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The Impact of Environmental Taxation on Wage Inequality in the Presence of Subsidizing Renewable Energy

  • Jiancai Pi EMAIL logo and Yanwei Fan
Published/Copyright: March 31, 2023
The B.E. Journal of Economic Analysis & Policy
From the journal The B.E. Journal of Economic Analysis & Policy Volume 23 Issue 2

Abstract

This paper explores how environmental taxation affects wage inequality in the presence of subsidizing renewable energy. It is necessary to take both traditional dirty energy and renewable energy into account. Take the case where the renewable energy sector is more skill-intensive than the traditional energy sector as an example. If the final product sector is more skill-intensive than the whole energy sector, an increment of the output tax in the traditional energy sector will widen wage inequality unambiguously. However, if the final product sector is less skill-intensive than the whole energy sector, an increment of the output tax in the traditional energy sector may narrow down wage inequality when the substitution elasticity between energy and labor in the final product sector is sufficiently large. The interaction between environmental taxation and subsidization on renewable energy plays a key role in the mechanism. We also analyze the relationship between environmental taxation and welfare.

Keywords: environmental taxation; subsidization on renewable energy; wage inequality; welfare
JEL Classification: J31; O15; Q52; Q58
Corresponding author: Jiancai Pi, Department of Economics, Nanjing University, Nanjing, P.R. China, E-mail:

Acknowledgment

We are very grateful to the editor Till Requate and two anonymous reviewers for their insightful comments and detailed suggestions on improving this paper.

Appendix A: The Detail of the Empirical Analysis

We consider some reduced-form regressions of wage inequality on the energy structure.[12] The results are shown in Table A1. In Panel A, we use the database covering G20 nations to investigate the correlation between wage inequality and the energy structure. In Panel B, the database is extended to all the countries that we have obtained the data.

Table A1:

Wages inequality regressed on the energy structure.

Dependent variable: industrial theil index of wage
(1) (2) (3) (4)
Panel A: data from G20
Renewable energy consumption share 0.00112b 0.00100b
(16.88) (7.00)
Renewable energy output share 0.00035b 0.00038b
(5.98) (4.80)
Skilled labor share −0.00059b −0.00098b
(−4.16) (−7.20)
Observations 413 413 123 123
R-squared 0.41 0.08 0.52 0.44
Countries 19 19 15 15
Panel B: data covering countries beyond G20
Renewable energy consumption share 0.000478b 0.000422a
(9.119) (2.465)
Renewable energy output share 0.000412b 0.000412b
(9.727) (3.991)
Skilled labor share −0.000636a −0.000608a
(−2.542) (−2.488)
Observations 1976 1976 486 486
R-squared 0.040 0.046 0.033 0.053
Countries 117 117 82 82

  1. t-statistics in parentheses. ap<0.05, bp<0.01.

In columns (1) and (2), we regress industrial wage inequality on the energy consumption structure and the energy output structure, respectively. In both Panel A and Panel B, the coefficients of the energy structure are significant. However, once more countries are considered in Panel B, the coefficients are much smaller. The reason is that the energy structure and wage inequality in most less developed countries change little in our sample.

In columns (3) and (4), we control for the labor structure. We define skilled labor as workers who at least have completed post-secondary education. The share of skilled labor in the population over 25 years old are used to represent the labor structure.[13] A higher share of skilled labor implies a relative higher skilled labor supply, which may generate a negative effect on the skilled wage and thereby on wage inequality. The results show that the coefficients of the energy structure are significant and stable with respect to columns (1) and (2). The coefficients of the skilled labor share are negative, which is in accordance with our intuition.

Appendix B: The Impacts of Environmental Taxation on the Wages and the Wage Gap

Totally differentiating Eqs. (4)–(10) and rearrange the results into the matrix form, we obtain:

(A1) 0 0 0 − θ U C − θ S C 1 0 0 0 0 − θ U R − θ S R 1 ϕ R 0 0 0 − θ U X − θ S X − θ E X 0 λ U C λ U R λ U X K 1 K 3 θ E X λ U X σ LEX 0 λ S C λ S R λ S X K 2 K 4 θ E X λ S X σ LEX 0 − λ C − λ R 1 θ L X θ ULX σ LEX θ L X θ SLX σ LEX − θ L X σ LEX 0 1 − 1 0 0 0 − η F − 1 × C ̂ R ̂ X ̂ w ̂ U w ̂ S p ̂ E s ̂ R = θ F C ϕ F 0 0 0 0 0 − η F t ̂ F + ϕ C 0 0 0 0 0 − η C t ̂ C ,

