We study behavioral responses to personal wealth taxes in Colombia. We utilize tax microdata from 1993 to 2016 linked with the leaked Panama Papers to investigate offshoring to the country’s key tax havens. We leverage variation from discrete jumps in tax liability and four major reforms to the wealth tax system, including changes in tax rates and duration, using bunching and difference-in-difference techniques. We find compelling evidence that taxpayers instantly reduce the wealth they declare in response to a wealth tax. Moreover, these effects can persist for years even after the wealth tax is no longer in place, providing the first evidence of a hysteresis effect for a temporary tax policy. The response is driven by misreporting items that authorities cannot cross-verify, such as overstating debt and understating non-third-party-reported business assets. Additionally, the wealthiest taxpayers respond to wealth tax increases by hiding assets in hard-to-track entities in tax havens.