Problem Set #3
Sonoma State University
Economics 462-Quantitative Marketing II
Dr. Cuellar
The data set for problem set #5 contains data on daily store sales for six stores in a trading area for the period December 27,
2010 to March 5, 2014. Store #6, however, opened 11/8/12. We want to analyze the effect of the new store opening on sales
at existing stores. As a control group, the data set also includes daily sales for a peer group of stores which experienced no new
store openings in that same period.
1.
2.
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5.
Store Level Analysis.
a. Compare mean sales at Store #3, the closest store to the new store (Store #6), before and after the grand
opening of Store #6. Do mean daily sales change?
Difference-in-Difference.
a. For the six stores in the trading area with the new store, compare mean daily sales.
b. For the six stores in the trading area with the new store, compare the distribution of mean daily sales.
Show graphically using histograms and box plots.
c. Choose one of the four other existing stores as a control for Store #3. Hint, Store #1.
d. Conduct a difference-in-difference analysis of sales at Stores #1 & #3. Explain your results. Does your
choice of a control make sense? Are your results significant? Use a table such as:
Control Group
Treatment Group
Before
After
Difference (After-Before)
Difference-in-Difference
Trend Analysis
a. For the six stores in the trading area with the new store, show graphically daily store sales over time. Hint,
use the “by” function in your graph. Do you see any signs of cannibalization at the store level?
b. To more clearly see any pattern in sales, use a simple (2 1 2) moving average smoother on sales. Do you
observe any discernable pattern in sales?
c. To more clearly see any pattern in sales, use a simple (3 1 3) moving average smoother on sales. Do you
observe any discernable pattern in sales?
d. To more clearly see any pattern in sales, use a lowess smoother on sales. Do you observe any discernable
pattern in sales?
e. Run a regression on sales for each store (Store #1 through Store #5) to examine the effect of the new store
(Store #6) opening. Explain your results. Be sure to use “outreg.”
f. Run a regression on the natural log of sales for each store (Store #1 through Store #5) to examine the effect
of the new store (Store #6) opening. Explain your results. Be sure to use “outreg.”
Trading Area Level Analysis-Simple Before and After Trend Analysis
a. Construct a graph showing total daily sales (i.e, the sum of all six stores) in the trading area over the period
of the data. You may want to use a data smoother to better illustrate any trend in daily sales. Does the
trend in sales appear to change after the new store opening?
b. Construct a regression model to test for a structural change in the time trend of total sales before and after
the new store opening. Show your model and regression results.
c. Discuss the results of your model. Specifically, what was the daily dollar rate of growth in sales before the
new store opening? What was the daily dollar rate of growth in sales after the new store opening?
d. Show your regression results graphically along with the actual sales (smoothed) data.
e. Re-run your regression using log(sales). Show your model and regression results.
f. Discuss the results of your model. Specifically, what was the annualized percentage rate of growth in sales
before the new store opening? What was the annualized percentage rate of growth in sales after the new
store opening?
Trading Area Level Analysis-Before and After with a Control versus Treatment Before Trend Analysis
a. Construct a graph showing total daily sales (i.e., the sum of all six stores) of the trading area as well as total
daily sales (i.e., the sum of all eight stores) of the control group stores over the period of the data. Hint, use
the “by” function in your graph and smoothed sales. Does the trend in sales in either treatment or control
group of stores appear to change after the new store opening?
b. Construct a regression model to test for a difference in the time trend of sales of the treatment group
stores compared to that of control group stores. Hint, use the “Cuellar Test” as defined in the Sideways
paper by Cuellar et. al., which was taught in class by Cuellar. Show your model and regression results.
c. Discuss the results of your model. Specifically, what are the daily dollar rates of growth for the treatment
and control groups before and after the new store opening? What are the changes in growth rates before
and after the new store opening? What is the difference in the change in growth rates? Use the same type
of table as above to show your results.
d. Show your regression results graphically.
e. Re-run your regression using log(sales). Show your model and regression results.
f. Discuss the results of your model. Specifically, reproduce the above table using annualized percentage rate
of growth in sales.