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# &quot;Introduction to normalization of demand data

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&quot;Introduction to normalization of demand data – The first step in isolating the effects of price on demand,&quot; Journal of Revenue and Pricing Management, Vol. 9, No. 1/2, pp. 4–22

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### &quot;Introduction to normalization of demand data

2. 2. Introduction to normalization of demand data OPPORTUNITY We often refer to demand as being either elastic ‘Ceterıs paribus’ is fundamental to price ¯ ¯ or inelastic. Elastic demand means that the elasticity theory. Ceterıs paribus is Latin for ¯ ¯ quantity demanded is sensitive to the price. ‘with other things [being] the same’ or ‘all Inelastic demand means that the quantity other things being equal.’ For example, an demanded is not very sensitive to the price. increase in the price of beef will result, ceteris Demand also responds to exogenous and paribus, in less beef being sold to consumers. endogenous factors. Parameters or variables are Putting aside the possibility that the prices of said to be endogenous when they are predicted chicken, pork, fish and lamb have simulta- by other variables in the model; variables are neously increased by even larger percentages, exogenous if they are entirely outside the or that consumer incomes have also jumped model. For example, a primary factor in any sharply, or that CBS News has just announced business is the ‘traffic’, that is, the number of that beef prevents AIDS, and so on – an guest/customers visiting a location or store. increase in the price of beef will result in less If more people visit a location, then generally beef being sold to consumers. the location sells more products. For the same Unfortunately, there are rarely instances in price, demand is higher with higher traffic which everything else remains the same. counts, and thus traffic can be an exogenous Normalizing the demand data helps us satisfy variable. For many businesses, the traffic itself is the ‘ceteris paribus’ requirement. We can also a function of the price: lower advertised accomplish normalization through techniques prices drive more traffic into the store, and thus such as ordinary least squares, whereby the traffic is also an endogenous variable. If this is demand is regressed against the demand true for a business, then advertising versus drivers. Price can be included in the model, traffic alone may need to be employed as an or a two-stage approach can be taken whereby independent variable to isolate the price effect, the normalized means from a primary model as advertised prices are having an impact on without price as a covariate are regressed traffic. If independent variables, such as traffic against price. By incorporating the drivers of and advertised prices, are related, there are demand for products into the modeling a variety of statistical procedures that you process, we can more accurately model the might use to isolate the effects; Bascle (2008) price–demand relationship for products. offers a methodology to control for endogene- ity through the use of instrumental variables. The different types of consumers visiting FACTORS INFLUENCING a location may also influence a product’s DEMAND demand; for instance, if more high-income Will a change in the price of a good or service consumers visit a location, we may find change the quantity demanded? Understanding a higher proportion of high-end products the price–demand relationship is the central sold. Consumer demographics capture the goal to price a product or service correctly. intrinsic variability that influences price elasti- At any given time, demand can be influenced city, and can vary over time, affecting the by several factors beyond price. Traffic and quantity demanded for a product. In addition customer demographics are just a couple of to the demographics of consumers varying over factors that influence demand. The impact of time, consumer demographics typically vary price on product demand is isolated when we by location. identify significant explanatory variables (other For any given traffic level or demographic than price) and remove their effect. mix, we can make a difference to the bottom How sensitive is the quantity demanded to line by adjusting price to maximize profits. a change in the price of the good or service? Understanding the factors that influence actual r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22 5
3. 3. Quillinan consumer behavior and applying the informa- called herding instinct. People tend to follow tion to maximize profits is the fundamental the crowd without examining the merits of value of normalization. There are numerous a particular object. studies on drivers that affect the demand of K Prices of related goods: When a fall in the price products. We will discuss some of the factors of one good reduces the demand for another in the literature review; however, most of the good, the two goods are called substitutes factors were not applicable to specific imple- (for example, pork and beef). When a fall mentation. in the price of one good increases the demand for another good, the two goods are called complements (for example, cars and A LITERATURE REVIEW OF gasoline). FACTORS INFLUENCING K Availability of (number of and closeness of) DEMAND substitutes: The greater the number of The literature was reviewed for studies of substitute products, the greater the elasticity. factors that influence product demand. We will The closer the substitutes for a good or touch on some of the noteworthy or more service, the more elastic demand will be in frequent factors found in the literature. response to