Exploring price promotions in Dutch deodorant industry with the use of a Dynamic Hierarchical Factorial Model

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Exploring price promotions in Dutch deodorant industry

with the use of a Dynamic Hierarchical Factorial Model

Master thesis, MSc Marketing, specialisation Marketing Intelligence

University of Groningen, Faculty of Economics and Business

-June, 2017-

Author: Supervisor/University

DANA CRISTINA ILIE Dr. Keyvan Dehmamy Student number: 3217256 University of Groningen e-mail: d.c.ilie@student.rug.nl

Second supervisor Dr. Felix Eggers

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1. Introduction & Previous research

In this century, personal image and branding has become more and more important. Consequently, consumers pay more attention to their personal care since they consider personal presentation important. The deodorant market is currently estimated at $252.9 million in The Netherlands. Due to population and income expansion, this market is foreseen to grow in the following years. The market is almost fully penetrated, about 90 %, which makes it difficult for manufacturers to innovate in order to boost sales. For this reason, in this industry, advertisement and promotions are very important drivers (“Deodorants in The Netherlands”, May 2017) Promotions are a very important part of the marketing mix. Their main role is to drag customers’ attention and motivate them into buying the product. In order to plan a successful and effective promotion, research and strategic planning are required. Being able to anticipate competitors’ actions and reactions is the key to a successful business.

Blattberg, et al. (1995) define price promotions as “temporary price discounts offered to a customer”. They are seen as a very important part of the marketing-mix giving the fact that price promotions raise the price sensitivity in general. The main finding of the paper written by Hanssens, et al. (1998) is that price promotions have a positive short-term effect, which does not last in the long run. This is why it would be useful to forecast promotions and act accordingly. The study of Kuntner and Teichert (2016) was meant to analyse the current literature regarding price promotions. They applied quantitative biometric analysis and text-mining techniques in order to extract the most important findings about price promotion. However, in the concluding remarks the following is stated: “The findings suggest that price promotion is an important, well-established, and differentiated scientific field that still has substantial research potential. In particular, applying behavioural economic theory and accounting for dynamics of promotional effects when answering existing and new research questions would offer promising opportunities.” This motivated me to investigate more about this field, looking at it from a different perspective as well.

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3 awareness and price sensitivity increase. Sotgiu, et al. (2015) found that price promotions reduce the perceived gains of sustained price reductions and the perceived losses of regular price increases. As expected, price promotions mitigate the negative effects of price increases in the aftermath of the price war. However, it would be more interesting to look at how different retailers are about to apply price promotion in case of such a shock. Having these insights about competitors, supermarket managers could foresee their competitors’ moves and use this for their gains.

In the current study, the following research questions will be investigated and answered:

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2. Data

2.1 Data exploration

The data set consists of weekly observations between the following periods: week 46, 2003 until week 12, 2006. There are five chains: Albert Heijn, Edah, Super de Boer, Jumbo and C1000, and for each of them, price information for eight brands: Dove, Fa, NIVEA, REXONA, VOGUE, Sanex, 8X4 and AXE. So for each brand, there are 124 weekly observations for each of the five chains. The price war starts with Albert Heijn in week 57 and is followed by the other chains in the upcoming weeks. The variables which will be used are the regular price, the weekly price and the sales. After obtaining the common factor using the Dynamic Hierarchical Factorial Model (DHFM), a Factor Augmented Vector Autoregressive (FAVAR) will be conducted in order to predict the sales.

Figure 1 First series of each block

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5 Albert Heijn C1000 Super de Boer Edah Jumbo Market share 38 % 32 % 13 % 11 % 7 %

Table 1 Market shares of supermarket chains

REXONA AXE Fa Sanex 8x4 Dove NIVEA VOGUE Market share 22 % 21 % 11 % 11 % 11 % 9 % 8 % 7 %

Table 2 Market shares of the deodrant brands

In order to get more insights about the observed variables, the market shares of both the chains and the brands have been presented in tables 1 and 2. Albert Heijn is the market leader among supermarkets, whereas REXONA and AXE are fighting for this position in the deodorant market.

2.2 Data preparation

At first, the data was analysed to find inconsistencies and outliers. It was noted that the regular price of some brands includes zeros. Since this variable is weighted, this happens if a brand was sold in a week in all supermarkets. Furthermore, this variable automatically smooths outliers. This means a value after an outlier (“0”) is not the real observed value, it is turned down to smooth the break. In this case it was decided to replace the “0” value and the value right after it with the mean of the previous three and the next three values in the specific column. Another issue was encountered within brand VOGUE observations. There were 23 values of “0” for each of the following variables: VOGUE sales, VOGUE Regular Price and VOGUE price- all in Edah supermarket. These values were replaced by the mean of all the other values in that specific supermarket.

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3. Dynamic Hierarchical Factorial Model (DHFM)

The aim of this thesis is to obtain latent factors that represent the general dynamics of price promotions. It is also interesting to explore if there are significant differences among the different chains regarding price promotions and the way they react to a price war.

The variance of price promotion will be analysed using a dynamic hierarchical factorial model (Moench et al. (2013)). I will investigate how deodorant price promotions of eight different deodorant brands vary across five supermarket chains from the Netherlands. Price promotions of the brands in each of the chains have dynamics that are common in that chain, but also have idiosyncratic dynamics. Moreover, all the chains may follow one common dynamic, but also have their own idiosyncratic dynamics. So, the variation of the price promotions will be decomposed into common, chain specific and brand specific. Using impulse response function, I will investigate how price promotions react to an exogenous shock (e.g. price war) in Dutch supermarket industry according to the chains and the brands.

Model

structure

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7 A three-level DHFM with five blocks will be considered as shown in figure 2. The three-level dynamic factor model consists of B=5 blocks, each of them corresponding to a chain, and Nb=8 time series (b=1,…, B) in each of the blocks corresponding to the brands. There are

N= 40 (N=Nb x B=8 x 5) time series with T=124 observations (weekly monetary value of the

discount). All time series are assumed to be stationary and have a mean of 0 and variance of 1. It is assumed as well that N and T are large and B<<T. All N time series are grouped in a TxN matrix X.

The first level of the model consists of the common factor, which accounts for the common movements of the dataset. The second level consists of the block specific factor and the third level contains the 40 time series.

𝑋

_𝑏𝑛𝑡

= 𝛬

_𝐺_𝑏𝑛

(𝐿)𝐺

_𝑏𝑡

+ 𝑒

_𝑋_𝑏𝑛𝑡

𝐺

_𝑏𝑡

= 𝛬

_𝐹_𝑏

(𝐿)𝐹

_𝑡

+ 𝑒

_𝐺_𝑏𝑡

Notations:

𝑋𝑏𝑛𝑡 – the standardized monetary value of the price promotion of the n-th brand of block b at

time t

𝐺_𝑏𝑡- is a vector of block factors of block b at time t 𝐹_𝑡- vector of common factors at time t

𝛬_𝐺_𝑏𝑛, 𝛬_𝐹_𝑏– matrix polinomials in L 𝑒_𝑋_𝑏𝑛𝑡- idiosyncratic residuals

𝑒_𝐺_𝑏𝑡- block-specific residuals

εFt – common residuals

𝜀

_𝐺_𝑏𝑛𝑡

= 𝜓

_𝐺_𝑏

(𝐿)𝑒

_𝐺_𝑏𝑡

𝜀

_𝐺_𝑏𝑡

~𝑁(0, 𝜎

_𝐺2_𝑏

)

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8 The model is flexible to draw the variance paramenters σF and σG , but the values were set to

be fixed to 0.1.

