Spatiotemporal analysis of Korean ginseng farm productivity

The past two decades has seen new methodological debates on the identification of production function. Olley and Pakes (J Polit Econ 101(6):1149–1164, 1996), Levinsohn and Petrin (Rev Econ Stud 70(2):317–340, 2003), and Ackerberg et al. (Econometrica 83(6):2411–2451, 2015) introduced nonparametric approaches to control for the unobserved productivity in the estimation of production function, which requires the availability of panel data. There has been an another body of the literature that argued that models that are typically estimated on the basis of panel data can also be identified with repeated cross-sections under certain conditions (Verbeek and Vella, 2005). The objective of this paper is two-fold. First, built on the insight of Verbeek and Vella (2005), this paper proposes a new approach to estimate the nonparametric control function based on repeated cross-sections. This is important because in many studies there is a lack of panel data where agents are followed over time, while repeated cross-sections may be available. Second, using cross-sections of Korean ginseng farms over 2006 to 2013, we apply our method to examine the evolution of farm-level productivity over time and across major production regions. Comparing our method with the pooled OLS regressions, the results show that the materials input coefficients are underestimated in the OLS regressions, which is consistent with the data where farms in the large ginseng production regions use relatively less materials than those in the other regions.