Tom Mroz


Table 1
Normal 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 2.274 0.176 1.653 [2.15,2.28,2.37] 2.302 0.168 1.724 [2.19,2.30,2.44]
Two Stage 0.872 0.731 0.546 [0.42,0.91,1.36] 1.102 0.894 0.801 [0.61,1.11,1.77]
Normal MLE 0.921 0.650 0.424 [0.47,0.89,1.39] 1.172 0.704 0.519 [0.67,1.09,1.63]
2 pt. Factor 1.537 0.569 0.608 [1.11,1.44,1.89] 1.762 0.700 1.066 [1.27,1.70,2.21]
3 pt. Factor 1.028 0.707 0.496 [0.45,0.94,1.56] 1.431 0.886 0.963 [0.88,1.23,1.78]
4 pt. Factor 0.935 0.734 0.537 [0.43,0.79,1.47] 1.217 0.903 0.855 [0.62,1.15,1.63]
n = 2,000
OLS 2.294 0.111 1.685 [2.21,2.29,2.36] 2.226 0.105 1.513 [2.15,2.22,2.30]
Two Stage 1.088 0.523 0.279 [0.79,1.17,1.39] 0.901 0.744 0.557 [0.36,0.77,1.39]
Normal MLE 1.073 0.489 0.242 [0.74,1.05,1.43] 0.976 0.597 0.354 [0.51,0.91,1.32]
2 pt. Factor 1.526 0.373 0.414 [1.27,1.49,1.72] 1.600 0.512 0.618 [1.21,1.65,2.03]
3 pt. Factor 1.191 0.509 0.293 [0.83,1.19,1.49] 1.082 0.607 0.372 [0.61,1.03,1.58]
4 pt. Factor 1.074 0.556 0.312 [0.66,1.05,1.38] 0.985 0.687 0.467 [0.53,0.82,1.56]
n = 3,000
OLS 2.306 0.090 1.715 [2.25,2.29,2.36] 2.276 0.107 1.640 [2.19,2.28,2.35]
Two Stage 0.974 0.470 0.219 [0.65,0.96,1.30] 0.886 0.590 0.358 [0.50,0.81,1.35]
Normal MLE 0.954 0.419 0.176 [0.70,0.92,1.20] 0.933 0.358 0.131 [0.67,0.89,1.15]
2 pt. Factor 1.484 0.317 0.333 [1.25,1.43,1.64] 1.445 0.389 0.348 [1.14,1.42,1.64]
3 pt. Factor 1.059 0.454 0.208 [0.73,1.01,1.35] 1.043 0.438 0.192 [0.67,0.97,1.34]
4 pt. Factor 0.991 0.511 0.258 [0.66,0.95,1.37] 0.882 0.461 0.224 [0.48,0.85,1.22]
n = 5,000
OLS 2.286 0.068 1.658 [2.24,2.28,2.33] 2.327 0.085 1.769 [2.26,2.33,2.38]
Two Stage 0.941 0.320 0.105 [0.74,0.97,1.18] 0.988 0.424 0.178 [0.69,1.04,1.25]
Normal MLE 0.963 0.268 0.073 [0.76,1.00,1.17] 1.007 0.339 0.114 [0.82,0.97,1.17]
2 pt. Factor 1.420 0.203 0.217 [1.27,1.43,1.55] 1.499 0.337 0.361 [1.24,1.44,1.67]
3 pt. Factor 1.040 0.271 0.074 [0.90,1.05,1.23] 1.113 0.365 0.144 [0.87,1.07,1.31]
4 pt. Factor 0.967 0.298 0.089 [0.78,0.99,1.18] 1.017 0.414 0.170 [0.74,0.98,1.20]



