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QUESTION:

In “Testing for Imperfect Competition at the Fulton Fish Market”(RAND Journal of Economics, 1995) and later work, Kathryn Graddy studies demand and competition in the main market for whiting — a type of fish — in New York City in 1992. The author spent a lot of time at the market and hand- collected daily observations on the quantity sold and the average price, as well as the quantities and prices separately for Asian and white buyers. The data include 97 daily observations.

The Stata data file FISH .dta contains observations on the variables of interest. Specifically:

• t: day of observation, excluding weekends (and running from 1 to 100, with three days excluded because the data are missing);

• totqty, ltotqty: total quantity sold (to Asian + white buyers) and its log;

• avgprc, ltotprc: average per-unit price and its log;

• mon,  tues,  wed,  thurs: indicator variables for the day of the week of the observation (with Friday as an omitted category);

• wave2: average max wave height at sea over last 2 days, measured in feet;

• wave3: lagged average wave height (two days prior to those in wave2);

• prca: price paid by Asian buyers;

• prcw: price paid by white buyers.

The Stata data file FISH panel .dta is a panel version of FISH .dta, with separate observations for each day for both Asian and white buyers (with 2 × 97 observations in total):

• t: day of observation;

• asian: indicator equal to 1 if observation is observation is for Asian buyers, 0 for white buyers;

• lprc: log of price for given group of buyers;

• lqty: log of quantity for given group of buyers;

• mon,  tues,  wed,  thurs,  wave2,  wave3: described above.

Some Stata hints:

• Command test allows you to compute F-statistics and perform two-sided tests on (single or multiple) coefficients or their linear combinations.

• Type help  command to get more details on how a particular command works, e.g. help  test.

• Type gen  varname  =  f(x) to generate a new variable equal to the function f(x).

• Type tsline  varname1  varname2  . . . to plot the time series of the selected variables. Before running, type tsset  varname to use varname as the time variable.

• Type predict  varname after a regression to generate predicted values and name them varname.

• Type predict  varname,  resid after a regression to generate predict residuals and name them varname.

• L .varname is the first lag of varname.

• ac  varname plots the autocorrelation function of varname.

•  c(pi) is the π = 3.14 ...  constant.

• To compute Newey-West standard errors with the ivreg2 command, replace the r for robust in the syntax with bw(auto).

Answer the following questions:

1. Run a regression to test whether log total quantity depends on the day of the week. (Allow for heteroskedasticity in all of your analyses, and assume for now that there is no serial correlation in the errors.) Report the F-statistic and p-value testing the null hypothesis that the log total quantity is the same on all days of the week, on average. What do you conclude? Describe any seasonal pattern you find.

2. Recall that another way to account for seasonality is to use trigonometric functions.  Generate two new deterministic season variables as a function of time,  t, with a weekly  (i.e.,  5-day)

frequency:

sin5 = sin ( ) ,   cos5 = cos ( ) .

Regress log total quantity on these two variables (and a constant).   Compute the estimated seasonal “trend”in this regression and that in the regression of question 1 and plot them together. What do you conclude about the two approaches?

3. Estimate an OLS regression of log total quantity on log average price, controlling for day-of-the- week dummies. (Keep using these controls in all regressions below.) Report the slope coefficient with 3 significant digits.   Under which (strong) condition is this estimate consistent for the demand elasticity?

To deal with simultaneity of demand and supply, Graddy uses instrumental variables which measure the conditions at sea.  Specifically, she uses lagged wave heights (wave2 and wave3).1 Winds above 4.5 feet make fishing more difficult.

4. Estimate the demand elasticity, using wave2 as a single excluded instrument. Report the elas- ticity estimate and its standard error with 3 significant digits.  Test whether the instrument is strong; report which test statistic you used, which value it takes, and which critical value you are comparing it to. Provide an argument for the exogeneity of this instrument.

5. Looking for stronger instruments for log price, you recall that waves are supposed to be bad for fishing only when they exceed 4.5 feet. You therefore conjecture that a dummy wave2high, indicating that wave2 > 4.5, may better predict log price than wave2 itself. Test this conjecture in the data. Should one use wave2high as an additional instrument when estimating the demand elasticity? (You need to generate the wave2high dummy.)

6. To estimate the inverse demand elasticity, swap log price and log quantity variables in your IV regression from question 4. Report the inverse demand elasticity estimate and its standard error with 3 significant digits.  Relate the estimate to the IV estimate of demand elasticity.  Which concerns may you have about this estimate, relative to the one in question 4?

7. Coming back to the demand elasticity in question 4, use both wave2 and wave3 as instruments for price. Report the elasticity and its standard error with 3 significant digits. Test the exogeneity of the two instruments; report which test statistic you used, which value it takes, and how you make the conclusion.

8. Are bad weather conditions persistent?  Estimate a probit regression of the indicator variable wave2high from question 5 on its first lag (with the standard controls). What is the estimated coefficient and its statistical significance?   What is the average partial effect of  wave2high yesterday on the probability that wave2high  =  1 today? Explain the intuition for your finding.

9. We have so far assumed that heteroskedasticity-robust standard errors were valid, implicitly assuming no autocorrelation in the errors.  To assess this assumption, first generate residuals from the model you estimated in question 4. Plot the autocorrelation function for the residuals. What do you observe? Test whether the errors are serially correlated in an AR(1) model. Report an appropriate test statistic and p-value. For this question, you can assume strict exogeneity.

10. Re-estimate the model in question 4 with heteroskedasticity and autocorrelation robust standard errors (using the default Newey-West bandwidth).  How does the estimated elasticity compare to that in question 4? How does the p-value compare?

11. How much does the mean (non-logged) price paid by Asian and white buyers differ?  Compute the means of prca and prcw and interpret their difference.  Now load the panel version of the dataset, FISH panel. Rerun the 2SLS regression in question 7 adding the ethnicity indicator as an exogenous regressor and the interaction of asian with lprc as a second endogenous regressor. You should also interact the instruments with asian to allow the first-stage coefficients to differ by ethnicity. Cluster standard errors at the day level. Is the price elasticity significantly different for Asian and white buyers?