مشخصات قیمت و کشش درآمد در مدل تعادل عمومی قابل محاسبه: استفاده از تفکیک نهفته

This paper contributes to the ongoing debate about the specifications of price and income effects in Computable General Equilibrium models. We detail a procedure which allows to implement in such models any regular configuration of price and income effects. This procedure exploits the advantages of latent separability. By allowing some overlapping in the grouping of commodities, this separability concept offers much more flexibility than other separability structures since substitution between goods runs through many channels. This paper also provides an empirical illustration which demonstrates the applicability of our procedure and which highlights the substantial bearing of these specifications on CGE results.

Computable General Equilibrium (CGE) models are now widely used in order to examine a wide array of economic issues (trade reform, economic integration, environmental policy, etc.). The popularity of these economic tools can be partly attributed to their ability to fully take into account inter-sectoral effects of economic shocks. These inter-sectoral effects mainly occur through prices (of goods, primary factors of production, etc.) and income, reflecting competition for scarce resources, limited disposable income, etc. Accordingly, the specification of price and income effects is a crucial factor for the relevance of CGE models. This specification of price and income effects is directly connected with the choice of functional forms used to represent production technologies of firms, preferences of households, etc. Several papers already highlight the substantial bearing of this choice upon CGE results. Let us mention four papers illustrating four different Flexible Functional Forms (FFF). The first paper by Hertel (1985) considers a CGE model of the New York State economy in order to examine the impact of a system of partial factor subsidies. In this framework, Hertel tests two specifications of production technologies. The first one is based on the Cobb–Douglas (CD) functional form, which can be easily introduced in the model but embodies restrictive hypotheses. The second uses the translog (TL) functional form, which is much less “convenient” but more flexible and adequate to capture patterns of substitution between production factors.1 As expected, this analysis shows the huge impacts of these two specifications on results. Moreover, Hertel compares these results with those obtained using a flexible partial equilibrium model. The simulations' results indicate that the flexible partial equilibrium model dominates its CD, general equilibrium counterpart, yielding a more accurate approximation to the TL, general equilibrium “base-line” model. This latter result obviously depends on the particular problem under consideration but leads the author to conclude that general equilibrium analysis with restrictive specifications may be of little value for some policy analysis. The second paper by Despotakis and Fisher (1988) focuses on the energy sectors in the California economy. Again two specifications of production technologies are contemplated. The first one uses the Generalized Leontief (GL) functional form while the second relies on fixed coefficients. The authors then simulate the long-run impacts of a doubling of oil price under these two specifications. It comes as no surprise that this experiment leads to a much larger drop in oil use with the GL specification (34%) than is obtained with the fixed-coefficients version of the model (11%). More interesting are the differences on aggregate variables and, as a result, policy recommendations. This experiment leads to a strong decrease of gross domestic output with the GL specification (4%) and a small increase with the alternative one (0.2%). The third paper by Robinson et al. (1991) investigates the role of functional forms for the specification of import demand functions.2 Using a three-country CGE model, they contrast the standard constant elasticity of substitution (CES) import-aggregation function with the almost ideal demand system (AIDS) formulation. Their analysis also demonstrates that, depending on simulation experiments, the choice of a particular specification has a strong impact on model results. Specifically, for experiments involving growth and tariff protection and thus generating significant income effects, the standard CES specification yields unrealistic terms-of-trade and trade-volume effects while the new AIDS specification does not. Finally, the fourth paper by McKitrick (1998) provides another robust and recent demonstration of the substantial role of functional forms. He developed a CGE model for the Canadian economy. Here the comparison is between the CES and the Normalised Quadratic (NQ) functional forms adopted to represent production technologies as well as consumers' preferences. Three fiscal experiments are simulated, reflecting “small”, “medium” and “large” policy shocks. It is again found that the choice of functional forms affects not only industry-specific results, but also aggregate results as well, even for the small policy shock. Despite these well-perceived results warning CGE modellers against the use of convenient/restrictive functional forms, many CGE applications still rely on them (like the CD system or the Linear Expenditure System (LES) at the final demand side). Here we make the assumption that two main reasons explain this unsatisfactory situation. Firstly, knowledge of substitution/price/income elasticities is limited. This justification may be relevant in some cases, but is clearly inappropriate in other cases. The second reason is more fundamental and is the core subject of this paper. Few modellers have adopted FFFs for the reason that they generally exhibit poor global properties. For instance, Caves and Christensen (1980) demonstrate that the TL and GL FFFs do not satisfy the restrictions of monotonicity and convexity of indirect utility function over all possible range of prices and income. Imposing global properties on FFF is not advantageous because this destroys their flexibility property (cf. Diewert and Wales, 1987 on the TL). This lack of global regularity is problematic for equilibrium models (either CGE or partial equilibrium), as it may cause numerical solution methods to fail. Aforementioned papers using FFFs in their CGE models acknowledge this potential issue. In practice, however, it seems that McKitrick only has to deal with the lack of global monotonicity in his experiments. Hence, he imposes some parameter restrictions that “reduce” the flexibility of its CGE model. But the “restricted” model still remains much more flexible compared to CGE models using traditional specifications. The critical issue of the introduction of FFFs in CGE models was first recognized by Whalley (1986), who considers this as a great challenge to CGE modellers. Accordingly, numerous works have been initiated to resolve this apparent trade-off between global regularity and flexibility of functional forms specified in these models. In particular, implicitly additive functional forms have been advocated and implemented in some well-known CGE models (for instance, the Constant Ratio Elasticity of Transformation Homothetic (CRETH) system in the ORANI model or the Constant Difference Elasticity (CDE) system in the GTAP model). Under implicit additivity, there are N independent substitution parameters, with N the number of goods in the system, and this still allows non-homothetic specification. Thus, this class of functional forms allows one to calibrate his consumer demand to a vector of own price and income elasticities which are the usual reported results of econometric estimation (for instance, see Seale et al., 2003). However, these functional forms impose cross-price relationships and moreover may not handle all configurations of own-price elasticities ( Hertel et al., 1991). To our knowledge, current efforts are mainly oriented towards the introduction of the An Implicitly Direct Additive Demand System (AIDADS) non-homothetic demand system pioneered by Rimmer and Powell (1996). This new demand system is globally regular and more flexible in its treatment of income effects than commonly demand systems used in CGE models, having Engel curve of rank three instead of, at must, two. Yu et al. (2003) detail the introduction of this demand system in the GTAP model and then compare it to several traditional demand systems in the context of projections for disaggregated global food demand. As anticipated, they show that the AIDADS demand system represents a substantial improvement, particularly for the rapidly growing developing countries, by allowing to capture changes in income elasticities of demand. However, this new demand system is based on the assumption of implicitly additive preference and therefore is not second-order flexible in its treatment of price effects. Our overall purpose in this paper is to contribute to this literature by suggesting to resort to the notion of latent separability, recently formalized by Blundell and Robin (2000) but applied for a long time. In a very general way, latent separability generalizes weak separability by allowing some overlapping in the grouping of commodities into different “sub-functions” of the main one (utility function, production function, expenditure function, profit function, etc.). Thus, latent separability offers much more flexibility than weak separability since substitution between goods runs through more than one channel. This advantage has been exploited in various econometric studies, performed both at the supply and demand side. Perroni and Rutherford (1995) (hereafter P&R) demonstrate theoretically that latent separability applied with CES-like functions overcomes the previous trade-off between flexibility and global regularity. More precisely, they define a class of Regular-Flexible Functional Forms (R-FFFs) which allows the introduction in an equilibrium model of any regular configuration of price and income elasticities. They furthermore illustrate, in the context of a three-input constant returns to scale production function, the relative performance of this family of R-FFFs over well-known FFFs (NQ, TL, GL) (Perroni and Rutherford, 1998). Then our contribution stands within this line of research which, to our knowledge, never really reaches CGE modelling. Our practical objectives in this paper are twofold. Firstly, we detail the implementation of a R-FFF in a typical CGE model (static, perfect competition, etc.), which allows us to capture any regular pattern of price/income effects. We focus our presentation on the representation of households' preferences. Extensions to production technologies, factor mobility, production differentiation by sources are straightforward. Secondly, we once again illustrate the substantial bearing of the specifications of price as well as income effects on CGE results by conducting a carefully designed set of experiments. In that respect, we make use of the simple and well-known CGE model of Harrison et al. (1997). This model is implemented using version 4 GTAP database, and we adopt a commodity/region disaggregation that allows us to introduce robust estimates of price and income elasticities. This paper is organized as follows. The first section briefly reviews the notion of latent separability and some econometric applications of this notion. The second section, which is the core of this paper, details the different steps required to implement an R-FFF. The third section provides an illustration of the applicability of this approach and of its usefulness. Conclusions and qualifications are offered in the final section.

The starting point of this research is the stimulating debate concerning the specifications of price and income effects in CGE models. We detail in this paper a procedure which allows to implement in such models any regular configuration of price and income effects. This procedure exploits the advantages of latent separability. By allowing some overlapping in the grouping of commodities, this separability concept offers much more flexibility than other separability structures since substitution between goods runs through many channels. This paper also provides an empirical illustration which demonstrates the applicability of our procedure. This illustration focuses on the demand side of the economy, and can be easily extended to production, trade or primary factor blocks. We contrast our proposed specification to traditional ones (Cobb–Douglas and Linear Expenditure System) with different experiments. In a general way, these experiments underline the substantial bearing of the specification on sectoral results. The results also suggest that the usefulness of the proposed specification depends on the simulations and the variables of interest. Accordingly, we do not consider our approach as a panacea. For example, if one contemplates one simulation with very strong income variation and very little price variations, then a rank three demand system, such as the AIDADS, may be more appropriate. The main difficulty here is to anticipate what will be the main effects and for many economic analyses conducted with CGE models, these are only revealed ex post. Therefore, we do believe that our proposed approach is potentially a good candidate in multi-sectoral analysis. Last, but not least, it allows reconciling CGE models with results of econometric analysis.