Model estimation

This model will be estimated using a Markov Chain Monte Carlo (MCMC) iterative method, namely Gibbs sampling. This method jointly draws the coefficients and the factors. Before estimating, some model parameters need to be specified. The model is chosen to have KF =1

common factor and KG,b =1 block specific factor for each of the five blocks. The transition

equation εFt= ψF(L)Ft and the AR model for eGbt to have lag orders of 1 whereas the lag order

of the idiosyncratic components eXbntwas set to be 1.The initial values for latent variables are

estimated by the principal components approach. In order to obtain reliable estimates, the first 50 000 out of the 100 000 draws will be discarded, and every 50th observation from the remaining 50 000 draws will be used for the analysis. In the end there will be 1000 draws for each parameter at each point in time. This model allows splitting the dynamics of an indicator or a time series into movements that it shares with other time series or factors and an idiosyncratic component. For instance, eGbt , the idiosyncratic component of block b is neither

correlated with the block specific common movements of the other blocks, nor with the economy-wide common movements Ft, nor with the idiosyncratic components of any block.

Doing this, one can shock a factor that stands for a certain economic concept and to see its isolated effect on the observed economic indicators which the conceptual factor is modelled to represent (Dehmamy and Halberstadt, 2015).

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4. Factor- augmented Vector Autoregressive (FAVAR) model

Bernanke, Bovin and Elisaz (2004) first proposed the Factor-augmented Vector Autoregressive model. Observable and latent factors follow a vector autoregressive process together, which then drives the comovement of a large number of observable variables. Including these unobserved factors, the FAVAR model is of rich information. (Bai, Li and Lu, 2014).

Let Yt be an M x 1 vector of observable economic variables. A VAR model would be estimated

using only this Yt vector. However, in many cases, this is not enough. Additional economic

information, which is not totally captured by Yt alone might be relevant for explaining and

forecasting the dynamics of this variable. Supposedly, this additional information can be summarized by the K x 1 vector of unobserved factors Ft, k being small. The joint variations of

(Ft, Yt) are explained by the following equation:

[

𝐹

𝑡

𝑌

_𝑡

] = µ + Φ(𝐿) [

𝐹

_𝑡−1

𝑌

_𝑡−1

] + 𝜈

𝑡

where µ is a (k+1) vector of constants , Φ(𝐿) is a conformable lag polynomial of finite order d, and the error term vt is mean zero with covariance matrix Q. However, this equation cannot

be estimated directly because the factors Ft are unobserved (Bernanke, Bovin and Elisaz, 2004).

In this paper, the actors Ft will be the common factor extracted with the help of the DHFM. The

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5. Results

5.1 Common factor F and chain-specific factors G

b

Figure 3 Common factor F

Figure 3 shows the common factor F, including the 5% confidence bands, which captures the common variance in the data. This factor is scaled according to the first standardized series. Hence, a value of 1 for F on the vertical axis represents the size of one standard deviation of that series, in this case Dove in Albert Heijn (standard deviation = 0.069). As expected, the common variance reaches a peak after the price war.

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11 Figure 4 illustrates the plots of the block specific factors Gb. All chains except Edah have the

same peak, which also overlaps with the one from F. Also what Jumbo and Edah have in common is the lack of much fluctuations over the period.

5.2 Variance decomposition

The model is able to quantify the importance of the variations at each level of the hierarchy through a variance decomposition analysis. The total variance of the price promotions, Var(Xbn), can be expressed as a weighted sum of the variances of the common, chain-specific

and brand-specific components:

𝑉𝑎𝑟(𝑋𝑏𝑛) = 𝛾𝐹(𝑉𝑎𝑟(𝐹)) + 𝛾𝐺(𝑉𝑎𝑟(𝑒𝐺𝑏)) + 𝛾𝑋(𝑉𝑎𝑟(𝑒𝑋𝑏𝑛))

where 𝛾_𝐹, 𝛾_𝐺 and 𝛾_𝑋 are composites of parameters. The shares of each component are illustrated in table 3, and for a better visualization the corresponding bar chart (Figure 5) is also included. The shares were calculated as follows:

𝑆ℎ𝑎𝑟𝑒_𝐹 = 𝛾_𝐹(𝑉𝑎𝑟(𝐹))/𝑉𝑎𝑟(𝑋_𝑏𝑛) 𝑆ℎ𝑎𝑟𝑒_𝐺 = 𝛾_𝐺(𝑉𝑎𝑟(𝑒_𝐺𝑏))/𝑉𝑎𝑟(𝑋𝑏𝑛) 𝑆ℎ𝑎𝑟𝑒_𝑋 = 𝛾_𝑋(𝑉𝑎𝑟(𝑒_𝑋𝑏𝑛))/𝑉𝑎𝑟(𝑋_𝑏𝑛) Block 𝑆ℎ𝑎𝑟𝑒_𝐹 𝑆ℎ𝑎𝑟𝑒_𝐺 𝑆ℎ𝑎𝑟𝑒_𝑋 Albert Heijn 0.0694 (0.0183) 0.0286 (0.0119) 0.902 (0.0248) Edah 0.0045 (0.0058) 0.1551 (0.0090) 0.8404 (0.0079) Super de Boer 0.1118 (0.0284) 0.0472 (0.0121) 0.841 (0.0264) Jumbo 0.1632 (0.0185) 0.0154 (0.0026) 0.8214 (0.0185) C1000 0.063 (0.0214) 0.0274 (0.0096) 0.9096 (0.0196)

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12 The variance decomposition does not vary much between the five chains. For each chain, the biggest part of the price promotion variance is explained by the brand specific component. This variance share takes values between 82 %, in Jumbo, and almost 91 %, in C1000. In Edah, the chain specific factor accounts for almost 16 % of the variance, while the common factor accounts for less than 1 %. Variables react strongly on an economy-wide shock if a large part of the group variance is explained by ShareF. In Jumbo and Super de Boer the common factor

accounts for 16 % and 11 % respectively. This means that price promotions in these chains are affected more by the common movement in the economy than the brands sold in the other three chains. In addition, looking at these results, Edah is the chain that takes the most “freedom” of dealing with the price promotions and seems to not be influenced by the common factor in the economy.

Figure 5 Variance decomposition

5.3 Impulse response analysis

After assessing the variance in each block, an impulse response analysis was conducted in order to see how an economy exogenous shock affects the price promotions of different brands in the different chains. The effect of one standard deviation shock on the common factor F is investigated. It is also interesting to see how this shock affects all levels of the hierarchy. Figure 6 illustrates how each chain specific factor is affected. A positive shock on the common factor will affect the chain specific factor of Albert Heijn, Super de Boer, Jumbo and C1000 positively. This means that in the time of the price war, price promotions’ depths will increase in these four chains. The effect lasts longer in Albert Heijn and C1000 and dies out more rapidly in Super de Boer and Jumbo. After about 40 weeks after the price war starts, all these chains

0% 20% 40% 60% 80% 100%

Albert Hijn Edah Super de Boer

Jumbo C1000

Variance decomposition

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13 return to the initial state before the price war. Nevertheless, the chain specific factor for Edah has a small and insignificant reaction to the shock. This was already expected, since less than .05% of the variance in this block was explained by the common factor.

Figure 6 Impulse response of the chain specific factors to a shock on the common factor F

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Figure 7 Impulse response of each brand from each chain to a shock on the common factor F

After assessing the impact that an exogenous shock would have on the chains and brands, it is also interesting to see how a shock on one chain specific factor affects the price promotions of the brands sold in that chain. For this analysis, Albert Heijn chain specific factor was chosen to have an exogenous shock applied. Figure 8 shows how this shock propagates through the brands. The only brands that are significantly influenced are Dove and Fa. These were the brands that would also have been affected by the shock applied to the common factor. Again, the positive effects die out after about ten weeks.

