ABTEILUNG ÖKONOMIE UND FINANZWIRTSCHAFT / DEPARTMENT OF ECONOMICS AND FINANCE
A Guide to ATCEM-E3:
A us T rian Computable Equilibrium Model for E nergy-E conomy-E nvironment interactions
Tamas Revesz, Corvinus University, Budapest, and Todor Balabanov, IHS, Vienna
This research was made possible by the financial support of the Austrian National Bank
September 2007
Table of Contents:
1 . I n t r o d u c t i o n ... 3
2 . 1 . T h e G e n e r a l E q u i l i b r i u m M o d e l l i n g A p p r o a c h ... 5
2 . 2 . M a i n C h a r a c t e r i s t i c s o f t h e ATCEM-E3 M o d e l ... 6
3 . O v e r v i e w o f t h e M o d e l ... 8
3.2. Descriptions of Selected Blocks and Features of the Model ... 10
3 . 2 . 1 . I m p o r t / E x p o r t V o l u m e s a n d P r i c e s ... 10
3 . 2 . 2 . P r o d u c t i o n T e c h n o l o g y ... 11
3 . 2 . 3 . P r o d u c t i o n D e c i s i o n s a n d R e l a t e d P r i c e s ... 12
3 . 2 . 4 . D e m a n d ... 15
3.2.5. Change i n Stocks ... 15
3.2.6. Private Consumption ... 15
3.2.7. Public Consumption ... 16
3.2.8. Investment... 16
3 . 3 . E n v i r o n m e n t ... 16
3.3.1. Emission Control Through Abatement ... 18
3.4 Balance (market clearing) Conditions ... 22
3.5. Income D i s t r i b u t i o n and Public Finance ... 22
4 . M o d e l ’ s I m p l e m e n t a t i o n ... 23
4.1. N o m e n c l a t u r e / D i m e n s i o n of the model ... 23
4.1.2. Agents and sectoral dimension ... 23
4.2. Model Output ... 24
5. Data base compilation for ATCEM-E3: sources and methods ... 24
5.1. Data sources ... 24
5.1.1. Data in industrial sector (or commodity group) break-down ... 24
5.1.2. Data in institutional sector break-down ... 25
5.2. Processing of the data ... 27
5.2.1. Computation of the Input-Output table ... 27
5.2.2. Construction of the input file of the model... 30
5.3. Construction of the SAM for ATCEM-E3... 35
5.4. Compilation of the electricity industry and emission related data of the model ... 38
5.4.1. Compilation of the electricity technologies related data of the model... 38
5.4.1. Compilation of the air pollution related data of the model... 39
6. Model Calibration and Use ... 40
6.1. Calibration of the data ... 41
6.2. Using the model... 42
6.3. Solution Algorithm ... 42
6.4. Description of model’s files and the order of their opening/run... 43
6.4.1. Data and Program files... 43
6.4.2. Running the model to reproduce the base year... 43
6.4.3. Simulations by the model ... 44
7. Validation of the model by Scenario building and analysis of the results... 45
7.1. Scenario building ... 45
7.2. Scenario assumptions for the 2000-2010 period: ... 45
7.3. Analysis of the results... 46
Main simulation results ... 47
References: ... 50
Glossary ... 51
ANNEX – Model’s Equations ... 53
1 . I n t r o d u c t i o n
This Guide describes the basic features and characteristics of ATCEM-E3 - Au sTr i a n Computable Equilibrium Model for Energy-Economy-Environment - interactions.
The ATCEM-E3 has been developed in cooperation between Prof. Ernö Zalai and Dr. Tamas Revesz from the Faculty of Mathematical Economics and Economic Analysis, Corvinus University, Budapest, and Dr. Todor Balabanov from the Institut für Höhere Studien (IHS), Vienna.
The model is to be applied for study of Austrian renewable energy options, trading with CO2
certificates and possibly as investigation tool for the impact of external shocks on the welfare.
The ATCEM-E3 model is a static computable general equilibrium model representing the Austrian economy through a Social Accounting Matrix (SAM) and is covering the interactions between the economy, the energy system and the environment.
The model computes simultaneously the competitive market equilibrium under Walra´s law and determines the optimum balance for energy demand/supply and emission/abatement.
The general features of the model are:
1. It is static in scope: it includes the domestic, EU and rest of the world (ROW) markets and represents the system at the appropriate level with respect to trade, the sub-system (energy, environment, economy) and the dynamic mechanisms of agent’s behaviour.
2. It formulates separately the supply or demand behaviour of the economic agents which are considered to optimise individually their objectives while market derived prices guarantee global equilibrium
3. It explicitly considers the market clearing mechanism and the related price formation in energy, environment and economy markets, i.e., prices are computed by the model as a result of supply and demand interactions at the market place and in addition to the perfect competition different market clearing mechanisms are allowed for
4. The model exhibits sufficient degree of disaggregation concerning sectors (25 economic sectors), structural features of energy/environment and policy instruments (e.g. taxation). The model formulates production technologies in an endogenous manner allowing for price-driven derivation of all intermediate consumption and the services from capital and labour. In the electricity sector, the choice of production factors can be based on explicit modelling of technologies. For the demand-side the model formulates consumer behaviour and distinguishes between durable (equipment) and consumable goods and services.
6. The model devises pollution permits for atmospheric pollutants and flexibility instruments allowing for a variety of options, including: allocation (grandfathering, auctioneering, etc.), user- defined bubbles for traders, various systems of exemptions, various systems for revenue recycling, etc.
The figure hereafter gives the basic scheme of the model
ATCEM-E3 - Social Accounting Matrix with 25 sectors
Producers Maximising Profits
Maximising Utility for varaible part of
consumption KLEM Production
Function
Consumption by purpose vesrsus Demand for goods Investment by origin
versus Investment by destination
Exports (EU, ROW imperfect substitutes)
Imports
(EU, ROW imperfect substitutes)
Market Equilibrium for producers & consumers Environment
CO2, SO2, NOX, Particles
Energy:Coal, Crude, and Feedstocks, Petroleum Products, Natural Gas, Hydro, Renewables and Waste, Electricity, Heat
Factors Capital
and Labour
Figure 1. The basic scheme of the ATCEM-E3 model
2 . D e s i g n P r i n c i p l e s f o r ATCEM-E3
2 . 1 . T h e G e n e r a l E q u i l i b r i u m M o d e l l i n g A p p r o a c h
The distinguishing features of general equilibrium modelling derive from the Arrow-Debreu1 economic equilibrium theorem and the constructive proof of existence of the equilibrium based on the Brower-Kakutani theorem2.
