sou · GQB3118d4 · 2003-01-01 00:00:00 — High-tech firms have experi- enced considerable productivity gains, and other firms have re- sponded to lower prices on high-tech capital by investing a great deal in high-tech equipment. Note, however, that the present analysis does not explain why measured total factor productivity growth has also been high in sectors outside of manufacturing.13 Can it be the case that the use of high-tech capital has also im- proved TFP growth, or is this just a matter of coincidence that has to do with other things (e.g., the business cycle)? This question cannot be answered in this article since the short time series data preclude an adequate analysis of whether or not the use of ICT capital has also contributed to TFP growth by means of, for exam- ple, productive spillovers and network effects (and not only to ALP growth through capital deepening).14 On the one hand, the 12One earlier Swedish study in which capital is divided into high-tech and non-high-tech capital is, as mentioned earlier, and (1999), who analyzed whether summation over factor inputs into aggregate input measures affects standard TFP calcula- tions. In a related study, et al. (2001) considered both high-tech and human capital when trying to determine the productivity effects of high-tech capital. In both these studies, the authors constructed their own data on computer capital by combining national accounts three-digit manufacturing data with annual investment surveys obtained from Sta- tistics . Data on computer investments were, for an unknown reason, excluded from these surveys in 1994, implying that there is to date no officially published information on Swedish computer investments for the period 1995–2002. 13This finding has been reported earlier (on U.S. data) by and Stiroh (2000), and and Sichel (2000). 14These potential productive benefits from an ICT investment may show up on the inside of (internal to) the economic agent that makes that particular investment (learning by doing), or they may spill over to the outside (i.e., an external effect) to other agents in the economy (learning by others doing). fact that high-tech capital deepening has contributed negatively to labor productivity growth in high-tech industries (where total fac- tor productivity has accelerated) seems to suggest that high-tech capital has rather to do with TFP growth. On the other hand, however, total factor productivity growth has, as mentioned above, been sizeable also outside of manufacturing. Much scope remains to distinguish between cyclical and struc- tural productivity gains in the Swedish economy during the 1990s. This is, of course, of importance when it comes to getting the mac- roeconomic picture right – bearing in mind that escaped from a large recession in the middle of the 1990s, this distinction between fluctuation and trend may in fact seem crucial. An ade- quate distinction between fluctuation and trend must however be postponed to future work when additional time series data are available. It is worth mentioning here that one prospective end result of a fast-growing high-tech sector need not always be that favorable: the reason is that offsetting productivity effects may dominate. For example, it may certainly be the case that high-tech expansion merely results in reorganization of market shares – for example when a traditional store loses business to an on-line equal. Another offsetting effect is the likely increase in useless on-the-job consump- tion, for example when employees use computers for video games. In addition, training costs that accompany high-tech capital invest- ments may reduce the output gains of these investments. If all of these counteracting effects are large, there may not be any linkage at all (or, for that matter, a negative linkage) between high-tech investments and total factor productivity gains. This article is part of the work of the Commission on the Re- view of Economic Statistics. The organization of this article is as follows. Section 2 outlines the analytical framework. This section can be disregarded by any- one familiar with standard growth accounting. Section 3 describes the data, and section 4 presents the central empirical findings. Concluding remarks close the analysis in section 5. Note that although some disagreement still remains about this in the literature, the most common finding seems to be that the TFP growth effect of high-tech capital deepening is very small (non-existent). There is by now a large and growing literature on the macroecono- mic implications of a growing ICT sector. The general approach in this literature is to begin by computing a measure of technological change by means of a traditional growth-accounting framework. This framework – which is simple enough to be useful, yet not dis- astrously at odds with reality – is functional, for example, when it comes to finding out if the recent productivity upturn is broad in the sense of including the universe of sectors and if sources of pro- ductivity growth differ between producers and users of high-tech equipment. If stronger labor productivity growth is broad, then, of course, this productivity revival is more likely to be long lasting than would otherwise have been the case. Indeed, if faster productivity growth were concentrated to a few sectors, the productivity revival would be at risk to a slowdown in these sectors. In addition, if a growing ICT sector is the prime driving force behind the produc- tivity revival, one would probably expect to find strong TFP (and hence ALP) growth in ICT producing sectors and ICT capital deepening in other sectors. Improvements in the production of computers would, for example, show up both in a growing per- formance-price ratio and faster growth in TFP (ALP). Users of high-tech equipment, in turn, take action in response to falling relative prices on high-tech equipment by investing in ICT – and this also boosts ALP growth. 2.1Comparing output and input growth Consider a general production function Y = F(K, L,V ) for a sing- le firm, where Y is value-added output (that is, gross output net of intermediate inputs).15 Capital and labor inputs are denoted by K and L, respectively. V is an index of the level of technology. Note that beneficial spillover effects that raise overall productivity in the 15 I take no account in this article of the potential measurement difficulties associated with the improper use of value-added data as an output measure, even though I do not doubt that value-added may sometimes fail to account correctly for the productive contribution of intermediate inputs. True value-added output should optimally be constructed by subtract- ing the productive contribution of intermediate inputs (that is, energy, materials, and busi- ness services) from gross output. However, as Basu and Fernald (1995) pointed out, when the contribution of intermediate inputs is measured by factor payments, real value-added may depend directly on parts of the intermediate inputs. economy could, of course, be explicitly modeled in this context – ICT capital equipment can, for example, give rise to production spillovers and a number of network externalities. The former effect is the usual learning-by-doing (investing) effects associated with capital that tend to boost overall productivity in the economy when knowledge is non-rival and protection of proprietary infor- mation is incomplete. The latter is a new effect originating from firms investing in comparable communication equipment. Now, let the production function F be homogenous of degree in capital and labor, and of degree one in V. Logarithmic differen- tiating of F yields equation (2.1) d lnY = d ln K + (d ln L d ln K) + where d lnY , d ln K , d ln L , and d lnV are the growth rates of Y, K, L, and V. FL is the marginal product of labor. I have used the homogeneity conditions (FK K + FL L) / Y = and FV V / Y = 1 in the derivation of (2.1). This model thus compares movements in output with movements in inputs and, accordingly, relates to the growth accounting literature originating from Solow (1957). The growth rate of technology ( d lnV ) is the Solow residual. Equation (2.1) can be further simplified by making the assump- tions that firms have some monopoly power in output markets (but not in the market for factor inputs), and that the behavior of firms can be approximated by a sequence of static problems. simple expression for the ratio FL L / Y can be found by assuming that a representative firm (now indexed by i) faces the demand (P / P) (M / P) . The price level of firm is output Pi , P is the general price level, M is the monetary base, and is the elasticity of demand. maximize the profit function wLi rKi with respect to labor and capital inputs in every time period. The wage rate w and the capital cost r are taken as given by the firms. The two first-order conditions are SOU 2002:118 Bilaga 5 where µ = /( 1) is the markup factor.16 Now, let v labors share in total value-added output, that is v = wLi / PiYi , and use the first relation in (2.2) to obtain F L / Y .17 By combining the two first-order conditions with condition (FK K + FL L) /Y = can, in turn, be rewritten in terms of the (internal) returns-to-scale parameter and labors share in total factor costs c where c wLi /(wLi + rKi ) . Substitution of (2.1) yields the equation that is used in this study d lnYit = it d ln X it + d lnVit , where dX it is a weighted index of input growth d ln X it cit d ln Lit + (1 cit c for FL L / Y in )d ln . The variables and parameters are now written with firm and time subscripts to emphasize that they can change across firms as well as over time. Equations (2.4) and (2.5) can easily be re-formulated in terms of average labor productivity growth by assuming returns to scale and subtracting the growth rate of worked hours from both sides. After doing this, it is clear that average labor productivity growth can be divided into total factor productivity growth and the contribution from so-called capital deepening d ln yit = d lnYit d ln Lit = d ln xit + d lnVit . Here, the growth of weighted inputs per worked hour is defined as 16Note that no assumption of of the markup factor is required. 17When output and input markets are competitive, the necessary conditions for producer equilibrium are that the share of every input in the value of output equals the output elastic- ity with respect to that input. It follows that under returns to scale (the elasticities Bilaga 5 SOU 2002:118 d ln X it d ln Lit (1 cit )d ln kit , d ln Lit . Equation (2.6) hence splits labor productivity growth into capital deepening in the sense of capital per hours worked (the more capi- tal there is per hours worked, the higher is labor productivity) and total factor productivity growth (higher TFP means higher ALP). This completes the description of the model. While simple, it cap- tures the essence of a number of different scenarios.18 Note that if the underlying assumptions in this model fail to hold, the Solow residual will include other things than just true technological change – for example, various distortions due to imper- fect competition and spillover effects in production (see, for exam- ple, (2000)), omitted intermediate input variables due to the improper use of value-added data (see Basu and Fernald (1995)), and cyclical effects ((2000)).19 Note also that even though various measurement difficulties may affect the Solow residual, it remains a useful indicator of pure technological change and welfare. Broadly defined capital – which may include, for example, physi- cal as well as human capital (human capital depends on education, on-the-job training, and research and development) – often plays an important role in growth-accounting exercises. In the next sec- tion, tangible capital is split into three parts. In the analysis below, the real stock of capital is divided into three subgroups: (i) (subscript B ), (ii) machinery and equip- ment exclusive of ICT equipment (subscript M ), and (iii) ICT equipment (subscript ICT ). ICT equipment is defined to include sum to one) the value of output is equal to the total cost of the production factors, and hence the share of labor in output then equals the share of labor in total factor costs. 