ICT and Total Factor Productivity Growth: Intangible Capital or Productive Externalities?

Ram C. Acharya
Industry Canada

Abstract

What accounts for the exceptional total factor productivity (TFP) growth performance of the United States and to some extent some of the other OECD countries after the mid-1990s? Most commentators have pointed to enormous productivity gains in the production of Information and Communications Technology (ICT) as the answer. But according to standard neoclassical theory, technical progress in one industry should not raise TFP growth in other industries. Yet the TFP acceleration is due mostly to industries that use, but do not produce, ICT capital. This paper investigates two explanations for this apparent puzzle, one based on the existence of intangible capital that is not measured in the National Income Accounts, and the other based on productive externalities. While both explanations can match the observed behavior of TFP growth, the two have very different implications for economic policy and welfare. We show that the two explanations can be distinguished using a cross-country, cross-industry data set. Using newly constructed very comprehensive data covering 16 OECD countries for 24 industries for a period of 32 years, we find evidence of intangible capital accumulation, but no evidence of positive spillovers to ICT investment. These results are robust across different estimation techniques and under different assumptions regarding market structure.

Table of contents

1. Introduction
2. The Basic Model
3. A Basic Identification Problem and its Solution
4. Data
5. Results
6. Conclusions

• References
• Tables
• Appendix A: Data Summary
• Appendix B: Derivation of the Estimating Equation
• Appendix C: Data Description

I. Introduction

After the mid-1990s, both labor and total factor productivity (TFP) accelerated in the United States and, to a lesser extent, in some other OECD countries. A large body of work has explored the sources and breadth of the U.S. acceleration and suggested reasons for the exceptionally good performance of the U.S. economy. Much of this research focuses on the role of information and communications technology (ICT)^{Footnote 1} Jorgenson, Ho and Stiroh (2006), for example, argue that the overall increase in the U.S. "speed limit" for growth is due to ICT. Growth accounting at an industry level for data from 1987-2004 shows that the simple explanation based on only ICT-producing industries for the U.S. TFP acceleration is incomplete at best. A growing body of literature finds that the TFP acceleration was, in fact, broad-based—not narrowly located in ICT production. Using industry-level data for the United States, Corrado et al (2006), and Bosworth and Triplett (2006) find that non-ICT-producing sectors saw a sizeable acceleration in TFP in the 2000s, whereas TFP growth slowed in ICT-producing sectors in the 2000s.

This finding is a puzzle. From the perspective of neoclassical economics, which underlies almost all the recent discussions of this issue, there is no reason to expect acceleration in the pace of TFP growth outside of ICT production. According to this theory, the fall in input prices do not shift production functions of the output sector. Of course, the fall in price leads to ICT capital deepening throughout the economy boosting labor productivity in ICT-using sectors—but does not change TFP in sectors that only use but do not produce ICT.

However, there are potentially two channels that the fall in the price of ICT could affect TFP of ICT-using industries. The first channel is that the resulting ICT deepening may lead to more use of complementary intangible capital, and the second channel is that there might be presence of positive externality of ICT use.^{Footnote 2} Let us discuss both lines of argument further.

Firm-level studies suggest that benefiting from ICT investments requires substantial and costly co-investments in complementary capital, with long and variable lags.^{Footnote 3} For example, firms that use computers more intensively may reorganize production, thereby creating 'intangible capital' in the form of organizational knowledge. The use of ICT may also prompt for more R&D investment some part of which might be intangible as well. The resulting "organizational capital" is analogous to physical capital that companies accumulate in a purposeful way. Conceptually, we think of this unobserved complementary capital as an additional input into a standard neoclassical production function.^{Footnote 4} In addition to the firm-level studies cited above, macro studies also argue that complementary investment is quantitatively significant (see, e.g., Laitner and Stolyarov, 2003).

The literature also suggests the likelihood of sizeable externalities to ICT. For example, successful new managerial ideas—including those that take advantage of ICT, such as the use of a new business information system—seem likely to diffuse to other firms. Imitation may be easier and less costly than the initial co-invention of, say, a new organization change, because one learns by watching and analyzing the experimentation, the successes and, importantly, the mistakes made by others.^{Footnote 5}

The first set of considerations is completely consistent with the growth accounting framework but suggest that the production function is mismeasured because we don't observe all inputs (the service flow from complementary, intangible capital) or all outputs (the investment in complementary capital). Hence, TFP is mismeasured. The second set of ideas, related to externalities, suggests that ICT might also explain "true" technology change (although the change would be endogenous, not exogenous). Empirically, the challenge is to infer the presence of ICT externalities while allowing for the existence of unobserved complementary investments.

This paper suggests a method to distinguish between these two explanations for the speedup of TFP in ICT-using industries. For that, the paper develops an estimating equation based on the model initiated by Basu, Fernald, Oulton and Srinivasan (2003; henceforth BFOS). In the BFOS model, reaping the full benefits of ICT requires firms to accumulate a stock of intangible knowledge capital. And, according to this model observed investments in ICT are a proxy for unobserved investments in reorganization or other intangible knowledge.

 Note that the BFOS story hews as closely as possible to neoclassical assumptions while explaining the puzzle of TFP growth in ICT-using industries. If growth accounting could include intangible capital as an input to production then it would show no technical change in ICT-using industries. (Of course, measuring intangible capital directly is very difficult at best; see Corrado, Hulten and Sichel (2006).) But the story can easily be extended to include non-neoclassical features that would explain true technical progress in ICT-using industries via other mechanisms, such as externalities. Indeed, to the extent that much of the intangible capital accumulated by ICT users is knowledge, which is a non-rival good, it would be natural to expect externalities. For example, the innovations that have made Amazon.com and Wal-Mart market leaders could presumably be imitated at a fraction of the cost it took to develop these new ideas in the first place, at least in the long run.

