Dynamic Luenberger Productivity Measures

The economics literature on efficiency has produced a wide range of productivity growth measures. The introduction of the directional distance function has led to the development of Luenberger productivity growth measures, either based directly on the static directional distance function or on its dual representation through static profit or cost function. However, currently available productivity measures including Luenberger measures generally ignore the costs of adjustment of quasi-fixed inputs like labor and capital to their long-run levels and the time interdependence of production decisions. Doing so is essential when analyzing productivity growth and its decomposition. Methodology This paper develops dynamic Luenberger productivity growth measures that are based on the dynamic directional distance function and intertemporal cost minimization. The directional distance function and the dynamic long-run cost function represent an adjustment cost technology in order to account for the presence of quasi-fixed factors of production. The Luenberger productivity growth measures are decomposed to identify the contribution of efficiency growth, scale, technical change, and identify impact the quasi-fixed factor disequilibrium. A quadratic specification is chosen for the dynamic directional distance function and the dynamic long-run cost function. The functions are estimated parametrically using stochastic frontier analysis. The dynamic directional distance function is estimated under a CRS and VRS assumption, to disentangle the scale contribution to dynamic TFP growth. Data The application focuses on a sample of Dutch dairy farms over the period 1995-2005. The dataset is an unbalanced panel that contains 2,614 observations on 639 farms that, on average, stay in the sample during 4 years. The model distinguishes one output, two variable inputs, two quasi-fixed inputs and two fixed inputs. Output is defined as a farm‘s total output and includes milk, livestock and livestock products, crops and crop products and other output. The two variable inputs are variable costs other than feed and feed expenses. Variable costs other than feed is an aggregate input that includes veterinary expenses, energy, contract work, crop-specific costs and other variable input costs. Breeding livestock is considered as a quasi-fixed input. Machinery and buildings are aggregated into one quasifixed input. Total utilized agricultural area, measured in hectares, and labor, which is mainly composed of family labor and measured in annual working units (AWU), are assumed to be fixed inputs. Country-level price indices are taken from Eurostat‘s. Netputs measured in monetary values are defined as implicit quantity indices by computing the ratio of value to its corresponding Tornqvist price index. The rental cost price of capital is defined as the sum of the interest rate plus the rate of depreciation. Results The application of the Luenberger productivity growth measures on panel data of Dutch dairy farms shows that productivity growth has been negative. The growth measures based on the dynamic directional distance function and the dynamic cost function are similar in size.