Tijdschrift voor Economie ei1 Managerrient
Vol. XLVII, 2, 2002
A General Test of Referente Price Theory
in the Presence of Threshold Effeets
B y K. RAMAN and F.M. BASS*
,
Kalyan Rainan
School of Management
University of Michingan Flint & Associate
Faculty, Center for Stiidy Of Complex Systerns
University of Micliigan Aiin Arbor, USA
Frank M. Bass
University of Texas System Eugene McDern~ott,
School of Management,
Tlie University of Texas at Dallas, USA
ABSTRACT
The theory o f reference prices has great theoretica1 appeal and considerable
managerial sigilificance. This paper provides a test o f reference price theory in
a geiieral setting allowing for threshold effects and asyininetric inarltet response
with respect to the thresliold. The theory is rigorously evaluated o n the basis of
predictive tests using the methodology o f switching regressions, and the empirical results show strong conoboration for it. Tlie paper concludes wit11 a disclission of managerial iinplications o f refereilce price theory for pro~notionaland
pricing strategy.
*
The authors are grateful to Marnik Dekiriipe, Russ Winer, Robert Meyer, Alan Sawyer,
Chaluavarthi Narasiiilhaii, Gerard Tellis and Dan Putler for conlrileiits on previous versioiis of this manuscript. A previous version of this article was presented at pricing
seminars at AT&T Bel1 Laboratories, Murray Hill, New Jersey, U.S.A. and DuPont
Company in Wilniington, Delaware, U.S.A.
I. TNTRODUCTION
This paper incorporates the concept of reference price in an aggregate
model of market share response. The behavioral pricing literature suggests that the attractiueness of a market price is deteriliined by a comparison of the market price to an intesnal standard known as the reference price. 111 cor~trast,classical Hicks-Qpe ecoiioiiiic models list:
actual retail prices, thus providing no infonnation about the effect on
aggregate demaiid of the psychological aspects of price. The notion of
a reference price is grounded in considerations of the psychological
dimeilsions of price perception. Many p~iblishedpapers in marltetíiig
have examined individual os household level models of reference
price (Janiszewski and Lichtenstein (1999), Kumar, Karande and
Weinartz (1998), Lattin and Bucklin (1989), Kalwani and Yim (1992),
Krishnamui-thi, Mazumdar and Raj (1992)) but none have established
asymmetric reference price effects at the aggregate level.
The theory of reference prices implies the following phenomena:
l . The existence of a range of acceptable prices.
2. The existence of a non-zero price threshold, as a consequente of 1.
3. Asyrnmetric market response to the reference price above and
below the threshold.
Therefore, a valid model of the inlpact of reference price on market
share must incorporate the above effects. Our model accommodates
the above requirements by using switching regressions, a methodology
originally developed by Quandt (1958), later gei~eralizedby Goldfeld
and Quandt (1973), and recently applied to predict consuiner choice in
a stochastic prefereilce framework (Lau, Yang and Post (1996)).
The theory of reference prices offers a nuinber of inanagerial iinplications:
1. The timing and magnitude of price promotions should ideally be
iililuenced by the existence of reference prices and their effect on
consuiner demand (Kalyailaram and Winer (1995)).
2. The existence of reference prices and the manner iil which they
are formed influences brand choice and purchase quantity (Kumar,
ICirande and Reiilax-tz (1998)).
3. Macro-econornic factors such as inflation, unemployment and
interest rates impact reference price forniation and hence sliould
be considered in the evaluation of alternative pricing scenarios
(Estelami, Lehmann and Holdeii (2001)).
4. The range of evoked prices inoderates the effect of reference price
and hence has implications for "every day low price" (EDLP) and
"high-low" pricing strategies (Janiszewski and Lichtenstein (1999)).
