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1 Introduction

“Verhouten, a family company founded in 1899 by Cornelis Verhouten in Haarlem, is a chocolate factory which has grown continuously. In 1899 the company only consisted of two employees, where at this moment this is 125. In the beginning, Verhouten only sold chocolate bars of 75 grams. Currently, the assortment consists of four product classes: chocolate bars, candy bars, specialties and seasonal products. The chocolate bars carry the brand name Verhouten and they are available in three weight classes (100, 200, and 400 grams), and four flavours: mil, pure, almond-milk, and white. Seasonal products are sold in December (chocolate letters, and Christmas chocolates), and around Easter (chocolate Easter eggs and Chocolate Easter bunnies). In this case, we focus on the most important category for Verhouten: chocolate bars” .

“There exist several usage motives for chocolate bars: (1) the functional motive (i.e. to satisfy appetite), (2) the threat-oneself motive, (3) the sharing-motive, and (4) the give-away motive. With exception for the last one, chocolate bars are often purchased by impulse. Not surprisingly, this purchase behaviour can be influenced by sales promotions. To anticipate the expected effects of sales promotions, good sales predictions are needed. For that reason, we develop a model, based on ‘chain-level scanner data', describing the influences on sales for chocolate bars. It should be mentioned that the model is a test case for Verhouten, and therefore only the 100 grams milk chocolate, sold at Albert Heijn, is taken into consideration. This due to the fact it has the largest turnover of all products in all channels. This test case, if successful, is to be extended to all products in all chains” .

The remainder of this paper is divided into seven chapters. First, the data is examined by exploratory data analysis. Second, the price-elasticity for Verhouten is estimated and interpreted in a simple linear regression model. In the following three chapters, control variables, competition variables and dynamics, respectively, are added to the model. In chapter 7, the predictive validity is assessed.  Finally, the conclusion summarizes the main findings of the paper and a critical reflection is provided.

2 Exploratory Data Analysis

There exist different types of data, and two key characteristics here is the observation level and the time dimension of the data. The data we have observed is collected at the aggregation level, also known as the market level. Additionally, observations of weekly prices and sales of Verhouten are obtained through repeated measures over time. The availability of the collection of these data items makes the data a time series. The data is collected weekly over a timespan of 68 weeks, starting from 1 December 1997 until 21 March 1999.

During the screening and cleaning process of our data analysis, the frequencies statistics table showed 68 valid values and 28 missing values. The missing values existed due to a mistake in the data set which consisted of 28 empty rows and were evidently deleted, without impairing the time series collected.  Table 1, descriptive statistics, shows under Valid N listwise that we have 68 observations, which indicates that the dataset is complete without any more missing values.The descriptives table furthermore reveals the minimum, maximum, mean, and standard deviation values. In the specific period of time, the minimum amount of sales was 60.36 in hundreds of kilos for Verhouten, with a maximum of 530.87; on average, Verhouten sold 127.4497 in hundreds of kilos per week. The standard deviation of Sales confirms that the data points are spread out over a wider range of values. Next, for Verhouten the minimum price was 1.02 in guilders per unit and the maximum 1.55, with a mean of 1.4692. The low standard deviation indicates that the data points tend to be close to the mean. The dataset indicates two extreme low prices (1.02 and 1.03) which could possibly be seen as outliers. However, the sales value of those specific price units is extremely high, which makes sense. It could be the case that these values indicate two extreme price drops in terms of promotions. Besides, due to the fact the data set is a time-series, those possibly outliers should not be left out.

From the competitors, Baronie has the widest range in terms of price, with a minimum of 0.81, a maximum of 1.75 and a mean of 1.65. A rationale behind these values is that Baronie is possibly one of the more luxious brands, but tends to compete due to extreme price promotions. Furthermore, the variables for feature, display and feature and display show the weighted distribution figure means with the store-level dummy variables  weighed with the turnover of the Albert Heijn stores. No data is collected for feature and display for Droste.

The temperature in degrees Celsius was on average 9.74, with a minimum of minus 2 and a maximum 25 degrees Celsius. No other particularities could be detected in the data.

