The Price Consideration Model of Brand Choice

1
The Price Consideration Model of Brand Choice

• Andrew Ching, University of Toronto
• Tulin Erdem, UC-Berkeley
• Michael Keane, U of Technology Sydney

2
Motivation

• Workhorse brand choice models in marketing
• Multinomial Logit (MNL)
• Nested Multinomial Logit (NMNL)
• Multinomial Probit (MNP)
• These models have been extended to allow for
• Correlation among unobserved attributes of choice
  alternatives
• Consumer taste heterogeneity
• State dependence
• No-purchase option

3
A common drawback of these models

• They all make strong (albeit different)
  assumptions about when consumers see prices, and
  when they consider purchasing a category.
• A model without no-purchase option implicitly
  assumes the consumer only sees prices after
  he/she has already decided to buy in a category,
  and the decision to buy is exogeneous.
• A model with no-purchase option assumes that
  consumers see prices every week.

4
Main features of the Price Consideration model

• Consumers make a weekly decision whether to
  consider a category.
• This decision is made prior to seeing prices.
  However, it does depend on inventory, and
  promotion activity.
• Only after the consumer decides to consider a
  category does he/she see prices. In this second
  stage, the consumer decides whether and what
  brand to buy.
• The Price Consideration Model (PC) provides a
  middle ground between the extreme price awareness
  assumptions of conventional models.

5
Research goals

• Investigate whether the PC model performs better
  than the conventional brand choice models. If
  so, why?
• Using Nielsen Scanner data for ketchup and peanut
  butter, we estimate
• The PC Model
• MNL with a no-purchase option
• NMNL with the category purchase decision at the
  upper level of the nest
• All three models incorporate
• State dependence in brand preferences a la
  Guadagni and Little (1983),
• Dependence of the value of no-purchase on
  duration since last purchase (to capture
  inventory effects),
• Unobserved heterogeneity in brand intercepts.

6
Summary of Results

• The PC model dominates both MNL and NMNL on
  likelihood, AIC and BIC criteria.
• Simulation of data from the models reveals that
  the PC model produces a dramatically better fit
  to observed inter-purchase spell lengths than do
  the MNL and NMNL models.
• In particular, the conventional models greatly
  exaggerate the probability of short spells. For
  the PC model, this problem is much less severe.

7
Summary of Results (contd)

• The severe failure of conventional MNL and NMNL
  choice models to fit inter-purchase spell
  distribution has not been previously noted.
• Why? It is uncommon in marketing to evaluate
  models based on fit to choice dynamics.
• The PC model is as easy to estimate as the
  conventional models, so it should be viewed as a
  serious alternative to MNL and NMNL.

8
Why does the PC Model Fit Better?

• It generates a more flexible relationship between
  purchase incidence and brand share price
  elasticities than conventional models.
• The conventional models greatly overstate the
  frequency of short inter-purchase spells.
• Because they have difficulty reconciling the
  observed high sensitivity of brand shares to
  price with low sensitivity of purchase incidence
  to price in the period shortly after a purchase
  (when the inventory is high).

9
The Price Consideration Model

• Consider a simple case where price is the only
  covariate.
• Category has J brands. At each t, prior to
  seeing prices, consumer decides whether to
  consider the category.
• PCt probability consumer considers category in
  week t. (This may depend on inventory,
  promotional activity, etc.)
• If he/she considers the category, then consumer
  looks at prices, and a MNL with a no-purchase
  option governs choice behavior.

10
The PC Model (contd)

• Utility of purchase brand j at time t
• Ujt aj ßpjt ejt
• where ejt is an extreme value error.
• Let Pt(jC) denote the probability the consumer
  chooses brand j at time t, conditional on
  considering the category
• (1) for j1,..,J,

11
The PC model (contd)

• Let option J1 be no-purchase, with utility set
  to zero.
• (2)
• Then, the unconditional choice prob.
• (3)
• (4)

12
PC Model properties

• In PC, IIA holds among brands, but it does not
  hold between brands and the no-purchase option.
• But in MNL,IIA holds among brands and the
  no-purchase option.
• Nested MNL could deviate from IIA. But it can
  only achieve this by raising the correlation
  among the extreme value error terms in the second
  stage, i.e., it forces brands to be close
  substitutes.
• PC can generate this departure without requiring
  that brands be close substitutes making it more
  flexible.

