Introducing Firm Heterogeneity in a CGE Model for Europe

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Introducing Firm Heterogeneity in a CGE Model for Europe

Authorsand e-mail of all:

Javier Barbero Jiménez

Francesco Di Comite

Department:

Directorate B – Growth and Innovation, Territorial Development Unit, Edificio Expo, C/ Inca Garcilaso 3, E-41092 Seville/Spain.

University:

European Commission, DG Joint Research Centre (JRC)

European Commission, DG Economic and Financial Affairs (ECFIN)

Subject area: 1. Spatial economic analysis, methods of regional analysis and spatial econometrics

Abstract:

Different methodological approaches have been proposed recently to introduce firm heterogeneity á la Melitz in computable general equilibrium models, thus providing additional depth to the currently popular combination of Armington assumptions and Krugman's new trade theory. However, these extensions have been mainly tested with simulated data or applied to settings characterised by a scarcity of granular data, such as global trade and general economic integration trends. In this paper, we build upon the European Commission efforts to build up Europe-wide Social Accounting Matrices for every EU region and sector and show how a spatial computable general equilibrium model can be enhanced with a heterogeneous-firms module at different levels of spatial aggregation, discussing its data requirements and the computational challenges involved.

The explicit introduction of heterogeneous firms in the picture affects significantly the outcomes of policy simulations for at least two orders of reasons. The first one is related to the channels through which policy shocks affect trade flows, which are in this setting the result of individual decisions of firms across the productivity distribution in ways that can actually partially offset each other. This means that even a shock bringing about overall increases in bilateral trade flows may be the result of the combination of very different patterns, with some firms expanding, others exiting the market. The dynamics generated by such a model are therefore closer to what can be observed empirically in the international trade literature at the firm level. The second concerns within- and between-sectors firm reallocations, as policy shocks can lead the a reduction in the number of firms in sectors characterised by less productive firms and an increase marketshares for sectors characterised by highly productive firms, which in turn bid up input prices and affect firms in all the other sectors and territories. This latter effect cannot generally be observed in analytical general equilibrium models with heterogeneous firms because of the computational complexities linked to the input price response to increases in demand.

A notable example of how to introduce firm heterogeneity á laMelitz in a computable general equilibrium framework can be found in Balistreri and Rutherford (2013), who develop a model where different sectors of the economy are modelled according to the industrial structure assumptions of Armington (1969), Krugman (1980), or Melitz (2003) trade theories. To avoid the computational difficulties usually found in large models with heterogeneous firms due to their dimensionality and non-convexities, they rely on the solution of Balistreri, Hillberry and Rutherford (2011) to use a decomposition algorithm to solve the model by iterating over a Melitz partial equilibrium and an Argminton general equilibrium. By contrast, Dixon, Jerie and Rimmer (2016) develop an Armingon-Krugman-Melitz Encompassing (AKME) model than encompass the three trade theories as particular cases of a general model. Using a different software to solve the model, Dixon, Jerie and Rimmer (2016) do not experience the computational difficulties encountered by Balistreri and Rutherford (2013) and Balistreri, Hillberry, and Rutherford (2011), but still exploit the decomposition algorithm proposed by the latter as a way to interpret Melitz results as the outcome of an Argminton simulation with additional shocks.[1]Roson and Oyamada (2014) use the Metlitz model by Dixon, Jerie and Rimmer (2016) as a starting point and enrich it by including multiple factors and intermediate inputs. Akgul, Villoria and Hertel (2016) integrate the firm heterogeneity model of Dixon, Jerie and Rimmer (2016) into the GTAP Model.

In our model, consumers and firms follows the standard behavioural assumptions employed in models with firm heterogeneity. Consumers are characterized by love-of-variety and preferences take the form of a Constant Elasticity of Substitution (CES) function over a continuum of horizontally differentiated varieties within each sector. Varieties are produced using a composite factor of production, which is an aggregate of value added from primary factors and intermediate inputs. Following Melitz (2003), the production of each variety involves a fixed production cost paid by the firm on set-up and a variable cost inversely related to firm productivity, both in terms of the composite factor of production. Notice that in the standard Melitz (2003) model the set-up costs are a simple sunk cost subtracted from firm profits and the overall economy, but in a computable general equilibrium setting is actually being spent on the purchase of the same composite goods used as a variable cost, implying that set-up costs can be actually interpreted as a reduction in firm productivity affecting all firms equally (at least in levels).As in Melitz (2003), within a given sector and region, productivity is the only dimension of differentiation analysed in this exercise so that all firms with the same productivity behave symmetrically, each one producing unique, horizontally differentiated variety.

In making their business decisions in the model, firms adopt the following timing. First, they observe market conditions and, based on their knowledge of the ex-ante Pareto distribution of firm productivities in their region and sector, they calculate their expected profits after entry. If entry is expected to be profitable, firms pay the fixed set-up cost and discover their actual productivity leveldrawn from the correspondingPareto distribution. At this point, subject to their productivity level, firmshaveto decide whether to continue operating or to exiting the market. When the productivity of firms is lower than what would allow them to make sufficient operating profits to repay the fixed set-up cost, the firm exits the market. On top of set-up costs, firms have to pay a fixed costto operate onaspecific trade link. Set-up and trade-link-specific costs are both expressed in terms of the composite factor of production in computable general equilibrium settings.[2]Notice that the productivity thresholds to operate in each market are then endogenously determined and are time-varying, as changes in overall market conditions (number of competitors and their efficiency levels) can tip individual firms in the distribution from profitability to generating losses. Only firms with productivity higher than the threshold for a specific market will operate in that market. Thus, the combination of the two types of fixed costs in the model implies that, out of the total number of firms observed in each region, a different subset of them is serving each other market of the economy, with the most efficient firms serving the highest number of markets and the least efficient (and smaller) being able to serve only the domestic regional market.

