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Intermediate Goods–Skill Complementarity

  • Kozo Kiyota and Yoshinori Kurokawa EMAIL logo
Published/Copyright: October 27, 2023
The B.E. Journal of Macroeconomics
From the journal The B.E. Journal of Macroeconomics Volume 24 Issue 1

Abstract

Recent research has begun to imply intermediate goods–skill complementarity; however, this possible complementarity has been hypothesized but not statistically tested, despite the increasing importance of intermediate goods in production. This study provides statistical evidence regarding whether intermediate goods are more complementary with skilled labor than with unskilled labor. Using panel data from 40 countries over the period 1995–2009, we estimate a two-level constant elasticity of substitution (CES) production function. Our major findings are fivefold. First, at the aggregated one-sector level, the elasticity of substitution between intermediate goods and unskilled labor is 1.22, which is significantly greater than that between intermediate goods and skilled labor of 1.05, indicating intermediate goods–skill complementarity. Second, at the disaggregated level, such complementarity is primarily observed in heavy manufacturing industries and the service sector, whereas complementarity is observed between intermediate goods and unskilled labor in the primary sector and light manufacturing industries. Third, the normalization of the data and the cumulant estimators exhibit stronger results. Fourth, our baseline results are confirmed applying several robustness checks, such as switching skilled and unskilled labor or considering capital–skill complementarity. Finally, intermediate goods–skill complementarity tends to be higher for industries that use more imported intermediate goods.

Keywords: intermediate goods–skill complementarity; elasticity of substitution; CES; skill-biased technological change; imported intermediate goods
JEL Classifications: E23; O47; J31; F10
Corresponding author: Yoshinori Kurokawa, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8571 Japan, E-mail:

Funding source: Japan Society for the Promotion of Science

Award Identifier / Grant number: JP18H03637

Award Identifier / Grant number: JP19H00598

Award Identifier / Grant number: JP22H00063

Funding source: Japan Society for the Promotion of Science

Award Identifier / Grant number: Unassigned

Acknowledgments

We thank Mons Chan, Kazunobu Hayakawa, Jean Hindriks, Manuel Jimenez, Hayato Kato, Ryo Kato, Daiji Kawaguchi, Toshiyuki Matsuura, Yasusada Murata, Yukihiro Nishimura, Susana Peralta, Sergio Perelman, Pierre Pestieau, Sergio Salgado, Motohiro Sato, Eiichi Tomiura, Tatsuma Wada, Hakan Yilmazkuday, Taiyo Yoshimi, the editor Árpád Ábrahám, and two anonymous referees for their useful comments. We also thank seminar participants at CORE, JEA Meeting, JSIE Meeting, Midwest International Trade Conference, SAET Conference, and WEAI Conference. Kiyota gratefully acknowledges the financial support of the Japan Society for the Promotion of Science Grants-in-Aid (JP18H03637, JP19H00598, and JP22H00063). The usual disclaimers apply.

Appendix A
Table A1:

Industry classification.

Code Industry Aggregate
1 Agriculture, hunting, forestry, & fishing Primary
2 Mining & quarrying Primary
3 Food, beverages, & tobacco Manufacturing
4 Textiles & textile products Manufacturing
5 Leather & footwear Manufacturing
6 Wood & products of wood & cork Manufacturing
7 Pulp, paper, printing, & publishing Manufacturing
8 Coke, refined petroleum, & nuclear fuel Manufacturing
9 Chemicals & chemical products Manufacturing
10 Rubber & plastics Manufacturing
11 Other non-metallic mineral Manufacturing
12 Basic metals & fabricated metal Manufacturing
13 Machinery, nec Manufacturing
14 Electrical & optical equipment Manufacturing
15 Transport equipment Manufacturing
16 Manufacturing, nec; recycling Manufacturing
17 Electricity, gas, & water supply Services
18 Construction Services
19 Sale, maintenance & repair of motor vehicles, & motorcycles; retail sale of fuel Services
20 Wholesale trade & commission trade, except of motor vehicles & motorcycles Services
21 Retail trade, except of motor vehicles & motorcycles; repair of household goods Services
22 Hotels & restaurants Services
23 Inland transport Services
24 Water transport Services
25 Air transport Services
26 Other supporting & auxiliary transport activities; activities of travel agencies Services
27 Post & telecommunications Services
28 Financial intermediation Services
29 Real estate activities Services
30 Renting of M & Eq & other business activities Services
31 Public admin & defense; compulsory social security Services
32 Education Services
33 Health & social work Services
34 Other community, social, & personal services Services

  1. Note: Aggregate industries are based on our own classification. Source: Socio Economic Accounts of the World Input–Output Database (WIOD) released in July 2014.