11. REFERENCE PFUCE ISSUES
A. Psychologieal Foundations of Refevence Prices and
theiv I~nplicationsfov Conszrmer Response
Intuitively, a reference price is an internal standard against which
consuiners compare observed prices. Since price is the most conspicuous of al1 the marketing variables, one would expect consumers to
form an idea of the "right" price for a brand, based on their past
observations of that brand's prices. Of course, such an expectation
assumes that consumers remember past prices. Iii a much-cited study,
Dickson and Sawyer (1990) showed that most consumers showed
extreinely poor recall of prices that they had just paid, a finding that
seems to cast doubt on the notion of reference price. However, as
Kalyanarain and Winer (1995) note, a substantial number of respondents in price recall surveys do recall past prices with reasonable
accuracy. Moreover, recent research on meinory suggests that there
are two types of inemory, explicit and implicit; and while consumers
may not explicitly recall the exact price, they are generally capable
of forining vague juciginents such as '-t00 high," os "a good deal"
(Monroe (1999)). The concept of reference prices thus has a great
deal of intuitive appeal and face validity. Indeed, Kalyanaram and
Winer (1995) note that considerable theoretica1 support exists for refereiice price aiid that its effect on consumer demand may be regarded
as an established empirica1 generalization. At least four different psychological theories substantiate this concept, as iioted by Winer
(1988), and reviewed in Sawyer and Dickson (1984). These are
briefly described below, iogetlieï with their implications for aggregate market response.
1. The Weber-Fechner Law
This law relates changes iii a stimulus to the evolted response as follows: AS/S = k, where S is tlie stilnulus, AS is the "just rioticeable
difference" (i.e. so that S + AS is perceived to be different from S),
and k is constant for each sensory stimulus. Fechner analyzed subjective sensations using differential increments and derived the
Weber-Fechner law (see Monroe (197 1)).
Several authors have applied the Weber-Fechner law in the investigation of price thresholds (Adam (1970), Gabor and Granger
(1966), (1971), Monroe (1 973)). The empirica1 evidence reported in
these papers supports the hypothesis of upper and lower price
thresholds and thus a range of prices which is considered acceptable.
The Weber-Fechner law provides a means of experimentally determining such thresholds. Prices below the lower threshold are considered too low (quality is suspect) and prices above the upper threshold
are considered too high. This was empirically demonstrated by Adam
(see Monroe (1973)).
2. Assimilation-Contrast Theory
This is closely related to the implications of the Weber-Fechner law.
Developed by Sherif and Hovland (1961), this theory hypothesizes a
range of prices called a lattitude of acceptance, which is similar to the
acceptable price ranges discussed in Gabor and Granger (1966) and
Monroe (1973). According to this theory, consumers tend to assimilate prices within the lattitude of acceptance and perceive them as
acceptable. Prices falling outside the range are contrasted to prices
within the acceptable range and their impact is strongly perceived.
3. Adaptation-Level Theory
Developed by Helson (1964), this theory hypothesizes that the
response to a stimulus depends on its relationship to preceding stimuli. Consumers form "adaptation levels" through exposure to the
stimuli. The response to the current stimulus is a function of the relationship between the stiinulus level and the adaptation level. In the
context of price response, Emory (1970) calls this adaptation level
the norrnal or standard price. Thus, in studying the consumer's
response to price, we ought to consider the relationship of the current
price level to the adaptation level. Niedrich, Sharma and Wede11
(2001) show good empirical support for adaptatation-level theory in
their experiinental study of exemplar and prototype models of reference price.
4. Prospect Theory
This was developed by Kahneman and Tversky (1979) to explain the
choices made by economic agents in risky situations. It is an alternative to traditional utility theory (von Neumann and Morgenstern
(1944)) in that it assigns a value to gains and losses, and not just to
the final outcome. The behavioral rationale for this is that most people are more strongly affected by losses rather than gains, even if the
amounts involved are the Same. In the context of price response, we
may view a price higher than the reference price as a "loss" (fiom the
consumer's perspective), and a price lower than the reference price as
a "gain." Prospect theory implies that consumers would be more
strongly affected in the former than in the latter situation. Winer
(1985) describes a price higher than the reference price as a "stickershock effect." Mayhew and Winer (1992) provide empirica1 evidence
of the different psychological effects of the gains and losses proposed
in prospect theory. Putler (1992) shows theoretically how a price
change effect may be decomposed int0 a gain and loss effect, using a
generalized Slutsky equation.