Figure 2: Fixed-point and tâtonnement process
The Arrow-Debreu theorem considers the economy as a set of agents, divided in suppliers and demanders, interacting in several markets for an equal number of commodities. Each agent is a price- taker, in the sense that the market interactions, and not the agents, are setting the prices. Each agent is individually defining his supply or demand behaviour by optimising his own utility, profit or cost objectives.
The theorem states that, under general conditions, there exists a set of prices that bring supply and demand quantities into equilibrium, and all agents are fully (and individually) satisfied. The Brower- Kakutani existence theorem is constructive in the sense of implementing a sort of tâtonnement process around a fixed point where the equilibrium vector of prices stands (see figure 2). Models that follow such a process are called computable general equilibrium models.
It has been demonstrated that the Arrow-Debreu equilibrium can also be obtained from global (economy-wide) optimisation that implements Pareto optimality and uses the equilibrium characterisation introduced by Negishi3. Models that follow this methodology have the form of mathematical programming5 and are called optimisation equilibrium models6.
In applied policy analysis, the so-called “closure rule4” problem has often been taken as a drawback of general equilibrium models, as the results are depending on the choice of the closure rule. As a matter of fact, a number of earlier approaches have been classified according to the type of closure rules that they were adopting (neoclassical, neokeynesian etc.).
A recent trend in computable general equilibrium modelling consists of incorporating an IS-LM mechanism (termed also macro-micro integration), which has been traditionally used in Keynesian models. J. De Melo, Branson and F. Bourguignon, P. Capros and others5 have independently proposed the ensuing hybrid models. The IS-LM closure of computable equilibrium models overcomes the limitation of an arbitrary closure rule that must otherwise be adopted. In addition it provides insight into financial market mechanisms and related structural adjustment, allowing for a variety of choice of
1 See Arrow K.J. and G.Debreu (1954)
2 See Kakutani S. (1941)
3 See Negishi (1962)
4 or example Dorfman et.al. (1958), Ginsburgh and Waelbroeck (1981)
5 In theory, the computable and the optimisation equilibrium models are equivalent: the former, represented as a system of simultaneous equations, correspond to the first order optimum conditions of the mathematical programming problem.
Motivated by the long-term character of the climate change issue, several new optimisation models have been constructed recently. The computable general equilibrium models however, are more common for two reasons: their computer solution is easier; they enable a straightforward representation of policy instruments and market-related institutional characteristics, therefore they enrich policy analysis
a free monetary variable that can then determine the level of inflation.
The IS schedule is downword sloping curve and represent the locus of all equilibria where total spending (Consumer spending + planned private Investment + Government purchases + net exports) equals an economy's total output (equivalent to income, Y, or GDP). Alternatively the IS curve can represent the equilibria where total private investment equals total saving, where the latter equals consumer saving plus government saving (the budget surplus) plus foreign saving (the trade surplus).
Thus the IS schedule is a locus of points of equilibrium in the "real" (non-financial) economy. Given expectations about returns on fixed investment, every level of interest rate (i) will generate a certain level of planned fixed investment and other interest-sensitive spending: lower interest rates encourage higher fixed investment and the like. Income is at the equilibrium level for a given interest rate when the saving consumers choose to do out of that income equals investment (or, more generally, when
"leakages" from the circular flow equal "injections"). A higher level of income is needed to generate a higher level of saving (or leakages) at a given interest rate. Alternatively, the multiplier effect of an increase in fixed investment raises real GDP. Either way explains the downward slope of the IS schedule. In sum, this line represents the line of causation from falling interest rates to rising planned fixed investment (etc.) to rising national income and output.
The LM schedule is an upward-sloping curve representing the role of finance and money. The initials LM stand for "Liquidity preference/Money supply equilibrium" but is easier to understand as the equilibrium of the demand to hold money (as an asset and for use in everyday transactions) and the supply of money by banks and the central bank. The interest rate is determined along this line for each level of real GDP.
The IS-LM mechanism in the equilibrium models has been often used for the evaluation of stabilisation packages. These models often incorporate additional features that enhance their short/medium term analysis features such as financial and monetary constraints and dynamically adjusting expectations.
Facilitated by the explicit representation of markets, the computable general equilibrium models have often been extended to model market imperfections in the goods or labour markets and other economic mechanisms that deviate from the Pareto optimality frontier.
Some authors used the term “generalised equilibrium modelling” to underline the flexibility of the computable equilibrium paradigm, regarding the extensions aforementioned, but also the possibility to represent and even mix different market clearing regimes within a single model. In general, these possibilities enrich the analytical capability of the model regarding structural change and its relation to market distortions, for example price regulations, cost-depending price setting, etc.
The current stream of CGE models, through its modular design, encompasses the whole area of modern economics going much beyond the standard neo-classical economics on which the first generation of CGE models was confined. This new generation of model design is the inspiration behind the development of the ATCEM-E3 model.
2 . 2 . M ai n C h a r a c t er i st i c s o f t h e ATCEM-E3 M o d e l
The design of ATCEM-E3 model has been developed following three main guidelines:
1. Model design around a basic general equilibrium core in a modular way so that different modelling options, market regimes and closure rules are supported by the same model specification.
2. Fully flexible (endogenous) coefficients in production and in consumer’s demand.
3. Calibration to the base year (2000) data set, incorporating detailed Social Accounting Matrices as statistically observed.
The ATCEM-E3 model starts from the same basic structure as the standard W o r l d B a n k m o d e l s.
Following the tradition of these models, ATCEM-E3is built on the basis of a Social Accounting Matrix and explicitly formulates demand and supply equilibrium. Technical coefficients in production and demand are flexible in the sense that producers can alternate the mix of production not only regarding
At the same time consumers can also endogenously decide the structure of their demand for goods and services. Their consumption mix is decided through a flexible expenditure system involving durable and non-durable goods. The specification of production and consumption follows the generalised Leontief type of models as initiated in the work of D. Jorgenson.
