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Version 7 of the database, which is benchmarked to 2004, identiﬁes 113 countries and regions and 57 commodities. The IMPLAN data speciﬁes benchmark economic accounts
for the 50 US states (and the District of Columbia). The dataset includes input-output tables for each state that identify 509 commodities and existing taxes. The base year for the IMPLAN accounts in the version we use here is 2006. To improve the characterization of energy markets in the IMPLAN data, we use least-square optimization techniques to merge IMPLAN data with data on physical energy quantities and energy prices from the Department of Energy’s State Energy Data System (SEDS) for 2006 (EIA, 2009).2 Data for trade between regions outside of the US are taken from GTAP and reﬂect bilateral ﬂows from the United Nations Commodity Trade Statistics Database. Bilateral stateto-state trade data in the IMPLAN database are derived using a gravity approach described in Lindall, Olson and Alward (2006).3 As our results depend on benchmark electricity trade ﬂows between California and neighboring states, we replace state-to-state electricity ﬂows from IMPLAN with modeled data from the National Renewable Energy Laboratory’s ReEDS model (Short et al., 2009). The ReEDS model simulates electricity ﬂows between Aggregation and reconciliation of IMPLAN state-level economic accounts to generate a micro-consistent benchmark dataset which can be used for model calibration is accomplished using ancillary tools documented in Rausch and Rutherford (2009).
The IMPLAN Trade Flows Model draws on three data sources: the Oak Ridge National Labs county-tocounty distances by mode of transportation database, the Commodity Flows Survey (CFS) ton-miles data by commodity, and IMPLAN commodity supply and demand estimates by county.
136 Power Control Areas (PCAs) and represents existing transmission constraints. Bilateral US state-to-country trade ﬂows are based on the US Census Bureau Foreign Trade Statistics State Data Series (US Census Bureau, 2010). Bilateral exports and imports are taken from, respectively, the Origin of Movement (OM) and State of Destination (SD) data series.4 The OM and SD data sets are available at the detailed 6-digit HS classiﬁcation level, which permits aggregation to GTAP commodity categories.
We integrate GTAP, IMPLAN/SEDS, and US Census trade data by using least-square optimization techniques. Our data reconciliation strategy is to hold US trade totals (by commodity) from GTAP ﬁxed and to minimize the residual distance between estimated and observed US Census state-to-country bilateral trade ﬂows and estimated and observed SAM data from IMPLAN, subject to equilibrium constraints.
For this study, we aggregate the dataset to 15 US regions, 15 regions in the rest of the world, and 14 commodity groups (see Table 2). Countries identiﬁed in the model include Brazil, Canada, China, India, Japan, Mexico and Russia. EU member states are included in a composite region and several other composites are included for other world regions. The composition of US regions is illustrated in Figure 1. A separate region is included for some states, including California and states that trade electricity with California, but most US regions include several states. Our commodity aggregation identiﬁes ﬁve energy sectors and nine non-energy composites. Primary factors in the dataset include labor, capital, and The OM series does not necessarily represent production location as states with important ports of entry or exit might be over-represented relative to their actual trade specialization. Cassey (2006) uses additional destination-less estimates of state-level trade to test whether the origin of movement is a suitable proxy for production location. He ﬁnds that while there exist signiﬁcant differences at the 6-digit commodity level for some states, the data is generally of good enough quality to represent the state of origin.
Moreover, we argue that our relatively coarse aggregation of commodities and states is likely to smooth out this bias.
fossil-fuel resources. Labor and capital earnings represent gross earnings denominated in 2004 US dollars. The calculation of gross returns to each fossil-fuel resource is outlined in Section 3.2.5.
3.2 The numerical model Our modeling framework draws on a multi-commodity, multi-region static numerical general equilibrium model of the world economy with sub-national detail for the US economy.
The key features of the model are outlined below.
3.2.1 Production and transformation technologies For each industry (i = 1,..., I, i = j) in each region (r = 1,..., R) gross output (Yir ) is produced using inputs of labor (Lir ), capital (Kir ), natural resources including coal,
natural gas, crude oil, and land (Rir ), and produced intermediate inputs (Xjir ):5
For simplicity, we
from the various tax rates that are used in the model. The model includes ad-valorem output taxes, corporate capital income taxes, payroll taxes (employers’ and employees’ contribution), and import tariffs.
We employ constant-elasticity-of-substitution (CES) functions to characterize the production technologies and distinguish six types of production activities in the model: fossil fuels (indexed by f ); reﬁned oil, electricity, agriculture, and non-energy industries (indexed by n). All industries are characterized by constant returns to scale (except for fossil fuels, agriculture and renewable electricity, which are produced subject to decreasing returns to scale) and are traded in perfectly competitive markets.
Fossil fuel f, for example, is produced according to a nested CES function combining a
fuel-speciﬁc resource, capital, labor, and intermediate inputs:
where β is the labor share.