B . Operationalization of the Reference Price
Having established that the reference price is an important variable in
determining market response, we now discuss its operationalization.
Several operationalizations have been proposed. Uh1 (1970) used
the last period's actual price as this period's reference price.
Helson (1964) suggested a weighted log mean of several actual
prices as the current period's reference price. Rinne (1981) has used
an adaptive expectations model to operationalize the reference price.
Hardie, Johnson and Fader (1993) and Greenleaf (1994) use an adaptive expectations model. It can be shown that al1 these models may be
accommodated in the more genera1 framework of the Rational
Expectations Hypothesis (REH), developed by Muth ((1960), (1961)).
Jacobson and Obermiller (1990) have questioned the appropriateness
of the REH framework; however, as Krishnamurthi et a1.(1992) note,
researchers are not in complete agreement over this issue.
Furthennore, several researchers have implicitly used REH by operationalizing reference price as the previous period's price (Uh1 (1970),
Gabor (1977), Mayhew and Winer (1992), Krishnamurthi et al.
(1992), and Kalwani, Yim, Rinne and Sugita (1990)).
Denoting the actual price by P, and the reference price by R,,
define R, to be the expected price, given al1 the past observed
prices.
R, = E(P, j P,, s < t)
The conditional expectation utilizes the inforination contained in
al1 past observed prices, Of course, consiimers observe not only the
brand's own past prices but also the prices of competing brands.
Therefore, relative rather than absolute price levels are used in the
empirica1 estimation of the reference price. In the context of the
REH, the adaptation level (reference price) formed by consumers is
influenced by the decision rules used by managers to set the levels of
expectational variables, i.e. price levels. In our context, the essence
of the REH is that economic agents act as iftheir expectations were
formed on the basis of the decision rules used by managers to
set prices. Thus, assuming that expectations are formed rationally
(i.e. each consumer's expectation is an unbiased estiinate of the tme
value) a model describing how price levels are adjusted over time by
management would also be the model utilized by consumers to form
their expectations. We note that we do not claim to capture the cognitive algebra of consumers: the REH is simply a theoretica1 description that generates an empirically testable theory by operationalizing
the reference price construct. Although consumers' behavior inay be
consistent with the theory's predictions, this does not iinply that they
are actually canying out detailed iilathematical computations. To use
a physical analogy, planers do nor solve systems of differential equations to obtain their trajectories; however their orbits can be predicted
by Newton's laws which require solving such equations.
A good discussion of REH and its incorporation in econometric
models is available in Nerlove, Grether, and Carvalho (1979). When
the price series is a discrete, linear stochastic process, it can be analyzed by Box-Jenltins methods to evaluate the conditional expectation in (1). If the price series is a random walk, equation (1) is merely
the last period's price. As Section IV shows, the curreilt reference
price for each brand was operationalized as the last period's price in
this analysis.
It may be objected that aggregate data are being used to test an
individual level theory. However, the nature of this product class
is such that reference price adjustments for brands are likely to be
minima1 within the data interval (bimonthly) that was available for
analysis. Furthermore, one can employ the "representative consumer"
hypothesis to specify an aggregate demand functioil that is consistent
with the behavior of an idealized "represeiltative" consumer who lias
a specific representation of preferences. For exainple, Putler (1992)
uses a modified Klein-Rubin utility function to theoretically derive
such an aggregate demand function.
111. THE GENERAL MODEL AND ESTIMATION ISSUES
A. Model FOT-uliulation
Our nul1 model (i.e. the model against which tlie genera1 reference
price models wil1 be compared) is of the following type:
MS, = a.
+ u,R, + a,Xt + E,
(2)
This is a model in the classica1 Hicks tradition and has been used
by many authors (Guadagni and Little (1983), Raj (1982), Winer
((1980), (1988)). Here R, denotes the reference price, X, a promotional variable and MS, the market share. While the economie literature uses the actual price P,, we use the reference price R, in order to
directly measure the effect of the reference price. We also estimated
a iiull model with actual prices P, as an independent variable.