a change in price. K Newness of the product: When first introduced, K Product utility, that is, the usefulness of the demand for a product can be highly product features, can influence product inelastic and gradually gain elasticity at demand. Incremental utility can translate maturity. This reflects a compound of into incremental demand. primary demand of the product and impact There are two measurable types of utility of cross price elasticity. Normalization of gained from the use of any product or the price demand function must take the service: utilitarian, which is the utility product’s lifecycle into account. directly provided to the user, and conspic- K Product presentation quantity and shelf space uous, which is the utility provided to the allocation (placement): Altering the product user as a result of being seen consuming the presentation quantity (within the same product or service (Basmann et al, 1988). location and across multiple locations) will The second type of utility is based on the alter demand. Dreze et al (1994) found that concept of ‘conspicuous consumption’, product location had a large impact on sales, which was coined by Thorstein Veblen whereas changes in the number of facings (1912). Demand for some kinds of luxury allocated to a brand had much less impact goods, like luxury automobiles, actually goes as long as a minimum threshold (to avoid up as prices rise. When prices increase, out-of-stocks) was maintained. demand increases instead of dropping or K Degree of necessity or luxury: Luxury products staying the same; this is referred to as the tend to have greater elasticity than neces- Veblen effect. found evidence that offers sities. The demand for necessities tends to be much support for the presence of status inelastic to price, whereas luxury goods and motives in the behavior of women who buy services tend to be more elastic to price. For cosmetics. Materialism, reference group and example, the demand for opera tickets is even education have been associated with more elastic than the demand for urban rail conspicuous consumption (Schor, 1998). travel. The demand for vacation air travel Conspicuous consumption is also linked to is more elastic than the demand for business the bandwagon effect, that is, purchasing a air travel. good because others are purchasing that After examining 101 different studies on good (Leibenstein, 1950). The effect is often gasoline, Espey (1996) found that while 6 r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22
4. 4. Introduction to normalization of demand data gasoline demand appears to be inelastic negative, and that long-run price elasticity over the short term, over the long term was twice as large as the short-term price the effect is not the same. Goodwin et al elasticity. (2004) could not predict with absolute Some studies suggest that the demand for certainty what effect a rise in the price of alcohol is price inelastic; others suggest it is gas would have on quantity demanded. price elastic. This is a signal that perhaps the Goodwin et al observed that the demand demand for alcohol is being impacted by for fuel decreased by a greater percentage factors other than price that have not been than the volume of traffic. This is probably incorporated in demand models. Fogarty because all else was not equal (a violation (2004) concluded that the year of the study, of our ceteris paribus requirement). The the length of study, the per capita level of reason why fuel consumed decreases by alcohol consumption and the relative etha- more than the volume of traffic is probably nol share of a beverage are important factors that price increases trigger more efficient when explaining variations in estimates of use of fuel (by a combination of tech- the price elasticity of demand for alcohol. nical improvements to vehicles, more fuel- Again, the price elasticity of alcohol is being conserving driving styles and driving in impacted by other factors, which when not easier traffic conditions). taken into account lead to poor estimates of K Proportion of income required by the item: elasticity. Products requiring a larger portion of the K Time period consumed or time elapsed since a consumer’s income tend to have greater price change: Demand tends to be more elastic elasticity. in the long run than in the short term. The As incomes grow, increases in status con- more time consumers have to adjust to a sumption will be pursued. Chao and Schor price change, the more elastic the demand (1998) found that income and occupational for that good. Becker et al (1994) and Espey status were positively associated with the (1996) found this to be the case for cigarettes propensity to engage in status purchasing. and gasoline, respectively. K Habit-forming goods: Goods such as cigarettes Fibich et al (2005) found that price elasticity and drugs tend to be inelastic in demand. is very sensitive to the time that has elapsed Preferences are such that habitual consumers since the price change. The effect of of certain products become de-sensitized to reference price is most noticeable immedi- price changes. Cigarettes and alcohol have ately after a price change. A better estima- been the topics of numerous studies, includ- tion of elasticity can be derived when the ing their joint demand. Goel and Morey time dependencies are accounted for. Fibich (1995) concluded that cigarettes and liquor et al derive an expression for the price are substitutes in consumption; in other elasticity of demand in the presence of words, an increase in the price of cigarettes reference price effects that includes a leads to an increase in the consumption of component resulting from the presence of liquor and conversely. gains and losses in consumer evaluations. Lyon and Simon (1968) reviewed results K Permanent or temporary price changes: A 1-day from prior cigarette elasticity studies, which sale will result in a different response than vary widely, ranging from À0.10 to À1.48, a permanent price decrease of the same and suggested that temporal changes magnitude. Blattberg et al (1995) found may explain some of the variation. Becker that temporary retail price promotions cause et al (1994) found that the empirical results a significant short-term sales spike. tend to support the implication of addi- K Price points: Schindler (2006) showed the 99¢ ctive behavior that cross-price effects are price ending is a signal of low price appeal. r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22 7
