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hw6 solution

# hw6 solution - Econ 444 Elementary Econometrics Fall 2007...

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Econ 444 Elementary Econometrics Fall 2007 Homework Exercise Solution: 6 (a-c) The solutions are computer files included as excel and word docu- ments. (d) The results are identical. (e) ˆ log ( Q i ) = - 0 . 01 + 0 . 29 log ( L i ) + 0 . 34 log ( K i ) + 0 . 37 log ( Mi ) (0 . 02) (0 . 04) (0 . 06) (f) ˆ log ( Q i ) = 0 . 03 + 0 . 43 log ( L i ) + 0 . 57 log ( K i ) (0 . 00) (0 . 00) (g) The point estimates in Regression (1) suggest that if labor, capital, and materials inputs were all zero, output would be slightly negative. This makes sense because firms have fixed costs which are independent of output. Given a 1% increase in labor input, we expect a 0 . 3% increase in output. Given a 1% increase in capital, we expect output to increase by 0 . 34% increase in ouput. Lastly, we expect a 1% increase in material inputs to increase output by 0 . 34%. (h) The regression has 2000 - 1951 + 1 = 50 observations and it follows that there are 50 - k - 1 = 46 degrees of freedom. The .95 critical value for 40 dof is 1.684. Our 90% confidence interval is 0 . 29 ± 1 . 684 * 0 . 02 = ( . 256 , . 323). 1

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(i) Using the 2-tailed test is as simple as seeing if the t-statistic falls within the 90% confidence interval calculated above. t = 0 . 29 0 . 023 = 12 . 61. Of course this number is very sensitive to the rounding we’ve done, but it is
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hw6 solution - Econ 444 Elementary Econometrics Fall 2007...

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