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| RE: Coefficient Restrictions - Cobb douglas- [ Reply ] By: Arne Henningsen on 2019-11-03 13:47 | [forum:47114] |
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It seems that your production frontier is: log( Output ) = a0 + a1 * log( Capital )+ a2 * log( H ) + a3 * log( Labour ) + a4 * trend and you want to impose constant returns to scale by the restriction: a3 = 1 - a1 - a2, right? You can impose this restriction in the following way: log( Output ) = a0 + a1 * log( Capital )+ a2 * log( H ) + ( 1 - a1 - a2 ) * log( Labour ) + a4 * trend log( Output ) = a0 + a1 * log( Capital )+ a2 * log( H ) + 1 * log( Labour ) - a1 * log( Labour ) - a2 * log( Labour ) + a4 * trend log( Output ) - log( Labour ) = a0 + a1 * ( log( Capital ) - log( Labour ) ) + a2 * ( log( H ) - log( Labour ) ) + a4 * trend log( Output / Labour ) = a0 + a1 * log( Capital / Labour ) + a2 * log( H / Labour ) + a4 * trend which you can estimate by: Reg_PCA <- sfa( log(Output/Labour) ~ log(Capital/Labour) + log( H / Labour ) + trend | PCA1, data = DataPanel ) and then calculate the coefficient of labour by: a3 = 1 - a1 - a2 The procedure to impose constant returns to scale in a Cobb-Douglas production function is equivalent to imposing linear homogeneity in input prices in a Cobb-Douglas cost function as explained, e.g. in my "Introduction to Econometric Production Analysis with R", which is available for download at: https://leanpub.com/ProdEconR (for free if you set the price to zero). |
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| Coefficient Restrictions - Cobb douglas- [ Reply ] By: taggero taggero on 2019-08-21 14:21 | [forum:46926] |
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Hi, Is it possible to restrict a coefficient to be a specific value? For example: Reg_PCA <- sfa( logOutput ~ logCapital)+logH+logLabour+trend|PCA1,data = DataPanel) where I want the parameter estimate, logLabour, to equal -(1-coef(logOutput)-ceof(logH)) Thanks in advance |
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