5. 5. Quillinan Figure 1: Any change that alters the quantity demanded at every price results in shifts in the demand curve. Decreasing the price from US\$2.00 to \$1.99 increased by 222 per cent. Eighty-nine to may result in greater increase in quantity seventy-one cents played on consumers’ demanded than decreasing it from \$1.99 to left digit effect. Eighty-nine to sixty-nine \$1.98. cents played on consumers’ right digit signal Thomas and Morwitz (2005) conducted as well as left digit effect to result in a experiments with graduate students and phenomenal increase of 222 per cent. showed that the greatest impact of price K External factors: Weather (temperature and ending comes when it changes the leftmost precipitation) can influence consumer pur- digit in the price – \$19.99 versus \$20, chase behavior. Bottled water and flashlights for instance, as opposed to \$3.49 versus are typical pre-hurricane items. In 2004, \$3.50. ‘Generally, it can be said that this Wal-Mart (Hays, 2004) learned from Hurri- happens because we read from left to right,’ cane Charley demand data that sales for Dr Thomas said, and we place extra strawberry Pop-Tarts increase seven times importance on the first number we see. their normal sales rate ahead of a hurricane, When he asked students to compare the and that beer was the top-selling pre- prices of \$99.99 with \$150 and then hurricane item. compare \$100 with \$150, they rated the K Advertising: Becker and Murphy (1988) gap between \$99.99 and \$150 as being have argued that advertising works by significantly larger, even though there was raising marginal consumers’ willingness to only a penny’s difference. pay for a brand. Advertising actually raises Blattberg and Wisniewski (1989) showed each individual consumer’s willingness that when the price of margarine was to pay for a brand (Erdem et al, 2008), lowered from 89 to 71 cents, sales volume and shifts the whole distribution of increased 65 per cent, but when it was willingness to pay in the population (see lowered from 89 to 69 cents, sales volume Figure 1). 8 r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22
6. 6. Introduction to normalization of demand data Table 1: Theme park visitation statistics Attendance – Visitor traffic at a theme park Origin – Visitor’s permanent residence Group type – Composition of the group visiting (family versus non-family) Accommodations area – Where the visitor is staying overnight Ticket type – Type of theme park ticket a visitor is using Ethnicity – Ethnic origin of visitor Household income – Household income of visitor Last trip/repeat visitation behavior – Last time visitor was at theme park Household segment – Segment into which household of a visitor falls Table 2: Resort demographics Resort population – Number of guests staying at a resort Average length of stay by resort – Number of nights on average that a guest stays overnight Average room rate by resort – Rate that a guest pays for room on average per night Percent of children by resort – Based on the reported number of children staying at a resort Although any of the above-described factors We started out with a larger list of business could be examined to help isolate the effect of metrics, and narrowed down the lists tabulated price on demand, for this study, in a theme in Tables 1 and 2. The demand drivers were park and resort context, we focused on two identified through interviews with merchants as exogenous explanatory factors, visitation well as insights from financial analysts support- and demography. In our study, the normal- ing merchandise, and ultimately statistically ization process was successfully applied to validated through multivariate regression ana- the merchandise line of business, dramatically lysis. The demand drivers are often referred improving the fit of the model relating demand to as explanatory variables or covariates in the to price. The normalization process can be normalization. applied to other lines of business, such as We selected different demand drivers for restaurants or service industries, where demand sales of merchandise in the theme parks and is price-able. Though the demand drivers may resorts. We will discuss each separately to give change, the approach remains the same. the reader a background on these drivers. The reason behind the separation of demand drivers is that the theme park visitation statistics (see THE STUDY: IDENTIFYING Table 1) cannot be reasonably applied to the APPLICABLE BUSINESS sales of merchandise in resorts, because these METRICS FOR DEMAND statistics are collected through attendance-based DRIVERS theme park research surveys. We carry out The application of normalization to the sales of a different set of surveys on guests staying merchandise at theme parks began with at resorts, and they therefore have their own investigation of what business metrics were set of descriptive statistics. Because not all collected. Many of these business metrics were resort guests visit the theme parks, it is already accepted in terms of describing the inappropriate to infer that theme park visitation cycle and trends of the theme park and resort statistics affect sales of merchandise at resort businesses. locations. r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22 9
