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  Fiscal policy

$$ \newcommand{\tsum}{\textstyle\sum} \newcommand{\extern}[1]{\mathrm{\mathbf{{#1}}}} \newcommand{\local}{\mathrm{local}} \newcommand{\roc}[1]{\overset{\scriptsize\Delta}{#1{}}} \newcommand{\ss}{\mathrm{ss}} \newcommand{\aa}{\mathrm{aa}} \newcommand{\bb}{\mathrm{bb}} \newcommand{\E}{\mathrm{E}} \newcommand{\ref}{{\mathrm{ref}}} \newcommand{\blog}{\mathbf{log}\ } \newcommand{\bmax}{\mathbf{max}\ } \newcommand{\bDelta}{\mathbf{\Delta}} \newcommand{\bPi}{\mathbf{\Pi}} \newcommand{\bU}{\mathbf{U}} \newcommand{\newl}{\\[8pt]} \newcommand{\betak}{\mathit{zk}} \newcommand{\betay}{\mathit{zy}} \newcommand{\gg}{\mathrm{gg}} \newcommand{\tsum}{\textstyle{\sum}} \newcommand{\xnf}{\mathit{nf}} \newcommand{\ratio}[2]{\Bigl[\textstyle{\frac{#1}{#2}}\Bigr]} \newcommand{\unc}{\mathrm{unc}} \notag $$

The government controls the following fiscal policy quantities

  • Government debt placed in local currency, \(dg_t\)

  • Government consumption, \(cg_t\)

  • Two types of lump-sum taxes, \(tx1_t\) and \(tx2_t\)

  • Import tariffs, \(txm_t\)

Household behavior (utility function) modified to induce

  • Fiscal crowding-in in the short run

  • Fiscal crowding-out in the long run

\[ \newcommand{\xnetf}{\mathit{netf}} \newcommand{\xnetfg}{\mathit{netfg}} \newcommand{\xdg}{\mathit{dg}} \newcommand{\xrg}{\mathit{rg}} \]

Dynamic fiscal budget

Government debt issued in local-currency, \(\xdg_t\)

\[ \begin{aligned} \xdg_t &= \xdg_{t-1} & \text{Rollover} \\[10pt] &+\ (\xrg_{t-1}-1) \ \xdg_{t-1} &\text{Interest} \\[10pt] &-\ tx1_t - tx2_t - txm_t &\text{Receipts} \\[10pt] &+\ pc_t \cdot cg_t &\text{Outlays} \\[10pt] \end{aligned} \]

Government expenditures on goods and services

Real government consumption, \(cg_t\)

\[ \begin{aligned} \log cg_t &= \rho_{cg} \cdot \log\left( cg_{t-1}\cdot \roc{cg}_\ss \right) &\text{Autoregressive} \\[15pt] &+\ \left(1-\rho_{cg}\right) \, \log \Bigl( \ratio{ngdp}{pc}_t \cdot \ratio{ncg}{ngdp}_\ss \Bigr) &\text{Govt consumption target} \\[15pt] &+\ \tau_{cg} \, \left( \ratio{dg}{ngdp}_{t+1} - \ratio{dg}{ngdp}_\ss \right) &\text{Debt target} \\[15pt] &+\ \epsilon_{cg,t} &\text{Govt consumption shock} \end{aligned} \]

Government type 1 lump-sum taxes

Type 1 lump-sum taxes, \(\mathit{tx}1_t\)

\[ \begin{aligned} \ratio{tx1}{nch}_{t} &= \rho_{tx1} \ \ratio{tx1}{nch}_{t-1} &\text{Autoregressive}\\[15pt] &+\ \left(1-\rho_{tx1}\right)\, \ratio{tx1}{nch}_\ss &\text{Type 1 tax target} \\[15pt] &+\ \tau_{tx1} \ \left( \ratio{dg}{ngdp}_{t+1} - \ratio{dg}{ngdp}_\ss \right) &\text{Govt debt target} \\[15pt] &+\ \epsilon_{tx1,t} &\text{Type 1 tax shock} \end{aligned} \]

