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Environmental Taxes and Economic Growth with Multiple Growth Engines

  • Hamid Beladi , Ping-ho Chen , Hsun Chu EMAIL logo , Mei-ying Hu and Ching-chong Lai
Published/Copyright: April 23, 2021
The B.E. Journal of Macroeconomics
From the journal The B.E. Journal of Macroeconomics Volume 21 Issue 2

Abstract

We develop an endogenous growth model in which long-run growth is driven by three engines: private abatement R&D, expanding-variety R&D, and capital accumulation. We show that an environmental tax activates private abatement by directing researchers from the variety R&D sector to the abatement R&D sector, which helps the economy avoid the environmental disaster. Our results also show that the effect of the environmental tax on long-run growth is uncertain, depending mainly on the relative productivity between the two R&D sectors. If the abatement R&D sector is sufficiently productive, increasing the environmental tax will enhance the balanced output growth rate and social welfare.

Keywords: private abatement R&D; endogenous growth; environmental tax; innovation
JEL Classification: H23; O32; Q56
Corresponding author: Hsun Chu, Department of Economics, Tunghai University, No. 1727, Sec. 4, Xitun Dist, Taiwan, E-mail:

Funding source: Ministry of Science and Technology

Award Identifier / Grant number: 105-2410-H-029-005-MY2

Acknowledgments

The authors are deeply indebted to the Editor, Arpad Abraham, and two anonymous referees for their constructive comments that substantially improved the paper. We would also like to thank Chu-chuan Cheng, Wei-chi Huang, Wen-chieh Lee, and participants at Tamkang University, 2020 Taiwan Economic Association Annual Conference, for helpful comments regarding earlier versions of this paper. Financial support from the Ministry of Science and Technology [Grant MOST 105-2410-H-029-005-MY2] is gratefully acknowledged. The usual disclaimer applies.

Appendix A: Derivation of Eqs. (20a)–(20d)

In the steady state, the labor allocations are stationary. Accordingly, by using (3), (5) and the resource constraint Y t = C t , we can obtain:

(A1) w ̇ t w t = Y ̇ t Y = C ̇ t C t = r t − ρ .

Inserting the above equation into the zero profit conditions in the variety R&D sector, capital-producing sector, and abatement R&D sector, and by using N ̇ / N = φ N L N , t , K ̇ / K = φ K L K , t and A ̇ / A = φ A L A , t , we can obtain:

(A2) r t − ρ − φ N L N , t = V ̇ N , t / V N , t ,

(A3) r t − ρ − φ K L K , t = V ̇ K , t / V K , t ,

(A4) r t − ρ − φ A L A , t = V ̇ A , t / V A , t .

Inserting (A2)–(A4) into the no-arbitrage conditions (11), (14) and (15) yields:

(A5) ρ + φ N L N , t = π x , t / V N , t ,

(A6) ρ + φ K L K , t = q t / V K , t ,

(A7) ρ + φ A L A , t = N t p A , t / V A , t

Again, by using the zero profit conditions, the above equations can be alternatively expressed as:

(A8) ρ / φ N + L N , t = N t π x , t / w t ,

(A9) ρ / φ K + L K , t = q t K t / w t ,

(A10) ρ / φ A + L A , t = N t p A , t A t / w t .

By applying symmetric condition and manipulating (4) and (6) to eliminate L Y,t and E t , we can obtain N t p t x t = αY t . Then, inserting (9) and the condition N t x t = K t into this equation, we obtain:

(A11) q K t ( 1 + τ / A t θ ) = α 2 Y t .

By using (A11), together with (8), (9), (17), and T t = τq t , after some calculation we can further obtain:

(A12) N t π x , t = 1 + τ A t θ 1 + τ α / ( 1 − α ) 1 − α α α 2 Y t ,

(A13) N t p A , t A t = 1 − 1 + τ A t θ 1 + τ α / 1 − α 1 − α α α 2 Y t .

Then, substituting (5) and (A11)–(A13) into (A8) and (A9) yields:

(A14) L N , t = 1 + τ A t θ 1 + τ α / ( 1 − α ) α L Y , t − ρ φ N ,

(A15) L K , t = α 2 1 + τ A t θ ( 1 − α ) L Y , t − ρ φ K ,

(A16) L A , t = 1 − 1 + τ A t θ 1 + τ α 1 − α α L Y , t − ρ φ A .

Inserting (A14)–(A16) into the labor market clearing condition L Y,t + L N,t + L A,t + L K,t = 1, we obtain:

(A17) L Y , t = 1 + δ 1 + α + α 2 ( 1 + τ A t θ ) ( 1 − α ) .

In the steady state, the abatement technology grows to become enormously large, and hence τ / A t θ in Eq. (A17) fades away. Then, we derive (20a)–(20d) in the main text.

Appendix B: Proof of Proposition 3

As discussed in the main text, to prevent an environmental disaster it is required that g E = g K − θg A ≤ 0. Using g K = φ K L K , g A = φ A L A , (20b) and (20c), the condition for g E ≤ 0 can be expressed as:

(B1) α 2 φ K − 1 − 1 1 + τ α 1 − α α θ φ A ( 1 − α ) ( 1 + δ ) − ρ 1 − θ ≤ 0 .

After further calculation, this condition can be alternatively expressed as:

(B2) τ ≥ α θ φ A ( 1 − α ) ( 1 + δ ) α θ φ A ( 1 − α ) ( 1 + δ ) − α 2 φ K ( 1 + δ ) + ρ 1 − θ 1 − α α − 1 ,

and thus Proposition 3 is proved.□

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Received: 2020-05-19
Revised: 2021-02-01
Accepted: 2021-04-06
Published Online: 2021-04-23

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Contributions
  3. Occupational Choice and Investments in Human Capital in Informal Economies
  4. Asymmetric Effects of Monetary Policy
  5. Trend Growth and Robust Monetary Policy
  6. Delegating Optimal Monetary Policy Inertia in a Small-Open Economy
  7. Dating Structural Changes in UK Monetary Policy
  8. International Historical Evidence on Money Growth and Inflation: The Role of High Inflation Episodes
  9. Inequality, Growth, and Congestion Externalities
  10. The Neoclassical Growth Model and the Labor Share Decline
  11. Environmental Taxes and Economic Growth with Multiple Growth Engines
  12. Macrodynamic Modeling of Innovation Equilibria and Traps
  13. Advances
  14. Unraveling News: Reconciling Conflicting Evidence
  15. Did the FED React to Asset Price Bubbles?
  16. Agricultural Trade and Structural Change: Evidence from Paraguay
https://doi.org/10.1515/bejm-2020-0108
Keywords for this article
private abatement R&D; endogenous growth; environmental tax; innovation

Articles in the same Issue

  1. Frontmatter
  2. Contributions
  3. Occupational Choice and Investments in Human Capital in Informal Economies
  4. Asymmetric Effects of Monetary Policy
  5. Trend Growth and Robust Monetary Policy
  6. Delegating Optimal Monetary Policy Inertia in a Small-Open Economy
  7. Dating Structural Changes in UK Monetary Policy
  8. International Historical Evidence on Money Growth and Inflation: The Role of High Inflation Episodes
  9. Inequality, Growth, and Congestion Externalities
  10. The Neoclassical Growth Model and the Labor Share Decline
  11. Environmental Taxes and Economic Growth with Multiple Growth Engines
  12. Macrodynamic Modeling of Innovation Equilibria and Traps
  13. Advances
  14. Unraveling News: Reconciling Conflicting Evidence
  15. Did the FED React to Asset Price Bubbles?
  16. Agricultural Trade and Structural Change: Evidence from Paraguay
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