26 See Fig. 2 in UNFCC (2015). As seen by comparing it with Fig. 5.6 in Nordhaus (2008), the NDC path is similar to the optimal path of the DICE model.

#### References

effect of the intended nationally determined contributions (FCCC/CP/2015/7). Accessed on 1 June 2021. http://unfccc.int/resource/docs/2015/cop21/eng/07.pdf

Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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Part III For Prosperity (SDGs 8 and 9)

# **9 Economic Growth:Why Are There Rich and Poor Countries?**

Koki Oikawa

#### **Abstract**

Sustainable economic growth is one of the main goals of SDGs. To achieve this goal, we need to know what drives the long-run dynamics of the wealth of nations. In this chapter, we first learn how to measure the level of a country's wealth and its growth from data, as well as some widely observed facts such as steady growth in some developed countries, the huge international difference in economic growth, and so forth. Next, we develop theoretical models to explain those observations. We present a basic theory of growth with capital accumulation as the driving force and check the consistency with the observed data. Further, we consider firms' investments into research and development (R&D) and see how innovations drive economic growth. It also tells us the effects of growth policies. Lastly, we discuss other factors that create international difference in economic growth such as education, institution, and misallocation of resources. This chapter contributes to Goal 8 (economic growth) and 9 (innovation) in SDGs.

Waseda University, Tokyo, Japan e-mail<EMAIL_ADDRESS>
#### **Keywords**

Economic growth · Catch-up · Productivity · Technological progress

#### **9.1 Introduction**

People living in the United States earn about 100 times the income of people in the poorest countries, after adjusting for price levels.Why are some countries so rich? Why do some countries grow faster than others? Can a poor country become rich in the future? If they can, how? These are questions in macroeconomics since our predecessors began to study the mechanism of economic growth and development. Honestly speaking, we do not have quick answers to those questions yet. However, accumulated knowledge in this academic field gives us a good perspective on the appropriate approach to tackle them. Learning the fundamental framework to analyze economic growth, which is developed in this chapter, definitely helps us achieve the sustainable development.

In this introduction, we review several important facts about economic growth using worldwide time-series data. Let us start by introducing the data we focus on. The wealth of a nation is usually measured by its gross domestic products (GDP, hereafter), which captures how much final goods and services are produced in a year. Because we are more interested in people's liv-

K. Oikawa(B)

© The Author(s) 2023

S. Urata et al. (eds.), *Sustainable Development Disciplines for Society*, Sustainable Development Goals Series, https://doi.org/10.1007/978-981-19-5145-9\_9

ing standards rather than the aggregate size, we divide the total GDP by the population to obtain per-capita GDP. Additionally, we remove the effect of price changes from GDP to avoid misinterpreting an increase in GDP owing to inflation as real economic growth. Finally, we adjust for differences in the price level between international economies to compare multiple countries that use different currencies.

Figure 9.1 shows the histograms of real GDP per capita across countries in 1960 and 2019.1 We need to clarify how to read this graph. Because the numbers for real GDP per capita are too diverse, for example, from 500 to 23,000 in 1960 (in US dollars based on 2017), to depict in an easy-to-read graph, one can make such a graph readable and concise by taking the logarithm of the numbers. Here, we use a logarithm with the base of 10, or log10 *yt* , where *yt* is real GDP per capita in year *t*. Note that the logarithm converts 10*x* to *x*, or, in equation, log10 10*x* = *x*. This *x* is taken as the horizontal axis in Fig. 9.1. So, if a country has *x* = 4 on the axis, its real GDP per capita is *y* = 104 = 10,000. If country A has 4 and country B has 3 on the horizontal axis, country A is 10 times larger than country B.

The takeaways from this figure are threefold. First, both histograms in 1960 and 2019 have wide ranges on the horizontal axis, implying that there exists a sizable dispersion in the level of per-capita real GDP. Second, the observed dispersion is persistent. Third, the histogram shifts rightward from 1960 to 2019, implying that the real GDP per capita is growing over time on average.

Next, Fig. 9.2 shows a histogram of the average annual growth rate of real GDP per capita from 1960 to 2019. The growth rates are mainly positive, but, again, there is a significant dispersion. Can you imagine how much difference there is between a country with a growth rate of 5% and another with 1% over 60 years? Even though the initial levels are common, the faster-growing country becomes more than 10 times richer than the other after 60 years, as shown in the calculation of (1 + 0.05)60/(1 + 0.01)60 ≈ 10.28.

Figure 9.3 illustrates the relationship between the initial level of real GDP per capita (in 1960) and the average growth rates afterward, using the same data in Figs. 9.1 and 9.2. This figure tells us about international convergence more clearly. If poor countries catch up with rich countries, a

PWT10.0

**Fig. 9.1** Histograms of log of real GDP per capita in 1960 and 2019. *Source*

1The data source is Penn World Table (PWT), version 10.0. You can download the worldwide data related to economic growth from https://www.rug.nl/ggdc/productivity/ pwt/. The histograms consist of 111 countries and regions that have GDP data in both years.

**Fig. 9.2** Histogram of growth rate. *Source* PWT10.0

**Fig. 9.3** Catching up? *Source* PWT10.0

low initial GDP level (horizontal axis) should be associated with a high growth rate (vertical axis). Indeed, some countries around the top-left corner in the figure, such as Botswana (BWA) and South Korea (KOR), have been catching up during these past several decades. However, it does not hold in general. The countries in the bottom-left area in the figure have low initial levels and low or negative growth rates. Some of those countries are lagging, rather than catching up with the richer countries.

In the next section, we argue about the mechanism behind these observations. To see how the long-run growth is determined, we first introduce a basic economic growth model in Sect. 9.2. The basic model explains some aspects of economic growth but, at the same time, casts a light on what we are ignorant of to explain economic growth. Hence, in Sect. 9.3 and subsequent sections, we dig deeper into the growth mechanism.

#### **Basics in Macroeconomics**

Here, we quickly review the definitions and ideas in macroeconomics used in the following discussions. If you are familiar with introductory macroeconomics, you can jump to the next section.

First, GDP is constructed to represent output, expenditure, and income using a single statistic. The idea is as follows. Produced final goods (output) are purchased by someone (expenditure). Moreover, cash flows to firms through sales are distributed as income to households in various forms such as wages, interests, and dividends (income). The amount of cash flows calculated from the three aspects is identical.

Second, four sectors construct macroeconomy: households, firms, governments, and foreign countries. Each of them purchases goods and services from the market. The expenditure of households in year *t* is called consumption *Ct* , expenditure of firms is investment *It* , expenditure of the government is *Gt* , and the net expenditure of foreign countries is net export *NXt* (export minus import). From the expenditure view of GDP, we have the following identity in the national accounts:

$$Y\_l = C\_l + I\_l + G\_l + NX\_l,$$

where *Yt* stands for GDP. In the following arguments, however, we consider the domestic private sectors in the economy, namely households and firms, to focus on the essence of the growth mechanism. Hence, the above identity becomes *Yt* = *Ct* + *It* , and then the saving equals investment, i.e., *St* = *Yt* − *Ct* = *It* , because *Yt* is also the aggregate income by definition, as mentioned in the previous paragraph.

The mechanism behind the equality of saving and investment is the supply–demand equilibrium in the funds market, where saving is the supply of funds and investment is the demand for them. Because high interest rates are a burden for fund-rasing firms, they do not execute investment projects whose expected returns are not large enough, relative to the interest payments. In other words, investment decreases with the interest rate. When the supply of funds is greater than its demand, the interest rate declines so that firms become able to afford to invest more. With the interest rate as the adjusting device, the demand– supply equilibrium in the funds market guarantees the equality of saving and investment.

Third, we consider a production function that generates real GDP, such as *Yt* = *At K*α *t L*1−α *t* , where *Kt* is capital equipments, *Lt* is labor force, and *At* is productivity. In particular, *At* is called *total factor productivity* (TFP). In the following arguments, we suppose that this production function determines the level of GDP, implying that GDP depends solely on capital and labor endowments and the technology in year *t*. Note that we care about only the supply-side conditions and do not consider the demand-side conditions, whereas a shrink in demands is considered significant for economic fluctuations. The reason why we ignore the demand-side conditions is that we deal with the long-run behaviors of economies, as we observe economic growth over several decades in the above figures. In the standard arguments in macroeconomics, the long-run trend of an economy is considered to be determined by the supply side conditions, and short-run business cycles, where demand side conditions matter, are considered diversions from the long-run trend.

#### **9.2 Basic Theory of Economic Growth**

#### **9.2.1 Solow Model**

Sustained growth can be explained by a simple model established by Robert Solow. Figure 9.4 shows the time series of the log of the real GDP per capita in the United States as a typical example of frontier economies, with the fitted linear line showing the long-run trend. The linear trend shows a good fit to the actual GDP data, which implies that the growth rate is constant in the long run. Moreover, we can extend this trend line dating

back to the mid-nineteenth century. The average growth rate is slightly less than 2% for over 150 years in the United States. There must be a rationale to support such a strikingly long-lasting steady growth. This is our starting point in the theoretical approach.

The Solow model supposes capital accumulation as the main factor to drive the dynamics of economies. To relate capital formation and economic growth, Fig. 9.5 shows the scatter plot of the average growth rate and the average investment shares in GDP from 1960–2019, with the fitted line. There clearly exists a positive correlation between the average investment shares and the average growth rates, implying that countries with large investments tend to grow faster.

To focus on the essential mechanism, we make the model as parsimonious as possible. Let there be only the domestic private sectors in the economy: households and firms. The real GDP in year *t*, *Yt* satisfies

$$Y\_t = C\_t + I\_t,$$

where *Ct* and *It* are the real consumption and investment, respectively. We assume a constant saving rate of households, *s*, so that *Ct* = (1 − *s*)*Yt* and

$$I\_{\mathbf{l}} = Y\_{\mathbf{l}} - C\_{\mathbf{l}} = \mathbf{s}Y\_{\mathbf{l}}, \qquad \mathbf{0} < \mathbf{s} < 1. \tag{9.1}$$

Investment, *It* , is the amount of newly equipped machines in year *t*, which constructs the real capital in the next year, *Kt*+1, which is the total amount of machines at period *t* + 1. Assuming that machines are broken in each period at the rate of δ, we represent capital accumulation as

$$K\_{l+1} = (1 - \delta)K\_l + I\_l \qquad 0 < \delta < 1. \quad (9.2)$$

Outputs are produced with capital and labor as inputs according to the production function,

$$Y\_t = K\_t^\alpha L\_t^{1-\alpha}, \qquad 0 < \alpha < 1,\tag{9.3}$$

where α represents capital share in the sense that α of total income is distributed to capital owners (and 1 − α goes to workers).2 For simplicity, we assume no population growth. *Lt* is constant over time, and, more specifically, we set *Lt* = 1. Then, *Yt* is equivalent with real GDP per capita. The production function (9.3) becomes

$$Y\_l = K\_l^\alpha. \tag{9.4}$$

2From the viewpoint of income distribution, real GDP satisfies *Yt* = *rt Kt* + w*t Lt* , where *rt* and w*t* are the real interest rate and the real wage, respectively. The capital share is measured by *rt Kt Yt* , and the labor share is measured by w*t Lt Yt* .

**Fig. 9.5** Average investment share and average growth rate (1960–2019). *Source* PWT10.0

Substitute equations (9.1) and (9.4) into (9.2), we have

$$K\_{l+1} - K\_l = sY\_l - \delta K\_l = \underbrace{sK\_l^\alpha}\_{\text{investment}} - \underbrace{\delta K\_l}\_{\text{depreciation}},\tag{9.5}$$

which determines the law of motion of capital. We find that there are two opposing forces at work. If investment is greater than depreciation, capital increases such that *Kt*+1 > *Kt* . Contrarily, if investment is smaller than depreciation, *Kt*+1 < *Kt* . Figure 9.6 illustrates how these two forces balance. As drawn in the figure, when capital is *K A t* , investment is greater than depreciation. Then, capital increases in the next period. However, if capital is at *K B t* , depreciation excesses investment, and the capital stock will decrease. Figure 9.6 also depicts *K*∗ at which investment equals depreciation so that the capital stock remains constant. Such *K*∗ is called the *steady state*. If the economy is at the steady state, nothing changes over time unless a shock perturbs the state of the economy. Moreover, Fig. 9.6 tells us that, starting from any positive level of capital stock, the economy converges to the steady state *K*∗. If the capital is less than *K*∗, like *K A t* , the capital increases and approaches *K*∗. If it is higher than *K*∗ like *K B t* , it decreases and gets closer to *K*∗. Hence, the economy is in the steady state in the long run. In the current setting, the steady-state level of capital is

$$K^\* = \left(\frac{s}{\delta}\right)^{\frac{1}{1-\alpha}}.\tag{9.6}$$

Note that the output *Yt* is determined by the level of capital *Kt* . Thus, at the steady state of capital, the output is also in the steady state, meaning no changes over time. The output attains *Y* ∗ = *K*∗α, and the per-capita real growth rate is zero in the long run.