Unfortunately, once one allows for the existence of intangible capital, accumulated in proportion to investment in ICT, it is very difficult to detect externalities using conventional techniques. The paper documents this basic identification problem. But allowing for intangibles is important, as a variety of papers have made a strong case for its existence. The paper then suggests that international industry data can help distinguish the effects of intangibles from true externalities. This method is particularly appropriate for OECD countries which are more trade oriented and are leaders in the business applications of ICT. Accordingly, we use data for 16 OECD countries () for 24 industries covering the period 1973 to 2004.^{Footnote 6}

Indeed, we find evidence that firms accumulate intangible capital in the way our theory predicts. We find evidence of positive spillovers to ICT investment neither within a country nor across national boundaries. Reassuringly, we do find positive and statistically significant spillover effects of R&D investment at the domestic level and also at the foreign level in recent decades. These findings are robust with different estimation techniques. The result that there is no ICT spillover remains unchanged whether we impose or relax the assumptions of perfect competition and constant return to scale. However, the presence of intangible capital story survives only if we do not impose the assumptions of CRS and perfect competition.

The rest of the paper is structured as follows. First, we review the basic intangible-capital model presented in BFOS, and derive an estimating equation. In Section III, we show that it is difficult to use the basic BFOS framework to identify externalities—there is an identification problem. We then show that the problem can be solved by using cross-country, cross-industry data. Section IV gives an overview of the data we use. Section V discusses the results. Section VI concludes.

II. The Basic Model

We now turn to a formal model which is based on the model by Basu, Fernald, Oulton and Srinivasan (2003; henceforth BFOS). In the BFOS model, capturing the full benefits of ICT requires firms to make intangible investment. The assumption that complementary investments are needed to derive the full benefits of ICT is supported both by GPT theory and by firm-level evidence.^{Footnote 7} These investments may include resources diverted to learning; they may involve purposeful innovation arising from R&D. Since (intangible) capital accumulation is a slow process, the full benefits of the ICT revolution show up in the ICT-using sectors with significant lags.

Formally, value added in industries $i$ at time $t$ that use, but do not produce, ICT is given by (we suppress the country subscript):

(1) $Q_{it}\equiv Y_{it}+A_{it}=F(Z_{t}G(K_{it}^{IT},C_{it}),K_{it}^{NT},L_{it}),i=1,\dots ,N$

where $Q$ is total output; the difference in terms of measurement is that $Y$ is observable output by national accountants, and $A$ is the investment flow that is not measured.^{Footnote 8} It is the time and resource cost of training and creating new business structures.^{Footnote 9} Each industry hires labor L and rents ICT capital $K^{IT}$ and non-ICT capital $K^{NT}$ in competitive, economy-wide markets. $Z$ is a technology term that each industry takes as exogenous. $F$ and $G$ are homogeneous of degree 1 in their arguments. For simplicity, we ignore materials input, imperfect competition, increasing returns, and capital adjustment costs. All could be added, at the cost of considerable notation. But it is straightforward to include all of these features in the empirical work, and we do.

Industries forego producing market output $Y$ to accumulate complementary $C$ capital as follows (for the rest of the theoretical model, we suppress industry subscript $i$):

(2) $C_t=A_t+\left(1-{\Delta }_c\right)C_{t-1}$,

where ${\Delta }_C$ is the depreciation rate of investment $A$. The economic difference between $A$ and $NT$ capital is that they interact in different ways with ICT capital. The main economic implication of the separability assumption built into is that the marginal productivities of $K^{IT}$ and $C$ are closely tied to one another. We assume that the elasticity of substitution between the two inputs in the production of $G$ is relatively small. We also assume Inada-like conditions to the effect that the marginal productivity of each input is very low if the level of the other is close to zero. Thus, when the GPT arrives and ICT capital starts getting cheap, the incentive to also accumulate $C$ is very strong.

Note that conceptually, innovation as traditionally construed can take two forms. First, we lump purposeful unmeasured innovations into $C$ (indeed, we have assumed that all purposeful innovation is closely linked to ICT). Second, we interpret $Z$ as all exogenous increases in technology, including the component of organizational change that spills over as an externality from the sector of origin for example, the idea of using individual electric motors at each workstation in a factory, rather than relying on the single drive train of a steam engine.

Differentiating (1), imposing constant returns to scale and perfect competition assumptions, and manipulating the expression algebraically, we have an expression for the measured Solow residual:

(3) $\Delta y^{NT}-\frac{P_{K^{IT}}{K}^{IT}}{PY}\Delta k^{IT}-\frac{P_{K^{IT}}{K}^{NT}}{PY}\Delta k^{NT}-\frac{WL}{PY}\Delta l\equiv \Delta TPF=\frac{F_{C}C}{Y}\mathrm{\Delta c}-\frac{A}{Y}\Delta a+s_Z\Delta z$,

where $P$, $P,P_{K^{IT}},P_{K^{NT}}$ are prices of output, ICT capital and non-ICT capital respectively; $\Delta x=d\log \raisebox{1ex}{$X$}\!\left/ \!\raisebox{-1ex}{$dt$}\right.$, and $s_Z\equiv \left(F_Z\raisebox{1ex}{$Z$}\!\left/ \!\raisebox{-1ex}{$Y$}\right.\right)$. Note that in this model, TFP growth is not equal to technological change (as in traditional neoclassical model), that is, $\Delta T\mathrm{FP}\ne s_Z\Delta z$. Hence, omission of complementary inputs can cause either overestimate or underestimate of TFP growth. When unmeasured output is growing $(\Delta a>0)$, TFP growth is underestimated (the 1974 story) as resources are diverted to investment. When unmeasured input is growing $(\mathrm{\Delta c}>0)$, TFP growth is overestimated. This point is simple but important. Of course, if one corrects only output mismeasurement $(\Delta a)$, then ICT will appear fantastically productive, far beyond what is ordinarily measured. But firms divert resources to unobserved investment $\Delta a$ in order to create an intangible capital stock, which contributes to future production. The resulting unmeasured flow of capital services implies a bias in the other direction.

The net bias may be either positive or negative at a point in time, but in a dynamically efficient economy the mismeasurement is necessarily positive: True steady-state TFP growth is lower than measured, not higher.^{Footnote 10} In steady state, of course, the accumulation equation implies that $\Delta c=\Delta a$. Hence, steady-state mismeasurement depends on $g$, the steady-state rate of growth, and $r^{*}$, the steady-state real interest rate.

We now seek an observable proxy for unobserved investment in, and growth in the stock of, complementary capital. As shown in Appendix B, with the assumption that the production function of $G$ is CES in inputs $C$ and ICT, equation (3) becomes:

(4) $\Delta TF{P}_t=\left[F_C-1\right]\beta {\stackrel{\sim }{k}}_t^{IT}+\left[\frac{\left(1-{\Delta }_C\right)}{1+g}\right]\beta {\stackrel{\sim }{k}}_{t-1}^{IT}+s_G\Delta z_t$

where $\beta ={\left(\frac{1-\alpha }{\alpha }\right)}^{\sigma }\left(\frac{P}{P_C}\right){\left(\frac{P_{K^{II}}}{P_C}\right)}^{\alpha -1};{\stackrel{\sim }{k}}_t^{IT}=s_{K^{IT}}\left[k_t^{IT}+\sigma \Delta \ln {\left(\frac{P_{K^{IT}}}{P_C}\right)}_t\right]$, and $s_{K^{IT}}=\raisebox{1ex}{$P_{K^{IT}}{K}^{IT}$}\!\left/ \!\raisebox{-1ex}{$PY$}\right.$

So ceteris paribus the mismeasurement of complementary capital is more important in those industries where $s_{K^{IT}}$, the share of ICT in revenue, is high.

Finally, the TFP growth represents more than just pure technological change, including positive externality created by some factors. In accordance with this fact, we decompose the $\Delta z$ term to represent externalities, $\Delta e$, as well as exogenous technical change, $\Delta t$. So far we have suppressed industry subscript $i$, but now need to introduce them for estimation using a panel of industries (we still continue to suppress country subscript). Hence,

(5) $\Delta TF{P}_{it}=\left[F_C-1\right]\beta {\stackrel{\sim }{k}}_{it}^{IT}+\left[\frac{\left(1-{\Delta }_c\right)}{\left(1+g\right)}\right]\beta {\stackrel{\sim }{k}}_{i,t-1}^{IT}+s_G\Delta e_{it}+s_G\Delta t_{it}$

This model has several general implications. First, one might find a link between ICT use and measured TFP even if there are no externalities to ICT use. Second, the correct proxy for ICT use involves the interaction of ICT-intensity (the ICT share) and the growth rate. Third, one needs to control for both current and lagged $\stackrel{\sim }{k}$ Since these values are correlated in the data, if one omits one of them, then the regression has an omitted variable problem. Fourth, the first term on the right-hand side of (5) is proportional to $(r^{*}+{\Delta }_c-1)$, so under reasonable circumstances it is negative. The second term, on the other hand, is clearly positive. Hence, other things equal, the productivity acceleration should be positively correlated with lagged ICT capital growth but negatively correlated with current ICT capital growth (with these growth rates scaled by the share of ICT capital in output).^{Footnote 11}

III. A Basic Identification Problem and its Solution

There are a number of challenges in implementing this framework empirically. First, it is unclear how long the lags are between ICT investment and complementary investment. In other words, the length of a period is a free parameter, and theory gives little guidance. The lagged $\stackrel{\sim }{k}$ may be last years ICT capital accumulation, or the last decades. Furthermore, the equation for the accumulation of complementary capital has no adjustment costs, or time-to-build or time-to-plan lags in the accumulation of $C$. But such frictions and lags are likely to be important in practice, making it even harder to uncover the link between ICT and measured TFP.

Second, if we estimate the coefficient of $\stackrel{\sim }{k}$ (our main variable of interest) to be positively significant, interpretation of the results may be clouded by uncertainty of whether our proxies are capturing only unobserved organizational capital, or whether the proxies are affecting TFP directly through spillovers. Since the coefficient of $\stackrel{\sim }{k}$ represents the impact of the product of ICT share and ICT growth on same industry's TFP growth, its positive significance may imply that there are intra-industry (within firms) ICT spillovers. That is, the firm cannot reap all the benefits of its ICT use and part of it is spilled to firms within the same industry. Alternatively, its significance might be an outcome of unmeasured intangible capital that went along with ICT use. In other words, one can no longer tell whether the $\stackrel{\sim }{k}$ terms represent intra-industry externalities that are internalized within the industry or accumulation of other private capital stock. Similarly, if we find that lagged $\stackrel{\sim }{k}$ is important for explaining current productivity growth we do not know whether that finding supports the theory we have outlined, or whether it indicates that the externality is a function of lagged capital.

