The topic of this paper has been motivated by the rising unemployment rate of low-skilled relative to high-skilled labour in Switzerland. Between 1991 and 2014, Switzerland experienced the highest relative increase in the low-skilled unemployment rate among all OECD countries. A natural culprit for this development is "globalization" as indicated by some mass layoffs in Switzerland and as commonly voiced in public debates all over the world. Our analysis, which is based on panel data covering the years 1991 to 2008 and approximately 33,000 individuals employed in the Swiss manufacturing sector, does not, however, confirm this presumption. We do not find strong evidence for a positive relationship between import competition and (low-skilled) individuals' likelihood of becoming unemployed.