Macro-Economic Growth Module (01_macro)

Description

The macro module allows for the implementation of different macro-economic modules.

Interfaces

Input

Output

Realizations

(A) singleSectorGr

The singleSectorGr realization corresponds to a neo-classical, single sector growth model.

The singleSectorGr realization corresponds to a neo-classical, single sector growth model.

Usable macroeconomic output - net of climate change damages - is calculated from the macroeconomic output, taking into account export and import of the final good, taking specific trade costs into account, which are assigned to the importer. The resulting output is used for consumption, for investments into the capital stock, and for the energy system cost components investments, fuel costs and operation & maintenance. Other additional costs like non-energy related greenhouse gas abatement costs and agricultural costs, which are delivered by the land use model MAgPIE, are deduced from disposable output. Net tax revenues and adjustment costs converge to zero in the optimal solution (equilibrium point).

\[\begin{multline*} vm\_cesIO(ttot,regi,"inco") \cdot vm\_damageFactor(ttot,regi) - vm\_Xport(ttot,regi,"good") + vm\_Mport(ttot,regi,"good") \cdot \left(1 - pm\_tradecostgood(regi) - pm\_risk\_premium(regi)\right) \geq vm\_cons(ttot,regi) + \sum_{ppfKap(in)} vm\_invMacro(ttot,regi,in) + \sum_{ppfKap(in)} v01\_invMacroAdj(ttot,regi,in) + \sum_{in} vm\_invRD(ttot,regi,in) + \sum_{in} vm\_invInno(ttot,regi,in) + \sum_{in} vm\_invImi(ttot,regi,in) + \sum_{tradePe(enty)\$\left(NOT tradeCap(enty)\right)}\left( pm\_costsTradePeFinancial(regi,"Mport",enty) \cdot vm\_Mport(ttot,regi,enty)\right) + \sum_{tradePe(enty)\$\left(NOT tradeCap(enty)\right)}\left( \left(pm\_costsTradePeFinancial(regi,"Xport",enty) \cdot vm\_Xport(ttot,regi,enty)\right) \cdot \left( 1 + \left(\frac{ pm\_costsTradePeFinancial(regi,"XportElasticity",enty) }{ sqr\left(pm\_ttot\_val(ttot)-pm\_ttot\_val(ttot-1)\right) } \cdot \left(\frac{ vm\_Xport(ttot,regi,enty) }{ \left( vm\_Xport(ttot-1,regi,enty) + pm\_costsTradePeFinancial\left(regi, "tradeFloor",enty\right) \right) }- 1 \right) \right)\$\left( ttot.val ge max\left(2010, cm\_startyear\right) \right) \right) \right) + \sum_{tradeSe}\left( pm\_MPortsPrice(ttot,regi,tradeSe) \cdot vm\_Mport(ttot,regi,tradeSe)\right) - \sum_{tradeSe}\left( pm\_XPortsPrice(ttot,regi,tradeSe) \cdot vm\_Xport(ttot,regi,tradeSe)\right) + \sum_{tradeCap} vm\_costTradeCap(ttot,regi,tradeCap) + vm\_taxrev(ttot,regi)\$\left(ttot.val ge 2010\right) + vm\_costAdjNash(ttot,regi) + \sum_{in\_enerSerAdj(in)} vm\_enerSerAdj(ttot,regi,in) + \sum_{teEs} vm\_esCapInv(ttot,regi,teEs) + vm\_costpollution(ttot,regi) + pm\_totLUcosts(ttot,regi) + \sum_{enty\$\left(emiMacSector(enty) \& \left(NOT emiMacMagpie(enty)\right)\right)} pm\_macCost(ttot,regi,enty) + vm\_costEnergySys(ttot,regi) \end{multline*}\]

The labor available in every time step and every region comes from exogenous data. It is the population corrected by the population age structure, which results in the labour force of people agged 15 to 65. The labor participation rate is not factored into the labour supply (as it would only imply a rescaling of parameters without consequences for the model’s dynamic). The labour market balance equation reads as follows:

\[\begin{multline*} vm\_cesIO(t,regi,"lab") = pm\_lab(t,regi) \end{multline*}\]

The production function is a nested CES (constant elasticity of substitution) production function. The macroeconomic output is generated by the inputs capital, labor, and total final energy (as a macro-ecoomic aggregate in $US units). The generation of total final energy is described by a CES production function as well, whose input factors are CES function outputs again. Hence, the outputs of CES nests are intermediates measured in $US units. According to the Euler-equation the value of the intermediate equals the sum of expenditures for the inputs. Sector-specific final energy types represent the bottom end of the `CES-tree’. These ‘CES leaves’ are measured in physical units and have a price in $US per physical unit. The top of the tree is the total economic output measured in $US. The following equation is the generic form of the production function. It treats the various CES nests separately and the nests are inter-connetected via mappings. This equation calculates the amount of intermediate output in a time-step and region from the associated factor input amounts according to:

\[\begin{multline*} vm\_cesIO(t,regi,out) = \sum_{cesOut2cesIn(out,in)}\left( pm\_cesdata(t,regi,in,"xi") \cdot \left( pm\_cesdata(t,regi,in,"eff") \cdot vm\_effGr(t,regi,in) \cdot vm\_damageProdFactor(t,regi,in) \cdot vm\_cesIO(t,regi,in) \right) ^{ pm\_cesdata(t,regi,out,"rho") }\right) ^{ \left(\frac{1 }{ pm\_cesdata(t,regi,out,"rho")}\right) } \end{multline*}\]

