Border carbon adjustment and tax revenue redistribution in MPSGE

Problems with modeling
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Richard_59
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Border carbon adjustment and tax revenue redistribution in MPSGE

Post by Richard_59 »

Hi everibody,
I'm trying to implement a border carbon adjustment in an MPSGE model. I'd like to introduce a tariff on imports arriving in a country depending on the carbon content of the imported good.
I'm using an Armington specification of international trade between two regions. The production function of the generic good in region r is the following :

$PROD:GENERIC(r) s:1 t:1
O:PGENERIC(r)
I:PL(r) t:
I:PK(r) t:
I:PF(r)

$PROD:GENERIC_ARMINGTON(r) s:1
O:PGENERIC_ARMINGTON(r)
I:PGENERIC(rr)

$PROD:F(r) s:1
O:PF(r)
I:PK(r)
I:PL(r)

Where L is for Labor, K for capital and F for fossil energy, and rr is an alternative name for r. So I would like to introduce an endogenous tax proportional to the fossil content of the generic arriving from region rr in r, i.e. F(rr) / GENERIC(rr), where F(rr) is the fossil input used in sector GENERIC(rr).
So I tryed to use an auxiliary variable to do so :

$PROD:GENERIC_ARMINGTON(r) s:1
O:PGENERIC_ARMINGTON(r)
I:PGENERIC(rr) N:BCA(r,rr)

$CONSTRAINT:BCA(r,rr)
BCA(r,rr) = (Tax_carbon(r) * F(rr) / GENERIC(rr)) / PGENERIC(rr) ;

Tax_carbon(r) being the exogenous carbon tax on quantity existing in region r and BCA the border carbon adjustment in r. The problem is that doing this I don't get the good values of F(rr). What I would like to get is not the total produced quantity of F (which can also be used outside of the GENERIC sector in my model) but only the quantity of F used as an input in the GENERIC(rr) sector. Does anyone know how I could do this in MPSGE ?

My second and last question would be on the way to redistribute a tax revenue otherwise than through a lump-sum redistribution. For example, if I wanted to use my whole carbon tax renvenue to reduce taxation on labour, I could add a constraint such as :

$CONSTRAINT:Tax_L_endogenous(r)
( Tax_L_exogenous(r) - Tax_L_endogenous(r)) * PL(r) * L(r) = PT(r) ;

where PT is the transfer of the carbon tax to households. It makes it possible to reduce the taxation on L by as much as the revenue of the carbon tax. But then, how can I cancel any redistribution of PT(r) to the household ? Because in my MPSGE model, the taxes are imposed by the government and then redistributed automatically to the household who has the tranfer as an endowment.

Any help on these two topics would be so much welcome !
Thanks a lot to anybody ready to share with me some ideas on how I could do this.

Richard
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