Development of a Large-scale Single US Region CGE Model using IMPLAN Data: A Los Angeles County Example with a Productivity Shock Application

Abstract This paper details the construction of a large-scale computable general equilibrium (CGE) model for a single US region. The model contains a detailed treatment of margins and taxes, features not typically given prominence in US regional CGE models. The starting point for the core of the CGE model's data base is information from IMPLAN, producers of regional I/O data at the US county and state levels. IMPLAN's I/O tables, however, are in producer prices with aggregated treatment of margins and taxes. The methods for reconfiguring the I/O data into basic price flows with direct allocation of imports and a disaggregated treatment of taxes and margins are described. The method is applied to construction of a Los Angeles County model. An illustrative simulation of a productivity improvement in the Los Angeles County economy is then discussed. Développement d'un modèle GCE (modèle d’équilibre général) à grande échelle pour une région unique des États-Unis, à l'aide de données IMPLAN: un exemple dans le comté de Los Angeles avec une application à choc de productivité Résumé La présente communication illustre en détail la construction d'un modèle informatisé d’équilibre général (GCE) pour une région unique des États-Unis. Ce modèle contient un traitement détaillé de marges et taxes, des aspects auxquels on n'accorde généralement pas une importance prédominante dans les modèles GCE régionaux aux États-Unis. Le point de départ pour la partie essentielle de la base de données du modèle CGE se situe au niveau des informations provenant d'IMPLAN, des producteurs de données d'Entrée/Sortie régionaux à l’échelon du comté et de l’état, aux États-Unis. Toutefois, les tableaux d'entrée/sortie d'IMPLAN portent sur des prix de producteur avec traitement agrégé des marges et des taxes. Les méthodes de reconfiguration des données d'E/S dans des flux de prix de base, avec affectation directe des importations, et un traitement désagrégé de taxes et marges, sont décrits. La méthode est appliquée à la construction d'un modèle du comté de Los Angeles. Une simulation illustrative d'un renforcement de la productivité est ensuite discutée. Desarrollo de un modelo CGE a gran escala para una región estadounidense única utilizando datos IMPLAN: un ejemplo de Los Angeles County con una aplicación de choques de productividad Extracto Este trabajo detalla la construcción de un equilibro general computable (CGE) a gran escala para una sola región estadounidense. El modelo contiene un tratamiento detallado de márgenes e impuestos, características que típicamente no reciben prominencia en los modelos CGE regionales estadounidenses. El punto inicial para el núcleo de la base de datos del modelo CGE es información procedente de IMPLAN, productores de datos I/O (input–output) regionales a los niveles de condado y estado estadounidenses. No obstante, las tablas I/O de IMPLAN aparecen en precios de productores con tratamiento agregado de márgenes e impuestos. Se describen los métodos para reconfigurar los datos I/O en flujos de precios básicos con asignación directa de importaciones y un tratamiento desagregado de impuestos y márgenes. El método se aplica a la construcción de un modelo de Los Angeles County. Seguidamente, se discute una simulación ilustrativa de la mejora de productividad en la economía de Los Angeles County.


Introduction
IMPLAN (Minnesota IMPLAN Group, 1997) is a widely used data resource for undertaking inputÁoutput analysis at the US sub-regional level. ORANI-G (Horridge, 2003) is a widely used template for a detailed single-region CGE model. This paper uses IMPLAN data, together with share and parameter values from USAGE, 1 to construct a single-region CGE model for a small US region. To make ORANI-G (a single country model) suitable for implementation at the small region level, a number of theoretical modifications to the standard ORANI-G framework are necessary. These are described in Section 2. We call the resulting regional model ORANI-R. Section 3 describes the development of the ORANI-R database from IMPLAN data. The specific implementation is Los Angeles County. Section 4 presents an illustrative simulation with the new model: short-run and long-run productivity growth in the Los Angeles County economy.