Government type 2 lump-sum taxes

Type 2 lump-sum taxes, \(\mathit{tx}2_t\)

\[ \begin{aligned} \ratio{tx2}{nch}_{t} &= \rho_{tx2} \ \ratio{tx2}{nch}_{t-1} &\text{Autoregressive}\\[15pt] &+\ \left(1-\rho_{tx2}\right)\, \ratio{tx2}{nch}_\ss &\text{Type 2 tax target} \\[15pt] &+\ \epsilon_{tx2,t} &\text{Type 2 tax shock} \end{aligned} \]

Import tariffs

Import tariff rate, \(trm_t\)

\[ \begin{aligned} trm_t &= \rho_{trm} \ trm_{t-1} &\text{Autoregressive}\\[15pt] &+\ \left(1-\rho_{trm}\right)\, trm_\ss &\text{Tariff target} \\[15pt] &+\ \epsilon_{trm,t} &\text{Tariff shock} \end{aligned} \]

GEES Fiscal policy module

Define quantities

!variables

    "Government debt interest rate" rg
    "Government consumption" cg
    "Government debt to GDP ratio" dg_to_ngdp
    "Net lump-sum tax 1 to consumption ratio" txls1_to_nc
    "Net lump-sum tax 2 to consumption ratio" txls2_to_nc
    "Government consumption, Y/Y" roc_cg
    "Import tariff rate" trm


!log-variables !all-but

    txls1_to_nc, txls2_to_nc, dg_to_ngdp, trm


!parameters(:fiscal :steady)

    "S/S Government debt to GDP ratio !! $\tratio{\mathit{dg}}{\mathit{ngdp}}_\ss$" ss_dg_to_ngdp
    "S/S Government consumption to GDP ratio !! $\tratio{\mathit{ncg}}{\mathit{ngdp}}_\ss$" ss_ncg_to_ngdp
    "S/S General import tariff rate !! $\mathit{trm}_\ss$" ss_trm


!parameters(:fiscal :dynamic)

    "Response in government consumption to government debt !! $\tau_\mathit{cg}$" tau_cg
    "Response in type 1 lump-sum tax rate to government debt !! $\tau_{\mathit{txls},1}$" tau_txls1
    "Autoregression in government consumption !! $\rho_\mathit{cg}$" rho_cg
    "Autoregression in type 1 lump-sum tax rate !! $\rho_{\mathit{txls},1}$" rho_txls1
    "Autoregression in type 2 lump-sum tax rate !! $\rho_{\mathit{txls},2}$" rho_txls2
    "Autoregression in generate import tariff rate !! $\rho_\mathit{trm}$" rho_trm


!shocks

    "Shock to government consumption" shk_cg
    "Shock to type 1 lump-sum taxes" shk_txls1
    "Shock to type 2 lump-sum taxes" shk_txls2
    "Shock to general import tariff rate" shk_trm

Define equations

!equations

    rg = r;

    "Dynamic fiscal budget constraint"
    dg_to_ngdp*ngdp = ...
        + rg{-1}*dg_to_ngdp{-1}*ngdp{-1} ...
        + pc*cg ...
        - (txls1_to_nc + txls2_to_nc) * pc*ch ...
        - (pmm - fob_pmm) * mm;


    "Fiscal reaction function for government consumption"
    log(cg) = ...
        + rho_cg * log(cg{-1}*&roc_cg) ...
        + (1 - rho_cg) * log(ss_ncg_to_ngdp*ngdp/pc) ...
        - tau_cg * (dg_to_ngdp{+1} - ss_dg_to_ngdp) ...
        + shk_cg ...
    !! pc*cg = ss_ncg_to_ngdp*ngdp;


    "Fiscal reaction function for type 1 net lump-sum taxes"
    txls1_to_nc = ...
        + rho_txls1 * txls1_to_nc{-1} ...
        + (1-rho_txls1) * &txls1_to_nc ...
        + tau_txls1 * (dg_to_ngdp{+1} - ss_dg_to_ngdp) ...
        + shk_txls1 ...
    !! dg_to_ngdp = ss_dg_to_ngdp;


    "Fiscal reaction function for type 2 net lump-sum taxes"
    txls2_to_nc = ...
        + rho_txls2*txls2_to_nc{-1} ...
        + shk_txls2 ...
    !! txls2_to_nc = 0;


    "Fiscal reaction function for import tariffs rate"
    trm = ...
        + rho_trm * trm{-1} ...
        + (1 - rho_trm) * ss_trm ...
        + shk_trm ...
    !! trm = ss_trm;