Unit 9 ECON16 (assignment answer key)

# I using the barium data run the regression model

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(i) Using the barium data, run the regression model given in your textbook for [10.22] (p. 362) and confirm you get the same results. Using the estimated residuals from this model, conduct a “four-step hypothesis test” for AR (1) serial correlation as described in your textbook on pp. 416 – 418. AR (1) test for serial correlation Step #1 Ho : ρ = 0 Ha : ρ≠ 0 Step #2 7

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This hypothesis test is based on the t-distribution (asymptotically) with df = 128 α = 0.05 Reject the Ho if the t-stat < -1.979 or > 1.979 and p-value < 0.05. EXCEL command for the critical value: =T.INV.2T(0.05,128) Step #3 Looking at the STATA output for this question: t = 3.18 p-value = 0.002 Step #4 Since 3.18 > 1.979 AND 0.002 < 0.05 Reject the Ho. This test does provide evidence for serial correlation. (According to the textbook, p. 417, rejecting the Ho at α = 0.05 usually means the conclusion that “serial correlation is a problem to be dealt with …”) (ii) Using the same regression model, conduct a “four-step” Durbin-Watson test for serial correlation, described in your textbook pp. 418 - 419. You can use the STATA for Step #3 but will need this resource ( ) for the rejection criteria (Step #2) and for your conclusion (Step #4). As with the Chow test, you may find the Wikipedia entry for the Durbin-Watson test to be a good resource to describe this test and its implementation. Durbin-Watson test for serial correlation Step #1 Ho : ρ = 0 Ha : ρ > 0 8
Step #2 This hypothesis test is based Durbin-Watson test and critical values taken from: for t = 131, k = 7. Reject the Ho if the DW stat < 1.62017 ; Fail to reject the Ho if DW > 1.81132. Step #3 Durbin-Watson d-statistic( 7, 131) = 1.458414 . estat dwatson (IMPORTANT: You must run this command directly after the full regression, it seems many of you ran this command on the wrong regression, for example a regression of the saved residuals) Looking at the STATA output for this question: DW = 1.46 Step #4 Since 1.46 < 1.62 Reject the Ho. This test does provide evidence for serial correlation. 9

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Software output: #1. . generate t = _n _cons -2.367526 20.78216 -0.11 0.909 -43.50455 38.7695 t .0127058 .0038443 3.31 0.001 .0050963 .0203153 afdec6 -.3515018 .2825417 -1.24 0.216 -.9107758 .2077722 affile6 .0970062 .2573131 0.38 0.707 -.4123294 .6063417 befile6 .09047 .2512887 0.36 0.719 -.4069406 .5878805 lrtwex .0782237 .47244 0.17 0.869 -.8569423 1.01339 lgas .4656786 .8761779 0.53 0.596 -1.268662 2.200019 lchempi -.6862364 1.239711 -0.55 0.581 -3.140169 1.767696 lchnimp Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 63.6522483 130 .489632679 Root MSE = .5748 Adj R-squared = 0.3252 Residual 40.6379584 123 .330389906 R-squared = 0.3616 Model 23.0142898 7 3.28775569 Prob > F = 0.0000 F(7, 123) = 9.95 Source SS df MS Number of obs = 131 . . regress lchnimp lchempi lgas lrtwex befile6 affile6 afdec6 t 10
_cons 27.30007 31.39707 0.87 0.386 -34.90919 89.50934 dec .0965326 .2615525 0.37 0.713 -.4217002 .6147654 nov -.2603032 .2530623 -1.03 0.306 -.7617136 .2411073 oct .0797627 .2570514 0.31 0.757 -.4295517 .5890771 sep -.0751929 .2583502 -0.29 0.772 -.5870807 .4366949 aug -.1271137 .2677917 -0.47 0.636 -.6577086 .4034812 jul .0111115 .2683777 0.04 0.967 -.5206446 .5428675 jun -.20095 .2592134 -0.78 0.440 -.7145481 .312648 may .031299 .2591998 0.12 0.904 -.4822721 .5448702 apr -.4406149 .258398 -1.71 0.091 -.9525974 .0713676 mar .062566 .254858 0.25 0.807 -.4424025 .5675345 feb -.3554148 .293754 -1.21 0.229 -.9374507 .2266211 t .0123389 .0039163 3.15 0.002 .0045793 .0200985 afdec6 -.2950163 .2994276 -0.99 0.327 -.8882937 .298261 affile6 .1534004 .2719856 0.56 0.574 -.3855043 .692305 befile6 .1648509 .2569789 0.64 0.523 -.3443198 .6740216 lrtwex -.1971415 .5295314 -0.37 0.710 -1.24634 .852057 lgas -.820624 1.345056 -0.61 0.543 -3.485679 1.844431 lchempi -.4516555 1.271528 -0.36 0.723 -2.971026 2.067715 lchnimp Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 63.6522483 130 .489632679 Root MSE = .57878 Adj R-squared = 0.3158 Residual 37.5185675 112 .33498721 R-squared = 0.4106 Model 26.1336807 18 1.45187115 Prob > F = 0.0000 F(18, 112) = 4.33 Source SS df MS Number of obs = 131 > jun jul aug sep oct nov dec . regress lchnimp lchempi lgas lrtwex befile6 affile6 afdec6 t feb mar apr may #2 _cons 107.0563 6.049651 17.70 0.000 94.98754 119.125 tsq -.0079591 .0050771 -1.57 0.122 -.0180876 .0021693 t .0716968 .3824461 0.19 0.852 -.6912622 .8346559 gfr Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 27847.8954 71 392.223879 Root MSE = 16.638 Adj R-squared = 0.2942 Residual 19100.5397 69 276.819415 R-squared = 0.3141 Model 8747.35576 2 4373.67788 Prob > F = 0.0000 F(2, 69) = 15.80 Source

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