Econometric take home APPS_Part_21

# Econometric take home APPS_Part_21 - lnL -.200 -13.6284...

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λ ln L -.200 -13.6284 -.150 -12.8568 -.100 -12.2423 -.050 -11.7764 0.000 -11.4476 .050 -11.2427 .100 -11.1480 .110 -11.1410 .120 -11.1378 .121 -11.1377 .122 -11.1376 .123 -11.1376 .124 -11.1375 .125 -11.1376 .130 -11.1383 .140 -11.1423 .200 -11.2344 .300 -11.6064 .400 -12.8371 The output elasticities for this function evaluated at the sample means, K = .175905, L = .737988, Y = 2.870777, are ln Y / ln K = b k ( K / Y ) λ = .2674 ln Y / ln L = b l ( L / Y ) λ = .9017. These are quite similar to the estimates given above. The sum of the two output elasticities for the states given in the example in the text are given below for the model estimated with and without transforming the dependent variable. Note that the first of these makes the model look much more similar to the Cobb Douglas model for which this sum is constant. State Full Box-Cox Model lnQ on left hand side Florida 1.2840 1.6598 Louisiana 1.2019 1.4239 California 1.1574 1.1176 Maryland 1.1657 1.0261 Ohio 1.1899 .9080 Michigan 1.1604 .8506 Once again, we are interested in testing the hypothesis that λ = 0. The Wald test statistic is W = (.123 / .2482) 2 = .2455. We would now not reject the hypothesis that λ = 0. This is a surprising outcome. The likelihood ratio statistic is based on both models. The sum of squared residuals for the restricted model is given above. The sum of the logs of the outputs is 19.29336, so the restricted log-likelihood is ln L 0 = (0-1)(19.29336) - (25/2)[1 + ln(2 π ) + ln(.781403/25)] = -11.44757. The likelihood ratio statistic is -2[ -11.13758 - (-11.44757)] = .61998. Once again, the statistic is small. Finally, to compute the Lagrange multiplier statistic, we now use the method described in Example 11.8. The result is LM = 1.5621. All of these suggest that the log-linear model is not a significant restriction on the Box-Cox model. This rather peculiar outcome would appear to arise because of the rather substantial reduction in the log-likelihood function which occurs when the dependent variable is transformed along with the right hand side. This is not a contradiction because the model with only the right hand side transformed is not a parametric restriction on the model with both sides transformed.

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## This note was uploaded on 11/13/2011 for the course ECE 4105 taught by Professor Dr.fang during the Spring '10 term at University of Florida.

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Econometric take home APPS_Part_21 - lnL -.200 -13.6284...

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