TABLE 1

DESCRIPTIVE STATISTICS

N Minimum Maximum Mean Standard Deviation

Sales 68 60.36 530.87 127.4497 100.53926

Price Verhouten 68 1.02 1.55 1.4692 0.14134

Price Droste 68 1.26 1.67 1.5612 0.07982

Price Baronie 68 0.81 1.75 1.6487 0.14055

Price Delicata 68 1.19 2.12 1.8544 0.24734

Feature Verhouten 68 0.00 0.74 0.1300 0.19664

Feature2 Droste 68 0.00 0.35 0.0257 0.06523

Feature Baronie 68 0.00 0.88 0.1751 0.22253

Feature Delicata 68 0.00 0.79 0.1532 0.19621

Display Verhouten 68 0.00 0.87 0.0271 0.13768

Display Droste 68 0.00 0.62 0.0176 0.09815

Display Baronie 68 0.00 0.85 0.0469 0.17612

Display Delicata 68 0.00 0.52 0.0179 0.07920

Fand* Verhouten 68 0.00 0.53 0.0135 0.07654

Fand Baronie 68 0.00 0.86 0.0326 0.13493

Fand Delicata 68 0.00 0.91 0.0343 0.16430

Temperature C 68 -2 25 9.74 7.243

Week 68 1 52 24.38 16.689

Valid N listwise 68

* Fand stands for the combination of Feature and Display promotions

When looking to the scatterplot, see appendix fig. 1, a linear relationship (R2 = .884) between the variables price and volume sold can be indicated. There seems to be a high negative correlation between the two variables; a price increase of the chocolate will be followed by a sales decrease.

3 Price Elasticities

Elasticities express by what constant percentage the dependent variable changes in response to a one-percent change in the marketing instrument. In other words, price elasticities are unit free and can be easily compared throughout different context. Besides, they can be used to express the effectiveness of marketing instruments. In this case we want to estimate the relevant price elasticity for Verhouten. Therefore, our output measure will be the log of sales of Verhouten in hundreds of kilos, whereas our input measure will be the log of price of Verhouten in guilders per unit. The model (1) is as follows:

Log 〖Sales〗_t= β_0+ β_1 Log〖Price〗_t+ε_t

with 0 indicating the constant, t indicating the weeks and  indicating the error term, which accounts for the possibility that the model does not fully represent the actual relationship between price and sales of Verhouten.

Before running the simple linear regression model, particular regression assumptions were tested: (1) all independent and dependent variables are metric; at least intervally scaled, (2) the values should be normally distributed, (3) independent random sample (4) homogeneity of variance, (5) no multicollinearity, (6) the model is correctly specified. All assumptions turned out to be met. For normality, the histogram is being observed, which turns out to be normally distributed with a little skewness to the left. For the homogeneity of variance, the scatterplot is observed.

Table 2 demonstrates the outcome of the simple linear regression, model 1. The fit of the model is explained by R2, which describes the amount of variance in the dependent variable sales that can be explained by the independent variable price. We can assume a good fit of the model with an R2 of 0.835.  In other words, the model explains 83.5% of sales through the independent variable price. This result is rather high. Overall the model is significant with an F value of 334. 337 and a p-value of <0.001.  The individual regression coefficient, which explains the relationship between sales and price is also significant, with a t-value of -18.285 and a p-value of <0.001.  A log-log model was used in order to estimate the price elasticity directly. The log indicates that we have a curvilinear relationship, additionally it indicates that the same input change constantly leads to the same output change.  In this model, we can observe a price elasticity of -3.938. In other words, an increase in price by 1 is going to lead to a 3.938 decrease in sales.

TABLE 2

REGRESSION MODEL PRICE ON SALES

Model Unstandardized B Significance

11 (Constant) 6.185** .000

Log Price -3.938* .000

1 R2 .835, p<0.001

* two-sided p-value  .05

** two-sided p-value . 001

In conclusion, it can be that there is an elastic demand, since a percentage decrease in price leads to a percentage increase in sales. Our analysis finds an elasticity of -3.938, which is substantially larger than the average price elasticity found of -2.62 by Bijmolt et al. (2005).

… how can this difference be explained…?

4 Adding Control Variables

Additional to price, there are several other aspects that could influence the sales of Verhouten. Especially when working with time series data, few issues could be encountered. One of these is seasonality, which is a characteristic of a time series in which specific events reoccur every year. Any pattern or change in a time series that repeats or reoccurs every year, can be said to be seasonal. By adding seasonality, the model will be improved and the estimated elasticities will be enhanced. Naturally, each year knows four seasons and the certain possibility exists that temperature has an influence on the number of sales for the 100-gram milk chocolate bar of Verhouten. For that reason, we included the log of temperature as a control variable in our model. Due to the fact that the data contains some negative values in terms of degrees Celsius, the data needed to be transformed before taking the log of temperature. The technique used to handle these negative values was the transformation of degrees Celsius to Kelvin . A value of 273.15 was added to all values of temperature before taking the logarithm.