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5.4 Forecast

In the last step of the DHFM analysis, a forecast for the future was developed. The extracted factors from the first 100 weeks were used in order to generate the forecast for the future. Figure 8 shows the forecast for the common movement and the group specific movements for each chain. This prediction starts at week 100 and goes 100 weeks ahead. However, these predictions do not account for any exogenous shock like in the case of the impulse response analysis. The upper part of figure 9 illustrates the predicted common movement. The price promotions are about to raise steadily for fifteen weeks and then settle back to the normal. The lower part, where the forecasts for the chain specific movements are shown, includes the first 100 weeks as well. The real forecasted values start after week 100. Price promotions for the deodorant brands sold in Albert Heijn will keep a steady movement, which will be almost equal to the mean values of the price promotions before the price war started. Right in the first predicted week, deodorant price promotions will raise significantly in Edah. However, after less than 15 weeks, they are predicted to remain stable at a value which is slightly higher than the mean before and during the price war. Super de Boer and C1000 common movement are almost the same as the Albert Heijn one. The depth of the price promotions in Jumbo is expected to get a little higher than what it used to be before the price war.

Figure 9 Forecast of the common movement and each group specific movement

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16 common factor and one group specific factor per chain. Apart from this, the actual data is still inside the confidence spans of the forecasting for most of the brands.

Figure 10 Predictions for all brands in Albert Heijn

The forecasting for all brands in the remaining four chains are shown in the Appendix 1.

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6. FAVAR predictions

Before running the FAVAR analysis, the relationship between the sales and the common factor F and chain specific factor G were assessed using scatter plots. Only the scatter plots for Dove Sales in Albert Heijn will be presented.

Figure 11 Scatter plots between Dove sales and factor F and G

Figure 11 shows a slightly positive correlation between the sales and the factors F or G. The unobserved factors that were extracted after the DHFM analysis can be further used in a FAVAR. In this case, only the common factor F and each chain specific factor G will be used in order to predict the upcoming sales for the deodorant brands. The latent factors will add extra information and will improve predictions compared to a simple AR model. In order to prove this, five time series were selected to be predicted. Dove sales in each of the five chains will be forecasted using both an AR and the FAVAR (using both the F and the specific G).

The AR equation:

𝑌_𝑡 = 𝛼𝑌_𝑡−1+ 𝜀 The FAVAR is composed by the following two equations:

𝑌_𝑡 = 𝑐₁+ 𝛼₁𝑌_𝑡−1+ 𝛽₁𝐹_𝑡−1+ 𝜀_𝑌 𝐹𝑡 = 𝑐2+ 𝛼2𝑌𝑡−1+ 𝛽2𝐹𝑡−1+ 𝜀𝐹

So in the end, four coefficients and two constants for each FAVAR will be estimated. After the Gibbs method, 1000 different values for the F factor were obtained for each period in time. All values were used for estimating the FAVAR. So, instead of obtaining one α1 coefficient, a

vector of 1000 values for α1 was obtained. For each model, six histograms were generated in

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18 coefficients for each FAVAR and AR are showed in table x. After the table, the histograms and a graph are presented. The graph plots the FAVAR predicted sales (one FAVAR with the F, and the other one with the G), the actual data and the AR predictions for the next 23 weeks.

Dove in Albert Heijn

FAVAR (F) 𝑌_𝑡−1 𝐹_𝑡−1 c 𝑌_𝑡 0.393 (0.374,0.409) 6.995 (5.174,9.438) 28.476(27.793,29.46 ) 𝐹𝑡 0.0007(-0.0005,0.002) 0.848 (0.805,0.885) 0.848(0.805,0.885) FAVAR (G) 𝑌𝑡−1 𝐹𝑡−1 c 𝑌𝑡 0.397(0.339,0.434) 6.42(1.579,11.083) 28.399(26.663,31.10 2) 𝐹_𝑡 0.001(-0.001,0.004) 0.672(0.517,0.783) -0.067(-0.199,0.07) AR 𝑌𝑡−1 - - 𝑌_𝑡 0.443 (p-value=4.00e-06) - -

Table 4 Estimates of the FAVAR and AR model for Dove sales in Albert Heijn

All coefficients are signifficantly different from 0, except α2 .