Table 2
Normal 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 1.918 0.127 0.858 [1.81,1.93,2.01] 1.914 0.131 0.853 [1.84,1.90,1.99]
Two Stage 1.024 0.487 0.235 [0.71,1.03,1.34] 0.983 0.573 0.325 [0.63,0.99,1.43]
Normal MLE 1.044 0.415 0.172 [0.83,1.08,1.31] 0.970 0.414 0.170 [0.68,0.92,1.25]
2 pt. Factor 1.359 0.342 0.244 [1.13,1.32,1.56] 1.401 0.390 0.312 [1.10,1.33,1.66]
3 pt. Factor 1.097 0.410 0.176 [0.85,1.09,1.29] 1.068 0.473 0.226 [0.74,1.00,1.24]
4 pt. Factor 1.049 0.472 0.223 [0.80,1.06,1.29] 1.022 0.482 0.230 [0.74,0.97,1.28]
n = 2,000
OLS 1.944 0.079 0.898 [1.91,1.95,2.00] 1.876 0.093 0.776 [1.81,1.88,1.94]
Two Stage 0.943 0.329 0.110 [0.71,0.94,1.18] 0.952 0.390 0.153 [0.71,0.96,1.19]
Normal MLE 0.951 0.280 0.080 [0.78,0.94,1.12] 0.949 0.277 0.078 [0.79,0.97,1.09]
2 pt. Factor 1.283 0.200 0.120 [1.17,1.25,1.39] 1.334 0.254 0.176 [1.15,1.31,1.46]
3 pt. Factor 0.996 0.276 0.076 [0.81,0.99,1.16] 1.031 0.281 0.079 [0.84,1.01,1.19]
4 pt. Factor 0.939 0.280 0.081 [0.76,0.95,1.10] 0.970 0.326 0.106 [0.79,0.98,1.12]
n = 3,000
OLS 1.933 0.063 0.874 [1.89,1.94,1.98] 1.913 0.077 0.839 [1.86,1.92,1.97]
Two Stage 1.007 0.287 0.082 [0.82,1.03,1.22] 0.997 0.291 0.084 [0.80,1.02,1.19]
Normal MLE 1.011 0.247 0.061 [0.80,1.04,1.19] 1.004 0.217 0.047 [0.85,1.00,1.14]
2 pt. Factor 1.293 0.174 0.116 [1.16,1.28,1.40] 1.316 0.189 0.135 [1.17,1.28,1.42]
3 pt. Factor 1.043 0.248 0.063 [0.85,1.03,1.22] 1.079 0.228 0.058 [0.97,1.05,1.23]
4 pt. Factor 1.010 0.262 0.068 [0.82,0.99,1.24] 1.040 0.229 0.054 [0.89,1.05,1.19]
n = 5,000
OLS 1.933 0.049 0.874 [1.90,1.94,1.96] 1.920 0.053 0.849 [1.89,1.92,1.95]
Two Stage 1.004 0.210 0.044 [0.83,0.97,1.20] 0.986 0.224 0.050 [0.82,0.99,1.14]
Normal MLE 1.003 0.188 0.035 [0.87,0.99,1.15] 1.013 0.181 0.033 [0.87,1.00,1.13]
2 pt. Factor 1.291 0.114 0.098 [1.22,1.27,1.38] 1.323 0.159 0.129 [1.22,1.32,1.42]
3 pt. Factor 1.036 0.177 0.032 [0.90,1.05,1.15] 1.094 0.191 0.045 [0.97,1.08,1.21]
4 pt. Factor 1.002 0.198 0.039 [0.85,0.99,1.15] 1.017 0.188 0.035 [0.88,1.01,1.16]