Besides temperature, other events could possibly have an effect of the sales of Verhouten. As this study assesses the influence on sales for chocolate bars, which could be considered as a gift-giving good, we take both Christmas and Easter into consideration for the model. To account for these events in our model, dummy variables are created for both the Christmas and Easter period. In this case, a dummy variable is 1 when an event occurs, and 0 otherwise. By deciding which weeks to include as a dummy for both Christmas and Easter, we plotted sales and weeks for Verhouten. Remarkably, the scatterplot, see Appendix fig. 2, shows no extreme peaks in the expected weeks of Christmas and Easter, nonetheless several random peaks can be detected. For Christmas, a dummy variable of 1 is assigned to the weeks 49 up to and including 52, which is considered as the typical Christmas-shopping period. It has to be stated, that the Dutch event of Saint Nicholas takes place in rarely the same period, namely on the fifth of December. Knowing this, sales could also be influenced by this event.  For Easter, which in 1998 was on the 12th of April, a dummy variable of 1 is assigned to the weeks 13 up to and including 15. By including these weeks, the week of the event itself, and the previous two weeks are taken into consideration.

Not surprisingly, own marketing activities could affect the output measure of sales. Possible promotions are feature-only, display-only and feature and display advertisements. A ‘feature-only' means special outside-store attention for Verhouten, either in the store flier or in an ad in a newspaper or a magazine.  A ‘display-only' means special inside-store attention for Verhouten: a temporary shelf in the one of aisles, or a change in the brand's regular shelf. Obviously, feature and display advertisement is a combination of the two mentioned above.

After including all the control variables, the model (2) is:

〖LogSales〗_t= β_0+ β_1 〖LogPrice〗_t+β_2 〖Logtemperature〗_t+β_3 〖Christmas〗_t+β_4 〖Easter〗_t+β_5 〖Feature〗_t+β_6 〖Display〗_t+β_7 〖FandD〗_t+ε_t

For this model (p < 0.001), the adjusted R2 is .882, which is higher than the first model with an R2 of .83. This means that the overall fit of the model improved, and the model accounts for 82,2% of the variance. In table 2, the results of the linear regression analysis for the second model are presented. Surprisingly and contradicting our expectations, the inclusion of own marketing activities – feature, display, and feature and display – has no significant effect on the sales of Verhouten. Even more surprisingly is the fact that by the inclusion of either feature or display, sales go down by .038 and .153 respectively. However, as stated before, this effect is not significant. In terms of face validity, these coefficients do not make sense, as one would expect that promotions would increase sales. A possible reason behind this could be competitors promoting at the same time. Another rationale could be that due to frequent promotions, consumers have adapted their purchase behaviour, and do not react heavily to future promotions anymore.

Besides, the results show that an increase in temperature by 1 is going to lead to a 1.971 decrease in sales, with a significance of .045. Remarkably, sales decline during the Easter and Christmas period with -.202 and -.192 respectively, which both are significant. At first sight, it would be expected that sales would increase during these specific periods, as the usage of chocolate bars also serves the give-away motive (as a present). However, the data only takes the sales of 100-gram milk chocolate, sold at Albert Heijn, into consideration. As mentioned before, Verhouten also sells specialities and seasonal products. A logic rationale behind this would be that during both the Christmas and Easter period, Verhouten offers special seasonal products, which then serve as a substitute for the regular 100-gram milk chocolate bar. In terms of face validity, these coefficients do make sense, as the sales for the seasonal products would probably increase, which explains the decrease in sales for the regular products.

In the second model, the log of price coefficient decreases a little, but still is highly significant (p<0.001). In other words, after adding control variables to the model, an increase of 1 in price will lead to 3.902 in sales. This shows that price is still the most important variable, but other variables increase the power of price slightly.

