• Conduct a Monte Carlo exercise to observe the sampling distribution of simple regression slope and intercept estimates when the population regression function is characterized by heteroscedasticity.
• Reinforce the idea that OLS and WLS are both unbiased estimators, but WLS is more efficient (has lower variance) when there is heteroscedasticity

• Read about the Fall 1997 Econ 1 "Stapler Experiment"
• Explore the data for viable functional forms
• Assess the data for multicollinearity, heteroscedasticity

1. The program entitled wls_eff.sha does the following things:

1. "Creates" population data for the revenues and fund-raising expenditures of 55 non-profit organizations. If these data were real, we would worry that they are jointly determined, but here, we will assume that fund-raising expenditures depend upon available revenues (and not vice-versa).
2. Checks the PRF - it will be different for everybody, because everybody will have a different set of population data.
3. As in the plotsrf.sha program, we will then draw 100 different samples of size 10 from this population. For each sample, we will fit a regression slope and intercept by OLS and also by WLS using the weight that should be appropriate, given the way the data were created.
4. We will then look at the average point estimates of the regression parameters produced by each method, and also (most importantly) at the standard deviations in these point estimates. The standard deviations for the WLS estimators should be smaller than those for the OLS estimators...this is what we mean by WLS being a "more efficient" estimator in the presence of heteroscedasticity.

2. In the Fall quarter of 1997, I taught an Economics 1 course wherein I put the students to work in order to generate a "real" production function. In each of eleven discussion sections, most with approximately 36 students, students organized themselves into "firms" of about nine people. Each firm was asked to produce "tri-fold mailers." These consist of a piece of letter paper, folded into thirds and stapled at each end. Each firm started with one stapler and one worker and did a production run of 60 seconds. Then they increased the labor to two workers, then three, and so on. Then they moved to two staplers and added incremental units of labor. The complete description of the experiment can be found at my 1997 Econ 1 Website. The unit of observation is a 60-second workshift. Data from the experiment can be read as follows:

sample 1 254

read(e1prod.dat) firm shift staplers qcon  coo &

    labor totalq goodq rejectq

sample 3 254

* The first two observations are "fake" observations so that some plots

* would come out nicely.  They force zero output with zero inputs

For our purposes, the relevant variables are:

• STAPLERS = number of staplers used on this shift
• LABOR = number of workers used on this shift
• TOTALQ = total units produced
• GOODQ = total units produced that meet quality control requirements
• REJECTQ = total units produced that do not meet quality control requirements

1. Explore these data, selecting a reasonable production function for tri-fold mailers. Justify your choice.

2. These are cross-sectional data. What common data pathologies might you be on the lookout for? Are they present here? Explain.