Decomposing technical change.

• Author: Gort, Michael

1. Introduction

   Within the conventional neoclassical framework, a distinction is sometimes made between product-augmenting and factor-augmenting technical change. A parallel distinction is commonly made between embodied and disembodied technical change with the former associated with factor, and the latter with product, augmentation. Disembodied change is commonly assumed to arise from increases in the stock of knowledge, independently of the characteristics of the inputs used, while embodied change relates to increases in the efficiency of inputs, that is, labor skills or the productivity of physical capital.

   Unfortunately, this distinction is ambiguous. Changes in the efficiency of the inputs used are usually accompanied - indeed made possible - by increases in knowledge. And conversely, increases in the stock of knowledge often favor some inputs more than others, including the capital goods of one vintage relative to those of another.

   Notwithstanding the ambiguity, the concept of embodiment has intuitive appeal and this partly explains the focus on decomposing the sources of technical change that followed Solow's [6] seminal paper. But by the late 1960s, a reader of the literature might have concluded that such decomposition was impossible. For with merely time series data on inputs and output, product-augmenting and factor-augmenting technical change are empirically indistinguishable.

   In an important paper, Hall [3] showed that with data on used equipment prices and the interest rate, embodied technical change and the deterioration function can, in principle, be calculated. However, the paucity of data on the price of used capital goods has allowed little progress in this direction. The new Longitudinal Research Database created by the U.S. Bureau of the Census now permits still another approach to the estimation of "embodied" technical change associated with capital, both physical and human. In addition, it casts light on a perplexing problem that has plagued econometric estimates of production relations based on changes in inputs and output as distinct from levels of both.

   This new body of information consists of time series and cross-section data for individual manufacturing plants for the period 1972 to 1986. The time series permit us to derive indexes of the vintage of capital for each plant. This, in turn, allows us to estimate the effects of vintage of capital on productivity from strictly cross-section data. And since these effects are estimated at a common point in time, temporal shifts in productivity divorced from vintage are excluded by definition.

   Moreover, we are also able to distinguish between "new" plants - that is, plants without endowments of capital accumulated in earlier periods - from "old" plants. The analysis of data for old plants allows the test of a hypothesis, and yields an explanation, of why estimates based on changes in inputs and output generally lead to very different coefficients from those based on levels of the variables. The latter is an issue with important policy implications given that most investment in developed economies takes the form of expansion - that is, changes in inputs - for existing (old) plants.

   The remainder of the paper is divided into six sections. In section II we present our principal model and the definitions of variables in our production function. Section III reports the estimates for technical change in the context of levels of inputs and output for new plants. Section IV discusses the implications of measuring production relations for changes in inputs and output as distinct from levels while section V presents estimates for old plants based on changes in the relevant variables. Section VI compares the results for new and old plants while section VII is a brief summary of principal conclusions.

2. Model for Measuring Technical Advance and Definition of Variables

   We start with a general model

   [Mathematical Expressions Omitted]

   Where [O.sub.[tau]] is output, [A.sub.[tau]] is a shift parameter that is assumed to affect the productivity of all vintages of capital and all labor skills symmetrically, [e.sup.a[tau]] is disembodied technical change at rate a, [L.sup.[tau]] is labor, [Q.sup.[tau]] is human capital, and [SYMBOL NOT CONVERTED] is a vector of investment streams.

   [Mathematical Expressions Omitted]

   Where [tau] is the vintage year in which investment is measured, and [gamma] is the age of the plant.

   As is commonly hypothesized, we expect each successive vintage of investment to be more productive than the last so that,

   [Mathematical Expressions Omitted]

   We next assume a standard production function approach of substituting an aggregate capital stock variable for the vector of investments and take due account of the effect of embodiment by measuring the average vintage of the stock. Accordingly, we have

   O = [Ae.sup.a[tau]] F [(K.sub.v.e.sup.kv], L, Q) (4)

   Where K is the sum of investments of various vintages, the subscript v is the weighted average vintage of the stock with weights based on the investment of each vintage relative to K, and [e.sup.kv] is an index of productivity enhancement at constant rate k from "embodied" effects of vintage (the subscripts of [tau] are omitted). The capital stock term of the production function, [K.sub.v.e.sup.kv], is thus converted into efficiency units based on average vintage.

   The resulting model differs in several respects from production functions that are commonly estimated. First, human capital (labor skills) enters as a separate argument in the production function rather than as an adjustment to the measure of labor input. Second, capital is composed of gross investment streams, rather than net investment, so that the effect of vintage (that is, obsolescence plus decay) is estimated within the framework of the model. In this respect, our approach accords with that of Prucha and Nadiri [5], though we do not follow them in their assumption that the depreciation rate is endogenous. It contrasts with the conventional method of inferring obsolescence and deterioration from assumed economic lives and decay functions.

   Our conceptual framework makes no distinction between the accumulation of knowledge and changes in the physical attributes of capital associated with vintage as long as new knowledge is uniquely related to vintage. Similarly, if new knowledge is uniquely related to labor skills, no distinction is made between the two. Changes in the shift parameter, [A.sub.[tau], disappear within a crosssection framework and only interplant variations in "disembodied" technical change remain.

   Differences across plants in blueprint technology, and in the knowledge associated with it, are almost certainly uniquely related to either labor skills or the vintage of physical capital. What, then, is there left of disembodiment in the context of a cross-section model? It appears that only the effects of organizational capital, largely in the form of firm-specific information, remain unaccounted.

   We next turn to a more detailed discussion of the variables in equation (4).

   Physical Capital and Vintage

   The stock of capital in equation (4) is the sum of deflated gross investments from the year following the birth of the plant to the year in which output is measured.(1) Obsolescence is then measured directly via the production function through estimates of the effect of vintage on output.

   The effects of vintage arise from obsolescence + (physical decay - maintenance outlays). If, however, as is plausible, maintenance outlays roughly offset the effects of physical decay at least on current production (if not also on earnings), the principal source of difference in the relative efficiency of capital of different vintages is obsolescence. The implied depreciation rate then, correctly measured, becomes roughly the dual of capital augmenting technical change.

   The foregoing indicates that the assumptions necessary to construct a net capital stock require implicitly a measure of embodied technical change of capital. And if physical decay roughly equals maintenance outlays, then obsolescence is all that needs to be measured to transform gross into net stocks.

   Vintage was measured as the weighted average of the years of the investment stream for each plant, with weights based on the ratio of the annual investment for each plant to its total investment over the relevant period. By definition, a higher average indicated more recent vintage. Thus vintage measured (inversely) the average age of physical assets.

   Since the productivity of an asset has a lower bound of zero, in principle, only non-retired assets should be included in the computation of average vintage. Otherwise, a systematic relation between the stock of retired assets and average vintage might lead, in the context of a production function, to distortions in the coefficients of both physical capital and vintage. However, since the period over which average vintage was computed was limited to 1973-86, retirements of assets from the relevant investment streams (as our tests showed) were not large enough to distort the estimates significantly and were, therefore, ignored.

   Excluded from the model is circulating capital (that is, inventories). This is justified since inventory accumulation is, at least partly, unintended and is also a function of expected future rather than merely current output.

   Labor and Human Capital

   Our labor variable was intended to approximate pure labor independently of human capital (labor quality) and was thus measured by the number of employees for each...