Answer All of the Following Questions. If You Do Not Have the Text You Should Borrow One

ABIZ 3080 Fall 2013

Assignment #6

Due Date: 29 Nov. 2013

Answer all of the following questions. If you do not have the text you should borrow one or use one of the copies on reserve in the Agriculture library. Assignments should be typewritten or neatly handwritten, and are due at the beginning of class on the due date.

1. An important measurement problem in economics is the relationship between price and quality (Berndt 1991, Ch. 4). The first empirical study relating price to quality appears to be that of Waugh (1928) who attempted to explain price variation in vegetable lots sold in a wholesale market in downtown Boston. He investigated three different vegetables; following Berndt (1991), we focus on one of them, asparagus. Over the period May 6 to July 2, 1927, 200 individual lots of asparagus were inspected. The data recorded were (1) the selling price per bushel box, (2) the number of inches of green color on the asparagus, (3) the number of stalks in an 18 ounce bunch, and (4) the quartile coefficient of dispersion of the diameters of the stalks. The last three variables were regarded as perceived quality indicators. More green color was seen as desirable. Bigger stalks were preferable to smaller stalks, and so the fewer the number of stalks per bunch the greater the quality. Uniformity of stalk size was also seen as desirable, and so the greater the dispersion of the stalk diameters, the lower the quality. Consider the model

Pt = b1 + b2GREENt + b3STALKSt + b4DISPERSEt + et

where Pt is price per bushel box in cents, GREENt is the number of inches of green color, STALKSt is the number of stalks per bunch and DISPERSEt is the dispersion of stalk diameters. Data on these variables can be found in the file asparas.dat. (Waugh used price relative to an average. We have converted his data to the actual price. This conversion has no substantive implications.)

(a) Estimate the relationship between price and the quality characteristics. Interpret the estimates and construct 95% interval estimates for them. In the context of the example, do you think the interval estimates are sufficiently narrow to provide valuable information for asparagus producers.

(b) Find the sample means, minimums and maximums for the quality variables.

(c) Suppose the perfect asparagus is that with the most green, the lowest number of stalks and the lowest dispersion in the sample. What is the price premium for the perfect asparagus relative to asparagus with average quality characteristics?

(d) What price would you expect to receive for asparagus with the worst quality characteristics in the sample?

(e) Suppose that you are an asparagus producer who is producing asparagus with 5 inches of green, 20 stalks per bunch and a stalk-diameter dispersion of 20. For an additional cost of $1 per bushel box, you can produce asparagus with 7 inches of green and a stalk-diameter dispersion of 10, while retaining 20 stalks per bunch. Is it profitable for you to produce the better quality asparagus?

2. The file meat.dat on the course webpage contains data on per capita consumption of beef (in pounds), per-capita disposable income ($), beef price (cents/pound), lamb price (cents/pound), and pork price (cents/pound) for a seventeen year period, with all prices and income inflation-adjusted. You decide to estimate a log-log demand model.

(a) what will your log-log demand model for beef look like in econometric notation?

(b) what are the expect signs for all your coefficients? Carefully explain each.

3. Previous assignment questions have investigated the relationship between starting salary (Y) and years of education (X) for employees in a Chicago bank for 93 employees that were hired during the period 1969-71. It was discovered in these earlier examples that there is a clear positive relationship between starting salary and years of education, but the estimated relationship was a poor model for predicting starting salary. The poor predictive ability could be attributable to the fact that there are variables other than education that influence starting salary. In addition to observations on Y and X, the file salary.dat contains observations on number of months of previous work experience (E) and the number of months after January 1, 1969 that the individual was hired (T).

(a) Before estimating the model, do you think E and T could be relevant variables for explaining variation in Y? Why or why not?

(b) Estimate a linear equation relating Y to X, E and T and report the results. Test (individually and jointly) the relevance of including E and T. (Use a 5% significance level.)

4. Suppose we have data where starting salary (Y) is related to years of education (X), previous work experience (E) and hiring time (T) for 93 employees of a Chicago bank. Suppose that you have been hired by the Equal Opportunity Office to investigate whether there has been any salary discrimination on the basis of gender. In the file salary.dat the first 61 observations are for female employees and the last 32 observations are for male employees. Let Gt be a gender dummy variable that is equal to 1 for the males and 0 for the females.

(a) Estimate the model Yt = b1 + dGt + et . How would you test whether male salaries are significantly greater than female salaries? Carry out this test at the 5% level of significance. What criticism could be levelled at this test?

(b) Estimate the model

Yt = b1 + dGt + b2 Xt + b3Et + b4Tt + et

Repeat the test performed in part (a). Why is the test based on this model an improvement over that done in part (a)? What would you report to the Equal Opportunity Office?

5. In the file pubexp.dat on the course homepage there are data on public expenditure on education (EE), gross domestic product (GDP), and population (P) for thirty-four countries in the year 1980. It is hypothesized that per-capital expenditure on education is a linear function of per capita GDP.

(a) would you expect heteroskedasticity to be present in this model? Why or why not?

(b) use the GQ test to find out whether there is heteroskedasticity.

(e) test the null hypothesis that per-capita GDP affects per-capita education expenditure using White’s standard errors. Choose your alternative hypothesis carefully.

(f) calculate a 95% confidence interval using White’s standard errors

(g) re-estimate the equation assuming proportional heteroskedasticity. Now re-test the hypothesis outlined in part (e) and re-calculate the confidence interval you did in part (f). How do the new results compare?

Please do not hesitate to consult myself or Mr. Choi if you have questions.