor 1.177 0.170 0.060 [1.06.1.17,1.31] 1.148 0.206 0.064 [1.02,1.20,1.31]
n = 2,000
OLS 2.829 0.112 3.357 [2.76,2.82,2.89] 2.468 0.099 2.166 [2.41,2.48,2.53]
Two Stage 1.014 0.489 0.237 [0.70,0.98,1.31] 1.009 0.645 0.412 [0.64,1.00,1.48]
Normal MLE 0.205 0.656 1.059 [-.30,0.07,0.65] -1.791 0.163 7.814 [-1.9,-1.8,-1.7]
2 pt. Factor 1.511 0.111 0.274 [1.43,1.52,1.60] 1.446 0.104 0.210 [1.36,1.45,1.51]
3 pt. Factor 1.291 0.117 0.098 [1.19,1.30,1.38] 1.263 0.109 0.081 [1.19,1.26,1.33]
4 pt. Factor 1.199 0.134 0.057 [1.10,1.20,1.30] 1.163 0.124 0.042 [1.08,1.17,1.24]
n = 3,000
OLS 2.825 0.092 3.338 [2.76,2.82,2.90] 2.525 0.082 2.331 [2.45,2.53,2.57]
Two Stage 1.002 0.441 0.192 [0.68,1.03,1.33] 0.995 0.542 0.291 [0.64,0.96,1.41]
Normal MLE 0.126 0.494 1.005 [-.23,0.01,0.41] -1.82 0.152 7.984 [-1.9,-1.8,-1.7]
2 pt. Factor 1.496 0.081 0.252 [1.44,1.49,1.55] 1.453 0.093 0.214 [1.39,1.45,1.51]
3 pt. Factor 1.285 0.091 0.089 [1.22,1.29,1.35] 1.274 0.098 0.084 [1.20,1.27,1.34]
4 pt. Factor 1.197 0.105 0.050 [1.13,1.19,1.28] 1.195 0.109 0.050 [1.12,1.19,1.27]
n = 5,000
OLS 2.873 0.078 3.515 [2.83,2.88,2.92] 2.458 0.061 2.128 [2.41,2.46,2.49]
Two Stage 1.031 0.328 0.107 [0.79,1.03,1.23] 0.991 0.432 0.185 [0.69,0.99,1.32]
Normal MLE 0.364 0.401 0.563 [0.10,0.34,0.63] -1.71 0.113 7.383 [-1.8,-1.7,-1.6]
2 pt. Factor 1.527 0.070 0.283 [1.48,1.53,1.57] 1.448 0.069 0.206 [1.40,1.45,1.50]
3 pt. Factor 1.299 0.076 0.095 [1.25,1.30,1.34] 1.271 0.076 0.079 [1.22,1.28,1.33]
4 pt. Factor 1.219 0.074 0.053 [1.17,1.22,1.26] 1.205 0.080 0.048 [1.16,1.20,1.26]



Appendix Table A.7
Normal Distributions

Correlation of Regressors: 0.80
Error Correlation: 0.00
R2's: 0.20

----------------- E[d] = 0.50 ------------------------------------ E[d] = 0.75 -----------------
Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

 Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

n = 1,000
OLS 0.994 0.144 0.021 [0.89,0.98,1.10] 1.021 0.172 0.030 [0.90,1.04,1.13]
Two Stage 1.138 0.832 0.704 [0.63,1.07,1.64] 1.051 0.921 0.842 [0.30,1.03,1.71]
Normal MLE 1.131 0.828 0.695 [0.66,1.11,1.73] 0.998 0.948 0.890 [0.22,0.93,1.81]
2 pt. Factor 1.095 0.653 0.432 [0.63,1.06,1.59] 0.927 0.733 0.537 [0.50,0.83,1.39]
3 pt. Factor 1.081 0.907 0.822 [0.40,1.06,1.82] 0.839 0.956 0.930 [0.07,0.79,1.71]
4 pt. Factor 1.048 0.946 0.889 [0.31,1.11,1.80] 0.965 0.993 0.977 [0.21,0.99,1.71]
n = 2,000
OLS 0.997 0.101 0.010 [0.93,1.00,1.06] 1.012 0.108 0.012 [0.93,1.00,1.09]
Two Stage 1.018 0.465 0.215 [0.65,1.06,1.26] 1.072 0.634 0.403 [0.58,1.06,1.55]
Normal MLE 1.006 0.455 0.205 [0.72,1.03,1.26] 0.057 0.613 0.375 [0.65,1.07,1.52]
2 pt. Factor 0.964 0.398 0.158 [0.73,1.03,1.19] 1.023 0.492 0.240 [0.72,1.03,1.38]
3 pt. Factor 0.878 0.526 0.289 [0.51,0.86,1.21] 0.996 0.714 0.505 [0.40,1.04,1.47]
4 pt. Factor 0.897 0.513 0.271 [0.55,0.88,1.26] 1.010 0.746 0.551 [0.49,1.02,1.51]
n = 3,000
OLS 0.990 0.087 0.008 [0.94,0.99,1.04] 1.000 0.096 0.009 [0.93,1.00,1.07]
Two Stage 1.000 0.387 0.148 [0.71,0.91,1.30] 1.007 0.564 0.315 [0.68,0.96,1.36]
Normal MLE 0.985 0.394 0.154 [0.70,0.94,1.25] 1.016 0.483 0.231 [0.70,1.00,1.34]
2 pt. Factor 0.964 0.400 0.160 [0.71,0.94,1.20] 0.950 0.404 0.164 [0.66,0.99,1.24]
3 pt. Factor 0.944 0.445 0.199 [0.58,0.92,1.28] 0.930 0.543 0.297 [0.50,0.92,1.34]
4 pt. Factor 0.920 0.466 0.221 [0.58,0.87,1.21] 0.978 0.559 0.310 [0.62,0.99,1.36]
n = 5,000
OLS 0.999 0.066 0.004 [0.95,1.00,1.05] 0.986 0.081 0.007 [0.93,1.00,1.05]
Two Stage 0.977 0.316 0.099 [0.75,0.98,1.20] 1.006 0.461 0.210 [0.71,1.02,1.29]
Normal MLE 0.969 0.316 0.100 [0.75,0.98,1.18] 1.011 0.428 0.181 [0.70,1.05,1.28]
2 pt. Factor 0.990 0.283 0.080 [0.85,1.01,1.15] 1.026 0.374 0.139 [0.81,1.04,1.24]
3 pt. Factor 0.970 0.364 0.132 [0.72,1.00,1.22] 1.008 0.504 0.251 [0.69,1.07,1.37]
4 pt. Factor 0.951 0.364 0.133 [0.71,0.97,1.23] 1.009 0.493 0.241 [0.67,1.02,1.34]



