In the context of growing societal demands for land-based products, crop production can be increased through expanding cropland or intensifying production on cultivated land. Intensification can allow sparing land for nature, but it can also drive further expansion of cropland, i.e. a rebound effect. Conversely, constraints on cropland expansion may induce intensification. We tested these hypotheses by investigating the bidirectional relationships between changes in cropland area and intensity, using a global cross-country panel dataset over 55 years, from 1961 to 2016. We used a cointegration approach with additional tests to disentangle long- and short-run causal relations between variables, and total factor productivity and yields as two measures of intensification. Over the long run we found support for the induced intensification thesis for low-income countries. In the short run, intensification resulted in a rebound effect in middle-income countries, which include many key agricultural producers strongly competitive in global agricultural commodity markets. This rebound effect manifested for commodities with high price-elasticity of demand, including rubber, flex crops (sugarcane, oil palm and soybean), and tropical fruits. Over the long run, strong rebound effects remained for key commodities such as flex crops and rubber. The intensification of staple cereals such as wheat and rice resulted in significant land sparing. Intensification in low-income countries, driven by increases in total factor productivity, was associated with a stronger rebound effect than yields increases. Agglomeration economies may drive yield increases for key tropical commodity crops. Our study design enables the analysis of other complex long- and short-run causal dynamics in land and social-ecological systems.