The Box-Cox test for functional form: (See GHJ: pp. 345-346.) ♦There are two candidate models: a linear form and a log-log form. The latter would come from a Cobb-Douglas specification, but you could also use a semi-log model – the key is that the dependent variable is in natural log form: (1) 01122iiiiYXXuβββ=+++(2) 122lnlnlniiXuααα++♦Estimate each model, save the residual sums of squares: RSSLis the residual sum of squares from the linear model, and RSSLLis the residual sum of squares for the log model. ♦Transform the residual sum of squares for the linear model: 2LGRSSY, where 12nGnYYYY=⋅"♦Calculate the test statistic: 22(1)ln2LGLLRSSYnlRSSχ⎛⎞⎜⎟=⎝⎠∼Or: ()22(1)lnln2LLLGnRSSlRSSY=−∼♦Compare – the key is to check the terms within the absolute value bars, because the test
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