13
Elaborating the PC Model

• The simple PC model in (1)-(6) can be elaborated
  in obvious ways
• consumer heterogeneity in the brand intercepts,
  aj
• state dependence in brand preferences
• letting the category consideration probability
  PCt be a function of feature and display
  indicators, ad exposures, household size and time
  since last purchase (to proxy for inventories).
• This is what we do now.

14
Econometric Specification for the PC Model

• In week t, consumer is consideration prob.
  depends on category promotional activity
  variables (Xct), household size (memi) and time
  since last purchase (purch_gapi)
• (7)
• Xct includes indicators for if any brand in the
  category is on feature or display - these
  promotional activities may draw consumers
  attention to the category.
• ?i0 is a random coefficient and we assume that it
  is normally distributed.

15
Econometric Specification (contd)

• Second stage consumer has decided to consider
  (but not necessarily buy) in the category.
• Let Uijt denote utility to consumer i of
  purchasing brand j at time t. For j 1,, J,
  let
• (8)
• Xjt is a vector of observed attributes of brand j
  at time t.
• Zit of observed characteristics of consumer i at
  time t.
• GL(Hijt, d) is the brand loyalty variable
  defined by Guadagni and Little (1983).
• For j J1,
• (9a) PC I,
• (9b) PC II,

16
Specification of MNL and NMNL

• The specification of MNL is similar to PC II
  except that the prob. of considering a category
  is set to be 1.
• In NMNL, the no purchase option is only available
  in the first stage.

17
Data

• Nielsen scanner data on Ketchup and Peanut
  Butter, Sioux Falls, SD and Springfield, MO.
• Sample begins in week 25 of 1986 for both
  categories. Ends in week 34 of 1988 for ketchup,
  and in week 23 of 1987 for peanut butter.
• Ketchup category has 3189 households, 114 weeks,
  324,795 store visits, and 24,544 purchases.
• Peanut butter has 7924 households, 51 weeks,
  258,136 store visits, and 31,165 purchases.
• Major brands in ketchup Heinz, Hunts, Del
  Monte, Store Brand.
• Major brands in peanut butter Skippy, JIF, Peter
  Pan, and Store Brand.

18
Summary statistics
19
Goodness-of-fit, Peanut Butter
20
Simulated vs. Actual Brand Choice Frequency
21
Purchase Incidence Probabilities Conditional on
Lagged Choice
22
Inter-purchase time distribution
23
Purchase Hazard
24
Parameter Estimates

• Estimates for brand specific intercepts and price
  coefficients are similar across models.
• State dependence

25
More parameter estimates
26
What PC Model says about Consideration Probability

• Baseline no brand on display/feature, household
  of size 3 that bought last period (i.e.,
  purch_gapit 1). The PC model says the
  probability of considering peanut butter is
  39.7, on average.
• The consideration probability increases to 75.6
  if one or more brands is on display and feature.
  Note in peanut butter, the category display and
  feature indicators equal 1 in 4.63 and 9.04 of
  weeks, respectively
• Starting from the baseline, if we increase the
  purchase gap to 5 weeks, the probability of
  considering the category increases to 90.7.

27
Conclusion

• The PC model can accommodate a more flexible
  relationship between purchase incidence and brand
  share price elasticities than conventional MNL or
  NMNL.
• Using data from the peanut butter and ketchup
  categories, we show that the PC model produces a
  much better fit, particularly to inter-purchase
  spells.
• The PC model is as simple to estimate as standard
  models.
• The PC model is a viable alternative to the
  workhorse MNL and NMNL models in Marketing.