7. 7. Quillinan Visitation statistics are family and non-family. Family subgroups We intercepted guests visiting the theme parks, are based on the age of the oldest child. Non- and asked a series of questions. Attendance is family subgroups are based on the age of the the most important visitation metric. This is respondent. the total number of ‘unique’ daily entries into a park; it does not include re-entries, or cross- Accommodations area overs between parks. Because the other visita- The Accommodations Area is where the visitor tion statistics are reported at the individual park is staying overnight. Broadly, we classify visitors level, attendance is taken as the multiple-theme as staying either ‘On’ or ‘Off ’ of the theme park attendance. In this example, it is worth park-managed property/hotel. noting that attendance is truly exogenous – it is determined by factors unrelated to the prices Ticket types of merchandise and foods; traffic to the theme Ticket types are classified according to the parks as a whole is typically driven by academic number of days over which a ticket can be used. calendars (of school-age children, entrance ticket prices and theme park/resort promo- tions). As discussed earlier, this assumption may Ethnicity not be true for other retail businesses. Ethnic origin is classified into Caucasian, Other visitation statistics include origin, African-American, Hispanic and All Other; group type, accommodation area, ticket type, ethnic origin does not include international ethnicity, household income, repeat visitation tourists. behavior and household segment. Household income Origin Household income is based on the household Origin is the guest’s permanent residence, income reported. and is derived from the guest’s zip code. The highest-level classifications for origin are Last trip/repeat visitation behavior Domestic Tourists, International Tourists and Repeat visitation behavior is when the guest Local Residents. Domestic Tourists are from was on their last trip to the theme park; for any of the 49 United States (not local). instance, was the guest here less than a year ago, International Tourists live outside of the between 1 and 2 years ago, 2 and 3 years ago, 3 United States. Local Residents live locally. and 5 years ago, or more than 5 years ago. Last Origin data are used to classify data such trip excludes first-timers. as attendance. By being able to cut the data by origin or even finer, we can see patterns Household segment emerge. In the normalization process, we do Household segment is a classification of a not use all of the highest-level classifications, guest’s household based on life stage, and but rather employ the classification that is most visitation behavior. Similar to group type, life significant and has the highest influence on stage classification is based on presence of demand. These classifications are determined children in the household (family versus pre- through statistical selection methods, such as family and post-family) and ages of the children backwards-stepwise linear regression. or adults. There are six life stage segments: Young Family, Tween Family, Teen Family, Group type Pre-Family, Post-Family and Seniors. Group type represents the composition of The visitation statistics discussed thus far are the group visiting. The primary categories categories selected by the theme park’s research 10 r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22
8. 8. Introduction to normalization of demand data department to measure and understand a theme process, and, typically, each guest receives a park business. As a first pass, they are being room key with their name on it. leveraged to normalize merchandise demand. We did not create the categories and classifications Weather statistics for the normalization of merchandise demand. We introduced weather statistics, such as We did not use all classifications of the maximum temperature and total rainfall, which categories in the normalization process. We are self-explanatory explanatory variables. selected the following classifications of the categories because of their statistical METHODOLOGY: AGGREGATION significance: OF DEMAND DATA Normalization can occur on whatever level of K local residents; time that the demand data and drivers co-exist. K families with children 0–13; In the case of our study of merchandise K guests on 1-day park tickets; demand, normalization occurred on a weekly K caucasian; level. This is primarily because the theme park K household income > \$60 000; and demographics were deemed only significant at K guests whose last trip was less than 5 years ago. the weekly level. We aggregated all data to the weekly level, even though in some cases such as Resort demographics demand for merchandise products and park Resort demographics, listed in Table 2, were attendance, the data were available on a daily obtained from the resort occupancy statistics. basis. We selected weekly theme park demo- While surveys of resort guests are conducted, graphics. We produced weather variables, such these descriptive statistics were not employed in as the minimum, maximum or average, to the normalization owing to a more than 1- represent the entire week. month lag in receiving this information, and to Normalization occurred within a demand concerns that the statistics are not valid on a zone, or grouping of locations. The purpose weekly level. The resort occupancy statistics was to use only applicable explanatory