We develop a simple model of value added tax (VAT) compliance, and estimate it using widely available national accounts data to learn about compliance in countries where little is currently known. International border controls improve VAT compliance, generating a correlation between imports and aggregate VAT revenues that is informative about domestic noncompliance. Estimates suggest that revenue lost due to domestic non-compliance is large, particularly in countries with low perceived institutional quality. We analyze how our estimates are related to institutional differences among countries, and discuss the implications for tax policy.