ORANI-R Model Overview
The well-known ORANI-G model is used as the starting point for the development of a single-region sub-national model, ORANI-R. Full documentation of the theoretical structure of ORANI-G and its antecedent, ORANI, are available in Horridge (2003) and Dixon et al. (1982), respectively. The structure of ORANI-R is identical to that of ORANI-G in all respects other than those outlined in Section 2.2.
ORANI-R is a single-region sub-national comparative-static computable general equilibrium model. The model features detailed sectoral disaggregation. For example, the Los Angeles County implementation developed in this paper covers 436 sectors and 19 margin commodities. Familiar neoclassical assumptions govern the behaviour of the model's economic agents. Decision-making by firms and households is governed by optimizing behaviour. Each representative industry is assumed to minimize costs subject to constant returns to scale production technologies and given input prices. Household commodity demands are modelled via a representative utility-maximizing household. Units of new industry-specific capital are assumed to be cost minimizing combinations of commodities sourced from the local region, the rest of the US and overseas. Imperfect substitutability between local, rest-of-US and foreign varieties of each commodity are modelled via CRESH (Hanoch, 1971) aggregation functions. Inter-regional and foreign export demands for local commodities are modelled via commodity-and destinationspecific constant elasticity export demand schedules. The model recognizes the consumption of commodities by state and federal government. A variety of direct and indirect taxation instruments are identified. Domestic commodity markets are assumed to clear and to be competitive. Purchasers' prices differ from basic prices by the value of indirect taxes and margin services. The model is solved using the GEMPACK economic modelling software (Harrison & Pearson, 1996).

Development of a Sub-national Implementation of ORANI-G
To date, ORANI has only been implemented as a national model. To implement the ORANI model at the sub-national level, new theory must be added to the core model to determine: (i) short-run and long-run regional labour supply; (ii) the price of interstate imports; (iii) the price of interstate exports; and (iv) imperfect substitution between commodity varieties.
These developments are discussed below.
2.2.1. Short-run and long-run regional labour supply. A typical labour market closure for a single-country short-run implementation of the ORANI model assumes endogenous national employment with an exogenous real consumer wage. This setting is suitable for short-run modelling of countries with centralized wage setting arrangements and moderate or high unemployment. It is less suitable in situations of decentralized wage setting and low unemployment. As such, the single-region US implementation of ORANI-G proposed in this paper establishes a regional labour market theory and closure that allows simultaneous stickiness in short-run employment and wages. This better-reflects a short-run situation of low unemployment, stickiness in regional migration, and wage flexibility: characteristics of the typical US labour market. 2 The following equations describe the regional labour market: where: pprate is the percentage change in the regional participation rate; realwage is the percentage change in the regional real wage; f PPRATE is a shifter on Equation (1), typically exogenous; emprate is the percentage change in the regional employment rate (1Áthe unemployment rate); f EMPRATE is a shifter on Equation (2), typically exogenous; hours is the percentage change in hours worked per worker; f HOURS is a shifter on Equation (3), typically exogenous; pop is the percentage change in the regional population; frealwage is a vertical (regional wage premium) shifter on Equation (4); f POP is a shifter on Equation (4); shwrkage is the percentage change in the share of the regional population that is of working age; employ is the percentage change in regional employment; a PPRATE is the elasticity of the regional participation rate to the real wage; a EMPRATE is the elasticity of the regional employment rate to the real wage; a HOURS is the elasticity of hours worked per worker to the real wage; and a POP is the elasticity of regional population to the real wage.
A short-run closure of Equations (1)Á(5) has f PPRATE , f EMPRATE , f HOURS , frealwage, pop and shwrkage exogenous, with pprate, emprate, hours, f POP and employ endogenous. realwage is determined endogenously in ORANI-R, but largely outside the system of Equations (1)Á(5). Under this labour market closure, regional population is fixed. This largely ties-down regional employment via Equation (5). However, some scope for short-run regional employment change is nevertheless provided by Equations (1)Á(3). These allow for short-run movements in participation, the employment rate, and hours worked per worker, in response to movements in the real consumer wage. The long-run labour market closure is identical to the short-run closure in all respects other than provision for regional population to be a positive function of the regional real wage via activation of Equation (4). Equation (4) is activated by exogenous determination of f POP and endogenous determination of pop. Note that Equation (4) can be interpreted as modelling long-run location preference in household decision making, since a POP can be interpreted as the reciprocal of the percentage change in the regional wage required to induce a one percentage point movement in regional population.
2.2.2. The price of interstate and foreign imports. To reflect the large size of the US economy as a whole, we begin by assuming that foreign import supply schedules to the USA are upward sloping. As such, foreign import supply schedules to any region in the USA are also upward sloping. In like fashion, we assume that interregional import supply schedules to any region within the USA are upward sloping. This reflects resource constraints in the rest of the US economy. We implement upward sloping import supply schedules for each commodity, c, via Equation (6): c;s ðs ¼ rest-of -US; foreignÞ ðt ¼ short-run; long-runÞ (6) where: is the reciprocal of the elasticity of supply of imported commodity c from source s over length of run t. For g t c;foreign we use USAGE database values for the elasticity of US foreign import prices to US import demand. For g short-run c;rest-of -US we derive short-run US commodity-specific supply elasticities from the USAGE database via the formula of Dixon et al. (1982, p. 309). For long-run applications, we set g short-run c;rest-of -US at one third of its short-run value. This reflects long-run elasticity of capital supply to industries in the rest of the US; GRP r =GDP US is the ratio of regional GDP in the region for which the ORANI-R model is implemented relative to total US GDP. For example, in the Los Angeles County implementation reported in Sections 3 and 4, this value is 0.037; and x ð0Þ c;s is the percentage change in demand for commodity c from source s.