Table 3
Normal 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 1.608 0.089 0.378 [1.55,1.61,1.66] 1.593 0.098 0.361 [1.52,1.57,1.66]
Two Stage 1.011 0.266 0.070 [0.80,1.01,1.20] 0.943 0.281 0.081 [0.76,0.95,1.13]
Normal MLE 1.010 0.231 0.053 [0.85,1.00,1.20] 0.967 0.234 0.055 [0.83,0.97,1.12]
2 pt. Factor 1.206 0.177 0.073 [1.08,1.20,1.33] 1.176 0.213 0.076 [1.03,1.18,1.30]
3 pt. Factor 1.048 0.229 0.054 [0.88,1.01,1.21] 1.018 0.263 0.069 [0.85,0.97,1.20]
4 pt. Factor 1.014 0.251 0.063 [0.82,0.99,1.23] 0.988 0.286 0.081 [0.80,0.95,1.22]
n = 2,000
OLS 1.601 0.062 0.365 [1.56,1.60,1.63] 1.623 0.072 0.393 [1.58,1.63,1.67]
Two Stage 0.991 0.172 0.029 [0.88,0.99,1.12] 1.000 0.211 0.044 [0.84,1.02,1.15]
Normal MLE 0.993 0.137 0.019 [0.90,1.00,1.08] 0.990 0.184 0.034 [0.87,0.97,1.12]
2 pt. Factor 1.183 0.118 0.047 [1.11,1.18,1.25] 1.189 0.149 0.058 [1.08,1.18,1.29]
3 pt. Factor 1.025 0.158 0.025 [0.91,1.01,1.14] 1.026 0.182 0.034 [0.90,1.02,1.13]
4 pt. Factor 1.000 0.154 0.023 [0.89,1.00,1.12] 0.987 0.195 0.038 [0.85,0.99,1.11]
n = 3,000
OLS 1.621 0.053 0.388 [1.59,1.62,1.65] 1.583 0.043 0.342 [1.55,1.58,1.61]
Two Stage 1.016 0.161 0.026 [0.90,1.03,1.12] 0.975 0.172 0.030 [0.84,0.98,1.11]
Normal MLE 1.015 0.140 0.020 [0.90,1.02,1.10] 0.988 0.143 0.020 [0.88,0.98,1.09]
2 pt. Factor 1.196 0.104 0.049 [1.13,1.20,1.25] 1.164 0.116 0.040 [1.07,1.14,1.26]
3 pt. Factor 1.038 0.141 0.021 [0.94,1.04,1.14] 1.021 0.136 0.019 [0.93,1.01,1.11]
4 pt. Factor 1.014 0.143 0.020 [0.90,1.02,1.10] 0.995 0.160 0.025 [0.88,0.98,1.11]
n = 5,000
OLS 1.589 0.045 0.348 [1.56,1.59,1.62] 1.596 0.041 0.357 [1.56,1.59,1.63]
Two Stage 0.991 0.111 0.012 [0.91,0.99,1.07] 1.007 0.138 0.019 [0.91,1.01,1.08]
Normal MLE 0.992 0.103 0.011 [0.92,0.99,1.07] 0.988 0.124 0.015 [0.90,0.99,1.07]
2 pt. Factor 1.165 0.072 0.032 [1.11,1.17,1.21] 1.170 0.093 0.037 [1.11,1.16,1.23]
3 pt. Factor 1.015 0.096 0.009 [0.95,1.01,1.09] 1.021 0.115 0.013 [0.94,1.01,1.10]
4 pt. Factor 0.987 0.106 0.011 [0.91,0.99,1.06] 0.994 0.130 0.017 [0.91,1.00,1.07]