The model is limited to comparative static evaluation of policies.
The model is calibrated to a data set for the base year 2000 that comprises a full Social Accounting Matrix that is built by combining Input-Output tables (as published by STATISTIK Austria) with national accounts data. Trade flows are also calibrated for each of the 25 sectors represented in the model, taking into account trade margins and transport costs. Consumption and investment is built around transition matrices linking consumption by purpose to demand for goods and investment by origin to investment by destination. The initial starting point of the model therefore, includes a very detailed treatment of taxation and trade.
Total demand (final and intermediate) is optimally allocated between domestic and two kind of imported goods (EU and ROW, under the hypothesis that these are considered as imperfect substitutes (the “Armington” assumption). To this respect the model follows the methodology of the models that are developed to study tax policy and international trade.
ATCEM-E3 considers explicitly market clearing mechanisms, and related price formation, in the economy, energy and environment markets. Following a micro-economic approach, it formulates the supply or demand behaviour of the economic agents regarding production, consumption, investment, employment and allocation of their financial assets. The model computes prices as a result of supply and demand interactions in the markets. Through its flexible formulation, it also enables the representation of perfect and imperfect competition, as well as hybrid or regulated situations. The current model version for example, incorporates sectors in which only a limited number of firms operate under oligopoly assumptions.
Recently some CGE models with imperfect competition have been developed and this feature could be included in the next generation of ATCEM-E3 model. The imperfect competition is usually based on the concept of product varieties as this derived from the theory of industrial organisation and the concept of economies of scale that provides for an elegant micro-economic framework for including non-linearities in production and consumption. Such models have been developed mainly in Europe to study the impact of European unification. Similar techniques have been utilised to study the labour market imperfections. The concept of product varieties has also been utilised to endogenise technical progress in a number of theoretical models.
Firms in these sectors operate under non-constant returns to scale involving a fixed cost element, endogenously determine their price/cost mark-ups based on Nash-Bertrand or Nash-Cournot assumptions. Firms in these sectors can make profits/losses that will alter the concentration and firm size in the sector. Demand then is also firm specific in the sense that changes in product varieties are directly affecting the utility of the consumers.
Institutional regimes, that affect agent behaviour and market clearing, are explicitly represented, including public finance, taxation and social policy. All common policy instruments affecting economy, energy and environment are included. Model closure options mainly investments/savings equality are varied according to capital or labour mobility across the sectors, the external sector , possibility of adjustment, etc.
The present ATCEM-E3 model is general and complete, in the sense that it includes all agents and markets that affect Austrian economic equilibrium. The model attempts also to represent goods that are external to the economy as for example damages to the environment.
The internalisation of environmental externalities is conveyed either through taxation or global system constraints, the shadow costs of which affect the decision of the economic agents. The current version of ATCEM-E3 is linking together the global constraints to environmental emissions changes in consumption or production patterns, the external costs/benefits, the taxation issues, as well as the pollution abatement investments and pollution permits. It evaluates the impact of policy changes on the environment by calculating the change in atmospheric emissions and damages and determines costs and benefits through an equivalent variation measurement of global welfare (inclusive environmental impact). The recent awareness about the greenhouse problem motivated the emergence of several empirical models for analysis of the economy-environment interactions. For example, the work of W.
N o rd h au s , D. Jorgenson and Wilcoxen, A. M an n e and Richels, B l it z e r and E c k au s , K. Conrad, L. Bergman, S. Proost and Van Regemorter22 have focused on the economic conditions for obtaining CO2 reduction by means of a carbon-related tax. Such a policy issue needs to be addressed by ensuring consistent representation of the interactions between the economy, the energy system and the emissions of CO2.
A counterfactual simulation is characterised through its impact on consumer’s welfare or through the equivalent variation of his welfare function. The equivalent variation can be, under reasonable assumptions, directly mapped to some of the endogenous variables of the model such as consumption, employment and price levels. The sign of the change of the equivalent variation gives then a measure of the policy’s impact and burden sharing implications.
The ATCEM-E3model is built in a modular way around its central CGE core. This modular structure allows for the definition of several alternative regimes and closure rules without the need for re- specification or re-calibration of the model.
The most important of these Alternative b e h a v i o u r a l / c l o s u r e options in GEM-E3 are Capital mobility across sectors
Flexible or fixed current account (with respect to the foreign sector) Flexible or fixed labour supply
Market for pollution permits national/international, environmental constraints Fixed or flexible public deficit
Perfect competition or Nash-Cournot competition assumptions for market competition regimes
3 . O v e r v i e w o f t h e M o d e l
The ATCEM-E3 is based on the conventions accepted by the HUGE model and by the EU GEM-E3 family of models (see Ref. 1, 6 & 12) and is aiming at the use of the general equilibrium theory as an operational tool in empirically oriented analyses of resource allocation, energy, environmental and income distribution issues.
The model is in fact a model family, i . e . , within certain limits the user can modify the specification of the model.
In the following description by indicating the most important alternative specifications of the individual equations the most interesting model versions will be discussed.
In the subsequent text the term “model” refers to ATCEM-E3.
1. The model is a system of (partly non-linear) equations.
2. The model is just identified, i . e . ,the number of variables equals to the number of equations.
3. The first 81 equations (seen ANNEX – Model’s Equations) - - or more precisely blocks of equations since one equation may represent identical formula for each elements of a given set – are forming the core of the model.
all variables are determined explicitly by assignment statements that in turn can be either definitional or behavioural equations.
6. The variables for which the core of the model does not contain explicit equations are CGOV, CLg, , CONSC, IFTX, IPTX, IWG, L A M B D A , LUMTOT, Q , R , RSi, V , W , C R E S C . To make the system precisely identified the user has to choose further 14 equations from the menu shown in the closure (Equations (82a), (95a) ).
7. To avoid under- and over identification (redundancy and contradiction) the user is recommended to start with the so-called EPM (Equilibrium Programming Model) version which consists of Equations (82a), (83a), (84a), (85a), (86a), (87a), (88a), (89c), (90a), (91a), (92a), (93c), (94b), (95a). Then, the user can replace these equations one-by one with the desired alternative in order to get the required specification. Each specification corresponds to certain theoretical assumptions or to the choice of exogenously determined variables.