Imperfect substitution between commodity varieties.
The ORANI-G model identifies two commodity sources: domestic and foreign. ORANI-R identifies three commodity sources: local, inter-regional and foreign. In ORANI-R, imperfect substitution between competing sources for the same commodity is modelled via CRESH aggregation functions (Hanoch, 1971). 3 2.2.4. Interstate and foreign export demand. Prices of regional exports, foreign and domestic, are determined via constant elasticity export demand functions, as follows: In evaluating g ð4Þ c;RUS , we assume that agents in the rest of the US (RUS) face CRESH substitution possibilities across three commodity sources: the ORANI-R region, the rest of the US, and overseas. This is consistent with the modelling of commodity sourcing for agents within the region of ORANI-R implementation (see Section 2.2.3 above). With demands for the region's commodities determined via CRESH aggregation functions in the rest of the US, demands for the region's exports in the rest of the US (RUS) are determined by where, Assuming x ðRUSÞ c is independent of activity in the region of focus, Equation (8) implies an inter-regional export demand elasticity for good c of: In evaluating Equation (9), the CRESH substitution elasticity on cross-border intra-US sourcing in the rest of the US r ðRUSÞ c;interregional is set at the same value as that in the region of focus. 5 The share of the f.o.b. price of c in the purchaser's price U ð4Þ c;RUS is set at 0.8. The share of c in the rest of the US that is sourced from the region of focus S ðRUSÞ c À Á is evaluated via comparison of USAGE values for US demand for c and IMPLAN values for inter-regional exports of c by the region of focus.
In evaluating g ð4Þ c;foreign , use is made of commodity-specific export demand elasticities from the economy-wide model USAGE. At the same time, a floor is placed on the potential elasticity value via an assumption that agents in other countries face CES inter-regional substitution possibilities. Hence, g ð4Þ c;foreign is set via: where: A floor of (6.4 is set on foreign export demand elasticities by reference to Anderson et al. (2008). They show that if foreign agents face sourcing substitution possibilities described by the World Bank's LINKAGE model (van der Mensbrugghe, 2005), the minimum export demand elasticity is given by / ð2Þ i is the elasticity of substitution between alternative foreign sources of supply for imported good i, and S FOB i is the share of the f.o.b. price in the foreign country purchaser's price of good i (see Anderson et al., 2008, pp. 29Á31). A typical LINKAGE value for / ð2Þ i is 8. With S FOB i set at 0.8, this establishes the (6.4 floor on commodity-specific foreign export demand elasticities in Equation (10).