The firm heterogeneity framework á la Melitz (2003) can be reduced to a firm homogeneity framework á la Krugman (1980)by focusing on expected outcomes for average firms and on aggregate market statistics.Given the assumption of firm homogeneity, there are no productivity differences between firms and all firms operating in the same trade link set the same price. Furthermore, no fixed operating costs are assumed, so all existing firms operate in all trade links. With further simplifications, the model can also be reduced to the Armington (1969) assumption, the most widely used assumption in computable general equilibrium models, in which products traded are differentiated by country of origin rather than by variety. Therefore, Krugman (1980) and Armington (1969) can essentially be treated as special cases of Melitz (2003) and the three different trade theories can be incorporated into a full computable general equilibrium model at the same time, with different sectors working under different assumptions.

The introduction of firm heterogeneity in a CGE model is computational challenging as the number of variables and equations increases with respect to when firm homogeneity or the Armington assumption is used. In a model of R regions and S sectors, the number of trade equation is 2 under the Armington assumption, under the Krugman trade theory of homogeneous firms, and if firm heterogeneity is assumed. To get a better idea, in a model of 267 regions, the number of trade related equations under the standard Armington assumption would be 534 per sector, whereas under firm heterogeneity the number of trade related equations would raise to 285,957 per sector.

The trade module is integrated into a full-fledged general equilibrium model that incorporates savings, investment, the government, and the rest of the world. In addition, intra-EU inter-regional bilateral trade costs are sector specific and borrowed from transport models calibrated on micro data.[3] The government collectstaxes from household income and from firm sales, spending it on goods consumption, transfers to households and investment. Investment is modelled thought a virtual investment agent, as it is commonly done in the CGE literature, which collects savings from the households, the government and the rest of the world and invests it in goods from the different sectors.

Regional data at the NUTS 2 level comes from the regionalizedSocial Accounting Matricesfrom Álvarez-Martínez and López-Cobo(2016), and interregional trade data from Thissen et al. (2015). Data on number of firms and survival rates is taken from the EUROSTAT-OECD Business Demography Statistics. A firm is considered to survive if it is still operating business after three years from their entrance into the market.

With a series of policy shocks simulations that are relevant in the European Union policy context, mainly related to transport infrastructure investment targeted at improving market integration and accessibility of the regions, we show how the model performs under the three different trade theories. Focusing on heterogeneous firms, different policy shocks can lead to a within- and to a between-sectors firms reallocations. With regard to the within-sector firm reallocation, policy shocks can lead the less productive firms to exit the market resulting in higher market-sector shares for highly productive firms, which in turn bid up input prices and affect firms in all the other sectors and territories. This feature can only be observed in a heterogeneous firms framework.

References:

Akgul, Z; Villoria, N. B; Hertel, T. W., (2016), GTAP-HET: Introducing Firm Heterogeneity into the GTAP Model. GTAP Journal of Global Economic Analysis, 1(1): 111-180.

Álvarez-Martínez, M.T. and López-Cobo, M. (2016). "National Social Accounting Matrices for the EU-27 in 2010: Building a new database for RHOMOLO," IPTS Working Papers, JRC101673, European Commission, DG Joint Research Centre

Armington P. S., (1969), A Theory of Demand for Products Distinguished by Place ofProduction, IMF Staff Papers, Palgrave Macmillan, 16(1): 159-178.

Balistreri, E. J. & Hillberry, R. H. & Rutherford, T. F., (2011), Structural estimation and solution of international trade models with heterogeneous firms, Journal of International Economics, Elsevier, 83(2): 95-108.

Balistreri, E. J.; and Rutherford, T. F., (2013), Computing General Equilibrium Theories of Monopolistic Competition and Heterogeneous Firms, Handbook of Computable General Equilibrium Modeling, Elsevier.

Dixon, P; Jerie, M; and Rimmer, M (2016), Modern Trade Theory for CGE Modelling: The Armington, Krugman and Melitz Models, GTAP Journal of Global Economic Analysis, Center for Global Trade Analysis, Department of Agricultural Economics, Purdue University, 1(1): 1-110.

Krugman, P, (1980), Scale Economies, Product Differentiation, and the Pattern of Trade, American Economic Review, American Economic Association, 70(5): 950-59.

Melitz, M.J., (2003), The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity, Econometrica, Econometric Society, 71(6): 1695-1725.

Roson, R.; and Oyamada, K., (2014), Introducing Melitz-Style Firm Heterogeneity in CGE Models: Technical Aspects and Implications, IEFE Working Papers 63, IEFE, Center for Research on Energy and Environmental Economics and Policy, Universita' Bocconi, Milano, Italy.

Thissen, M., Lankhuizen, L., and Jonkeren, O. (2015). "Multi-regional trade data on Europe in 2010," PBL Report, 1753, Netherlands Environmental Assessment Agency.

Keywords:Firm Heterogeneity, Trade, Computable General Equilibrium, Modelling, Spatial

JEL codes: C68, D58, F12, R13

[1]Balistreri, Hillberry and Rutherford (2011) and Balistreri and Rutherford (2013) solve the model in levels using the GAMS software, whereas Dixon, Jerie and Rimmer (2016) solve a linear percentage-change representation of the model using GEMPACK.

[2]Alternative ways to determine the composition (and therefore the price) of composite factors of production can be explored and can even be differentiated between variable and fixed costs (and, even within fixed costs, between set-up and trade-link-specific costs). For example, some of these costs may be allocated more capitals goods intermediate consumption, or a higher level of labour intensity. However, the use of a single composite factor of production for the different types of costs simplify the numerical computations without affecting the generality of the results obtained.

[3]See TRANSTOOLS: