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Quantitative Methods

Problem Set 3

Due in Class Thursday, June 8, 2017

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 Shazam output.  You must submit this problem set on time to receive full credit. Answers will be posted promptly, so late problem sets cannot be accepted. Maximum: 10 points per question.

http://shazam.ucdavis.edu/

[Important: Copy your output into a text file, like notepad, to print out. This will preserve the formatting. Upload your command file on Canvas as usual.]

I.            Tanzania Cotton Production: Heteroskedasticity & Testing Functional Forms

You have cotton production data “tanzaniacotton.txt” for the year 2014 on 355 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;

* hilabor (HL): hired labor days;

* hhlabor (HHL): household 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:

      i.            Estimate this regression equation, using ordinary least squares in SHAZAM.  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 household labor?

  iii.            Do you agree with your friend’s suggestion about using the above functional form? Critique the use of the above functional form by econometrically testing for heteroskedasticity. (Hint: Use White’s test for heteroskedasticity. Show your work to obtain full credit)

  iv.            Test the null hypothesis that the marginal products of household and hired labor are equal to each other, at the 1% significance level. Show your work.

2.      Now consider the following, alternative specification for your regression equation:

      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 “tanzaniacotton.txt” data set to estimate this production function. Report your results in table form.

  iv.            Now what are your estimates of the output elasticities of land, hired and household labor? Are they significantly different from zero at the 5% significance level?

    v.            Test for heteroscedasticity using White’s test and comment on your findings, drawing comparisons. 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.

II.            Estimating a Demand Function: Serial Correlation

The data set “corndemand.txt” contains 89 observations on production (Q, in billions of bushels), price (P, in dollars per bushel), and the consumer price index (CPI) for the United State from 1926 through 2014.  We will use this dataset to estimate a demand curve for corn. Here’s a plot of the data.

3. The value of a dollar changed a lot from 1926 to 2014, so we need to use real prices rather than nominal prices. Run the regression:

where  is the real price and . Report your results in table form.  What is your estimate of the elasticity of demand?

4. Test for autocorrelation in the errors of your regression in (3). What are the implications of your test result for interpreting your findings in (3)?

5. Now reconfigure the model as a one-period distributed lag model. Write down your new regression equation and estimate it using OLS.

6. Test for autocorrelation and report your results in table form. Did reconfiguring the model as a distributed lag model solve the serial correlation problem?

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