However, both inodels perform equally wel1 (or poorly) in al1 cases.
This is easily explainable statistically: the variatioa of the reference
price series is practically identical to that of the actual price series
since al1 the price series were random walks, and consequently the
reference price series was the actual price series lagged by a single
period. Al1 variables are measured at relative rather thaii at absolute
levels to account for competitive effects. X, and MS, are the brand's
shares of the promotional expenditure and sales respectively.
Economie theory predicts u, < O and a, > 0.
In order to capture the elements of reference price theory, our genera1 model is defined as follows.
Let A, = P, - R,, where P, is the actual and R, the reference price,
and let K be an unknown, strictly positive constant.
Next we postulate:
Equations (3A) and (3B) constitute a switching regression, a t e m
coined by Quandt (1958). The variable A, and parameter K control
the switching between the two regimes; the periods when A, > K is
commonly referred to as Regime l , and its complement as Regime 2.
Using A, as a switching control rather than as an explanatory variable
avoids potential multicollinearity problems. This model accoinmodates the essential i-equirements of reference price theory as wil1 be
shown in the next section in which we discuss the rationale behind
our predictive tests of the theory.
B. Predictive Tests
The concept of predictive testing is to deduce specific implications
from explicit premises; if the predictions are fulfilled, then the data
support the underlying theory, and if the predictions are not, then
tlie underlying theory is falsified. This notion was advocated
by Basmann ((1965), (1968)), used by Bass ((1969A), (1969B)),
Bass and Parsons ((1969), (1971)), and fits into the logica1 positivist
school of theory-testing (Hanssens, Parsons and Schultz (1990),
p. 2-83).
1. K > O. We expect the parameter K to be strictly positive. As noted
in Section 11, the Weber-Fechner law, adaptation-level theory,
assimilation-contrast theory and prospect theory al1 imply a range
of prices considered acceptable. This implies that consumers are
not sensitive to every positive deviation A,. To use Winer's (1985)
tenninology, the "Sticker-Shock" effect A, must be large enough
to provolte a reaction. This requirement is conipactly suminarized
by this test, i.e. K > 0.
2. B, < O, y, < O, P 2 > O, Y2 > O
These are obvious requireinents deduced froin basic economie
theoiy.
3. I P i > IYil
This is a direct consequence of prospect tlieory. Regime 1 defines
the periods when consumers perceive a "1oss"--the observed price is
greater than the reference price and exceeds it by the threshold
amount K. Regime 2 defines the periods when consumers perceive
a "gain"--the difference between observed price and the reference
price falls within tlie latitude of acceptance. Since a loss is generally
perceived more harshly than a gain, we expect the slope of the reference price to be more negative in the first regime.
The switching regression defined in equations 3A and 3B provides
tlie natura1 framework for these predictive tests; the conventional
constant parameters regression defined iil equation 2 cannot handle
the phenoinena implied by reference price theory. Notice that
the switchii~gsystem implies that inarket response switches discoritinuously between the two regimes. This is in fact lcnown to be
appropriate at the individual level - Laining ((1986), pp. 18) notes:
"The essential notioil of classical threshold theory is that the threshold is a point of discontinuity in sensory experience. Stimuli below
the threshold are not perceived; they have no effect on the organism."
It is possible that the aggregate response may uildergo a smoother
transition than the discontinuity found at the individual level we are not aware of any research addressing this interesting possibility. Lilte al1 models, the switching system described in 3A-3B is an
approximation of reality; it is a useful approximation because it captures the essential aspects of reference price theory which are
neglected by the classical model specified in equation (2).
C. Estimation Issues
If the threshold K were known a priori, estimation of 3A - 3B would
be simple. The data set could then be partitioned int0 two subsets
on the basis of K, and OLS regressions perfonned on each subset.
A Chow test could be used to test for the existence of two separate
regimes. Since K is unknown, estimation of 3A - 3B is non-trivial,
and we use the inethod proposed by Goldfeld and Quandt (1973).
