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a) A researcher investigating the factors determining wages estimates models (1) and (2) below using information on a cross-sectional sample of data on wages
a) A researcher investigating the factors determining wages estimates models (1) and (2) below using information on a cross-sectional sample of data on wages for 525 US workers recorded in 2005. Note that below In stands for natural logarithm and is the subscript denoting the i-th cross-sectional unit i.e. worker. InWAGE=0.28 +0.09EDUC +0.01EXPER, -0.03FEMALE InWAGE =-1.14 +0.941nEDUC, +0.16 InEXPER-0.02FEMALE where: WAGE is the hourly wage in US$ EDUC is the number of years of education of the worker (1) (2) EXPER is the number of years of working experience the worker has FEMALE is a dummy variable that equals 1 if the worker is female and equals 0 if they are male. Clearly explain what the estimated values of the slope coefficients in the two models imply about the relationship between each explanatory/independent variable and wages (you do not need to discuss the intercept/constant coefficient in each model). (20 marks) b) The researcher is unsure which of the two functional forms above is more appropriate and so applies Ramsey's RESET using the estimation results from both models. While performing the RESET tests two powers of the fitted values (i.e. and Y) are included in the RESET regression. The values of the RESET test F-statistics are 4.71 for model (1) and 2.26 for model (2). What are the outcomes of the two RESET tests and what do these results imply about the suitability/unsuitability of the functional forms used in models (1) and (2)? Explain how you reach your conclusions. (12 marks) c) What are the likely consequences of using an incorrect functional form for a regression model? Besides the RESET tests used above, describe in detail one other possible method of testing for incorrect functional form. What advantages and/or disadvantages does this have compared to the RESET test used above? (18 marks) [TOTAL 50 MARKS] TABLE of CRITICAL VALUES for STUDENT'S t DISTRIBUTIONS Column headings denote probabilities (a) above tabulated values. 0.40 0.25 0.10 0.325 1.000 3.078 0.05 0.04 0.025 6.314 7.916 12.706 2.920 3.320 4.303 2.353 2.605 0.289 0.816 1.886 0.277 0.765 1.638 3 3.182 4.849 3.482 2.999 3.747 4.604 4 0.271 0.741 1.533 2.132 2.333 2.776 8.610 5 0.267 0.727 1.476 2.015 2.191 2.571 2.757 6.869 6 5.959 7 5.408 8 9 0.02 0.01 0.005 0.0025 0.001 0.0005 15.894 31.821 63.656 127.321 318.289 636.578 6.965 9.925 14.089 22.328 31.600 4.541 5.841 7.453 10.214 12.924 5.598 7.173 3.365 4.032 4.773 5.894 0.265 0.718 1.440 1.943 2.104 2.447 2.612 3.143 3.707 4.317 5.208 0.263 0.711 1.415 1.895 2.046 2.365 2.517 2.998 3.499 4.029 4.785 0.262 0.706 1.397 