For a customer in a grocery store, the greater the number of purchases the longer the shopping path. On the other hand, the longer the shopping path the greater the number of goods to which the shopper is exposed and thus the greater the number of purchases made. A high degree of correlation between the path length and the number of purchases is envidence of both effects but how to understand which of these two effects is stronger or at least are they both significant? Assume that one can employ any required data on shopping paths and purchases.

  • $\begingroup$ I'd recommend taking a look at Hill's criteria for causation borrowed from epidemiology. Many of his criteria can help pinpoint the direction of causality: en.wikipedia.org/wiki/Bradford_Hill_criteria $\endgroup$ – StatsStudent Jan 9 at 1:40
  • $\begingroup$ @StatsStudent Thanks. Could you give an example how these criteria can be applied in my situation. $\endgroup$ – 8k14 Jan 15 at 6:18

You need to find an instrumental variable: something that definitely causes more or less wandering, but is not related to the unobservables, like intent, that lead the consumer to fill his shopping cart more. You can find many examples and explanations of IV analysis under that tag on CV.

None of the ideas below are particularly iron-clad since good instruments are hard to find, but perhaps they can inspire you to find something that actually works in your setting.

If you have variation in placement from a promotional campaign or a store reorganization, that could create exogenous variation in path length. One example might be when a product is taken off the shelf and placed on an end cap. If the consumer has to go somewhere unusual to find the product (because he cannot find it and has to wonder around or simply because it further/closer), that would create variation that is arguably random and leads to more/less incremental exposure for other products along the way. Using promotional relocations as an instrumental variable may work here for exposure to products that are not complements or substitutes for the promoted product and if the price discount is not big enough to alter the budget constraint in a way that leads to additional purchases.

Maybe you can use the handing out of samples in a similar manner if that is available in your data. The problem with that is that this might be correlated with being hungry, which could also lead to higher purchases. My grocery store hands out wine, beer, and even liquor on occasion (or will even sells you some to drink as you shop), which would be an even worse example.

Another kind of example is a consumer that buys milk. Milk is typically placed in the back of the store since the cooler needs to be connected to the AC system, so you could have additional exposure if you walk through to the back of the store. However, maybe the milk trips are also the big purchase trips, so this variation is problematic.

Staffing variation might also work if it is random (say someone calls in sick). If fewer staff makes it harder to find products and cause more wandering, that could work. On the other hand, fewer staff might also reduce purchases overall, so this could also be problematic.

  • $\begingroup$ Thank you. In your opinion, is using IV is the only way to answer my question? $\endgroup$ – 8k14 Jan 15 at 6:11
  • $\begingroup$ This is the usual approach without some sort of experimental variation. I am not aware of others. $\endgroup$ – Dimitriy V. Masterov Jan 15 at 6:48
  • $\begingroup$ When a dependent variable is potentially endogenous, people also look for a proxies that does not suffer from that problem. The most common approach is to lag the suspect variables by one or more periods. I don't think that can help in this setting. $\endgroup$ – Dimitriy V. Masterov Jan 15 at 17:23

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