Accounting for Growth with New Inputs: Theory and Evidence

by Robert C. Feenstra, James R. Markusen, William Zeile
Accounting for Growth with New Inputs: Theory and Evidence
Robert C. Feenstra, James R. Markusen, William Zeile
The American Economic Review
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Accounting for Growth with New Inputs: Theory and Evidence

Since the work of Robert M. Solow (19571, it has been known that technological change accounts for a significant portion of GNP growth in industrialized economies. This technological change has been measured either by the estimated time trend in regres- sions of aggregate output on inputs or by indexes of total factor productivity. Since under either method productivity is measured as a residual, it incorporates all fac- tors that influence GNP growth other than the increase in measured inputs. Despite various refinements to the measurement of total factor productivity, there still is no convincing explanation for its source (see Dale W. Jorgenson and Zvi Griliches, 1967; Solow, 1988).

Recent literature has suggested a poten- tial source of productivity gains: the creation of new inputs under monopolistic competition. Wilfred Ethier (1982) has ar- gued that the development of new interme- diate inputs leads to greater specialization in the use of resources and to higher pro- ductivity (see also Markusen, 1989). Subse- quent authors, including Paul M. Romer (1990) and Gene Grossman and Elhanan Helpman (19911, have examined models in which continuous growth is made possible by the creation of new inputs. Romer (1987) has considered the form of the aggregate

* Feenstra: Department of Economics, University of California, Davis, CA 95616; Markusen: Department of Economics. University of Colorado, Boulder, CO 80309; Zeile: Bureau of Economic Analysis, U.S. Department of Commerce, 1401 K Street, N.W., Washington, DC 20230. Views expressed in this paper are those of the authors and should not be attributed to the Department of Commerce. This paper originated with discussions on the no. 4 and no. 9 buses in Jerusalem, while the first two authors were Visiting Fellows at the Institute for Advanced Studies. The authors thank the Hebrew University for support and the Egged Bus Company for generously providing so much time. if not seats.

production function in such an economy and has argued that conventional growth accounting, assuming constant returns to scale, may be incorrect.

In this paper we shall examine how to account for growth when new inputs are being created. In particular, we are inter- ested in obtaining a decomposition of growth into that due to a higher quantity of existing inputs, and that due to a greater range of inputs. In Section I, we show how this de- composition can be obtained for a constant- elasticity-of-substitution (CES) production function, obtaining an exact quantity index in the presence of new inputs. In Section I1 we examine the CES cost function, and show how an implicit quantity index is con- structed. In Section 111 we consider an em- pirical application to the productivity growth of industries within the major business groups (chaebol) of South Korea. We find that productivity is significantly correlated with the entry of new input-producing firms into the chaebol, as expected from our theo- retical results.

I. Production Function

We shall consider a CES production function:

where xi is the quantity of input i = 1,.. .,M, x =(x ,,...,x,) denotes the vector of inputs, and y is the output. The parameter 8 is related to the elasticity of substitution u by u = 1/(1-8). We shall denote the prices of the inputs as pi > 0 and suppose that the quantities x, > 0 are cost-minimizing for these prices and output y.

We will suppose that the range of inputs is expanding over time, and let M, denote the number of inputs available in period t = 0,1, with Mo IMI. Then x, and p, are MI-dimensional vectors, where x, > 0 is cost-minimizing for prices p, > 0. We are interested in comparing the outputs f(x,, M,) obtained with the full range of period-1 inputs, to f(xl, Mo) obtained with the artificially restricted range M,. The fol- lowing result is established in Feenstra and Markusen (1991).



MI I Mfl

This result shows that the outputs obtained with the ranges of inputs M, and M, are related by the factor A'/' 21. This vari- able is endogenously determined by the cost-minimizing input choices of the firm. It can be easily measured as the ratio of expenditure on the full and restricted set of inputs at the common period-1 prices, raised to the 1/6 power. As 9 becomes smaller then the new inputs are less close substi- tutes for existing ones, leading to a larger increase in output.