Note that:
All but the last equations of the model are homogenous in respect to the nominal (price or value type) variables. That is, once the equations hold they would continue to do so even if all nominal variables were multiplied by the same scalar. That is the reason why for the Equation (95a) the price level should be set exogenously.
The models equations satisfy Walras law, which implies that the sum of the net monetary savings are equal to zero
∑
∑
= + +g
g j
j SGOV SROW SHOU
CREDIT where:
CREDITi - Sectoral net borrowing (= - savings), i∈ℑ SGOV - Governmental savings
SROW – Savings of the Rest of the Word (= - foreign balance of payments) SHOUg - Households savings, g∈ G
Grossly speaking by including the real investment among the savings, one can say that total savings equals total investments (the well-known S = I relationship in the macroeconomic textbooks) - so its explicit prescription is unnecessary.
3.1 Theoretical Characteristics
Essentially, the model follows the Walrasian or neoclassical tradition. However, several versions of the model allow for certain deviations from the standard neoclassical approaches. For example, one can define alternative models with disequilibria in the resource markets, or irrational consumer behaviour or models with exogenous (e.g. investment) goals that cannot be described analytically.
The model at this stage is static which implies that instead of sophisticated inter temporal decision rules, the savings and consumption are determined by simplified rules of thumb. For more realistic treatment of these problems a dynamic model and a monetary module of the model are under development.
The production function of the model is of the so-called Johansen type which assumes Leontief-type fixed input coefficients but allows for smooth substitution between:
Domestic and imported goods, Various types of energy,
Aggregate energy and labour and Energy-labour composite and capital.
The substitution possibilities are represented by isoelastic (nested) C E S functions.
Similar substitution p o s s i b i l i t y e x i s t s between imported and domestic goods i n consumption (and final uses in general). In addition, in the case of the personal consumption (the variable part, i.e., in
excess to the exogenously given consumption) the sectorial import-domestic composites (which are defined simply by their sectorial origin) are combined by a C E S aggregator function thus allowing for substitution.
Export supply i n each industry is determined by a CET function, which allows for transformation in the production process between goods produced for the domestic and foreign markets.
Although by assuming that the “small country” world prices for imports are exogenous (not influenced by the domestic demand) then the export prices may depend on the exports volume. This can be explained either by assuming that the domestic products are to be different from similar products from the rest of the world (ROW) or by taking into account the higher short run transportation and marketing unit costs when larger amounts are to be sold. the price concept used in the model is that these unit costs are diminishing the FOB prices of exports.
Labour is homogenous or mobile across sectors but following Johansen [1960], exogenous sectorial wage differentials are used to allow for sectorial variations in wage rates. However, the general index of wages is uniform unless one exogenously changes the wage differentials.
Capital is either mobile or sector specific depending on the choice of the user. Producers are assumed to minimize costs. Possible monopolistic behaviour is represented by mark-ups in the production price formula.
Households are maximizing their utility measured by the aggregate level of the variable consumption or the aggregate utility of consumption leisure and environmental quality (in most versions seen as a higher level aggregate).
The income distribution is described in details, i.e., sectorial income distribution includes p r o f i t taxes, dividends, and various earmarked or in-kind (mainly investment) transfers. Therefore we can derive the disposable income for the individual sectors. However, in the present (static) version of the model we assume that the shares of the sectors in the total investment are exogenously given, which in turn is determined by the macro closure rule of the model. As a result, credits are needed to bridge the gap between disposable incomes and consumption so that the investment level is determined endogenously (residually). An investment matrix is used in the model to show the shifts in fina l demand structure resulting from the different buildings and machine intensities of the sector specific investments.
3.2. Descriptions of Selected Blocks and Features of the Model 3 . 2 . 1 . I m p o r t / E x p o r t V o l u m e s a n d P r i c e s
Commodities supplied to the domestic markets are in the most of the sectors composites of domestically produced and imported goods. As to the imported goods our model can distinguish between two d i f f e r e n t markets, namely the EU import/export market and the ROW. These markets can be assumed to behave in d i f f e r e n t ways and the user has some freedom to decide on the s p e c i f i c nested structure of substitution between the domestic products and various imports.
In most of the models the substitution possibilities would be d e f i n e d at the level of the total sectorial use, as if the mix of imported and domestically produced goods would be the same across d i f f e r e n t uses or users. But in the ATCEM-E3 model in order to allow for more realistic representation of the substitution opportunities, and if needed to be able to apply d i f f e r e n t i a t e d import duties, we have three distinguished categories, namely, consumption, investment and other uses.
The supply of imported goods is considered to be i n f i n i t e l y elastic (the so called small country assumption), which means exogenous world market prices of imported commodities.
According to the A r m i n g t o n assumption, domestic products and imports of the same sectorial origin are considered to be d i f f e r e n t i a t e d products of the same variety. The model users have to decide on the special aggregation rule (simple or nested C E S functions) in order to d e f i n e the volume of the composite supply. Also, for a given sectorial commodity one has to specify the allocation
u i MEL
u t i u
t i
i u
t i u
t
i XD
PWM TXM
V MH P
M
u t i
, ,
, ,
, ,
, ,
,
*
*
* *
, ,
⎟⎟
⎠
⎞
⎜⎜
⎝
= ⎛ ( 2 3 )
It is also possible to apply a d i f f e r e n t rule, namely, EU imports are to be treated as perfect substitutes for the composite of the ROW i m p o r t s and the domestic supply, though their ratio, as in the case of imperfect substitutes, is still a function of their relative prices. Such demand function can be interpreted as r e f l e c t i n g imperfect adjustment to changing relative prices, rather than imperfect substitutability,
(
iu iu iWBETAu iu)
BETAiuBETA u i u i u
E i u
i M AH XD AM M
HTS , , ,
1 ,
, , ,
, ,
,
, = +
*
− + + − − (28)There is some asymmetry between the treatment of exports and of imports. In the case of exports, unlike imports, the s m a l l c o u n t r y assumption is usually dropped. Given the price of the competing exports from the rest of the world and the total demand of the given export market one can assume an inverse correspondence between the volume and the unit price of exports (direct or inverse export demand function). That brings special terms of trade effects into the model which has to be carefully checked for its order of magnitude,
t i ZELD
t i t i t
i PWZ
ZD PZ Z
t i
, 1
, ,
, *
,
⎟⎟
⎠
⎞
⎜⎜
⎝
=⎛ (22)
One way to avoid large changes in terms of trade that would be d i f f i c u l t to explain and still constrain effectively changes in the export volume is to match the above export demand functions with export supply functions. They can be d e f i n e d in a fashion similar to those of the import demand functions. Exports can be treated as imperfect substitutes to similar goods sold on domestic markets, aggregated into a composite sectorial output by appropriately chosen CET (transformation) functions,
(
ZBETA)
ZBETA iEW i i ZBETA i i
i AD XDT AZ Z Z
X i i i ,
1
*
,*
+ += − − − (27)
One can, thus, derive the decomposition of the sectorial output as if it were the result of an income maximizing choice. Here again the ATCEM-E3 model also allows for non-neoclassical export supply determination,
i T
I ZXEL
i i ZELS
i t i t
i t
i t
i XDT
XDT P
PZ V Z TXZ
Z ⎟⎟⎠
⎜⎜ ⎞
⎝
⎟⎟ ⎛
⎠
⎜⎜ ⎞
⎝
= ⎛
−
* 0
*
* * 0
;
, ,
,
, ( 2 4 )
3 . 2 . 2 . P r o d u c t i o n T e c h n o l o g y
The representation of production possibilities in our CE model is based on the combination of the input- output models and smooth production functions. We utilize the conventions and database of the input- output tables but depart from the traditional input-output models by allowing for various kinds of (imperfect) substitutability between inputs and outputs groups.
