Does the productivity J-curve exist in Japan?-Empirical studies based on the multiple q theory

doi:10.1016/j.jjie.2021.101137

Journal of the Japanese and International Economies

Volume 61, September 2021, 101137

https://doi.org/10.1016/j.jjie.2021.101137 Get rights and content

Highlights

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Brynjolfsson et al. (2021) argued that the movements of the standard TFP growth look like J-curve due to the accumulation of unmeasured intangibles during the investment boom for new technologies.
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Following their arguments, we revise the standard TFP growth rate and measure the gap between the standard TFP and the revised TFP using the estimated parameters of adjustment cost function of investment.
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When we focus on the IT-intensive industries, we find the J-curve in the period when the IT revolution started.

Abstract

Brynjolfsson, Rock, and Syverson (2021) argued that the standard TFP growth is low during an investment boom for new technology such as the IT revolution. As the new capital is operated and productivity improves, the shape of the movements in the standard productivity growth resembles a J-curve. However, when costs associated with investment for new technology are recognized as intangible investment - which is not counted in the conventional value added –, the revised TFP growth including these unmeasured intangibles show different movements from the standard TFP growth. Following Brynjolfsson, Rock, and Syverson (2021), we examine the gap between the standard TFP growth and the revised TFP growth. According to their theory, unmeasured intangibles are estimated by the gap between the shadow value and the price of investment goods. We obtain this shadow value of investment through an estimated parameter in each asset using listed firm-level data and revise the standard TFP growth rate. In the case of all industries, the standard TFP growth is overestimated in most years in the late 1990s and the 2000s, because the growth in intangible investment associated with measured investment is lower than measured capital accumulation rate. When we focus on the IT-intensive industries, we find the productivity J-curve in the late 1990s, at the early stage of the IT revolution, as indicated by Brynjolfsson, Rock and Syverson (2021).

Introduction

When the IT revolution started in the late 1990s, many expected the increase in IT investment to lead to improvements in productivity. While in the US, labor productivity growth accelerated from 1.49% in the period from 1973 to 1995 to 2.30% from 1995 to 2006,¹ productivity growth in Japan and the EU countries did not grow at a faster rate. As shown in Fig. 1, Total Factor Productivity (TFP) growth in Japan was almost 0% in the late 1990s, although the share of IT capital formation (information and communication machineries and software) in all capital formation grew from 8.7% to 13% for the same period. Van Ark et al. (2008) also showed that the US GDP per man-hour accelerated from 1995 to 2006, while for the EU 15, GDP per man-hour slowed for the same period.

Most researchers have agreed that intangibles are the key factors explaining the disconnect between IT capital formation and productivity growth. For example, intangibles such as software and skilled workers are indispensable for productivity growth when we use IT facilities effectively. This complementary role of intangibles is emphasized in the Economic Report of the President 2007 of the US government, where it was noted that “Only when they made intangible investments to complement their IT investments did productivity growth really take off.” Bloom, et al. (2011) showed that management practices in the US contributed more to the efficient use of IT within a firm than management practices in European firms. In this case, intangibles represented by management practices contribute to an improvement in firm performance. According to this argument, the slower productivity growth in Japan and major EU countries compared to the US can be explained by the lack of accumulation of intangibles.

Brynjolfsson et al. (2021) developed the above discussions to explain the secular stagnation of the US economy. They pointed out that slow productivity growth in the US is inconsistent with new technological advances such as in Artificial Intelligence and robots. They argued that official statistics do not account for the effects of intangibles such as the training of skilled laborers and organizational changes associated with the introduction of AI and robots. To conceptualize their arguments, they combine growth accounting with the standard investment theory with adjustments costs developed by Lucas (1967); Uzawa (1969), and Hayashi (1982). Investments with new technological innovation require large adjustment costs that should be accounted for as intangible investment in the System of National Accounts. This leads to productivity growth being underestimated when measured by the standard growth accounting when investments with new technological innovation are carried out aggressively. It is then overestimated after the capital with new technology is sufficiently accumulated. As a result, the movements in standard productivity growth resemble a J-curve. Based on their findings, they conclude that the slow productivity growth in the US after the Global Financial Crisis should be revised upward, because many innovative activities such as AI, robots and sharing services were carried out in the US in the 2010s and should have led to higher productivity.

Following Brynjolfsson et al. (2021), we also examine how unmeasured intangibles affect productivity growth in Japan. The adjustment costs of investment provide key parameters for the measurement of intangibles. Using estimated results of adjustment costs of investment, we measure the gap between the standard TFP growth and the revised TFP growth. Unfortunately, in the case of the whole economy, the standard TFP growth is overestimated in almost all years in the late 1990s when the IT revolution started. However, we find that the movements in the gap seem to follow a J-curve in the IT-intensive industries in the late 1990s. We also find the productivity J-curve in two other periods (from the mid to late 2000s and from the mid to late 2010s), although the scales of these curve are smaller than in the late 1990s.

Our paper consists of six sections. In the next section, we review the related literature. We focus on two research fields: the recent empirical studies on the multiple q theory of investment, and the recent issues in productivity measurement. In the third section, following Brynjolfsson et al. (2021), we introduce a revised growth accounting equation using a standard investment theory with adjustment costs. In this section, we show that the standard TFP growth is underestimated when large adjustment costs associated with new technological investment are accounted for as intangibles. In the fourth section, we explain our dataset to estimate adjustment costs using firm-level data. Then in the fifth section, we estimate the adjustment costs of multiple capital goods. Based on these estimation results, we measure our revised productivity growth in the sixth section. Although the productivity J- curve in the late 1990s is not found in the case of the whole economy, we find the productivity J-curve in the 1990s in the IT intensive industries. Then in the last section, we summarize our results and discuss remaining questions to be researched.

