Results

USING A VENDING MACHINE “RETAILER" TO STUDY REPEAT PURCHASES IN CONSUMER BEHAVIOR

Hypothesis 3: The total number of unique customers will increase during the Sale period

4.6 Results

In the following section, we present results testing the five hypotheses laid out earlier in the paper. We first show that the standard economics predictions about behavior during the Sale period were all born out in the data. We then take a look at the Post-Sale data.

Sale Increases Purchases of Discounted and Non-Discounted Items

Consistent with H1 and H2, there is an increase in discounted and non-discounted items during the Sale. The Sale period saw an increase in purchases as compared to the Pre-Sale period, across both discounted and non-discounted items, as can be seen in Table 4.5.

Table 4.5: Weekly Transaction Summary by Treatment Period

Mean SD Q1 Median Q3

Pre-Sale Discounted 27.75 4.92 25.50 26.00 28.25 Pre-Sale Non-Discounted 38.00 11.83 30.50 34.00 41.50 Pre-Sale Total Weekly Purchases 65.75 11.64 56.50 64.50 73.75 Sale Discounted 65.50 14.85 60.25 65.50 70.75 Sale Non-Discounted 54.00 7.07 51.50 54.00 56.50 Sale Total Weekly Purchases 119.50 21.92 111.80 119.50 127.20 Post-Sale Discounted 40.25 16.21 32.00 41.50 49.75 Post-Sale Non-Discounted 46.25 22.98 43.50 56.50 59.25 Post-Sale Total Weekly Purchases 86.50 38.00 75.50 98.5 109.50

Consistent with the loss leader hypothesis, consumers purchase more items per visit during (and after) the Sale. Aggregating individual-level purchases up to bundles, we compare the number of items purchased prior to the sale period with the number of items purchased during and after the sale. The number of items purchased during Sale is higher than Pre-Sale and this remains elevated during the Post-Sale period, increasing overall Post-Sale revenue, as seen in Table 4.6.

While the composition of individual bundles between product categories does not shift dramatically (the percentage of the bundle which represents discounted items is slightly higher during the Sale, but comes back to Pre-Sale levels following), the bundles become and remain slightly larger Post-Sale, meaning customers are spending more per bundle on average ($2.20 vs $1.95 Pre-Sale). However, none of the differences were statistically significant using a Mann–Whitney U test.22

22The Mann–Whitney U test is a nonparametric test of the null hypothesis that, for randomly selected values from two experimental periods, the probability of one value being greater than the other value is equal to the probability of the latter value being greater than the former. Using this test, we find no significant differences between the number of items per bundle nor the percent of the bundle which is discounted items for each pair of experimental periods. Furthermore, we do find a significant difference between the dollar amount spent per bundle between Pre-Sale and Sale (𝑝 <0.01%) and Sale and Post-Sale (𝑝 <0.01%), but not between Pre-Sale and Post-Sale periods.

Table 4.6: Bundle-Level Summary by Treatment Period

Mean SD Q1 Median Q3

Pre-Sale items per bundle 1.49 0.93 1.00 1.00 2.00

Pre-Sale dollar amount spent per bundle 1.91 1.26 1.00 1.50 2.13 Pre-Sale percent of bundle which is discounted items 0.41 0.46 0.00 0.00 1.00

Sale items per bundle 1.93 1.69 1.00 1.00 2.00

Sale dollar amount spent per bundle 1.67 1.51 0.75 1.00 2.00 Sale percent of bundle which is discounted items 0.48 0.47 0.00 0.50 1.00

Post-Sale items per bundle 1.82 1.73 1.00 1.00 2.00

Post-Sale dollar amount spent per bundle 2.20 1.99 1.00 1.50 2.00 Post-Sale percent of bundle which is discounted items 0.39 0.44 0.00 0.00 1.00

Post-Sale Purchases of Discounted Items Increase Compared to Pre-Sale Consistent with H4a, purchases of discounted items increaseduring the Post-Sale period. As can be seen in Table 4.5, the Post-Sale period saw a 48% increase in purchases of previously discounted items as compared to the Pre-Sale period, from a customer base which was comparable to baseline.

