Efficiency and Productivity Estimation with a Hierarchical Data Structure: An Aggregation Perspective

Repeated measurements on a subject of interest are statistically preferable than cross-sectional data due to confoundment of effect estimates in the latter. The confoundment is brought about due to between-subject heterogeneity which arises from the possibility that repeated measurements on the same subject tend to be more similar (as indicated by high correlation) as compared to measurements across different subjects. The method of hierarchical modelling entails varying coefficients by subject in order to account for the heterogeneity in carrying out causal inference. This dissertation unites hierarchical modelling with efficiency estimation by formulating a methodological research objective in the first paper. It verifies the potential of hierarchical modelling in efficiency aggregation by using hierarchical data. Further, in the second paper, the role of temporal land use and fertilizer as an input have been studied in determining the scope for sustainable intensification, with the use of hierarchical modelling. The third paper applies Stochastic Frontier Analysis for estimating the production frontier and technical efficiency with the aim of studying the elasticity of inputs. The modelling context as well as the results of the second and third paper are specific to paddy production in Bangladesh. The first paper is a comparison of two independent modelling approaches in the aggregation of technical efficiency scores. The first approach is an estimation of a stochastic frontier model at the lowest level of observation (a plot). Technical efficiency scores obtained at this level are aggregated to the next level of observation (a farm) by applying composite indices such as the arithmetic mean and its weighted variants. The second approach is the direct estimation of technical efficiency scores at the farm level using a hierarchical model. With Monte Carlo simulation, the paper concludes that while both approaches can preserve the ranking of the true efficiency scores, it is only the hierarchical model which accurately estimates the level of the true efficiency scores. The second paper is an empirical study of the potential of temporal land use and its interaction with fertilizer in bringing about sustainability in intensification as against the choice of keeping the plot fallow in paddy cultivation in Bangladesh. The question of whether fertilizer as an input, conditional on land use choice, is instrumental in ensuring sustainable intensification, is addressed with the application of hierarchical models. Specifically, the Random Intercept and Random Coefficients Model (with cross level interaction) have been used to conclude that potato cultivation in Rabi season increases paddy production in the succeeding Boro season and also enhances the effect of fertilizer as an input in driving paddy production. The third paper is an application of the Stochastic Frontier model to a large sample of plots which cultivate paddy in the immediate time span following the food price crisis of 2007-08. The estimation and inference indicated that since most of the plots operated close to the production frontier, there is a need to bring about a shift in the production frontier to increase production. Increased fertilizer and labour application is expected to bring gains in the quantity of output.

2021-04-21