18Note, however, that although this type of neoclassical analysis can illustrate what has hap- pened in the economy as regards productivity growth it cannot explain why it happened. 19Note also that more thorough representations of the production process may include, for example, dynamic cost function models in which variable and quasi-fixed inputs are explic- itly taken into account within a micro foundation framework. For details, see and Siegel (1999). computer hardware and software as well as telecommunications equipment. Dividing total capital into these three parts yields a de- tailed analogue to equation (2.7) d ln xi Bi d ln kBi + Mi d ln kMi + ICTi d ln kICTi , (2.9) where the beta coefficients represent each factors share in total cost ji = (1 it )S ji , j = B, M , ICT. Time subscripts have been suppressed in equation (2.9). sent study, SBi , SMi , and SITCi are computed as the current value shares of each of the three types of capital in total capital – they hence sum to one (for more information, see section 3). Equations (2.6) and (2.9) hence capture the essence of the growth-accounting approach. 2.3Going to the aggregate level Basu and Fernald (1997) showed that substantial heterogeneity across sectors in terms of returns to scale and factor cyclicality may have cyclical implications at higher levels of aggregation. If aggre- gation bias is present, then standard aggregate production function regressions may suffer from an omitted-variable bias. This bias contributes positively to output growth if firms with higher than average returns to scale have higher than average growth in inputs, and it is procyclical if firms with above-average input cyclicality have above-average returns to scale. To see this, consider first ag- gregate value-added and weighted inputs computed as so-called Divisia of firm-level value-added20 d lnYt = it d lnYit , d ln X t = it d ln X it . The share of firm is nominal value-added in one-digit industry value-added is denoted by i . Then substitute the expression for 20 To facilitate exposition, I only illustrate the aggregation effect while going from the firm level to the one-digit level. The same reasoning can of course be applied to any data aggrega- tion. firm-level output growth in (2.4) into the first equation in (2.11) to obtain d lnYt = i it ( it d ln X it + it ) . Some algebraic manipula- tions of this expression and the use of the second equation in (2.11) yield t d ln X t + Rt + t , is a weighted average of returns to scale and Rt Rt = it ( it t )d ln X it . According to (2.13), the aggregation effect Rt contributes positively to output growth if firms with above-average returns to scale have higher than average growth in inputs, and the aggregation effect is procyclical if firms with above-average returns to scale have above- average input cyclicality. , if heterogeneity is cyclical, esti- mates of the returns-to-scale parameter from different levels of aggregation may differ. It thus follows that if Rt is omitted from the regression of the baseline equation (2.6), aggregate estimates of the returns-to-scale parameter can be biased. To control for this aggregation effect, one can try to estimate aggregation-bias-corrected value-added (that is, an output measure obtained by subtracting Rt from actual value-added growth) on the growth of the primary in- puts. Equation (2.12) hence shows that simple data aggregation may cause measurement difficulties also in a traditional growth-accounting framework that does not include traditional econometrics in the sense of parameter estimation. For example, if firms with above- average returns to scale for some reason are characterized by above- average input cyclicality, equation (2.6) suffers from an omitted variable (the aggregation term Rt ) that may, or may not, have an effect on the residually computed total factor productivity growth. The next section presents the data at hand and discusses some other possible measurement worries and data limitations. 21 Note again that because the current data lack information on intermediate inputs, I formulate this model in terms of value-added (rather than gross output). According to Basu and Fernald (1997), equation (2.6) should, in effect, include an additional term capturing the difference between the growth of value-added output and the growth of intermediate inputs. However, since this difference in growth rates cannot be computed here (given the available data), I implicitly assume that value-added output moves one-to-one over time with inter- mediate inputs. The current data set represents a sub-sample of the officially pub- national accounts data from 1993 through 1999, provided by Statistics , supplemented by new time-series records on annual investments in high-tech equipment. The addi- tional information on high-tech capital has been produced spe- cifically for the present analysis and the Commission on the Re- view of Economic Statistics. The ambition is to show what can be accomplished with these new data and to give special attention to the usual problems as regards the measurement of effective factor inputs and how these problems are affected by a fast-growing high- tech sector. The perpetual inventory method is used to compute the stock of each of the three assets (subscript B ), machinery and equipment exclusive of high-tech capital ( M ), and high-tech capi- tal ( ICT ) K jt = (1 j )K jt 1 + I jt 1 , j = B, M , ICT, where j is the economic rate of annual depreciation and the gross investment in asset j in period t 1. I jt 1 is While constructing these data, special care was taken to account for differences in the depreciation rates and price deflators for computer hardware and software (see also section 4.3). 3.1The share of capital and labor In order to derive an indicator of firm-level input activity, dxit , capital and labor are, according to equation (2.9), weighted by their shares in total factor costs. Total labor compensation (that is, total wage expenses, social security contributions, and mandatory insur- ance fees) is used here for the labor cost. Labor is measured by the number of hours worked per year. One way to assess the user cost of capital is to follow and (1967) – firm is user cost of asset j can then be com- puted according to22 22 The user cost of capital is the price that would be charged if capital was rented for one period of time. Bilaga 5 SOU 2002:118 ( j + j ). The economic rate of annual depreciation j typically lies in the interval 0.10–0.15, and the real rate of return required on capital is normally approximated by subtracting the CPI inflation rate from the required nominal and tax-adjusted rate of return on capital (that is, j ). The investment tax credit ITCij , in turn, meas- ures the proportion of the original investment cost that is subsi- dized by the government. The present value of depreciation allow- ances for an investment is captured by j . The required payment for the jth asset then equals r j K j , where K j is the current value of the stock of this particular asset. The total cost of employing capital in production, broadly measured as the sum of all types of capital, then equals the sum of the required payment for each of the assets. The share of capital (broadly measured) can then be obtained by dividing the total cost of capital by the sum of total capital and labor costs. Another route is to approximate the total cost of employing broadly measured capital by the operation surplus.23 This surplus, which is sometimes directly available in the data at hand, is defined as the value of output net of all labor costs. Asset js share in total costs can then be computed as j = (1 ) , J = B, M , ICT, where is labors share in total costs, defined as total labor costs divided by the sum of total labor costs and the operation surplus, and K j is the current stock value of asset j. Table 3 shows the real value shares of each of the three types of capital input in total capi- tal. According to the table, in the business sector the share of ICT equipment increased from 3.2 percent in 1993 to 5.2 percent in 1999. In the goods sector this share increased from 4.0 percent to 5.9 percent, and in the service sector it increased from 2.9 to 5.0 percent. The ICT capital share increased from 7.4 in 1993 to 10.1 percent in 1999 in the manufacturing sector, and, interestingly, it 23 To be perfectly accurate, this approximation requires zero profits. If this were not the case, this measure of the cost of employing capital would overestimate the true cost since it would also include profits. decreased from 32.9 to 31.3 percent among ICT-producers. Here, this sector is defined to include manufacturing of (i) office machinery and computers, (ii) cables and wires, (iii) radio, television and com- munication equipment, (iv) , surgical and orthopedic in- struments, (v) telecommunications equipment measured by radio transmit, operation of cable-television, and the use of electric power, and (vi) data processing and computer (hardware and soft- ware) consulting. In the current analysis, equation (3.3) is used for measuring each assets share in total costs. Table 3 Capital stock shares Note: The shares are computed from real SEK values. B stands for , M for machin- ery and equipment exclusive of ICT, and ICT for ICT equipment. Source: Statistics and authors calculations. Note that due to various measurement difficulties, estimates of the cost of capital are at best good approximations of the true cost of capi- tal. It is normally safer to underestimate this cost than the opposite since capital is in general less cyclical than labor. The reason why this is safer is that spurious cyclical measurement errors in the base- line equation (2.6) are less likely to show up when labors share in total costs is large.24 A closer look at data (not reported here) reveals that capitals share in total factor costs is in fact high (about 0.5 in the business sector in 1999 and a few percentage points larger in earlier years). A more plausible range for capitals share in total factor costs would probably be around 30–40 percent (see, for example, Bento- lila and (1998)). In the appendix, I have experimented with different cost shares without qualitatively affecting the re- sults. Apart from potential stochastic measurement errors and the possi- ble omitted-variable bias caused by simple data aggregation (see section 2.3), one limitation of the available data is that differences in the quality of the production factors are not accounted for. In particular, the measure of labor input does not consider the distri- bution of competence levels among the employees. It is also rather likely that quality differences among different types of capital in- puts are not satisfactorily considered even though capital inputs are split into three parts.25 In Basu and Fernald (1995), however, similar results were obtained when using quality-adjusted workforce and capital data on non adjusted data, suggesting that the induced error of not taking into account input qualities might not be crucial. Another limitation is the lack of information on the factor utili- zation rates. Labor input is computed as the volume of labor in the sense of hours worked. , this measure only matches effective labor input to the extent that it accounts for variations over the business cycle in labor effort. This is, of course, ever the case. Similarly, the measure of capital inputs does not take into ac- count variations in utilization rates.