Assignment 6.9. Artūras Dulko & Gust ė Zefaitė 2012. Exercise 6.9. Data. Production function. K = an index of capital L = an index of labor E = an index of energy use M = an index of intermediate materials Y = an index of output. Cobb-Douglas.
Artūras Dulko & Gustė Zefaitė 2012
K = an index of capital
L = an index of labor
E = an index of energy use
M = an index of intermediate materials
Y = an index of output
where Q stands for output, L for labor, and C for capital. The parameters a, b, and c (the latter two being the exponents) are estimated from empirical data.
F has Fisher’s distribution Fr,N-(k+1)
r-number of restrictions
N- sample size
k - number of x variables in general
Numerator degrees of freedom = r
Denominator degrees of freedom = N– (k + 1)
Test following hypothesis:a) H0: 2=0 H1: 20
To test this hypothesis we are going to use Fisher or F − test.
b) H0:2=0, 3=0
H1: 20 and/or 30
Test following hypothesis:c) H0: 2=0, 4=0
H1: 20 and/or 40
Test following hypothesis:
d)H0:2=0, 3=0, 4=0
H1: 20 and/or 30 and/or 40
Test following hypothesis:e) H0 : 2+ 3+ 4+ 5=1 H1 : 2+ 3+ 4+ 51
Collectively, all the variables produce a model with a high level of explanation and a good predictive ability. Furthermore, our economic theory tells us that all the variables are important ones in a production function. However, we have not been able to estimate the effects of the individual explanatory variables with any reasonable degree of precision.