Table A2:

Estimated elasticities by aggregate sector: alternative estimation method.

Sector b ̂ θ ̂ N and Wald a ̂ ρ ̂ N and Wald ρ ̂ − θ ̂
All 0.951 −0.270 600 0.765 −0.001 600 0.268
[0.007] [0.035] 185.3 [0.010] [0.019] 210.5 (0.000)
Primary 0.977 −0.204 600 0.609 0.067 600 0.272
[0.012] [0.108] 539.7 [0.020] [0.028] 257.2 (0.007)
Manufacturing 0.990 −0.261 600 0.862 −0.031 600 0.230
[0.003] [0.045] 195.3 [0.008] [0.017] 245.3 (0.000)
Services 0.916 −0.290 600 0.745 −0.034 600 0.255
[0.011] [0.035] 204.3 [0.010] [0.019] 189.6 (0.000)

  1. Notes: Figures in brackets indicate standard errors that are based on 100 bootstrap replications. Figures in parentheses are the p-values of the z test. Wald indicates the first-stage Wald statistics. Source: Socio Economic Accounts of the World Input-Output Database (WIOD) released in July 2014.

Table A3:

Estimated elasticities by manufacturing industry: alternative estimation method.

Industry b ̂ θ ̂ N and Wald a ̂ ρ ̂ N and Wald ρ ̂ − θ ̂
Food, beverages & tobacco 1.0000 −0.404 600 0.999 −0.071 600 0.332
[0.0000] [0.033] 332.3 [0.000] [0.016] 191.5 (0.000)
Textiles & textile products 0.9997 −0.159 600 0.997 0.043 600 0.202
[0.0001] [0.044] 324.8 [0.000] [0.024] 187.3 (0.000)
Leather & footwear 0.9997 −0.097 584 0.998 −0.019 584 0.078
[0.0001] [0.061] 311.9 [0.000] [0.027] 185.8 (0.122)
Wood, products of wood & cork 0.9999 −0.345 600 0.998 −0.065 600 0.279
[0.0000] [0.046] 243.0 [0.000] [0.013] 154.6 (0.000)
Pulp, paper, printing & publishing 0.9998 −0.214 600 0.998 −0.106 600 0.107
[0.0001] [0.061] 268.6 [0.000] [0.021] 162.4 (0.048)
Coke, refined petroleum & nuclear fuel 1.0000 −0.248 569 1.000 −0.020 569 0.228
[0.0000] [0.174] 782.2 [0.000] [0.134] 417.8 (0.149)
Chemicals & chemical products 1.0000 −0.385 600 0.999 −0.114 600 0.272
[0.0000] [0.074] 412.1 [0.000] [0.023] 355.9 (0.000)
Rubber & plastics 1.0000 −0.433 600 0.999 −0.150 600 0.283
[0.0000] [0.045] 340.2 [0.000] [0.035] 310.7 (0.000)
Other non-metallic mineral 0.9999 −0.262 600 0.998 −0.058 600 0.204
[0.0001] [0.062] 225.2 [0.000] [0.013] 271.0 (0.001)
Basic metals & fabricated metal 0.9999 −0.390 600 0.999 −0.138 600 0.252
[0.0000] [0.078] 984.5 [0.000] [0.018] 262.5 (0.001)
Machinery, nec 0.9997 −0.155 600 0.997 0.025 600 0.179
[0.0001] [0.032] 524.1 [0.000] [0.023] 440.3 (0.000)
Electrical & optical equipment 0.9997 −0.089 600 0.998 0.035 600 0.123
[0.0001] [0.047] 225.4 [0.000] [0.015] 318.0 (0.006)
Transport equipment 0.9999 −0.192 600 0.998 0.048 600 0.240
[0.0000] [0.053] 275.7 [0.000] [0.046] 273.8 (0.000)
Manufacturing, nec; recycling 0.9999 −0.346 600 0.998 −0.185 600 0.161
[0.0000] [0.071] 371.4 [0.000] [0.054] 374.0 (0.035)

  1. Notes: Figures in brackets indicate standard errors that are based on 100 bootstrap replications. Figures in parentheses are the p -values of the z test. Wald indicates the first-stage Wald statistics. Source: Socio Economic Accounts of the World Input-Output Database (WIOD) released in July 2014.