Third and more fundamentally, consider the problem of estimating the externalities represented by $\Delta e$ in equation (5). Besides the possibility of intra-industry ICT spillovers, there could be presence of inter-industry spillovers (firms in one industry benefits from ICT use by firms in other industries) as well. We can estimate this inter-industry ICT spillover by using aggregate ICT capital in the economy (more precisely ICT of all other industries in the economy). However, there are other factors that are considered to have spillovers to TFP, and we need to control these factors so that their effects are not erroneously captured by ICT variables. R&D is considered one such variable that spills positive affects to TFP. Hence, we can measure the $\Delta e$ by the growth rate of economy-wide aggregate ICT $(\Delta k_t)$, own industry R&D growth $(\Delta r_{it})$, and all other industries (within a country) aggregate R&D growth $(\Delta r_t)$ such that $\Delta e_{it}=\gamma \Delta k_t^{IT}+{\lambda }_1\Delta r_{it}+{\lambda }_2\Delta r_t$. In this case, equation (5) can be written as:

(6) $\Delta TF{P}_{it}=\alpha +{\beta }_1{\stackrel{\sim }{k}}_{it}^{IT}+{\beta }_2{\stackrel{\sim }{k}}_{i,t-1}^{IT}+\lambda \Delta k_t^{IT}+{\lambda }_1\Delta R_{it}+{\lambda }_2\Delta r_t+s_G\Delta t_{it}+u_{ijt}$

So, if coefficient $\gamma$ is significant then it would mean the presence of domestic inter-industry ICT spillover. In that case, if both or one $\beta$ is also significant, we would have reason to believe that $\stackrel{\sim }{k}$ more likely captures intra-industry ICT spillover rather than intangible, as firms potentially learn more from the activities of other firms in their own industry than from other random firms in the economy. If $\gamma$ is not significant but $\beta$ is, we still face the same problem of whether $\stackrel{\sim }{k}$ captures the effect of intangible capital or intra-industry ICT spillover. In this case, the country dimension of the data allows us to cut through the confusion so that we can estimate externalities that is robust to the existence of intangible capital. If there are industry-level externalities at the domestic level (the possible explanation of the positive $\beta$), it is reasonable to expect that they do not stop at national boundaries. Indeed, Stockman (1988) defines technology change (including the effects of possible externalities) as shocks that change output in the same industry across a group of countries. Hence for positive $\beta$ to imply intra-industry ICT spillover, one would like to see positive impact of foreign intra-industry ICT. If $\beta$ is significant but the coefficient on foreign intra-industry is not, then the story is more in line with intangible capital.

Hence, we estimate the equation by adding ICT growth in the same industry in a foreign country. Besides, we also control for foreign intra-industry R&D $\left(\Delta r_{it}^{*}\right)$ R&D in all foreign countries in the same industry, foreign aggregate ICT in all other industries $\left(\Delta r_t^{*}\right)$ and foreign aggregate R&D in all other industries $\left(\Delta r_t^{*}\right)$. Note that the variables with "star" as superscript are respective foreign variables. Thus the full form estimating equation (with country subscript j added) would be

(7) $\Delta TF{P}_{ijt}=\alpha +{\beta }_1{\stackrel{\sim }{k}}_{ijt}^{IT}+{\beta }_2{\stackrel{\sim }{k}}_{ijt-1}^{IT}+{\gamma }_1\Delta k_{jt}^{IT}+{\lambda }_1\Delta r_{ijt}+{\lambda }_2\Delta r_{jt}$
$+{\gamma }_1^{*}\Delta k_{ijt}^{IT*}+{\gamma }_2^{*}\Delta k_{jt}^{IT*}+{\lambda }_1^{*}\Delta r_{ijt}^{*}+{\lambda }_2^{*}\Delta r_{jt}^{*}+u_{ijt}$

Intuitively, the reason that equation (7) is robust to intangible capital accumulation is that intangible assets should be accumulated in proportion to ones own investment, but not to the investment of an industry in another country. Thus, cross-country data can solve the identification problem. Of course, one might argue that the externality from foreign capital is not quite as large as the externality to investment in ones own home industry. To that extent, estimates of (7) will represent a conservative lower bound to the external effects of domestic ICT investment.

We run regression of equation (5) as a first step. Then we estimate equation (6) using both aggregate and industry-level data for the countries in our sample (note that $\Delta k_t$ and $\Delta r_t$ appear without industry subscript). Finally, we estimate the full equation (7) with foreign variables included.

IV. Data

The data used in this paper are from the EUKLEMS database compiled by the Groningen Growth and Development Centre (GGDC), the OECD's Analytical Business Expenditure for Research and Development (ANBERD) database. For few countries, several data series have been supplemented from national statistical agencies. We use data for 16 OECD countries (Australia, Belgium, Canada, Denmark, Finland, France, Germany, Ireland, Italy, Japan, South Korea, the Netherlands, Spain, Sweden, the United Kingdom and the United States) and 24 industries covering the period 1973 to 2004. Among the 24 industries, 13 are manufacturing, nine are services industries, one is electricity, gas and water supply industry and the remaining one is construction industry. The only industries that are missing from the study are agriculture, fishing and forestry industries, as they do not have R&D data available (the industry list is given in Appendix A, Table A1).

Data on gross output, value added, intermediate input, hours of work, ICT capital, non-ICT capital are taken from the EUKLEMS database. The detailed description of the EUKLEMS data is available in Inklaar, Timmer and van Ark (2006). Data on R&D stock is taken from OECD's ANBERD database. Again, in several cases, both these data have been supplemented by national statistical agencies (see Appendix B for data description). In the database, output is defined at constant price. Labor input is measured as composition-adjusted hours worked. This is the product of total hours worked and an adjustment for differences in the marginal product of heterogeneous workers based on their relative wages.

Instead of using data on capital services we use data on capital stock. Capital services data are available only in index form and capital stock data are available in levels. Since we estimate production function also at the level form and it is not straight forward to derive level from capital services in index, we prefer to use capital stock (rather than capital services). However since ICT capital stock was computed by adding three separate assets and non-ICT capital was obtained by adding five different assets (with different depreciation rates), there is no additional benefit of data precision in using capital services over capital stock.

We use three types of ICT capital stock both individually and also by aggregating them into one series. The three types of ICT capital are computers, communication equipment and software. The non-ICT capital is used only as an aggregate series. For detail on how these capital stock data are estimated, see Timmer et al (2007).

The R&D expenditure data are in national currency current price which were converted to constant price using industry value added deflators then transferred to PPP at 1997 rate (using industry level PPP for each country) and constructed capital stock with 15% depreciation rates.

Appendix A presents average data across time (1973–2004) for 16 countries and 24 industries, with data availability information in Table A1. With 24 industries and 32 years of data, there are maximum of 768 observations for each country. Similarly with 16 countries, for each industry, the maximum number of observation is 512. Among the 24 industries, 23 are ICT-using industries and electrical and optical equipment industry is the only one that is ICT-producing. As our focus is on ICT-using industries, we will exclude ICT-producing industry from our estimation.

Looking at the upper panel, the data on value added and labor are complete for all countries. The data availability is quite good for both types of capital for all countries except for Ireland and Sweden. For Ireland, the capital stock data starts only from 1995 and those for Sweden only from 1993. On R&D variable, Korea has the smallest number of observation, as its data start only from 1995. By industry, the data points for value added, labor, ICT and non-ICT capital are almost similar (although not complete for capital stock as some countries' data are missing for the earlier years as mentioned above). The data availability on R&D, however, varies by industry, with minimum observation of 204 for hotel and restaurant industry.

An inspection at the data shows that there is quite a variation across industries and countries in value added (Table A2), hours of work (Table A3), R&D capital stock (Table A4), ICT capital stock (Table A5), non-ICT capital stock (Table A6), share of ICT to total capital stock (Table A7) ICT intensity in terms of value added, (Table A8) and R&D intensity in terms of value added (Table A9). The share of ICT to total capital stock ranges from 0.1% in real estate activities to 28% in post and telecommunications (Table A6). The industry mean of share of ICT to total capital stock is 3.6% with median of 4.5%. Taking industry median value as a cut off point, 11 industries have the share higher than median and 12 industries have share lower than median. Only four manufacturing industries have ICT to capital share higher that that of industry median. The country median ranges from a low of 2% for Canada and Belgium to a high of 8.2% for Sweden.

Looking at ICT intensity (ICT to GDP share) in Table A8, we see that it ranges from as low as 1.2% for real state activities industry to as high as 147% to post and telecommunication industry in the US. Almost similar variation is noticed across countries in the same industry. For example, in renting of M&E and other business industry, (the industry with second highest ICT share after post and telecommunication industry) the ICT intensity varies from low of 6% in Belgium to high of 51% in Korea. Most of the industries that have higher share of ICT in total capital stock are also the industries which have higher share of ICT capital stock to value added. There are few exceptions. For example, the electricity, gas and water supply is highly capital-intensive in terms of value added (11%) but has a very low share of ICT in total capital stock (1.8%). A more pronounced difference in two shares is found for transport storage (19% vs. 5%). It implies that both these industries have very high capital to value added ratio. There are only two industries whose ICT share in total capital is higher than their respective capital to value added shares. They are construction and wholesale trade. As a result, they have the lowest capital to value added shares.

Finally, one might argue that using firm-level data would allow us to avoid the complexity of using cross-country data sets. Returning to equation (7), the beneficial externalities to a firm presumably come from the investments of other firms within the same industry. So why not estimate (7), with i indexing firms, and the externality coming from industry-level ICT investment?

The main reason why firm-level data are not suitable for the purpose of estimating externalities in our framework is the lack of true price deflators for firm-level output. In the realistic case where firms within an industry produce heterogeneous output, Klette and Griliches (1996) have shown that the procedure of replacing the true firm-level deflator with an aggregate industry deflator leads to an omitted variable problem that is particularly worrisome for the purpose at hand. They show that the omitted variable is correlated with industry inputs, even controlling for firm inputs that is, it has exactly the characteristics of an externality! But the source of the correlation with industry inputs is the mismeasurement of real output, not a true productive externality. Thus, using firm-level data which would be preferred according to theory, will not give useful answers as long as one needs to deflate firm revenues with an aggregate industry price index.

Although industry data have other problems, including the problem of distinguishing own unobserved investment from a productive externality, there are true price deflators for industry output, and thus the Klette-Griliches problem does not apply. Furthermore, the industry level data makes it possible to use data for so many countries, industries and across years.

V. Results

At the beginning, we omit controls for intangible capital; those will be added later. For most part of the analysis, we allow for non-constant returns to scale and perfect competition. Thus, our dependent variable is output rather than TFP, and we enter the inputs separately on the right-hand side. Towards the end of the paper, we impose CRS and perfect competition and use TFP as dependent variable. To begin with we estimate level equation and revert to growth one subsequently. We use OLS for most of the estimation and use GMM as robustness check. We also decompose the most preferred estimation in two ways: first, into decade-long three sub-periods and second aggregate ICT into three components: software, information technology and communication technology.

The results for level equation are presented in Table 1, using all industries (both ICT-producing and ICT-using) in specifications 1–6 and using only ICT-using industries (dropping one industry ICT-producing, electrical and optical equipment industry) in specifications 7 and 8. For the first seven specifications, we use gross output as the dependent variable and value added for the last specification. We also augment our basic estimating equation with own industry domestic R&D (specifications 6-8).

We estimate fairly standard coefficients for all the inputs except labor, whose coefficient seems too low. The coefficient for non-ICT capital is also implausibly low once we introduce industry fixed effects. Since the variation in capital and especially in non-ICT capital is across industries (cross-section) rather than across time within the same industry (time series), the use of industry fixed effect as a control lowers the magnitude of its coefficient. The estimation of low coefficients, especially on capital, is a common outcome from fixed effects regression (see Griliches and Mairesse 1998). On the other hand, the coefficient of intermediate input is quite high once the industry fixed effect is introduced.

Overall, the labor and capital coefficients are generally smaller than their respective average factor shares, whereas the coefficient of intermediate input is larger than its average factor share in the raw data. The sum of coefficients is very close to unity in all specifications except for specifications when we start having all three (country, industry and time) effects (in specifications 5). The sum of coefficient falls further with the introduction of R&D variable (specification 6), with the dropping of ICT-producing industry (specification 7) and value added as dependent variable (specification 8). The data reject the null hypothesis that there is constant return to scale, i.e. the sum of coefficients (labor, capital and intermediate input) is unity in all specifications. All the coefficients, including those on R&D capital, are significant at the 1% level.

Results in Table 2 are in some way repetition of the specifications of Table 1, but now estimated using growth rates and considering only ICT-using 23 industries (dropping ICT-producing, electrical and optical equipment, industry from the estimation sample). Here, as expected, the estimated coefficients on the capital input variables fall and are often close to zero. This is particularly true for ICT capital, which of course has a smaller share to start with. The coefficient of non-ICT capital is significant once we introduce time fixed effect and insignificant when industry or country fixed effect is introduced. Domestic R&D continues to be significant in most specifications.^{Footnote 12} Even though industry and country fixed effects are wiped out in first difference equation, we still carry them in some specifications in this table. But our preferred specification is (3) with only time fixed effect and we continue this method for the rest of the estimations.

In Table 3, we introduce the variables that should proxy for intangible capital accumulation, as required by the model in Section II. We extend the growth equations that provided results for Table 2 by adding first the ICT capital share in gross output (specification 1) and then the product of the ICT ratio to gross output and ICT capital growth (specification 2). Then we check the impact of this product variable in one period lag (spec. 3). Although the theory we have developed is not a guide on how far the lags should, it suggests that to control for intangible capital accumulation we need enter the variable for two time periods. Accordingly, we extend the estimation to include contemporaneous and one-period lags (spec. 4). As the theory suggests, regarding the control for intangible, the more recent variable should have a negative sign and the longer lag should have a positive sign. This is exactly the sign pattern we find in specification 5, although only the longer lag is statistically significant. Specification (6) shows that the data do not advise further longer lags.

Number 5 is our preferred specification, where first term enters with no effect (negative coefficient) and second term implies positive impact (as suggested by the theory) at 10% level. For the rest of the analysis, we will extend this specification to the full form as given in equation (7). Without further control, the difficulty with this estimation is that there is no way of knowing whether the significance of this variable indicates the impact of intangible or the benefits of ICT use of one firms spills to other firms in the same industry (called within-industry ICT spillover). If there are spillovers at the industry level (if the full reward of ICT use is not captured at the firm level), then the coefficient will show up with positive sign indicating industry level ICT use efficiency.

Besides, there is also the case that the ICT spillovers might be across industries. That is, a firm in an industry may benefit not only from the ICT use of firms within the same industry, but also from ICT use of firms in other industries (called inter-industry spillover). We want to estimate this channel of ICT spillover as well. Furthermore, along with intra-industry R&D spillover, we would like to control for inter-industry R&D spillover.

We begin to look for external effects, using as a baseline our results from Table 3, where we allow for intangible capital accumulation. We take the specification 5 in Table 3 and estimate equation (7) in its full form except for the fact that the different price levels that appear in the equation are not considered. However, as one does not expect the relative price of ICT in the sample countries to be very different, their exclusion should not bias our results. We begin by looking for within-country spillovers by adding aggregate ICT which is the domestic total ICT of all other industries (named inter-industry aggregate ICT), and aggregate R&D in specification 1. These two variables are significant at the 10% and the 1% levels, respectively, implying that there are spillovers from other industries' use of ICT and other industries' R&D capital.

