Econometrics Problem Set

Econometrics Problem Set

This project requires the use of the program SHAZAM

the data file needed is attached as well as the file with the project instructions/ questions.

Please only bid if you are confident you know how to do the problem set.

*86 observations
*Variables:
*Year=1 if 1983, 2 if 1989
*Output (Q) Output in Metric Tons
*Land (T) Land Input in Hectares
*Labor (L) Labor Input in Person-Days
2 2.43 1 79
2 7 5 150
2 1.12 4 24
2 0.7 0.5 14
2 6.8175 3 74
2 3.85 3.5 33
2 4.2 2.5 70
2 8.1 4.25 127
2 0.7 1 19
2 0.28 0.5 14
2 1.54 0.75 20
2 0.2025 0.5 2.2
2 3.4425 4.5 25
2 14 7 499
2 8.4375 5 108
2 4.455 2.5 101
2 1.62 1.5 35
2 3.4425 2 50
2 1 1 69
2 3.13875 1.75 255.5
2 0.54 0.25 26
2 2.025 1 34.5
2 2.025 2 123.5
2 1.2825 1 27
2 2.94 1.5 78
2 2.9025 2 171
2 2.16 1 60.5
2 0.81 1 62
2 4.3875 2 310
2 8.1 4 192
2 1.6875 1.5 119.5
2 4.3875 3 148
2 0.43875 0.25 4.5
2 0.945 1.5 156
2 3.375 2 80
2 0.27 1 80
2 2.7 2 118
2 0.4725 0.06 25
1 3.104 2.5 92
1 0.7425 0.5 46
1 1.35 1 21
1 0.96525 1 47
1 3.78 0.75 58.5
1 1.5525 0.75 42.5
1 0.7425 0.5 17
1 9.45 4 196
1 2.025 1.5 47.5
1 1.0125 1.5 48
1 2.835 2 110
1 1.5525 0.5 42.75
1 0.81 1 47
1 3.0375 3.5 264
1 4.05 2 84.5
1 0.945 1 28
1 0.30375 0.25 26
1 1.8225 1 42
1 1.35 1 28.5
1 0.6075 1 22
1 0.54 0.5 44
1 0.4725 1 49
1 4.3875 3 50
1 1.215 3.25 60.95
1 4.05 2 150
1 12.015 2.5 74.75
1 1.89 4 369
1 1.62 1 101
1 1.35 1 32
1 1.2825 3 100.5
1 30 6 130.5
1 0.67 1.25 33.75
1 10.8 4.5 64.75
1 0.81 1 60
1 10.935 5.5 90.75
1 1.08 1.5 48.2
1 0.27 0.5 16.5
1 0.54 2 95.9
1 1.35 1 36
1 2.025 1.5 24
1 5.4 5.5 114
1 1.35 3 31
1 0.8775 1 7
1 1.08 1 25
1 0.2025 0.25 12.65
1 0.2025 2.5 66
1 10.8 5 220
1 1.8225 1.25 60
*Insert commands below:
STOP

ARE 106 Quantitative Methods Problem Set 2 Due in class on Monday, February 27, 2017
Be sure to write your name on this page. You can either enter your answers onto this Word document, expanding it to create the space you need, or else attach it to

your answers on other sheets. Please answer each question completely, show your work, and attach 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 Function The data set “maize.shz” contains 86 observations on output, Q (in metric tons), land input T (in hectares), and labor input L (in

person-days) for a random sample of maize farms 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 the variables in this data set:
Variable Description Year 1 if 1983, 2 if 1989 Output (Q) Output in Metric Tons Land (T) Land Input in Hectares Labor (L) Labor Input in Person-Days
1. Estimate a 95-percent confidence interval for expected maize output (no econometrics yet!). Looking at your confidence interval, what would you say about 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:
iiii uLTQ ++=+ 12 ββ α
where ui is a stochastic error term assumed to be distributed independently and identically as ~N(0,σ2). Estimate this regression equation, using ordinary least

squares in SHAZAM. Report your results in table form.
J. Edward Taylor Winter 2017
2
3. What is your estimate of the elasticity of output with respect to land for this sample? The elasticity of output with respect to labor? Are they significantly

different from zero at the 10% significance level? 4. Test the null hypothesis that the marginal products of land and labor are equal to each 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 the producer theory you learned in your microeconomics course. 7. Now consider the following, alternative specification for

your regression equation: iu iii eLATQ 12 ββ = i. What kind of production function does this regression equation correspond to? ii. How can you modify this equation so

that it can be estimated using ordinary least squares? iii. Use the “maize.shz” data set to estimate this production function. Report your results in table form. iv.

Now what is your estimate of the output elasticity of land? The output elasticity of labor? Are they significantly different from zero 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 are

constant returns to scale in maize production amongst the population of farmers from which this sample was drawn. 10. Consider whether the output elasticity of land

and labor parameters different in 1983 than in 1989? i. Describe how can you modify your model to test for different elasticities in the two years ii. Use the

“maize.shz” data set to estimate your model. Report your results in table form. iii. At the 10% significance level, test whether the elasticities are significantly

different across years

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