Assume the Cobb-Douglas production function for a country is estimated as where

Question

Assume the Cobb-Douglas production function for a country is estimated as where Y_t is real GDP, X, is national labor input, and X_2, is the stock of fixed capital. Please answer the following is the coefficient of labor input statistically different than 0.5? is the coefficient of the capital Input statistically different than 0.75? if we know that the Cos (beta_1, beta_2) = .15, can we test the hypothesis that the Cobb-Douglas production function has constant returns to scale? If so, please perform the test at the 5% level of significance.

Explanation / Answer

Part-a

Test statistic is t= (beta_x1-0.5)/SE(beta_x1) =(0.3397-0.5)/0.1857=-0.8632

As magnitude of this is less than 2.0, we conclude that coefficient of x1(labor input) is not statistically different than 0.5

Part-b

Test statistic is t= (beta_x2-0.5)/SE(beta_x2) =(0.8460-0.5)/0.09343=3.7033

As magnitude of this is greaater than 2.0, we conclude that coefficient of x2(capital input) is statistically different than 0.5

Part-c

This can not be tested until we know the regression ANOVA table

Part-d

For this also we need ANOVA table of results.

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