Agricultural Total Factor Productivity (TFP) Convergence in the United States and the Role of Patents in TFP Growth

This study examines long-run convergence in U.S. state-level agricultural total factor productivity (TFP) and investigates the role of patent-based technological knowledge in explaining persistent productivity differences across states. Using annual agricultural TFP data for 48 contiguous U.S. states from 1960 to 2015, we assess convergence dynamics through σ-convergence tests and the club convergence approach proposed by Phillips and Sul (2007). We then use a two-way fixed effects (TWFE) panel framework to examine whether patent-based knowledge stocks are associated with state-level agricultural TFP. Patent stocks are constructed for six agricultural technology subsectors under alternative assumptions regarding knowledge depreciation and lag structures. The results indicate that U.S. agricultural TFP does not converge toward a common steady state but instead exhibits multiple convergence clubs, suggesting persistent heterogeneity in long-run productivity paths across states. Patent-based knowledge accumulation also displays substantial sectoral heterogeneity. Plants, research tools, animal health, and machinery patent stocks are positively associated with agricultural TFP across most specifications, whereas fertilizer-related patent stocks are negatively associated. These patterns remain broadly robust across alternative constructions of the patent stock. Overall, the findings highlight the importance of technological heterogeneity in long-run agricultural productivity and suggest that accumulated patent-based technological knowledge is associated with agricultural productivity in distinct ways across innovation sectors.