Econometrics-I-15

# Shephard’s lemma states that the cost minimizing

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Unformatted text preview: Shephard’s Lemma states that the cost minimizing factor demands are given by Xm = C(…)/Pm. Take logs gives the factor share equations, logC(…)/logPm = Pm/C C(…)/Pm = PmXm/C which is the proportion of total cost spent on factor m. &#152;&#152;&#152;&#152;™ ™ 32/45 Part 15: Generalized Regression Applications Translog &#152;&#152;&#152;&#152;™ ™ 33/45 Part 15: Generalized Regression Applications Restrictions &#152;&#152;&#152;&#152;™ ™ 34/45 Part 15: Generalized Regression Applications Data – C&G, N=123 &#152;&#152;&#152;&#152;™ ™ 35/45 Part 15: Generalized Regression Applications &#152;&#152;&#152;&#152;™ ™ 36/45 Part 15: Generalized Regression Applications---------------------------------------------------------------------- Ordinary least squares regression ............ LHS=C Mean = -.38339 Standard deviation = 1.53847 Number of observs. = 123 Model size Parameters = 10 Degrees of freedom = 113 Residuals Sum of squares = 2.32363 Standard error of e = .14340 Fit R-squared = .99195 Adjusted R-squared = .99131 Model test F[ 9, 113] (prob) = 1547.7(.0000)--------+------------------------------------------------------------- Variable| Coefficient Standard Error t-ratio P[|T|>t] Mean of X--------+------------------------------------------------------------- Constant| -7.79653 6.28338 -1.241 .2172 Y| .42610*** .14318 2.976 .0036 8.17947 YY| .05606*** .00623 8.993 .0000 35.1125 PK| 2.80754 2.11625 1.327 .1873 .88666 PL| -.02630 (!) 2.54421 -.010 .9918 5.58088 PKK| .69161 .43475 1.591 .1144 .43747 PLL| .10325 .51197 .202 .8405 15.6101 PKL| -.48223 .41018 -1.176 .2422 5.00507 YK| -.07676** .03659 -2.098 .0381 7.25281 YL| .01473 .02888 .510 .6110 45.6830--------+------------------------------------------------------------- Least Squares Estimate of Cost Function &#152;&#152;&#152;&#152;&#152;™ ™ 37/45 Part 15: Generalized Regression Applications Criterion function for GLS is log-likelihood. Iteration 0, GLS = 514.2530 Iteration 1, GLS = 519.8472 Iteration 2, GLS = 519.9199---------------------------------------------------------------------- Estimates for equation: C......................... Generalized least squares regression ............ LHS=C Mean = -.38339 Residuals Sum of squares = 2.24766 Standard error of e = .14103 Fit R-squared = .99153 Adjusted R-squared = .99085 Model test F[ 9, 113] (prob) = 1469.3(.0000)--------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X--------+------------------------------------------------------------- Constant| -9.51337** 4.26900 -2.228 .0258 Y| .48204*** .09725 4.956 .0000 8.17947 YY| .04449*** .00423 10.521 .0000 35.1125 PK| 2.48099* 1.43621 1.727 .0841 .88666 PL| .61358 1.72652 .355 .7223 5.58088 PKK| .65620** .29491 2.225 .0261 .43747 PLL| -.03048 .34730 -.088 .9301 15.6101 PKL| -.42610 .27824 -1.531 .1257 5.00507 YK| -.06761*** .02482 -2.724 .0064 ....
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Shephard’s Lemma states that the cost minimizing factor...

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