Thus, like in the input-output models, the base production units are the sectors. The level of sectorial aggregation and breakdown depends on the purpose of the model and the availability of data, e.g., in our case there are 25 sectors. The sectorial production functions take the form of multi-stage nested C E S functions of the intermediate inputs (sectorial commodities) and primary inputs (labour and capital).
Sectorial indices are denoted by i and j ( i,j∈ℑ), X stands for production, XHM for intermediate inputs, L for labour and K for capital.
Johansen [1960] has introduced the simplest extension of the linear input-output model to allow for price driven production structure.
In his solution, at the lower stage, labour and capital (L and K) define a composite primary input in the form of a Cobb-Douglas production function (volume aggregator). At the upper stage, this composite primary input and the intermediate inputs together determine then (as perfect complements) the sectorial output according to a Leontief production function. In an open economy the intermediate inputs ( X H M ) themselves are as a rule treated as composite commodities, as C E S aggregates of domestic and imported commodities of the same sectorial origin ( A r m i n g t o n assumption).
This Johansen-type production specification has been adopted in the ATCEM-E3 model variants, replacing the Cobb-Douglas with a general C E S function (allowing for capital and labour substitution elasticities smaller than one). However, because of our particular concern on energy/economy/environment issues, we employ more complex production functions allowing for a more differentiated treatment of input substitution possibilities. I n particular, the intermediate inputs are further subdivided into energy inputs ( X H Mi j i∈
ε
Ν,
j∈ℑ) and non-energy (material) inputs ( X H Mi j i∈Νε
Ν,
j∈ℑ).Figure 3: The nesting structure of the sectoral production functions
The demand for non-energy intermediate inputs is computed by assuming Leontief-type fixed input- output coefficients. Energy inputs define a composite input according to a C E S volume aggregator.
At the next stage energy and labour are aggregated into a higher level composite input (LE) which is then combined with capital in a similar way to define the sectorial output, which - as discussed later - is in turn a composite of domestic output (XD) and exports (Z) (see Figure 3).
3 . 2 . 3 . P r o d u c t i o n D e c i s i o n s a n d R e l a t e d P r i c e s
The u s e r s price of the import-domestic composite sectorial commodity is determined as the weighted average of the prices of the composing sources, which are, as a rule, modified by appropriate (consumption) taxes and subsidies,
u i
u t i u
t i i
u i u
i HTS
PWM V
M P
XD PHM
,
, , ,
, ,
,
*
*
*
+∑
= (21)
where:
PHMi,u – Composite good price, i∈ℑ, u∈U
XDi,u – Domestic sales from production, i∈ℑ, u∈U
PWM i,t,u – World market prices of imports, i∈ℑ, t∈ℑ, u∈U HTS i,u – Domestic use, i∈ℑ, u∈U
As a result of the above description the price level of domestic sales and exports changes at different rates even if the rate of export tariffs/subsidies remains unchanged. Therefore, unlike the traditional input-output models, the average wholesale price in the CGE model becomes the weighted average of the domestic and export prices, where the world market price of the export of the modelled economy (own world market export price) may change as the volume of exports changes.
i t
t i t i t
i i
i
i XDT
Z PZ V TXZ X
PA P
∑
−
= . , ,
*
*
*
*
(20)
As a result of the elaborate treatment of foreign trade several price indices will appear in the ATCEM-E3 for the same sectorial commodity, e.g., exogenously defined world market export and import prices;
endogenous own world market export price; domestic export price (the former multiplied by the exchange rate and the tariff/subsidy factor); domestic import price and their various averages.
Production decisions are represented as if the sectors acted as cost minimizing single producers. Thus, at any level of production, X j and input prices,
PHMi,u – Composite good price, i∈ℑ, u∈U PLi – Calculative labour costs, i∈ℑ
PKi – Calculative capital costs, i∈ℑ
the level of inputs used are defined by minimizing total cost ( T C j) ,
*
,* *
j i i j j j j j
i
TC =
∑
PHM XHM +PL L +PK K subject to the constraint defined by the production function.The multi-stage, separable nature of the production function implies a process of sequential minimization, i.e., the determination of the minimal cost for each separate group of inputs. In the formal description of the model the cost minimization is usually represented stage by stage, defining various composite inputs and their minimum unit cost. I f the production function is lineary homogenous, as it is usually assumed, the minimum average cost is the same as the marginal cost, and they are independent of the level of production. In competitive equilibrium, under constant returns to scale, the unit cost is, at the same time, the equilibrium price level.
As it is known, the C E S form allows the model builder to use explicit dual C E S forms to define the minimum cost and the implied factor demand as functions of the level of production and the input prices. As a matter of fact various alternative forms can be used to characterize the cost minimizing solution. The choice among the alternative primal or dual forms, or their various combinations may be important from the point of view of the stability or the speed of the solution algorithm.
