Box-Cox test for functional form

Box-Cox test for functional form - The Box-Cox test for...

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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) 01 1 2 2 ii i i YX X u β ββ =+ + + (2) 1 2 2 ln ln ln i i X u α αα + + Estimate each model, save the residual sums of squares: RSS L is the residual sum of squares from the linear model, and RSS LL is the residual sum of squares for the log model. Transform the residual sum of squares for the linear model: 2 L G RSS Y , where 12 n Gn YY Y Y =⋅ " Calculate the test statistic: 2 2 (1) ln 2 L G LL RSS Y n l RSS χ ⎛⎞ ⎜⎟ = ⎝⎠ Or: () 2 2 (1) ln ln 2 L LL G n RSS lR S S Y =− Compare – the key is to check the terms within the absolute value bars, because the test
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