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UC Davis ARE 106 – Quantitative Methods Problem Set 2

Your Name____________________________________ ARE 106Quantitative MethodsProblem Set 2Due in class on Monday, February 27, 2017Be sure to write your name on this page. You can either enter your answers onto thisWord document, expanding it to create the space you need, or else attach it to youranswers on other sheets. Please answer each question completely, show your work, andattach your Shazam output. You must submit Problem Set 2 on time to receive credit.Answers will be posted promptly, so late problem sets cannot be accepted.Estimating a Production FunctionThe data set “maize.shz” contains 86 observations on output, Q (in metric tons), landinput T (in hectares), and labor input L (in person-days) for a random sample of maizefarms in the Mexican state of Michoacán, during each of two years (1983 and 1989).These data were collected by your own Professor Taylor! The following table defines thevariables in this data set:VariableYearOutput (Q)Land (T)Labor (L) Description1 if 1983, 2 if 1989Output in MetricTonsLand Input inHectaresLabor Input inPerson-Days 1. Estimate a 95-percent confidence interval for expected maize output (noeconometrics yet!). Looking at your confidence interval, what would you sayabout the variability of maize output from this sample of farms? Is it high or low?2. Let’s use our econometric tools to estimate the output elasticity of land and labor.A friend suggests that you estimate a regression equation of the following form:Qi 1Ti 2 Li ui where ui is a stochastic error term assumed to be distributed independently andidentically as ~N(0,2). Estimate this regression equation, using ordinary leastsquares in SHAZAM. Report your results in table form. J. Edward Taylor Winter 2017 3. What is your estimate of the elasticity of output with respect to land for thissample? The elasticity of output with respect to labor? Are they significantlydifferent from zero at the 10% significance level?4. Test the null hypothesis that the marginal products of land and labor are equal toeach other, at the 10% significance level.5. Now test whether your R-squared is significantly greater than zero, at the 10%significance level.6. Critique the use of this functional form for the regression equation, in light of theproducer theory you learned in your microeconomics course.7. Now consider the following, alternative specification for your regressionequation: Qi ATi 1 Li 2 e uii.ii.iii.iv. What kind of production function does this regression equationcorrespond to?How can you modify this equation so that it can be estimated usingordinary least squares?Use the “maize.shz” data set to estimate this production function.Report your results in table form.Now what is your estimate of the output elasticity of land? Theoutput elasticity of labor? Are they significantly different fromzero at the 10% significance level? 8. Which of these two regression equations do you think is “better?” Explain.9. Using the regression model in question 7, test the null hypothesis that there areconstant returns to scale in maize production amongst the population of farmersfrom which this sample was drawn.10. Consider whether the output elasticity of land and labor parameters different in1983 than in 1989?i.Describe how can you modify your model to test for differentelasticities in the two yearsii.Use the “maize.shz” data set to estimate your model. Report yourresults in table form.iii.At the 10% significance level, test whether the elasticities aresignificantly different across years 2

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