The production decisions determine the producers´ supply and demand of goods and they imply changes in their costs of production as well as in their prices, since, as mentioned above, the producer’s price (PP) in competitive equilibrium is defined by the unit cost (due to the assumption that production functions are homogeneous of degree 1),
(
j j j j)
jj i i
i
i PHM AHM PL L PK K X
PP =
∑ *
, +*
+* /
where:
AHMi,j – Domestic sales from production, i,j∈ℑ
In the model specification, however, this definition would as a rule take a different form, making use of the dual forms and the possibility for stage-by-stage definition of the cost function’s components.
For example, in the case of the Johansen production function the value added part, ( P L j * L j + P K j
* K j ) / X j can be represented by an explicit (dual C E S ) function of P L j and P K j. In the
case of the multistage C E S production function the cost price definitions appear in the form of a sequence of dual C E S functions that are defining stage by stage the minimum cost of the separate input groups (Equations (29)(33)).
Changes in sectorial producers prices reflect variations in the unit cost of sectorial inputs, labour and capital costs and/or changes in the composition of the inputs (e.g., domestic and imported goods, labour and capital) in response to relative price changes, depending on the model specification. If no substitution possibility is allowed for, the price definition coincides with the familiar price equations of the input-output models. Thus, the lower the substitution elasticities are set, the closer one stays to the classical analysis of price changes, in which distributional effects (changes in wage and p r o f i t rates) are at the heart of explaining changes in relative (sectorial) prices. This approach can be utilized in some versions of the ATCEM-E3, in which changes in the wage and/or p r o f i t rates are set exogenously and capital/labour substitutability is neglected.
Price changes will then reflect the simultaneous changes in the various cost components (labour, capital, material, energy). Wage costs, may change both endogenously, as a result of changes in the relative scarcity of labour (the general wage level, W) or in the consumer price index, CPI (in the case of wage indexation) and exogenously, for example because of changing wage tax rates (W G ). A typical formulation of the sectorial unit wage cost (PL) would be as follows,
) 1
(
* 0
*
j ji W WT WG
PL = + (41)
where WT0j is the sectorial wage differential.
(Strictly speaking, the assumption of homogenous labour - mobile across sectors - would imply the same wage in all sectors in the spirit of pure competitive equilibrium.
So the use of wage differentials is a practical compromise introduced by Johansen [1960].)
The cost of capital may change as the average price of capital goods changes or the rate of return changes (reflecting, for example, a change in the relative scarcity of capital),
P Kj = P I N V S j (AMRj + R Sj) (42)
In some variants of the model we would depart from the neoclassical price formation rule and allow for profit mark-ups even in equilibrium with constant return to scale (Major [1999]). In such case part of the net earning on capital will show up in the model as pure p r o f i t rather than the cost of the capital.
Such choice of specification reflects the belief that producers can successfully protect their relative income position by passing at least part of the changes in their costs over to the users of their commodities. (The choices of the initial value of the normative rate of return can reflect producers’
belief on how much of these changes can be passed on to customers.)
Taking into account the amortization as well, the cost of capital, together potentially with some pure p r o f i t (which corresponds roughly to the concept of operating surplus) will consist of the following components,
(
j j)
j j j jj j
j
j K X PINV PROFC AMR RS PINVS K X PINV PROFC
PK
* /
+*
= +* * /
+*
where P I N V and PINVSj stand for the general and the sectorial price index of capital, AMRj for the sectorial rate of amortization, RSj for the sectorial rate of return on capital and PROFCj for the sectorial p r o f i t mark-up.
One would derive Johansens solution by setting the p r o f i t mark-ups at zero and the sectorial rates of return on capital, R Sj as the product of a variable general rate of return (R) and fixed sectorial differential, RS0j, assuming that capital is mobile across sectors. If sectorial capital were fixed, the sectorial return on capital would be defined by the scarcity of the sectorial capital (in a way, as a residual variable). Assuming that the producers can fully pass increases in their costs on to the buyers,
relative scarcity of capital.
Apart from pure cost and price considerations, the eventual income position of enterprises (sectors in our models) is also influenced by various taxes and subsidies in all economies. Some taxes are clearly meant to take away rent-like income (extra p r o f i t ) ; some of them are pure excise type of taxes to collect income for the state budget.
The basic question the modeller has to address in this respect is: what part of the net income should be considered as return on the capital? Thus, he has to decide which taxes/subsidies affect the users prices and which are to be considered as pure income transfers (having no impact on prices), affecting only the retained earning of the sectors (added to or subtracted from their operating surplus). Clearly, these decisions determine what will be the size of the sectorial operating surplus.
Having determined the net rate of taxes/subsidies ( P T X ) that is modifying users prices one could define the average wholesale price as follows,
P Aj =P Pj / (1 - P T X j ) or, alternatively,
i
i i
i i i i i i j
O j
j PTX
PROFC X PINV
K PK L PL E AHM PE
PHM PA
i j
−
+ + + +
=
∑
Ν Ν
∈
1
* *
*
* *
, ,
ε (19)
3 . 2 . 4 . D e m a n d
Final demand is broken down into the usual major components in our model:
Changes in stocks, Private consumption, Public consumption, Investments, and Exports
3.2.5. Change i n Stocks
The stocks change exogenously provided because it is included in the model in order to complete the commodity balances.
3.2.6. Private Consumption
Private consumption is modelled by means of one representative household group.
The household behaviour in the model can be described according to a neoclassical approach, making use of the extended linear expenditure system. The nested utility function includes the choice between labour, leisure (thus resulting in variable labour supply) and environmental quality.
1 ) 1 /(
1 1 1 1
1
)
*
* (
1 1
ELCW ELCW
ELCW
ELCW CLTOT SHW LQ ELCW SHC
UTIL − −
+ −
= (75)
where the LQ composite is defined as
1 ) 1 /(
1 1 1 1
1
)
*
* (
1 1
ELQ ELQ
ELQ
ELQ ELQ
LQ SHW
LEIS SHL
LQ
−
− −
+
= (76)
As to the determination of consumption, a generalized Linear Expenditures System is used in the ATCEM-E3 model (the substitution elasticity in a Stone-Geary type utility index function is different from one),
The parameters of the above LES demand functions are not estimated by econometric techniques. Instead, the fixed (committed) part of consumption is set to reflect the degree to which the consumption of the given good is considered to be demand driven or supply constrained. Lower (higher) levels allow for relatively larger (smaller) shifts in demand as prices or income change. The smaller possibilities for change can be regarded as reflecting some short term, non-price rigidities in the adjustment of supply.