**Exogenous Technological Progress** The above simple model can easily incorporate exogenously growing factors. If we introduce population growth such that *Lt*+1 = (1 + *n*)*Lt* , the per-capita output remains constant while the aggregate real output grows at the rate of *n* in the steady state.

Similarly, we can introduce exogenous technological progress in the form of

$$Y\_l = K\_l^\alpha \left(A\_l L\_l\right)^{1-\alpha},\qquad(9.7)$$

where *At* represents the effectiveness of one unit of labor. We assume that *At* grows at the rate of *g*, or *At*+1 = (1+ *g*)*At* . Then, in the steady state,

the per-capita output grows at the rate of *g* and the aggregate output grows at the rate of *n* + *g*.

Now, we got the theoretical result of steady growth observed in Fig. 9.4. The growth rate is stable because the economy is in a steady state. Positive growth in the per-capita term occurs because of technological progress. If the technological progress rate is not that turbulent, the economy grows at a constant rate on average.

#### **9.2.2 Conditional Convergence Across Countries**

Although the Solow model presents an explanation of economic growth in some frontier economies such as the United States, is it consistent with the international difference in the GDP levels and growth rates, observed in Figs. 9.1, 9.2 and 9.3? Here, we consider whether a poor country will catch up with a rich one in the Solow model.

Let *gK t* be the growth rate of capital from year *t* to *t* + 1. In an equation, it is given by

$$g\_{l}^{K} = \frac{K\_{l+1} - K\_{l}}{K\_{l}}.$$

The relationship between the level and growth in the Solow model is depicted in Fig. 9.7. It is simply from the law of motion of capital, equation (9.5), such that

$$\mathbf{g}\_{l}^{K} = \frac{K\_{l+1} - K\_{l}}{K\_{l}} = \mathbf{s}K\_{l}^{\alpha - 1} - \boldsymbol{\delta},$$

which is decreasing in *Kt* because α − 1 < 0. Therefore, a country with lower capital stock, *Ka* in the figure, has a higher growth rate than countries with abundant capital stock.

So far, it seems like poor countries will eventually catch up with the frontier economies that are considered to be around the steady state, *K*∗. However, it is the case only when every country has an identical steady state.

As shown in Eq. (9.6), the steady-state level of capital per capita is determined by parameters *s*, δ, and α. If we incorporate population growth and technological progress, it also depends on the population growth rate, *n*, and the technological progress rate, *g*, too. Since those parameters vary from country to country in reality, the steady state also varies.

For example, suppose that countries A and B are different in their saving rates, say *sA* > *sB*, while the other parameters and the initial capital stock, *K*0, are the same. From Eq. (9.6), the steady-state levels of capital per capita are *K*∗ *A* > *K*∗ *B*. Even though the initial capital is the same across the two countries, the distance from the initial position to the steady-state level is greater in country A, or *K*∗ *A*/*K*0 > *K*∗ *B*/*K*0. Now apply Fig. 9.7 to each country separately. In the figure for country A, the initial capital is small relative

**Fig. 9.7** Level and growth of capital in the Solow model

to the steady state as if *K*0 is around *Ka*. On the other hand, in the figure for country B, the initial capital is close to the steady state as if *K*0 is around *Kb*. Then, country A has a higher growth rate than country B even though the initial capital levels are the same.

Therefore, the distance to the steady state is significant in the relationship between GDP levels and growth rates. Low growth countries have low levels of steady state. If this is the case, such a poor country never catches up with a rich country unless there occurs a shock or policy intervention on some parameters such as the saving rate, technological progress rate, and so forth.

#### **Poverty Trap**

While we divert a bit from the main context in this chapter, here, we present another way to explain the stagnation of a poor country by extending the Solow model. Suppose that there is a subsistence level of consumption *C*¯. When the income level is less than or equal to *C*¯, they cannot afford to save and just consume all the income. They have positive savings (and investment) only when *Yt* > *C*¯. This situation is described by the investment function,

$$I\_l = \begin{cases} 0 & \text{if } Y\_l \le \bar{C}, \\ s \left( Y\_l - \bar{C} \right) & \text{otherwise.} \end{cases}$$

The other settings are the same as in the baseline model.

The diagram for this modified Solow model is illustrated in Fig. 9.8. The difference from Fig. 9.6 is that the intercept of the investment curve lies at a positive value on the horizontal axis, which creates two intersections with the depreciation curve. The upper intersection at *K*∗ is similar to the steady state in the basic model. The lower intersection at *K*ˆ indicates the divide between the shrinking economy and the growing economy. If *Kt* is greater than *K*ˆ , the investment is more than depreciation, and the economy grows. If *Kt* is less than *K*ˆ , investment is not enough to compensate the amount of depreciation, and capital stock decreases over time.

Even though the upper steady state *K*∗ is potentially possible, a country may be trapped on the left side of the divide at *K*ˆ if it initially lacks a sufficient amount of capital stock. This case is called a *poverty trap*. In order for a developing country to escape from the poverty trap, it needs a big push via official development assistance (ODA) or foreign direct investments with which the capital level is pushed up beyond the dividing border, *K*ˆ . 3

3Although the poverty trap discussed here gives us an insight about economic development, it is difficult to estimate how big is the required push to go across *K*ˆ . Evidencebased policy evaluation is hard without tracking how foreign aids are distributed into the economy. In response

**Fig. 9.8** Poverty trap

#### **9.2.3 Growth Accounting**

The Solow model focuses on capital accumulation as the growth engine, and population and productivity growth are exogenous factors. However, how important is those exogenous growing factors in the data? In this subsection, we run *growth accounting* to investigate the contribution to the growth of each factor that determines GDP.

We consider a slightly different production function such that

$$Y\_l = A\_l K\_l^\alpha L\_l^{1-\alpha},\qquad(9.8)$$

where *At* is TFP.4 We calculate the relationship among growth rates of variables in this production function. Consider the change rate from *t* to *t* + 1 such that

$$\frac{Y\_{t+1}}{Y\_t} = \frac{A\_{t+1}}{A\_t} \left(\frac{K\_{t+1}}{K\_t}\right)^{\alpha} \left(\frac{L\_{t+1}}{L\_t}\right)^{1-\alpha}.$$

Define the growth rates *gx t* = *xt*+1/*xt* −1, where *x* can be *Y* , *A*, *K*, and *L*. Then,

$$\mathbf{1} + \mathbf{g}\_t^Y = \left(\mathbf{1} + \mathbf{g}\_t^A\right) \left(\mathbf{1} + \mathbf{g}\_t^K\right)^\alpha \left(\mathbf{1} + \mathbf{g}\_t^L\right)^{1-\alpha}.$$

It is well known that the above equation is approximately equal to the following relationship,5

$$\mathbf{g}^{Y} = \mathbf{g}^{A} + \alpha \mathbf{g}^{K} + (1 - \alpha)\mathbf{g}^{L},\qquad(9.9)$$

where the aggregate data of GDP and related variables are open to the public in many countries. *gY* is the real GDP growth, *gK* is growth in real capital stock, *gL* is growth in total working hours, and α is the average capital share. Only *gA* can

$$\begin{aligned} \log\left(1+\mathbf{g}^{\boldsymbol{Y}}\right) &= \log\left(1+\mathbf{g}^{\boldsymbol{A}}\right) + \alpha \log\left(1+\mathbf{g}^{\boldsymbol{K}}\right), \\ &+ (1-\alpha)\log\left(1+\mathbf{g}^{\boldsymbol{L}}\right), \end{aligned}$$

where the base of the logs is *e*, i.e., natural logarithm, and we drop time subscript for notational simplicity. Next, we use approximation such that log(1 + *x*) ≈ *x* if *x* is sufficiently close to 0, which comes from the first-order Taylor expansion.

to those critiques, the recent development studies focus on micro-evidences using randomized controls to obtain evidence-based policy evaluation. I recommend Banerjee and Duflo [3] to interested readers.

4Note that this function form is interchangeable with Eq. (9.7), where we can define TFP as *A*1−α *t* .

5To derive Eq. (9.9), we take the logarithm of both sides such that

**Fig. 9.9** Shares of contribution of capital, labor, and TFP to economic growth. *Source* PWT10.0

not be observed directly, but it is calculated from Eq. (9.9) as *gA* = *gY* − α*gK* − (1 − α)*gL* .

We are interested in what percentage of economic growth remains unexplained by observable factors such as capital and labor. So, we define the share of contribution of capital accumulation real economic growth as α*gK* /*gY* when all growth rates are positive. When some growth rates are negative, we define the contribution as

$$\frac{\alpha|\mathbf{g}^K|}{|\mathbf{g}^A| + \alpha|\mathbf{g}^K| + (1-\alpha)|\mathbf{g}^L|},$$

where |*g*| is the absolute value of *g*. 6

Figure 9.9 shows the result of growth accounting for the sample periods of 1960–2019 in 13 countries/regions.7 The set of the countries/regions is limited mainly due to the lack of data required to conduct the above procedure. The figure confirms that capital accumulation is important, as the Solow model supposes. However, at the same time, it also implies that the contribution from TFP is significant in many countries.8 The average contribution of TFP in the current sample is about 35%. In some countries, it amounts to 50% or more. This result motivates us to take a closer look at TFP. However, what the Solow model tells us is that per-capita real GDP has steady growth if productivity grows at a given constant rate. It is nothing about what determines the level and evolution of the productivity. We are going to address this question in subsequent sections.

#### **9.3 Endogenous Growth: How Is the Growth Rate Determined?**

As discussed above, we need to explain TFP growth to uncover the mechanism of economic growth and to obtain an insight for growth policy. In this section, we introduce a new framework, an *endogenous growth model*, in which the economic growth rate is endogenously determined.

6Consider the case in which *gY* = 0, α*gK* = 0.05, and (1 − α)*gL* = 0. In this case, *gA* = −0.05 and the contribution ratios of capital and TFP are 1/2 for each (and zero for labor). This number is generated by |0.05|/ (|0.05|+|− 0.05|).

7The national account data for Germany (DEU) before the integration at 1991 are estimates based on the growth rates recorded for West Germany (Groningen Growth and Development Centre [5]).

8There is a discussion on the undervaluation of the contribution of TFP in the procedure described here. Because TFP includes technological progress, newly introduced machinery embodies higher quality, which increases capital contribution. Thus, part of the contribution of the capital comes from the increase in TFP. Taking this relationship into account, the true contribution of TFP is even higher (and the true contribution of capital is lower) than the shares observed in Fig. 9.9.

Although there are a variety of models of endogenous growth, we mainly focus on productivity growth driven by corporate research & development (R&D) activities, which accumulates ideas, knowledge, and techniques for more efficient production in the society.

#### **9.3.1 Economy of Ideas**

Before jumping into the new growth model, it is convenient to discuss an important feature of knowledge or ideas.  You have come up with a new idea for making a light bulb. This new idea, or innovation, is "yours" in the sense that the patent system prohibits any other person or company from commercializing it without permission. However, the idea itself can be shared with thousands of people who will try to create the next generation of light bulbs based on your idea, including ones that last longer, are safer, and are brighter. An inventor who significantly improves your light bulb will obtain a new patent.