vari- came directly from the hotel/resort operational ables. We used theme park visitation statistics to systems for checking guests in and out. normalize merchandise demand observed within the theme park. We used resort drivers Resort population to normalize merchandise demand observed at Resort population is the number of guests resorts locations. We later aggregated the results staying at a resort. from the demand zones to the price zone level for price differentiation. Average length of stay Stage-wise regression (Alley, 1987) is one of Average length of stay is the number of nights the statistical approaches that are available for on average that a guest stays overnight. use. Analysis of Covariance in conjunction with meta-analysis techniques (Thompson and Average room rate Sharp, 1999) is just one approach of the many Average room rate is the rate that a guest pays that are available. In the merchandise example, for a room on average per night. we implemented a two-stage linear regression with backward selection. The first-stage regres- sion normalized the demand using all available Percentage of children explanatory variables in the following form: Percentage of children is based on the reported number of children staying at a resort; this information is collected during the reservation ^ d ¼ a þ b1 x1 þ b2 x2 þ Á Á Á þ bn xn þ e r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22 11
9. 9. Quillinan ^ where d ¼ total demand owing to explanatory where Z ¼ profit function; P0 ¼ optimal price; variables, excluding price effect; a ¼ base C ¼ cost (landed cost or procurement cost); demand; bi ¼ rate at which demand changes ^ d0 ¼ normalized demand predicted with with explanatory variable i; xi ¼ explanatory respect to price effect; j ¼ secondary demand variables i; n ¼ number of explanatory variables intercept; and d ¼ rate at which demand i; and e ¼ error term. changes with respect to price. We then subtracted the fitted/predicted de- ^ mand calculated from the first step dt from actual NORMALIZATION USING ALL observed demand, and added this residual to the EXPLANATORY VARIABLES average demand over the life of the product. Normalization is a better alternative to how the Pn dt merchandise demand and price changes were 0 dt ¼ t¼i ^ ^ þ ðdt À dt Þ ¼ d þ ðdt À dt Þ measured in the past. Historically, merchants in n the theme park business measured their success where dt0 ¼ secondary stage demand at time t; based on per capita spending. Per capita is dt ¼ actual observed demand at time t; dt0 ¼ - ^ simply the demand divided by the theme park demand predicted by first-stage regression for attendance. ‘Per cap’ is the ‘average’ amount time t, which is estimated using a þ b1x1t þ demanded per guest per day. All guests count, ¯ b2x2t þ ? þ bnxnt; d ¼ average demand over even those who do not spend any money at all. life of the product; xjt ¼ explanatory variable j Per capita is analogous to normalization using at time t; i ¼ first time period; n ¼ number of attendance alone. historical weeks available; and t ¼ time period. d In the second-stage regression, the secondary Per cap ¼ A stage demand, which we refer to as the normalized demand, was regressed against price where d ¼ demand; and A ¼ attendance. to calculate the price coefficient, d. Attendance alone does not explain the variability in merchandise demand as accurately ^ d 0 ¼ j þ dP þ e as an estimate based on normalization. We find ^ that guests of different origins spend different where d 0 ¼ normalized demand predicted with amounts, and therefore per caps actually vary respect to price effect; j ¼ base demand; by origin. This is fairly intuitive if you think d ¼ rate at which demand changes with respect about it – let us use food and beverages as an to price; P ¼ price; and e ¼ error term. example. When you are a tourist, you are likely The price coefficient is that amount by to eat in the theme park, as you probably which demand changes with regard to price. It do not have anywhere else to go (unless you is not the price elasticity estimate of demand, have brought in food or are in a timeshare re, that is the rate by which the percentage of where you can cook). Conversely, when you demanded changes with respect to percentage are a local resident, you have the ability to eat of change in price. The above equation at home, and thus you might spend very little estimated from the second-stage regression, on food and beverages in the parks. which represents the price-demand function, To illustrate the need to normalize using more was then used to calculate the price elasticity of than attendance in the merchandise business, we demand. This is a form of function that is choose a commonly purchased product for ultimately passed to the price optimization obtaining character signatures: a vacation auto- system to find the optimal price. graph book. We compare (1) normalization using ^ attendance only (per cap); and (2) normalization Max Z ¼ ðP0 À CÞd 0 using all explanatory variables including price. ¼ ðP0 À CÞj þ dðP0 À CÞ2 The measure of fit is the adjusted R2. 12 r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22
