HW03_answers_Econ140A_2011Fall

HW03_answers_Econ140A_2011Fall - Economics 140A Fall 2011...

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Unformatted text preview: Economics 140A Fall 2011 Professor Startz Sketched Answers to Homework 3 1. Your profit function is ¡ ¢£√( ¤ ¥ ¦§ ¨ ¥ ) © ª « ¦ ¬ ¬¦ ¡ ­ ¡ ®¢ « √( § ¨ ¥ ¤ ¥ ) ¯ ° ± ² ¦ ³ ´ ¥ µ © ª ¦ ¡ ¶ · ¸ ²ª (¢ « ¹° § ¨ ¥ ¤ ¥ µ ) º » ¼ ³¥ ¡ ¢ ¥ ° § ¨ ¥ ¤ ¥ µ ½²ª¾ ¥ 2. We have ¿̂ ¡ À ´ Á À ¥ ² ¡ ½¿ Á  ´ ¾ Á ½¿ Á  ¥ ¾ ² ¡ ¿ Á  ´ Á  ¥ ² From earlier results, we know ÃÄŽ¿̂¾ ¡ ¤ ¥ £² . Write an alternative estimator, ¿̃ , as a linear function of À . ¿̃ ¡ Æ ´ À ´ Á Æ ¥ À ¥ ¡ ½Æ ´ Á Æ ¥ ¾¿ Á Æ ´  ´ Á Æ ¥  ¥ For ¿̃ to be unbiased we need Æ ´ Á Æ ¥ ¡ ± . We get ÃÄŽ¿̃¾ ¡ Æ ´ ¥ ¤ ¥ Á Æ ¥ ¥ ¤ ¥ Á ²Æ ´ Æ ¥ « ­ ¡ ¤ ¥ ½Æ ´ ¥ Á Æ ¥ ¥ ¾ Now write Æ Ç ¡ ´ ¥ Á ÈÆ Ç © ´ ¥ É The variance is ¤ ¥ (*° ± ² µ ¥ Á °Æ ´ © ± ² µ ¥ Á ² « ± ² °Æ ´ © ± ² µ+ Á *° ± ² µ ¥ Á °Æ ¥ © ± ² µ ¥ Á ² « ± ² °Æ ¥ © ± ² µ+) If we add the terms closest to the square brackets we get ¤ ¥ [°Æ ´ © ± ² µ Á °Æ ¥ © ± ² µ] ¡ ¤ ¥ ½Æ ´ Á Æ ¥ © ±¾ ¡ ­ What’s left is the ols variance, Ê Ë ¥ , plus a positive term. 3. a. ÃÄÅÌÍ Î ´ © Í Î ¥ Ï ¡ ÃÄÅÌÍ Î ´ Ï Á ÃÄÅÌÍ Î ¥ Ï © ² ÐÑÃÌÍ Î ´ Ò Í Î ¥ Ï . b. ÃÄÅÌÓ ´ Í Î ´ Á Ó ¥ Í Î ¥ Ï ¡ Ó ´ ¥ ÃÄÅÌÍ Î ´ Ï Á Ó ¥ ¥ ÃÄÅÌÍ Î ¥ Ï Á Ó ´ Ó ¥ ÐÑÃÌÍ Î ´ Ò Í Î ¥ Ï page 2 4. The regression looks like Dependent Variable: COST Method: Least Squares Date: 04/07/11 Time: 13:14 Sample: 1 6 Included observations: 6 Variable Coefficient Std. Error t-Statistic Prob. C 418.2603 63.58245 6.578235 0.0028 CDS 0.735207 0.024831 29.60832 0.0000 R-squared 0.995458 Mean dependent var 1864.167 Adjusted R-squared 0.994322 S.D. dependent var 1323.656 S.E. of regression 99.73734 Akaike info criterion 12.30416 Sum squared resid 39790.14 Schwarz criterion 12.23475 Log likelihood -34.91248 Hannan-Quinn criter. 12.02629 F-statistic 876.6523 Durbin-Watson stat 1.895811 Prob(F-statistic) 0.000008 The t- stat look is | ¡¢£¤ ¡£...
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HW03_answers_Econ140A_2011Fall - Economics 140A Fall 2011...

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