midterm1_2012_solutions

A 10 test the hypothesis of the increasing return to

This preview shows page 3 - 4 out of 4 pages.

a) (10) Test the hypothesis of the increasing return-to-scale, that is ε(L) + ε(K) > 1, if the estimate of ε(L) is 0.807 with a standard error of 0.151. The estimate of ε(K) is 0.233 with a standard error of 0.070. And the total variance-covariance matrix of (ε(K), ε(L)) is: ε(K) ε(L) ------------------------------------------------- ε(K) 0.00494695 ε(L) -0.00961159 0.02289165 ANSWER: H0: ε(L) + ε(K) = 1 Ha: ε(L) + ε(K) > 1 Significance level is 5% t-stat = (0.807 + 0.233 – 1)/ s.e. s.e = sqrt(Var(ε(L)) + Var(ε(K)) + 2cov(ε(L), ε(K))) = = sqrt(0.151^2 + 0.070^2 + 2*(-0.00961159)) = 0.092075078 t-stat = (0.807 + 0.233 – 1)/ 0.092075078 = 0.434428087 95% CI is [-∞, 1.64] T-stat is in CI, we fail to reject the H0. Thus, there is no enough statistical evidence to support the increasing return-to-scale hypothesis.
Image of page 3

Subscribe to view the full document.

b) (10) Test the hypothesis that “is we increase labor input twice and also capital input twice, then the output will also increase twice”. ANSWER: This is a constant return-to-scale hypothesis. H0: ε(L) + ε(K) = 1 Ha: ε(L) + ε(K) ≠ 1 Significance level is 5% t-stat = 0.434428087 (same) 95% CI is [-1.96, 1.96] T-stat is in CI, we fail to reject the H0. Thus, the data supports the constant return-to-scale hypothesis. c) (5) Construct 99% Confidence Interval for ε(L). [0.807 -2.57* 0.151, 0.807 + 2.57* 0.151].
Image of page 4

{[ snackBarMessage ]}

Get FREE access by uploading your study materials

Upload your study materials now and get free access to over 25 million documents.

Upload now for FREE access Or pay now for instant access
Christopher Reinemann
"Before using Course Hero my grade was at 78%. By the end of the semester my grade was at 90%. I could not have done it without all the class material I found."
— Christopher R., University of Rhode Island '15, Course Hero Intern

Ask a question for free

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern