Income Distribution, Factor Endowments, and Trade Revisited: The Role of Non-Tradable Goods

Sebastian Galiani; Daniel Heymann; Nicolas E. Magud

doi:10.1515/jgd-2016-0028

Article

Income Distribution, Factor Endowments, and Trade Revisited: The Role of Non-Tradable Goods

Sebastian Galiani , Daniel Heymann and Nicolas E. Magud

Published/Copyright: July 14, 2017

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From the journal Journal of Globalization and Development Volume 8 Issue 1

Abstract

We return to the traditional theme of the distributive consequences of international prices and trade policies, focusing on economies relatively abundant in natural resources with a large non-tradable-goods sector. Changes in international prices create an aggregate demand effect which impacts on the earnings of factors employed in the non-traded goods sector. We show that, in economies highly specialized in the production of tradable goods and where the import-competing sector is small, under standard assumptions, terms-of- trade shifts have a neutral effect on factor prices and thus lack distributive effects, quite differently from Stolper-Samuelson scenarios. In economies with sizable import-competing sectors and two “urban” productive factors (e.g. skilled and unskilled labor), changes in the terms of trade do induce distributional tensions through two channels: (i) the exogenous shift in the relative price of tradable goods, and (ii) the endogenous displacement of the demand for non-tradables. We illustrate how, according to the structure of the economy, different patterns of income distribution may arise. Next, we analyze the introduction of trade duties. Trade taxes change relative prices between tradable goods as a terms-of-trade shock does, but also introduce an additional demand mechanism, that depends on the use the government gives to the revenues. If the tax revenues are transferred back to the private sector, the resulting reallocation of spending favors those factors used intensively in the production of non-tradables.

Keywords: income distribution; international trade; non-tradable goods; Stolper-Samuelson effects

JEL Classification: F16; F13; D33

Acknowledgment

We would like to thank Daniel Aromi, Sebastian Bauer, Joaquin Endara, Martin Guzman, Pablo Mira, Gustavo Montero, Santiago Cesteros, Guido Zack, and an anonymous referee for their comments and suggestions. The usual caveat applies.

A Appendix

Imports as Production Inputs in the Two-Sector Case

Good M is now not only a consumer product but is also used as an input in the production of goods A and N. The proportional change in intermediate imports after a change in the price of A (with p^M=0):

M^=λMA(p^A+y^A)+λMN(p^N+y^N)−p^M

The supply-demand conditions for primary factors L, T and H are still given by:

L^=0=λLA(p^A+y^A)+λLN(p^N+y^N)−w^T^=0=p^A+y^A−t^H^=0=λHN(p^N+y^N)−h^

The trade balance condition:

p^A+y^A=(1−m)γA(p^A+c^A)+(1−m)γMc^M+mM^

Cost-price equations:

p^A=θTAt^+θLAw^+θMAp^Mp^N=θLNw^+θHNh^+θMNp^M

It can be seen that these equations are satisfied if:

t^=w^=h^=p^A+y^A=p^N+y^N=c^M=p^A+c^A=M^=11−θMAp^A

and:

p^N=1−θMH1−θMAp^A, y^N=θMH1−θMAp^A, y^A=θMA1−θMAp^A

The change in the price of the exportable good has, as in the case in which there are no intermediate imports, neutral effects on the returns to the domestic factors. However, now factor earnings rise more than in proportion to the price of good A because of the expanded production opportunities created by the relative reduction in the cost of international inputs.

B Appendix

Derivation of the Reduced System involving the Sign of the Determinant in the Three-Goods Case

The supply-demand equations for production factors can be written as follows:

L^=0=λLA(p^A+y^A)+λLN(p^N+y^N)+λLMy^M−w^T^=0=p^A+y^A−t^H^=0=λHN(p^N+y^N)+λHMy^M−h^

Price equations for A and M:

p^A=θTAt^+θLAw^p^M=0=θLMw^+θHMh^

Trade balance:

χA(p^A+y^A)+χMy^M=γA(p^A+c^A)+γMc^M

Taking into account the assumed consumption demand functions and the supply-demand balance of non-tradable-goods:

p^N+y^N=p^N+c^N=p^A+c^A=c^M

The system then reduces to:

λLAt^+λLNc^M+λLMy^M=p^A−θTAt^θLAλHNc^M+λHMy^M=−θLMθHMp^A−θTAt^θLAχAt^+χMy^M=c^M

or:

