Dear all,

I have been running into a problem when trying to implement an **equal yield constraint** (i.e. keeping public goods provision constant per period) in a standard Ramsey-dynamic CGE model written in MPSGE.

The model runs over the time period from 2020 to 2050. It entails benchmark taxes, Armington trade and sector-specific capital. At the moment, there are 6 sectors: 2 industry sectors, 2 service sectors, one electricity and one fuel sector.

I implemented an equal yield constraint that adjusts the income tax (i.e. the labor tax) in the sectoral production block with the corresponding constraint and initialization of the benchmark variable as follows:

I:PL(t) Q:(fd0(“L”,i)) p:pf0(“L”) A:GOV T:(2*ftax0(“L”)) N:TAU(t) M:(-1)

$CONSTRAINT:TAU(t)

GVNT(t) =E= QREF(t);

TAU.L(t) = ftax0(“L”);

In simulations (e.g. a 10% increase in the annual fuel tax over the entire time horizon), the resulting labor tax oscillates heavily and in an erratic manner. In other cases, e.g. where the tax is only introduced for a ten-year period in 2030, the solver returns “locally infeasible”. My investment / capital accumulation / terminal condition is modelled as follows:

$PROD:Kpt(cs,t)

O:PK(cs,t+1) Q:((1-delta)*KptShare(cs)*KPT0)

O:PKT$TLAST(t) Q:((1-delta)*KptShare(cs)*KPT0)

O:RK(cs,t) Q:(KptShare(cs)*VK0)

I:PK(cs,t) Q:(KptShare(cs)*KPT0)

$PROD:Inv(cs,t)

O:PK(cs,t+1) Q:((delta+growth)*KptShare(cs)*KPT0)

O:PKT$TLAST(t) Q:((delta+growth)*KptShare(cs)*KPT0)

I:PA(i,t) Q:(KptShare(cs)*I0(i))

$CONSTRAINT:TK

sum(t$TLAST(t), sum(cs, Inv(cs,t)*KptShare(cs))/sum(cs,Inv(cs,t-1)*KptShare(cs)) - sum(i, Y(i,t)*y0(i)) /sum(i, Y(i,t-1)*y0(i))) =G= 0;

I have tested a wide range of elements in order to find the problem, such as the following:

• Rearranging the two equations for constraints for TK and TAU, respectively.

• Modelling the weight KptShare(cs) explicitly, as: sum(i$mapcap(i,cs),i0(i)))

• Without the equal yield constraint, the model successfully converges towards the steady-state after the implementation of a wide range of taxes (and also with almost prohibitively high

tax rates).

• Removing the sector-specific capital and tested the equal yield constraint likewise leads to erratic labor tax movements

All of this was unfortunately to no avail and I would be delighted if someone could be of any help, in case you have run into similar problems before. If you need any additional information, please let me know. Many thanks!

Best regards,

Michel