Construction of an ORANI-R Database from IMPLAN Data
The ORANI-R model described in Section 2 has the following characteristics: (1) the structure of capital formation is distinguished by industry; (2) there are three sources of commodity supply: local, rest-of-US, and foreign; (3) there are two export destinations: rest-of-US, and foreign; (4) public consumption is distinguished by whether it is undertaken by the regional government or the federal government; and (5) purchasers' prices differ from basic prices by the value of margins and indirect taxes.
An initial solution to such a model is provided by a balanced inputÁoutput table with the following characteristics: (1) a basic price valuation basis; (2) use of services as margins distinguished from direct use of those commodities; (3) investment demand disaggregated by industry; (4) public consumption demand, distinguished by level of government; (5) export demand, distinguished by destination; and (6) commodity, source and user specific taxes and margins.
Such an inputÁoutput table is described by Figure 5. Sections 3.1Á3.5 describe steps in constructing such a table, using IMPLAN producer price tables and relevant shares from the USAGE database. Figure 1 reports the structure of the most disaggregated single-region inputÁoutput table that can be extracted from IMPLAN data. The table is at producer prices, with disaggregated treatment of imports but aggregated treatment of margins. Figure 1 is evaluated using input from the IMPLAN 26 file report, the structure of which is described in the MIG IMPLAN Technical Report TR-98002, pp. 3Á4 (Minnesota IMPLAN Group, 2009). Table 1 describes the mapping between the components of the IMPLAN SAM tables and Figure 1.

Step 1: A Single Region Producer Price IO Table from IMPLAN
The IMPLAN data follows a producer price valuation basis, and does not distinguish use of commodities as margin services from their direct use. The IMPLAN data are based on BEA national IO data. As such, they replicate the misallocation of indirect taxes in the BEA national IO data. In the BEA IO data, most indirect taxes are attributed to the institutions collecting the taxes, not the institutions producing the commodities on which the taxes are levied, as conventionally required by a producer price valuation basis. Hence, most taxes appear on output of the retail and wholesale margin industries (Dixon & Rimmer, 2002). To allow this tax misallocation to flow into the CGE database will cause at least two problems when the CGE model is used for applied policy analysis: (a) CGE model results for welfare measures will be incorrect, because indirect tax wedges are allocated to the wrong commodities; and (b) CGE model results for shocks to indirect tax rates will generate perverse industrial composition effects.
Correction of BEA misallocation of indirect taxes is among the tasks in transforming the IMPLAN data described by Figure 1 to the ORANI-R data described by Figure 5. The following sections describe how: (a) the IMPLAN producer price table is converted to a basic price table; (b) independent data are used to re-estimate tax rates and generate tax matrices; and (c) independent data are used to estimate margin matrices.
Step 2 begins by converting the IMPLAN data to a basic price valuation basis.