This story highlights three things. First, ideas are *non-rival* goods in the sense that its use by someone else does not prevent others from using the same goods. So, ideas have an aspect of public goods.9 Second, ideas are inputs for subsequent idea creation. An inventor or researcher learns the existing ideas developed by predecessors and tries to create a new idea relying on them. A little dwarf on the giant's shoulder can see further than the giant.10 New ideas are born on the giant's shoulder, and these ideas accumulate to make the giant even bigger. Third, as suggested by the above two characteristics, the private and social benefits of innovation are different. The private value is the profit derived from the product designed by the idea, which is only a part of the social value of innovation. The social value also depends on future innovations inspired by the current idea. In the story at the beginning of this subsection, Edison and the subsequent inventors pursue rents from commercializing a new idea, which is the private benefit. If you predict sufficiently large rents, it is worth investing money, time, and effort. However, the innovation is public in some sense because it will be used extensively in subsequent idea creation. Even if the private benefit is negligible, the social benefit might be large. For example, the formula for solving quadratic equations hardly yields profits, but it will help much subsequent research. Because the social benefit of an innovation is greater than the private benefit in many cases, investment for idea creation tends to be smaller than the socially desirable level. This is where we should consider a policy intervention to encourage R&D in the following model.11

#### **9.3.2 R&D-Driven Growth**

We consider the economy with two sectors in which workers find a job: One is the production sector and the other is the research sector. We assume no skill difference between the sectors for simplicity. Denote *LY t* and *L At* as the production workers and researchers, respectively. Assuming that *Lt* = 1 and define the share of researchers as ρ*t* , we have *L At* = ρ*t* and *LY t* = 1 − ρ*t* .

The production sector is the same as in the Solow model with technological progress,

$$Y\_l = K\_l^\alpha \left( A\_l L\_{Yl} \right)^{1-\alpha},$$

but now *At* does not grow automatically; it grows in response to the researcher's work.

Because productivity *At* reflects scientific and technological knowledge in the society, we suppose that *At* is the stock of ideas and R&D activity increases *At* . As discussed in the previous subsection, the input of idea creation is the stock of ideas, *At* , and researchers, *L At* . Let μ > 0 be the efficiency in the research sector, and we suppose that *At* evolves according to

9The other aspect of public goods is non-exclusiveness. If goods are exclusive, it is possible to prevent someone from using them if the person does not pay the price. Intellectual property rights give exclusivity to an idea.

10Such a metaphor, famously described by Isaac Newton as "by standing on the shoulders of Giants," dates back to the Middle Ages in Europe.

11Jones and Williams [8] estimate that actual R&D investment is less than half of the optimal R&D investments.

$$A\_{I+1} = A\_I + \underbrace{\mu A\_I L\_{AI}}\_{\text{new ideas}}.\tag{9.10}$$

In other words, one researcher creates μ*At* units of ideas.12 Then, the growth rate of *At* is given by

$$\mathbf{g}\_{I}^{A} = \frac{A\_{I+1} - A\_{I}}{A\_{I}} = \mu L\_{AI} = \mu \rho\_{I}.$$

Now, we focus on a *balanced growth path*, generalization of steady state, where each variable has a constant growth rate over time. Note that the steady state in the Solow model is a balanced growth path because the output per capita has a constant growth rate of zero. On a balanced growth path, *gA t* is fixed at some constant so that ρ*t* must be a constant. Let ρ be the number of researchers on a balanced growth path, and we have *gA* = μρ. Then, applying the last argument in Sect. 9.2.1, we have *gY* = μρ.

The argument so far lets us know that what determines the growth rate is the share of researchers or the intensity of R&D activity in the economy. If an economy is more R&D-intensive, it grows faster. However, in what case, is ρ > 0 supported? It depends on the balance between the value of a new idea and the cost to create it. When there is a limited labor supply, wages become higher. A very high wage implies that research costs do not meet the reward from the research, which is the future monopoly rents protected by patents. In such a case, there is no incentive to carry out R&D projects, and ρ turns out to be zero on a balanced growth path. Therefore, we need a sufficient amount of potential resources employed in the research sector to have a positive growth rate in the long run. Certainly, the strength of patent protection is another factor to motivate R&D. Without patent protection, innovators cannot monopolize the market for the product they created because imitators enter the market without paying R&D costs or license fees. The reward for innovation is limited under weak patent protection.13

The R&D-driven endogenous growth model opens the black box of TFP at least partly. It illustrates the mechanism that long-run economic growth is achieved by R&D activities. Moreover, it implies that the more the R&D, the higher the growth rate. Hence, the policy implication is straightforward: Encouraging investment in R&D will lead to rapid economic growth. As argued in the previous subsection, promoting R&D is desirable from the social viewpoint.

There are several ways to promote R&D, such as R&D subsidy, R&D tax credit, patent reform, easing of financial constraints on firms, and so forth. Some policies could affect the efficiency in the research sector, μ. Because a better collaboration of researchers can create better ideas, a matching mechanism may help increase research efficiency at the aggregate level. We need to exclude discrimination when building research teams. A researcher with appropriate expertise should be employed as a team member regardless of gender, nationality, or skin color, which increases the efficiency of researcher allocations in the aggregate economy.

#### **9.3.3 Growth Without Scale Effect**

The model in the previous subsection has one deficit. If we remove the simplifying setting of *L* = 1, the growth rate becomes μρ*L* instead of μρ. Thus, the above model implies that the scale of the economy matters for its economic growth rate. This is called the *scale effect*. But, if there were two identical countries, would merging the two

12One may be wondering how we define the unit of ideas. A standard way to keep track of ideas in empirical research is by counting the number of quality-adjusted patents. Quality adjustment is important because many patents are not used to produce any goods while some patents are essential.

13There are many discussions about the patent system. Patents provide an incentive to innovate, but it sometimes imposes a cost for the next innovations. When strong protection is given to existing patents, inventors have to present significant novelty and originality to get a new patent successfully. A company adopting a new technology would have a higher risk of litigation from an existing patent holder. Hence, the optimal design of a patent is a controversial issue. See Jaffe and Lerner [7] for more discussion. Some researchers argue that innovations will continue to occur even without a patent system, using the development of open-source software as an example Boldrin [4].

produce a country with double the growth rate? Moreover, the above model suggests that the real growth rate increases over time if we allow a positive population growth rate instead of a constant *L*. Is it plausible?

Figure 9.10 scatters the average growth rates and the average total working hours across countries and regions, and we see no significant correlation between the two variables.14 Perhaps, the above model overemphasizes non-rivalry and the idea production process, although it captures an important aspect of technological progress. Here, we modify the model to get rid of the scale effect.

The idea production function, equation (9.10), is linear in the stock of ideas. As scientific knowledge evolves, however, it is getting more complicated and catching up with the frontier knowledge requires more effort of learning for researchers than before. It is natural to consider that creating a new idea is getting harder as knowledge accumulates. Then, research productivity is not linearly increasing in the existing knowledge. This situation can be captured by the following slightly modified idea production function such that

$$A\_{l+1} - A\_l = \mu L\_{AI} A\_l^{\phi}, \qquad \phi < 1.$$

The parameter φ stands for an increasing difficulty along with knowledge accumulation.

With this idea production function, the productivity growth on a balanced growth path is

$$\mathbf{g}^{A} = \frac{A\_{I+1} - A\_I}{A\_I} = \mu L\_{AI} A\_I^{\phi - 1} = \frac{\mu L\_{A1}}{A\_I^{1 - \phi}},\tag{9.11}$$

where *L At* /*A*1−φ *t* must be constant over time. To keep it constant, the numerator and the denominator must have the same growth rate. Since *L At* stops growing if there is a constant upper bound of *L*, we allow *Lt* to grow at rate of *n*. Then, the balanced growth is achieved when all the growth rates of *Lt* , *L At* , and *LY t* are *n*. Hence, *A*1−φ *t* also grows at *n* to keep the fraction in the right-hand side of Eq. (9.11) constant, that is,

$$\left(\frac{A\_{l+1}}{A\_l}\right)^{1-\phi} = 1+n$$

$$\Rightarrow \quad \left(1+g^A\right)^{1-\phi} = 1+n.$$

Then, from a similar procedure in deriving Eq. (9.9), we obtain

14It depends on the era on which we focus, though. In the eighteenth century after the Industrial Revolution, the world population and output start to rise explosively, where population size and output growth have a positive correlation. However, the reverse causality could be true, i.e., rapid growth may result in more capacity to increase the population.

$$g^A \approx \frac{n}{1 - \phi}.$$

Moreover, since per-capita real GDP grows at the same rate of *gA*, economic growth depends not on population size but its growth rate, *n*.

This modification successfully removes the scale effect. However, it erases the R&D policy implication obtained in the original model. Because the growth rate is determined by population growth rate, a policy promoting R&D activity does not increase the growth rate in the long run, while it leaves short-run impacts on the number of researchers and outputs. Any increase in the policy-promoted research outcomes will be offset by the difficulty in developing more complex R&D projects, leaving no impact on the growth rate.

#### **9.4 Other Factors: Look Inside of** *At* **more deeply**

In this section, we discuss three factors other than technology that construct TFP.

#### **9.4.1 Education and Human Capital**

The level of education of the people involved in the labor is one of the important factors that determines production efficiency. Before we look at the overall productivity of a country, let us consider the productivity of individual workers. In the first place, why are you reading this and why are you spending your time and paying for your education? It is probably because there is a return from education. The returns may not always be translatable into money, but there is no denying that getting the job you want and increasing your chances of earning a higher income are important returns. Why do firms pay you a high wage?  Education increases productivity at the individual level.

Figure 9.11 shows a scatter plot of the average level of education (years of schooling) and real GDP growth rates in each country,15 showing a clear positive correlation. As with the investment in physical capital, investment in education is expected to contribute to economic growth by improving *human capital* and raising productivity. Let us formulate this situation in a simple model to see the link between education and growth.

The production function in this context is

$$Y\_l = K\_l^\alpha \left(\mu H\_l\right)^{1-\alpha},\qquad(9.12)$$

where *Ht* represents human capital and *u* is the share that human capital employed in the production sector. The rest of human capital, (1 − *u*) *Ht* , goes to the education sector, or school teachers, that contributes human capital accumulation. Suppose that human capital accumulates according to

$$H\_{l+1} - H\_l = \phi \,(1 - \mu) H\_l,$$

where φ > 0 is the efficiency in the education sector.

In this economy, for a given *u*, the growth rate of human capital is

$$\mathbf{g} = \phi(1-\mu).\tag{9.13}$$

This human capital growth rate turns out the growth rate of the economy. Let us see how it comes. Similar to the growth rate relationship derived at growth accounting in Sect. 9.2.3, we have

$$\mathbf{g}^{\boldsymbol{Y}} = \alpha \mathbf{g}^{\boldsymbol{K}} + (\mathbf{l} - \alpha)\mathbf{g},$$

for a constant *u*. Because the real output and physical capital should have the same growth rates,16

15Data on education are from Barro-Lee Education Attainment Data, which are available from http://www.barrolee. com.

16From the national income identity, *Yt* = *Ct* + *It* . To keep the balance, these three variables must have the same growth rate. Further, capital accumulation equation *Kt*+1 = *It* + (1 − δ)*Kt* implies that *Kt* and *It* also have the same growth rate. Therefore, *gY* = *gC* = *gI* = *gK* on a balanced growth path.

we have *gY* = *gK* = *g*. All growing variables have identical growth rates.

The balanced growth implies that

$$\frac{H\_l}{K\_l} = \text{constant, say } \hat{A}$$

because the numerator and denominator change at the same rate. Using this constant *A*ˆ with the production function, (9.12), we obtain

$$Y\_l = K\_l^\alpha \left(\hat{A}\mu\right)^{1-\alpha} K\_l^{1-\alpha} = \left(\hat{A}\mu\right)^{1-\alpha} K\_l.$$

In other words, production in this economy shows a constant marginal product of physical capital on a balanced growth path, unlike in the Solow model. The Solow model investment curve depicted in Fig. 9.6 has a curvature because the marginal product of capital decreases with the capital level. In the current human capital model, the diminishing marginal product of physical capital is offset by the human capital accumulation to keep the marginal product of physical capital at constant *Au*ˆ 1−α . No matter how much is accumulated, the marginal value of capital does not fall, so the economy will continue to grow. Importantly, when more human capital is employed in the education sector, the growth rate is higher.

#### **9.4.2 Institution**

Differences in productivity among nations that cannot be explained by the production factor endowments or technology are also created by differences in institutions. At the beginning of their book, Acemoglu and Robinson [1] talk about a region divided by the artificially drawn border between the United States and Mexico. Originally, there was little difference between the north and south of the border, and similar people lived similar lives. However, 100 years after the border was drawn, there appeared a marked difference in the standard of living across the border. The gap in North and South Korea is another example. The border between the two countries was artificially drawn for political reasons due to the Korean War, and there was no intrinsic difference. Seventy years later, however, the difference in wealth between them is enormous.

Such artificial borders are grand social experiments that give us insights. If there is a big difference between two countries that are not different by birth, the cause is the environment in which they grew up. In other words, the laws, rules, political systems, and customs of the countries to which the residents happen to belong are of decisive importance. Are private property rights guaranteed there? Does it allow for free market transactions? Do successful entrepreneurs get paid what they deserve? What kind of education system does it have? How well developed is its social infrastructure? Is its political system democratic?

This argument suggests that some part of TFP, *At* , should be explained by institutions. A more efficient institution results in higher *At* , leading to a greater real output and possibly real growth rate. However, it is not easy to pinpoint what exactly is good and what is bad in the institutions. It is not necessarily true that transplanting the institutions of frontier economies, such as the United States, directly to developing countries will work. It is easier said than done.

#### **9.4.3 Misallocation**

One of the most important findings in recent economic growth studies is the impact of *misallocation* of resources on aggregate productivity. Suppose that there are two types of firms operating in the market: One is highly productive and the other is less. Then, it seems efficient to transfer resources employed by low-productivity firms to high-productivity firms. However, such reallocation could not smoothly occur in the market because we observe wide productivity dispersion across firms even within narrowly defined industries. When the misallocation of resources significantly reduces aggregate productivity, policy interventions that promote the reallocation of resources are desirable to improve people's wellbeing.

Hsieh and Klenow [6] is the seminal work to measure the degree of misallocation. It should be noted that simple observation of productivity dispersion is not an evidence for misallocation. The coexistence of large high-productivity firms and small low-productivity firms may be efficient because of declining marginal products and capacity constraints such as plant size. To quantify misallocation inefficiency, they consider "revenue" productivity instead of the usual TFP, which is coined as TFPR.

The logic is simple and interesting. Suppose that a firm has the production function of *Y* = *AL*, where *A* is the firm-level TFP and *L* is employment, hired at the wage rate of w. The cost to produce one unit of goods is w/*A*. If this firm determines its price with some markup margin, at the rate of *m* ≥ 1, the price of the goods is *P* = *m*w/*A*. Then, the TFPR of this firm is

$$\text{TFPR} = \frac{PY}{L} = PA = mw.$$

Therefore, TFPR is independent of *A*. This result holds even with more general production function such as the Cobb–Douglas type with physical capital as in Eq. (9.3).

This simple calculation implies that all firms should have the common TFPR in theory after controlling markups and wages. Then, if we find a dispersion in TFPR, some wedge exists to generate a gap from the theoretical outcome. Based on this logic, Hsieh and Klenow [6] define the degree of misallocation as the observed dispersion in TFPR. According to their estimates, China and India have higher degrees of misallocation compared to the United States in the manufacturing industries. They also estimate the aggregate productivity of both countries when they have the same degree of misallocation as the United States. The results show that aggregate productivity is expected to increase by 30–50% in China and 40– 60% in India, strikingly large numbers.

Reducing misallocation of resources across firms may have a significant impact on the aggregate economy. However, designing a reallocation policy is not simple because the sources of misallocation can be diverse. Adjustment costs such as firing costs would make reallocation slow. Protective policy for small firms would matter. The institution discussed in the previous subsection also matters. Taxation, financial constraint, or any distortions may affect the degree of misallocation in one country. So far, there is no consensus on the most important factor to explain misallocation. Rather, the main source seems different across countries and periods.

#### **9.5 Conclusion**

A country does not become rich overnight, and when it starts, the process of steady growth depends largely on historical circumstances. So, it is natural that there are variations in the level of economic wealth or real GDP per capita. The more important question is whether poor countries will turn into rich countries, that is, whether a poor country attains rapid growth and will catch up with the group of rich countries or not. To catch up with and hopefully overtake rich countries in the long run, poor countries need to achieve sustained economic growth rather than a temporary hike in the GDP levels. If a poor country has a growth rate that is 2% higher than a rich country that initially had twice the GDP, it will take 35 years to catch up. If the growth rate gap is 5% instead, it will only take about 14 years. This is not just a play on numbers. It is what actually happened in Japan in the 1960s and in China since the 1990s.

In this chapter, we have outlined the typical mechanisms of economic growth in as simple a model as possible while sorting out the facts related to economic growth.We have covered the accumulation of physical and human capital, technological progress, institutions, and misallocation, but which factors constitute the main problems will vary depending on the country being addressed. Since policies for economic growth will vary accordingly, we must first carefully observe the conditions of the country or region we are dealing with. In this sense, this chapter can be seen as providing a list of points to pay attentions to.

However, there are other factors that we could not cover in this chapter due to space limitations. In particular, trade and cross-border technology transfer are important in international economic interdependence. Trade with technologically advanced countries and direct investments from them cause an influx of ideas and technology to developing countries. Technology adoption and learning through imitation are typical steps in catching up.17

Finally, having clarified the causes of economic growth throughout this chapter, we should also remark the consequences of economic growth. Increased GDP leads to higher consumption and living standards, but thriving economic activity places a greater burden on the global environment. We need to consider the balance between economic growth and the environment from multiple perspectives. There is also the issue of inequality: Even if the size of GDP expands, not everyone will necessarily benefit from it. We must always pay attention to the distribution of wealth to ensure that economic growth does not widen the gap and leave some people behind.

#### **References**

17See Baldwin [2] for arguments about trade, global supply chains, and international convergence.

**Open Access** This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

# 10 Structure of Development in a Smart Society: An Application of Input–Output Analysis

Ayu Washizu and Satoshi Nakano

#### Abstract

The construction of a smart society utilizing information and communication technology (ICT) is attracting attention to simultaneously achieve various Sustainable Development Goals (SDGs). Using input–output analysis, this chapter elucidates the economic structure of a smart society. This content is an extension of Leontief's "Structure of Development" study of the 20th-century industrial society. Here, a smart society enables waste to be eliminated and the utility of people to be increased by strengthening management in all fields of society using ICT. It is shown that a smart society will achieve an industrial structure with a lighter environmental load and sustain moderate economic growth. Therefore, the movement aiming to build a smart society in Asia and other regions of the world is deemed beneficial and expected to contribute to achieving the SDGs. Additionally, Japan is a

S. Nakano Nihon Fukushi University, Tokai, Japan e-mail<EMAIL_ADDRESS>
developed country with advanced ICT in Asia, and improving the efficiency of Japan's ICT has been found to profoundly affect the entire Asian region. Japan plays a key role in building a smart society in the Asian region. This chapter is not only directly related to SDG9, but also to SDGs2, 5, 7, 8, 11, 12, and 13.

#### Keywords

Input–output table Smart society Information and communication technology Structure of development

#### 10.1 Introduction

In his (1994) book, The Digital Economy, Tapscott states that information technology brings new social norms for wealth creation and social development. This suggests that economic development in the information society requires an analytical perspective that is different from the conventional economic growth theory. Furthermore, Jorgenson and Vu (2016) report that a wide range of policy considerations are needed to guide economic growth through the information and communications technology (ICT) revolution. Jorgenson and Vu (2016) measure the contribution of ICT investment to economic growth and show that China and India are driving the world economy. On the one hand, Kooshki and Ismail (2011) empirically show that

A. Washizu (&) Waseda University, Tokyo, Japan e-mail<EMAIL_ADDRESS>
ICT investment has a positive impact on economic growth in newly industrialized countries in Asia. On the other hand, Pradhan et al. (2015) state that the construction of ICT infrastructure alone does not guarantee economic growth and must be accompanied by financial development. Vu (2013) also states that ICT use contributes to economic growth, while the contribution of ICT manufacturing to economic growth is limited (in the presence of China and India) based on empirical research on economic growth in Singapore. To clarify the effects of the spread of ICT on economic growth, these previous studies show that it is insufficient to investigate the effects of physical production and investment in ICT devices.

To verify the effects of ICT use, it is necessary to study the effects of services that utilize ICT. Toh and Thangavelu (2013) analyze the impact of the information sector on Singapore's economy using an input–output approach, which provides them with a framework for analyzing the linkage between the manufacturing and service sectors. A recent study (Tripathi and Inani 2020; Usman et al. 2021; Murshed 2020) has reported that informatization also contributes to economic growth in South Asia, and the effect of informatization is widespread throughout Asia, thereby suggesting expansion. Moreover, several studies (Usman et al. 2021; Murshed 2020; Lu 2018) argue that ICT contributes not only to economic growth but also to the mitigation of global warming.

Based on the aforementioned points, the following submissions are made: (1) research on the effects of introducing ICT requires an analytical framework that integrates various sectors and regions, (2) the effect of introducing ICT is greater when it is used than when producing ICT devices or investing in ICT infrastructure, and (3) it is necessary to grasp the value of ICT use that exceeds the economic value captured by conventional statistical indicators. Regarding point (1), the input–output framework used by Toh and Thangavelu (2013) is considered to be an appropriate analytical approach for analyzing the effects of ICT introduction. Notably, the framework for international input–output analysis, e.g., World Input–output Database (WIOD),1 enables the evaluation of interdependencies between regions as well as sectors. At that time, in relation to point (2), it is necessary to consider how to describe the economic activity of ICT use within the framework of input–output analysis. In relation to point (3), it is necessary to expand the sector classification of the conventional input–output database. As Watanabe et al. (2018) indicate, ICT contributes beyond conventional economic values, thereby resulting in uncaptured gross domestic product.

In Japan, a new society that makes advanced use of ICT is referred to as a smart society, and the Japanese government has set the building of a smart society as one of its policy goals.2 Currently, the building of smart societies is ongoing in other Asian countries. A theoretical understanding of the effects of building a smart society on the economy and how it contributes to regional economic development is an important issue in Asian development studies. Thus, directly related to SDG9, this chapter aims to explain the structure of development in a smart society that utilizes ICT using the input–output analysis framework.

The structure of this chapter is as follows: Sect. 10.2 explains the framework of the input– output analysis. Section 10.3 describes the structure of development theory using the input– output framework proposed by two representative input–output researchers (Professors Leontief and Ozaki), while Sect. 10.4 considers how their theory can be extended to explain the structure of the development of smart societies that utilize ICT. Section 10.5 uses the WIOD to provide an overview of the current state of interdependence between regions and sectors in Asia, including the relationship between the ICT manufacturing and ICT use sectors. Finally, a summary of the chapter is presented in Sect. 10.6.

1 World Input–output Database, http://www.wiod.org/ home.

2 Cabinet Office, Government of Japan, "Society5.0", https://www8.cao.go.jp/cstp/society5\_0/.

#### 10.2 Input–Output Framework3

Figure 10.1 is a conceptual diagram of the input–output table used for the analysis. It was originally developed by Prof. Wassily Leontief in the 1930s (see Leontief 1986). This table is a matrix that summarizes the annual transactions between sectors within an economy. The vertical columns show how each sector obtains the required inputs from others. Conversely, the horizontal rows show how the output of each sector of the economy is distributed among the others. This input–output table that describes the relationship between the product of one sector and the input of another sector reveals the interdependence in the economic sectors. In recent years, input–output tables4 have been used to analyze the effects of sustainable economic structures using renewable energy on the economy and the environment (Washizu and Nakano 2021a).

In this figure, xij is the component of the intermediate transaction matrix, X, and represents the monetary amount of the ith good consumed by activity j; P i xij þ vj ¼ xj is the sum of xij in terms of the ith good and the value-added, vj, and it represents the total output for activity j; the ratio of xij to xj, aij ¼ xij=xj, is called the input or technical coefficient; and the set of input coefficients of activity j, i.e.,

$$\mathbf{a}\_{j} = \begin{pmatrix} a\_{1j} \\ a\_{2j} \\ a\_{3j} \\ \vdots \\ a\_{mj} \end{pmatrix} \tag{10.1}$$

is called the activity vector of activity j. Leontief defines vector Eq. (10.1) as the representation of

Fig. 10.1 Conceptual diagram of an input–output table

the production technology of activity j. A full set of input coefficients of all sectors is described by the symbol A and is called the input coefficient matrix. Using an input coefficient matrix, we can express the demand and supply balance as follows (the LHS of Eq. (10.2) is the sum of the intermediate and final demand):

$$\underbrace{\mathbf{Ax} + \mathbf{f}}\_{\text{demand}} = \underbrace{\mathbf{x}}\_{\text{supply}} \tag{10.2}$$

Here, x is the output vector (monetary units), A is the input coefficient matrix, and f is the vector of the final demand (monetary units).

Solving Eq. (10.2) for x, we can obtain the Leontief inverse matrix ð Þ I A 1 . According to Eq. (10.3), we can see the direct and indirect effects induced by the given final demand vector. The effects contain all production amounts of goods and services directly and indirectly needed throughout the supply chain of goods and services included in the final demand vector.

$$\begin{aligned} \mathbf{x} &= (\mathbf{I} - \mathbf{A})^{-1} \mathbf{f} \\ &= \underbrace{\mathbf{If}}\_{direct} + \underbrace{\left(\mathbf{A} + \mathbf{A}^2 + \mathbf{A}^3 + \cdots\right) \mathbf{f}}\_{indirect}, \quad (10.3) \end{aligned}$$

where I denotes the unit matrix. Figure 10.2 is a conceptual diagram of the direct and indirect effects induced by the final demand of the automobile (the induced effect when the component of the f vector in Eq. (10.3) is only the

3 See Nakano et al. (2015) in relation to this section.

4 Institute for Economic Analysis of Next-generation Science and Technology, input-output table for analysis of next-generation energy system, http://www.f.waseda. jp/washizu/table.html.

automobile). Figure 10.2 can be interpreted as an illustration of the automobile supply chain.

The international input–output table analyzes the economic interdependence between sectors as well as between regions by combining the input–output tables of several countries. Figure 10.3 is a conceptual diagram of the international input–output table among three countries A, B, and C. Using this table, we can analyze the effect of the final demand by the people of Country A, for example, on the production activities of the sectors in Countries B and C through international intermediate transactions.

#### 10.3 Structure of Development Theory

This chapter describes the mechanism of economic growth (led by manufacturing), which has been elucidated in previous studies under the framework of input–output analysis. It explains the structure of the development theory proposed in the past by two representative input–output researchers (Professors Leontief and Ozaki).

#### 10.3.1 Leontief's Structure of Development Model5

Wassily Leontief is the founder of the input–output table and has been awarded the Nobel Prize in Economics for his work. He said, "It was the labor of computation that promoted the first systematic studies of the structural characteristics of an economy as they are displayed in an input–output table. (The members of US government's project) undertook to rearrange the rows and columns in a table of the US economy in such a way as to minimize the computation required to yield numerical solutions. Such rearrangement brought into sharper relief the inter-industry and intersectoral transactions that tie industries and sectors together in the subunits of the total structure of the economy" (Leontief 1986, p. 166).

According to Leontief, each sector does not have a uniform intermediate relationship with other sectors in the input–output table. Leontief submits that the input–output table can be organized in a form similar to Fig. 10.4 by

Fig. 10.2 Conceptual diagram of the direct and

final demand of the automobile

5 For the contents of this subsection, see Chap. 8 "Structure of Development" in Leontief (1986).

Fig. 10.3 Conceptual diagram of an

table

international input–output

rearranging the row and column sector array in the actual table because there are some parts where there are almost no intermediate transactions between sectors. He refers to such a structural feature in the input–output table as "triangularity."

Figure 10.4 shows the case where the structural relationships between sectors have the most complete hierarchical relationship. In Fig. 10.4, the first sector purchases inputs from all other sectors, while the tenth sector supplies inputs to all other sectors. The other sectors are arranged in the order of proximity to each role. The first sector, i.e., the automobile sector, produces complex goods with a large number of parts, and the tenth sector, i.e., the energy or corporate services sector produces general purpose and basic intermediate goods. Figure 10.4 illustrates the process whereby the intermediate goods of the sector at the bottom of the triangle are sequentially processed into the goods of the sector at the top of the triangle which are used for final consumption. The actual input–output table is composed of several blocks with a triangular structure shown in Fig. 10.4. For example, there is a machine block and a food block, and each block has a strong interdependence within itself, but the interdependence between blocks is relatively weak. Such a situation whereby the actual input–output table is composed of triangular blocks is called "block-triangularity" of the industrial structure.

According to Leontief, these structural features are discovered in the process of rearranging the order of sectors in the input–output table to simplify computer calculations.

#### 10.3.2 Structure of Development During Japan's High Economic Miracle Period

Ozaki (2004) further extends Leontief's structure of development theory discussed in the previous section and clarifies the structure of development during Japan's high economic miracle period. This section describes Ozaki' s structure of development theory.

#### <IP_ADDRESS> Rearrangement of Input– Output Sectors Based on Supply Chain

Ozaki (2004) initially considers the factors that cause block-triangularity in the industrial structure mentioned in the previous theory. Leontief (1986) does not explicitly discuss why the industrial structure has the block-triangularity properties. To explore the causes of blocktriangularity, Ozaki (2004) assumes that manufacturing industries in each field need to build

their own efficient supply chains in order to establish economic growth through industrialization. He rearranged Japan's input–output table after a period of high economic miracles based on the following theoretical hypothesis:

In an economic structure, there are several supply chains that connect and integrate multiple sectors. In the process of economic development, limited resources, labor, capital, etc. are sequentially invested along this chain, and one economic structure is formed.

As a result of this rearrangement, he discovers the nature of block-triangularity in the Japanese industrial structure. Ozaki's research process leading up to this discovery is presented as follows:

As a working hypothesis that embodies the aforementioned theoretical hypothesis, Ozaki assumes four supply chains based on the type of natural resource of their origin. They are supply chains from metal ores, natural crops, nonmetal minerals, and crude oil. In each supply chain, starting from the input of natural resources, related industries are ranked according to the processing stage of the product, leading to the final products. The more sophisticated the technology, the more diversified the sectors involved in one supply chain, but the number of main inputs for each final product is relatively limited. Leontief has established that the industrial structure is divided into blocks, and each block has triangularity. Ozaki extends Leontief's theory and clarifies that the blocks in the industrial structure are divided based on the type of raw material and that the triangularity of the industrial structure results from the rearrangement of the sectors according to the processing path of each supply chain. Generally, as technology becomes more sophisticated, the processing stage (supply chain) is extended, and more valueadded is created. Therefore, if the technology becomes more sophisticated as the economy develops, the triangularity of the industrial structure will become clearer. At that time, the interdependence within one block will be strengthened, and the interdependence between blocks will simultaneously and gradually occur. For example, a food supply chain originating from agricultural products (natural crops) requires chemical fertilizers (products of the supply chain originating from nonmetallic minerals), and thus, interdependence will occur between a block originating from natural crops and that from nonmetallic minerals.

Based on the aforementioned working hypothesis, Ozaki closely tracks the supply chain originating from different raw materials found in Japan's 1965 input–output table and rearranges approximately 450 sectors therein.

Figure 10.5 shows a conceptual diagram of the sectoral rearrangement according to the supply chain. Starting from a certain raw material input (RM), products are sequentially processed in the order of the main material input (MM) according to the processing route of the supply chain, and the final product is produced. The sectors that support this mainstream concept include energy supply (E), auxiliary material input (Aux) (general-purpose goods and services used in the production of various industries), repair services (Rep), and various other services (S). The goods and services produced by these support sectors are introduced at all stages of the supply chain.

When the input–output sectors are rearranged according to the aforementioned hypothesis, the industrial structure shown in Fig. 10.6 is confirmed. The colored part in Fig. 10.6 shows that the intermediate transactions between sectors are solid, and the white part shows that virtually no transactions are found between the sectors. The six parts of the MM, RM, E, Aux, Rep, and S in Fig. 10.6 correspond to the rectangle of the same name in Fig. 10.5. In Fig. 10.6, the MM part is further divided into five subparts: machinery/ metal, food, ceramic, textile, and chemical. Each subpart corresponds to one of the four supply chains (as shown in Fig. 10.5) originating from four types of RM inputs.6 Figure 10.6 confirms the block-triangularity property. In other words, it has been confirmed that the industrial structure of Japan, which has been completed since the period of high economic miracle, has blocktriangularity properties based on the supply chain originating from different raw materials.

Leontief discovers the block-triangularity nature of the industrial structure in the process of rearranging the sectors of the input–output table to simplify computer computation, while Ozaki establishes a similar block-triangularity property by rearranging the sectoral arrangements in the input–output table based on the theoretical hypothesis of the supply chain. Ozaki's work justifies Leontief's discovery.

#### <IP_ADDRESS> Technology Classification of the Input–Output Sector

Following the rearrangement of the input–output sector, Ozaki measures the production functions of each input–output sector and classifies the sectors based on the measurement results, i.e., based on the nature of the technology.

The most basic production function traditionally used in microeconomics assumes that the factors of production can be flexibly substituted. For example, when the factors of production are labor and capital, if labor is relatively cheap, the technology of using a relatively significant amount of labor will be adopted (and vice versa). However, according to Ozaki, it is unlikely that the production function that allows flexible factor substitution is applicable to heavy industry, which has rapidly developed since the high economic miracle period. Heavy industries require large-scale capital equipment. For example, the steel industry requires the construction of largescale blast furnaces, and even in countries where capital is scarce, labor cannot be substituted for capital. Moreover, once a capital facility, such as a blast furnace, is constructed, the relationship between the required factor input and production is fixed to some extent by the design value. When the demand is extremely low, it becomes difficult to reduce production according to the demand. Ozaki submits that capital equipment in the heavy industry has such a fixed production scale, and he refers to it as "plant indivisibleness."

Based on these, Ozaki measures the following two types of production functions for all sectors using microdata from industrial statistics.

6 The textile supply chain is an extension of the chemical supply chain originating from crude oil. Ozaki posits that during the period of high economic miracle, a material revolution occurred, and natural fibers used as textile raw materials were replaced by chemical types.

Fig. 10.6 Japan's industrial structure after the high economic miracle period

The factor-limitational production function is that whereby the input of labor and capital is determined independently according to the level of production, and no factor substitution is allowed between labor and capital. Furthermore, when bL or bK\1, economies of scale work on labor or capital input. The Cobb–Douglas production function, which allows for factor substitution, is traditionally used in microeconomics. Ozaki empirically estimates the two aforementioned types of production functions for all input– output sectors and examines which production function is more applicable to each sector. He further evaluates the parameters of the estimated production function in detail and classifies all industrial sectors into five subgroups according to the estimated parameters of the production functions. He argues that such a classification is based on the "technical characteristics" of each sector. Table 10.1 shows the names given to the "technical characteristics" of each subgroup and a summary of each technical characteristic.

#### <IP_ADDRESS> Mechanism of Japan's High Economic Growth

Ozaki's structure of development model can be summarized using the industrial structure diagram (Fig. 10.6), in which the order of the sectors is rearranged, and the technical characteristics of each sector (Table 10.1). Figure 10.7 shows a redrawn diagram of Fig. 10.6 for explanation. As mentioned previously, the filled parts in the figure indicate that there are many intermediate transactions. The block-by-block triangular-filled area shows the supply chain inside each block. The wide square-filled area below indicates that energy, auxiliary materials, etc., are universal inputs to various industries. Moreover, the rectangular filled area that extends to the left of the chemical block shows a material revolution, which is a characteristic technological change in the era of high economic growth. In other words, natural materials, such as natural fibers and wood, have been replaced by artificial materials, such as chemical fibers and resins. As a result of this replacement, chemical raw materials have become universal inputs to other sectors. Additionally, after high economic growth, the weight of the machinery and steel industries in the top block of the diagram significantly increases. Furthermore, from the 1970s to the 1980s, the weight of the assembly machinery industry (automobile, electronic/electrical machinery industry), which is located at the top of the top block, increases, and the industrial structure became more sophisticated.

Of the filled parts in Fig. 10.7, the dark-filled blocks are sectors with capital-intensive technical characteristics, in which economies of scale work strongly (sectors with K (I)-type technology). Figure 10.7 shows that the blocks with strong economies of scale are located at the top and bottom of the block-triangularity structure of the MM part. The blocks, such as the food and textile industries, sandwiched between them are a group of sectors with labor-intensive (L-type) technology. Focusing only on the machine-metal refining block located at the top of Fig. 10.7, the assembly machinery industry is located at the top of this block, while the metal refining industry is located at the bottom. These are the sectors with the K (I)-type technology defined by Ozaki. Sectors that produce mechanical parts are located in the middle of these sectors. Mechanical parts are often produced in small-town factories that have labor-intensive technical characteristics.7

To summarize the aforementioned, in Fig. 10.7, the capital-intensive sectors with economies of scale are located above and below the block-triangularity structure of the MM part, and the labor-intensive sectors are located between them. The same positional relationship applies to the internal structure of the machinemetal refining block that has driven the Japanese economy since the high economic miracle period.

The industrial structure diagram shown in Fig. 10.7 helps to explain the mechanism of the high economic miracle in Japan. A major feature of this period was the bullish and active investment motivation of companies that "investment calls for investment." The willingness to invest created a high demand for the assembly machinery industry, located at the top of the industrial structure. Large-scale production to meet this demand brought efficiency to the assembly machinery industry with the K (I-M)-type technology by pursuing economies of scale. The large-scale demand generated in the upper part of the block-triangularity structure returned to the supply chain and spread to the sectors in the lower part of the triangularity structure. In other words, the large-scale production of final products also caused the mass production of raw materials and intermediate parts. Consequently, mass production occurred even in the chemical block with the K (I-B)-type technology located at the bottom of the block-triangularity structure, and great economies of scale also occurred in that block. A similar spillover effect was true for the internal structure of the machinery–metal refining block,

7 Workers in these labor-intensive town factories producing mechanical parts possess sophisticated skills for delicate work. These skills are one factor which supported the international competitiveness of Japanese-made machines. It is desirable to digitize the professional skills of these workers to ensure they are passed on efficiently to future generations. This is also one of the purposes of a smart society described in a later chapter.

Table 10.1 Classification of the technical characteristics of sectors

Fig. 10.7 Mechanism of high economic growth

which has been a major part of the Japanese economy during the high economic miracle period. In other words, the economies of scale of the assembly machinery industry at the top of the block triggered economies of scale in the metal refining industry at the bottom of the block.

However, the pursuit of economies of scale is essentially a labor-inhibiting phenomenon. In particular, a major feature of the K (I)-type technology is that economies of scale in labor input work strongly, and the larger the production scale of sectors with the K (I)-type technology, the more labor-saving progresses. When sectors with the K (I)-type technology mainly drive economic growth, it is not expected that labor demand will increase with economic development. In Fig. 10.7, it is important that a labor-intensive sector exists in the middle of the triangularity structure. This is because the spillover effect of large-scale demand generated in the upper part of the triangularity will surely extend to labor-intensive sectors. Large-scale labor absorption occurs in the middle block through the spillover effect from the triangularity upper sectors. An increase in labor demand will lead to an increase in consumer demand through an increase in employee income. In Japan, during the high economic miracle period, this consumption demand formed a large domestic market for products of assembly machinery industries. Certain terms, such as "three sacred treasures (electric refrigerator, electric washing machine, black and white TV)" and "3C (car, cooler, color TV) era," are slang terms that refer to the domestic market for home appliances formed in this way. Apparently, the formation of such a domestic market further strengthened the effect of the previously mentioned ripple mechanism. Similarly, a large-scale employment absorption effect occurred at a small machine parts factory located in the middle of the machine-metal refining block, which was a major part of the Japanese economy during the high economic miracle period.

To summarize, in the Japanese economy during the period of high economic miracle, the expansion of demand for the upper triangularity sectors spread to the lower triangularity sectors, and economies of scale were pursued in those sectors. Meanwhile, large-scale labor absorption occurred in the middle sectors of the triangularity. This mechanism has arisen technically through the transaction of intermediate goods along the supply chain, and thus, it can work in any country, not just Japan. However, in the case of Japan, this technical mechanism was reinforced by the institutional mechanism of affiliated relationships with Keiretsu between companies. In general, when discussing Japan's period of high economic miracle, the affiliation relationship between companies centered on banks, remaining from the prewar conglomerate, is emphasized. This affiliated relationship is the relationship between large enterprises and small and medium-sized enterprises (SMEs). The upper and lower sectors of the block-triangularity are dominated by large enterprises. Notably, SMEs dominate the middle sector of the triangularity. Accordingly, the affiliation relationship corresponds exactly to the block-triangularity of the input–output relationship. Therefore, in order to maintain this relationship properly, the Ministry of International Trade and Industry (MITI)8 took measures to support SMEs as part of its industrial policy during the high economic miracle period. Thus, during the period of Japan's high economic growth, the efficient economic cycle mechanism functioned by mutually reinforcing the technical input–output relationships and institutional corporate relationships.

The key to this efficient economic cycle mechanism is the high final demand for the machinery sector located at the top of the triangularity structure. This stimulus of final demand generated an efficient cycle in the entire economic system through input–output relationships, and Japan's high economic growth was realized. However, when the high economic growth ended, domestic investment demand for machinery stagnated. Rather, from the late 1970s to the 1980s, the international competitiveness of Japan's machinery sector increased, and export demand replaced domestic investment demand, thereby driving the economy. However, in the 1990s, the catch-up of Asian countries reduced the international competitiveness of Japan's machinery sector, thus resulting in a decline in export demand for the upper sectors of the triangularity structure. Thereafter, the economic

8 The predecessor of the current Ministry of Economy, Trade and Industry (METI).

circulation mechanism malfunctioned, and the economy stagnated. This is one of the causes of the stagnation of the Japanese economy in the 1990s, which is referred to as the "lost decade."

#### 10.4 Structure of Development of a Smart Society

In the analysis of a modern economic society, wherein the weight of production activities in the service industry has increased, it is necessary to pay more attention to the input–output relationships between the service sectors located in the Aux, R, and S parts and to expand the discussion in Figs. 10.6 and 10.7 accordingly. Especially in recent years, with the development of ICT, new business services (information processing services, data provision services, etc.) that have never existed in the past are developing. Therefore, it is necessary to consider the role of ICTrelated service sectors in the entire industrial structure. As mentioned in the introduction, it is important to focus on the economic activity of ICT use. Moreover, ICT will create unprecedentedly new economic values such that it may be necessary to expand the conventional input– output database. Section 10.4.1 explains how the structure of development theory presented in Sect. 10.3 is extended when focusing on the service industry of ICT use. Section 10.4.2 provides a perspective on how to expand the conventional input–output database for the analysis of a smart society.

#### 10.4.1 Information Service Industry and Industrial Structure

Nakano and Washizu (2018) focus on the smart food industry and divide ICT-related industries into manufacturing sectors necessary for ICT infrastructural development and service sectors that utilize it. Furthermore, the latter is divided into sectors that provide general purpose and basic ICT services such as communication services, i.e., the primary information service (PIS) part, and sectors that provide ICT utilization services customized for each customer in detail according to user requests, i.e., the secondary information service (SIS) part.

Subsequently, Nakano and Washizu (2018) visualize the emergence of new input–output relationships between ICT-related (manufacturing and service) industries and food-providing sectors. In a smart society, it is expected that such new input–output relationships between ICT-related sectors and those that produce goods and general services are progressing in various industries other than the food industry. Figure 10.8 is a conceptual diagram of the input– output structure of such a smart society, which is created by extending Figs. 10.6 and 10.7. In Fig. 10.8, the service sectors at the bottom of Figs. 10.6 and 10.7 are expanded to the PIS, SIS, and general service sectors.

Here, the PIS sector refers to those that produce the basic information services necessary for the production of the SIS described below, such as the Internet, communication, broadcasting, as well as research and development. Secondary information services are sectors that produce application services customized for industry, such as wholesale/retail, finance, advertising, transportation, and legal/accounting services, which are produced by combining information goods and the PIS. The information goods sector is the manufacturing sector of MM parts that produces sensors and computer equipment. General services are other service sectors that are not included in the PIS and SIS sectors, and the quality of services provided can be improved by utilizing information goods as well as PIS and SIS. It can be thought of as a production sector for more highly customized services for end consumers, including households.

In the MM part, rearranging the sectors to trace back to the final goods production process shows a triangularity structure. Similarly, if we rearrange the service sectors in the order of general services ! SIS ! PIS, a triangularity structure will be shown in the service part as well. Furthermore, large IT companies, such as GAFA (Google, Apple, Facebook, and Amazon), are currently attracting attention. Our empirical study using the Basic Survey of Corporate

Fig. 10.8 Conceptual diagram of the input–output structure of a smart society

Activities in Japan suggests that the PIS sector, which provides the communications infrastructure (platform), is capital-intensive and is increasing returns to scale (Washizu and Nakano, 2021b). This property is similar to that found in large-scale equipment industries, such as the steel and chemical sectors in the MM part. Washizu and Nakano (2021b) also suggest that not only the information service sectors but also the general service sectors are shifting to a capital-intensive industry through the strengthening of equipment related to computerization.

The economic cycle in the industrial structure shown in Fig. 10.8 can be explained as follows: a variety of end services that are customized for individual service consumers have a continuous end demand (arrow 1). The final demand induces economies of scale for the PIS block below the triangle of the service part and increases the productivity of the block. Increased productivity of the PIS block located in the lower triangle will contribute to lower prices of general services in the upper triangle of the service part through the supply chain of the service part (arrow 2). According to Ozaki (2004), the service industry is a basic input in all industries, including the MM part sector (arrow 3), so the effect of increasing the efficiency in service sectors and lowering service price will bring cost reduction effects and productivity increase effects to the sectors in the MM part. The decrease in the price of information materials in the MM part increases the capital intensity of the service part, including the general service sectors, and activates the flow of information equipment input from the MM part to the service part (arrow 4). As the demand for general services is less likely to be saturated than the demand for goods and is considered to be continuous, the economic effects of the previously mentioned economic cycle are also expected to be continuous.

#### 10.4.2 Toward the Input–Output Analysis of a Smart Society

Watanabe et al. (2018) report that ICT may create new economic values that cannot be captured by means of conventional economic indicators. Nakano and Washizu (2018) also attempt to capture such a new economic value. They define a smart society as that wherein management is highly sophisticated by utilizing ICT. They focus on "management activities" as economic activities that create new value using ICT. However, it can be difficult conceptually and statistically to estimate the actual size of those activities and values because they are not properly captured in conventional input–output tables, and they are often buried beneath the surface of an industry. Nakano and Washizu (2018) undertake this difficult task by referring to Porat (1977).

It is useful to review Porat (1977) when considering the estimation method of the actual size of information activities and those values that are buried beneath the surface of other industries and not captured at present. In the late 1960s, Porat set out to quantitatively measure what fraction of the gross national product (GNP) in the USA is related to information activities. He proposes a new definition for "information industry" and measures the amount of value-added by information industry, finding that these industries' proportion of the overall GNP is 46%. According to Porat, information activities can be divided into two types: activities of primary information sectors already on the market and activities carried out in secondary information sectors within each industry. The GNP of primary information sectors can be measured by clarifying the definition of "information industry." Meanwhile, a secondary information sector is buried inside an industry, and thus, it is more difficult to define and measure. Porat separates the internal information activities of each industry from the industry's main business based on each industry's occupation composition ratio. He defines "occupation to process information" and separated value-added as a result of information activities from value-added as a result of noninformation activities according to the proportion of employees engaged in those occupations within each industry. For example, as a physician, in addition to the technical work of patient treatment, there are many tasks related to information activities, such as collecting patient information, conducting medical research, and processing patient accounts. Porat investigates the average time allocation of doctors' daily tasks and estimates the allocation ratios for time related to technical work vs. time related to information work. Using these ratios, Porat separates the value-added by internal information activities from that of the medical industry as a whole.