On the higher level, optimal household behaviour can also be described as cost minimizing behaviour.
Optimal behaviour (including demand for aggregate consumption, environment and leisure) is determined by Equations (64) and (72). Non-optimal behaviour means that some (or all) of the first order conditions for optimality (Equations (90a), (91a) and (92a)) are replaced by arbitrary behavioural functions, e.g. by exogenous or simply wage-elastic labour supply.
Household monetary saving in the ATCEM-E3 model is either assumed to be proportional to the disposable incomes or alternatively, private saving can be determined as a residual by fixing the level of consumption exogenously. Being a static, short to medium term focused model, saving (investment into housing) is treated exogenously.
3.2.7. Public Consumption
Public consumption is modelled by an exogenously given structure ( f i x e d coefficients). In most cases the expenditure level is also exogenously defined. Public savings/deficits on the other hand are usually determined as residual variables (what remains after accounting for all incomes and expenditures of the public sector). Alternatively, the model user can choose government consumption level to be a variable and prescribe a given level of d e f i c i t . Also, in some applications of the models one can compute the
“budget n e u t r a l ” e f f e c t of certain changes in the tax and benefit system. Endogenising some tax or benefit rates can easily do this.
3.2.8. Investment
The investment demand for sectorial commodities is determined by splitting total investment into various areas. The model follows the input-output modelling tradition and uses an investment coefficient matrix to determine investment demand. Depending on the eventual sectorial character of the investment, all investments are grouped by production sectors. The investments made by the state and private households are, in this solution, translated into sectorial investments by means of investment transfers.
The fixed sectorial coefficients d e f i n e in each investment area a specific composite capital good and a corresponding price index. The prices of these capital goods are used to d e f i n e the current value of the area specific capital stock, the volume of which is measured by its value at base prices.
The determination of the investment level can take d i f f e r e n t forms depending on model specification. In particular, gross investment may be either fixed or can be treated as a freely adjusting variable, depending on the adopted macro-closure rule. The sectorial shares in total investment are considered constant in the model, as the sectorial decomposition of total investment has limited effect in a static model, given that there are no future periods in which capital accumulation would be i n f l u e n t i a l .
3 . 3 . E n v i r o n m e n t
The figure bellow provides a general scheme of the structure of the environmental submodel
of ATCEM-E3.
the users prices ( P H M U and P H M U C ) are computed. If switch E3 is equal to 0 then the tax and abatement cost component of their formulas (Equation (15) and (16) ) are dropped.
At present the model can deal with the problem of air-pollution caused by emissions of C O2, S O2, N Ox and suspended particles. While some natural, non-energy, and non-pyrogeneous emissions take place, most man-made emissions of the four pollutants are associated with combustion of energy carriers.
Thus the vast majority of the four air pollutant emissions we are investigating are associated with energy use.
Figure 4. The structure of the environmental submodel of ATCEM-E3
The baseline combustion emissions were further decomposed by fuel type so as to obtain estimates of emissions originating with each of the energy inputs that entered into production of j or consumption of g. These pollutant and fuel-specific emission estimates were divided by the monetarized input of each fuel used by each sector in the baseline yielding baseline emission coefficients for each fuel input.
These coefficients, CE p o i j and CEHpoig (i∈
ε
Ν) are used as parameters in the model. They allow for increasing emissions with increasing scale of production and associated increases in use of energyinputs. Even more important, these coefficients link emissions to the energy mix used in production.
Thus the inter fuel s u b s t i t u t i o n s is one of the main ways in which producers can change air pollutants emission.
Making reference emissions proportional to the fuel use is not an entirely satisfactory approach in those sectors such as pharmaceuticals that are using energy carriers as process feedstock and not for combustion.
In such sectors we made rough adjustments upwards to the emission coefficients while at the same time trying not to overstate the opportunity for emission reductions in that sector due to factor
substitution or pollution abatement. The assumption of proportionality, while not perfect, does allow us to model emissions reductions via inter fuel s u b s t itu t io n s as an economic rather than administrative phenomenon.
Other means of emissions reduction that are incorporated into the model by virtue of this assumption of proportionality are via general reduction in energy use by domestic industry or consumers, i.e., factor substitution, and, as discussed below, abatement of emissions due to process equipment modifications or extensions, e.g., addition of end-of-pipe pollution abatement equipment.
3.3.1. Emission Control Through Abatement
The baseline emission c o e f f i c i en t s CEpoij and CEHpoig (i∈
ε
Ν) represent the potential for pollutant abatement beyond existing levels of control for each pollutant, p o , associated with energy input, i, in production of output j. Such abatement, however, is costly and the greater the extent of abatement, for example as a fraction of potential emissions, the more costly abatement becomes. Following C a p r o s , et.al. [1995] we introduce decision variables AEIpoj ranging between 0 and 10, into F E I M . These variables are d e f in ed as proportion (based on the abatement level) of emission p o selected by the industry j. These proportions are embedded in average or unit cost of emissions-abated functions of the following sort,
j po GC
j po j
po j
po AEI KC
GC
CAB BCpoj , 1 poj ,
, ,
, ,
) 1
(
1 * − +
+
= − + (7)
These average cost emissions-abated functions are increasing and monotonic, that is
≥
0
∂
∂ AEI
CAB and 2
0
2 ≥
∂
∂ AEI
CAB .
The abatement cost functions are embedded in the model using the C a p r o s et. al. s [1995] so-called c o s t - p r i c e s t r a t eg y 4 . His report also provide a summary of the methods used to estimate costs, to rank technologies, and to estimate a set of points on air pollution abatement average cost functions for the sectors and major air pollutants. These data were used in the cost functions like Equation (7) and Figure 5 and 6 for each sector of the model.
For the households a similar abatement cost function can be specified but for the time being it is not e f f e c t i v e in the model.
Figure 5
Figure 6.
Marginal abatement costs of NO
xS o u r c e : P . C a r p o s a n d a l .