3.2.
Step 2: Conversion of the IMPLAN Producer Price Table to a Basic Price Table   Figure 2 describes a single region inputÁoutput table, valued at basic prices, with disaggregated treatment of imports and aggregated treatment of margins. In moving from Figure 1 to Figure 2, we begin by noting that in Figure 1 VPRDMAKE c; j is the value at producer prices of output of commodity c by industry j. We begin by defining TAXMAKE c; j , the value of indirect taxes in the make matrix, as: where VTOT1 j is the value at producer prices of industry j's output, defined as: We define the make matrix valued as basic prices, VBASMAKE c; j , as: Next, we define TAXRATE c , a vector of commodity-specific tax rates (defined as shares of producer values represented by indirect tax), implicit in the initial IMPLAN data:  We define an array of tax payments on source-specific commodities VTAX1 c,s,j . Tax payments on locally sourced commodities are defined as: Given the format of the data in Figure 1, we have insufficient information to retrieve a tax matrix on domestic and foreign imports. A proportion of the tax currently allocated to retail and wholesale trade is likely to be tax collected on imports. As such, the matrices VPRD1 c,foreign,j and VPRD1 c,rest-of-US,j must already be close to a basic price valuation basis. Hence, for the moment we assume: Intermediate flows at basic prices are now defined as: We define tax payments on sales of locally sourced commodities to final demand as: Again, we have little information on which to form a judgement on tax paid by final demanders on commodities sourced from the rest of the US or overseas. As such, we initially assume: Purchases by final demanders at basic prices are now defined as: completing the evaluation of all arrays in Figure 2. (b) margins are directly allocated to margin commodity sales in the matrices VBAS1 and VBASF; and (c) investment does not have an industry dimension.
In Step 3 we make a first effort at margin disaggregation. Figure 3 describes a single region inputÁoutput table, valued at basic prices, and with disaggregated treatment of imports and incomplete margin disaggregation. In Figure 3, the basic value of use of margin commodity m by producers ðVMAR1 m;j Þ and final demanders VMARF ðAÞ m;j has been removed from the basic value flow matrices VBAS1 c,s,j and VBASF ðAÞ c;s;t , respectively. As such, for c0m, VBAS1 c;s;j and VBASF ðAÞ c;s;t contain only direct use of c. Use of c as a margin service appears in the rows of ðVMAR1 m;j Þ and VMARF ðAÞ m;j . Generation of Figure 3 is described below. We define MARSHARE m,u as the share of commodity m by user u that is margin use of m, by user u (u# USER). USER, a new set of length 8, is comprised of all elements of FINA plus one new element, industry. MARSHARE m,u is evaluated from the full 500 sector USAGE database (Dixon & Rimmer, 2002). The USAGE database shares a very similar disaggregated structure to that described by Figure 5. Moreover, in the work of Dixon & Rimmer, the creators of the USAGE database, substantial effort has gone into considered evaluation of detailed US tax and margin matrices. As such, the USAGE database is an excellent source for the shares required to reconfigure the data presented in Figure 1 to a format described by Figure 5. The construction of the USAGE database is described in Dixon & Rimmer (2002).

Step 3: Preliminary Identification of Margin Matrices
Using MARSHARE m,u , we define the margin matrices VMAR1 m,j and VMARF   In Step 4, the investment column of Figure 3 is disaggregated in the industry dimension.

Step 4: Disaggregation of Investment by Industry
In Figure 3  disaggregated treatment of imports, identification of investment by industry, and incomplete margin disaggregation. We begin by calculating aggregate regional investment in the IMPLAN database, ITOT:  (27) We define industry-specific investment/capital ratios, IKR j . These are evaluated using USAGE database values. Using IKR j , we calculate target values for investment by industry I j as follows: The USAGE database recognizes that inputs to capital formation differ across industries. Using USAGE database shares, we calculate B2 c,s,j , the share of industry j's investment represented by the basic value of inputs of commodity c from source s. 6 B2 c,s,j is then used to calculate initial values for the basic values of inputs to industry j's capital formation as follows: To calculate investment tax matrices, we begin by evaluating from the USAGE database T2 c,s,j , the rate of indirect tax on inputs of source-specific commodity c,s to capital formation by industry j. T2 c,s,j is then used to calculate initial values for indirect tax collected on inputs to capital formation as follows: To calculate investment margin matrices, we begin by evaluating from the USAGE database M2 c,s,j,m , the ratio of use of margin commodity m to the basic value of inputs of source-specific commodity c,s to capital formation by industry j. M2 c,s,j,m is then used to calculate initial values for margin services required to facilitate purchases of source-specific inputs to capital formation by each industry as follows: Our manipulations in Step 4 introduce a small amount of imbalance to Figure 4. The imbalance arises because, in applying USAGE shares to assumed values for industry-specific total investment, we have as yet done nothing to ensure that the sum across investors of source-specific commodity demands corresponds to the values given in Figure 3. In compiling the database, one option might be to reimpose balance at this step. However the imbalance introduced in this step has no direct consequences for subsequent data manipulations. Hence, we leave correction of the imbalance for the end of Step 5. Otherwise, the database described by Figure 4 has two limitations: (a) indirect taxes remain miscalculated for all non-investment users, since they continue to reflect the BEA/IMPLAN misallocation of indirect taxes to retail and wholesale trade; and (b) margins are separately identified, but are allocated to source-specific commodity flows for investment users only. In Step 5, we seek to improve the tax and margin matrices relating to intermediate input purchases and final demands.

