The gist: there is complementarity if you live near, but cannibalization if you live far.

The local average treatment effects models suggest that once induced to buy online, consumers who live near the retailer’s physical store tend to increase their offline spending and total sales by 47% (i.e., complementarity effects for nearby consumers). However, for consumers who live far away from the brick-and-mortar store, inducing them to buy online can backfire by reducing offline and total sales by approximately 5.7% for each additional kilometer of distance (i.e., cannibalization effects for distant consumers). Explorations of these mechanisms suggest that distant consumers who are induced to buy online may fail to return to shop in the offline store and purchase less experiential category products with a smaller basket size than other customers, thus leading to a negative net impact on the total sales

The study is a RCT using a loyalty program: the treatment group receives a promotion via SMS to buy in the online channel.