Statistical Journal of the IAOS 34 (2018) 235–253 235 DOI 10.3233/SJI-160327 IOS Press The value added and operating surplus deflators for industries: The right price indicators that should be used to calculate the real interest rates Itsuo Sakumaa, Masako Tsujimurab;c and Kazusuke Tsujimurad;∗ aFaculty of Economics, Senshu University, Tokyo, Japan bFaculty of Economics, Rissho University, Tokyo, Japan cKeio Economic Observatory, Keio University, Tokyo, Japan dFaculty of Economics, Keio University, Tokyo, Japan Abstract. After the global financial crisis of 2008–2009, many advanced economies are suffering from a dearth of domestic investment opportunities. It has been said that lowering real interest rate is the best policy to boost the capital investment. The problem is what inflation rate they have in their mind when the entrepreneurs make investment decisions. Not only the output prices, but also the composition of inputs differ from one industry to another. Therefore, the value added deflator or even the operating surplus deflator for each industry are better alternative to calculate the real interest rate. In the first half of the paper, we examine the theoretical meaning of the value added deflators using a highly simplified symmetric input output table. In the latter half, we will use so-called SNA-IO, the input-output table published as a part of Japanese SNA, to experimentally estimate both value added and operating surplus deflators. The study reveals that if lowering interest rate depreciate the local currency, it will depress value added deflators, and in turn, will discourage capital investments. In this sense, lowering interest rate is a double-edged sword; the governments and central banks should think twice before taking such a policy. Keywords: National accounts, use table, symmetric input-output table, double deflation, GDP deflator JEL Classification: C43, C67, E31 1. Introduction (natürliche Kapitalzins) as the physical rate of return on capital investment at the time. If the market rate of With slowly growing or declining workforces, as interest on loans (Darlehnszins) is below the natural well as high capital-labor ratios, many advanced econ- rate, entrepreneurs will borrow funds and make profit omies face an apparent dearth of domestic investment by investing in capital goods. On the contrary, if the opportunities, while the ageing society calls for more market rate is above the natural rate, the entrepreneurs savings (i.e. future consumption) to prepare for the re- will be hesitant to borrow so that capital investment tirement (Bernanke [1]). Traditionally, it was thought will stagnate. However, Wicksell also asserted that, that if you wanted to boost the capital investment, the even in such a situation, the entrepreneurs are willing central bank would reduce interest rates. Wicksell [2] to invest if they face an inflation because it will in- (Chapters VIII and IX) defined natural rate of interest crease the monetary return. Therefore, he concluded that capital investment will increase as the real rate of interest, which is market rate of interest less the rate of ∗ Corresponding author: Kazusuke Tsujimura, Faculty of Eco- inflation, declines. The problem is what inflation rate nomics, Keio University, 2-15-45 Mita, Minato, Tokyo 108-8345, Japan. Tel.: +81 3 5427 1597; Fax: +81 3 5427 1640; E-mail: they have in their mind when the entrepreneurs make [email protected]. investment decisions. 1874-7655/18/$35.00 c 2018 – IOS Press and the authors. All rights reserved This article is published online with Open Access and distributed under the terms of the Creative Commons Attribution Non-Commercial License (CC BY-NC 4.0). 236 I. Sakuma et al. / The value added and operating surplus deflators for industries A price index is a measure of the proportionate, or count, the value added consists of three major com- percentage, changes in a set of prices over time; usu- ponents: compensation of employees, taxes/subsidies ally it consists of per-unit transaction value of spe- on production and imports, and gross operating sur- cific product (prices) and some indicator of the pro- plus/mixed income. As paragraph 14.155 asserts, cal- portionate composition of the products (share weight) culating compensation of employees in volume terms among the group of products in question. For example, is possible if enough information is available on wage a consumer price index (CPI) measures changes in the rates and numbers employed by category of worker. prices of goods and services that households consume If it is possible, it is an easy task to obtain the defla- (ILO [3]). In an analogy, so called producer price in- tor for compensation of employees. However, it seems dex (PPI) measures changes in the prices of goods and far more difficult to know the taxes less subsidies on services that domestic producers produce. However, as production in volume terms. To obtain the deflator IMF [4] asserts, the producers are at the same time pur- for gross operating surplus, we have to overcome this chasers of goods and services because they consume critical problem. Despite all the difficulties, we tenta- other producers’ outputs as intermediate inputs – mate- tively obtained the deflator for gross operating surplus rials, components, fuels, etc. The value added deflator / mixed income for the Japanese industries to find out is a price indicator that takes this two-sidedness of the further problems we may encounter in practice. producers; it is defined as the proportion of the nom- inal value added to the real value added, which is ob- tainable by dividing both the output and the intermedi- 2. Value added deflator ate inputs in nominal terms by the appropriate price in- dices.1 The remaining problem is that the value added 2.1. Definitions deflator does not take the wage rate and other produc- tion factor cost into consideration; in this context, it is Before going into the empirical evidence, we exam- desirable to obtain the operating surplus deflator rather ine the theoretical meaning of the value added defla- than the value added deflator. This paper discusses the tors using a highly simplified use table in which one issues concerning the measurement of the deflators for industry produces only one product so that the table both value added and operating surplus for each indus- reduces to a symmetric input output table as shown in try. Table1 in current values (i.e. VAT inclusive). Note that After the tradition of the SNA 1968 (paragraphs 8.44 paragraph 5.2 of SNA 2008 basically defines industry through 8.47) and 1993 (15.162 through 15.164), the as a group of establishments engaged in the same pro- SNA 2008 discusses value added deflator in paragraphs duction activity. Let subscripts i; j = 1; : : : ; n and 14.153 through 14.157; it is defined using double de- k; l = 1; : : : ; n denote inputs and outputs respectively. flation method2 in the framework of the supply and use While Xik denotes intermediate input of i into k; Di, tables. The proportion of the domestic total of nomi- Ei, Mi and Ti indicate domestic final uses, exports, nal value added to that of real value added is casually imports and total domestic output of product i respec- referred to as GDP deflator (SNA 2008, 15.235); not tively. Vk is the gross value added generated in the pro- a few statistical authorities publish it as a part of GDP duction process of output k, which is defined as total statistics. Simple mathematics tells us that, as shown domestic output less intermediate inputs; the definition in Eq. (24) below, the GDP deflator is the weighted is equivalent to that at producer prices described in the harmonic mean of the value added deflators. However, SNA 2008, paragraph 6.78. As in the Chenery-Moses the meaning of the value added deflator for each indus- input-output model,3 which Table1 resembles to, we try is far more complicated because the weight for one assume that the domestic and imported products are in- particular item involves the prices of other items. different, and distributed among the domestic users at In addition to the value added deflator, the SNA a constant ratio that reflects the ratio of total imports to 2008 mentions the operating surplus deflator in 14.157. the domestic production. We assume that only the do- In the framework of the generation of income ac- mestic products are exported. Although the Chenery- Moses input-output model usually assumes ‘one price for one product’, we will assume that the import prices 1According to the definition of IMF [4], PPI includes not only output PPI but also input PPI and value-added PPI. 2Double deflation method is originally proposed by Fabricant [5] and sophisticated by Stone [6]. 3See Moses [7] and Chenery and Clark [8]. I. Sakuma et al. / The value added and operating surplus deflators for industries 237 Table 1 Symmetric use table at current prices Industries (production activities) Domestic Exports Imports Total domestic output 1 ··· k ··· n final uses Products 1 X11 ··· X1k ··· X1n D1 E1 −M1 T1 . .. .. i Xi1 ··· Xik ··· Xin Di Ei −Mi Ti . .. .. n Xn1 ··· Xnk ··· Xnn Dn En −Mn Tn Value Added V1 ··· Vk ··· Vn Total Output T1 ··· Tk ··· Tn Table 2 Symmetric use table presented in constant prices Industries (production activities) Domestic Exports Imports Total 1 ··· k ··· n final uses domestic output pd1 Products 1 p1x11 ··· p1x1k ··· p1x1n p1d1 1+τ e1 −pm1m1 pd1t1 . .. .. pdi i pixi1 ··· pixik ··· pixin pidi 1+τ ei −pmimi pd iti . .. .. pdn n pnxn1 ··· pnxnk ··· pnxnn pndn 1+τ en −pmnmn pd ntn Value Added pv1v1 ··· pvkvk ··· pvnvn Total Output pd1t1 ··· pdktk ··· pdntn are different from domestic prices following the obser- The above assumption tells us that the domestic and vations by Diewert and Nakamura [9] and Reinsdorf imported products are supplied to the domestic users at and Yuskavage [10] that the former affects the latter.