TABLE 3

INCLUDING CONTROL VARIABLES

Model Unstandardized B Significance

11 (Constant) 6.185** .000

Log Price -3.938* .000

22 (Constant) 17.320** .001

Log Price -3.902** .000

Feature Verhouten -.038 .816

Display Verhouten -.153 .700

Feature and display Verhouten 1.388 .059

Temperature in Kelvin -1.971* .045

Easter -.202* .010

Christmas -.192* .036

1 R2 = .835, p<0.001

2 adjusted R2 = .882, p<0.001

* two-sided p-value  .05

** two-sided p-value . 001

5 Adding Competition

The prior models were purely focused on the own-marketing efforts of Verhouten. Naturally, Verhouten is not the only manufacturer of chocolate bars in the market. In the time series of 68 weeks, the data of three competitors – Droste, Bronie, and Delicata – is captured and available for interpretation. The model is extended by adding the price variables and all feature and display variables for these competitors. For every competitor, the log prices are calculated in order to make them comparable to the price elasticities of Verhouten.  All price,

feature, feature, and feature and display variable for each competitor are added separately to the model  (3):

〖LogSales〗_t= β_0+ β_1 〖LogPrice〗_t+β_2 〖logtemperature〗_t+β_3 〖Christmas〗_t+β_4 〖Easter〗_t+β_5 〖Feature〗_t+β_6 〖Display〗_t+β_7 〖FandD〗_t+β_8 LogPrice〖Competition〗_t+β_9 Feature〖Competition〗_t++β_10 Display〖Competition〗_t++β_11 FandD〖Competition〗_t+ε_t

where, for example, β_9 Feature〖Competition〗_t includes all variables for each competitor separately. For this model (p < 0.001), the adjusted R2 is .894, which is again higher than the second model with an R2 of .882. Yet again the overall fit of the model improved, and the model accounts for 89,4% of the variance. In table 3, the results of the linear regression analysis for the third model are presented.

Model 3 decreases the price elasticity down to -.383, which means that an increase in price of 1 will lead to 3.683 decrease in sales. As could be seen in table three, the price elasticity is less strong than the price elasticity of model 2 and model 1. This means that by adding more variables to the model, price becomes less important. However, it should be stated that price overall is still the biggest influence on sales of chocolate, with a significance of p<0.001. When adding competition variables to the model, we see that Easter and Christmas become insignificant. In the previous chapter, we already explained why Christmas and Easter did not have the expected effect on sales. More interesting is that solely the price of Droste has a significant effect on the sales of Verhouten. In other words, with an increase of 1 in price of Droste, the sales of Verhouten decline with 1.252. It could be assumed that Droste is the biggest competitor of Verhouten. Equally to the non-significant effects of feature and display for Verhouten, the feature and display promotions of competitors do not have a significant effect on the sales of Verhouten. Again, it could be concluded that price is the most important aspect regarding to the sales of the 100-gram chocolate bar

TABLE 4

MODEL 3, INCLUDING COMPETITION

Model Unstandardized B Significance

1 (Constant) 6.185** .000

Log Price -3.938* .000

2 (Constant) 17.320** .001

Log Price -3.902** .000

Feature Verhouten -.038 .816

Display Verhouten -.153 .700

Feature and display Verhouten 1.388 .059

Temperature in Kelvin -1.971* .045

Easter -.202* .010

Christmas -.192* .036

3 (Constant) 20.866** .004

Log Price -3.683** .000

Feature Verhouten .054 .763

Display Verhouten .128 .758

Feature and display Verhouten .868 .259

Temperature in Kelvin -2.581* .041

Easter -.199 .152

Christmas -.133 .054

Feature Droste .067 .847

Feature Baronie .179 .118

Feature Delicata .059 .771

Display Droste -.260 .283

Display Baronie -.208 .619

Display Delicata .588 .237

Feature and display Baronie .357 .500

Feature and display Delicata -.039 .867

Log Price Droste -1.252* .020

Log Price Baronie .404 .072

Log Price Delicata .067 .495

1 R2 = .835, p<0.001

2 adjusted R2 = .882, p<0.001

3 adjusted R2 = .894, p<0.001

* two-sided p-value  .05

** two-sided p-value . 001

6 Adding Dynamics

The time series models allow for the inclusion of dynamics in order to account for the effect of events that happened in the past or that will happen in the future. Two possible ways to add dynamics are to add lead and/or lags to a model, or to use the stock variable approach. Both methods have their advantages and disadvantages and a careful analysis should be done in order to choose the most appropriate way. The addition of lead and/or lags to the model defines a certain distribution of the effects over time. In this case, we would see how much the sales of Chocolates Verhouten would be influenced not only by the current price, but also by the past price and/or the future price of the chocolates. β_1 Log〖Price〗_t represents the contemporaneous effect while the β_2 Log〖Price〗_(t-1) and β_2 Log〖Price〗_(t+1) are the lagged and leading effect respectively. However there is a loss of observations when including multiple leads and lags, this is a very flexible way of accounting for dynamics since it allows for the combination of leads and lags in one model. Therefore, it is possible to account for past events and future events.

Lead (3):

Log 〖Sales〗_t= β_0+ β_1 Log〖Price〗_t+ β_2 Log〖Price〗_(t+1)  +ε_t

Lag (4):

Log 〖Sales〗_t= β_0+ β_1 Log〖Price〗_t+ β_2 Log〖Price〗_(t-1)  +ε_t

Another way to account for dynamics is by adding a stock variable. This method is built under the assumption that knowledge is accumulated over time and measures the influence of events from the past in our output variable. The effect of input depends on the level of input in the same period and on the stock of previous periods. In this case the value of sales of chocolate Verhouten would be influenced by the price at time t, but also by the price of past periods.

In the particular case of the Chocolates Verhouten, we have decided to use the first approach, since we consider that future price values can also influence the current value of sales. Therefore, in order to account for past and future values of price, we opted for adding leads and lags to our model. However, when we added the lag price variable of t-1 to our model we obtained a non-significant value, β=0.134 (p=0.540). The same happened when we added the lead price of t+1, obtaining a β=0.044 (p=0.840). Therefore, we did not add leads and lags from other periods, since these first values were not significant. The results obtained mean that we cannot state that the past and future values of Chocolate Verhouten price influence the current value of the sales. Our final model will thus be model 3, as the model fits the data the best.

7 Assessing Predictive Validity

In order to assess the predictive validity of our model we used our final model (3), as this is the one with the highest adjusted R square (R2=0.894). The R square shows how close the data is to the fitted regression line. Therefore, in general the higher R square, the better the model fits the data.

We started by using the 60 observations of the model, in order to estimate the model for the training sample and use it to generate predicted scores. The obtained 8 last values can be compared to the real data values to check the predictability of the model.  We obtained also predicted values for new observations that were not used for model estimation (holdout sample). By having a first look at the obtained values we can conclude that in general they do not differ significantly from the real values.

The next step was to compute some statistics to help judge the predictive fit. Hence, the MAE and the MAPE were calculated. The former shows the average of the absolute value of the differences between the observed and predicted values, while the latter is defined similarly but that difference is also divided by the observed value and multiplied by 100% to get a percentage error.

Mean absolute error (MAE): Mean absolute percentage error (MAPE)

MAE =   MAPE =   x 100%

We obtained a MAE value of 0.09 for the training sample and a MAE value of 0.25 for the holdout sample. Similarly, we obtained a MAE value of 2.12% for the training sample and a MAPE value of 5.63% for the holdout sample. As we expected, the values of the holdout sample are slightly larger than the ones of the training sample, since we also used the last 8 observations to estimate the model. However, in general, the differences observed between these measures values of both samples are small, which let us conclude that the model presents a good internal validity. Moreover, since the percentage errors are also small, the model has a good external validity. This allows to conclude that our model is suitable to forecast sales and delivers good predictive performance.

8 Critical Reflection and Conclusion

Throughout this assignment we added some factors that could affect the output measure, such as seasonal, marketing and competition effects. The goal was to improve the model and to enhance the estimated elasticities. However, the added variables were not always significant, which can mean that the factors do not influence the sales of the Chocolates Verhouten or it can be explained by other factors, such as the number of observations studied or the period used in the analysis. Overall, we think that the modelling steps performed were of relative importance, since theoretically they have an influence on sales. The non-significance of some of the results obtained, such as the factor of competition, can be explained by some further details that we do not have access to, such as the level of brand equity of the different brands.

After the estimation of the different models, we can conclude that in this case, price is the factor that influences sales of the chocolates the most. Therefore, Verhouten should plan to do promotions of his Chocolate and to use feature and display advertising to promote its reduction of price, as we saw that it has an effect on sales.

We suggest that more factors should be taken into account to build a more complete response model, such as the level of brand equity of the different brands. We also think it would be relevant to analyse the other product classes of the brand, like specialities and seasonal products, since we expect that Christmas and Easter significantly influence the value of sales of these products. Moreover, other distribution channels should also be studied, like the gasoline stations and the tobacco stores. We think that advertisement would have a higher impact in these stores, due to their considerably lower number of marketing campaigns, which can result in customers that are more perceptive to marketing elements.

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