where K 1 = − λ U C θ SLC σ USC − θ S R λ U R σ USR − λ U X θ E X θ ULX σ LEX + θ SLX σ USX < 0 , K 2 = λ S C θ ULC σ USC + θ U R λ S R σ USR + λ S X − θ E X θ ULX σ LEX + θ ULX σ USX , K 3 = λ U C θ SLC σ USC + θ S R λ U R σ USR + λ U X − θ E X θ SLX σ LEX + θ SLX σ USX , and K 4 = − λ S C θ ULC σ USC − θ U R λ S R σ USR − λ S X θ E X θ SLX σ LEX + θ ULX σ USX < 0 .

We use Δ to denote the determinant of the coefficient matrix of Eq. (A1). When t ̂ F = 0 , solving Eq. (A1), we obtain the impacts of the output tax t C on the wages:

(A2) w ̂ S t ̂ C = 1 Δ 1 − η F ϕ R θ L X θ ULX + θ E X θ U R A 1 ϕ C + η C θ L C θ E X θ ULC + θ L X θ ULX A 1 ϕ R − θ ULX λ S X − λ U X σ LEX − θ E X A 2 ϕ C ϕ R ,

(A3) w ̂ U t ̂ C = 1 Δ − 1 − η F ϕ R θ L X θ SLX + θ E X θ S R A 1 ϕ C − η C θ L C θ E X θ SLC + θ L X θ SLX A 1 ϕ R − θ SLX λ U X − λ S X σ LEX − θ E X A 2 ϕ C ϕ R ,

where A 2 = θ ULX λ S X + θ SLX λ U X σ USX + θ ULC λ S C + θ SLC λ U C σ USC + θ U R λ S R + θ S R λ U R σ USR .

Combining Eqs. (A2) and (A3), we obtain the impact of t C on the wage gap:

(A4) w ̂ S − w ̂ U t ̂ C = 1 Δ η C 1 − θ E X θ F C ϕ R + 1 − η F θ L X ϕ R ϕ C A 1 + λ U X − λ S X σ LEX ϕ R ϕ C .

From Eq. (A4), as Δ < 0 holds (see Appendix C), when A 1 < 0 and λ UX − λ SX < 0, then w ̂ S − w ̂ U t ̂ C > 0 . However, when A 1 < 0 and λ UX − λ SX > 0, then w ̂ S − w ̂ U t ̂ C > 0 if and only if − η C 1 − θ E X θ F C ϕ R + 1 − η F θ L X ϕ R ϕ C A 1 λ U X − λ S X ϕ R ϕ C > σ LEX . The situation where A 1 > 0 is similar. Thus, Proposition 1 is proved.

When t ̂ C = 0 , solving Eq. (A1), we obtain the impacts of the emission tax t F on the wages:

(A5) w ̂ S t ̂ F = 1 Δ θ F C θ E X θ U R + 1 − η F ϕ R θ L X θ ULX A 1 ϕ F + η F θ E X θ L C θ ULC + θ L X θ ULX A 1 ϕ R − θ F C θ ULX λ S X − λ U X σ LEX − θ E X A 2 ϕ R ϕ F ,

(A6) w ̂ U t ̂ F = 1 Δ − θ F C θ E X θ S R + θ L X θ SLX 1 − η F ϕ R A 1 ϕ F − η F θ E X θ L C θ SLC + θ L X θ SLX A 1 ϕ R − θ F C θ SLX λ U X − λ S X σ LEX − θ E X A 2 ϕ R ϕ F .

Combining Eqs. (A5) and (A6), we obtain the impact of t F on the wage gap:

(A7) w ̂ S − w ̂ U t ̂ F = 1 Δ η C 1 − θ F C θ E X ϕ R + θ F C 1 − η F θ L X ϕ R ϕ F A 1   + θ F C λ U X − λ S X ϕ F ϕ R σ LEX .

From Eq. (A7), when A 1 < 0 and λ UX − λ SX < 0, then w ̂ S − w ̂ U t ̂ F > 0 . However, when A 1 < 0 and λ UX − λ SX > 0, then w ̂ S − w ̂ U t ̂ F > 0 if and only if − η C 1 − θ F C θ E X ϕ R + θ F C 1 − η F θ L X ϕ R ϕ F A 1 θ F C λ U X − λ S X ϕ F ϕ R > σ LEX . The situation where A 1 > 0 is similar. Thus, Proposition 2 is proved.

Appendix C: The Dynamic Adjustment Process of the Model

Following the method of Konishi, Okuno-Fujiwara, and Suzumura (1990) and Beladi, Chaudhuri, and Yabuuchi (2008), we construct the dynamic adjustment system according to Eqs. (4)–(10) as follows:

(A8) C ̇ = d 1 p E ( 1 − t C ) − a U C w U − a S C w S − a F C p F ( 1 + t F ) ,

(A9) R ̇ = d 2 p E ( 1 + s R ) − a U R w U − a U S w S ,

(A10) X ̇ = d 3 p X − a S X w S − a U X w U − a E X p E ,

(A11) w ̇ U = d 4 a U C C + a U R R + a U X X − U ̄ ,

(A12) w ̇ S = d 5 a S C C + a S R R + a S X X − S ̄ ,

(A13) p ̇ E = d 6 a E X X − C − R ,

(A14) s ̇ R = d 7 t F p F a F C C + t E p E C − s R p E R ,

where d i (i = 1, …, 7) denotes the speed of adjustment and d i > 0. The notation “⋅” denotes the differentiation with respect to time t (e.g. C ̇ = d C d t ). Linearizing the adjustment system in the neighborhood of equilibrium, we obtain the determinant of the Jacobian matrix:

(A15) J = ( 1 − t E ) ( 1 + s R ) p E 2 p X U ̄ S ̄ ( C + R ) C X w U w S ∏ i d i × 0 0 0 − θ U C − θ S C 1 0 0 0 0 − θ U R − θ S R 1 ϕ R 0 0 0 − θ U X − θ S X − θ E X 0 λ U C λ U R λ U X K 1 K 3 θ E X λ U X σ LEX 0 λ S C λ S R λ S X K 2 K 4 θ E X λ S X σ LEX 0 − λ C − λ R 1 θ L X θ ULX σ LEX θ L X θ SLX σ LEX − θ L X σ LEX 0 1 − 1 0 η F θ L C θ ULC σ LFC η F θ L C θ SLC σ LFC − η F − 1 = ( 1 − t E ) ( 1 + s R ) p E 2 p X U ̄ S ̄ ( C + R ) C X w U w S ∏ i d i Δ ⋅

According to the Routh–Hurwitz theorem, J < 0 ensures the local stability of the system consisting of seven equations, and thereby we have Δ < 0.

Appendix D: The Impacts of Environmental Taxation on Emissions

Differentiating Eqs. (7)–(9), we have:

(A16) λ U C a ̂ U C + C ̂ + λ U R a ̂ U R + R ̂ + λ U X a ̂ U X + X ̂ = 0 ,

(A17) λ S C a ̂ S C + C ̂ + λ S R a ̂ S R + R ̂ + λ S X a ̂ S X + X ̂ = 0 ,

(A18) a ̂ E X + X ̂ = λ C C ̂ + λ R R ̂ .

Combining Eqs. (A16)–(A18) and solving the subsystem, we obtain:

(A19) C ̂ = 1 A 1 λ S R + λ R λ S X a ̂ U C λ U C + a ̂ U R λ U R + a ̂ U X λ U X − λ U R + λ R λ U X a ̂ S C λ S C + a ̂ S R λ S R + a ̂ S X λ S X + a ̂ E X λ S X λ U R − λ U X λ S R .

Since a ij is a function of prices w S , w U , and p E , Eq. (A19) can be rewritten as:

(A20) C ̂ = 1 A 1 A 3 w ̂ S − w ̂ U + σ LEX λ S R λ U X − λ S X λ U R   × p ̂ E − w ̂ S θ SLX − w ̂ U θ ULX ,

where A 3 = θ SLC λ S R + λ R λ S X λ U C + θ ULC λ S C λ U R + λ R λ U X σ USC + θ S R λ S R + λ R λ S X λ U R + θ U R λ S R λ U R + λ R λ U X σ USR + θ ULX λ S X λ U R + θ SLX λ S R λ U X + θ SLX + θ ULX λ R λ S X λ U X σ USX .

If σ LEX = 0, combining Eqs. (A4), (A7) and (A20), we obtain:

(A21) C ̂ t ̂ C = 1 Δ η C 1 − θ E X θ F C ϕ R + 1 − η F θ L X ϕ R ϕ C A 3 < 0 ,

(A22) C ̂ t ̂ F = 1 Δ η C 1 − θ F C θ E X ϕ R + θ F C 1 − η F θ L X ϕ R ϕ F A 3 < 0 .

