The value added and operating surplus deflators for industries: The right price indicators that should be used to calculate the real interest rates

2.1Definitions

Before going into the empirical evidence, we examine the theoretical meaning of the value added deflators using a highly simplified use table in which one industry produces only one product so that the table reduces to a symmetric input output table as shown in Table 1 in current values (i.e. VAT inclusive). Note that paragraph 5.2 of SNA 2008 basically defines industry as a group of establishments engaged in the same production activity. Let subscripts i,j=1,…,n and k,l=1,…,n denote inputs and outputs respectively. While Xi⁢k denotes intermediate input of i into k; Di, Ei, Mi and Ti indicate domestic final uses, exports, imports and total domestic output of product i respectively. Vk is the gross value added generated in the production process of output k, which is defined as total domestic output less intermediate inputs; the definition is equivalent to that at producer prices described in the SNA 2008, paragraph 6.78. As in the Chenery-Moses input-output model,33 which Table 1 resembles to, we assume that the domestic and imported products are indifferent, and distributed among the domestic users at a constant ratio that reflects the ratio of total imports to the domestic production. We assume that only the domestic products are exported. Although the Chenery-Moses input-output model usually assumes ‘one price for one product’, we will assume that the import prices are different from domestic prices following the observations by Diewert and Nakamura [9] and Reinsdorf and Yuskavage [10] that the former affects the latter.

Let pd⁢i and pm⁢i be the current prices of domestic and imported products respectively while taking the domestic price of the base period to be unity. Under this assumption, the domestic and imported products are supplied jointly at a composite price pi, which is the quantity-weighted average of the domestic and import prices. Therefore, we can rewrite the current nominal values in Table 1 in the constant prices as in Table 2 if pd⁢i and pm⁢i are observable:

where τ is the standard VAT rate. Since zero-rating VAT is applicable to exports of goods, we assume the export prices to be lower than the domestic prices to the extent of the VAT. The input-output balance of product i at current price is as follows:

The balance at constant price is as follows:

The above assumption tells us that the domestic and imported products are supplied to the domestic users at a price, which is the quantity-weighted average of the domestic and import prices:

Therefore

and

The input deflator for product k is defined as

Likewise, the input deflator for all domestic products as a composite commodity is obtainable:

The output deflator for product k is by definition:

Furthermore, by assuming tk=ti and Tk=Ti where k=i, we obtain the output deflator for all domestic products in the following manner:

As we have described already, in this model, gross value added for product k is defined as total domestic output less intermediate inputs:

By summing up the above equation over k=1,…,n, we have the gross domestic product or GDP at current prices, which is often referred to as nominal GDP:

The above equation proves that GDP is equivalent to the sum of domestic final uses and exports less imports so that GDP can be obtained either in the production approach by summing up value added or in the expenditure approach using the latter relations. We further define real value added for product k in an analogy to Eq. (11):

By summing up the above equation over k=i=1,…,n, we have GDP at constant prices, which is also known as real GDP:

According to the traditional double deflation method, as described in Paragraph 15.162 of the SNA 1993, the value added deflator for product k is defined as the ratio of nominal value added Vk to real value added vk:

Likewise, we define GDP deflator as the ratio of nominal GDP to real GDP:

Therefore, in most cases, the expenditure approach is a more convenient way to get real GDP and the GDP deflator.

2.2Decompositions

The value added deflator for product k could be decomposed in the following manner from Eq. (15):

The last line of the above equation shows that the value added deflator for product k can be decomposed into (i) output price effects and (ii) input price effects. Equation (2.2) can be rewritten as:

so that output price is a weighted average of the input prices and the value added deflator. Alternatively, we can decompose the value added deflator for product k into three parts. Again from Eq. (15) by substituting Eq. (4):

The last line of the above equation tells us that the value added deflator for product k consists of three portions: (i) output price effects, (ii) domestically-produced input price effects, and (iii) imported input price effects. Since

we can safely conclude that the effects of import prices on the value added deflator is negative.

Likewise, the GDP deflator (for all the domestic products as a composite commodity) could be decomposed in the following manner from Eq. (16) by substituting Eq. (4):

In other words, the GDP deflator consists of two portions: (i) that depends on the domestic factors, and (ii) that depends on the import prices. It should be noted that, since

the effects of import prices are inevitably negative.

Alternatively, we can decompose the GDP deflator into consisting products:

It means that the GDP deflator is a constant-price value-added weighted average of the value added deflator of each product. The problem of the above equation is that vk is not directly observable so that the following equation is more widely used:

In other words, the GDP deflator is simply regarded as a weighted harmonic mean of the value added deflators.

4.1Value added and operating surplus deflators

We will use so-called SNA-IO,55 the input-output table published as a part of Japanese SNA, to experimentally estimate both value added and operating

surplus deflators. The SNA-IO is an input-output table that consists of the same number of products and corresponding industries.66 Note that the Input-Output Table for Japan, on which SNA-IO is constructed, is based on the concept of cost accounting so that each column represents the production activity of the corresponding product except for the case of joint production such as oil refinery. Although more detailed table that consists of 87 products is also available, the SNA-IO table we use is a smaller version that consists of 24 products; there is no jointly produced products at this level of aggregation. They also publish the output deflator for each product. Since import prices are not available in the framework, we used the price indices published by the Bank of Japan. We adjusted the import price indices using the international comparative price level data published by OECD77 so that the domestic price of the product at the base year is unity. Since import price index is not available for services, we simply used the exchange rate as a proxy. In the SNA-IO, the gross value added consists of three portions: compensation of employees, taxes of production

Figure 1.

