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ARE 106

Quantitative Methods

Problem Set 2

Due Online 11:59PM Friday May 19, 2023

Be sure to write your name on this page.  Enter your answers onto this Word document, expanding it to create the space you need.  Please answer each question completely, show your work, and attach your Stata output for the relevant questions.  You must submit this problem set on time on Gradescope to receive full credit. Answers will be posted promptly, so late problem sets cannot be accepted. Maximum: 10 points per sub-question.

[Important: Copy your Stata code and paste at the end of your answer document.]

You have cotton production data in a Stata data (.dat) file called “Cotton S23.dat” for the year 2014 on 344 randomly chosen cotton farmers from the Lake Zone of Tanzania. The data set contains information on total output (in kg), land (in acres) and labor inputs for each cotton farmer. The labor input in this data set is disaggregated into household labor, i.e., labor input by members of the farmer-household and hired labor that the farmers obtain locally. In this exercise, you will be estimating several specifications of the production function testing for functional forms and heteroskedasticity in the data.

Definitions of the variables in our Tanzania data set are:

* output (Y): cotton output in kg;

* land (T): land input in acres;

* labor (L): labor in days

1. 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; we call this “Model 1”:

i. Estimate this regression equation, using ordinary least squares in Stata.  Report your results in table form and interpret the parameter estimates.

ii. What is your estimate of the elasticity of output with respect to land for this sample?  The elasticity of output with respect to labor?

iii. Please test this regression for heteroskedasticity. (Hint: Use White’s test for heteroskedasticity, using p=.01 for your test. Show how you did this test to obtain full credit. Do not use the “canned” White’s test in Stata, because we want to see how you did it.)

iv. Do you agree with your friend’s suggestion about using Model 1 to estimate this production function? Why or why not?

2. Now consider the following, alternative specification for your regression equation, which we call “Model 2”:

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 Tanzania cotton data set to estimate Model 2 using Stata. Report your results in table form, and briefly explain what each estimated coefficient means.

iv. What are your estimates of the output elasticities of land and labor in Model 2? Are they significantly different from zero at the 5% significance level?

v. Test Model 2 for heteroscedasticity using White’s test and comment on your findings, comparing with the test results you got with Model 1. Does this transformation of the equation solve your heteroscedasticity problem?

vi. Test the null hypothesis that there are constant returns to scale in Tanzania cotton production, using Model 2. Use p=0.05.

vii. Test the null hypothesis that the marginal products of family and hired labor are the same, using Model 2. Use p=0.10.