Furthermore, even in the presence of these two variables, the ICT ratio and ICT growth (product) term is negative in one year lag and positively significant (at 10% level) in 2 years lag. The significance of this variable may indicate either intra-industry ICT spillovers or presence of intangible. More importantly, in the presence of the positive inter-industry ICT spillovers that we have estimated, it is hard to believe that there is no intra-industry spillover, as firms generally learn from firms in the same industry than firms in other industries. Hence, the significant result on the coefficient of the product of ICT ratio and ICT growth in specification 1 is more in line with domestic intra-industry ICT spillover rather than intangible capital story.

To explore further, we introduce foreign intra-industry ICT in the estimation. As explained above, our line of reasoning is that if the spillovers indicate domestic intra-industry efficiency, then foreign intra-industry variable should also be significant. The notion is that unless there is a convincing case that spillovers stop at the border (which is not the case in R&D as several studies have shown) then foreign intra-industry spillover should be present (may be in lower magnitude) if there is domestic intra-industry ICT spillover.

When we add foreign intra-industry ICT growth variable (spec. 2) ICT capital growth in the same industry in all foreign countries the domestic aggregate ICT variable loses its significance. Next we add foreign intra-industry R&D, foreign inter-industry ICT (ICT in all other industries in all foreign countries) and foreign inter-industry R&D (spec. 3). None of them are significant; all of them have wrong sign except for inter-industry R&D and oddly intra-industry R&D variable is statistically significant. In this full specification 3, the two-period lag of the product of ICT ratio and ICT growth is significant but neither domestic inter nor foreign intra and inter industry ICT variables are significant. Since there is no trace of domestic inter and foreign intra- and inter-industry ICT, the positive impact of the variable product of ICT ratio and ICT growth implies the impact of intangible capital that goes along with the ICT investment.

In specification (4), we remove all R&D related variables (both domestic and foreign) and estimate the impact of ICT. Interestingly, the product term loses its significance. Even more interesting is the case that the aggregate domestic ICT variable is quite significant, whereas the foreign ICT variables are not significant. This is a perfect case of domestic inter-industry ICT spillovers, and no trace of intangible capital impact. However, this is an outcome of model misspecification, as R&D, the TFP spillers, is taken out of the estimation.

Thus, we find some qualified support for positive externalities from aggregate domestic ICT growth (specification 1). That support vanishes, though, while we introduce the foreign ICT variables, which themselves are not significant either. Hence there is no support for the proposition that foreign within-industry and foreign inter-industry ICT usage has positive externalities (specifications 2 & 3). The significance of the ICT variable at the domestic level but insignificance at the foreign level indicates that the positive impact on productivity might be generated by intangible capital than by ICT spillovers. Another finding is that once we remove R&D variable, the aggregate ICT growth spillover becomes stronger (specification 4) suggesting that while estimating the impact of ICT on TFP, the control of R&D is essential otherwise the result would be biased. Furthermore, the models that do not control for R&D while measuring impact of ICT would be wrongly ascribing R&D spillovers to ICT spillovers.

The domestic aggregate R&D is consistently significant in all specifications, whereas own-industry R&D is positively significant only if domestic aggregate R&D is taken out from the estimation. While introduced together, the inter-industry R&D growth nullifies the impact of own industry R&D growth as these two variables own industry R&D and domestic inter-industry R&D are positively related. A higher inter-industry R&D growth rate leads to higher TFP growth, whereas own industry's higher R&D growth rate does not reflect into higher TFP growth.

An important question is whether the nature of ICT spillover has changed over time. To test this, we decompose the estimation in specification (3) into three sub-periods with 10 years each (1975–1984, 1985–1994 and 1995–2004; the samples from 1973 and 1974 are excluded) and present results in specifications 5 through 7. This sub-division allows us to evaluate whether there was anything different in the post 1995 period the time when both the US average labor productivity growth and TFP growth accelerated. In none of the three decades domestic aggregate (inter-industry) ICT variable is significant. The foreign intra-industry ICT is positive (insignificant) for the first decade, negative (insignificant) for the second decade and negatively significant at the 10% level for the last decade (1995–2004). The foreign inter-industry ICT coefficients are negative but insignificant in all three decades. For R&D, however, the situation is different. The coefficient on aggregate domestic R&D is significant for the last two decades; foreign intra-industry R&D is negative throughout and (wrongly) significant in the first decade, whereas foreign inter-industry R&D is positively significant for the recent decade.

As far as the ICT story is concerned, this decomposition confirms the finding in previous specification that there is no ICT spillovers, neither inter nor intra; neither domestic nor foreign. Any indication of positive ICT spillovers can occur due to either misspecification of the model or due to missing measurement of intangible capital.

What is somewhat surprising is the negatively significant coefficients of ICT capital in specifications 1 through 3 (at 10% level) of Table 4 (spec. 4 is not the preferred model as R&D variables are excluded). Taken literally, this could mean that the ICT capital is unproductive. This is not the first time the own industry ICT capital growth is found to be negatively correlated with its own TFP growth. In the US data from 1984 to 1999, Stiroh (2002), under different estimation techniques, finds that ICT growth is negatively related with TFP growth even at the lower level of significance. In his study, the strong negative effect is driven by telecom capital, as the coefficient of computer capital is negative but not significant. In our case, the decomposition shows that this negative coefficient was caused by the situation in the first decade of the study (Spec 5); in the last two decades, the impact of ICT capital growth on TFP growth was nil (Specs 6 and 7).

To understand if any of the three ICT assets have spillover and which asset types caused this negative impact we decompose the ICT capital into: information technology (IT), communication technology (CT) and software.^{Footnote 13} Results in Table 5 show that the negative coefficient on ICT in Table 4 was driven only by CT whose coefficient is negatively significant at the 5% level for the sample of entire study period. Furthermore, the regression results for three sub-periods show that the coefficient was negative only for the first sub-period, 1975–1984 (results not reported to avoid clutter) and that too only for CT. During the periods 1985-1994 (again results not reported) and 1995–2004 (reported in Table 5), none of the three ICT assets were significant. To sum up, the ICT capital is not a drag in TFP growth especially not so in the more recent years, but the industries with higher ICT growth may not be the ones which necessarily acquire higher TFP growth. The results at the domestic aggregate category show that none of the three assets generated spillover type effects.

In Table 6, we conduct a robustness check using generalized method of moment (GMM) system estimation to address the potential issue of endogeneity in the above panel (within) estimation. The first specification is copied from specification (3) of Table 4. Specifications 2-4 use system GMM and treat different variables as endogenous. In specification (2), we treat two variables, intermediate input and labor hour, as endogenous and use their lags of two period and back as GMM-type instruments. All other variables are used as exogenous and the difference of each of these variables (difference of the difference as these variables are already in difference form) is used as standard instrument. All of these are instruments for difference equation. For the level equation, we use the second lag of the difference of all endogenous and exogenous variables as instruments. Only the second lags of the variables are used because the moment conditions using the higher lags are redundant (Blundell and Bund, 1998). The model is estimated using two-step GMM and the standard errors are robust. The p-value for AR(1) shows that, as required by theory, there is first order serial correlation (the null is rejected), but the null that there is no second order correlation is not rejected at 10% and higher level, contrary to what theory requires us to do.

In specification (3), we use only intermediate input as endogenous. All instruments are as explained above. The non-rejection of AR(2) at 7% level and above strongly rejects the model. In Specification (4) we use only labor hour as endogenous. In terms of AR(2), this specification is better because as required by theory we cannot reject the null that there is no second order serial correlation at least for the 11% level. Among the three specifications in GMM, our preferred and theoretically sound model is specification (4).

The major difference in the results between OLS and GMM estimations are the following: (i) the coefficients on non-ICT is significant in OLS and turns insignificant in GMM, (ii) the lag effects strengthens (iii) the strong positive coefficient on domestic aggregate R&D in OLS either loses strength or becomes nil in GMM, (iv) the foreign intra-industry ICT which was insignificant in OLS turns significant in spec. (4) and (v) the negatively significant coefficient on foreign intra-industry R&D in OLS turns insignificant in GMM. In terms of the impact of ICT, the prime interest for this paper, none of these differences qualitatively cast doubt on the previous finding that any potential spillover impacts of ICT abode well with the intangible capital story but not with the presence of its spillovers. Overall, the GMM estimations suggest that the OLS results were not driven by simultaneity issue; even when we control for potential endogeneity, the results qualitatively remain the same.

Finally, in Table 7, we run regressions similar to those of Table 4, but now using TFP growth rather than output growth as the dependent variable (and removing own-inputs from the right-hand side of all the specifications). Using TFP rather than estimating the coefficients on the inputs is an attempt to gain power by imposing the conditions for cost minimization (although, since we do not include an input aggregate on the right-hand side, as in Hall (1990), we are also imposing constant returns to scale). The qualitatively new result is that when we estimate using TFP, the share-weighted lags of own ICT investment retain the negative and positive signs predicted by theory, although, none of the lags is significant. Second, looking at the full specification (4), we see that foreign intra-industry ICT and foreign inter-industry R&D which were insignificant in Table 4, turns negatively significant with TFP as dependent variable which is difficult to rationalize. As before within a country, R&D has spillovers that are statistically significant. Impact of foreign aggregate ICT growth is insignificant. In specification (5), we introduced cross country aggregate R&D and ICT as an interaction term, and as a result, the oddly negative coefficient (inter-industry aggregate R&D) turns insignificant. Among the four foreign variables only intra-industry ICT is (negatively) significant. In the last specification, we take out all R&D related variables and as a result both domestic and foreign aggregate ICT variables become significant. This result is capturing the positive impact of excluded variable R&D. Overall, the story holds; there is no evidence of aggregate ICT positive externalities, either within or across countries.

VI. Conclusions

Using a simple model, we show that it is difficult to estimate ICT spillovers when one also allows for intangible investment that is complementary to ICT. Yet a variety of evidence, both micro and macro in nature, suggest that intangible investment is very important, and is particularly strongly associated with ICT investment. We then propose a solution to this problem, if ICT spillovers operate across borders. Since intangible capital investment is confined within country boundaries, using cross-country, cross-industry data allows us to solve this fundamental identification problem.

We assemble a large data set for 24 industries in 16 OECD countries over 32 years. This rich data set allows us to test for externalities even if there is intangible capital accumulation. Indeed, we find evidence that firms accumulate intangible capital in the way our theory predicts. Allowing for the intangible capital accumulation—which might otherwise be mistaken for positive externalities to lagged ICT capital investment—we find no evidence of positive spillovers to ICT investment across national boundaries and within countries. This is true across two estimation techniques we have used. This is also true whether we use gross output or TFP growth (imposing the conditions for cost minimization) as our dependent variable.  Reassuringly, we do find positive and statistically significant effects of R&D investment at the domestic level and at the international level in more recent period. This finding, in keeping with the large literature on R&D spillovers, suggests that our failure to find ICT externalities is not due to some quirk of our data or specification.

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Tables

Appendix A: Data summary