A skeptical note on the role of constant elasticity of substitution in labor income share dynamics

Paul, Saumik Working Paper A skeptical note on the role of constant elasticity of substitution in labor income share dynamics ADBI Working Paper Series, No. 944 Provided in Cooperation with: Asian Development Bank Institute (ADBI), Tokyo Suggested Citation: Paul, Saumik (2019) : A skeptical note on the role of constant elasticity of substitution in labor income share dynamics, ADBI Working Paper Series, No. 944, Asian Development Bank Institute (ADBI), Tokyo This Version is available at: https://hdl.handle.net/10419/222711 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/igo/ ADBI Working Paper Series A SKEPTICAL NOTE ON THE ROLE OF CONSTANT ELASTICITY OF SUBSTITUTION IN LABOR INCOME SHARE DYNAMICS Saumik Paul No. 944 April 2019 Asian Development Bank Institute The Working Paper series is a continuation of the formerly named Discussion Paper series; the numbering of the papers continued without interruption or change. ADBI’s working papers reflect initial ideas on a topic and are posted online for discussion. Some working papers may develop into other forms of publication. Suggested citation: Paul, S. 2019. A Skeptical Note on the Role of Constant Elasticity of Substitution in Labor Income Share Dynamics. ADBI Working Paper 944. Tokyo: Asian Development Bank Institute. Available: https://www.adb.org/publications/skeptical-note-role-constant-elasticitysubstitution-labor-income-share-dynamics Please contact the author for information about this paper. Email: pauls[email protected] Saumik Paul is a research economist at the Asian Development Bank Institute in Tokyo, Japan. The views expressed in this paper are the views of the author and do not necessarily reflect the views or policies of ADBI, ADB, its Board of Directors, or the governments they represent. ADBI does not guarantee the accuracy of the data included in this paper and accepts no responsibility for any consequences of their use. Terminology used may not necessarily be consistent with ADB official terms. Working papers are subject to formal revision and correction before they are finalized and considered published. Asian Development Bank Institute Kasumigaseki Building, 8th Floor 3-2-5 Kasumigaseki, Chiyoda-ku Tokyo 100-6008, Japan Tel: +81-3-3593-5500 Fax: +81-3-3593-5571 URL: www.adbi.org E-mail: [email protected] © 2019 Asian Development Bank Institute ADBI Working Paper 944 Paul Abstract The constancy of the elasticity of factor substitution (σ) makes its role as a driver of the labor income share exogenous. The constant elasticity of substitution (CES) (Arrow et al., 1961) production function has predominantly been used to support this causal relationship. This paper argues that (i) capital-labor ratio determines the value of σ, and (ii) both capital-labor ratio and σ vary over time. I use a variable elasticity of substitution (VES) production framework that allows both labor income share and σ to change over time. Statistically significant empirical support is provided using the Japanese industrial productivity (JIP) data. This suggests that the CES model may not be an ideal choice to examine the factor income share dynamics. Keywords: substitution elasticity, labor income share, production function parameters JEL Classification: E21, E22, E25 ADBI Working Paper 944 Paul Contents 1. INTRODUCTION ......................................................................................................... 1 2. A BRIEF HISTORY OF THE EVOLUTION OF THE VES PRODUCTION FUNCTIONS ...................................................................................... 4 3. EMPIRICAL ANALYSIS .............................................................................................. 6 3.1 Data and Descriptive Statistics ........................................................................ 6 3.2 Empirical Model ............................................................................................... 9 3.3 Empirical Outcomes ...................................................................................... 10 4. CONCLUSION .......................................................................................................... 13 REFERENCES ..................................................................................................................... 15 APPENDIX 1 ......................................................................................................................... 18 APPENDIX 2: SECTORAL LABOR INCOME SHARES ....................................................... 21 ADBI Working Paper 944 Paul 1 1. INTRODUCTION “…the production function has been a powerful tool of miseducation.” The Production Function and the Theory of Capital Joan Robinson (1953–54, page 81) The elasticity of factor substitution plays an important role in the analysis of factor income shares. For example, the assumption of a non-unitary elasticity of substitution (𝜎𝜎𝐾𝐾𝐾𝐾) between capital and labor explains the changes in the labor income share over time. A production technology that shows how the allocative efficiency of factor inputs relates to the rate of productivity per worker, on the other hand, governs the characteristics of the elasticity of factor substitution. More than a half-century ago, Liu and Hildebrand (1965) suggested a three-variable relationship between value added per unit of labor (𝑌𝑌𝐾𝐾), the wage rate (𝑊𝑊) and the capital–labor ratio (𝐾𝐾𝐾𝐾), which has, since then, served as the basis of estimating a production framework. Equation (1) replicates this relationship in a log-linear form, including a constant term (𝛽𝛽0) and an error term (𝜀𝜀): 𝑙𝑙𝑙𝑙𝑙𝑙𝑌𝑌𝐾𝐾=𝛽𝛽0+𝛽𝛽1𝑙𝑙𝑙𝑙𝑙𝑙𝑊𝑊+𝛽𝛽2𝑙𝑙𝑙𝑙𝑙𝑙𝐾𝐾𝐾𝐾+𝜀𝜀 (1) Arrow et al. (1961) assumed 𝛽𝛽2= 0 , and propounded the constant elasticity of substitution (CES) production function based on the goodness of fit of the empirical relationship between 𝑙𝑙𝑙𝑙𝑙𝑙𝑌𝑌𝐾𝐾 and 𝑙𝑙𝑙𝑙𝑙𝑙𝑊𝑊. The CES production function has, since then, become a prominent model in the studies of economic theory (equation 2). It is a generalized version of the Cobb–Douglas (CD) production function (Cobb and Douglas 1928),1 and reduces to the CD form when σ= 1. 𝑌𝑌=𝐴𝐴�𝜃𝜃𝐾𝐾σ−1 σ+ (1 −𝜃𝜃)𝐿𝐿σ−1 σ�σ σ−1; 𝛽𝛽2= 0 and σ𝐾𝐾𝐾𝐾=σ (2) In equation 1, σ represents the elasticity of substitution between capital and labor, and 𝜃𝜃 and 1−𝜃𝜃 are the factor cost share of capital and labor, respectively. Equation (1) also serves as the basis for a class of production functions with variable elasticity of factor substitutions (VES) that assumes 𝛽𝛽2≠0. This makes 𝜎𝜎𝐾𝐾𝐾𝐾 a function of the capital–labor ratio. Moreover, studies show that factor income shares can also vary with the capital– labor ratio. Karagiannis, Palivos, and Papageorgiou (2005) consider a VES framework (Equation 3) assuming 𝜎𝜎𝐾𝐾𝐾𝐾 as a linear function of the capital–labor ratio (Revankar 1971), and provide empirical support to it. Taken together, it points to the advantages of a VES framework in addressing movements in the labor income share with varying levels of capital per unit of labor. 𝑌𝑌=𝐴𝐴𝐾𝐾𝛼𝛼�1−𝜃𝜃σ−1 σ���1−2𝜎𝜎 𝜎𝜎�𝐾𝐾σ−1 σ+𝐿𝐿�𝛼𝛼�𝜃𝜃σ−1 σ�; 𝛽𝛽2≠0 and σ𝐾𝐾𝐾𝐾= 1 + 1−2σ 𝜎𝜎−𝜃𝜃(1−𝜎𝜎)𝐾𝐾𝐾𝐾 (3) 1 A standard form of a CD production function can be written as 𝑌𝑌=𝐴𝐴𝐾𝐾𝛼𝛼𝐿𝐿1−𝛼𝛼, where the elasticity of substitution (𝜎𝜎𝐾𝐾𝐾𝐾) between capital and labor is equal to unity. ADBI Working Paper 944 Paul 2 However, most of the studies (Bentolila and Saint-Paul 2003; Elsby, Hobijn and Sahin 2013) that derive a theoretical relationship between factor income shares and σ𝐾𝐾𝐾𝐾 rely on a CES production function. In a CES production function (equation 2), assuming constant returns to scale and perfectly competitive factor markets, there is a stable relationship between the labor income share, the elasticity of substitution (σ) and capital– output ratio. Under these assumptions and using the aggregate production function (2), the labor income share can be derived as 𝐿𝐿𝑆𝑆=(𝐾𝐾)σ−1 σ (𝐾𝐾)σ−1 σ+(𝐾𝐾)σ−1 σ (4) and the capital-output ratio as 𝑘𝑘=�(𝐾𝐾)σ−1 σ (𝐾𝐾)σ−1 σ+(𝐾𝐾)σ−1 σ�σ σ−1. (5) Combining (4) and (5), I get 𝐿𝐿𝑆𝑆= 1 −(𝑘𝑘)σ−1 σ. (6) The expression for the labor income share in equation (6) is known as the “SK” schedule (Bentolila and Saint-Paul 2003), which shows a functional relationship between the labor income share, σ, and capital–output ratio. When σ > 1, i.e., labor and capital are gross substitutes, availability of more capital per unit of labor reduces the labor income share as the capital price goes down. This is known as “accumulation view.” Similarly, when σ < 1, i.e., labor and capital are gross complements, a higher k increases the labor income share. Both Piketty (2014), and Karabarbounis and Neiman (2014), estimate 𝜎𝜎𝐾𝐾𝐾𝐾to be greater than unity. A CES production function assumes (i) the existence of the relationship between value added per unit of labor and the wage rate independent of the changes in the stock of capital (i.e., 𝛽𝛽2= 0) and (ii) the elasticity of substitution between factor inputs as a constant (but not unity) along the isoquant. Both assumptions appear unrealistic in the presence of an upward trend in the capital–labor ratio as documented by many studies (Acemoglu and Guerrieri 2008). Nonetheless, it remains an empirical question whether a VES is a more realistic model compared to CES to study changes in the factor income shares. The recent growth in the labor income share literature mostly relies on the CES model to derive the relationship between the elasticity of factor substitution and the labor income share. The literature that provides empirical validity to the usefulness of VES production technology predates the recent growth in the labor income share research. While most of the studies (Sato and Hoffman 1968; Diwan 1970; Kazi 1980; Meyer and Kadiwala 1974; and Revankar 1971) reject CD and CES model specifications in favor of the VES model, Lovell (1973), Tsang and Yeung (1976) and Zellner and Ryu (1998) provide evidence that in certain sectors the CES model provides a better fit to the data compared to VES. Since these studies use various estimation strategies methods and different sets of data (both cross-sectional and time-series) at different levels of aggregation (from industries within a country to cross-country countries using aggregate data), it becomes difficult to ascertain a definite answer. ADBI Working Paper 944 Paul 3 In this paper, I argue that the VES model specification is preferred to the CES to explain the movements in the labor income share. I work with a production function where 𝜎𝜎𝐾𝐾𝐾𝐾 is a non-linear function of 𝐾𝐾𝐾𝐾 (𝛽𝛽2≠0 in equation 1). I build on the variable elasticity of factor substitution production framework originally developed by Lu and Fletcher (1968), which allows 𝜎𝜎𝐾𝐾𝐾𝐾 to vary with the factor shares as the availability of capital per unit of labor changes. I perform two empirical exercises. First, I test whether 𝛽𝛽2= 0 using a panel data on 108 Japanese industries throughout almost 40 years (1970 – 2012).2 Second, I derive 𝜎𝜎𝐾𝐾𝐾𝐾 for the industries at a disaggregated level of classification. The empirical findings suggest a consistent and statistically significant role that the capital–labor ratio plays in explaining the variation in output per worker over time and across sectors. This suggests a variable elasticity of substitution between capital and labor as a function of the capital per unit of labor. Almost 40% of the industries show a statistically significant variation in 𝜎𝜎�𝐾𝐾𝐾𝐾 around its average value, which supports the role of capital per unit of labor in the movement of the elasticity of factor substitution over time. Also, 15 out of 23 industries have the average estimated elasticity of substitution between capital and labor greater than unity. This indicates that capital and labor are gross substitutes in most of the sectors. The substitutability between capital and labor is more prevalent among service industries compared to those in manufacturing or agriculture. Overall, the findings suggest that the CES model may not always be an ideal choice to examine the drivers of the labor income share. Movements in the labor income share have direct bearings on income distribution and input use, and the findings in this paper suggest more careful attention to model selection in order. This paper is directly related to the recent debate on the role of the elasticity of factor substitution behind the secular decline in the labor income share. Using the CES production framework, Piketty (2014) and Karabarbounis and Neiman (2014) estimate the values of elasticity of substitution between capital and labor to be greater than unity. However, many studies find an estimate of σ to be less than one (Leon-Ledesma, McAdam and Willman 2015; Oberfield and Raval 2014; Chirinko and Mallick 2017). These findings point to an apparent puzzle. I mention two recent studies that attempt to resolve this puzzle. Grossman et al. (2017) show that a decline in the labor income share is feasible with 𝜎𝜎 < 1 if there is a slowdown of labor productivity growth. Paul (2018), in another study, drawing insights from the literature on differential capital–skill substitutability (Krusell et al., 2000) and the estimation of different elasticity of substitution parameters using the Morishima elasticity of substitution, shows that it is possible to have a decline in the labor income share resulting from a fall in the relative price of capital when 𝜎𝜎𝐴𝐴𝐴𝐴𝐴𝐴< 1. This study provides another alternative to address this puzzle using the VES framework. This paper is also related to the literature on the endogenous elasticity of factor substitution. Miyagawa and Papageorgiou (2007) build a static factor-endowment model where 𝜎𝜎𝐾𝐾𝐾𝐾 in each period is endogenously determined by the existing endowments of capital and labor and their equilibrium inter-sectoral allocation. Duffy and Papageorgiou (2000), in another paper, show that 𝜎𝜎𝐾𝐾𝐾𝐾 increases as the economy grows. This line of literature does not assume that capital per unit of labor and 𝜎𝜎𝐾𝐾𝐾𝐾 are related based on any functional form. Rather, such a relationship is determined by the market equilibrium conditions of a growing multi-sectoral economy. This paper is directly linked to the endogenous elasticity of factor substitution but unlike Miyagawa and Papageorgiou (2007), it assumes a non-linear relationship between 𝜎𝜎𝐾𝐾𝐾𝐾 and capital per unit of labor. 2 The Japanese Industrial Productivity (JIP) database. ADBI Working Paper 944 Paul 4 The rest of the paper is organized as follows. In section II, I provide a brief discussion of the evolution of VES production functions since the 1960s. I then discuss a VES framework that I empirically test in this paper. Section III provides empirical evidence using the Japanese Industrial productivity (JIP) database, which is followed by a concluding remark. 2. A BRIEF HISTORY OF THE EVOLUTION OF THE VES PRODUCTION FUNCTIONS A production function portrays the techniques of how inputs are used to produce the output. It shows both the technical efficiency and allocative efficiency of the inputs. Production function has been an important tool of economic analysis in the neoclassical tradition. Economists have typically assumed that the factor inputs are technically efficient, and as a result, production functions in economic analysis focus on the allocative efficiency of the factor inputs. Philip Wicksteed (1894) was the first economist to algebraically formulate the relationship between output and n inputs as 𝑌𝑌=𝑓𝑓(𝑥𝑥1,𝑥𝑥2,..,𝑥𝑥𝑛𝑛), while some sources suggest that Johann von Thünen first formulated it in the 1840s (Humphrey 1997). A standard CD (Cobb-Douglas, 1928) production function (equation 4) demonstrates allocative efficiency from changes in the input uses and how it affects the output, which is otherwise assumed to be technically efficient. 𝑌𝑌=𝐴𝐴𝐾𝐾𝛼𝛼𝐿𝐿1−𝛼𝛼. (7) In a CD production function (equation 7), the elasticity of substitution (𝜎𝜎𝐾𝐾𝐾𝐾) between capital and labor is equal to unity. Unitary 𝜎𝜎𝐾𝐾𝐾𝐾 supports Kaldor’s stylized facts on constant factor income shares, and for several years it has been considered as a “deep” parameter. The growing dissatisfaction with the Cobb–Douglas production function led to the invention of the CES production function. The CES production function was derived almost 33 years after the formulation of the CD production function based on the goodness of fit of the empirical relationship as shown in equation (1) with 𝛽𝛽2= 0 (Arrow et al. 1961). The CES production allows for non-unitary values of 𝜎𝜎𝐾𝐾𝐾𝐾. However, it does not allow 𝜎𝜎𝐾𝐾𝐾𝐾 to vary with changes in the capital per unit of a worker. In other words, 𝜎𝜎𝐾𝐾𝐾𝐾 remains constant across the isoquants independent of the size of the output and inputs in the production function. Since the formulation of the CES production function, several attempts3 have been made to accommodate the variability of 𝜎𝜎𝐾𝐾𝐾𝐾in the production function. Mukerji (1963) generalized the CES production function based on constant ratios of 𝜎𝜎𝐾𝐾𝐾𝐾. Revankar (1967) developed a generalized CES production function with variable returns to scale and elasticity of substitution. Revankar’s VES, or the generalized CES production function (equation 3), does not contain the Leontief production function but shows the Harrod–Domar fixed coefficient model, the linear production function and the CD production function as its special cases. In this model, 𝜎𝜎𝐾𝐾𝐾𝐾varies linearly with the capital per unit of labor. However, it does not allow the value of 𝜎𝜎𝐾𝐾𝐾𝐾to cross over from one side of the unity to the other in the relevant range of the capital–labor ratio. Bruno (1968) 3 Bruno (1962); Brown and Cani (1963); Mukerji (1963); Nerlove (1963); Ringstad (1967); Revankar (1967); Lu and Fletcher (1968); Sato and Hoffman (1968); Revankar (1971) and Kadiyala (1972), among others. Please see Mishra (2007) for a comprehensive analysis of the evolution of production functions in economic analysis. ADBI Working Paper 944 Paul 11 of the substitution parameter ranging between –2 and 3. Thus, the relationship between factor inputs not only varies over time but it also exhibits mixed trends of complementarity and substitutability over time. Figure 5: Elasticity of Substitution between Capital and Labor in Heavy Manufacturing Sectors Note: Author’s calculation. Figure 6: Elasticity of Substitution between Capital and Labor in Light Manufacturing Sectors Note: Author’s calculation. Figure 6 plots the elasticity of substitution between capital and labor for the light manufacturing sectors. The left-hand panel of Figure 6 exhibits substitution elasticity for mining, food, textiles, pulp and non-metal industries. The trends of substitution ADBI Working Paper 944 Paul 12 elasticity over time suggest it shows constant trends for most of the sectors except textiles. The right-hand panel of Figure 6 shows the same for other light-manufacturing sectors. The trends based on the estimated elasticity of substitution for sectors such as electrical, transportation equipment, precision instrument, other manufacturing and construction show greater variation over the period from 1970–2012, and the average values of the values of 𝜎𝜎�𝐾𝐾𝐾𝐾 tend to vary between 1 and 2. I return to this point with a more elaborated discussion using Table 2. Among the three sectors in commerce, the variation in the elasticity of substitution for the wholesale and retail trade sector is far greater than finance and insurance and real estate (the left-hand panel of Figure 7). Among the sectors in utilities and services, only transport and communications show significant variation in 𝜎𝜎�𝐾𝐾𝐾𝐾. The average value of 𝜎𝜎�𝐾𝐾𝐾𝐾 in most of these sectors tends to be greater than unity. Figure 7: Elasticity of Substitution between Capital and Labor in Commerce, Utilities and Services Note: Author’s calculation. To conclude, I summed the statistical outcomes on labor income share, 𝜎𝜎�𝐾𝐾𝐾𝐾, and the nature of the substitutability between capital and labor across 23 broad Japanese sectors (R-JIP classification) for the period from 1970 to 2012. The third column in Table 2 shows the average labor income share over the period for each sector. As discussed earlier, the average share of labor’s income is much lower in industries in agriculture and heavy manufacturing compared to the same in light industry, commerce and services. And, 15 out of 23 industries have the average estimated elasticity of substitution between capital and labor greater than unity (the fourth column, Table 2). Almost 40% of the industries show a statistically significant variation in 𝜎𝜎�𝐾𝐾𝐾𝐾 around its average value, which supports the role of capital per unit of labor in the movement of the elasticity of factor substitution over time. The empirical findings also suggest that the relationship between capital and labor in most of the sectors is as substitutes. If the estimated value of the elasticity parameter is above unity in more than 60% of the years in the period between 1970 and 2012, then I consider capital and labor as gross substitutes. On the other hand, capital and labor are gross complements if 𝜎𝜎�𝐾𝐾𝐾𝐾> 1 in less than 40% of the times in the study period. Using this rule of thumb, only four industries, namely agriculture, textiles, primary metals and transport equipment, appear in the borderline case. There is complementarity between capital and labor in four industries: petroleum and coal products; fabricated metal; machinery and transport; and communication. The capital and labor are substitutes in ADBI Working Paper 944 Paul 13 the rest of the 15 industries. Substitutability between capital and labor, on average, is higher among the industries in services compared to manufacturing or agriculture. Table 2: Substitutability of Sectoral 𝝈𝝈�𝑲𝑲𝑲𝑲 and Its Variability over Time R-JIP 23 Sectors Average Labor Income Share Mean of 𝝈𝝈�𝑲𝑲𝑲𝑲 t-Statistic (Mean/SD) of 𝝈𝝈�𝑲𝑲𝑲𝑲 Percentage of Years (1970–2012) 𝝈𝝈�𝑲𝑲𝑲𝑲>𝟏𝟏 The Nature of the Relationship between K and L 1 Agriculture, Forestry and Fishery 0.48 0.54 0.54 41% Borderline 2 Mining 0.55 1.14 5.50* 85% Substitutes 3 Food products and beverages 0.44 1.14 9.63* 100% Substitutes 4 Textiles 0.94 –0.15 –0.11 40% Borderline 5 Pulp, paper and paper products 0.52 1.13 9.69* 98% Substitutes 6 Chemicals 0.37 1.96 4.87* 98% Substitutes 7 Petroleum and coal products 0.08 0.94 22.86* 7% Complements 8 Non-metallic mineral products 0.60 1.20 3.38* 88% Substitutes 9 Primary Metals 0.43 0.77 0.60 51% Borderline 10 Fabricated metal products 0.81 –0.33 –1.46 0% Complements 11 Machinery 0.71 –0.73 –0.83 10% Complements 12 Electrical machinery, equipment and supplies 0.64 1.27 3.20* 93% Substitutes 13 Transport equipment 0.57 0.98 1.47 49% Borderline 14 Precision instruments 0.72 1.58 4.82* 100% Substitutes 15 Other manufacturing 0.73 1.42 1.47 85% Substitutes 16 Construction 0.78 1.17 1.23 88% Substitutes 17 Electricity, gas and water supply 0.30 1.24 3.22* 95% Substitutes 18 Wholesale and retail trade 0.69 1.05 14.64* 98% Substitutes 19 Finance and insurance 0.50 1.02 328.5* 100% Substitutes 20 Real estate 0.32 1.02 455.4* 100% Substitutes 21 Transport and communication 0.69 0.39 0.35 34% Complements 22 Service activities and producers of private nonprofit services to households 0.72 1.09 9.80* 88% Substitutes 23 Producers of government services 0.75 1.05 4.03* 78% Substitutes Note: Author’s calculation. 4. CONCLUSION The crucial role of σ in analyzing the factor income shares has been noted since the seminal work of Hicks (1932) and Robinson (1953). The CES production function has predominantly been used to derive the relationship between σ and the labor income ADBI Working Paper 944 Paul 14 share. Assuming constant returns to scale and perfectly competitive factor markets, there is a stable relationship between factor income shares and σ. And, the constancy of the elasticity of factor substitution makes its role as a driver of the labor income share exogenous. This paper suggests that more careful attention must be paid in the modeling choice. The empirical findings using the Japan Industrial Productivity database at the disaggregated level of industry classification suggest a consistent and statistically significant role that capital–labor ratio plays in explaining the variation in output per worker over time and across sectors. This validates the existence of a variable elasticity of substitution between capital and labor. Almost 40% of the industries show a statistically significant variation in 𝜎𝜎�𝐾𝐾𝐾𝐾 around its average value. Also, capital and labor