Table 4
Normal Distribution

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 2.942 0.147 3.795 [2.84,2.94,3.03] 2.973 0.160 3.919 [2.88,2.98,3.07]
Two Stage 0.949 0.790 0.621 [0.58,0.96,1.33] 0.912 1.032 1.063 [0.15,0.94,1.62]
Normal MLE 1.067 0.582 0.340 [0.65,1.04,1.40] 1.057 0.536 0.288 [0.66,1.05,1.39]
2 pt. Factor 2.006 0.458 1.220 [1.67,1.89,2.24] 2.124 0.559 1.574 [1.76,2.10,2.41]
3 pt. Factor 1.402 0.601 0.519 [1.00,1.30,1.75] 1.406 0.657 0.593 [1.01,1.25,1.75]
4 pt. Factor 1.229 0.640 0.458 [0.79,1.23,1.52] 1.210 0.741 0.588 [0.77,1.11,1.67]
n = 2,000
OLS 2.986 0.108 3.955 [2.92,2.98,3.05] 2.943 0.117 3.788 [2.86,2.94,3.03]
Two Stage 1.063 0.553 0.307 [0.68,1.10,1.47] 1.028 0.673 0.449 [0.59,0.98,1.50]
Normal MLE 1.048 0.369 0.137 [0.78,1.03,1.31] 1.010 0.438 0.190 [0.72,0.97,1.29]
2 pt. Factor 1.906 0.325 0.925 [1.66,1.85,2.09] 2.027 0.484 1.287 [1.67,1.96,2.25]
3 pt. Factor 1.322 0.385 0.250 [1.04,1.31,1.56] 1.323 0.478 0.331 [1.01,1.29,1.59]
4 pt. Factor 1.088 0.420 0.183 [0.78,1.06,1.35] 1.086 0.575 0.335 [0.79,1.05,1.41]
n = 3,000
OLS 2.948 0.089 3.801 [2.88,2.94,3.01] 2.961 0.099 3.857 [2.90,2.96,3.01]
Two Stage 1.065 0.416 0.176 [0.79,1.05,1.37] 0.900 0.613 0.382 [0.59,0.89,1.32]
Normal MLE 1.015 0.303 0.091 [0.78,0.99,1.20] 1.004 0.336 0.112 [0.74,1.00,1.25]
2 pt. Factor 1.892 0.227 0.847 [1.75,1.90,2.03] 1.927 0.356 0.985 [1.68,1.84,2.12]
3 pt. Factor 1.242 0.315 0.157 [1.03,1.24,1.46] 1.281 0.357 0.205 [1.03,1.27,1.46]
4 pt. Factor 1.066 0.344 0.122 [0.88,1.09,1.27] 1.061 0.427 0.184 [0.79,1.03,1.35]
n = 5,000
OLS 2.928 0.077 3.723 [2.88,2.92,2.97] 2.906 0.072 3.636 [2.86,2.91,2.95]
Two Stage 0.956 0.324 0.106 [0.77,0.97,1.15] 0.999 0.417 0.172 [0.73,1.00,1.29]
Normal MLE 0.995 0.251 0.063 [0.82,1.00,1.18] 0.950 0.215 0.048 [0.78,0.96,1.10]
2 pt. Factor 1.839 0.168 0.732 [1.73,1.85,1.95] 1.903 0.218 0.862 [1.77,1.90,2.02]
3 pt. Factor 1.212 0.256 0.110 [1.03,1.25,1.35] 1.268 0.213 0.117 [1.10,1.25,1.41]
4 pt. Factor 1.050 0.267 0.073 [0.87,1.02,1.21] 0.990 0.230 0.053 [0.82,0.99,1.18]



Table 5
Normal 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 2.453 0.185 2.146 [2.33,2.44,2.60] 2.303 0.157 1.722 [2.16,2.32,2.43]
Two Stage 1.244 7.218 51.63 [-3.7,0.32,6.80] 0.883 3.067 9.327 [-.85,1.27,2.55]
Normal MLE 1.632 2.030 4.479 [-.02,1.12,3.20] 1.294 1.231 1.587 [0.38,1.00,1.81]
2 pt. Factor 2.659 0.982 3.706 [1.98,2.55,3.39] 2.116 0.858 1.973 [1.46,2.13,2.58]
3 pt. Factor 2.333 1.698 4.623 [1.13,2.32,3.89] 1.908 1.217 2.291 [0.89,1.77,2.66]
4 pt. Factor 2.053 1.930 4.796 [0.36,1.94,3.58] 1.665 1.433 2.474 [0.59,1.41,2.58]
n = 2,000
OLS 2.404 0.126 1.988 [2.32,2.41,2.49] 2.370 0.119 1.891 [2.30,2.36,2.45]
Two Stage 1.386 4.408 19.39 [-1.8,1.05,4.81] 0.551 2.112 4.618 [-.55,0.64,2.09]
Normal MLE 1.624 1.674 3.163 [0.18,1.19,2.66] 1.262 0.960 0.982 [0.51,1.09,1.76]
2 pt. Factor 2.558 0.772 3.015 [2.05,2.49,3.15] 2.194 0.775 2.020 [1.66,2.19,2.51]
3 pt. Factor 2.191 1.443 3.480 [1.08,2.02,3.37] 1.716 1.111 1.734 [0.91,1.44,2.31]
4 pt. Factor 2.048 1.763 4.176 [0.60,1.71,3.42] 1.438 1.064 1.312 [0.54,1.29,2.27]
n = 3,000
OLS 2.325 0.087 1.764 [2.27,2.32,2.40] 2.332 0.104 1.785 [2.24,2.33,2.40]
Two Stage 0.861 3.617 12.97 [-1.4,1.50,3.69] 0.936 1.640 2.665 [-.33,1.01,2.13]
Normal MLE 1.388 1.390 2.065 [0.24,1.03,2.44] 1.229 0.976 0.996 [0.57,1.05,1.47]
2 pt. Factor 2.480 0.696 2.669 [2.02,2.40,3.19] 2.167 0.737 1.900 [1.56,2.12,2.43]
3 pt. Factor 2.097 1.247 2.742 [1.12,1.94,3.18] 1.568 0.951 1.218 [0.86,1.44,2.10]
4 pt. Factor 2.012 1.556 3.421 [0.78,1.89,3.36] 1.182 1.006 1.035 [0.58,0.97,1.52]
n = 5,000
OLS 2.389 0.083 1.936 [2.34,2.39,2.45] 2.397 0.092 1.959 [2.33,2.39,2.46]
Two Stage 1.114 2.758 7.546 [-.80,1.54,2.82] 1.145 1.249 1.565 [0.24,1.12,1.73]
Normal MLE 1.307 1.205 1.533 [0.53,0.94,1.78] 1.096 0.546 0.305 [0.70,1.02,1.46]
2 pt. Factor 2.470 0.717 2.668 [2.06,2.34,3.18] 2.204 0.775 2.044 [1.50,2.16,2.65]
3 pt. Factor 2.084 1.214 2.634 [1.14,1.89,2.99] 1.467 0.829 0.900 [0.88,1.22,1.80]
4 pt. Factor 1.840 1.383 2.597 [0.77,1.56,2.72] 1.274 0.848 0.787 [0.73,1.13,1.55]



