Frequentist and Bayesian Methods for Mixed Discrete and Continuous Outcomes with Selection, Heteroscedasticity and Lagged Effects

Abstract

Farmers in Sub-Saharan Africa have lower agricultural technology adoption rates compared to the rest of the world. Production risk is one of the inhibiting factors of improved technology adoption. Quantifying this effect on adoption is a challenging task due to the endogenous effect of the technology on yield. We quantify this effect through lagged crop yield and lagged crop variance by developing two models for mixed discrete and continuous outcomes while accounting for endogenous effect of technology on yield. We use maximum likelihood method for the estimation in Chapter 1 and bayesian estimation in Chapter 2. The first model does not include the lagged variance in the adoption equation since variance is constant at the household level. In this model 1, we quantify the effect of past season yield on improved corn seed use in future seasons while addressing the impact of the seed variety on yield. We develop a maximum likelihood method that addresses the fact that farmers self-select into a technology resulting in its effect on yield being endogenous. The method is unique since it models both lagged and endogenous effects in correlated discrete and continuous outcomes simultaneously. Due to the presence of the lagged effect in a three year dataset, we also propose a solution to the initial conditions problem and demonstrate with simulations its effectiveness. We use survey longitudinal data collected from Kenyan corn farmers for three years. Our results indicate that higher past season yield increased the likelihood of adoption in future seasons. The simulation and empirical studies indicate that ignoring the self selection of improved seed use biases the results; we obtain a different sign in the covariance. In model 2, we extend model 1 above to include household specific variance and lagged variance in the technology adoption model. The results showed that variance was household specific and that the lagged corn yield variance negatively affected the probability of adoption in line with the risk aversion behavior of farmers. However, the lagged crop yield was no longer a significant determinant of improved corn seed adoption in model 2. We also found the evidence that improved seed use was endogenous and significantly increased the corn yield. Comparison of the two models using likelihood and BIC also confirmed that model 2 specification was more robust than model 1. Finally, using non-informative priors we confirmed that the maximum likelihood estimates and bayesian estimates were virtually identical.