The algorithin, adapted to the present context, works as follows.
l . The observations are arranged in descending order of A,.
2. Each value of A, determines a partition of the data set into two
subsets. OLS regressions can be perfortned on each subset, provided each subset has a sufficieiit nuniber of degrees of freedoni to
allow estimation of al1 the parameters.
3. The total sum of squared errors (SSE) is computed for each partition.
4. The value of A, at whicli we get the smallest SSE provides the best
estimate of K, in the least-squares sense. The values of the other
parameters in the two regimes corresponding to this value of A,
are their least-squares estimates.
The standard OLS assumptions of zero mean and uncorrelated error
terms are made. For purposes of inference, we also need another
standard assumption, i.e., that the errors are normally distributed.
In order to test the nul1 hypothesis that there is no switching (i.e.
a single regression suffices for al1 the observations), a Chow test is
used. This is defined as follows:
F,, m + I, -,P
=
{(SSEI - SSE~)Ip}I{SSEll(n+ m
-
p)}
where,
SSE, = Sum of Squared Ei-sors when a single regression is
used for al1 the observations
SSE, = Suin of Squared Errors when two regressions are used,
n
= number of observations in Regime 1
m
= number of obsesvations in Regime 2
= nuinber of explanatory variables
p
Chow (1960) proved that the above ratio follows an F distribution
with parameters p, m + n - 2p. Strictly speaking, the Chow test was
designed for situations where the two regimes are known a priori.
However, the alternative to the Chow test is the conveiltional likelihood ratio test which is reported by Quantimesgre (1960) to have
some problems - it has been found to be of use only for certain
ranges of the irue value of the threshold. Goldfeld and Quantimesgre
(1973), and Bhattacharya and Johnson (1968) report that the Chow
test, used with caution and as if the threshold value were h o w n a
priori is satisfactory.
IV. EMPIRICAL RESULTS
A. Description of Data
Five brands in a class of frequently bought consumer non-durables
were ailalyzed. Specific brand name os product class ii~forniationis
confidential and we have therefore coded the brand names as A, B, C,
D and E. The available data contain inforination on sales (in units
and in dollars), price, promotion and advertising levels. The variable
X, in equations 2, 3A, and 3B was talten to be promotional share
level since advertising was not used by al1 tlie brands. Market
share was measured in tesms of units rather than dollars since the former measure tends to be more stable over time and is not subject to
fluctuations arising froni varying costs of production inputs over time.
The variable R, is an expectational variable and depends on the stmcture of the price series P,. Since consumers compare prices between
brands as wel1 as over time, P, was taken to be a relative rather than
an absolute price level. This is defined as the ratio of the brand's price
to the average price of competing brands. Relative price levels have
the further statistical advantage of remaining fairly stable over time
since price competition is generally avoided by firnis. Thus, we
expected the relative prices to closely follow a random walk, i.e.
where e, is a white-noise term. Inspection of the autocorrelation and
partial autocorrelation plot for each brand confirmed this. This immediately leads to:
R, = E(P,I P,, s < t) = P,-
l
Other researchers who have used this operationalization include Uh1
(1970), Gabor (1977), Mayhew and Winer (1992), Krishnamurthi et
al. (1992), and Kalwani et al. (1990).
B. Estimated Models
1. Description of Tables
The empirica1 results are displayed in Tables 1-5. In Table 6, we have
reported the R2 values for the constant parameter regression for each
brand. R2 values are geilerally not reported for switching regressions,
since such systeins are non-linear and consist of a pair of straight
lines. Formally, one can thiiik of the R2 for a switching regression in
the traditional way by coilsidering the total error involved in using
the switching systein. Thus,
R,,'
=
R,,'
SSE
SSY
SSE
= R'
1 - SSEISSY
where,
for the switching regression
Total Suin of Sq~iaredErrors for the switching regression
= Total Sum of Squares for the dependent variable
= SSE, + SSE,, where SSE, and SSE, are the sum of
squared errors for each meinber of the switching system.