To show how Proposition 1 can be used

to obtain a decomposition of the growth in

output, write the ratio of outputs in the two

periods as functions with the same number of inputs, where the inputs x, and xo are cost-mini- mizing for the prices p, and p,, respectively. Then we can use the formula of Kazuo Sato (1976) and Yrjo 0. Vartia (1976) to express f(x,, Mo)/ f(x,, Mo) as an exact quantity index, denoted by Q(x,, po,xl, p,; M0 The formula for this quantity index is


Q(~O,P~,~~,P~;n (xli /xO,)~'.



This is a geometric mean of the quantity ratios for each input, where the weights wi are logarithmic averages of the cost shares sir in the two periods, as follows:

As discussed by W. Erwin Diewert (1978 appendix 21, the quantity index Q(x,, po,xl,pl; M,) will show similar behavior over time even if simpler weights w, are used, such as wi =(so;+ sli)/2 which corre- sponds to a translog index. The main point of our results is that, if we multiply this index by the factor A'/', we then obtain an exact quantity index which takes into account the new inputs.

Defining total factor productivity (TFP) as the difference between the growth in outputs and an index of inputs, we can use

(2) and (3) to write

The first line of (3) is an identity, and the second line is obtained from Proposition 1. To obtain the third line, we note that f(xl, M,)/f(x,, Mo) is the ratio of two CES The expression in the final line of (4) equals the expenditure on new inputs relative to all inputs, and the approximation holds so long as this ratio is small. This result shows that total factor productivity should be correlated with the share of expenditure on new inputs available to a firm or industry.

Our results can be readily extended to the case in which some inputs are disappearing, while others are new (Feenstra, 1991). The results can also be extended to an economy-wide GNP function, in which there are many sectors using intermediate inputs whose ranges change over time (Feenstra and Markusen, 1991). We shall discuss only one extension here, and that is the measurement of total factor productivity using an implicit quantity index. To moti- vate this, suppose that a new input added in period 1 is a perfect substitute for the exist- ing inputs, meaning that 8 = 1 in the pro- duction function (1). Intuitively, we would not expect this new input to result in any productivity gain. However, if a positive amount is purchased by the firm, then a positive level of TFP would be measured in (4). This undesirable result will not appear when we instead compute the price index of inputs and use this index to deflate nominal expenditure, obtaining an implicit quantity index. The price index for the inputs is obtained from the CES cost function, which we turn to next.

11. Cost Function

The CES unit-cost function correspond- ing to (1) is


c(pl, M,) = c(pl, ~~)h-('-@)/@

where (1 -8)/8 = l/(a -1).

Thus, as inputs expand from Mo to MI, unit costs fall by the factor A-('-@)/@ -< 1. If the new inputs are perfect substitutes for exist- ing inputs, so that 8 = 1, then unit costs would not be reduced at all from their in- troduction.

An exact price index which takes into account the new inputs can be obtained from Proposition 2 as


is the Sato-Vartia formula for the exact CES price index when the number of inputs is fixed at Mo. We can use this index to define the implicit quantity index of inputs as

where E, denotes total expenditure over all inputs available in period t = 0,l.

In contrast to (31, let us define total factor productivity as the difference between the growth in outputs and the implicit quantity index. In many applications, this definition will be closest to the actual method used, and this method for treating new inputs has been recommended by Diewert (1980 pp. 498-501). Then, using (6) and the fact that expenditure equals E, = y,c(p,, MI),we obtain:

As above, we shall let Mo IM, denote the number of inputs in the two periods, and suppose that x, > 0 is cost-minimizing for prices p, > 0. Defining A as in (21, we are interested in comparing the unit costs c(pl, M,) obtained with the full range of period-1 inputs to c(p,, Mo) obtained with the restricted range Mo. The following re- sult is established in Feenstra (1991).

