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I have a Cobb-Douglas equation I am modelling in R:

$$ \ln⁡(Y) = β + β_a \ln⁡(A) + β_l \ln⁡(L) + β_f \ln⁡(F) + β_o \ln⁡(O) + u $$

Is there an easy way of testing the hypothesis about whether the betas sum to one; less than one; more than one?

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    $\begingroup$ The car package has the linearHypothesis function that enables you to test the claim that all betas sum to 1 easily. If mod is your model, then use the following command: linearHypothesis(mod, "1 = beta_a + beta_l + beta_f + beta_o") where beta are the names of your variables $\ln(A)$ etc. as entered in the regression command. Have a look at the help page of linearHypothesis for more examples. $\endgroup$ – COOLSerdash Jul 13 '13 at 8:50
  • $\begingroup$ Cool! Please ask again if you need further help. $\endgroup$ – COOLSerdash Jul 14 '13 at 7:07
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    $\begingroup$ Does this answer your question? Testing linear restriction in R $\endgroup$ – luchonacho Nov 7 '20 at 2:10