Smallholders Are Not the Same: Under the Hood of Kosovo Agriculture

Economists and policy makers are interested in producers' responses to policies in order to achieve some national or sectoral objectives, e.g., growth, employment, food security. The way producers respond to policy depends on their production function. If producers do not have homogenous production function, policy responses will be heterogeneous. We use the underlying functional relationship to derive homogenous groupings. The paper employs finite regression mixture models to specify and estimate farm groups with regard to pre-specified functional relationship. The proposed approach is illustrated with regard to the aggregate production function of Kosovo agriculture, characterised by high prevalence of small farmers. The results point out to two farm clusters. The first one extracts more output from labour and intermediate consumption. The second one makes a better use of land. Perhaps, surprisingly, both clusters appear quite similar in terms of their stock of production inputs. Cluster 1 however appears to be more specialised. We can conclude that in Kosovo agriculture appearances and size are not primary determinants of productivity.

Mixture regression for longitudinal data based on joint mean-covariance model

In the process of modeling longitudinal data, we focus on the case that the studied population is comprised of different groups of individuals and individuals within the same group share the similar kind of mean progression trajectories, where finite mixture models (FMM) are often used to address this kind of unobserved heterogeneity in terms of mean. Existing methods, such as parametric and semiparametric mixture regression, usually model the mean in each subpopulation with assumption that observations sharing a common trajectory are independent or their covariance structure is pre-specified, but less research considers modeling of covariance structures while accounting for heterogeneity. In this paper, we introduce a joint model which models the mean and covariance structures simultaneously in a finite normal mixture regression, demonstrating how important the within-subject correlation is in clustering longitudinal data. Model parameters are estimated with an iteratively re-weighted least squares EM algorithm (IRLS-EM). Our estimators are shown to be consistent and asymptotically normal. We can identify different mean trajectories and covariance structures in all clusters. Simulations show that the proposed method performs well and gives more accurate clustering results by introducing covariance modeling. Real data analysis is also used to illustrate the usefulness of the proposed method, and it presents good performance in clustering COVID-19 deaths for European countries in terms of progression trajectory.