1.860 2.004 2.306 2.449 2.896 3.355 0.261 0.703 1.383 1.833 1.973 2.262 2.398 2.821 3.250 0.260 0.700 1.372 1.812 2.359 2.764 3.169 0.260 0.697 1.363 1.796 2.328 2.718 3.106 0.695 1.356 1.782 2.303 2.681 3.055 1.350 2.282 2.650 3.012 1.345 2.264 2.624 2.977 0.258 0.691 1.341 2.249 2.602 2.947 2.235 2.583 2.921 2.224 2.567 2.214 2.552 10 1.948 2.228 1.928 2.201 11 12 0.259 13 0.259 0.694 14 0.258 0.692 1.771 1.912 2.179 1.899 2.160 1.761 1.887 2.145 1.878 2.131 1.869 2.120 15 16 0.258 0.690 1.337 1.753 1.746 1.740 17 0.257 0.689 1.333 2.898 3.222 3.646 18 0.257 0.688 1.330 3.610 19 0.257 0.688 3.174 3.579 3.153 3.552 3.850 3.135 3.527 3.819 3.119 3.505 3.792 0.256 0.685 3.768 0.256 0.685 1.711 1.828 3.745 25 0.256 0.684 1.316 1.708 1.825 26 0.256 0.684 1.706 1.822 2.056 2.763 3.047 27 0.256 0.684 28 0.256 0.683 29 0.256 0.683 30 0.256 0.683 31 0.256 0.682 32 0.255 0.682 33 0.255 0.682 34 0.255 0.682 35 0.255 0.682 1.862 2.110 1.734 1.855 2.101 2.878 3.197 1.328 1.729 1.850 2.093 2.205 2.539 2.861 0.257 0.687 1.325 1.725 1.844 2.086 2.197 2.528 2.845 0.257 0.686 1.323 1.721 1.840 2.080 2.189 2.518 2.831 0.256 0.686 1.321 1.717 1.835 2.074 2.183 2.508 2.819 1.319 1.714 1.832 2.069 2.177 2.500 2.807 3.104 3.485 1.318 2.064 2.172 2.492 2.797 3.091 3.467 2.060 2.167 2.485 2.787 3.078 3.450 3.725 1.315 2.162 2.479 2.779 3.067 3.435 3.707 1.314 1.703 1.819 2.052 2.158 2.473 2.771 3.057 3.421 3.689 1.313 1.701 1.817 2.048 2.154 2.467 3.408 3.674 1.311 1.699 1.814 2.045 2.150 2.462 2.756 3.038 3.396 3.660 1.310 1.697 1.812 2.042 2.147 2.457 2.750 3.030 3.385 1.309 1.696 1.810 2.040 2.144 2.453 1.309 1.694 1.808 2.037 2.141 2.449 1.308 1.692 1.806 2.035 2.138 2.445 1.307 1.691 1.805 2.032 2.136 2.441 1.306 1.690 1.803 2.030 2.133 2.438 1.306 1.688 1.802 2.028 1.687 1.800 2.026 1.686 1.799 2.024 2.023 1.796 2.021 3.646 3.633 2.744 3.022 3.375 2.738 3.015 3.365 3.622 2.733 3.008 3.356 3.611 2.728 3.002 3.348 36 0.255 0.681 37 0.255 0.681 2.724 2.996 2.131 2.434 2.719 2.990 2.129 2.431 2.715 2.985 2.127 2.429 2.125 2.426 2.708 2.976 2.123 38 1.305 1.304 1.304 1.685 1.798 0.255 0.681 0.255 0.681 2.712 2.980 39 0.255 0.681 1.303 1.684 2.423 2.704 2.971 3.307 3.551 2.099 2.660 2.915 3.232 3.460 3.416 3.390 40 60 0.254 0.679 1.296 1.671 1.781 2.000 2.390 80 0.254 0.678 1.292 1.664 1.773 1.990 2.088 2.374 2.639 2.887 3.195 100 0.254 0.677 1.290 1.660 1.769 1.984 2.081 2.364 2.626 2.871 3.174 120 0.254 0.677 1.289 1.658 1.766 1.980 2.076 2.358 2.617 2.860 3.160 3.373 140 0.254 0.676 1.288 1.656 1.763 1.977 2.073 2.353 160 0.254 0.676 1.287 1.654 1.762 1.975 2.071 2.350 180 0.254 0.676 1.286 1.653 1.761 1.973 2.069 2.347 200 0.254 0.676 1,286 1.653 1.760 1.972 2.067 2.345 250 0.254 0.675 1.285 1.651 1.758 1.969 2.065 2.341 inf 0.253 0.674 1.282 1.645 1.751 1.960 2.611 2.852 3.149 