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Figure 13 Histograms of FAVAR model coefficients for Dove in Albert Heijn using the chain specific factor G

Figure 14 Predictions of the next 23 weeks of Dove sales in Albert Heijn

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7. Conclusion and managerial implications

The aim of the thesis was to explore the price promotions for the deodorant industry using a dynamic hierarchical factorial model. One of the main advantages of using such a model is that the variance of price promotions can be decomposed into common (economy wide), chain specific and idiosyncratic. The common movement was explained by the latent factor F. The common movement illustrates a peak right after the start of the price war. This was expected, since during a price war, regular prices drop significantly. All chain specific latent factors showed same peaks, except the one for the Edah supermarket. Interestingly, this chain had some peaks before the price war started.

The variance decomposition did not differ much across the five chains. For all of them, the biggest share was represented by the idiosyncratic movement. From The deodorant brands sold in Jumbo seem to be have the highest percentage of explained variance by the common factor F, approximately 16 %, while this common movement accounts for less than .05% for the deodorant brands sold in Edah.

In order to see how the price promotions might react to an exogenous shock, an impulse response analysis was performed. Looking at the impulse response graphs, a brand manager can foresee how his competitor would react to such a shock. For instance, Rexona and AXE are the market leaders in this industry. After a possible shock, the price promotions for Rexona sold in Super de Boer and Jumbo tend to raise and then settle after approximately 10 weeks. In order to outperform their sales, AXE could keep its price promotions going for two more weeks. This is a small example to show how the impulse analysis can serve, especially for future strategy purposes.

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8. Limitations and further research

This study has several limitations, providing leads for further research. The data illustrates the price promotions of eight brands from five chains from only one country, The Netherlands. Further studies could establish whether these findings can be generalized to other price war situations. Moreover, the deodorant industry has changed in the past 12 years, and also the supermarkets in The Netherlands. Edah was closed down after this price war and Super de Boer was bought by Jumbo.

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9. References

Bai, J., Li, K., & Lu, L. (2016). Estimation and inference of FAVAR models. Journal of Business & Economic Statistics, 34(4), 620-641.

Bernanke, B. S., Boivin, J., & Eliasz, P. (2005). Measuring the effects of monetary policy: a factor-augmented vector autoregressive (FAVAR) approach. The Quarterly journal of economics, 120(1), 387-422.

Blattberg, R. C., Briesch, R., & Fox, E. J. (1995). How promotions work. Marketing science, 14(3_supplement), G122-G132.

Dehmamy Keyvan and Halberstadt Arne (2015), “Modelling the term structure of interest rates in a Dynamic Hierarchical Factorial Model”.

Dekimpe, M. G., Hanssens, D. M., & Silva-Risso, J. M. (1998). Long-run effects of price promotions in scanner markets. Journal of econometrics, 89(1), 269-291.

Van Heerde, H. J., Gijsbrechts, E., & Pauwels, K. (2008). Winners and losers in a major price war. Journal of Marketing Research, 45(5), 499-518.

Heil, O. P., & Helsen, K. (2001). Toward an understanding of price wars: Their nature and how they erupt. International Journal of Research in Marketing, 18(1), 83-98.

Kuntner, T., & Teichert, T. (2016). The scope of price promotion research: An informetric study. Journal of Business Research, 69(8), 2687-2696.

Moench, E., Ng, S., & Potter, S. (2013). Dynamic hierarchical factor models. Review of Economics and Statistics, 95(5), 1811-1817.