Step 5: Construction of Tax and Margin Matrices Related to Intermediate Inputs and All Remaining Final Demand Categories
At the beginning of Step 5, taxes on intermediate inputs VTAX1 c;s;j and purchases by final users other than investors VTAXF ðBÞ c;s;j ) continue to reflect the implicit BEA/IMPLAN rates derived in Step 2. As such, both VTAXI c,s,j and VTAXF ðBÞ c;s;j presently reflect the misallocation of indirect taxes discussed in Section 3.1. In Step 5, we re-evaluate VTAX1 c,s,j and VTAXF ðBÞ c;s;j . We begin by evaluating from the USAGE database two arrays of indirect tax coefficients: T1 c,s,j the rate of indirect tax on inputs of source-specific commodity c,s to current production by industry j; and TF c,s,t the rate of indirect tax on purchases of source-specific commodity c,s by final user t. 7 Next, T1 c,s,j and TF c,s,t are used to calculate initial values for indirect tax collected on inputs to current production and final demand as follows: To calculate matrices of margins on inputs to current production and purchases by final users other than investors, we begin by evaluating two arrays of margin coefficients from the USAGE database: M1 c,s,j,m the ratio of use of margin commodity m to the basic value of inputs of sourcespecific commodity c,s to current production by industry j; and MF c,s,t,m the ratio of the use of margin commodity m to the basic value of purchases of source-specific commodity c,s for use by non-investor final user t.
Next, M1 c,s,j,m and MF c,s,t,m are used to calculate initial values for margin services required to facilitate purchases of source-specific inputs to current production and non-investment final demands as follows:  Figure 5 is to individually identify the basic value flows to non-investor final demands, as follows: The input data for the table described by Figure 5 (namely, Figure 4

) began
Step 5 imbalanced. Inputting the new matrices described by Equations (32)Á(49) generates further imbalance in the dimensions of: industry costs, individual final demand totals, and the values of margin commodity sales. The final database manipulation is re-imposition of balance, via either bi-proportional scaling, or a simultaneous equation simulation such as described by Horridge (2004Horridge ( , 2009.
Step 5 brings us to the end of our inputÁoutput table manipulations: Figure 5, a balanced disaggregated basic price table representing an initial solution to the ORANI-R model. For this paper, Steps 1Á5 above have been applied to 2007 IMPLAN data for Los Angeles County to produce a 436 sector, 19 margin ORANI-R model. In Section 4, we use this model to investigate the consequences for the LA County economy of primary factor productivity growth.