Nakano and Washizu (2018) employ the same method as Porat to identify and isolate internal ICT-based management activities within an industry. They focus on the food industry and separate the internal management activities according to the proportion of occupation to process information in that sector. By applying the separation method developed by Nakano and Washizu (2018) to all sectors, internal management activities in all industries can be separated. These are economic activities that are not identified in the conventional input–output table. By explicitly separating these activities, it is possible to analyze the effects of management activities that utilize ICT, and eventually the effects of building a smart society. By separating the internal management activities of all sectors according to the proportion of occupation to process information in specific sectors and incorporating this into the service part in Fig. 10.8, the structure of the economic cycle indicated by arrows in this figure will become clearer. We will undertake this task in future research.

#### 10.5 International Interdependence of Information Society in Asia

Figure 10.3 in Sect. 10.2 explains the international input–output table. Based on the discussions so far, this section attempts to analyze some of the international interdependencies in the modern Asian region that have been informatized. One international input–output table is the WIOD created by the University of Groningen. The WIOD (2016 Release) describes the transactions of goods and services between 43 countries and 56 sectors in 2014. In the table, six countries—China, Indonesia, India, Japan, South Korea, and Taiwan—are listed for Asia. Using the international input–output table, it is possible to calculate the amount of production and income (value-added) that the final demand of one

Table 10.2 Amount of production and value-added that the final demand of China and Japan has induced in their own country and others

MM: main material input, RM: raw material input, E: energy supply, Aux: auxiliary material input, S: general service, SIS: secondary information service, PIS: primary information service

a Asia: China, Indonesia, India, Japan, Korea, Taiwan

country has induced in the sectors of the country and other countries through the worldwide supply chain. Table 10.2 shows the results of calculating the amount of production and valueadded that the final demand of China and Japan has induced in the industries of their own country and other countries using the WIOD in 2014.9

According to Table 10.2, the final demand in China induces a production of US\$ 28.3 trillion worldwide, while the final demand in Japan induces a production of US\$ 8.8 trillion, and the amount of added values generated by these induced productions is US\$ 9.7 trillion and US\$ 4.5 trillion, respectively. In China, the induced value-added is 34.2% of the induced production value, while in Japan it is 51.1%. Of the valueadded induced by final demand, the domestic induction is 86.2% in China and 85.1% in Japan; that is, the former is slightly higher. The composition ratios of value-added by the sector part induced by the final demand of China and Japan significantly differ. The value-added induced for the MM part of the home country is 27.5% in China and 8.8% in Japan. However, the valueadded induced for the domestic information service (SIS and PIS) parts is 21.3% in China and 40.3% in Japan. It is also interesting to compare the value-added composition ratio that the final demand of each country induces in the other country. The composition ratio that China's final

9 See the appendix for the specific calculation formula.

Fig. 10.9 Impacts of increased productivity in the "manufacture of computer, electronic, and optical products" sector in China and Japan on the manufacturing cost of each sector in other countries10

demand induces in Japan is only 0.98%, while the composition ratio that Japan's final demand induces in China is 3.1%. Upon considering the extent to which one country's production activity is affected by the final demand of another, it is observed that Japan's impact on China is higher than the other way around.

Figures 10.9 and 10.10 show the results of an analysis of the cost reduction effects of improved labor productivity in the information-related sectors of China and Japan on the production sectors of each country in the Asian region. Figure 10.9 shows how much the production cost of each sector in the Asian countries (China, Indonesia, India, Japan, Korea, and Taiwan) featured in the WIOD will decrease when labor productivity increases by 30% in the "manufacture of computer, electronic, and optical products" sector of the MM part in China and Japan. If a sector in a country has a "manufacture of computer, electronic, and optical products" sector in China or Japan involved in its supply chain, the production cost of that sector is expected to drop significantly. Figure 10.9 shows that the increase in labor productivity in the "manufacture of computer, electronic, and optical products" sector in Japan and China affects the manufacturing unit price of sectors of the information service part as well as sectors of the MM part in Asian countries. In particular, price declines in various sectors of China are significant. China's sectors are more affected by the productivity gains of Japan's "manufacture of computer, electronic, and optical products" sector than by the productivity gains of the same sector in China. This tendency is the same in other countries. It can be inferred that Japan's "manufacture of computer, electronic, and optical products" sector is deeply involved in the supply chains of many sectors in Asian countries.

Figure 10.10 shows how much the production cost of each sector of the Asian countries (China, Indonesia, India, Japan, Korea, and Taiwan) featured in the WIOD will decrease when labor

10 The abbreviations on the horizontal axis consist of country and sector part names. The abbreviations for country names are as follows: China (CHN), Indonesia (IDN), India (IND), Japan (JPN), Korea (KOR), and Taiwan (TWN). The abbreviations for sector part names are the same as those in Table 10.2.

Fig. 10.10 Impacts of increased productivity in the "computer programming, consultancy, and related activities; information service activities" sector in China and Japan on the manufacturing cost of each sector in other countries11

productivity increases by 30% in the "computer programming, consultancy, and related activities; information service activities" sector of the PIS part in China and Japan. The increase in productivity in this sector in Japan has a considerable impact on the production prices of the service and manufacturing sectors in Japan. However, its impact on other Asian countries, including China, is not as high as in the case of increased productivity in the "manufacture of computer, electronic, and optical products" sector. Increasing labor productivity in the same sector in China has a minor impact on Asian countries. The impact of increased productivity in this sector in China on the production prices of each industry in China is approximately the same as the impact on them by this sector in Japan.

In short, Japan is more informatized than China. Japan's information goods manufacturing sector influences the supply chains of various Asian sectors. The productivity improvement of the information service sector in Japan will spread to the supply chains of Asian countries, but the extent will be minor compared to the effect of the information goods manufacturing sector. However, the scope of the production sector, which is affected by productivity improvements in the information service sector, seems to be broader.

#### 10.6 Concluding Remarks

In this chapter, based on the recognition that the analysis of the effects of ICT use requires an analytical framework that integrates various sectors and regions, using the input–output framework, we explain the structure of development in a smart society utilizing ICT.

This chapter first clarified the structure of development theory of industrial society, developed by Leontief and extended by Ozaki. Subsequently, it was suggested that the structure of development mechanism of the industrialized society has major drawbacks: When the final demand for industrial products at the end of the supply chain disappears, it becomes dysfunctional.

Next, we considered how the structure of development theory would be extended in a smart society using ICT. Previous studies have pointed out that the effect of using ICT is greater than the effect of producing ICT materials and investing in ICT infrastructure, and that ICT creates values that exceed the economic value captured by means of conventional statistical indicators. Based on these points, we have rearranged the relationship between the information

11 The abbreviations on the horizontal axis are the same as in Fig. 10.9.

Fig. 10.11 Relationship between information goods manufacturing sector and information service sector

goods manufacturing sector and the information service sector, as shown in Fig. 10.11.

Specifically, the products produced in the information goods manufacturing sector of the MM part are input into the service industry of the PIS part that produces primary information services (e.g., communication services). At this time, economies of scale operate in the production process of the primary information services. Furthermore, the service industries in the SIS part use the primary information services produced in the PIS part to generate more customized secondary information services (e.g., legal and accounting services). The management department inside each industry (including the manufacturing industry of the MM part) creates efficient management services by combining information goods, primary information services, and secondary information services. The management service within each industry eliminates the waste in various supply chains and greatly contributes to improving the efficiency of the entire industrial structure. Furthermore, it creates new types of services (e.g., sharing services) which did not exist before the smart society and contributes to people's welfare.

Based on the inter-industry relationships in Fig. 10.11, we rearranged the input–output table and presented the structure of development mechanism of a smart society. Here, the continuous final demand for smart services makes it easier to maintain an economic cycle and avoid dysfunction.

Finally, using the WIOD, we analyze the current state of interdependence in the Asian region regarding the ICT material manufacturing sector and the ICT use sector. Consequently, it is shown that Japan is an informatized economy in the Asian region. Japan's information manufacturing sector has influenced the supply chains of various sectors in Asian countries. The productivity improvement of the information service sector in Japan also affects the supply chains of Asian countries, but the extent is minor compared to the effect of the information goods manufacturing sector. However, the range of production sectors affected by productivity improvements in the information service sector is wider.

This chapter analyzes the input–output effects of the smartening of society through technological innovations in ICT directly related to SDG9. However, ICT advances have spillover effects that cannot be discussed under this topic alone. For example, it is necessary to build smart energy management systems to more efficiently utilize renewable energy sources, which are variable and decentralized. Therefore, this chapter is also related to SDG7. Similarly, advances in ICT have made it possible to strengthen the management of production systems and ensure improvements in resource efficiency (SDG8). They have also contributed to the realization of sustainable consumption by making it possible to replace the consumption of people's "things" with the consumption of "services" produced by things (sharing services, etc.) (SDG12). Advanced utilization of renewable energy, improvements in resource efficiency, and the construction of sustainable production and consumption systems are indispensable means of reducing greenhouse gas emissions (SDG13). Advances in ICT are also useful for solving various other social issues. For example, they can contribute to community development that is favorable for the elderly and people with disabilities through the provision of appropriate smart transportation services (SDG 11) and will streamline food production and contribute to addressing the problems of hunger and poverty through the development of smart agricultural machinery and precision agriculture technology (SDG2). Furthermore, it has been pointed out that improved ICT will increase employment opportunities for women and empower them, thereby contributing to gender equality (SDG5). Thus, this chapter is not only directly related to SDG9, but also to SDGs 2, 5, 7, 8, 11, 12, and 13.

#### Appendix

This appendix shows the formula for the analysis in Sect. 10.5 using the WIOD in 2014. The formula for Table 10.2 is as follows: Eq. (10.4) is for calculating the amount of production that the final demand in a specific region r induces in all regions. This formula calculates all the production inducements that individual goods in the final demand in region r cause worldwide through the supply chains.

$$\mathbf{x} = (\mathbf{I} - \mathbf{A})^{-1} \mathbf{F}^{\mathbf{r}} \tag{10.4}$$

x: vector of the production induced in all sectors in all regions

Fr : vector of final demand in region r(r = 1, …, k)

A: inter-regional input coefficients matrix of the WIOD

By using the calculation results of Eq. (10.4), the value-added (income) induced by the final demand in region r in all regions is calculated using Eq. (10.5).

$$\mathbf{VA} = \mathbf{v}'\mathbf{x} \tag{10.5}$$

VA: vector of the gross value-added induced in all sectors in all regions

v0 ¼ vr j 0 : vector of the gross value-added ratio of all sectors in all regions

vr j ¼ VAr j . Xr j VAr j : the gross value-added of sector j in region r in the WIOD

Xr j : control total of sector j in region r in the WIOD

In Sect. 10.5, the case of r = China, Japan is calculated.

The method of calculating the cost reduction effect of improving labor productivity in the information-related sectors of China and Japan on the production sectors of Asian countries is presented as follows: The production unit price p by country/sector is calculated by the following Eq. (10.6) using the traditional equilibrium price model of input–output analysis:

$$\mathbf{p} = (\mathbf{I} - \mathbf{A}')^{-1}\mathbf{v} \tag{10.6}$$

Here, p is the price vector by country/sector, I is the identity matrix, A' is the transposed matrix of the input coefficients matrix of WIOD, and v is the vector of gross value-added ratio by country/sector.

We assume that labor costs, which are components of value-added, will decrease and the value-added coefficient will decrease through the increase in labor productivity in the information goods manufacturing sector or information service sector in China or Japan. In the text, the analysis is performed based on the assumption that the rate of decrease in the value-added coefficient is 30%. That is, the value-added coefficient v of the information-related sector in China or Japan is reduced by 30%, and the change in manufacturing unit price p by country/sector is calculated.