With respect to purchases of non-discounted substitute items, the sales here increase during the Post-Sale period, but decrease on a relative basis compared to discounted items. As can be seen in Table 4.5, the Post-Sale period saw an increase in purchases of items that were not discounted during the Sale period, albeit at a lower rate (a 24% increase).

We complement all of these descriptive statistics with regression results estimating model 4.1. In our purchase regression specification, 𝑦_𝑡 is the total number of purchases made at time t. We regress 𝑑 𝑢𝑟 𝑖𝑛𝑔 𝑠𝑎𝑙 𝑒_𝑡 and 𝑝 𝑜 𝑠𝑡 𝑠𝑎𝑙 𝑒_𝑡, which are binary indicators of whether the purchase was made during the Sale or Post-Sale, respectively, and𝑤 𝑒 𝑒 𝑘_𝑡, which is the number of the week of the experiment (1-10) and is intended to capture any time trends influencing the results. 𝜖_𝑡is our error term, which we assume is uncorrelated with the regressors. These regressions collapse all purchases at the individual day level. Specifically, we calculate the number of purchases made in each day over the observed 10-week time period. We then regress the number of purchases on indicators of whether it was a Sale period or Post-Sale period at the time of purchase.

𝑦_𝑡 =𝛼+𝛽₁𝑑 𝑢𝑟 𝑖𝑛𝑔 𝑠𝑎𝑙 𝑒_𝑡 +𝛽₂𝑝 𝑜 𝑠𝑡 𝑠𝑎𝑙 𝑒_𝑡+𝛾(𝑤 𝑒 𝑒 𝑘_𝑡)²+𝜖_𝑡 (4.1)

The regression results can be found in 4.7. We can see from this regression that purchases significantly increase during the Sale period, as compared to both Pre- and Post-Sale. When both time periods enter into our regression, Post-Sale purchases remain elevated compared to Pre-Sale as well.

Table 4.7: Purchases During Sale and Post-Sale Periods

Dependent variable:

Total Purchases

(1) (2) (3)

DuringSale 4.614^∗∗∗ 7.115^∗∗∗

(1.524) (1.999)

PostSale −1.716 6.775^∗

(2.920) (3.595)

week² 0.043^∗∗ 0.061 −0.048

(0.021) (0.047) (0.053)

Constant 8.374^∗∗∗ 9.403^∗∗∗ 8.576^∗∗∗

(1.054) (1.100) (1.039)

Observations 68 68 68

R² 0.159 0.045 0.203

Adjusted R² 0.133 0.016 0.166

F Statistic 6.136^∗∗∗(df = 2; 65) 1.543 (df = 2; 65) 5.436^∗∗∗(df = 3; 64) Note: ^∗p<0.1;^∗∗p<0.05;^∗∗∗p<0.01, two-tailed test of hypothesis

We run this regression including interaction terms for discounted items (“SaleItem"

in our regression) to see whether the Sale had a disproportionate impact on dis- counted items versus non-discounted items. We do not find such an effect, and the results from this regression can be found in Table 4.8.23

Total Customers Increases with Sale and Remains Unchanged Post-Sale Consistent with H3, the total number of customersincreasesduring the Sale period.

As can be seen in Table 4.9, the Sale period saw a 42% increase in total unique customers as compared to Pre-Sale. The number of unique customers purchasing discounted items went up even more significantly, at a 73% increase. This finding

23Difference-in-difference regressions, another way to measure the impact of the Sale treatment on future purchases of discounted items, also found no significant effect and can be found in Appendix E.

