Question

A researcher wishes to estimate a Cobb-Douglas production function for a microprocessor company of the form
                                                            Y = β₁ X₂^β2 X₃^β3 X₄^β4u
where Y = #microprocessors; X2 = units of capital; X₃ = units of labour; and X₄ = # computer science staff involved in research and development. The researcher has n=30 observations and estimates the following unrestricted regression with OLS:

                              LnY = 1.2 + 0.6ln X₂ + 0.2ln X₃ + 0.3ln X₄                                   RSS=3157.2

In order to test the validity of the SINGLE linear restriction of constant returns to scale,
Ho: β2+β3+β4 = 1, the researcher substitutes the restriction into the regression and estimates the restricted regression below:

               Ln(Y/X₄) = 0.8     + 2.2ln(X₂/X₄)   + 1.3ln(X₃/X₄)    RSS=3683.4
(1.2)       (1.0)                   (0.6)                   

The restriction is valid at a level of significance of 5%.

True

False

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