Families originally living in public housing were assigned housing vouchers by lottery, encouraging moves to neighborhoods with lower poverty rates. Although we had hypothesized that reading and math test scores would be higher among children in families offered vouchers (with larger effects among younger children), the results show no significant effects on test scores for any age group among more than 5,000 children aged six to 20 in 2002 who were assessed four to seven years after randomization. Program impacts on school environments were considerably smaller than impacts on neighborhoods, suggesting that achievement-related benefits from improved neighborhood environments alone are small. (Contains 9 tables, 1 figure and 18 footnotes.)