=
However, it should be borne in mind that there is no statistica1
basis for interpreting the R' associated with a switching regression.
We have provided this information purely to illustrate the reduction
in total error when one passes from a constant parameter system to a
switching system in which the values of the parameters depend on
the level of a threshold variable.
Tables 1-5 provide the following information for each brand:
he estimated threshold K, the P-value for the Chow statistic, the
number of observations in each regime, the parameter estimates and
their P-value in the two regimes and the nul1 model (i.e. the constant
parameter regression).
2. Discussion of Results
Inspection of Tables 1-5 shows that the brands analyzed provide
strong support for the theory. For every brand, the Chow statistic is
strongly significant (ranging from a P-value of 0.0001 for Brand C to
0.1262 for Brand D). Thus, in each case, the switching regression
performs significantly better than the constant parameter regression.
The parameter K (threshold level) is strictly positive for each brand,
as predicted by the psychological theories discussed in Section 11.
This is an important empirical confirmation of the threshold implications of these theories.
For Brands A to D, the coefficient of R, is more negative in
Regime 1 than in Regime 2. This confirms our prior expectation that
market response would be sharper in Regime l (due to the "stickershock effect" of larger than expected prices) than in Regime 2. This
fact furnishes strong empirical confirmation of the implications of
prospect theory for reference price theory.
Al1 variables have the expected sign in each model. Note (Table 4)
that R, has a positive sign in Regime 2 and the constant parameter
regression for Brand D. However, it has the correct sign and is
strongly significant (P-Value = 0.002) in Regime 1 when price deviations exceed the threshold. The promotional variable X, has a negative sign in Regime 1 for this brand, but its P-value (0.128) indicates
that it is only weakly significant.
Note that the results of Brand E are not supportive of reference
price theory. Although the threshold is positive, the Chow Statistic is
significant, and al1 variables have the expected sign, the direction of
inequality between the slope of R, in the two regimes is wrong.
Estimated Thueslzold K
=
No. Of Obseniations
Intercept
Rt
X,
TABLE 1
Brand A
0.0077 - P-Value For Chow Statistic
=
0.0183
Regime 1
Regime 2
(P, - R, > 0.0077)
28
(P, - R, 5 0.0077)
98
Estimate
0.5135
(10")
-0.3645
( 104)
-0.1326
(0.4356)
Estimate
0.4741
(10-'j)
-0.3285
(10-'O)
0.0026
(0.7478)
Constant Parameter Regression
Estimate
0.4739
(0.0001)
-0.3309
(0.0001)
0.0054
(0.5004)
Intercept
Rt
x,
Inspection of the correlation inatrix showed that X, was uncorrelated
with MS, (r = -0.08301, P-value = 0.4882) and weakly correlated
with R, (r = 0.24136, P-value = 0.041 1). We therefore dropped X,
froin the inarket share equation and re-estiinated the switching
regression. This produced the following results:
Regime 1
Coefficient Of R,
P-value for Chow = 0.4469
-2.284
(10-'O)
Regime 2
TABLE 2
Brand B
Estrmatecl Thl*esholdK = O 0039 - P-Jhlzie Fo7- C h o ~Statrstzc
No. Of Observations
Intercept
R,
X,
=
O 0142
Regiine I
Regime 2
(P,-R,> 0.0039)
19
(P, - R, I
0.0039)
20
Estimate
1.233
(0.00002)
-0.3963
(0.0142)
-0.0653
(0.0178)
Estimate
0.7105
(0.00009)
-0.0536
(0.5884)
O. 1524
(1o-8)
Constant Parameter Regression
Intercept
Estimate
1.0613
(0.0001)
-0.2869
(0.0066)
o. 1002
(0.0001)
Here, the coefficients are very strongly significant, and the direction
of inequality is as expected. However, tlie Chow statistic is insignificant, which means that we cannot reject the nul1 hypothesis of "No
Switching." Based on the statistica1 evidence, we therefore have to
conclude that a constant parameter regression sufices for Brand E. It
appears that Brand E customers are not very sensitive to the discrepancies between the reference and actual price. Winer (1986) found
this to be the case for one of the brands he analyzed. His explanation
was that consumers were probably not devoting much price infomation processing time to its purchasing. Interestingly, in both Winer's
(1986) analysis and ours, the brand insensitive to switching is a low
share brand.
