I have been unable to find one, yet my suspicion is that the proportion of citizens who smuggle can be very high, in Canada for example through cross-border shopping
Dear Alan, people would probably not be willing to admit that they smuggle, which may explain why it is difficult to find a survey (but I am certain you considered that!). I found this an interesting topic and did a brief search on Google Scholar, I however, did not check for the use of surveys. An interesting topic!
I've been working on research on the topic of cross-border shopping for a while. I checked my citations database and found 10 articles that deal with smuggling and/or contraband (see attached). Most of the articles are from Nordic countries. I published a paper in 2016 (see attached) that examined Canadian news coverage of cross-border shopping; there were a few stories, but it was not a dominant theme. Finally, I have another article under review that is based on 450+ interviews with cross-border shoppers. Reports of smuggling were very few – likely for reasons of social desirability, as mentioned by Linda. That being said, besides cigarettes and booze, certain pharmaceutical, homeopathic remedies, and muscle-enhancement offerings are certainly in the mix, in addition to bringing everyday goods over the border without claiming them. Best wishes with your research – I’d love to hear/read more!
Another article: "The archaeology of illegal and illicit economies" has a section on smuggling: https://s3.amazonaws.com/academia.edu.documents/32185115/annurev-anthro-092412-155452.pdf?AWSAccessKeyId=AKIAIWOWYYGZ2Y53UL3A&Expires=1516376449&Signature=9fAUxy3xR9kV2GIbKTt87nICIHk%3D&response-content-disposition=inline%3B%20filename%3DThe_Archaeology_of_Illegal_and_Illicit_E.pdf