Simulation Design
We simulate a 1% improvement in primary factor productivity in all LA County industries other than dwellings services. The short-run and long-run impacts on LA County of such productivity improvement are reported in Tables 2 and 3. We choose productivity improvement as our illustrative simulation because it is a supply-side shock. IMPLAN data are typically used for regional input/output impact assessments. Input/output models are not suitable for analysis of supply-side shocks.
The short-run and long-run labour market closures are as described in Section 2.2.1. In both the short-run and long-run, household consumption spending is assumed to be a fixed proportion of household income.
In the short-run, industry-specific capital stocks are exogenous, with industryspecific rates of return on capital adjusting to clear industry-specific capital markets. In the long-run, rates of return on industry-specific capital are exogenous, with industry-specific capital stocks endogenous. Long-run industry-specific investment is determined via an assumption of exogeneity in industry-specific gross capital growth rates.
In the short-run, regional and federal government real public consumption spending are exogenous. In the long-run, the ratio of regional and federal government real public consumption spending to real regional private consumption spending is exogenous.

Short-run Consequences of a 1% Improvement in Primary Factor Productivity
The shock is a 1% improvement in the productivity of primary factors used in all Los Angeles County industries other than dwellings services. In the short-run, industry-specific capital stocks cannot adjust to the shock. Via Equation (5), shortrun employment is largely tied-down via the exogeneity of regional population. In the absence of any movement in regional factor employment, a 1% primary factor productivity improvement should increase regional real GDP by 1% (row 1, Table  2). However, with regional employment sticky via short-run exogeneity of regional population (row 4), the productivity improvement causes the regional real consumer wage to increase (row 13). Via Equations (1)Á(3) this induces small short-run increases in hours worked per worker, participation rates, and employment rates. This accounts for the small short-run increase in regional employment (row 3). The short-run increase in regional employment is responsible for real GDP increasing by more than the one percentage point attributable to productivity growth alone (row 1). With capital stocks fixed (row 2), but productivity and employment rising, rates of return on physical capital increase. This accounts for the short-run increase in real investment (row 4). Real private consumption is linked to real income. With real GDP higher (row 1) so too is real regional income. This accounts for the short-run increase in real private consumption spending (row 6). With regional economic activity higher than it would otherwise have been, so too are inter-regional and overseas imports (rows 10 and 11, respectively). Note that real public consumption spending is unchanged (row 7). As such, real GNE (rows 5Á7) increases by less than real GDP (row 1). This requires the regional real balance of trade to move towards surplus. Hence, the increases in real regional exports (rows 8 and 9) exceed the increases in real regional imports (rows 10 and 11). Movement towards surplus in the real regional balance of trade requires the regional price level to fall relative to the external price level (row 14). The expansion in regional export volumes involves movement down fixed interregional and international export demand schedules. Hence regional export price falls. The expansion in foreign and inter-regional imports exerts slight upward pressure on regional import prices. Together, these regional trade price movements cause the regional terms of trade to decline relative to what they would otherwise have been (row 15). The decline in the regional terms of trade explains why the increase in real private consumption (row 6) is less than the increase in real regional GDP (row 1). The LA County implementation of ORANI-R, ORANI-LA, contains 436 industries. Table 3 reports results for these industries aggregated to 15 broad sectors. Consistent with the uniform 1% improvement across industries in primary factor productivity, most industries expand by a little more than 1%. A notable exception is Dwellings (row 10), which experiences no expansion in output. This reflects the exclusion of this sector from the general increase in productivity experienced by all other sectors. Public administration (row 15) also experiences little output expansion. This reflects the exogeneity of aggregate real public consumption spending (Table 2, row 7). Prospects for the regional Construction sector (row 4) are largely determined by regional investment (row 5, Table 2). With regional real investment expanding by less than real GDP, the regional Construction sector is among the sectors experiencing the lowest expansion in output.