10. 10. Introduction to normalization of demand data Figure 2: Normalization using Attendance Only. When we fit a statistical model of demand 0 and 13; Family 0–13 ¼ percentage visitors that using only attendance as the explanatory are families with the oldest child between ages variable to our example product, the adjusted 0 and 13; b5 ¼ rate at which demand changes R2 is 0.64. In short, attendance helps to explain with respect to location exposure; location ¼ approximately 64 per cent of the variation in percentage exposure that product is given demand (Figure 2). across locations; and e ¼ error term. When the demand was normalized using all ^ d ¼ a þ bA þ e of the significant explanatory variables includ- ^ ing price, five variables were significant: theme where d ¼ total demand predicted; a ¼ base park attendance, Caucasian, First Trip, Family demand; b ¼ rate at which demand changes 0–13 and Location. This approach resulted in with attendance; A ¼ attendance; and e ¼ error an adjusted R2 of 0.85; 85 per cent of the term. demand variation is accounted for by the ^ d ¼ a þ b1 A þ b2 Cauc þ b3 FirstTrip explanatory variables. Thus, the equation using þ b4 Family 0 13 þ b5 Location þ e additional variables improved the explanatory power of the model from 64 per cent to 85 ^ where d ¼ total demand predicted; a ¼ base per cent, a dramatic change (Figure 3). demand; b1 ¼ rate at which demand changes The 21 per cent improvement in goodness of with attendance; A ¼ attendance; b2 ¼ rate at fit for the autograph book is a non-refutable which demand changes with respect to per- reason for including all significant explanatory centage Caucasian visitors; Cauc ¼ percent variables versus attendance only. Caucasian visitors; b3 ¼ rate at which demand Another example of where the goodness changes with respect to percentage visitors on of fit measure improved by incorporating First Trip; First Trip ¼ percentage visitors on all significant explanatory variables was a First Trip; b4 ¼ rate at which demand changes nighttime entertainment or ‘glow’ product. with respect to percentage visitors that are Considering attendance only to explain the families with the oldest child between ages variability in the demand, we end up with the r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22 13
11. 11. Quillinan Figure 3: Normalization using all significant explanatory variables including price. following model: Location ¼ percentage exposure that product is given across locations. ^ d ¼ 133:7688 þ 0:00008518 A þ e The first-stage-regression adjusted R2 for this product went from 0.9 per cent for ^ where d ¼ total demand predicted; A ¼ attendance only to 54.7 per cent for a full attendance level; and e ¼ error term. normalization model using all significant ex- When we added the significant explanatory planatory variables. variables to the model, we ended up with the In the second-stage regression for the sample following ‘full’ model: product in Figure 4, the normalized demand is computed from the first-stage regression ^ d ¼ À88:317348 þ 0:000102ÂA residuals and the means of the series. Figure 5 illustrates how the normalized demand for the þ 3:646500838ÂCauc superior model (that is, ‘full’ model) is then þ 5:715628ÂTourist Ticket regressed against the price to arrive at the þ 4:696201ÂLocal Resident predicted normalized demand with respect to price. À 6:176941ÂMax Temp þ 5:757854ÂLocation ^ d0 ¼ 372:0399 À 12:6762ÂP þ e ^ where d 0 ¼ normalized demand predicted with ^ where d ¼ total demand predicted; A ¼ respect to price effect; and P ¼ price. attendance; Cauc ¼ percentage Caucasian visi- Overall, there is a remarkable improvement tors; Tourist_Ticket ¼ percentage of visitors in model fit across all items available for on Tourist ticket; Local_Resident ¼ percen- normalization. The mean adjusted R2 goes tage of visitors that are local residents; from 6 per cent to approximately 50 per cent Max_Temp ¼ maximum temperature; and across the proportion of the products that are 14 r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22
12. 12. Introduction to normalization of demand data Figure 4: Normalization of Glow Product using Attendance Only and Full Model. Figure 5: Second-stage regression results using Full Model. available for normalization. We applied nor- improvement in adjusted R2 for a sample malization to analyze every item that had at of the products impacted. Normalized least 52 weeks of demand history and at least demand was calculated for the demand zone one price change. Figure 6 illustrates the exhibiting the most sales per item; alternatively, r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22 15
13. 13. Quillinan Figure 6: Distribution of adjusted R2 from Attendance Only to Full Model. normalized demand can be weighted by the multiplied by the pre-price-change normalized proportion of demand in a demand zone and demand, then the price change is concluded to summed up across all groupings of locations to be a success. The caveat to this test is that produce an estimate of normalized demand at product relationships should be taken into the price zone level, which represents the consideration when evaluating a price change. higher level of grouping of locations (above demand zone) where price differentiation occurs. NORMALIZATION REQUIRES Normalization is the first step in isolating the CONTINUAL PROCESS effects of price on demand. After normalized IMPROVEMENT demand, we can now go back and evaluate Normalization models must be updated reg- whether or not a price change was successful. ularly. This requires a Continual Process In Figures 2 and 3, the reader can see that Improvement. An organization that identifies a price change occurred at about week 71. explanatory variables upon implementation and A standard t-test was conducted on the means never goes back to update their models could of the fitted (‘normalized’) demand before and be facing a disaster. In our example, annual after the price change. If the means were audits to refresh models should be planned. statistically different, then a simple comparison In addition to annual audits, there should be of the pre- and post-price change normalized ongoing efforts to identify other explanatory profit was carried out. If the normalized variables. profit after the price change (that is, the new price less cost of goods sold multiplied by the K In the case of the glow product, park post-price change normalized demand) was operating hours and total hours of darkness greater than the old price less cost of goods sold during park hours were not available 16 r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22
14. 14. Introduction to normalization of demand data initially. However, later on, we evaluated location variable in the normalization mod- these data and found them to have merit in els, the average adjusted R2 was 0.35. Only the normalization process. approximately 25 per cent of the models had K The number and type of locations at which a R2 higher than 0.5. After we added the product is available change often, and there- location variable, the model performance fore are likely to influence the demand for improved significantly (see Figure 7). The the product. We introduced an additional average adjusted R2 increased to 0.52. More explanatory variable, which represents the than 50 per cent of the models had adjusted availability of a product at different locations, R2 that were higher than 0.5. to account for changes in product demand K Big-box locations utilize ShopperTrak hard- owing to changes in a product’s availability ware, which effectively counts the number at different locations. The location variable is of guests entering and exiting the location. the weighted number of locations at which a We leveraged the ShopperTrak guest counts product is available each week. We calculate collected on the hour to allocate labor the location variable for each item in each during heavy traffic periods. These guest demand zone. The weights for each location counts could be used in lieu of park atten- are the location’s percentage of contribution dance counts for demand at the big-box to total sales during the previous year. The store locations. ShopperTrak is common- weights are calculated at the sub-class level place at retail locations such as nationwide and applied to all items in the sub-class. We chains at indoor-shopping malls, and would update the weights every few months, to most likely be an ideal explanatory variable adjust for any location changes. Without the for a retailer to use in normalizing its Figure 7: Distribution of adjusted R2- for Without and With Location Variable. r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22 17
15. 15. Quillinan demand data. Improving upon the estimate K Grad Night of consumer traffic should have value for any K Father’s Day retailer. K Sci-Fi Weekend K Summer Vacation K Independence Day NEXT STEPS K Labor Day K Food and Wine Related products K October Fest The models presented in this article are K Fright Fest simplistic. Models that are more complex could K Halloween incorporate the prices of related goods, both K Thanksgiving complements and substitutes, and the number K Holiday Season of available substitutes. Market basket analysis is K Christmas one technique that can help understand demand dynamics. An example of the price of related products Diagnostic tests is how the price of the complement of a Finally, we have spent a lot of time explaining princess costume, the tiara, wand and novelty how adding all of the significant explanatory shoes impacts the demand of the princess cos- variables will result in better model fits. We do tume. The prices of other characters’ costumes not want to lose sight of the importance of may also influence the demand of other running diagnostics on our models. Therefore, costumes. Costume ensembles may cannibalize our last next steps are to incorporate diagnostics each other. in the regression processes. Some recom- mended diagnostics are: Special event indicators K Significance of explanatory variables: Are all of In spite of our best efforts to identify operating the explanatory variables significant? business metrics that explain merchandise K Collinearity: Predictors that are highly colli- demand, and incorporate product relationships, near, that is, linearly related, can cause we will always fail at coming up with models problems in estimating the regression coeffi- that result in high-adjusted R2. In some of cients. When more than two variables these cases, further work with indicator vari- are involved, this is often called multi- ables may be of some promise. Some products collinearity. The Variance Inflation Factor are seasonal or driven specifically by recurring (VIF) is a good metric to use to evaluate events. Some events that were identified in multi-collinearity. As a rule of thumb, a theme park example are: variable whose VIF values are greater than 10 may merit further investigation. K New Years Eves; K Normality: The errors should be normally K Presidents Day distributed – technically normality is neces- K Valentine’s Day sary only for the t-tests to be valid; esti- K Sports Weekend mation of the coefficients only requires that K Spring Break the errors be identically and independently K Easter distributed. The Kolmogorov-Smirnov test K Home and garden show compares the cumulative distribution of the K Earth Day data with the expected cumulative Gaussian K Mother’s Day distribution, and bases its P-value on the K Memorial Day largest discrepancy. 18 r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22
