To reduce deforestation rates in the Amazon forest, Brazil established in the period 2004-2010 conservation zones covering an area larger than Germany.  In the same period, Brazil experienced a large reduction in deforestation rates. We build a spatial economics model of land use, with endogenous location of conservation zones and imperfect enforcement, to predict the effects of the policy. By combining satellite data on deforestation with data on the location and timing of the conservation zones, we provide spatial regression discontinuity estimates and difference-in-difference estimates indicating that the policy cannot explain the large reduction in deforestation rates. Consistent with the theory, the reason is that the zones are located in areas where agricultural production is likely to be unprofitable. We also provide evidence that zones reduce deforestation if the incentives for municipalities to reduce deforestation are high, consistent with the enforcement predictions from the model. Our findings point to the need for other explanations than the conservation zones to explain the sharp decline in deforestation rates in the Brazilian Amazon since 2004. Joint with Liana O. Anderson (CEMADEN/Oxford), Samantha De Martino (Sussex), Karlygash Kuralbayeva (Grantham) and Andre Lima (Maryland).