Table 4.8: Purchases During Sale and Post-Sale Periods

Dependent variable:

Total Purchases

(1) (2) (3)

DuringSale 1.952^∗ 2.298^∗

(1.012) (1.188)

PostSale −1.925 1.042

(1.476) (1.716)

SaleItem −1.192^∗ −0.682 −1.241

(0.675) (0.770) (0.909)

week² 0.021^∗∗ 0.046^∗∗ 0.007

(0.010) (0.021) (0.023)

DuringSale:SaleItem 1.592 1.641

(1.427) (1.558)

PostSale:SaleItem −0.449 0.111

(1.314) (1.367)

Constant 4.958^∗∗∗ 5.161^∗∗∗ 5.035^∗∗∗

(0.604) (0.645) (0.683)

Observations 134 134 134

R² 0.139 0.053 0.143

Adjusted R² 0.113 0.024 0.102

F Statistic 5.217^∗∗∗(df = 4; 129) 1.819 (df = 4; 129) 3.520^∗∗∗(df = 6; 127) Note: ^∗p<0.1;^∗∗p<0.05;^∗∗∗p<0.01, two-tailed test of hypothesis

is in line with our standard economic prediction based on the law of supply and demand.

Table 4.9: Weekly Customer Summary by Treatment Period

Mean SD Q1 Median Q3

Pre-Sale Discounted 15.00 3.65 12.50 15.00 17.50 Pre-Sale Non-Discounted 19.00 2.94 16.75 19.00 21.25 Pre-Sale Total Weekly Purchases 34.00 4.24 32.25 33.00 34.75 Sale Discounted 21.00 2.83 20.00 21.00 22.00 Sale Non-Discounted 20.00 1.41 19.50 20.00 20.50 Sale Total Weekly Purchases 41.00 4.24 39.50 41.00 42.50 Post-Sale Discounted 14.75 5.32 13.75 16.50 17.50 Post-Sale Non-Discounted 15.75 6.18 13.75 17.50 19.50 Post-Sale Total Weekly Purchases 30.50 11.09 29.75 35.00 35.75

Inconclusively with H5a or H5b, the number of unique customers remainsunchanged in the Post-Sale period, as can be seen in Table 4.9. This finding is in contrast to both the prediction made by the brand loyalty/habit formation models (that total number of customers would increase post-sale) as well as the prediction made by the reference-dependence model (that total number of customers would decrease post-sale).

We complement these descriptive statistics with regression results estimating model 4.1. In this specification, 𝑦_𝑡 is now the total number of unique customers making a purchase at time t. As before, 𝑑 𝑢𝑟 𝑖𝑛𝑔 𝑠𝑎𝑙 𝑒_𝑡 and 𝑝 𝑜 𝑠𝑡 𝑠𝑎𝑙 𝑒_𝑡 are binary indicators of whether the purchase was made during the Sale or Post-Sale, respectively, and 𝑤 𝑒 𝑒 𝑘_𝑡is the number of the week of the experiment (1-10) and is intended to capture any time trends influencing the results. 𝜖_𝑡 is our error term, which we assume is uncorrelated with the regressors.

As observed in the Descriptive Analyses earlier, we find evidence in support of H3 - that total number of unique customers is significantly higher during the Sale period (𝛽 = 1.292, 𝑝 < 0.1). We further find that the total number of customers remains unchanged in the Post-Sale period (does not drop or increase significantly, compared to the Pre-Sale period, in contrast to our two hypotheses).

Table 4.10: Customer Composition During Sale and Post-Sale Periods Dependent variable:

Unique Customers

(1) (2) (3)

DuringSale 1.292^∗ 2.767^∗∗∗

(0.667) (0.855)

PostSale 0.695 3.998^∗∗

(1.231) (1.538)

week² −0.002 −0.014 −0.056^∗∗

(0.009) (0.020) (0.023)

Constant 5.301^∗∗∗ 5.741^∗∗∗ 5.420^∗∗∗

(0.461) (0.464) (0.444)

Observations 68 68 68

R² 0.057 0.007 0.147

Adjusted R² 0.028 -0.023 0.107

F Statistic 1.962 (df = 2; 65) 0.244 (df = 2; 65) 3.677^∗∗(df = 3; 64) Note: ^∗p<0.1;^∗∗p<0.05;^∗∗∗p<0.01, two-tailed test of hypothesis