are gross substitutes in most of the sectors. The substitutability between capital and labor is more prevalent among the industries in services compared to that in manufacturing. The topic of income distribution has always been at the center of economic policymaking, and the recent decline in the labor income share has generated concerns among researchers and policymakers, alike. And, the puzzling role of 𝜎𝜎 in explaining the movements in the labor income share as highlighted by some recent studies (Grossman et al. 2017; Paul 2018) adds to the misery. This study provides a novel mechanism to resolve this puzzle that allows 𝜎𝜎 to vary over time. 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ADBI Working Paper 944 Paul 18 APPENDIX 1 Broad Categories JIP Sectors JIP Code 1 Rice, wheat production 1 Miscellaneous crop farming 2 Livestock and sericulture farming 3 Agriculture services 4 Forestry 5 Fisheries 6 2 Chemical fertilizers 23 Basic inorganic chemicals 24 Basic organic chemicals 25 Organic chemicals 26 Chemical fibers 27 Miscellaneous chemical products 28 Pharmaceutical products 29 Petroleum products 30 Coal products 31 Pig iron and crude steel 36 Miscellaneous iron and steel 37 Smelting and refining of non-ferrous metals 38 Non-ferrous metal products 39 Fabricated constructional and architectural metal products 40 Miscellaneous fabricated metal products 41 General industry machinery 42 Special industry machinery 43 Miscellaneous machinery 44 Office and service industry machines 45 3 Mining 7 Livestock products 8 Seafood products 9 Flour and grain mill products 10 Miscellaneous foods and related products 11 Prepared animal foods and organic fertilizers 12 Beverages 13 Tobacco 14 Textile products 15 Lumber and wood products 16 Furniture and fixtures 17 Pulp, paper, and coated and glazed paper 18 Paper products 19 continued on next page ADBI Working Paper 944 Paul 19 Appendix 1 table continued Broad Categories JIP Sectors JIP Code Printing, plate making for printing and bookbinding 20 Leather and leather products 21 Rubber products 22 Glass and its products 32 Cement and its products 33 Pottery 34 Miscellaneous ceramic, stone and clay products 35 Electrical generating, transmission, distribution and industrial apparatus 46 Household electric appliances 47 Electronic data processing machines, digital and analog computer equipment and accessories 48 Communication equipment 49 Electronic equipment and electric measuring instruments 50 Semiconductor devices and integrated circuits 51 Electronic parts 52 Miscellaneous electrical machinery equipment 53 Motor vehicles 54 Motor vehicle parts and accessories 55 Other transportation equipment 56 Precision machinery and equipment 57 Plastic products 58 Miscellaneous manufacturing industries 59 Construction 60 Civil engineering 61 Publishing 92 4 Electricity 62 Gas, heat supply 63 Waterworks 64 Water supply for industrial use 65 Waste disposal 66 Railway 73 Road transportation 74 Water transportation 75 Air transportation 76 Other transportation and packing 77 Telegraph and telephone 78 Mail 79 continued on next page ADBI Working Paper 944 Paul 20 Appendix 1 table continued Broad Categories JIP Sectors JIP Code 5 Wholesale 67 Retail 68 Finance 69 Insurance 70 Real estate 71 6 Education (private and non-profit) 80 Research (private) 81 Medical (private) 82 Hygiene (private and non-profit) 83 Other public services 84 Advertising 85 Rental of office equipment and goods 86 Automobile maintenance services 87 Other services for businesses 88 Entertainment 89 Broadcasting 90 Information services and internet-based services 91 Video picture, sound information, character information production and distribution 93 Eating and drinking places 94 Accommodation 95 Laundry, beauty and bath services 96 Other services for individuals 97 Education (public) 98 Research (public) 99 Medical (public) 100 Hygiene (public) 101 Social insurance and social welfare (public) 102 Public administration 103 Medical (non-profit) 104 Social insurance and social welfare (non-profit) 105 Research (non-profit) 106 Other (non-profit) 107