Tobit estimation with unknown point of censoring with an application to milk-market participation in the Ethiopian highlands

Canadian Journal of Agricultural Economics;49(3): 293-311

Data augmentation is a powerful technique for estimating models with latent or missing data, but applications in agricultural economics have thus far been few. This paper showcases the technique in an application to data on milk market participation in the Ethiopian highlands. There, a key impediment to economic development is an apparently low rate of market participation. Consequently, economic interest centers on the 'locations' of non-participants in relation to the market and their 'reservation values' across covariates. These quantities are of policy interest because they provide measures of the additional inputs necessary in order for non-participants to enter the market. One quantity of primary interest is the minimum amount of surplus milk (the 'minimum efficient scale of operations') that the household must acquire before market participation becomes feasible. We estimate this quantity through routine application of data augmentation and Gibbs sampling applied to a random-censored Tobit regression. Incorporating random censoring affects markedly the marketable-surplus requirements of the household, but only slightly the covariates requirements estimates and, generally, leads to more plausible policy estimates than the estimates obtained from the zero censored formulation.