Aggregation issues in the estimation of linear programming productivity measures

This paper demonstrates the sensitivity of the linear programming approach in the estimation of productivity measures in the primal framework. Specifically, the sensitivity to the number of constraints (level of dis-aggregation) and imposition of returns to scale constraints is evaluated. Further, the shadow or dual values are recovered from the linear program and compared to the market prices used in the ideal Fisher index approach. Empirical application to U.S. state-level time series data from 1960-2004 reveal productivity change decreases with increases in the number of constraints. Divergence in productivity measures is observed due to the choice of method imposed, various levels of commodity/input aggregation, and technology assumptions. Due to the piecewise linear approximation of the nonparametric programming approach, the shadow share-weights are skewed leading to the difference in the productivity measures due to aggregation.