Table 6
Uniform 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 2.408 0.150 2.005 [2.32,2.40,2.51] 2.325 0.189 1.790 [2.19,2.32,2.45]
Two Stage 0.930 0.713 0.509 [0.29,0.92,1.37] 0.869 1.021 1.050 [0.15,0.84,1.70]
Normal MLE 1.082 0.644 0.418 [0.62,1.09,1.48] 1.069 0.756 0.570 [0.53,0.97,1.50]
2 pt. Factor 1.363 0.549 0.431 [0.92,1.27,1.72] 1.287 0.624 0.469 [0.90,1.24,1.63]
3 pt. Factor 1.103 0.816 0.670 [0.53,0.99,1.64] 1.116 0.883 0.786 [0.54,1.02,1.51]
4 pt. Factor 0.934 0.842 0.706 [0.38,0.83,1.38] 0.883 0.923 0.857 [0.21,0.79,1.30]
n = 2,000
OLS 2.342 0.113 1.812 [2.27,2.34,2.41] 2.333 0.114 1.791 [2.25,2.33,2.40]
Two Stage 1.051 0.552 0.305 [0.67,1.08,1.43] 1.084 0.663 0.442 [0.70,1.11,1.56]
Normal MLE 1.135 0.450 0.219 [0.80,1.14,1.53] 1.105 0.535 0.294 [0.73,1.13,1.39]
2 pt. Factor 1.287 0.369 0.217 [1.02,1.28,1.51] 1.320 0.452 0.305 [1.04,1.29,1.48]
3 pt. Factor 1.043 0.558 0.310 [0.64,1.02,1.43] 1.132 0.686 0.483 [0.64,1.01,1.42]
4 pt. Factor 0.995 0.579 0.332 [0.59,0.92,1.44] 0.998 0.683 0.462 [0.60,0.90,1.23]
n = 3,000
OLS 2.347 0.081 1.822 [2.29,2.35,2.41] 2.344 0.105 1.817 [2.28,2.35,2.41]
Two Stage 0.943 0.444 0.199 [0.59,1.05,1.29] 1.027 0.513 0.261 [0.72,1.02,1.32]
Normal MLE 1.026 0.328 0.107 [0.78,1.07,1.29] 1.040 0.421 0.177 [0.76,1.00,1.29]
2 pt. Factor 1.175 0.260 0.098 [1.00,1.16,1.33] 1.234 0.293 0.140 [0.99,1.26,1.43]
3 pt. Factor 0.912 0.374 0.146 [0.68,0.96,1.20] 0.939 0.408 0.169 [0.69,0.89,1.21]
4 pt. Factor 0.850 0.414 0.192 [0.58,0.85,1.12] 0.851 0.447 0.220 [0.54,0.81,1.12]
n = 5,000
OLS 2.308 0.061 1.714 [2.28,2.31,2.34] 2.260 0.071 1.593 [2.21,2.25,2.31]
Two Stage 0.973 0.383 0.146 [0.67,1.01,1.24] 0.975 0.385 0.147 [0.75,0.98,1.21]
Normal MLE 1.055 0.298 0.091 [0.88,1.06,1.24] 1.002 0.298 0.088 [0.80,1.02,1.20]
2 pt. Factor 1.226 0.230 0.103 [1.08,1.21,1.40] 1.204 0.222 0.090 [1.05,1.21,1.33]
3 pt. Factor 0.983 0.350 0.122 [0.79,1.05,1.25] 0.959 0.315 0.100 [0.75,0.98,1.14]
4 pt. Factor 0.930 0.321 0.107 [0.71,0.95,1.13] 0.884 0.314 0.111 [0.63,0.91,1.09]