Appendix Table A.8
Skewed Distribution in Probit

Correlation of Regressors: 0.80
Error Correlation: 0.33
R2's: 0.20

----------------- E[d] = 0.50 ------------------------------------ E[d] = 0.75 -----------------
Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

 Mean Standard

Deviation

 MSE Quartiles

[25,50,75]

n = 1,000
OLS 0.986 0.199 0.039 [0.84,0.98,1.10] 0.967 0.179 0.033 [0.85,0.97,1.08]
Two Stage 1.106 0.659 0.442 [0.62,1.07,1.63] 0.971 0.821 0.668 [0.53,0.98,1.56]
Normal MLE 1.122 0.610 0.384 [0.67,1.17,1.56] 1.015 0.702 0.488 [0.52,1.04,1.50]
2 pt. Factor 1.093 0.624 0.394 [0.73,1.07,1.42] 0.923 0.522 0.275 [0.69,0.94,1.22]
3 pt. Factor 1.087 0.761 0.580 [0.51,1.10,1.65] 0.657 0.777 0.716 [0.09,0.69,1.22]
4 pt. Factor 0.927 0.760 0.576 [0.41,0.91,1.48] 0.588 0.786 0.781 [0.09,0.55,1.02]
n = 2,000
OLS 1.001 0.112 0.012 [0.94,1.00,1.08] 1.014 0.120 0.015 [0.91,1.01,1.10]
Two Stage 1.018 0.556 0.306 [0.62,0.99,1.24] 1.013 0.526 0.274 [0.60,0.98,1.33]
Normal MLE 1.009 0.542 0.291 [0.65,0.98,1.28] 0.991 0.555 0.305 [0.66,1.04,1.37]
2 pt. Factor 1.008 0.463 0.213 [0.71,0.97,1.32] 1.032 0.492 0.241 [0.65,1.04,1.35]
3 pt. Factor 0.960 0.588 0.344 [0.55,0.89,1.40] 0.978 0.647 0.415 [0.49,0.98,1.47]
4 pt. Factor 0.940 0.627 0.392 [0.48,0.90,1.37] 0.948 0.642 0.411 [0.47,0.88,1.41]
n = 3,000
OLS 0.981 0.103 0.011 [0.91,0.99,1.05] 0.996 0.097 0.009 [0.95,1.00,1.06]
Two Stage 1.020 0.395 0.155 [0.79,1.04,1.26] 0.926 0.481 0.235 [0.66,0.97,1.25]
Normal MLE 1.036 0.372 0.138 [0.78,1.05,1.29] 0.978 0.441 0.193 [0.75,0.97,1.28]
2 pt. Factor 1.019 0.345 0.118 [0.77,1.03,1.24] 0.964 0.401 0.160 [0.69,1.00,1.20]
3 pt. Factor 1.042 0.457 0.208 [0.72,1.08,1.34] 0.976 0.512 0.260 [0.62,1.05,1.29]
4 pt. Factor 1.002 0.478 0.226 [0.68,0.99,1.33] 0.972 0.520 0.269 [0.59,0.99,1.36]
n = 5,000
OLS 0.979 0.078 0.006 [0.92,0.98,1.03] 1.015 0.079 0.006 [0.95,1.01,1.07]
Two Stage 0.968 0.360 0.130 [0.70,0.96,1.21] 0.962 0.344 0.118 [0.72,0.98,1.18]
Normal MLE 0.968 0.365 0.133 [0.73,0.98,1.21] 0.962 0.313 0.099 [0.73,0.95,1.18]
2 pt. Factor 0.974 0.318 0.101 [0.77,0.96,1.21] 0.982 0.277 0.076 [0.85,0.99,1.13]
3 pt. Factor 0.959 0.404 0.163 [0.67,0.94,1.23] 0.848 0.295 0.109 [0.66,0.83,1.00]
4 pt. Factor 0.943 0.412 0.171 [0.67,0.93,1.23] 0.823 0.322 0.134 [0.63,0.82,0.99]