3.361 3.352 2.607 2.847 3.142 2.603 2.842 3.136 3.345 2.601 2.838 3.131 3.340 2.596 2.832 3.123 3.330 2.576 2.807 3.090 3.290 2.054 2.326 d.f. 1 2 20 21 22 23 24 3.833 4.501 5.041 3.690 4.297 4.781 3.581 4.144 4.587 3.497 4.025 4.437 3.428 3.930 4.318 3.372 3.852 4.221 3.326 3.787 4.140 3.286 3.733 4.073 3.252 3.686 4.015 3.965 3.922 3.883 3.601 3.340 3.591 3.333 3.582 3.326 3.574 3.319 3.566 3.313 3.558 dfdf, Denominator Degrees of Freedom SHEMASA522 85832 38532 2982, 13 14 15 16 17 18 19 20 21 22 24 26 27 29 30 40 60 120 1 161.45 18.513 10.128 9.5521 7.7086 -9.9443 4.9646 4.1028 4.7472 4.6672 4.6001 199.50 4.5431 4.4940 4.4513 4.4139 4.3807 19.000 4.2417 4.2252 F- Distribution (-0.05 in the Right Tail) Numerator Degrees of Freedom 4 6 4.2100 4.1960 4.1830 4.1709 4.0847 4.0012 3.9201 3.8415 5.4095 5.1922 6.6079 5.7861 5.9874 5.1433 4.7571 4.5337 5.5914 4.7374 4.3468 4.1203 5.3177 4.4590 5.1174 4.2565 3.7083 4.8443 3.9823 3.5874 3.8853 3.8056 3.7389 3 215.71 3.4434 3.4221 3.4028 19.164 4.3512 3.4928 3.4668 4.3248 4.3009 4.2793 4.2597 3.3852 3.3690 3.3541 3.3404 3.3277 9.2766 6.5914 3.1504 3.0718 2.9957 224.58 3.6823 3.2874 3.0556 3.6337 3.2389 3.0069 3.5915 3.1968 2.9647 3.5546 3.1599 2.9277 3.5219 3.1274 2.8951 3.0984 3.0725 3.0491 19.247 3.4780 3.3567 3.4903 3.2592 3.4105 3.3439 9.1172 6.3882 2.9912 2.9752 2.9604 2.9467 2.9340 3.3158 2.9223 3.2317 2.8387 2.7581 5.0503 4.9503 4.3874 4.2839 3.9715 3.8660 4.0662 3.8379 3.6875 3.5806 3.8625 3.6331 3.4817 3.3738 2.8661 2.8401 2.8167 3.0280 2.7955 3.0088 2.7763 230.16 2.7587 2.7426 19.296 3.3258 3.2172 3.2039 3.0946 3.1059 2.9961 3.1791 3.0254 2.9153 3.1122 2.9582 2.8477 2.7278 2.7141 2.7014 9.0135 6.2561 2.7109 2.6848 233.99 2.6613 2.6400 2.6207 19.330 8.9406 6.1631 2.9013 2.7905 2.8524 2.7413 2.8100 2.6987 2.7729 2.6613 2.7401 2.5719 2.5581 2.5454 2.6896 2.5336 2.6060 2.4495 2.5252 2.3683 2.6802 2.4472 2.2899 2.6049 2.3719 2.2141 2.5990 2.5727 2.6030 2.4904 2.5868 2.4741 7 236.77 19.353 8.8867 6.0942 2.4205 2.3359 8 238.88 2.7066 2.6572 2.6143 2.5767 2.5102 2.6283 2.5435 2.4768 2.4047 2.3883 2.4591 2.3732 2.4453 2.3593 2.4324 2.3463 19.371 4.8759 4.8183 4.2067 4.1468 3.7257 8.8452 6.0410 3.7870 3.5005 3.4381 3.2927 3.2296 2.3343 2.2490 2.2541 2.1665 2.1750 2.0868 2.0986 2.0096 3.1355 3.0717 3.0123 2.9480 2.9134 2.8486 2.8321 2.7669 2.7642 2.6987 2.5140 2.4471 2.4876 2.4205 2.5491 2.4638 2.3965 2.5277 2.4422 2.3748 2.5082 2.4226 2.3551 2.6408 2.5911 2.5480 2.3371 2.3205 2.3053 2.2913 2.2783 2.2662 2.1802 2.0970 2.0164 1.9384 9 240.54 19.385 8.8123 6.9988 4.7725 4.0990 3.6767 3.3881 3.1789 3.0204 2.8962 2.7964 2.7144 2.6458 2.5876 2.5377 2.4943 2.4563 2.4227 2.3928 2.3660 2.3419 2.3201 2.3002 2.2821 2.2655 2.2501 2.2360 2.2229 2.2107 2.1240 2.0401 1.9588 1.8799
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