Do Age-Verification Bills Change Search Behavior? A Pre-Registered Synthetic Control Multiverse

Starting in January 2023, Louisiana and 17 other states passed laws requiring age verification for websites with substantial adult content. Using Google Trends data and a synthetic control design, we examine how these laws affect digital behavior across four dimensions: searches for compliant websites, non-compliant websites, VPNs, and adult content. Three months after the laws were passed, results show a 51\% decrease in searches for the main compliant platform, while searches increased for both non-compliant platform (48.1\%) and VPN services (23.6\%). Through multiverse analyses, we demonstrate the robustness of these findings to numerous model specifications. Our findings reveal that while regulations reduce traffic to compliant sites and likely decrease overall consumption, users adapt by shifting to providers without verification requirements. This approach provides valuable insights for policymakers considering similar legislative measures of digital content regulation. Our methodology offers a framework for real-time policy evaluation in contexts with staggered implementation.