Large Midwestern Grocery Chain Price Randomization, First and Second Waves

2019-07-10

2020-03-10

Changes in sales to price changes.

First wave. In the first wave, test prices were reviewed every Wednesday, for 11 consecutive weeks. Candy, shredded cheese, other cheese, pasta, and pasta sauce received their first test prices on July 10, 2019; butter spreads, sliced cheese, snacking cheese, and facial tissue received theirs one week later. We do not have access to the pricing-solutions company’s proprietary code for generating test prices. However, the company explained its pricing algorithm to us at a high level, and we verified its key statistical properties with the data. Approximately, a product–store’s first test price was created by multiplying its last observational base price by a random number, drawn roughly uniformly from [0.8, 0.98] ∪ [1.02, 1.2]. From the second test price onward, the next test price was set by drawing a multiplier from a similar nearly uniform distribution, but with a point mass at 1, which meant that there was only a 64.0% chance of a price change in a given week. This data-generating process held throughout the first wave, with two caveats: First, the test-price multipliers were slightly negatively autocorrelated within product–store (-0.2), so prices would not become too extreme over time. Second, toward the end of the first wave (around weeks 7 and 8) and continuing into the second wave, the distribution of multipliers became more concentrated at the 0.8, 1, and 1.2 modes, so that price changes became more extreme and prices were held for longer.

Second wave. In the second wave, the retailer continued with the first wave’s data-generating process, but with one crucial difference: it introduced price optimization. Specifically, in the first week of the second wave, the retailer randomly relabeled 50 out of 82 experimental stores from “test” to “optimal” by category, and in each subsequent week, it randomly swapped the labels of three “optimal” and three “test” stores, also by category. The retailer then treated the “test” store–categories as before, but assigned the “optimal” store–categories prices that the pricing-solutions company believed would maximize profits. This process started on September 25, 2019, and lasted until March 10, 2020, when the World Health Organization declared COVID-19 a global pandemic, and the retailer’s prices were frozen in place because of emergency anti-price gouging laws. Moreover, in the second wave (as at the end of the first wave), experimental prices continued to be randomly held for longer, and they were more skewed toward high and low values. Specifically, in the second wave, the probability of changing a test price in a given pricing decision (calculated over all product–stores and weeks) was 38.5%. Similarly, the probability a store–product’s price was the maximum or minimum price (across all test stores) was 70.4%, whereas it was just 23.5% in the first wave.

computer

store--product--week (except where indicated)

No

The sample contains 116 stores, of which 82 receive test prices, and 100,474 product–stores, of which 26,213 receive test prices.

These test products at test stores received 389,890 random, in-store prices over the 35 weeks of experiments.

The unit of observation in our core analysis is a product variant (UPC)–store–date. After applying the filters we describe in the paper, our sample comprises 42,352,031 observations; of which 28,388,810 involve test products; 20,148,823 involve test products and test stores; and 2,263,428 involve test products, test stores, and test prices. This core sample contains all 1,314 products in the 9 test categories, of which 409 received test prices. These experimental products represent the lion’s share of sales, accounting for $117.5 million out of the $147.3 million in revenue associated with the test categories.