16. 16. Introduction to normalization of demand data K Homogeneity of variance (homoscedasticity): One CONCLUSION of the main assumptions for the ordinary least squares regression is the homogeneity Greater confidence in price of variance of the residuals. If the model optimization is well fitted, there should be no pattern to The two-stage regression methodology results the residuals plotted against the fitted values. in a substantially improved model fit and thus If the variance of the residuals is non- in much stronger explanatory power. With this constant, then the residual variance is said greater explanatory power, pricing analysts to be ‘heteroscedastic.’ There are graphical have greater confidence in taking price recom- and non-graphical methods for detecting mendations from the price optimization. With- heteroscedasticity. The White Test (White, out this confidence, the pricing analyst could 1980) tests the null hypothesis that the take the price in the wrong direction or perhaps variance of the residuals is homogenous. in the right direction but could conclude that Therefore, if the P-value is very small, we the price change had a negative effect. would have to reject the hypothesis and accept the alternative hypothesis that the variance is not homogenous. Extensibility of normalization The concept of normalization can be applied to any line of business, where the demand is Don’t lose sight of the big picture price-able. Though the demand drivers may The pricing analyst should also incorporate change, the approach remains the same. impacts on the category when evaluating the The end-user needs only to identify and impact of price changes on individual products. apply those explanatory variables that are The objective is to improve overall economics, unique to their business: the general demand not the profitability of individual product lines. drivers that might influence demand, particu- An example: When a retailer increased the larly retail demand. In Table 3, I have attempted price on a leading brand of detergent, he saw to enumerate and classify possible explanatory a drop in the total gross margin; normally, variables, and identify which industries might the pricing analyst would have concluded that benefit from them. the price increase was a negative price test and that the company should take price in a different direction. However, when the Final diagnostic analyst looked at the category sales, he noticed While much of the process, for example, the that another detergent whose price remained selection of explanatory variables and diagnos- the same was gaining in higher gross margin tic tests, can be automated, this does not relax owing to increased sales. He concluded that the need for a pricing analyst to ensure that the the sales from the leading detergent had diver- inputs, that is, the explanatory variables, and ted to the lower-quality detergent, on which the price optimization results, make sense. the retailer happened to have a higher profit A pricing analyst provided three examples in margin. At one point, the retailer was con- which price elasticities were out of kilter, and sidering dropping the leading brand detergent, knowledge of consumer behavior or the but the pro forma became more complicated. assortment provided additional insights for The manufacturer of the leading brand deter- pricing decisions. gent gave the retailer off-invoice promotions One example was a price recommendation to keep their business; consequently, this allo- for a princess lightchaser (a glow product). The wed the retailer some options with product lightchaser was originally priced at \$14, pricing. changed to \$15, later to \$10, and then raised r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22 19
17. 17. Quillinan Table 3: Covariates across industries Seasonality covariates (most/all industries) K Fourier Filter-based Covariates (multiple yearly cycles) K Other Data-derived Covariates (such as monthly contribution ratios) K Day-of-Week Covariates K Holiday/Special Event 0/1 Indicator Covariates K Other User-defined Covariates Customer-based covariates (Retail, hotel/cruise, distribution, services, casino, theme park, manufacturing) K Customer Demographics (total number of customers, Age/Financial Distribution, etc) K Customer Survey Information K Information on Prior Customer Relationships Competition based covariates (Airline, petroleum, financial services, apartment leasing, distribution, any industry with access to competitive data) K Market Strength Indices K Price or Volume of a Competitor’s key products K Your company’s Price Rank among competitors Financial covariates (primarily financial services, petroleum, manufacturing, transportation, communications, others where appropriate). K Gross Domestic Product (GDP) K Index of Leading Indicators K Gross National Happiness , a new concept relating happiness to economic growth K Population K Labor Force: Employment, Unemployment rate, Average Weekly earnings, Job security K Public Expenditure, Revenues, Budget Surplus and Deficit, National Debt K Personal Income, Expenditure, Savings K Broadband Internet Penetration K International: Balance of Payments (Current Account Balance of Trade) K Productivity Survey K Manufacturing output, Capacity Utilization, Inventories K Money supply, Interest Rates (Fed Funds, Prime, Major Competitors), Yield on various financial Instruments and Yield Curves. K Stock Market Indices (Dow-Jones Industrial Average, SP 500, etc) K Inflation, Consumer Price Index, Producer Price Index K New Home Sales K Retail Sales, Auto Sales K Lagging indicator, a historical indicator following an event that reacts slowly to economic changes K Genuine Progress Indicator, a concept in ecological economics and welfare economics that has been suggested as a replacement metric for GDP K Spot market prices K Energy prices, supply and consumption (Source: US Department of Energy, Energy Information Administration, http://eia.doe.gov) Climate covariates (retail, healthcare, pipeline, any industry where relevant) K Daily Temperature (Low, High, Average, #consecutive cooling/heating days) K Rainfall 20 r 2010 Macmillan Publishers Ltd. 1476-6930 Journal of Revenue and Pricing Management Vol. 9, 1/2, 4–22