If σ LEX is large enough, C ̂ is approximate to:

(A23) C ̂ = σ LEX λ S R λ U X − λ S X λ U R p ̂ E − w ̂ S θ SLX − w ̂ U θ ULX .

Differentiating Eq. (4), we have:

(A24) p ̂ E = w ̂ S θ L C θ SLC + w ̂ U θ L C θ ULC + t ̂ C ϕ C + t ̂ F θ F C ϕ F .

Combining Eqs. (A2), (A3), (A23) and (A24), if σ LEX is large enough, the impact of t C on C is approximate to:

(A25) C ̂ t ̂ C = σ LEX λ S R λ U X − λ S X λ U R A 1 1 Δ θ SLC θ ULX − θ ULC θ SLX   × λ U X − λ S X θ L C σ LEX ϕ C ϕ R + ϕ C .

From Eq. (A25), if λ UX − λ SX = 0 and λ S R λ U X − λ S X λ U R A 1 < 0 , we have C ̂ t ̂ C < 0 . Note that θ SLC θ ULX − θ ULC θ SLX = 0 cannot ensure the sign of Eq. (A25) be negative. When θ SLC θ ULX − θ ULC θ SLX = 0, the term in Δ with σ LEX is equal to zero too. Similarly, when σ LEX is large enough, it can be proved that C ̂ t ̂ F < 0 if λ UX − λ SX = 0 and λ S R λ U X − λ S X λ U R A 1 < 0 . Thus, Proposition 3 is proved.

Appendix E: The Comparison Between Two Types of Environmental Taxation

Combining Eqs. (A4) and (A7), we have:

(A26) w ̂ S − w ̂ U t ̂ C − w ̂ S − w ̂ U t ̂ F = 1 Δ η F − η C ϕ R ϕ C A 1 + ϕ C − θ F C ϕ F   × 1 − η F θ L X ϕ R A 1 + λ U X − λ S X ϕ R σ LEX .

If η C = η F , we have:

(A27) η F = η C ⇒ t F p F a F C C = t C p E C ⇒ t F θ F C = t C .

Combining Eq. (A27), ϕ C = t C / 1 − t C , and ϕ F = t F / 1 + t F , we have:

(A28) ϕ C − θ F C ϕ F = ϕ C 2 1 + θ F C ϕ C + θ F C ϕ C + 1 > 0 .

Thus, when η C = η F , w ̂ S − w ̂ U t ̂ C − w ̂ S − w ̂ U t ̂ F > 0 if σ LEX is sufficiently small and A 1 < 0.

If ϕ C = θ FC ϕ F , combining with ϕ C = t C / 1 − t C and ϕ F = t F / 1 + t F , we have:

(A29) ϕ C = θ F C ϕ F ⇒ t C = t F θ F C 1 + t F + t F θ F C ⇒ η F η C = 1 + t F 1 + θ F C > 1 .

Thus, when ϕ C =θ FC ϕ F , w ̂ S − w ̂ U t ̂ C − w ̂ S − w ̂ U t ̂ F > 0 if σ LEX is sufficiently small and A 1 < 0.

If t C = t F , we have:

(A30) ϕ F = ϕ C 1 + 2 ϕ C ⇒ ϕ C − θ F C ϕ F = 2 ϕ C + θ L C 1 + 2 ϕ C > 0 ,

(A31) η F η C = t F θ F C t E ⇒ η F = θ F C η C < η C .

Appendix F: Discussion About the Rules of Taxation and Subsidization

To prove the equivalence between an increment of environmental taxation and an increment of the subsidy on renewable energy, we take the output tax on traditional energy for example.

When the government takes the output tax as an instrument, the impacts of the environmental tax are solved by the following system:

(A32) 0 0 0 − θ U C − θ S C 1 0 0 0 0 − θ U R − θ S R 1 ϕ R 0 0 0 − θ U X − θ S X − θ E X 0 λ U C λ U R λ U X K 1 K 3 θ E X λ U X σ LEX 0 λ S C λ S R λ S X K 2 K 4 θ E X λ S X σ LEX 0 − λ C − λ R 1 θ L X θ ULX σ LEX θ L X θ SLX σ LEX − θ L X σ LEX 0 1 − 1 0 η F θ L C θ ULC σ LFC η F θ L C θ SLC σ LFC − η F − 1 × C ̂ R ̂ X ̂ w ̂ U w ̂ S p ̂ E s ̂ R = ϕ C 0 0 0 0 0 − η C t ̂ C .

Thus, the impact of the output tax on the skilled wage can be written as w ̂ S t ̂ C = Δ S t C Δ , where

(A33) Δ S t C = 0 0 0 − θ U C ϕ C 1 0 0 0 0 − θ U R 0 1 ϕ R 0 0 0 − θ U X 0 − θ E X 0 λ U C λ U R λ U X K 1 0 θ E X λ U X σ LEX 0 λ S C λ S R λ S X K 2 0 θ E X λ S X σ LEX 0 − λ C − λ R 1 θ L X θ ULX σ LEX 0 − θ L X σ LEX 0 1 − 1 0 η F θ L C θ ULC σ LFC − η C − η F − 1 .

When the government takes the subsidy on renewable energy as an instrument, the impacts of the subsidy are solved by the following system:

(A34) 0 0 0 − θ U C − θ S C 1 − ϕ C 0 0 0 − θ U R − θ S R 1 0 0 0 0 − θ U X − θ S X − θ E X 0 λ U C λ U R λ U X K 1 K 3 θ E X λ U X σ LEX 0 λ S C λ S R λ S X K 2 K 4 θ E X λ S X σ LEX 0 − λ C − λ R 1 θ L X θ ULX σ LEX θ L X θ SLX σ LEX − θ L X σ LEX 0 − 1 1 0 − η F θ L C θ ULC σ LFC − η F θ L C θ SLC σ LFC η F − η C C ̂ R ̂ X ̂ w ̂ U w ̂ S p ̂ E t ̂ C = 0 − ϕ R 0 0 0 0 − 1 s ̂ R .

Thus, the impact of the subsidy on the skilled wage can be written as w ̂ S s ̂ R = Δ S s R Δ s R , where Δ s R is the determinant of the coefficient matrix of Eq. (A34), and

(A35) Δ S s R = 0 0 0 − θ U C 0 1 − ϕ C 0 0 0 − θ U R − ϕ R 1 0 0 0 0 − θ U X 0 − θ E X 0 λ U C λ U R λ U X K 1 0 θ E X λ U X σ LEX 0 λ S C λ S R λ S X K 2 0 θ E X λ S X σ LEX 0 − λ C − λ R 1 θ L X θ ULX σ LEX 0 − θ L X σ LEX 0 − 1 1 0 − η F θ L C θ ULC σ LFC 1 η F − η C = Δ S t C .

Therefore, it is clear that w ̂ S t ̂ C = Δ s R Δ w ̂ S s ̂ R . Note that Δ s R < 0 holds to ensure the stability of system (A34). Then, we have Δ s R Δ > 0 . Thus, the impact of an increment of the output tax on traditional energy is linear to the impact of an increment of the emission tax on renewable energy.

The situation where the emission tax is levied is similar.

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Received: 2022-06-29
Accepted: 2023-03-08
Published Online: 2023-03-31

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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  10. The Competitive Foundations of Price Cap Regulation
  11. Letters
  12. Exploring the Existence of a Short-Run Kuznets Curve: Does the Fourth Industrial Revolution Affect Income distribution?
  13. MRS Functions and the Pareto Interval in Public Good Provision
  14. Optimal Imprisonment with General Enforcement of Law
  15. Immigration and Perceived Social Position. Insights from an Unintended Survey Experiment
https://doi.org/10.1515/bejeap-2022-0236
Keywords for this article
environmental taxation; subsidization on renewable energy; wage inequality; welfare

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Overconfidence and Public Intoxication Arrest: Evidence from a University Town Police Log
  4. The Changing Determinants of Juvenile Crime
  5. Failing Young and Temporary Workers? The Impact of a Disruptive Crisis on a Dual Labour Market
  6. Productivity, Innovation Spillovers, and Mergers: Evidence from a Panel of U.S. Firms
  7. Trade Policies and FDI with an Endogenous Market Structure
  8. Is There a Business Cycle Effect on the Incidence of Dual Job Holding?
  9. The Impact of Environmental Taxation on Wage Inequality in the Presence of Subsidizing Renewable Energy
  10. The Competitive Foundations of Price Cap Regulation
  11. Letters
  12. Exploring the Existence of a Short-Run Kuznets Curve: Does the Fourth Industrial Revolution Affect Income distribution?
  13. MRS Functions and the Pareto Interval in Public Good Provision
  14. Optimal Imprisonment with General Enforcement of Law
  15. Immigration and Perceived Social Position. Insights from an Unintended Survey Experiment
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