In comparison with (41, we see that total factor productivity is again correlated with the share of expenditure on new inputs, but now with a coefficient equal to (1 -f3)/0. If the new inputs are perfect substitutes for existing ones, so that 6 = 1, then both TFP and its correlation with expenditure on new inputs is zero. Aside from this extreme case, we expect to find a positive relationship between TFP and the expenditure on new inputs available to a firm or industry, as we examine next for a sample of Korean industries.

111. Korean Business Groups and Industry Productivity

To apply our theoretical results, we need to observe new inputs provided to a firm or group of firms. This information was avail- able to us for business groups (chaebol) within the Korean economy. Each group is characterized by the central control of member firms through mutual shareholding or direct family ownership. In addition, each chaebol is characterized by strong vertical integration (Zeile, 1991a). We can therefore expect that a new member firm producing an intermediate input will supply that prod- uct to other member firms in the same chaebol. Provided that this new product is somewhat differentiated from other available inputs, it should provide a boost to the total factor productivity of the purchasing firms. For the chaebol as a whole, the final line of (7) could be measured as the sales of new input-producing firms in a chaebol, rel- ative to the total purchases of intermediates by firms in that group. We shall discuss below how this measure, called GNEW, was calculated for each business group.

Our theoretical results imply that GNEW should be correlated with TFP growth within each group. However, measures of TFP were only available at the industry level (Zeile, 1991b). We therefore took the variable GNEW and transformed it into a measure of the new intermediate inputs available to each industry, called NEW; the details of this transformation are also discussed be- low. We shall then test for the correlation between NEW and TFP growth across the industries.

We began with data on the member firms of the 45 business groups listed among Ko- rea's top 50 chaebol in both 1983 and 1986.' New member firms of the 45 chaebol are identified as firms that are listed as mem- bers of a given group in 1986 but not in 1983. In accordance with its assigned Ko- rean SIC code, each new member firm has been classified as a producer of either inter- mediate goods or final goods, using infor- mation from the Korean input-output tables. Then. the total value of sales in 1986 for all of the new group-member firms pro- ducing intermediate goods was calculated for each of the 45 chaebol. This figure is taken to represent the supply of new inter- mediate inputs to the member firms of the chaebol.

Next, the data on sales minus value added for the manufacturing firms were totaled for each of the 45 chaebol. The resulting figure is taken to represent the demand for intermediate inputs by the manufacturing member firms of the chaebol. The following ratio was calculated for each of the 45 busi- ness groups: GNEW =(1986 sales of all new firms producing intermediate inputs)/(sales minus value added in 1986 for all manufac-

'we draw on the data base of member firms of the top 50 chaebol in 1983 and 1986, constructed from Korean language sources at the Research Program in East Asian Business and Development (EABAD), In- stitute of Governmental Affairs, U.C. Davis.

turing firms). This ratio is interpreted as the supply of new intermediate inputs to the group relative to the demand for intermedi- ate inputs by the group's manufacturing firms, or the final line of (7).

Finally, to transform this measure to the 52 manufacturing industries for which we have estimates of TFP growth, the share of each industry's sales accounted for by each group was calculated for 1986. For example, special industrial machinery (Korean SIC 3824) is dominated by the Daewoo group, whose firms account for 60 percent of the 1986 industry sales. The electronic equip- ment and parts industry (Korean SIC 3832

+3834) has 35 percent of its 1986 sales attributable to firms in the Samsung chaebol, and 25 percent attributable to firms in the Lucky Goldstar group, with much smaller shares from other chaebol. All these shares can be arranged in a 52 x 45 matrix2 The 45 X 1 vector GNEW was premultiplied by the 52x45 share matrix, yielding the 52x1 vector NEW, our measure of new intermediate inputs for the 52 manufactur- ing industries (expressed in percentages). This will be the principal variable of interest used to explain TFP growth by industry.

Other control variables used in the regressions are described as follow^:^ (i) devi- ation of industry growth rate during 1983-1986 from its long-term trend, which is measured as the difference between the average annual rate of growth in industry output for 1983-1986 and the average for 1973-1986; (ii) the 1983 industry ratio of capital to labor; (iii) the 1983 industry ratio of imports to total consumption; and (iv) the 1983 ratio of research and development ex- penditures to industry sales.

