Convergence in recessions

Growth theory and data teach us that, at least in developed countries, economies tend to converge in the long run: the dispersion across regions or nations of per capita income (or similar indicators) tends to decline. While this is a long term phenomenon, there is a priori no reason to believe this is a constant process.

Eldon Ball, Carlos San Juan and Camilo Ulloa study total factor productivity in agriculture across US states. While they indeed find a general trend towards convergence, it turns out that its speed is much faster during recessions. Why would this happen? If we follow Schumpeter, the worst firms should be dropping out during a recession, thereby relatively increasing TFP in the worst areas. And voilà, you have faster convergence. But only farm-level data would tell whether my conjecture is true.