Table 7
Skewed Distributions

Correlation of Regressors: 0.80

Sample Size: 3000

----------------- E[d] = 0.50 ------------------------------------ E[d] = 0.75 -----------------
Mean Standard Deviation MSE Quartiles [25,50,75] Mean Standard Deviation MSEQuartiles [25,50,75]
R2 = 0.20
= 0.33
See Tab. A.3
OLS2.234 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]
R2 = 0.33
= 0.33
See Tab. A.4
OLS1.9120.0720.837[1.87,1.92,1.96]1.7230.0750.528[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]
R2 = 0.50
= 0.33
See Tab. A.5
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]
R2 = 0.20
= 0.50
See Tab. A.6
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]



Table 8

Number of Rejections out of 100 by Requested Sizes

E[d] = .50, Error Correlation = 0.50, R2 = 0.20, Normal Errors, 5,000 Observations

"Theoretical" Size

.05 .10 .25
Four Points of Support 76 83 91
Seven points of Support 16 17 28
25% Upwards Testing, Maximum 4 Points of Support 74 83 89
25% Upwards Testing, Maximum 7 Points of Support 45 49 65
50% Upwards Testing, Maximum 4 Points of Support 74 83 89
50% Upwards Testing, Maximum 7 Points of Support 30 31 44


Table 9

Estimates of the Impact of Marriage on Wages

Model Type points of support number of parameters marriage effect
(se, robust)		 log likelihood
DFM (indep) 1 (==> OLS
w/ Probit )		 24 .1061
(.0222)		 -2086.046
DFM 2 27 .1195
(.0220)		 -2068.277
DFM 3 29 .1275
(.0232)		 -2060.790
DFM 4 31 .1119
(.0368)		 -2058.079
DFM 5 33 .0230
(.0610)		 -2053.052
DFM 6 35 .0045
(.0424)		 -2050.238
DFM 7 37 -.00637
(.0487)		 -2049.437
DFM no exclusions 1(==> OLS
w/ Probit )		 34 .1084
(.0222)		 -2077.986
DFM no
exclusions		 6 45 -.0030
(.0434)		 -2041.198
DFM -no exclusions 7 47 -.0183
(.0480)		 -2039.701
Normal MLE --- 25 .0247
(.1206)		 -2085.824
Normal MLE no restric. --- 35 .63466
(.0937)		 -2076.268
2 stage w/
exclusions		 --- .0323
(.1266)		 accept exog, p-value: .55
2 stage w/o
exclusions		 .6288
(2.792)		 accept exog, p-value: .85

Test of exclusion restrictions in DFM(1): chi-square=16.12, 10df, (p=.13)
Test of exclusion restrictions in DFM(6): chi-square=18.08, 10df, (p=.07)
Test of exclusion restrictions Norm. MLE: chi-square=19.11, 10df, (p=.05)

Chisquare(2):
.25: 2.773
.50: 1.386