Constraints for perfect complements in the CES tree

\[\begin{multline*} vm\_cesIO(t,regi,in) = pm\_cesdata(t,regi,in2,"compl\_coef") \cdot vm\_cesIO(t,regi,in2) \end{multline*}\]

The capital stock is claculated recursively. Its amount in the previous time step is devaluated by an annual depreciation factor and enlarged by investments. Both depreciation and investments are expressed as annual values, so the time step length is taken into account.

q01_kapMo(ttot,regi,ppfKap(in))$( ( NOT in_putty(in)) AND (ord(ttot) lt card(ttot)) AND (pm_ttot_val(ttot+1) ge max(2010, cm_startyear)) AND (pm_cesdata("2005",regi,in,"quantity") gt 0))..
    vm_cesIO(ttot+1,regi,in)
  =e=
    (1- pm_delta_kap(regi,in))**(pm_ttot_val(ttot+1)-pm_ttot_val(ttot)) * vm_cesIO(ttot,regi,in)
$ifthen setGlobal END2110
  + pm_ts(ttot)*vm_invMacro(ttot,regi,in)*0.94**5 - (0.5*pm_ts(ttot)*vm_invMacro(ttot,regi,in)*0.94**5)$(ord(ttot) eq card(ttot));

Adjustment costs of macro economic investments:

\[\begin{multline*} v01\_invMacroAdj(ttot,regi,in) = sqr\left(\frac{\frac{ \left(vm\_invMacro(ttot,regi,in)-vm\_invMacro(ttot-1,regi,in)\right) }{ \left(pm\_ttot\_val(ttot)-pm\_ttot\_val(ttot-1)\right) }}{ \left(vm\_invMacro(ttot,regi,in)+0.0001\right) }\right) \cdot \frac{ vm\_cesIO(ttot,regi,in) }{ 11 } \end{multline*}\]

Initial conditions for capital:

\[\begin{multline*} vm\_cesIO(t,regi,in) = pm\_cesdata(t,regi,in,"quantity") \end{multline*}\]

Limit the share of one ppfEn in total CES nest inputs:

\[\begin{multline*} vm\_cesIO(t,regi,in) + pm\_cesdata(t,regi,in,"offset\_quantity") \leq pm\_ppfen\_shares(t,regi,out,in) \cdot \left(\sum\left(cesOut2cesIn(out,in2), vm\_cesIO(t,regi,in2) + pm\_cesdata(t,regi,in2,"offset\_quantity")\right)\right) \end{multline*}\]

Limit the ratio of two ppfEn:

\[\begin{multline*} vm\_cesIO(t,regi,in) + pm\_cesdata(t,regi,in,"offset\_quantity") \leq p01\_ppfen\_ratios(t,regi,in,in2) \cdot \left(vm\_cesIO(t,regi,in2) + pm\_cesdata(t,regi,in,"offset\_quantity")\right) \end{multline*}\]

Putty-Clay production function:

\[\begin{multline*} vm\_cesIOdelta(t,regi,out) = \sum_{cesOut2cesIn(out,in)}\left( pm\_cesdata(t,regi,in,"xi") \cdot \left( pm\_cesdata(t,regi,in,"eff") \cdot vm\_effGr(t,regi,in) \cdot vm\_cesIOdelta(t,regi,in) \right) ^{ pm\_cesdata(t,regi,out,"rho") }\right) ^{ \left(\frac{1 }{ pm\_cesdata(t,regi,out,"rho")}\right) } \end{multline*}\]

Putty-Clay constraints for perfect complements in the CES tree:

\[\begin{multline*} vm\_cesIOdelta(t,regi,in) = pm\_cesdata(t,regi,in2,"compl\_coef") \cdot vm\_cesIOdelta(t,regi,in2) \end{multline*}\]

Correspondance between vm_cesIO and vm_cesIOdelta:

\[\begin{multline*} vm\_cesIO(ttot+1,regi,in) = vm\_cesIO(ttot,regi,in) \cdot \left(1- pm\_delta\_kap(regi,in)\right)^{\left(pm\_ttot\_val(ttot+1)-pm\_ttot\_val(ttot)\right) }+ pm\_cumDeprecFactor\_old(ttot+1,regi,in) \cdot vm\_cesIOdelta(ttot,regi,in) + pm\_cumDeprecFactor\_new(ttot+1,regi,in) \cdot vm\_cesIOdelta(ttot+1,regi,in) \end{multline*}\]

Capital motion equation for putty clay capital:

q01_kapMo_putty(ttot,regi,in_putty(in))$(ppfKap(in) AND (ord(ttot) le card(ttot)) AND (pm_ttot_val(ttot) ge max(2005, cm_startyear)) AND (pm_cesdata("2005",regi,in,"quantity") gt 0))..
    vm_cesIOdelta(ttot,regi,in)
    =e=
             0
$ifthen setGlobal END2110
                  + pm_ts(ttot)*vm_invMacro(ttot,regi,in)*0.94**5 - (0.5*pm_ts(ttot)*vm_invMacro(ttot,regi,in)*0.94**5)$(ord(ttot) eq card(ttot));

The singleSectorGr realization corresponds to a neo-classical, single sector growth model.

Limitations There are no known limitations.

Definitions

Objects

Sets

Authors

See Also

02_welfare, 11_aerosols, 20_growth, 21_tax, 22_subsidizeLearning, 23_capitalMarket, 24_trade, 26_agCosts, 29_CES_parameters, 32_power, 35_transport, 36_buildings, 37_industry, 45_carbonprice, 50_damages, 51_internalizeDamages, 80_optimization, core

References