Most of the growth in agricultural output in the last thirty years comes from increases in the efficiency with which both land and non-land inputs are used. Recent work calls for a better understanding of whether this efficiency, known as total factor productivity (TFP), contributes to a more sustainable food system. Key to this understanding is the documented phenomenon that, instead of saving lands, the introduction of technologies that improve agricultural productivity encourage cropland expansion. We extend the results of a recently published econometric model of cross-country cropland change and TFP growth to explore the extent to which improvements in technology were associated with lower greenhouse emissions from land conversion to agriculture as well as with lower land conversion pressures in biodiversity-rich biomes. We focus on the decade of 2001-2010, a period in which our sample of 70 countries (≈75% of global croplands) experienced net land contraction. Except in sub-Saharan Africa and South and East Asia, regional TFP growth was associated with regional land expansion, thus confirming the existence of Jevons paradox in most regions of the world. However, such expansion was more than offset by indirect land use effects stemming from increases in productivity somewhere else. These indirect effects are far from trivial. In the absence of TFP growth, our estimates suggest that ≈125 Mha would have been needed to satisfy demand, half of which are in the four most biodiverse biomes of the world; estimated land use emissions from the ensuing changes in land use range from a lower bound of 17 Gt CO2eq to an upper bound of 84 Gt CO2eq, depending on whether the expansion would have occurred on pasturelands or forest, in contrast to the ≈1 to 15 Gt CO2eq imputed to observed cropland expansion. Our projections of the land needed to satisfy projected growth in TFP per capita during 2018-2023 indicate that current rates of TFP growth are insufficient to prevent further land expansion, reversing in most cases the in-sample trends in land contraction observed during 2001-2010.