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In this section, we perform some sensitivity analysis to test the robustness of our results. During this analysis we use different model specifications for hypothesis testing and alternate models to define some of our variables.

First, we checked the robustness of our results testing different traffic uncertainty models. Recall that we used as measure of traffic uncertainty the inter-day traffic variability across stores. For our core analysis we obtained this measure as follows: we calculated the coefficient of variation of traffic for each store over a week and then obtained the overall mean of the coefficient of variation across weeks for each store.

We calculated the inter-day traffic variability using three alternate approaches. In the first approach which we refer to as Model 1 we calculate the coefficient of variation of traffic for each store over a month and then obtain the overall mean across months for each store. In the second approach (Model 2) we calculate the coefficient of variation for each store over two weeks and obtain the overall mean for each store across the two- week periods. In the third approach (Model 3) we calculate the coefficient of variation of traffic for each store over the whole year.

Tables 3.15 and 3.16 present the results of regression equations (3.4) and (3.7). Table 3.15 shows that the results obtained from the three alternate model specifications for traffic uncertainty are robust. We find that traffic uncertainty is negatively correlated with conversion rate and sales under all model specifications. Similarly, we find that the coefficient estimates of Models 1-3 in Table 3.16 confirm support for Hypothesis 4. Second, we checked the robustness of our results using different labor mismatch models. In the main analysis we had used the following model to obtain mismatches:

LBRHRSit = b11T RAF F ICit−1+b12T RAF F ICit−2+b13T RAF F ICit−3

+ b₁₄T RAF F ICit−4+b15T RAF F ICit−5+b16T RAF F ICit−6

+ b₁₇T RAF F ICit−7+b18δh+b₁₉ dδd+b₂₀mδm+ηit (3.8)

We defined as a mismatch the residuals of the above regression which we convert into a single number for each store by obtaining the mean residual for each store in order to enable cross-sectional analysis to test our fourth hypothesis. The advantage of this

definition is that we do utilize longitudinal data to create the mismatch variable. To test the robustness we tried three alternative model specifications for mismatches. We first removed the dummy variable for holidays from the regression equation (3.8). We refer to this specification as Model 4. Models 5 and Model 6 were constructed sequentially from Model 4 by removing days of the week and months from the covariates respectively. Table 3.17 present the results of regression equation (3.7) for the three alternate model specifications for mismatches. Table 3.17 shows that our results support fully Hypothesis 4.

Third, we also tested the robustness of the results from the first stage model in which we removed one of the covariates at a time and rerun the model. First, we removed from regression equations (3.1)-(3.3) the dummy variable for holidays. This is refered to as Model 7. Second, we removed from regression equations (3.1)-(3.3) the month covariates (i.e., Model 8). The results of the estimation of the above models are presented in Table 3.17. We find under all alternate model specifications that traffic variability is negatively associated with store performance which is consistent with our previous findings.

3.9

Conclusion

Motivated by the increasing efforts that retailers make to track conversion rate and basket value and the importance that they place on such store performance metrics we conduct a descriptive study of these metrics for a retailer. Specifically, we consider

the correlation between store performance and intra-day traffic variability and traffic uncertainty. We also measure traffic-labor mismatches and study if they explain the observed correlations in our sample.

We report the following results in this chapter. First, we present the within-store results. We find that intra-day traffic variability is negatively correlated with both conversion rate and basket value. A 1% increase in traffic variability is associated with a 0.094% decrease in conversion rate in a store and 0.037% decrease in basket value. We also find that, for a given level of traffic, both conversion rate and basket value increase with an increase in store labor at a diminishing rate. A 1% increase in labor is associated with a 0.102% increase in conversion rate and 0.066% increase in basket value. In addition, we find that conversion rates are higher during holidays but basket values are lower suggesting that price promotions offered during the holiday season cause more customers to purchase but do not make the average customer purchase more. Moreover, we find that both conversion rates and basket values exhibit significant seasonality.

Next, we report the across-store results. We find that stores with higher traffic uncertainty have lower conversion rates but similar basket values. We also find that stores that have higher traffic variability and higher traffic uncertainty have higher mismatches between required labor and actual labor. Furthermore, our tests reveal that stores that have lower foot-traffic have higher traffic uncertainty resulting in mis- matches between required labor and actual labor. A surprising result of our analysis is that competition does not affect conversion rates and basket values. This suggests

that consumers decision to whether or not to purchase and how much to purchase is unaffected by the presence of other competitors once they are in the store. Finally, we find that stores located in neighborhoods with higher per capita income have higher conversion rates but similar basket values.

Although our analysis has provided several interesting insights related to the link- ages between staffing levels, traffic variability, traffic uncertainty, and store performance we need to acknowledge its limitations. One of the drivers of store performance is the availability of inventory at a store. Our stores are under the same ownership so one would expect that the target inventory levels should be similar in all stores. However, there could be large variations in the actual inventory levels across stores as well as within a store over time. Unfortunately, we could not obtain any information with respect to the inventory levels for the retailer we studied and as a result, we could not control for actual inventory in our analysis. Another information that we could not obtain pertains to the type and size of assortment. Even though the stores that we considered in our analysis are of the same type there could be large variations in the size as well as type of assortment that they offer.

Summarizing our study has the following implications for practitioners. First, ac- cording to our study retailers need to plan labor not only based on sales and traffic which has been the traditional approach but also take traffic volatility into account. Even though some part of traffic volatility is uncontrollable retailers need to handle volatilities that are under their control either using increased labor or through more flexible labor. Second, retailers often can induce traffic volatility through the actions

that they take. For example, several retailers have “early bird specials” that would cause traffic variability to increase substantially. Hence, our study shows that it is important to coordinate actions that drive store traffic with those that help manage the potential increase in volatility.