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Sub-regional dis-aggregation of production and factor markets in CGEBox

Background and motivation

Especially question around use of immobile natural resources such as land, minerals or water often ask for an analysis at regional level, especially if environmental consequences are to evaluated and externalities have a regional character. It is therefore not uncommon to find sub-regional detail in CGE work at single country level. We present in here a rather simplistic approach to add such detail to the CGE modelling framework.


We implement a rather basic dis-aggregation as a starting point for further work:

  1. Outputs are assumed homogenous at national level and no intra-national trade margins are introduced. Consequently, there is one uniform output price faced by all regions in the same nation.

  2. Commodity demand is accordingly modeled at national level.

  3. Factor markets however are depicted by a CET structure which hence allows for sluggish or even no factor mobility across regions.

  4. The tax system is not regionally differentiated.

As a consequence, the data requirements are relatively low, basically, data on output quantities and cost shares net of taxes are required for the framework.

Integration into the modeling framework

There were limited changes necessary to introduce regional detail for the supply side into the model and there were mostly realized via macros. In order to introduce the uniform output prices in the framework the following macro is used:

Where the cross-set r_r(r,rp) depict the relation between sub-region r and nation rp. In case of countries without regional detail, the cross-set depicts a diagonal relation, i.e. r_r(rNat,rNat) = yes.

In order to avoid problems with a simply linear aggregation from regions to nations, a CES-aggregator is used in the code:

Where omegasi and omegasa either aggregate product or activities from region to nation, both set to 10. That means that the national composition of output from the regions can change rather flexibly.

There are various equations which ensure that firm demand is aggregated over regions to country level, while it is assumed that all regions face the same prices for intermediate inputs. Factor prices clearly differ reflecting the assumption with regard to factor mobility across regions and sectors.

In order to ease reading the code and speeding up execution, the set disr depicts those nations which feature regional detail while the set subr depicts sub-regions. A second equation adds up intermediate input use in each region and sector to national level:

An additional equation was added which distributes the total national factor xft(disr) to the regional factor xft(subr):

Clearly, if the transformation elasticity across regions omegafr is set to zero, the regional factor stock is fixed. The last line in the equation depicts the case of inifinite transformation which leads to uniform prices. A matching dual price aggregator defines the price for mobile factors at national level:

Not that the last line provides the physical linear aggregation in case that the transformation elasticity is infinite.

In order to avoid that the tax income equation are changed to aggregate over sub-regions, factor use for each activities and matching prices are defined in two additional equations:

The code was updated at various places if $ rNat conditions to avoid that data transformation for sub-regional data are executed which do not relate to production or factor markets. During variable initialization and calibration, it is assumed that the regional data on intermediate input and primary factor use match the national totals (see next section for an implementation). Factor, production and immediate taxes rates are taken from the national SAMs.

The intermediate taxes are implicitly taken over by using the relation between the national Armington intermediate demands and the national SAM entries net of taxes:

There were otherwise very limited changes to the calibration code.

Implementation for European countries at NUTS2 level

The NUTS (Nomenclature des unités territoriales statistiques) system provides a classification of administrative units for the European Union and some further regions. After NUTS0 (= nation) and NUTS1 (=federal state or similar), NUTS2 provides already relatively small regional units for economy wide assessment and beyond. In the context of the EU funded research project CAPRI-RD (, regional SAMs at NUTS2 level and matching national ones for the EU member and candidates countries were compiled (Ferrari et al. 2012). The SAMs feature somewhat limited sector detail (Agriculture, Forestry, Other primary, Food processing, Other Manufacturing, Energy, Construction, Trade and transport, Hotels and restaurants, Education, Other Services) which reflects both data availability and the aim to model rural development policies under the Common Agricultural Policy (CAP). A specific feature of the SAMs is a dis-aggregation of intermediate demand to regional, national and imported origin. A matching single country CGE was developed (Törmä et al. 2010. 2010, Britz 2012) with a rather detailed driver to map individual rural development measures from the CAP into shocks for the model and an interface to the regional supply models and the market model of the partial equilibrium CAPRI modeling system. So far, the application of that model is rather limited (Schröder et al. 2015, Britz et al. 2015). We use here only the production data of these regionals SAMs which also breaks down demand to the regional level and provides also details on the national and regional government accounts.

The introduction of the list of sub-regions into the static set r (= all regions) which is used as the domain for various variables, equations and parameters requires that the list is available when the data from GTAPAGG are read. Accordingly, the data set program is partly read rather early in the program sequence:

To load the following list with the NUTS2 regions:

The actual data processing consists of the following steps:

  1. Defining the regional hierarchy. Currently, the program only introduces sub-regions if the related country is a separate region in the GTAPAGG data set:

From there, the regional hierarchy is defined:

And the list of regions which are dis-aggregated:

  1. As the regional SAMs will typically feature a differently detail sector list compared to what is used elsewhere in the model, a mapping and consistency check is required. First, the link between the original 57 GTAP sectors and the sectors in the regional SAMs is set-up:

First, SAM entries for intermediate input use are set up which assign the (sum of the) original regional SAM to the new commodities and sectors:

Next, a correction factor is defined and applied which ensures that the regional entries match the national ones:

The program is not fully shown here, it also removes tiny regional entries. Finally, the behavioral parameters are defined:


  1. The substitution elasticities at national level are also used for the regions, and

  2. Land cannot move between regions, capital is assumed as fully mobile and labor as sluggish. Note that natural resources are immobile at sector level.

Result exploitation

So far, there is only one specific view which uses a map with regional detail:


Britz W. (2012) WP3.2 Model development and adaptation – Regional CGEs Additional Deliverable: D3.2.4 RegCgeEU+ in GAMS, documentation including the Graphical User Interface, CAPRI-RD deliverable D3.2.4,

Britz, W., Dudu, H., Ferrari, E. (2015): Economy-wide Impacts of Food Waste Reduction: A General Equilibrium Approach, selected paper presented at the International Conference of Agricultural Economists (ICAE 2015), 8-14 August 2015, Milan (Italy).

Ferrari, E., Himics, M. and Mueller M. (2010): WP2.2 Databases – Regional Social Accounting Matrices Deliverable: D2.2.4, Procedure for the compilation of regional SAMs based on national SAMs and available regional datasets: dataset and documentation; CAPRI-RD deliverable D2.2.4,

Schroeder, L. A., Gocht, A., Britz, W. (2015): The Impact of Pillar II Funding: Validation from a Modelling and Evaluation Perspective, Journal of Agricultural Economics 66(2): 415–441

Törmä, H., Zawalinska, K., Blanco-Fonseco M., Ferrari, E., Jansspon T. (2010): WP3.2 Model development and adaptation – Regional CGEs Deliverable: D3.2.1 Regional CGE model layout with a focus on integration with the partial equilibrium models and modelling of RD measures; CAPRI-RD deliverable D3.2.1,