Measurement and Interpretation of Productivity (1979) / Chapter Skim
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Accounting for Intermediate Input: The Link Between Sectoral and Aggregate Measures of Productivity Growth
Accounting for Intermediate Input: The Link Between Sectoral and Aggregate Measures of Productivity Growth
Pages 318-333
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From page 318... ...
Accounting far Intermedlate Input: The Lluk Between Sectored and Aggregate Measures of Productlv~y Orowtb P~K H o0~0P An economies macro-economic o~ecdve ~ to maxlmlze aggregate output given supples of primal Actors of producdon.
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From page 319... ...
17) says: From a macroeconomic viewpoint, there are persuasive arguments for using real product estimates (i.e., real value added, in which real intermediate costs are deducted from the real value of total gross output)
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From page 320... ...
Moreover, should the restrictions prove inappropriate, a model excluding intermediate input maintains an incorrect description of not only producer behavior but technical change as well. PRODUCER BEHAVIOR As a general model, micro-economic theory requires a production function that includes among its arguments all factors of production, both primary and intermediate inputs.
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From page 321... ...
A supermarket manager can choose to have his own employee display frozen ice cream products in the frozen foods cabinet or he may contract with the raw materials supplier to have its delivery person display the product. The former is a direct labor cost to the supermarket; the latter is an expense related to intermediate input.
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From page 322... ...
Proposition 1 The rate of sectoral technical change derived from a model treating all inputs symmetrically is less than the corresponding rate resulting from a model maintaining value-added separability. The Hicks-neutrality maintains that technical change equally augments all inputs.
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From page 323... ...
. Proposition 3 Given estimates of sectoral technical change derived from a model excluding intermediate input, the correct measure of economy-wide productivity growth equals a weighted average of the sectoral rates of technical change with weights equal to the ratios of the value of each sector's net output (value added)
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From page 324... ...
Consequently, the output elasticities appearing in (2) can be characterized by factor income shares: ~ ln Xj P ki Kki = - = l k bln K,~j qjXj J k = 1,2, ·~.,m,
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From page 325... ...
~ Oil Xy ~ =,j _ ~L,j i (3) The rate of technical change ej for each sector can be expressed as the rate of growth of the corresponding sector's output less a weighted average of the rates of growth of capital, labor, and intermediate inputs into the sector.
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From page 326... ...
= ~ in Vj/8t. Under constant returns to scale and in competitive equilibrium, the implied rate of technical change for each sector j is defined as the rate of growth of the sector's net output less a weighted average of the rates of growth of the primary inputs ej*
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From page 327... ...
The appropriate macro-economic characterization of aggregate technical change begins with defining aggregate output as a proportion of all sectoral quantities of value added. The maximum value of aggregate ouput (^y)
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From page 328... ...
In contrast, since the sectoral model assuming value-added separability abstracts from all 3Under constant returns to scale, the elasticities with respect to all quantities of value added sum to minus unity; the corresponding value shares sum to unity. Similarly, the sum of the elasticities with respect to all components of capital and labor inputs and the sum of the corresponding value shares equal unity.
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From page 329... ...
A similar set of substitutions permits the rate of aggregate technical change E in (14) to be decomposed into terms identifying the transmission of advances in sectoral productivity through both inter-industry sales and direct deliveries to final demand.
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From page 330... ...
The weights are given by the ratios of the values of sectoral gross output to the value of aggregate output. The sum of these weights exceeds unity since each sector contributes to the rate of technical change for the aggregate economy through its deliveries to 'ooth final demand and intermediate demand.
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From page 331... ...
j J (21) The rate of aggregate technical change equals a weighted average of the sectoral rates of productivity growth where each rate is derived from a sectoral model maintaining value-added separability.5 4Note that an increase in ej does not necessarily imply that the intermediate input Xji will be more productive in sector i.
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From page 332... ...
J J J J (22) The appropriately weighted sum contribution of sectoral advances in technology to aggregate productivity growth is identical whether the sectoral rates of technical change are developed from models including or excluding intermediate input.
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From page 333... ...
(1957) Technical change and the aggregate production function.
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