The regression results are shown in Table 1, where the dependent variable is TFP percentage growth over 1983-1986 by in- dustry. In all the regressions, the deviation of output growth from its long-term trend is

2~otethat the rows of this matrix may sum to less than unity, as when some sales for an industry are accounted for by firms who were not among the top 50 chaebol in both 1983 and 1986.

'~hese data and a description of sources are avail- able from the authors upon request.




Variable (i) (ii) (iii) (iv) (v)
Constant 1.06 1.19' 1.11 1.66a 1.36'
  (1.33) (1.78) (1.66) (3.27) (2.07)
Growth 0.40" 0.40a 0.40a 0.39a 0.39=
deviation (10.28) (10.38) (10.05) (9.93) (9.84)

Imports/ 0.056' 0.059~ consumption (1.93) (2.14)

R&D 0.21 0.80 0.90 expenditure (0.31) (1.26) (1.40)

NEW inputs 0.33~ 0.35b 0.24 0.26'

(2.06) (2.19) (1.56) (1.68)

R2: 0.680 0.686 0.661 0.657 0.651

N: 52 52 52 52 52

Notes: Numbers in parentheses are t statistics.

"Significant at the 1-percent level.

'significant at the 5-percent level.

'Significant at the 10-percent level.

an important explanatory variable and can reflect the degree of capacity utilization in each industry. Provided that this variable is included, then the estimated effect of NEW inputs is also significant in most cases, de- pending on what other explanatory vari- ables are used. It is noteworthy that the NEW input variable is more significant than the R&D expenditures within each industry in explaining TFP growth (see especially the first regression). However, in current work over a longer time period (1972-1985) we have found that R&D expenditures do ac- count for a significant part of TFP growth, particularly when the R&D expenditures embodied in intermediate inputs are included.

Using our theoretical result in (71, we can interpret the regression coefficient of about

0.33 on the NEW inputs in terms of an elasticity of substitution between inputs. Since (1 -8)/8 = l/(a -11, the implied elasticity is cr = 4, which appears to be a quite reasonable estimate of the substitu- tion between new inputs and existing ones.

The contribution of the new inputs is fur- ther indicated by considering examples in our data of industries with significant pro- ductivity growth and the identity of new firms entering the corresponding chaebol.

Thus, the electronic parts and equipment industry has 25 percent of its 1986 sales accounted for by firms in the Lucky Goldstar group. Within this group, there were a number of new entrants between 1983 and 1986 producing intermediate in- puts useful to the electronic parts indus- try. These new firms (and their industry name) include Goldstar Micronix (electronic tubes), Lucky DC Silicon (semicon- ductors), Goldstar Fiber Optics (electrical wire), Sungyo Company (resistors), and Kukje Electrical Wire (electrical wire). The first three of these firms were established in 1983 or 1984, while the latter two were established at earlier dates but acquired by the Lucky Goldstar group between 1983 and 1986. The potential contribution of these firms to industry productivity is reflected by our regression results.

As a second example, the special indus- trial machinery industry is dominated by the Daewoo group, and within this group there were three firms acquired between 1983 and 1986 whose sales of intermediates could plausibly contribute to industry productivity: Orion Electric (electronic tubes), Daewoo Electrical Components (electrical capaci- tors), and Daewoo Carrier (industrial refrig- erators). In addition, there were three other newly established firms in this group which are listed in the "automobile parts industry," which may have also contributed to produc- tivity. Other plausible links between new input-producing firms and productivity in the purchasing industries can also be found in our data.

In summary, for our sample of Korean industries, new inputs are an important ex- planation for the productivity growth. We interpret these results as strongly supportive of the role of new inputs in explaining total factor productivity. Of course, the limited nature of our sample (two years for a single country) makes it difficult to generalize. Nevertheless, our empirical results lend support to the new growth models that use the creation of new inputs to generate con- tinuous growth, and they represent a first step toward a more systematic testing of these models.


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