Note that the promotional variable is insignificant for Brand A
(Table 1) in both regimes and insignificant for Brand C (Table 3)
in the first regime. Dropping the promotional variable and re-estimating the equations leads to even stronger results, as shown below.
TABLE 3
Braizd C
Estimated Tlz~esholdK = 0.0116 - P- Valzie FOTChow Statistic
Regime 1
No. Of Observations
R,
x,
0.0001
Regime 2
(P,-R, > 0.0116)
ll
Estimate
0. 1542
(0.0656)
-0.1306
(0.1343)
0.0365
(0.0545)
Estimate
0.3299
(0.1212)
-0.335 1
(0.1313)
0.4354
(0.25 16)
Intercept
=
Constant Parameter Regressi011
Intercept
Rt
x,
Coefficient
Of R,
P-Value
P-Value
For Chow
Brand A
Regime l
Regime 2
Brand C
Regime l
Regime 2
-0.3246
(0.00004)
-0.2360
(0.000003)
-0.4013
(0.0135)
-0.1258
(0.058)
(0.0273)
(l O-')
We discover an interesting empirica1 relationship between the estimated slope of the reference price in the constant paraineter regression a , , and its slope in Regime l@,) and Regime 2 (y,). In every
case (except Brand E) we find:
TABLE 4
Brand D
Estimated Thveshold K = 0.0104 - P-Value For Chow Statistic
Regime 1
No. Of Observations
Intercept
Rt
(0.002)
xt
=
0.1262
Regime 2
(Pt - R t > 0.0104)
1O
Estimate
0.2910
(0.0001)
-0.1321
(0.0920)
-0.0216
(0.128)
Estimate
0.0251
(0.6292)
0.0678
Constant Parameter Regression
Intercept
Estimate
0.2052
(0.0894)
-0.1885
(O. 1806)
0.0561
(0.0001)
The implication is that the constant parameter regression underestimâtes mârket response when price deviations are large enough to
exceed the threshold K and overestimates market response in the
other cases. In conclusion, the brands analyzed here al1 provide
strong evidence for reference price theory.
V. MANAGEMAL IMPLICATIONS
Our work establishes the existence of thresholds and reference prices
at an aggregate level of consumer demand. From a managerial standpoint, the presence of thresholds and reference prices has important
promotional implications (Lattin and Bucklin (1989)). The existence
of price thresholds and reference prices suggests that consumers will
not notice a price-promotion unless the price reduction exceeds a
minimum threshold. Furthermore, promoting more frequently will
TABLE 5
Bvaizd E
Estimated Threshold K = 0.0162 - P-Value For Chow Statistic
Regime l
No. Of Observations
Intercept
Rt
x,
=
0.0025
Regime 2
(P,-R, > 0.0162)
1O
Estimate
1.723
( l o-8)
-0.980
( i O-")
-0.048
(0.1552)
Estimate
1.972
(0)
- 1.127
(0)
0.045
(0.0145)
Constant Parameter Regression
Estimate
1.904
(0.0001)
- 1.086
(0.0001)
0.046
(0.0079)
Intercept
R,
xt
TABLE 6
R2 Values
Brand
A
B
C
D
E
Constant
Parameter
Switching
Regression
0.3876
0.7827
0.20
0.6106
0.6956
0.4389
0.8418
0.5015
0.6717
0.7600
R2 For The Switching Regression = 1-SSEISSY
SSE = SSE, + SSE,
where,
SSE, = Sum Of Squared Errors From Regime 1
SSE, = Sum Of Squared Errors From Regime 2
lower the reference price, thereby making it increasingly likely that
consumers wil1 not perceive future promotions to be as attractive as
earlier ones. Even worse, the consumer inay begin to perceive
the regular price as a price iiicrease. Our research sliowed that coiisumers react more strongly to a price increase thaii a price decrease.
