### Abstract

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.

Original language | English |
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Title of host publication | North American Productivity Workshop, Houston, 6-9 June 2012 |

Place of Publication | Houston, Texas |

Pages | 149-150 |

Publication status | Published - 2012 |

Event | Proceedings North American Productivity Workshop - Duration: 6 Jun 2012 → 9 Jun 2012 |

### Workshop

Workshop | Proceedings North American Productivity Workshop |
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Period | 6/06/12 → 9/06/12 |

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## Cite this

Oude Lansink, A. G. J. M., Serra, T., & Stefanou, S. E. (2012). Dynamic Luenberger Productivity Measures. In

*North American Productivity Workshop, Houston, 6-9 June 2012*(pp. 149-150).