As mentioned earlier, this strategy assumes a fix e d proportionality between energy use and emissions.
These coefficients, introduced above, can be used to transform energy consumption into emissions levels. Then, using the cost functions of Equation (7), converts the emission reductions into the total material input required to abate emissions due to energy use in production of Xj. Associated with abatement technologies are input coefficients for abatement, ABCpoij. These coefficients were based on emission control technology input cost data contained in sources used by T a j t h y [1996b] to construct input costs and recommended to us by him. In ATCEM-E3 these input shares are fixed across levels of pollution abatement for a given pollutant. A shortcoming of the model as currently formulated is that energy inputs are not directly included among the input shares. Another adjustment made in order to operationalize ATCEM-E3 is the characterization of investments in pollution abatement as being firstly amortized and then included as a cost along with current material inputs.
An expression for material inputs, ABIij required to abate emissions of all pollutants in sector j is shown by
In principle similar function can be used for the households too (Equation (11). The price indices for abatement inputs by pollutants and sectors are shown by
Remaining emissions after abatement is shown by
for sectors and
for households.
Based on a study (Kaderjak [1996]) environmental quality endowment ( Q E N D O W ) of the households is a (linearly approximated) function of (changes in) industrial emissions,
where the DAMAGIp o and DAMAGHp o – the marginal damage coefficients were estimated on the basis of the same study.
With this augmented price, the variables AEIpoj become decision variables and producers problem is constrained cost minimization with augmented energy prices. In the model equations, as implemented, more implicit forms of AEIpoi are used in order to assist numerical solution.
3.3.2 Environmental Load Fees
We model environmental load fees (ELF in the followings) as pollutant emission taxes. We compute the ELF payments of each sector as the product of the pollutants ELF tax rate and the sectors pollutant emissions.
We therefore characterize the ELFs as excise taxes with a single, uniform rate. This model structure allows one to specify different ELFs (tax rates) for each pollutant and each production sector.
Emission tax rates are either exogenous or endogenously computed so that a certain emission reduction target be met (Equations (1)(3) versus Equations (1)(3)).
The ELF revenues are inversely related to AEIpo,j. Thus, in selecting cost minimizing levels of AEIpo,j. the producers of the sector implicitly select optimal pollution abatement levels such that the marginal cost of a pollutants abatement is equal to the marginal savings from reductions in that pollutants ELF payments. Thus the abatement ratio is determined by the following alternative formulas,
where the marginal cost can be computed as
1. Energy
3.4 Balance (market clearing) Conditions
At the core of the CGE models there are various resource balances and accounting identities. In a fully neoclassical model the supply of various sectorial commodities has to match their total demand, labour and capital markets must clear, etc. By making use of the build in switches not strictly neoclassical variants of the ATCEM-E3 model can be formulated as well, i.e., in which labour and capital markets do not have to clear; instead it is to be assumed that the utilization level of the capacities would change.
These options are technically realized as if the overall productivity of labour and/or the efficiency of capital are endogenously changed.
Apart from the commodity balances there are various financial balances in the models as well, such as the balance of foreign trade, the balance of foreign payments, the budget of the private households, the state household and the production units (sectors).
3.5. Income D i s t r i b u t i o n and Public Finance
There as build in option in the model covering the major aspects of public finance including all substantial taxes, social policy transfers, public expenditures and deficit financing instruments. By switching in this option, given an appropriate database, a detailed investigation of the income distribution-redistribution components can be done.
Equations (35)&(38) represent the budgets of the economic agents (households, sectors, state household and foreigners) and are implicitly defining the monetary savings as the difference between disposable incomes and expenditures. As a result primary income is received not by labour and capital,
proportional to some activity level (and a price index for the valorisation). The transfer amounts are given exogenously only in few cases, namely when a simple behavioural rule cannot be identified or they are determined by some dynamic effects (past commitments and anticipations) that cannot be properly captured in a static model.
It is to be noted that the system of equations is satisfying the Walras-law as general equilibrium models usually do. As a result, total net monetary savings equals zero so that savings-balancing requirement is implicitly given.
Also to be noted is that all model equations introduced so far are homogenous in the nominal (price or value type) variables. That is, once the equations hold they would continue to do so even if the same constant multiplied all nominal variables.
Most C G E models exhibit such price homogeneity (money neutrality) , thus, there is a need to e x o g e n o u s l y set the general price level (choose a n u m e r a i r e ) ,
4 . M o d e l ’ s I m p l e m e n t a t i o n
4.1. Nomenclature/Dimension of the model 4.1.2. Agents and sectoral dimension
Economic agents
The model considers 4 economic agents: households, firms, government and foreign sector.
Government revenue and income flow categories:
Direct taxation, indirect and VAT taxation Energy and environmental taxation
Property taxes, capital taxes Social security, social benefits Production subsidies
Import duties and foreign sector transfers Revenues from state owned enterprises.
2 primary production factors: labour & capital Branches
The model code allows for a user-defined aggregation of sectors and traded products. The following table shows the industrial classification chosen for the model.
Table 1. The 25 sectors industrial classification of current ATCEM version
No Sector Name AT I/O table (year 2000, 2 digits code–see Table 6)
1. COAL 10
2. OIL and GAS 40b
3. ELECTRICITY 40a
4. REFINERIES 11, 23
5. FORESTRY 2
6. STEEL ½ from 27, ½ from 28
7. OTHER METALS ½ from 27, ½ from 28
8. ENGINEERING 29,30, 31,32,33,34,35
9. BUILDING MATERIAL 26
10. FERTILISERS ½ from 24
11. PLASTIC MATERIALS ½ from 24
12. OTHER CHEMICALS 25
13. LIGHT INDUSTRIES 17, 18, 19, 20, 21, 22
14. FOOD INDUSTRIES 15, 16
15. CONSTRUCTION 45
16. AGRICULTURE 1, 5
17. TRANSPORTATION 60, 61, 62, 63
18. OTHER MINING 14
19. TRADE 50, 51, 52, 55
20. WATER 41
21. OTHER MATERIALS 72
22. FINANCIAL SERVICES 65, 66, 67 23. OTHER SERVICES &
TELECOMMUNICATION 64, 70, 71, 73, 74, 93, 95
24. WELFARE 80, 85
25. PUBLIC SERVICES 90, 91, 92
