Trade linkages

  Algebra  Model source code

Assembly of non-commodity imports

Production function

\[ mm_t = F(mm_t^1,\ \dots,\ mm_t^A) \]

Demand for imports, ignoring adjustment costs

\[ \frac{mm_t^k}{mm_t}\ \propto\ \left( \frac{\frac{e_t}{e_t^k} \ pxx_t^k}{pmm_t} \right)^{-1} \]

Import tariffs

Demand for imports with tariffs

\[ \frac{mm_t^k}{mm_t}\ \propto\ \left[ \frac{pmm_t^{\mathrm{fob}, k}\ (1 + trm_t + trm_t^k) }{pmm_t} \right]^{-1} \]

Import price FOB destination

\[ pmm_t^{\mathrm{fob}, k} = \frac{e_t}{e_t^k} \ pxx_t^k \]

Import price including tariffs

\[ pmm_t^{k} = \frac{e_t}{e_t^k} \ pxx_t^k \ (1 + trm_t + trm_t^k) \]

Import price indicators

Price	Where placed in the model
\(pmm_t^{\mathrm{fob}, k}\)	Balance of payments
\(pmm_t^{k}\)	Input price facing local agents
\(pmm_t^k - pmm_t^{\mathrm{fob}, k}\)	Government revenues

GEES International trade linkages module

Declare quantities

!variables
    !for ?M=<areas> !do
        !for ?X=<setdiff(areas, "?M")> !do
            "Share of real imports from [?X] in total real imports to [?]"
            ?M_mm_sh_?X
        !end
    !end


!log-variables !all-but

    !for ?M=<areas> !do
        !for ?X=<setdiff(areas, "?M")> !do
            ?M_mm_sh_?X
            ?M_trm_?X
        !end
    !end


!parameters

    !for ?M=<areas> !do
        "Point of origination import adjustment costs !! $\xi_\mathit{mm}$"
        ?M_xi_mm

        !for ?X=<setdiff(areas, "?M")> !do
            "Share of nominal imports from [?X] in total [?M] nominal imports !! $\omega_\mathrm{?X}$"
            ?M_omega_?X
        !end
    !end

Define equations

!equations

    !for ?X=<areas> !do
        "Distribution of exports across areas"
        ?X_xx = !for ?M=<setdiff(areas, "?X")> !do + ?M_mm * ?M_mm_sh_?X !end ;
    !end


    !for ?M=<areas> !do
        "Assembly of total non-commodity imports"
        1 = 1 !for ?X=<setdiff(areas, "?M")> !do * (?M_mm_sh_?X / ?M_omega_?X)^?M_omega_?X !end;
        % 1 = 1 !for ?X=<areas> !do * ?M_mm_sh_?X^?M_omega_?X !end;

        !for ?X=<setdiff(areas, "?M")> !do
            "Demand for imports from [?X] in total [?M] non-commodity imports"
            ?M_omega_?X * ?M_pmm = ...
                (?M_e / ?X_e) * ?X_pxx * (1 + ?M_trm + ?M_trm_?X) * ?M_mm_sh_?X ...
                * [1 + ?M_xi_mm*(log(?M_mm_sh_?X)-log(?M_mm_sh_?X{-1})) - ?M_rdf*(log(?M_mm_sh_?X{+1})-log(?M_mm_sh_?X))] ...
            !! ?M_omega_?X * ?M_pmm = (?M_e / ?X_e) * ?X_pxx * (1 + ?M_trm + ?M_trm_?X) * ?M_mm_sh_?X;
        !end
        ?M_fob_pmm = !for ?X=<setdiff(areas, "?M")> !do + (?M_e / ?X_e) * ?X_pxx * ?M_mm_sh_?X !end; 
    !end



%% Tariffs 

!for ?M=<areas> !do
    !for ?X=<setdiff(areas, "?M")> !do
        !variables
            "Area specific import tariff rate" ?M_trm_?X

        !shocks
            "Shock to area specific import tariff rate" ?M_shk_trm_?X

        !parameters(:trade :steady)
            "S/S Area specific import tariff rate !! $\mathit{trm}_{\mathrm{?X},\ss}$" ?M_ss_trm_?X

        !parameters(:trade :dynamic)
            "A/E Area specific import tariff rate !! $\rho_{trm,\mathrm{?X}}$" ?M_rho_trm_?X

        !equations
            ?M_trm_?X ...
                = ?M_rho_trm_?X * ?M_trm_?X{-1} ...
                + (1 - ?M_rho_trm_?X) * ?M_ss_trm_?X ...
                + ?M_shk_trm_?X ...
            !! ?M_trm_?X = ?M_ss_trm_?X;
    !end
!end

Postprocessing equations outside model

!postprocessor

    !for ?M=<areas> !do
        !for ?X=<setdiff(areas, "?M")> !do
            "Imports from [?X] to [?M]"
            ?M_mm_?X = ?M_mm_sh_?X * ?M_mm;
        !end
    !end


!log-variables !all-but