Long-run Consequences of a 1% Improvement in Primary Factor Productivity
Column 2 of Tables 2 and 3 report the long-run impacts on the LA County economy of improved primary factor productivity. In the long-run, the regional capital market closure is equivalent to an assumption that the regional economy can source as much capital as required at exogenously determined real rates of return. In the long-run, Equation (4) is activated via exogenous determination of f POP and endogenous determination of pop. With very high values for a POP , this is almost equivalent to an assumption that the regional economy can source as much labour as required at an exogenously determined real regional wage. However, to reflect location preference, and some feedback to the national real wage from the regional economy, a POP is set at a high, but not infinite, value. 8 With exogenous regional rates of return, and near exogeneity of the regional real consumer wage, the increase in primary factor productivity generates sizeable long-run increases in employment of capital (row 2) and labour (row 3). However expansion of the long-run regional economy is limited by two factors. First, via Equation (4), the regional real wage must rise to attract population from outside the region. This accounts for the long-run increase in the LA County real wage (row 13). Second, expansion of the regional economy causes the regional terms of trade to decline (row 15) damping the potential increase in the values of the marginal product of capital and labour.
The increase in LA County primary factor productivity is projected to increase LA County real GDP by 3.1%. Just under one percentage point of this increase is directly attributable to the rise in primary factor productivity. The remainder is due to increased employment of capital (row 2) and labour (row 3). The capital/labour ratio increases slightly (compare rows 2 and 3) because the long-run regional real wage must rise to attract population to the regional economy (row 13).
Long-run private consumption is assumed to be a fixed proportion of long-run regional income. Hence, with long-run real regional GDP higher, so too is regional private consumption (row 6). However expansion of the long-run regional economy is associated with import and export expansion (rows 8Á11) and thus long-run terms of trade decline (row 15). This damps the increase in real (CPI-deflated) income relative to real GDP. This explains why the increase in private consumption (row 5) is less than the increase in real GDP (row 1). The long-run ratio of public to private consumption spending is exogenous. Hence the long-run percentage change in public consumption spending (row 7) is the same as that for private consumption spending (row 6). Hence the increase in real public consumption spending is also less than the increase in real GDP. Long-run industry-specific investment/capital ratios are exogenous. This accounts for why the increase in aggregate real investment (row 5) is very similar to the increase in the aggregate capital stock (row 2). Since productivity growth is contributing about one percentage point to the increase in real GDP (row 1) the increase in the capital stock (row 2), and thus so too, investment (row 4), must be less than that of real GDP (row 1). Hence, with real investment, real private consumption, and real public consumption all rising by less than real GDP, the real balance of trade must move towards surplus (rows 8Á11).

Conclusions
Computable general equilibrium models of sub-national regions are of three types: top-down multi-regional, bottom-up multi-regional, and bottom-up single region. The ORANI-R model developed in this paper is of the latter type. Multi-regional models, whether bottom-up or top-down, are particularly valuable where policy focus is on both the national and regional consequences of an economic shock. However, regional policy makers are often interested in analysis of economic impacts within a single region of focus only. In such cases, maintenance of the modelling overhead associated with a fully integrated multi-regional model may be unnecessary. Where there is interest in results for only one region of a multi-regional model, the benefits of the full multi-regional model lie chiefly in correct modelling of movements in this region's factor prices, factor supplies, import prices and export prices. As discussed in Section 2 of this paper, a satisfactory closure of regional factor markets and foreign and inter-regional commodity markets can be achieved in a single-region setting without resorting to the full complexity of an integrated multiregional model. That is, the functioning of a single regional economy within a multiregional environment can be replicated in a single-region model via appropriate modelling of import-supply schedules, export demand schedules, and regional factor supply schedules. This is achieved in this paper via additions to the theory of the wellknown and widely used template for detailed single-region CGE modelling, ORANI-G. Using data from IMPLAN, a widely used data resource for undertaking inputÁoutput analysis at the US sub-regional level, the regional CGE model was implemented for Los Angeles County. However, the data construction algorithm underlying the production of the LA-County database will accept input for any IMPLAN region, making the procedure readily generalizable to construction of a single-region bottom-up CGE model for any US region for which IMPLAN produces inputÁoutput data. This marriage of two widely used modelling resources*IMPLAN and ORANI-G*represents a substantial reduction in entry barriers to bottom-up CGE modelling of US regions.