This section describes the structure of the functional forms used in the Berau District static CGE model, see shown by Figure 4.2. Terms σ and η denote the elasticity of substitution of production function and the elasticity of
transformation respectively.
Source: Rutherford and Light, 2001 (see http://www.mpsge.org/dnp2001.pdf) Figure 4.2 General structure of the static model
Production function
In this model, every sector is assumed to act as a single representative producer whose production possibilities are characterised by multi-level production function. The production function follows a standard specification used in CGE models. Consider the Figure 4.2, a producing sector Y which produces output of commodities i. At the top level, to produce the commodities, each sector requires Armington aggregate intermediate inputs and aggregate primary inputs which are
C, G, I
RA, Gov.
Ai:
R ; Land V : Aggregate Primary Inputs
K:
Capital
L: Labour σ = CES/CD
Yi: Output
σ =0=Leontief
Ei : Exported
η = CET D: Domestic
goods Mi: Imported
goods
Ai: Armington products
Aj
Armington
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combined through a Leontief production function. The combination can be described in an algebraic form as:
At the second level, the primary inputs (value-added) of capital, labours and land are aggregated through a constant elasticity of substitution function (CES) specification, as follows. Note that this follows a specification available in the CGE models for Indonesia, see for example the works of Robinson et al. (1997), San et al. (2000) and Warr and Yusuf (2011)(Warr & Yusuf, 2011):
exported and locally produced goods (Armington goods) which are aggregated in a fixed proportion.
Factors of production
Embedded into the production function are factors of production whose mobility is an important feature of a general equilibrium system. Mobility is defined as the capacity of factors of production to be reallocated across economic activities (producing sectors) in response to changes in rates of return. The greater the mobility that is chosen for factors of production, the greater is the economy‘s capacity to respond to changes in the economy. Assumption of the degree of
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mobility should be consistent with the length of run that the problem/model is being analysed (Warr & Yusuf, 2011).
In the Berau District CGE model, all factors of production are assumed to be in a fixed supply. Labours is divided into agricultural and non-agricultural labour.
Each category is further detailed into paid worker and non-paid worker types.
Such classification is based on the Indonesian Labour Force Survey classification and the specification of labour in the Forestry Social Accounting Matrix of the Kutai Timur District (Pusat Rencana Kehutanan Departemen Kehutanan &
Direktorat Neraca Konsumsi Badan Pusat Statistik, 2001). While the paid worker type is interpreted as the labour that receives a formal wage and salary, the non-paid worker does not receive a formal wage. During the construction of the Berau District Social Accounting Matrix dataset, the non-paid worker is paid ‗an imputed wage‘, whose total value for every producing activity is excluded from
‗the operating surplus‘ category in the input-output table (Warr & Yusuf, 2011;
Yusuf, 2006). Also, the land factor of agricultural activity is further estimated using information on the net capital/land ratio of Kalimantan Island as depicted in the 2005 Indonesia Inter Regional Input Output Table28. Following Warr and Yusuf (2011), all labour categories are assumed to be less mobile across all sectors, while capital is assumed to be immobile. This reflects the short-medium run of the analysis.
Meanwhile, with regard to land factors specification in the Berau District CGE model, the specification of Warr & Yusuf (2011) was adopted. Land is assumed to non-homogenous and less-than perfectly mobile across sectors. For this purpose, an elasticity of land transformation of 0.5 is used. A transformation function representing how land is supplied into several agricultural activities is included in the model, as below.
28 The 2005 Indonesia Inter Regional Input Output Table was provided by Mr. Daniel Pambudi (MONASH) and Budy Resosudarmo (ANU).
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Where:
Nag
: benchmark value share of land used in agricultural sector out of total land used in all production (N),
Nag
1 : benchmark value share of land used in logging sector out of total land used in all production (N), and
ο is the elasticity of transformation for land.
According to Warr and Yusuf (2011), despite its uncertainty, elasticity of transformation between land use between forestry and crop production is 0.5.
Furthermore, within the land use for the crop production, the elasticity of transformation of land use between the crops is 0.75. In the Berau CGE model, it is simplified that the elasticity of land transformation in all agricultural activities is assumed 0.5, close to the parameter used in Warr and Yusuf (2011)).
Production output
Every sector‘s output Yi can be marketed locally as final and intermediate consumption (as domestic goods Di) and exported (Ei). The commodities are assumed to be imperfect substitutes and have a constant of elasticity of transformation η. An algebraic formulation of this transformation function is as follow:
11/ (1 ) 11/
1/(11/ ))
(
i i iD i iD i
i g DE D E
Y
Where δi D is the benchmark value share of output marketed domestically out of the total production for sector i and η represents to the elasticity of transformation.
The Berau District CGE Model has twenty three activities producing twenty three commodities. That is, there is one-to-one mapping between activities and commodities. The distribution of the sectors/activities and commodities can be seen in Table 6.6 of Chapter 6 and Appendix 6.2.
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Imports
The model includes an Armington representation of import demand. The Armington commodities Ai, are composite of domestic outputs and imports. The domestic and imported components of the same commodities are assumed to be imperfect substitutes and the choice between utilising these goods is assumed to be governed by a constant elasticity of substitution (CES) or the Armington elasticity. This is represented by an algebraic equation:
11/ (1 ) 11/ )111/
(
iD i iD i
ji D M
A
The Armington products are used for both final consumption that is, for private consumption, government consumption, and investment as well as for intermediate inputs in the production activities.
Final Consumption of Households, Government and Investor
Representative agents of household and government own endowment factors of primary inputs such as capital (K), labours (L), and (R) lands. The representative agents also demand investment (through saving) and consumptions (private and public goods for households and government respectively). In the regional CGE model, these institutions may both receive and transfer funds from rest of world‘s institutions, as well as exchange funds between the same institutions (trn).
All domestic demands (private and government consumption and investment demand and intermediate demand) require Armington products of imported and locally commodities. The domestic demand is determined by the assumption that the domestic consumers minimise cost subject to imperfect substitutability, captured by an Armington CES aggregation function.
Consumption by households is represented by a Cobb-Douglas utility function.
That is, the demand function is derived from utility function subject to budget constraint:
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) nettrn : net transfers between households and other institutions Ira : saving/investment of households.
Following the household specification of Pusat Rencana Kehutanan Departemen Kehutanan or Centre for Forestry Planning, the Indonesian Ministry of Forestry (2001), the Berau District CGE model features a simplified households grouping consisting of forestry households, other-agricultural households, and non-agricultural households, and other households type. Each group except the other household type is further divided into two types i.e. worker and self-employee household types. For example, the forestry household worker implies either head of the household‘s occupation is as worker at the forestry sector or the household‘s main income is derived from working at the sector. Thus, other types of households are interpreted in a similar fashion. Finally, the other household type is not detailed further.
Government
The government earns revenues from household and enterprise direct taxes, indirect taxes i.e. sales tax for the Armington commodities, capital rents and transfers from Rest of World (e.g. for the Berau District, it receives transfers from
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central government as well as transfers to RoW). The government uses revenues to purchase goods and services for consumption and investment. It is assumed that the government demands a fixed proportion of commodities29:
is the government‘s consumption, taxes government revenue from taxes, nettrn denotes for (net) transfers, and Igov denotes for government savings.
Investment Demand
Regional investment equals to regional saving and is financed by aggregate regional savings. The regional savings is derived from households saving, enterprise saving, government savings and foreign saving. The saving is used to purchase goods and services by maximise the investment demand through a fixed proportion aggregation of goods and services.
Macroeconomic closure
In addition to factors and commodity market clearings, there are three types of macroeconomic closure or constraints in the standard CGE model. They are foreign exchange balance, government balance and saving investment balance constraints (Lofgren et al., 2002).
In the Berau CGE model, the district is assumed to be a small open economy where imports and exports prices (p ,iE piM) are determined exogenously. The Berau CGE is a single region CGE model and has the same currency with the rest of the world (ROW). For this model, the initial exchange rate is set as unity (Burfisher, 2011). The exchange rate actually determines a real exchange rate,
29 Modified from An Emipirical Model. Markusen, J., Rutherford, T., & Light, M. (2004) in MPSGE: A user‘s Guide. 2004. . Markusen, J., and Rutherford, T. (2004). University of Colorado.
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which is the relative price of traded to non-traded goods. Note that the traded goods are products that are exported and imported; while the non-traded goods are commodities that are produced and sold in the domestic markets (Burfisher, 2011).
For the government balance condition, the model assumes that the (local) government uses the fixed direct tax rate (for all period) and the government saving is a residual after their earning is used for consumption. It is assumed that the government consumption is fixed (later in a dynamic model, the government consumption is assumed to grow at a fix rate). The government in the SAM Table is assumed to be only the local government of the Berau District; relationship with central government implicitly occurs within transfers with the rest of the world (ROW).
Finally, for the investment-saving closure, the regional investment adjusts to the level of regional savings (savings driven), where the regional savings is financed by private savings, government savings and foreign savings. In addition, these specifications follow those of existing CGE models for Indonesia such as in Dee (1991) and Warr and Yusuf (2011).