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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.

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assignment 6 9
Assignment 6.9

Artūras Dulko & Gustė Zefaitė 2012

production function
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
Cobb-Douglas
  • The simplest production function is the Cobb-Douglas model. It has the following form: Q=aLbCc

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.

  • If b + c = 1, the Cobb-Douglas model shows constant returns to scale. If b + c > 1, it shows increasing returns to scale, and if b + c < 1, diminishing returns to scale.
fisher or f test
Fisher or F-test

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)

facts about f distribution
Facts about F-distribution
  • The curve is not symmetrical but skewed to the right.
  • There is a different curve for each set of dfs .
  • The F statistic is greater than or equal to zero.
  • As the degrees of freedom for the numerator and for the denominator get larger, the curve approximates the normal.
exercise 6 9 a
Exercise 6.9 a)

Test following hypothesis:a) H0: 2=0 H1: 20

exercise 6 9 a1
Exercise 6.9 a)

To test this hypothesis we are going to use Fisher or F − test.

exercise 6 9 b
Exercise 6.9 b)
  • Test the following hypothesis

b) H0:2=0, 3=0

H1: 20 and/or 30

exercise 6 9 c
Exercise 6.9 c)

Test following hypothesis:c) H0: 2=0, 4=0

H1: 20 and/or 40

exercise 6 9 d
Exercise 6.9 d)

Test following hypothesis:

d)H0:2=0, 3=0, 4=0

H1: 20 and/or 30 and/or 40

exercise 6 9 e
Exercise 6.9 e)

Test following hypothesis:e) H0 : 2+ 3+ 4+ 5=1 H1 : 2+ 3+ 4+ 51

conclusion
Conclusion

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.

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