(λLAθLA+θTA)t^+θLAλLNc^M+θLAλLMy^M=p^A−θLMθTAt^+θHMθLAλHNc^M+θHMθLAλHMy^M=−θLMp^AχAt^+χMy^M=c^M

leading to:

((λLA+λLNχA)θLA+θTA)t^+θLA(λLM+λLNχM)y^M=p^A(θHMθLAλHNχA−θLMθTA)t^+θHMθLA(λHM+λHNχM)=−θLMp^A

The determinant of this system is:

Ω=((λLA+λLNχA)θLA+θTA)(λHM+λHNχM)θHMθLA−(θHMθLAλHNχA−θLMθTA)(λLM+λLNχM)θLA

It can be seen that the only negative term is a multiple of θ_HMθ_LAλ_HNχ_A. Collecting the terms in λ_HN:

(λLA+λLNχA)θLAλHNθHMθLAχM+λHNθHMθLAθTAχM−(λLM+λLNχM)θHMθLAλHNθLAχA=θHMθLAλHN(θLA((λLA+λLNχA)χM−(λLM+λLNχM)χA)+θTAχM)

This reduces to:

θHMθLAλHN((θLAλLA+θTA)χM−λLMθLAχA)

But:

χM=pMyMpMyM+pAyA=pMyMwLMwLMwLpMyMwLMwLMwL+pAyAwLAwLAwL=λLMθLAλLMθLA+λLAθLM=λLMθLAx

And a similar expression for χ_A.

Then:

(θLAλLA+θTA)χM−λLMθLAχA=λLMθLAx(θLAλLA+θTA−λLAθLM)=λLMθLAx(θTA(1−λLA)+λLAθHM)>0

Therefore, Ω is unambiguously positive.

C Appendix

Proof of Proposition 4 and Related Results

Proof that t^p^A>0 and y^Mp^A≤0

Using the reduced system shown in Appendix B, it follows that:

Ωt^p^A=θHMθLA(λHM+λHNχM)+θLMθLA(λLM+λLNχM)>0Ωy^Mp^A=−θLM((λLA+λLNχA)θLA+θTA)−(θHMθLAλHNχA−θLMθTA)=−θLM(λLA+λLNχA)θLA−θHMθLAλHNχA<0

Proof that t^p^A≥1

This result is equivalent to p^A+y^A≥p^A or y^A≥0. The system can be rearranged as:

((λLA+λLNχA)θLA+θTA)y^A+θLA(λLM+λLNχM)y^M=p^A(1−(λLA+λLNχA)θLA+θTA)(θHMθLAλHNχA−θLMθTA)y^A+θHMθLA(λHM+λHNχM)y^M=−p^A(θLM+(θHMθLAλHNχA−θLMθTA))

which implies:

Ωy^Ap^A=(1−((λLA+λLNχA)θLA+θTA))θHMθLA(λHM+λHNχM)+θLA(λLM+λLNχM)(θHMθLAλHNχA+θLMθLA)>0

because (λ_LA+λ_LNχ_A)θ_LA+θ_TA < 1

Expression for w^

The system can be rearranged (taking into account that t^=p^A−θLAw^θTA) to give:

((λLA+λLNχA)θLA+θTA)w^−θTA(λLM+λLNχM)y^M=p^A(λLA+λLNχA)−(θHMθLAλHNχA−θLMθTA)w^+θHMθTA(λHM+λHNχM)=−p^AλHNθHMχA

In a similar fashion to what was done before, it can be shown that the determinant of this system is positive:

Ω′=((λLA+λLNχA)θLA+θTA)θHMθTA(λHM+λHNχM)−θTA(λLM+λLNχM)(θHMθLAλHNχA−θLMθTA)>0

Then:

Ω′w^p^A=(λLA+λLNχA)θHMθTA(λHM+λHNχM)−λHNθHMχAθTA(λLM+λLNχM)

Which can be reduced to an expression with an ambiguous sign:

Ω′w^p^A=θHMθTA(λLA(λHM+λHNχM)+χA(λHMλLN−λHNλLM))

Limit cases

1. Sector A labor intensive: θ_LA ≈ 1

In the limit: w^=p^A, h^=−θLMθHMp^A

The value of spending on good N (in terms of M) and the volume consumption of M may increase or fall depending on the parameters. To clarify this, it is useful to rewrite the system as:

(λLA+λLNχA)c^M+(χAλLM−χMλLA)y^M=χAp^AθHMλHNc^M+θHMλHMy^M=−θLMp^A

The determinant Ω″ can be shown to be positive. Now:

Ω″c^Mp^A=θHMλHMχA+θLM(χAλLM−χMλLA)

Recalling the expressions for χ_A, χ_M:

Ω″c^Mp^A=θLMλLAx(θHMλHM+λLM(θLM−θLA))=θLMλLAxθHM(λHM−λLM)

So that the sign of c^M depends on that of the difference in factor uses in sector: λ_HM − λ_LM.

2. Sector A, with very low labor intensity: θ_LA ≈ 0, λ_LA ≈ 0

Now, t^p^A=1, y^A=0

The system can be written:

w^−(λLM+λLNχM)y^M=λLNχAp^AθLMw^+θHM(λHM+λHNχM)y^M=−θHMλHNχAp^A

The determinant Ω´´´ is positive. Now,

Ω‴w^p^A=θHMχA(λLN(λHM+λHNχM)−λHN(λLM+λLNχM))

Or:

Ω‴w^p^A=θHMχA(λLNλHM−λHNλLM)=θHMχA(λLN−λHN)

Then, w^p^A>0 if sector N is comparatively L-intensive. However, w^p^A<1 whatever the value of λLN−λHN.

It can also be shown that:

Ω‴p^Np^A=θLNΩ‴w^p^A+θHNΩ‴h^p^A>0

That is so because:

Ω‴p^Np^A=χA(λLN−λHN)(θLNθHM−θHNθLM)=χA(λLN−λHN)(θLN−θLM)>0

Also: p^Np^A<1 since, as indicated before, both w^p^A<1 and h^p^A<1.

It can also be seen that:

Ω‴c^Mp^A=χA(θHMλHM+θLMλLM)>0

and:

Ω‴c^Np^A=χA((θHMλHM+θLMλLM)−(λLN−λHN)(θLN−θLM))=χA(λHMθHN+λLMθLN)>0

D Appendix

Effects of the tax refund in the three-goods case

Recalling equations (34) and (35), the system that determines the effect of the trade tax and refund policy can be written as:

[(λLA+λLNχA)θLA+θTA]t^+(λLM+λLNχM)θLAy^M=−α−λLNδα(χA−γA)[λHNχAθHMθLA−θLMθTA]t^+(λHM+λHNχM)θHMθLAy^M=θLMα−λHNθHMθLAδα(χA−γA)

Thus, the change of the endogenous variables t^,y^M is a combination of the response that would hold in the case of a terms-of-trade shift of magnitude –α, and the effect of the refund δα(χ_A−γ_A):

Ωt^tax=Ωt^int+θHMθLA(λLMλHN−λLNλHM)θLAδα(χA−γA)Ωy^Mtax=Ωy^Mint−(θHMλHNθLA(λLAθLA+θTA)+θLMθTAλLNθLA))δα(χA−γA)

where Ω is the positive determinant. Similar expressions can be found for variables like w^ and c^M

Ωw^tax=Ωw^int−θHMθTA(λLMλHN−λLNλHM)δα(χA−γA)Ωc^Mtax=Ωc^Mint+((λLAθLA+θTA)θHMλHMθLA+θLMθTAθLAλLM)δα(χA−γA)

It can also be verified that t^taxα<0:

Ωt^taxα=−(λHM+λHNχM)θHMθLA−θLMθLA(λLM+λLNχM)+θHMθLA(λLMλHN−λLNλHM)θLAδ(χA−γA)

The only positive term is proportional to θ_HMθ_LAλ_HN. Comparing the analogous terms and remembering the expressions for χ_A, χ_M

θHMθLAλLMλHNθLAδ(χA−γA)−θHMθLAλHNχM<θHMθLAλHN(χAθLAλLM−χM)<0

Also: y^Mtaxα>0:

y^Mtaxα=χA(θLMθLAλLN+θHMθLAλHN)+θLM(λLAθLA+θTA)−θLMθTA−δ(χA−γA)((λLAθLA+θTA)θHMθLAλHN+θLMθTAθLAλLN)>χA((θLMθLAλLN+θHMθLAλHN)−(λLAθLA+θTA)θHMθLAλHN−θLMθTAθLAλLN)>0

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Published Online: 2017-7-14

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https://doi.org/10.1515/jgd-2016-0028

Keywords for this article

income distribution; international trade; non-tradable goods; Stolper-Samuelson effects