Supporting Information

1. Overview of Computable General Equilibrium Models

We present a brief description of the computable general equilibrium (CGE) method, followed by some specifics of the model. The basic CGE economic model consists of households and producing sectors, linked to one another and the rest of the world through commodity and factor markets. The rest of the world includes both domestic trade and foreign trade.

Profit-maximizing, price-taking firms employ capital, labor, and intermediate inputs to produce their outputs in a continuous, nonreversible, and bounded process. Outputs from each sector may be used as intermediate goods in production by other sectors, sold in regional markets and exported out of the region to domestic or foreign markets, while regional production is differentiated from aggregate imports following Armington (1969). Capital and labor are homogeneous, perfectly mobile within the region, and defined in service units per period. Substitution between regional supply and aggregate exports is given by constant elasticity of transformation (CET) functions as are the substitution possibilities between exports to domestic markets and exports to foreign markets. Firms smoothly substitute over primary factors as represented by constant elasticity of substitution (CES) functions, but employ intermediates in fixed proportions through Leontief functions.

Households are differentiated by their income category and demand composites of regionally produced goods and imports, where imperfect substitution possibilities are given by nested CES functions. Household demands are governed by CES functions over aggregated goods, in which the prices consumers face are indices of aggregate import and domestic prices, with domestic and foreign import prices taken exogenously. Substitution possibilities in demand between foreign and domestic imports are also governed by CES functions. Household incomes are derived through a two-stage process. Households are endowed with varying amounts of labor and capital. These factors are exchanged in factor markets, and through production generate value added. Value added expenditures flow first to the factor "institutions", and are then redistributed to households. Total factor payments to households from value added are net of factor taxes, depreciation allowances, rents attributable to the factor (which are distributed to households from corporations through enterprise income), and labor payments out-of-region.

Government behavior is admitted to the model in two layers: a Federal level and an aggregated State and Local government level. Government entities operate according to a balanced budget, produce and consume goods and activities related to tax and trade. Government revenues are from taxes (indirect business taxes, primary factor taxes, and income taxes all taken as fixed proportions of output), sales of governmentally produced commodities, and government borrowing and transfers. These revenues are then redistributed in lump sum to both consumers and producers.

Equilibrium conditions follow de Melo and Tarr (1992). Model closure follows Waters, Holland and Weber (1997) and Coupal and Holland (2002) in which net financial inflows (from foreign and domestic sources) adjust to balance the regional investment savings balance. The model specification follows standard methods as given by de Melo and Tarr (1992). We expand the de Melo and Tarr (1992) model to account for effects on firms’ production functions following a dreissenid invasion through sector specific factor productivity shocks that enter into the firms’ primary cost functions.

2. Model Specification

The model is a regional general equilibrium model consisting of nine sectors. The regional economy is modeled as a system of interacting institutions. The interactions come through product and factor markets, government redistribution schemes, and financial allocations (savings and investments). Institutions consist of heterogeneous household groups, industrial sectors, factors of production, and levels of government, all making optimal choices while linked to one another through the process of exchange.

Regional Production

For all producing sectors (given by the set i), the dual specification of cost minimization takes place through a bi-level nest. Primary factors and intermediate inputs are assumed to be strictly separable, and aggregated in the first level of the nest by a Leontief production function to produce output:

(S1)

Intermediate inputs from j, Vji (i≠j), are employed as fixed proportions aji of regional output DYi. Firms smoothly substitute over primary factors (capital Ki and labor Li) in the second level of the nest by means of CES value-added functions, VAi.

Under the assumptions of additively separable primary factor and intermediate costs, constant returns to scale, and perfect competition each industry minimizes costs subject to their respective production function. Through cost minimization the cost function of each industry CVi can be derived as a summation of primary factor costs PVCi, intermediate costs INTCi, and indirect business taxes IBTi. The Leontief assumption in technology implies that the cost function is additively separable in its primary and intermediate cost components:

(S2)

Primary factor costs PVCi for each sector i are derived to be:

(S3)

PVCi are a function of regional output DYi, regional rental rate of capital R, and the regional wage rate W. They are also dependent upon value added distribution parameters di, industry specific partial elasticities of substitution in value added si, and industry specific value added efficiency parameters fi.

The influence on industry costs by a dreissenid invasion is introduced to the model through factor productivity changes. Following an invasion, affected industries respond by installing mitigation equipment and hiring people to monitor and control the effects, leading to efficiency losses. The dual equivalent of these factor productivity shocks enter into the primary factor cost PVCk [1] functions’ efficiency parameters,

(S4)

where is the percentage change in industry k primary costs induced by the mussel invasion and is the sector’s efficiency parameter in the absence of any cost impacts. Sector specific factor demand functions can be readily derived by an application of Shepard's Lemma to the cost function, given output and factor prices.

Product differentiation is introduced to the supply side (for all sectors) through the use of constant elasticity of transformation (CET) functions following De Melo and Tarr (1992). Industry output for all sectors is allocated to regional consumption, XDi, or export (in aggregate to foreign and domestic markets), XEi, through constrained maximization of industry revenues given regional prices PDi and export prices PEi, subject to a CET function with substitution possibilities governed by elasticities of transformation. The CET function and resultant first order conditions determine the mix of goods allocated for regional consumption and exports:

(S5)

and

(S6)

The optimization allows for substitution between production for regional and export markets, driven by the relative prices of regional goods and exports, and the magnitude of substitution possibilities given by the elasticity of transformation siT (where i are distribution parameters and fiT are efficiency parameters). Regional producer prices PXi are composites of domestic and export prices.

Regional Demand

Regional demand is composed of household, investment, (regional) intermediate, and government demands. Households are assumed to have identical, homothetic within group preferences, where a "representative individual" maximizes a CES utility function over regionally and out-of-region produced goods, given endogenous income and prices:

(S7)

where XHih are household h demands for goods i, PQi the composite price of good i, HHIDh disposable income of h, HDSAVh total savings of h, and hhIMP are h’s expenditures on noncomparable imports. The ai,h are household group h's distributional share parameters for goods, and shH are household specific partial elasticities of substitution between goods. From the constrained utility maximization, optimal demand functions for the commodities are obtained that fulfill the necessary restrictions and are therefore "continuous, nonnegative and homogeneous of degree zero (in absolute prices)" (de Melo and Tarr, pg 43). Disposable household incomes are gross incomes net of household taxes, and with myopic decision makers, household savings are determined as a constant proportion of income net of exogenous expenditures on noncomparable imports.

Household incomes are derived through a two-stage process. Households are endowed with varying amounts of labor and capital. These factors are exchanged in factor markets, and through production generate value added. Value added expenditures flow first to the factor "institutions", and are then redistributed to households. Total factor payments to households from value added are net of factor taxes, depreciation allowances, rents attributable to the factor (which are distributed to households from corporations through enterprise income), and labor payments out-of-region.

Product differentiation in aggregate demand for all sectors Qi is achieved through the use of the "Armington assumption" (Armington 1969). Regional households and firms demand a composite of regional goods QDi consisting of domestic production, government supply, inventories, and imports QMi, where the differentiation is assumed to occur in perfectly competitive international markets. The blend of regional and imported goods is found through households minimizing the costs of meeting their composite commodity demands, given regional prices PDi and import prices PMi and substitution possibilities (from CES functions with elasticity of substitution siC). The CES functions and resulting first order conditions determine the mix of imports and regional production:

(S8)

and

(S9)

where i are distribution parameters and fiC are efficiency parameters.

The remaining components of demand, investment Ii, intermediate demands Vji, and government demands are modeled as fixed proportions of output. Demand prices of all goods are indices of import and regional prices, with import prices taken exogenously (following the "small" country assumption).

Government

Federal, state, and local governments operate under balanced budgets, produce and consume goods, and tax trade related activity. Government revenues are from taxes, sales of governmentally produced commodities, and government borrowing and transfers. These revenues are redistributed in lump sum to both consumers and producers to maintain a balanced budget.

Tax revenues are from indirect business taxes, primary factor taxes, and income taxes. Taxes are taken as fixed proportions of output. Indirect business taxes include sales and excise taxes, and other regionally specific taxes paid through day-to-day operations of industry (not including net income taxes). Profits are taxed similarly, found as a fixed proportion of rents to the factors of production. Factors are taxed according to the value of their employment. Labor, or payroll, taxes are determined from industry payments to labor while capital taxes are found in the same fashion.

The final sources of tax revenues are from household income taxes. Households are taxed on their gross incomes at differing rates, according to their income group. Government revenues are further supplemented through sales of government commodities, government interest received and amounts that the government borrows.

Expenditures by government are for government demand for commodities, transfers to households, and transfers to producers. A balanced budget is maintained through a balance of total revenues and expenditures.

Equilibrium

The system is in general equilibrium when all individuals of all sectors optimize, there exists a set of prices and level of output at which all firms just break even, Walras’ Law holds, and all markets clear. In commodity markets, total demand is comprised of household demand, intermediate demand, investment, government demand, and exports. Total supply comes from regional output, imports, intermediate supplies, and government supplies. Factors are supplied by households and demanded by firms. Simultaneously, given the set of market clearing prices consumers’ expenditures exhaust disposable income following Walras’ Law, there is a balance of trade in the current account, and the government preserves a balanced budget. In general, closure rules focus around the relationship in the model between savings, investment, and labor market clearing. Herein, the model is closed by net financial inflows (from foreign and domestic sources) adjusting to balance the regional investment savings balance (Waters, Holland and Weber, 1997, and Coupal and Holland, 2002). The model has 51 equations and variables, not accounting for differences in only variable and parameter indices. The system is solved using the mathematical programming software GAMS and the PATH solver.

3. Data and Parameterization

The model is based on a benchmark of 2001. The benchmark dataset is taken from an IMPLAN (MIG, 2004) derived social accounting matrix (SAM) for all counties in the Columbia River Basin, shown in Table S1. The region’s SAM is displayed in Table S2 with each account’s (numbered on the rows) receipts in rows and expenditures in columns.

Though deficient in many areas, IMPLAN data is the industry standard, it is more comprehensive than any other source and provides a decent building block. The industry sectors were aggregated down from IMPLAN's 509 sectors to eight sectors. These sectors consist of irrigated agriculture, other agriculture, fish hatcheries, independent power, municipal water, federal power, state & local power, and miscellaneous (a catchall for all other productive sectors in the region). IMPLAN differentiates households according to income class, and this classification was maintained. The federal government’s interactions with the state were kept distinct while city, county, and state governments were aggregated into a single institution labeled state and local government. Given the importance of trade flows into and out of the region, foreign and domestic trade were aggregated into a single sector.

The base IMPLAN dataset necessarily underwent some modification. Primary factors of labor and capital were disaggregated. IMPLAN’s employee compensation account was used to construct the labor account. Capital was similarly found as the summation of proprietary income and other property income. A recreational fishing sector was created out of the miscellaneous sector by taking constant proportions[2] of all economic flows. Final balancing was done by minimizing least square differences between regional supplies and demands.

Most parameters of the model (apart from elasticities of substitution) are found through calibration as in Ballard et al. (1985) and De Melo and Tarr (1992). The calibration routine sets benchmark input and output prices equal to unity (by constant returns to scale and the units of the initial data being in value terms). We use foreign prices as our numeraire, setting them equal to one. Using all first-order conditions from profit maximization, cost minimization, and utility maximization; and the benchmark data and prices, most parameters apart from the elasticities of substitution are found. Following standard practice, estimates of elasticities of substitution are taken from the literature and displayed in Tables S3 and S4. Sources for elasticities in demand and supply are displayed with the tables. All households are assumed to have an elasticity of substitution between consumption goods of 0.9.