A researcher wishes to estimate a CobbDouglas production
function for a microprocessor company of the form
Y = β_{1} X_{2}^{β2}
X_{3}^{β3} X_{4}^{β4}u
where Y = #microprocessors; X2 = units of capital; X_{3} =
units of labour; and X_{4} = # 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 X_{2} + 0.2ln X_{3} + 0.3ln X_{4} 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/X_{4}) = 0.8 +
2.2ln(X_{2}/X_{4}) +
1.3ln(X_{3}/X_{4}) RSS=3683.4
(1.2)
(1.0) (0.6)
The restriction is valid at a level of significance of 5%.

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