1. Impact of Sales Promotions on When, What, and How Much to Buy
Sunil Gupta, JMR, 1988
Presenter: Gabe Gonzales
MKTG 555

2. Research Question
When products are promoted, what explains the sales ‘bump’?
When to buy: Interpurchase time, the time between purchases of items in a category
What to buy: Brand-size switching (i.e., Guadagni and Little, 1983)
How Much to buy: Purchase quantity, here described as ‘stockpiling’
These three elements had not been observed/modeled together
Papers modeling promotions’ effect on 2 of 3:
Brand choice & Interpurchase time together (e.g., Little and Guadagni, 1986)
Interpurchase time & Quantity together (e.g., Neslin, Henderson, and Quelch, 1985)
Brand choice & Quantity together (e.g., Krishnamurthi and Raj, 1988)

3. Modeling Approach
Brand Choice and Purchase Quantity are conditional on purchase decision
So time is modeled separately from the other two
Brand Choice and Quantity are modeled separately
Brand Choice probability is a function of each week’s market conditions
Weak association between brand choice and purchase quantity ( U = .053) despite inherent connection (brand-size  volume)
Built 3 models

4. Brand Choice Model Multinomial Logit (e.g., Guadagni and Little, 1983)
Modeled brand-sizes of coffee, like G & L (1983)

5. Interpurchase Time Model
Modal interpurchase time > 0; Poisson distribution is inappropriate
People are not most likely to purchase again immediately as would be suggested by an exponential distribution
Other papers used Erlang-2 distribution as its mode is > 0
Use of this distribution was empirically supported by the scanner dataset

6. Purchase Quantity Model
Linear Regression of exogenous variables on Quantity?
Quantity is not continuous—so this is inappropriate
Instead, modeled underlying latent variable V for the regression [ V = B’Z + ε ]
Q is discrete purchase quantity—equations 7 & 8 are a cumulative logit model

7. Scanner Panel Data
Similar to Guadagni and Little (1983), used coffee purchases from one market (Pittsfield, MA) to test their models
Used random sample of 100 households
Dataset included weeks of panel
Weeks 30-59: Precalibration (for brand loyalty, inventory, etc)
Weeks : Calibration period
Weeks : Validation period
1526 purchases
4211 opportunities

8. Variables Brand-specific constant (0 or 1)
Regular brand price (¢/oz)—inferred from shelf price & promotions
Promotional price cut (¢/oz)
Feature-or-display (weighted average between 0 and 1)
Feature-and-display (weighted average between 0 and 1)
Brand loyalty (Exponentially weighted average of past purchases, 0-1)
Size loyalty (Exponentially weighted average of past purchases, 0-1)
Weekly inventory (oz) estimated:
Inventory = Inventory (w – 2) – Estimated weekly consumption + quantity purchased (w – 1)

9. Results (Brand Choice)
Hypothesized Signs:
Brand Loyalty: +
Size Loyalty: +
Feature-and-Display: +
Feature-or-Display: +
Price Cut: +
Regular Price: -
Large effects of brand switching!

10. Results (Interpurchase Time)
Hypothesized Signs:
Average Purch time: +
Feature-and-Display: -
Feature-or-Display: -
Inventory: +
Price Cut: -
Regular Price: +
Interpurchase time is relatively stable

11. Results (Purchase Quantity)
Hypothesized Signs:
Average Purch Quantity: +
Feature-and-Display: +
Price Cut: +
Regular Price: -
Family Size: +
Inventory: -
Feature-or-Display: +
Interpurchase time: +
Significant, but relatively small, stockpiling effects.

12. Model Validation Compared proposed models to 3 naïve models:
Interpurchase time, Quantity, and Brand Choice = averages in calibration period
Same as Naïve model 1, but brand shares updated after each purchase simulation
Same as Naïve Models 1 & 2, but using the logit model of brand choice
Demonstrates additional value of time & quantity models
Proposed model has lowest inequality coefficient U, meaning it produces the best predictions

13. Elasticity Analysis
A primary goal of the paper was to disentangle and compare the relative effect of promotions on What, When, and How Much consumers purchased.
Calculated elasticities for Feature-and-Display, Feature-or-Display, and Promotional Price Cut
Total Elasticity:
Almost all of promotional sales increase from price cuts (98%) is from brand switching (price cut has no effect on purchase time)
What When How Much

14. Conclusions/Implications
Promotion primarily affects brand switching
Effects weaker for purchase acceleration/stockpiling, which are not true incremental sales
Modeling approach can be used to compare effectiveness of different promotions
Determine which promotions add the most new customers vs. ‘accelerated’ loyal customers who would buy eventually