Table A4:

Estimated elasticities by aggregate sector with year dummies: reference year = 2009.

Sector b ̂ θ ̂ N and Wald ρ ̂ N and Wald ρ ̂ − θ ̂
All 0.793 0.088 560 0.126 360 0.038
[0.051] [0.071] 2472.2 [0.036] 1776.5 (0.316)
Primary 0.799 0.248 560 0.173 360 −0.075
[0.065] [0.069] 1365.2 [0.046] 930.6 (0.189)
Manufacturing 0.924 0.090 560 0.096 360 0.006
[0.027] [0.063] 2535.4 [0.026] 1450.2 (0.468)
Services 0.733 0.072 560 0.109 360 0.037
[0.057] [0.073] 2220.4 [0.036] 1383.0 (0.331)

  1. Notes: Figures in brackets indicate standard errors that are based on 100 bootstrap replications. Figures in parentheses are the p-values of the z test. Wald indicates the first-stage Wald statistics. Source: Socio Economic Accounts of the World Input-Output Database (WIOD) released in July 2014.

Table A5:

Estimated elasticities by aggregate sector with year dummies: reference year = 2001.

Sector b ̂ θ ̂ N and Wald ρ ̂ N and Wald ρ ̂ − θ ̂
All 0.831 0.088 560 0.113 360 0.025
[0.041] [0.071] 2472.2 [0.036] 1763.4 (0.378)
Primary 0.850 0.248 560 0.151 360 −0.097
[0.054] [0.069] 1365.2 [0.046] 932.0 (0.120)
Manufacturing 0.940 0.090 560 0.092 360 0.002
[0.021] [0.063] 2535.4 [0.026] 1449.7 (0.489)
Services 0.767 0.072 560 0.094 360 0.022
[0.049] [0.073] 2220.4 [0.035] 1371.9 (0.393)

  1. Notes: Figures in brackets indicate standard errors that are based on 100 bootstrap replications. Figures in parentheses are the p-values of the z test. Wald indicates the first-stage Wald statistics. Source: Socio Economic Accounts of the World Input-Output Database (WIOD) released in July 2014.

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Received: 2023-01-11
Accepted: 2023-09-07
Published Online: 2023-10-27

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/bejm-2023-0008
Keywords for this article
intermediate goods–skill complementarity; elasticity of substitution; CES; skill-biased technological change; imported intermediate goods

Articles in the same Issue

  1. Frontmatter
  2. Advances
  3. Optimal Taxation of Informal Firms: Misreporting Costs and a Tax Reform in Brazil
  4. Initial Beliefs Uncertainty
  5. Credit Resource Misallocation and Macroeconomic Fluctuations in China: From the Perspective of Heterogeneous Financial Frictions
  6. The Bitcoin Premium: A Persistent Puzzle
  7. Contributions
  8. Intermediate Goods–Skill Complementarity
  9. Perfect Competition and Fixed Costs: The Role of the Ownership Structure
  10. Optimal Monetary Policy with Government-Provided Unemployment Benefits
  11. Employment Protection in Dual Labor Markets: Any Amplification of Macroeconomic Shocks?
  12. A Tide that Lifts Some Boats: Assessing the Macroeconomic Effects of EU Enlargement
  13. Current Account Balances’ Divergence in the Euro Area: An Appraisal of the Underlying Forces
  14. Merging Structural and Reduced-Form Models for Forecasting
  15. Trust in Government in a Changing World: Shocks, Tax Evasion, and Economic Growth
  16. The Fiscal Multiplier of Public Investment: The Role of Corporate Balance Sheet
  17. Does Uncertainty Matter for the Fiscal Consolidation and Investment Nexus?
  18. Government Spending Between Active and Passive Monetary Policy: An Invariance Result
  19. A DSGE Model with Government-owned Banks
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