Sotgiu, F., & Gielens, K. (2015). Suppliers Caught in Supermarket Price Wars: Victims or Victors? Insights from a Dutch Price War. Journal of Marketing Research, 52(6), 784-800. Deodorants in the Netherlands. (2017). Marketresearch.com. Retrieved 20 April 2017, from

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APPENDIX 1

Figure 15 Predictions for all brands in Edah

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Figure 17 Predictions of all brands in Jumbo

Figure 18 Predictions for all brands in C1000

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25 𝑌_𝑡 0.168()0.157,0.176) -5.394(-6.114,-4,536 ) 13.180(13.067,13.337 ) 𝐹_𝑡 -0.009(-0.011,-0.008) 0.467(0.446,0.490) 0.178(0.157,0.209) AR 𝑌𝑡−1 - - 𝑌_𝑡 0.077 (p-value= 0.392 ) - -

Table 5 Estimates of the FAVAR and AR model for Dove sales in Edah

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Figure 20 Histograms of FAVAR model coefficients for Dove in Edah using the chain specific factor G

Figure 21 Predictions of the next 23 weeks od Dove sales in Edah

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27 𝐹_𝑡 -0.002 (-0.006,0.001) 0.855 (0.821,0.884) 0.044(-0.021,0.114) FAVAR (G) 𝑌𝑡−1 𝐹𝑡−1 c 𝑌_𝑡 0.551(0.547,0.555) 0.056(-0.696,0.758) 7.711(7.633,7.789) 𝐹𝑡 0.002(-0.005,0.008) 0.666(0.519,0.764) -0.029(-0.152,0.091 ) AR 𝑌𝑡−1 𝑌𝑡 0.541 (p-value=6.44e-1 1 )

Table 6 Estimates of the FAVAR and AR model for Dove sales in Super de Boer

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Figure 23 Histograms of FAVAR model coefficients for Dove in Super de Boer using the chain specific factor G

Figure 24 Predictions of the next 23 weeks od Dove sales in Super de Boer

Dove in Jumbo

FAVAR (F)

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29 𝑌_𝑡 0.744 (0.739,0.748) -0.017 (-0.101,0.069 ) 2.080(2.049,2.12) 𝐹_𝑡 -0.01 (-0.023,0.001) 0.853 (0.818,0.882) 0.089(-0.009,0.191) FAVAR (G) 𝑌_𝑡−1 𝐹_𝑡−1 c 𝑌𝑡 0.743(0.742,0.744) -0.016(-0.026,-0.003 ) 2.869(2.076,2.095) 𝐹_𝑡 -0.022(-0.027,-0.016) 0.817(0.809,0.827) 0.189(0.145,0.234) AR 𝑌_𝑡−1 - - 𝑌_𝑡 0.765(p-value < 2e-16) - -

Table 7 Estimates of the FAVAR and AR model for Dove sales in Jumbo

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Figure 26 Histograms of FAVAR model coefficients for Dove in Jumbo using the chain specific factor G

Figure 27 Predictions of the next 23 weeks od Dove sales in Jumbo

Dove in C1000 with F

FAVAR (F)

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31 𝑌_𝑡 0.685 (0.675,0.694) 0.57 (-0.137,1.291 ) 11.848(11.52,12.22) 𝐹_𝑡 0.003 (0.001,0.005) 0.84(0.805,0.876) -0.119(-0.196,-0.045 ) FAVAR (G) 𝑌_𝑡−1 𝐹_𝑡−1 c 𝑌𝑡 0.675(0.643,0.693) 1.025(-0.039,2.325 ) 12.228(11.56,13,497) 𝐹_𝑡 0.002(-0.002,0.008) 0.745(0.540,0.844) -0.099(-0.288,0.09) AR 𝑌𝑡−1 - - 𝑌_𝑡 0.778 (p-value < 2e-16) - -

Table 8 Estimates of the FAVAR and AR model for Dove sales in C1000

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32

Figure 29 Histograms of FAVAR model coefficients for Dove in C1000 using the chain specific factor G

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