From the excellent Doug Irwin:
Do trade reforms that significantly reduce import barriers lead to faster economic growth? In the twenty-five years since Rodríguez and Rodrik’s (2000) critical survey of empirical work on this question, new research has tried to overcome the various methodological problems that have plagued previous attempts to provide a convincing answer. I examine three strands of recent work on this issue: cross-country regressions focusing on within-country growth, synthetic control methods on specific reform episodes, and empirical country studies looking at the channels through which lower trade barriers may increase productivity. A consistent finding is that trade reforms have had a positive impact on economic growth, on average, although the effect is heterogeneous across countries. Overall, these research findings should temper some of the previous agnosticism about the empirical link between trade reform and economic performance.
Here is my much earlier CWT with Doug Irwin.