The fluctuations in the deflators for total outputs, intermediate inputs and value added.

Figure 1.

continued.

Figure 1.

continued.

(less subsidiaries), and the operating surplus (and mixed income). Since wage deflators are unavailable in the SNA, we used the data published by the Research Institute for Advancement of Living Standards, which is the only Paasche wage index available in Japan. We made the deflator for taxes on production in the procedure described in the previous section. Since the original data of taxes on production included both taxes on products and other taxes on production, we divided it proportionally using the data published for the total economy. The observation period is from 2001 to 2013 calendar year.

Figures 1-1 through 1-24 depict the fluctuations in the deflators for total outputs, intermediate inputs, and value added for each industry. The correlation coefficients between the deflators are listed in Table 3. The main findings from the figures and the table can be summarized as follows:

If you take look at the ‘electrical machinery and equipment’ (Figure 1-12), one of the dominant export industry of Japan, you will find a steep decline in the value added deflator during the first decade of the century because output price declined faster than the input prices. (See (i) above.) There is no wonder that the industry was reluctant to invest in new plants or equipment; gross capital formation of the sector at 2005 constant price declined by 31 percent between 2000 and 2013. This must be the reason why they lost their international competitiveness because new technologies are often embodied in the production facilities. It is a vicious circle because the lack of competitiveness depresses the value added deflator even further. In contrast to this, the value added deflator for ‘wholesale and retail trade’ (Fig. 1-18), a typical domestic industry, was more or less stable during the observation period. Gross capital formation of the industry at constant price rose 49 percent between 2000 and 2013, however, the value added of the industry at constant price increased merely 3 percent because of the sluggish economy.

Figure 3.

The fluctuations in the deflators for operating surplus, wage rate and the taxes across all the industries.

Figure 2 illustrates the fluctuations in the deflators for GDP, total outputs, intermediate inputs and operating surplus across all the industries. While output and input deflators peaked at 2008, the GDP deflator gradually declined throughout the observation period. It should be noted that, while the correlation coefficient between GDP and total output deflators is positive but not statistically significant, that between GDP and input deflators is not only negative as expected but also statistically significant at 5 percent level.88

The correlation coefficients between the operating surplus deflators and the value added and other related deflators are listed in Table 4. The main findings from the table are summarized as follows:

Figure 3 illustrates the fluctuations in the deflators for operating surplus, wage rate and the tax deflators, taxes on products and other taxes on production, across all the industries. While other three indicators are somewhat fluctuating during the observation period, the operating surplus deflator declined significantly. There is a high correlation between the value added and operating surplus deflators; the correlation coefficient is as high as 0.966. There is a negative and significant correlation between the input and operating surplus deflators. Although the operating surplus deflator is significantly correlated neither with the wage rate nor taxes-on-products deflator, we do not know why, but we found a significant positive correlation with the other-taxes-on-production deflator.

4.2Decomposition of the value added deflators

Figure 4 depicts the decomposition of the value added deflator for each industry for 2013 in terms of Eq. (2.2) above. The line that lies above zero suggests that the output price effect surpasses the input price effect in any of the 24 industries listed there. Although, the import prices forms the larger part of the input price effect in ‘petroleum and coal products’ and ‘electricity, gas and water supply’ industries, the domestic prices account for more than half in most of the industries. The ratio of the output price effects to the input price effects is larger in the service industries comparing to the other industries. The ratio is smaller in the industries that heavily depend on imports.

Figure 4.

Decomposition of the value added deflator for each industry (2013).

Figure 5.

Decomposition of the GDP deflator.

As shown in Fig. 5, the GDP deflator gradually declined during the observation period. The figure also depicts the decomposition of GDP deflator into domestic and import deflator effects. As Eq. (2.2) suggests, while domestic output deflator affects positively on the GDP deflator, import prices give negative effects on the deflator. Figure 5 clearly illustrates that the decline in Japanese GDP deflator during the observation period originated in the increase in the import prices. The decomposition of Eq. (2.2), which is illustrated in Fig. 6, tells us that only ‘transportation and communication’ significantly affected positively on the deflator. It should be noted however, this is not because the value added deflator of the industry rose, but because the production share of the industry increased considerably as the information technology and IT commerce rapidly advanced. In contrast to this, although the value added deflators for ‘mining’, ‘foods and beverages’ and ‘textiles’ increased as shown in Fig. 1, these industries affected negatively on the overall GDP deflator because of the decline in the production share. Summarizing Fig. 6, we can tell that the price drops in the domestic industries that supplies non-tradable goods and services were the direct cause of the decline in the GDP deflator. ‘Construction’ also negatively contributed to the GDP deflator despite its deflator hike because the real value-added share of the industry declined significantly during the observation period; ‘wholesale and retail trade’ also lost its share.

Figure 6.

Decomposition of the changes in the GDP deflator (2001–2013).

Figure 7.

Decomposition of the annual changes in the GDP deflator.

Figure 8.

The value of one U.S. dollar in Japanese yen (normalized to the 2005 exchange rate).

A great portion of the changes in the import prices is due to the fluctuations in the exchange rate because most of the Japanese imports are originally denominated in U.S. dollars. Thus, we decompose the import prices in Japanese yen as:

where ε is the dollar-yen exchange rate,99 and pμ⁢i is the import prices in U.S. dollars. Consequently, the last line of Eq. (2.2) is rewritten in the following manner:

We can decompose the changes in the GDP deflator from year y-1 to y using the above equation: