Question

# A researcher wishes to estimate a Cobb-Douglas production function for a microprocessor company of the form...

A researcher wishes to estimate a Cobb-Douglas production function for a microprocessor company of the form
Y = β1 X2β2 X3β3 X4β4u
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%.

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