Retail & Marketing Analytics Effectiveness of Marketing Activities at Local Level A Spatial Panel Autoregressive Model Andreas Georgopoulos CID: 01281486 Abstract Abstract At this project the effectiveness of different marketing acitivities and communication campaigns, of a fast-food retail chain at restaurant-level, on increasing daily net sales and total receipts count is assessed. Daily data is used and only fully operated restaurants from 2015-01-01 to 2016-12-31 are examined, resulting in a “same-store” analysis. Additional daily data that migh explain a lot of the response variables’ variation, such as weather data, sport events bank holidays and weekends, is also acquired. A Spatial Panel Autoregressive Model with Fixed Effects that accounts for spatial dependencies between restaurants is proposed. Each advertising activity is modeled separately as an adstock variable for each Italian Province, capturing the provincial carryover effect of alternative media on consumers’ decisions. With the adstock variables defined at a Province- level, the Advertising Elasticities of each Province of the statistically and economically significant marketing activities, e.g. GRP TV and Euro Spent in other Offline Campaigns, are computed, underlining the effectiveness of different media in the short and long run. The proposed model provides the potential of capturing the effect of a change in a marketing activity on net sales and/or foot traffic of specific “target” restaurants. Therefore, a focused budget allocation can be implemented in order to improve individual performance of specific restaurants based on their location (Province). ii Table of Contents Table of Contents 1 Introduction 4 2 Spatial Panel Model 5 2.1 Spatial Panel Autoregressive Model .......................................................................... 5 2.2 Spatial Weight Matrix ................................................................................................ 6 2.3 Spatial Autocorrelation .............................................................................................. 7 3 Explanatory Variables 8 3.1 Marketing Activities .................................................................................................. 8 3.2 Weather Data ............................................................................................................. 9 3.3 Additional Explanatory Variables ............................................................................. 9 4 Model Estimation 11 4.1 Regression Estimation ............................................................................................. 11 4.2 Advertising Elasticities ............................................................................................ 13 5 Recommendations 15 References 16 Appendices 17 A. Fixed Effects ............................................................................................................. 17 B. Advertising Elasticities per Province ........................................................................ 19 iii 1. Introduction 1 Introduction This project is considered a sequential analysis of the (Georgopoulos A., 2017) project, where the effectiveness of different media on net sales and foot traffic at an aggregated country-level was examined. At this project a restaurant-level analysis on daily data takes place. Therefore, a panel dataset with restaurants as cross-sectional that are fully operated for the entire time period from 2015-01-01 to 2016-12-31 is generated. In Figure 1, a data model that underlies the data preprocessing and aggregation procedures of the provided and newly constructed datasets, is presented. The final panel dataset, consists of � = 505 cross-sectional units (restaurants) with recorded information for � = 731 days, resulting in a total number of 369,155 observations. Figure 1. Construction of Final Panel Dataset 4 2. Spatial Panel Model Spatial Panel Autoregressive Model 2 Spatial Panel Model 2.1 Spatial Panel Autoregressive Model A Spatial Autoregressive Model with Fixed Effects (Spatial Error Model, SEM) controls for all space-specific time-invariant variables. More specifically, this model takes into consideration spatial effects through the error structure (LeSage, 2008). The fixed effects “absorb the effects of omitted variables that differ between cross-sectional units but are constant over time”, the absence of which cause bias in the estimated parameters (Elhorst, 2014). When specifying for such spatial dependencies between units, a SAR (SEM) model includes a spatial autoregressive process in the error term, known as the spatial autocorrelated coefficient or the spatial error (Elhorst, 2014) (Viton, 2010). A Spatial Panel Data Autoregressive Model with Fixed Effects of the previously