ON THE RELATION BETWEEN GROSS OUTPUT– AND VALUE ADDED–BASED PRODUCTIVITY MEASURES: THE IMPORTANCE OF THE DOMAR FACTOR

In this paper I consider the relation between gross output– and value added–based total factor productivity (TFP) measures. It appears that, without any (micro-)economic theory being required, a conditional relationship between TFP indices can be derived, in which the Domar factor plays an important role. At the same time it turns out that gross output– and value added–based TFP indicators (difference-type measures) always coincide. In the Divisia index framework and maintaining the classical assumptions (profit maximization and a production technology that exhibits globally constant returns to scale), it appears that both TFP indices measure technological change, albeit in a dual way. In establishing this result, no separability assumptions are involved. Both indices are in general path-dependent. Path independence of the gross output–based TFP index requires that the technology exhibit Hicks input neutrality, whereas path independence of the value added–based TFP index requires Hicks value-added neutrality. These two concepts of neutrality are, however, not dual.

[1]  B. Balk.  Divisia price and quantity indices: 80 years after , 2005 .

[2]  Alice Orcutt Nakamura,et al.  Index Number Concepts, Measures and Decompositions of Productivity Growth , 2003 .

[3]  Pirkko Aulin-Ahmavaara.  The Sna93 Values as a Consistent Framework for Productivity Measurement: Unsolved Issues , 2003 .

[4]  B. Balk,et al.  Industrial Price, Quantity, and Productivity Indices: The Micro-Economic Theory and an Application , 1998 .

[5]  G. Benston,et al.  The Residual: On Monitoring and Benchmarking Firms, Industries, and Economies with Respect to Productivity , 1997 .

[6]  B. Balk.  Axiomatic Price Index Theory: A Survey , 1995 .

[7]  D. Primont,et al.  Multi-Output Production and Duality: Theory and Applications , 1994 .

[8]  Frank M. Gollop.  MODELING AGGREGATE PRODUCTIVITY GROWTH: THE IMPORTANCE OF INTERSECTORAL TRANSFER PRICES AND INTERNATIONAL TRADE , 1987 .

[9]  L. Törnqvist,et al.  How Should Relative Changes be Measured , 1985 .

[10]  Thomas G. Cowing,et al.  Productivity Measurement in Regulated Industries , 1981 .

[11]  W. Diewert.  Superlative Index Numbers and Consistency in Aggregation , 1978 .

[12]  Kazuo Sato.  The Meaning and Measurement of the Real Value Added Index , 1976 .

[13]  C. Hulten.  Divisia Index Numbers , 1973 .

[14]  Z. Griliches,et al.  The Explanation of Productivity Change , 1967 .

[15]  E. Domar,et al.  ON THE MEASUREMENT OF TECHNOLOGICAL CHANGE , 1961 .

[16]  R. Solow.  TECHNICAL CHANGE AND THE AGGREGATE PRODUCTION FUNCTION , 1957 .

[17]  I. Fisher,et al.  The Mathematical Problem of the Price Index. , 1937 .

[18]  W. Diewert,et al.  Index Number Theory Using Differences Rather Than Ratios , 2005 .

[19]  Bert M. Balk,et al.  Industrial Price, Quantity, and Productivity Indices , 1998 .

[20]  G. Lorenzen.  Konsistent addierbare relative Änderungen , 1990 .

[21]  M. Slade.  Value-Added Total-Factor-Productivity Measurement: A Monte-Carlo Assessment , 1988 .

[22]  Wolfgang Eichhorn,et al.  Measurement in economics : theory and applications of economic indices , 1988 .

[23]  W. Diewert.  Hick's Aggregation Theorem and the Existence of a Real Value Added Function , 1978 .

[24]  D. McFadden,et al.  Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production , 1978 .

[25]  Yrjö Vartia.  Relative changes and index numbers , 1976 .