Section snippets

Related literature

In our study, we examine the fluctuations of TFP using the multiple q theory with an adjustment cost of investment. Our study here builds on two other areas of study: the recent empirical studies on the multiple q theory of investment, and recent issues in productivity measurement.²

The multiple q theory of investment was developed by Wildasin (1984). He showed that a

Summary of revised growth accounting using a standard investment theory

Following Brynjolfsson et al. (2021), we show how we revise the standard growth accounting framework using the neoclassical investment theory, with multiple capital goods. A production function with many capital goods is expressed as follows: $Y = A F (K, L)$ where $Y$ is value added, and K expresses a vector $K = K {(K_{1}, \dots, K_{j}, \dots K_{m})}^{T}$ and $K_{j}$ is jth measured capital input. L is labor input, and A is total factor productivity (TFP). The production function has constant returns to scale with respect to production

Estimation strategy and data construction

Brynjolfsson et al. (2021) estimated Eq. (15). However, the estimation of Eq. (15) is likely to be subject to heteroscedasticity. Therefore, we take a different approach to estimate the value of intangibles.

From Eq. (11) evaluated at $t = 0$ , we obtain: $p_{I_{j}} ϕ_{I_{j}} K_{j} = λ_{j} K_{j} - p_{I_{j}} K_{j .}$

We take the sum of (16) with respect to all assets. $\sum_{j = 1}^{m} ϕ_{I_{j}} ω_{j} = \frac{V}{p K} - 1$ where $ω_{j} = p_{I_{j}} K_{j} / pK$ . From $ϕ_{I_{j}} = γ_{j} \frac{I_{j}}{K_{j}}$ and $\frac{V}{p K} = q$ , Eq. (17) is rewritten as: $q - 1 = \sum_{j = 1}^{m} γ_{j} \frac{I_{j}}{K_{j}} ω_{j} .$

Eq. (18) implies that the marginal benefit of investment is equal to the

Estimations of adjustment cost functions of multiple assets

We estimate Eq. (18) assuming that firms have three types of investment/capital ratios multiplied by their capital shares: buildings and constructions ( ${(\frac{I}{K})}_{1}$ ), machineries ( ${(\frac{I}{K})}_{2}$ ), and R&D capital ( ${(\frac{I}{K})}_{3}$ ).¹⁰

Revision of the standard TFP growth

Based on Eq. (7), we revised the standard TFP growth rate ( $g_{A})$ . To revise the standard TFP growth, we need to measure growth in intangible investment ( $g_{I_{Z}}$ ) and the relative price of intangibles ( $μ)$ . As Brynjolfsson et al. (2021) show, intangibles are associated with normal investment, and so we assume that growth in intangible investment is the same as the growth in normal investment ( $g_{I}$ ).¹⁴

Concluding remarks and discussions for future research

Solow (1987) and Brynjolfsson et al. (2021) purported that the productivity growth evident in statistics is not consistent with the technological progress in the real economy. Brynjolfsson et al. (2021) argued that as the conventional value added does not reflect new capital formation, productivity growth is underestimated when aggressive capital formation for the new technology is undertaken. In addition, when the return of the new technology is generated and the new capital formation slows,

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: We thank two anonymous referees for their valuable comments for the improvement of our paper. As this paper is an extended version of RIETI Discussion Paper 19-J-041, we thank Dr. Yano (President of RIETI), Professor Morikawa of Hitotsubashi University, and Professor Fukao of Hitotsubashi University for their helpful comments on the early version of our paper. We also thank Professor Tokui of Shinshu University, Professor Kawakami of Toyo University, Professor Matsubayashi of Kobe University, Professor Mizobata of Kansai University and participants in the 21^st Macroeconomic Conference, the 14^th Young Macroeconomists Conference in Osaka and the 6^th World KLEMS Conference for their excellent suggestions. This study is supported by two types of Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (No.18H00852, and No. 16H06322) of Japan and Japan Securities Scholarship Foundation.

View full text

Does the productivity J-curve exist in Japan?-Empirical studies based on the multiple q theory

Highlights

Abstract

Introduction

Section snippets

Related literature

Summary of revised growth accounting using a standard investment theory

Estimation strategy and data construction

Estimations of adjustment cost functions of multiple assets

Revision of the standard TFP growth

Concluding remarks and discussions for future research

J. Japan. Int. Econ.

Return of the solow paradox? IT, productivity, and employment in US manufacturing

Am. Econ. Rev.

Missing growth from creative destruction

Am. Econ. Rev.

Survey of the Literature. Multiple q and Investment in Japan

Tochihyouka to Tobin's q/Multiple q no keisoku (The Land Value and Tobin's q: The measurement of Multiple q)

Econ. Today

The case of the missing productivity growth: or, does information technology explain why productivity accelerated in the United States but not in the United Kingdom?

NBER Macroeconomics Annual

Americans do IT better: US multinationals and the productivity miracle

Am. Econ. Rev.

Race against the Machine: How the Digital Revolution is Accelerating Innovation, Driving Productivity, and Irreversibly Transforming Employment and the Economy

The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies

Machine, Platform, Crowd: Harnessing Our Digital Future

The productivity J-curve: how intangibles complement general purpose technologies

Am. Econ. J.: Macroecon.

Does the United States have a productivity slowdown or a measurement problem?

Brook. Pap. Econ. Activity

On the nature of capital adjustment costs

Rev. Econ. Stud.

Intangible capital and U.S. economic growth

Rev. Income Wealth

Intangible investment in Japan: measurement and contribution to economic growth

Rev. Income Wealth

The Rise and Fall of American Growth: the U.S. Standard of Living since the Civil War