mentioned panel dataset with � = 505 cross-sectional units (restaurants) and � = 731 time periods, can be formulated as following: �!,! = �!,! ∙ � + �! + �!,!, ! �!,! = � ∙ �!,! ∙ �!,! + �!,!, !!! where: − � = (1, … ,505). Cross-sectional unit index for each restaurant of the retail chain. − � = (2015-01-01, … , 2016-12-31). Time period for years 2015 and 2016. − �!,!: observation on response variable, either net sales or receipt count, for restaurant � at time �. − �!,!: explanatory variable of restaurant � at time �. − �!": element of the Spatial Weight Matrix underlying if restaurants �, � are neighbors (spatial location of each restaurant). − �!,!: spatially autocorrelated error term. ! − �!,! ∼ (0, � ): independent and normally distributed error term equation restaurant � at time �. − �!: spatial fixed effects for each cross-sectional restaurant unit − �: spatial autocorrelated coefficient (spatial error) � �: vector of fixed but unknown parameters. 5 2. Spatial Panel Model Spatial Weight Matrix 2.2 Spatial Weight Matrix The spatial dependencies between the cross-sectional units (restaurants) have to be quantified into a Spatial Weight Matrix �, in order to indicate the neighboring relationships between all restaurants of the retail chain. The Spatial Weight Matrix is an � x � matrix (N: total number of restaurants) where: 1, if restaurants �, � are neighbors � = !,! 0, otherwise In order to define when two restaurants to be considered as “neighbors” a distance- based contiguity approach is implemented (Viton, 2010, Bivand, 2016). A threshold distance �!"# (bandwidth) is introduced in order to define the neighboring relationships between restaurants. More specifically, two restaurants are “neighbors” if the distance between their spatial locations is less or equal to the threshold distance, and thus: 1, �!,! ≤ �!"# �!,! = 0, �!,! > �!"# Since the location of each store is provided by latitude and longitude, the distance between all restaurants in space can be calculated. The Harvesine distance between restaurants in km is calculated. After computing the neighboring relationships between all restaurants, the Spatial Weight Matrix is “row-standardised” to remove any scale dependencies, resulting in a row-stochastic Weight Matrix (LeSage, 2008). In order to observe the “optimal” radius beyond which there is no spatial influence between restaurants, different weight matrices are generated with the threshold distance ranging from 1 to 10 km. The Spatial Panel Autoregressive model with Fixed Effects is estimated with the different Spatial Weight Matrices, and the regression Standard Error (SE) is observed. The Spatial Weight Matrix that resulted in the minimum SE corresponds to a threshold distance of 1km (Figure 2). Therefore, the final row-stochastic Spatial Weight Matrix with a threshold distance of 1km is computed in order to depict the spatial dependencies between the restaurants of the retail chain. Figure 2. Regression Standard Error for different Threshold Distances (km) 6 2. Spatial Panel Model Spatial Autocorrelation 2.3 Spatial Autocorrelation After defining the spatial dependencies between the restaurants, the panel data is tested for spatial autocorrelation through a series of Lagrange Multiplier (LM) tests (Breusch and Pagan, 1980, Baltagi et al., 2003). The LM2 Marginal Test assumes that random individual effects do not exist, whereas the Conidtional LM test assumes a possible existence (Baltagi et al., 2003). From the results shown in Table 1, someone can observe that both tests indicate the existence of spatial autocorrelation in the panel data model. Therefore, a spatial panel data model is needed, as the one proposed in this project, to account for spatial dependencies and control for all space-specific and time-invariant variables that result in biased estimations. Baltagi, Song and Koh LM2 Marginal Test Dependent variable: Total Net Sales Total Receipts Count LM2 116.2 156.28 p-value < 2.2e-16 < 2.2e-16 Alternative hypothesis: Spatial autocorrelation Baltagi, Song and Koh LM*-lambda conditional LM test Dependent variable: Total Net Sales Total Receipts Count LM2 105.86 100.34 p-value < 2.2e-16 < 2.2e-16 Alternative hypothesis: Spatial autocorrelation Table 1. Lagrange Multiplier Tests for Spatial Autocorrelation 7 3. Explanatory Variables Marketing Activities 3 Explanatory Variables 3.1 Marketing Activities Different communication campaigns have a different impact on consumers memory rate and thus on their final decisions. However, the effect of the same marketing activity on consumers’ behavior might vary with respect to local preferences and habits. In order to capture the regional carryover effect of alternative media on consumers’ decisions, each marketing activity is modeled separately