#### References

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# 11 Trade-Investment Nexus and Economic Growth in East Asia

Shujiro Urata

#### Abstract

SDG 8's goal is to promote sustained, inclusive, and sustainable economic growth; full and productive employment; and decent work for all. This chapter examines the experiences of East Asian developing countries in achieving rapid and inclusive economic growth by focusing on the role of international trade and foreign direct investment nexus created through global value chains (GVCs) by multinational corporations (MNCs). GVCs enabled participating companies and countries to improve productivity, contributing to economic growth. The factors attributable to the participation in GVCs include high competitiveness of local companies and open business environment created by the Asian government. Moreover, construction and maintaining well-functioning soft (e.g., education and legal systems) and hard (e.g., transportation and communication systems) infrastructure by the government and international donors contributed to the creation of business-friendly environment. Faced with growing protectionism and the threats of growing US-China rivalry, infectious diseases, climate change, etc., maintaining an open and transparent rules-based business environment is crucially important to further achieving sustained, inclusive, and sustainable economic growth. In the light of absence of effective global economic order, exemplified by ineffectiveness of the World Trade Organization in trade liberalization as well as dispute settlement, regional economic frameworks such as the CPTPP and RCEP in the Asia and Pacific region would be proven to be effective to achieve the goal.

#### Keywords

Global value chains Free trade agreements Infrastructure

#### 11.1 Introduction: Asia's Rapid Economic Growth

Among the United Nations' 17 sustainable development goals (SDGs), the objective of SDG 8 is to "promote sustained, inclusive, and sustainable economic growth; full and productive employment; and decent work for all." Among the world's developing countries and economies, those in East Asia have been relatively successful in achieving some of these objectives. The most

SDG 8: Promote sustained, inclusive and sustainable economic growth, full and productive employment, and decent work for all.

S. Urata (&) Waseda University, Tokyo, Japan e-mail<EMAIL_ADDRESS>
© The Author(s) 2023

S. Urata et al. (eds.), Sustainable Development Disciplines for Society, Sustainable Development Goals Series, https://doi.org/10.1007/978-981-19-5145-9\_11

Fig. 11.1 GDP growth rates for East Asia and the world (%).2 Source World Bank, World Development Indicators online

obvious indication of their success is that many of these countries have achieved high, sustained economic growth for several decades. This chapter examines how East Asian countries1 are achieving the objectives outlined in SDG 8 and attempts to provide guidance for other countries that are eager to achieve stronger economic growth. In our analysis, we focus on the roles of international trade and foreign direct investment (FDI), which have contributed significantly to development in East Asian countries.

We begin by presenting some facts about East Asia's rapid economic growth, and in the following sections, we analyze the role of foreign trade and FDI in achieving that growth.

East Asia has been an engine of economic growth for the world economy since the end of World War II although the main drivers of that growth have changed over time, shifting from Japan to the Newly Industrializing Economies, namely South Korea, Taiwan, Hong Kong, and Singapore, then to China, and the several member countries of the Association of Southeast Asian Nations (ASEAN), including Indonesia, Malaysia, Thailand, Vietnam, and the Philippines. As shown in Fig. 11.1, economic growth measured by the annual growth rate of gross domestic product (GDP) for East Asia has been higher than the rest of the world in the post-war period.

Rapid economic growth in developing East Asian countries has been accompanied by an improved quality of life. The number of people in poverty has declined significantly, based on declines in the percentage of people living below the poverty line for the East Asian countries for which data are available: China 66.3% (1990) to 0.5% (2016), Indonesia 68.5% (1984) to 2.7% (2019), Lao PDR 31.1% (1992) to 10% (2018), and Vietnam 52.3% (1992) to 1.8% (2018).3 From 1960 to 2020, GDP per capita in current US dollars for East Asian developing countries increased approximately 90 times, and the gap in GDP per capita in USD between East Asian developing countries and high-income countries declined sharply from 46 times in 1990 to 5.3 times in 2020. A large number of job opportunities were generated over the period from 1991 to 2019, with the number of employed workers increasing from 1.22 billion to 1.37 billion before declining to 1.34 billion in 2020 due to the

1 In this chapter, the term "East Asian countries" refers to developing countries in East Asia, specifically China, South Korea, and the members of the ASEAN: Brunei, Cambodia, Indonesia, Lao PDR, Malaysia, Myanmar, the Philippines, Singapore, Thailand, and Vietnam. It excludes Japan unless otherwise noted. Due to data availability, in some cases countries in the Pacific region are included.

2 East Asia includes developing countries in East Asia and the Pacific.

3 Data used in this paragraph are obtained from the World Bank's World Development Indicators online. Poverty here is defined as people living on less than US\$1.9 a day in 2011 purchasing power parity USD.

COVID-19 pandemic. Life expectancy at birth rose from 45 in 1960 to 75 in 2019, while the infant mortality rate declined from 45 per 1000 births in 1990 to 12 in 2019.

Various factors have been identified as drivers of the rapid economic growth in East Asia,4 including high savings and investment, sound macroeconomic policies, highly educated and dedicated workers, a well-functioning infrastructure, and others. Among these, outwardoriented development strategies such as import liberalization and export promotion, which are discussed later in this chapter, played an important role in achieving rapid economic growth.

Despite sharing the common characteristic of rapid economic development and growth, the East Asia region is a collection of diverse countries not only in economic terms but also in noneconomic aspects. The countries are diverse in size (measured in terms of GDP, population, and land area), level of economic development, and endowment of natural resources. Among East Asian countries, China has the largest population, GDP, and land area, while Brunei has the smallest population (3/10,000th the size of China) and GDP (8/10,000 as large as China), and Singapore is the smallest in terms of land area (8/100,000th of China). Among East Asian countries, Singapore has the highest income per capita and Myanmar has the lowest (1/50th of Singapore). Similarly, there is diversity with respect to noneconomic aspects such as religion, culture, and political system. It should be noted that the diverse economic characteristics found in East Asia have led to an interesting and unique economic development pattern, which we discuss later in this chapter.

The remainder of this chapter is structured as follows. Section 11.2 discusses the role of foreign trade and FDI in achieving rapid economic development and growth, with a focus on global value chains (GVCs) created through FDI by multinational corporations (MNCs). Section 11.3 examines the changing environment with respect to trade and investment policy in East Asia, which has seen an emergence of free trade

4 See, for example, the World Bank (1993) and Asian Development Bank (2020). 5 In Fig. 11.3, East Asia includes Japan.

agreements (FTAs). Section 11.4 concludes and provides several policy implications that would be helpful for other developing countries seeking to achieve economic development and growth. It also discusses challenges for East Asia to achieve inclusive growth.

#### 11.2 Nexus of Trade and Investment and Global Value Chains

One of the notable characteristics of the economic growth pattern in East Asia is the rapid expansion of trade and FDI during the period of high economic growth. According to Fig. 11.2, the ratio of trade (exports and imports) to GDP rose from 50% in 1980 to a high of 78% in 2006 before starting to decline, reaching 42% in 2020. This decline is mainly due to China's influence, which expanded domestic production and sales substantially as a result of its rapid economic growth. Somewhat in contrast to the pattern observed for the trade-to-GDP ratio, the ratio of inward FDI stock to GDP increased throughout the period 1980–2020, with some fluctuations, rising from 3% in 1980 to 26% in 2020. As we discuss more in detail later, trade and FDI increased more or less in tandem by interacting with each other.

#### 11.2.1 Expansion of Intra-regional and Machinery Parts Trade

International trade in East Asia has experienced several notable structural changes. First, intraregional trade, which refers to trade among East Asian countries, has expanded rapidly. The ratio of intra-regional trade to overall trade for East Asia increased from 25.7% in 1985 to 37.2% in 2012 and then declined slightly to 34.9% in 2019 (Fig. 11.3).5 Within East Asia, China has become an important source of import and a significant export destination for many East Asian countries. For China, the importance of

**Intra-regional trade share (left axis)**

**Share of parts in Asia's regional exports (right axis)**

countries outside of East Asia, such as the US and the European Union (EU), has also increased. This rapid expansion of intra-regional trade can be explained mainly by the rapid economic growth of East Asian countries. It is natural for a rapidly growing country to increase its demand for imports and its ability to supply exports, leading to an expansion of trade. However, it should also be noted that GVCs in East Asia, formed through FDI by multinational corporations (MNCs), also contributed to an expansion of intra-regional trade, as will be discussed later in this chapter.

Second, the product composition of trade for East Asian countries changed significantly. Specifically, the importance of manufactured products increased significantly for many countries in the region, which is attributable to successful industrialization. Specifically, the share of manufactured exports to total merchandise exports for East Asia's developing countries increased sharply from 27% in 1985 to 85% in

Fig. 11.2 Trade and inward FDI (% of GDP). Source World Bank, World Development Indicators online, UNCTAD, UNCTADstat online

2005 and remained at that level through 2020. Among manufactured exports, exports of machinery products, particularly electric and electronic machinery and their parts, expanded markedly (Fig. 11.3).

These two notable developments regarding international trade in East Asia, namely increases in intra-regional trade and parts and components trade, are the result of regional production networks known as GVCs, created by MNCs.

#### 11.2.2 Formation of Global Value Chains

Japanese MNCs that use a large number of parts and components began to establish factories in East Asia, in the early 1980s, undertaking FDI to take an advantage of low production costs. This process of internationalizing production was accelerated by a sharp appreciation in the Japanese yen in the mid-1980s, which increased the cost of Japanese products in foreign markets. Many Japanese MNCs implemented a fragmentation strategy, in which an integrated production system is fragmented into a number of production blocks. Each block specializes in producing one or a few specific parts, and the production blocks are connected by service links (Fig. 11.4), creating GVCs. MNCs in South Korea and Taiwan followed Japan's MNCs in implementing a fragmentation strategy as those countries' currencies appreciated. In implementing a fragmentation strategy, MNCs set up factories for part production in countries where those parts can be produced at a low cost. Through these GVCs, MNCs can achieve efficient production systems, in which production factors, such as labor, capital, and technology, are allocated and used efficiently.

Next, we examine how deeply East Asian countries are involved in GVCs. There are several ways to measure the extent of a firm's or county's participation in GVCs. One is to use information about a firm's transaction pattern. If a firm imports inputs and exports outputs, it is considered a participant in one or more GVCs. Another approach is to use information on international trade and production at sector level. More specifically, data on value-added trade constructed from world input–output tables are used to measure the extent of GVC participation by country.6 In this approach, GVC participation is generally assessed by two approaches, namely backward and forward participation. Backward participation refers to the ratio of the "foreign value-added content of exports" to the country's total gross exports.7 This is the "buyer" perspective or sourcing side of GVCs, in which a country imports intermediate

6 See, for example, the World Bank (2020) for useful information about GVCs with respect to economic development.

7 Adopted from WTO (2016).

inputs to produce its exports. Forward participation refers to the ratio of the "domestic valueadded sent to other countries relative to the country's total gross exports. It captures the domestic value-added contained in inputs sent to other countries for further processing and exporting through various value chains. This is the "seller" perspective or the supply side of GVCs. Total GVC participation is the sum of backward and forward participation.

Figure 11.5 shows GVC participation rates for ASEAN countries, China, Japan, and Korea (ASEAN+3 countries) in 1980 and 2018. Many countries increased the level of GVC participation, although there are some countries that experienced a decline in GVC participation. Singapore, Malaysia, and the Philippines show very high GVC participation rate, while Cambodia, Lao PDR, and Myanmar exhibit low GVC participation rate. Magnitude of backward and forward GVC participation rates reveals interesting patterns of GVC participation of a country. Countries with relatively high share of backward participation such as Singapore and Malaysia engage in assembling final products by importing intermediate goods. We may divide countries with relatively high share of forward participation into two groups. One group of countries includes Brunei, Indonesia, Lao PDR, and Myanmar, while the other group consists of China and Japan (1980). Countries in the first group mainly export raw materials, while those in the second group mainly export manufactured or processed intermediate goods such as parts and components. One cannot make judgment a priori as to which type of participation, high share of backward participation or forward participation, contributes more to economic growth. Having said this, one may observe that countries with high share of manufacturing tend to grow fast compared to those with high share of raw materials sector.

#### 11.2.3 Benefits of GVC Participation

In the early stages, GVCs were formed by MNCs to involve their foreign subsidiaries; over time, they expanded to include local companies. GVCs have brought many benefits to their participating companies and the countries in which they operate.8By participating in GVCs, local firms are able to import high-quality raw materials and components, which they use to produce and export their products. This export expansion not only increases production and employment, but also improves production efficiency and strengthens competitiveness. It is particularly important that superior technologies and management knowhow owned by MNCs are transferred to the participating local companies through these GVCs. To make this technology transfer possible, it is essential that local companies that participate in GVCs have capable employees with technological knowledge and managers who understand the importance of technology.