Consider the following "true" (Cobb-Douglas) production function:
ln Yi = α0 + α1 ln L1i + α2 ln L2i + α3 ln Ki + ui
where Y = output
L1 = production labor
L2 = nonproduction labor
K = capital
But suppose the regression actually used in empirical investigation is
ln Yi = β0 + β1 ln L1i + β2 ln Ki + ui
On the assumption that you have cross-sectional data on the relevant variables,
a. Will E(βˆ1 ) = α1 and E(βˆ2 ) = α3 ?
b. Will the answer in a hold if it is known that L2 is an irrelevant input in the production function? Show the necessary derivations.