Such asymmetric response must be taken iiito account when setting
dynamically optima1 priciiig and promotion policies. Greenleaf
(1994) Iinds that recurring promotioiis are more profitable than a
constant price, when the market is more sensitive to gaiiis than to
losses. Our findings have interestiiig iinplications for planning proinotions in the context of deal-prone segments. Blattberg and Neslin
(1990) define deal-proneness as the extent to whicli the consuiner is
influenced by sales promotion. ICumar, Karaiide and Reinartz (1998)
recoininend "liigh-low" pricing in deal-prone areas and EDLP strateg i e ~for non-deal-prone areas, based on their individual-level analysis
of IR1 scanner panel purchase data. Our study empirically validates
the existence of internal reference price and its atteiidant effects at
the aggregate market level, thus suggesting that the recomniendations
of Kumar et al. (1998) are likely to be applicable at the level of entire
market segments. Beatty and Smith (1987) have shown that price
information search declines with increased prosperity. On the other
hand, households face more severe budget constraints during times of
economic slow-down, resulting in an inverse relationship between
household prosperity and price sensitivity (Wakefield and Inman
(1993)). Thus, Estelaini et al. (2001) find that consumer knowledge
of prices is lower during periods of higher economic growth, high
inflation and lower interest rates. They suggest that comparitive pricing is likely to work better during such tiines because the success
of comparitive pricing is likely to depend on a lack of consuiner
knowledge of prices. Combining our deinonstration of reference
price effects at the aggregate level with the findings of Estelaini et al.
(2001), we suggest that comparative pricing tactics are likely to work
better in market segments characterized by high economic growth,
high inflation rates and low interest rates.
VI. CONCLUSION
We have presented the results of an empirica1 test of reference price
theory. Our paper has theoretical, methodological and managerial
contributioiis. Our model is based in psychological theories of consuiner response. We showed that switching regressions provide a liatural frainework for testing reference price theoiy. Reference price
forniatioii is a complex process, aiid it may be argued that the frequency and depth of promotions, and otlier contextual variables
would affect its dynamics (Kalwani and Yim (1992), Kalwani et al.
(1990), Mayhew and Winer (1992)). Our research suggests that there
is a basic asyminetry in market response. One should not expect this
to be tlie case for al1 product classes: the conclusions reported here
apply, strictly speaking, only for the product class considered in our
study. Generalizations to other product classes must carefully consider the iinportance of the price variable, and whether consumers
devote a significant ainount of information processing time to price
comparisons over time and across brands within the product class
(see Dicltson and Sawyer (1990) for more on this issue). If they do,
then this research has important implications for management: asyminetric response must be modeled when management attempts to
measure the impact of changes in a brand's price.
Monroe and Lee's (1999) recent research on key differences
between conscious and non-conscious processing of price information opens up a line of research that may uncover fresh insights int0
the effect of reference prices. Exact recall of prices requires remembering responses and retrieval of consciously processed information
whereas knowing responses are related to a sense of familiarity that
reflect non-conscious processing. Conscious processing is necessary
to transfer exact knowledge of price information to long-term memory whereas non-conscious or automatic information processing can
result in value judgments such as "too h i g h or "reasonable price."
The formation of such value judgments results in linguistically vague
rather than mathematically exact encoding of price information in
meinory, a situation that is remarkably well-suited to the methods of
fuzzy analysis (Raman (2002)). Thus, the methods of fuzzy logic are
relevant to study the manner in which price judgments are encoded in
memory and to quantitatively analyze their effect on consumer
demand.
In conclusion, we stress that statistica1 modeling should be based
on a sound theory of the phenomenon. Since the switching regressions have more parameters than a simple constant parameter regression, they may be expected in genera1 to improve the fit. This, in
itself, is not sufficient justification for the switching regressions.
Their appropriateness should be based on theoretica1 grounds.
We hope that other researchers dealing with interactive or threshold
effects-wil1 find interesting ideas in this paper and fresh approaches
to dealing with such problems.
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