Using administrative data on wealth, firm ownership structure, and migration in Sweden and Denmark, we document international migration patterns among the very wealthy, their impact on the economy, and how they respond to wealth taxation. We show that more than 20% of taxpayers liable to pay wealth tax are business-owners, and that the employment, investments, and value-added of these businesses are negatively affected when their owner migrates out of the country. Exploiting three large reforms, we then isolate the causal effect of wealth taxation on the international location choices of the wealthy. We find significant effects on out-migration flows from increases in the effective wealth tax. But, we also document that the overall level of these migration flows is remarkably small, with annual net-migration rates below .01%. As a result, we find that the aggregate economic effects of tax-induced migration are modest in Scandinavia: a one percentage point increase in the average wealth tax rate on the top 2% decreases the stock of wealthy taxpayers by at most 2% in the long run, and lead to a reduction of at most .03% in aggregate employment and at most .1% in aggregate value- added. Hence, our results suggest that trickle-down effects of tax-induced migration by the wealthy do exist, but that they are quantitatively small.