We adopt a putty-clay approach to model capital adjustments. Under this approach, a fraction φ of previously-installed capital becomes non-malleable and frozen into the prevailing techniques of production. The fraction 1−φ can be thought of as that proportion of previously-installed malleable capital that is able to have its input proportions adjust to new input prices. Vintaged production in industry i that uses non-malleable capital is subject to a ﬁxed-coefﬁcient transformation process in which the quantity shares of capital, labor, intermediate inputs and energy by fuel type are set to be identical to those in the
In each region, a single government entity approximates government activities at all levels—federal, state, and local. Aggregate government consumption is represented by a Leontief composite: Gr = min(G1r,..., Gir,..., GIr ).
3.2.2 Consumer preferences In each region r, preferences of the representative consumers are represented by a CES
utility function of consumption goods (Ci ), investment (I), and leisure (N ):
where µ and γ are CES share coefﬁcients, g(·) is a CES composite of energy and non-energy goods, and the elasticity of substitution between leisure and the consumption-investment composite is given by σl,r = 1/(1 − ρcr ).
3.2.3 Supplies of ﬁnal goods and intra-US and international trade With the exception of crude oil, which is a homogeneous good, intermediate and ﬁnal consumption goods are differentiated following the Armington assumption. For each demand class, the total supply of good i is a CES composite of a domestically produced variety and
where Z, C, I, and G are inter-industry demand, consumer demand, investment demand, and government demand of good i, respectively; and ZD, CD, ID, GD, are domestic and imported components of each demand class, respectively. The ψ’s and ξ’s are the CES share coefﬁcients and the Armington substitution elasticity between domestic and the imported
The domestic imported varieties are represented by nested CES functions. We replicate a border effect within our Armington import speciﬁcation by assuming that goods produced within the country are closer substitutes than goods from international sources.
We include separate import speciﬁcations for for US regions (indexed by s = 1,..., S) and international regions (indexed by t = 1,..., T ). The imported variety of good i is
1/(1 − ρSU ) is the elasticity of substitution across US origins. Figures 2 and 3 depict the i nesting structures described by Eqs. (4)–(9).
3.2.4 Equilibrium, model closures, and model solution Consumption, labor supply, and savings result from the decisions of the representative
household in each region maximizing its utility subject to a budget constraint that consumption equals income:
where pi, pc, pk, pV k, pR, and pl, are price indices for investment, labor services, household consumption (gross of taxes), capital services, rents on vintaged capital, and rents of fossil fuel resources, respectively. K, V K, R, L, and T are benchmark stocks of capital, vintaged capital, fossil fuel resources, labor, and transfer income, respectively.
Fossil fuel resources and vintaged capital are sector-speciﬁc in all regions. In international regions, malleable capital and labor are perfectly mobile across sectors within a given region but immobile across regions. In the US, mailable capital is perfectly mobile across US states and, as our model is intended to simulate a "medium-run" time horizon, we assume labor is mobile across sectors but not across states.
Given input prices gross of taxes, ﬁrms maximize proﬁts subject to the technology constraints Minimizing input costs for a unit value of output yields a unit cost indexes
their proﬁt by selling their products at a price equal to these marginal costs.
The main activities of the government sector in each region are purchasing goods and services, income transfers, and raising revenues through taxes. Government income is
aggregate government consumption.
Market clearance equations for factors that are supplied inelastically are straightforward. The other market clearing equations are: (1) Supply to the domestic market equals demand by industry, household, investment, and government, (2) import supply of good i satisﬁes domestic demand by industry, household, investment, and government for the imported variety, (3) trade between all regions in each commodity is balanced, and (4) labor supply equals labor demand.
Numerically, the equilibrium is formulated as a mixed complementarity problem (MCP) (Mathiesen, 1985; Rutherford, 1995). Our complementarity-based solution approach comprises two classes of equilibrium conditions: zero proﬁt and market clearance conditions.
The former condition determines a vector of activity levels and the latter determines a vector of prices. We formulate the problem using the General Algebraic Modeling System (GAMS) and use the Mathematical Programming System for General Equilibrium (MPSGE) (Rutherford, 1999) and the PATH solver (Dirkse and Ferris, 1995) to solve for non-negative prices and quantities.
3.2.5 Elasticities and calibration As customary in applied general equilibrium analysis, we use prices and quantities of the integrated economic-energy dataset for the base year (2004) to calibrate the value share and level parameters in the model. Exogenous elasticities determine the free parameters of the functional forms that capture production technologies and consumer preferences.
Reference values for elasticity parameters are shown in Table 3. Values for Armington trade elasticities are based on GTAP estimates. Given the lack of empirical estimates for
RU DU SUσi, σi, and σi we use a “rule of thumb” that hypothesizes that the value at a given nest is twice as large as the value at the parent nest. That is, we set the elasticity of substitution
simulates a de-facto "border effect", and the within-country trade response will be larger than the international response. Section 4.5 conducts a sensitivity analysis with respect to these parameters.