Key - Problem Set 5 - 2011

Key - Problem Set 5 - 2011 - Problem Set 5 Econometrics I...

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Problem Set 5 Econometrics I Resource Economics 702 1. Consider the following model of the aggregate US production: 3 12 4 exp t u tt t t t YA K L E M  ; where: Y t is an index of total US output in year t; K t is an index of capital input for year t; L t is an index of labor input for year t; E t is an index of energy input for year t; and M t is an index of materials input for year t. Data are on the course website and in the text (Table 9.10). (1) a. Estimate the population parameters using OLS. Interpret the estimates for the population parameters 123 4 , , , and . Do the estimates have the expected signs? The estimates are shown in the SAS output below. The REG Procedure Model: MODEL1 Dependent Variable: lny Number of Observations Read 25 Number of Observations Used 25 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 1.35654 0.33913 98.55 <.0001 Error 20 0.06882 0.00344 Corrected Total 24 1.42536 Root MSE 0.05866 R-Square 0.9517 Dependent Mean 0.37725 Adj R-Sq 0.9421 Coeff Var 15.55004 Parameter Estimates Parameter Standard Variance Variable DF Estimate Error t Value Pr > |t| Inflation Intercept 1 0.03516 0.04393 0.80 0.4329 0 lnk 1 0.05607 0.25927 0.22 0.8310 32.45951 lnL 1 0.22631 0.44269 0.51 0.6148 37.35267 lne 1 0.04358 0.38989 0.11 0.9121 76.81764 lnm 1 0.66962 0.36106 1.85 0.0785 62.09678 All estimates are elasticities: a 1% increase in capital input results in a 0.056% increase in output, holding labor, energy and materials constant; a 1% increase in materials results in a 0.67% increase in output, holding capital, labor and energy constant; etc.
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(1) b. Are the estimated parameters statistically significant ? Explain briefly for each. Review the calculated t-values. With 20 degrees of freedom and a 10% level of significance, the critical t-value is 1.325. Thus, only the effect of materials on output is statistically different from zero. Seems rather odd as R 2 = 95.2% and the calculated F-value is 98.55, highly significant. I’ve include the “variance inflation factors,” a quick check for multicollinearity problems. (2) c. Theory suggests that US aggregate production may be characterized by constant returns to scale . Derive the appropriate restriction for your empirical model that will be used as the null hypothesis for a test of constant returns to scale. Show clearly what “restriction” you will test and state the complete hypothesis.
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This note was uploaded on 12/08/2011 for the course ECON 702 taught by Professor Staff during the Spring '08 term at UMass (Amherst).

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Key - Problem Set 5 - 2011 - Problem Set 5 Econometrics I...

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