Does posting caloric information change consumers' caloric consumption?

I just came across a study entitled Menu Labelling and Calories Purchased at Chain Restaurants by Krieger et al. The authors investigated whether displaying caloric information on menus altered customers' food and beverage choices. They took advantage of a new regulation that requires certain food outlers to display caloric information on their menus. In particular, they interviewed a large number of customers before the regulation was implemented, and a large number afterward, and then looked to see whether there was a change in the mean number of calories purchased per customer. They found that, after 18 months, mean calories purchased per customer had decreased by about 4% in chain restaurants and about 14% in coffee shops. From the perspective of getting customers to buy less calorically dense foods, these results are quite encouraging.

However, there is one obvious limitation to the study. The authors had absolutely no way of knowing (as they acknowledge at the end of the paper) whether customers compensated for their choices by eating more at other meals. For example, the typical customer might have looked at the menu in the coffee shop and chosen the lower calorie option, only to then eat an extra portion of food at dinner. For this reason, I find these kind of studies largely uninformative for evaluating whether such interventions can alter consumers' caloric consumption.