CSAVE is a single-region multi-sector recursive dynamic computable general equilibrium (CGE) model interacting with the rest of the world through international trade. The model utilizes the subroutine of GTAPinGAMS to produce the desired sectoral aggregation using the GTAP-power database ([7]). The input-output table of the focused region is extracted from the aggregated dataset. In CSAVE, activities of various agents and their interactions are summarized by: 1) zero-profit conditions; 2) market-clearing conditions; and 3) income-balance conditions. For a producer, the economic activity is output, and for a household, the activity is utility. A zero-profit condition formulated as a Mixed Complementarity Problem (MCP) is:

For a production activity, if the equilibrium output Q > 0 , the first-order condition requires that the marginal cost equals the marginal revenue ( M C = M R ). Alternatively, if M C > M R in equilibrium, Q = 0 as there is no incentive to produce. Finally, M C < M R does not constitute an equilibrium since in that state it is profitable to increase the output Q until M C = M R . Other activities such as imports, exports, investment, and commodity aggregation have their own zero-profit conditions.

For each market-clearing condition, the price level is determined based on demand and supply. The market-clearing condition in MCP format can be written as:

The condition states that for each market, if there is a positive equilibrium price P , the price will make supply and demand equal ( S = D ). If S > D in equilibrium, P = 0 due to the excess supply. Similarly, S < D is not an equilibrium because in that case, suppliers are able to increase the price until the market is cleared.

The income-balance condition specifies the income supporting the household expenditure and savings. For consistency, the condition is expressed in MCP format as:

In Condition (3), E represents expenditure plus savings, and so the condition states that any positive expenditure plus savings equals the income I . In the model, the price of utility is chosen as the numeraire of the model, and all other prices are measured relative to it.

The core of CSAVE is formulated in MPSGE ([27]) and the rest is written in GAMS ([5]). The model structure is best described by the social accounting matrix (SAM) in a “micro-consistent matrix” format (Figure 1), where each row of SAM is associated with a market-clearing condition of a commodity or service (Condition 2), and each column corresponds to a zero-profit condition of an activity (Condition 1), except for the last column, which represents the income-balance condition of the economy (Condition 3). Cells in blue denote output of each activity, supply of each market, or endowment of the representative agent (those in the rightmost column); Cells in light orange are input of each activity, demand for the commodity of each market, or aggregate consumption of the representative agent (those in the rightmost column). Notations for elements in SAM are explained in Tables 1-5, and Table 6 presents tax revenue components of the income-balance condition, which is handled automatically in the background by MPSGE.

For instance, for a non-electricity sector j (see the column “ Y j | n o t   e l e c ” in Figure 1) without using fixed factors (land and natural resources), when a positive output v o m 0 j is produced in the base year, it would require the use of primary factor v f m 0 f , j and the intermediate input v a f m 0 i , j . The output and input values of the production activity are shown in (4) and (5), respectively:

The accounting identity (4) = (5) corresponds to a zero-profit condition with a positive output. Also taking the non-electricity sector j as an example, the market for the domestic output (the row labeled by P j ) is formed by: 1) the supply of the domestic output v o m 0 j , 2) the domestic demand of that output v d f m s j , which is the domestic component of the Armington good j , and 3) the foreign demand of that output e 0 j , which is just the exports of j . The positive output of j implies a positive price of j (i.e., P j > 0 ) in this market, which has the following equilibrium condition:

Finally, the column denoted by “RA” corresponds to an income balance condition of the representative agent (consumer), with the value of total expenditure (savings included) being:

The value of the endowment is the sum of the following terms

The income-balance condition is the following identity, which states that the consumer’s savings included total expenditure equals the value of the endowments he owns:

Following [11], CSAVE assumes that for a given commodity i , the domestic economy may face a negatively sloped export demand (i.e., demand for exports from abroad), due to product differentiation¹. Here, the price on the vertical axis is the foreign commodity price for exports from the country we model (See Equation (17)). The foreign commodity price here is the price the (hypothetical) foreign consumers face.

In addition, CSAVE also allows the domestic economy to face a positively sloped import supply (i.e., supply of imports from abroad) curves. Similarly, the price on the vertical axis is the foreign price of commodity imported by the country we model (See Equation (19)). The foreign commodity price here is the price the (hypothetical) foreign suppliers face. To elaborate the setting, let us denote P W E i as the foreign price index of commodity i exported from the domestic economy. Following notations defined in Table 1 and Table 5, P W E i can be expressed as:

Figure 1. SAM structure of CSAVE.

Table 1. Price indices.

Table 2. Activities.

Table 3. Sets.

Table 4. Parameters with base year values.

Table 5. Base year tax or subsidy rates.

*The base year carbon tax rate c t a x r ( i ) = 0 .

Table 6. Base year tax revenues.

*The base year carbon tax rate c t a x r ( i ) = 0 , and so in base year t a x _ A C ( i , g ) = 0 .

Equation (16) reveals that imposing export subsidy (setting r t x s e i < 0 ) and devaluation of domestic currency ( E R increases) will make the export of i more competitive. Let us denote the elasticity of export demand by α i :

P W E i in Equation (17) is the price faced by foreign consumers (not represented explicitly in the single country framework). The export demand for commodity i , denoted by E i , can be derived accordingly as:

Therefore, E i increases if there is: 1) a devaluation in domestic currency, 2) an increase in export subsidy ( r t x s e i < 0 but | r t x s e i | increases), and 3) a decrease in P E i (domestic price index of E i excluding the export subsidy). Equation (18) also shows that when α i → − ∞ , the home country is “small” for the export of i since other things being equal, even a tiny increase in P E i beyond the base year level will lose all of the exports. On the other hand, when α i → 0 , the home country is “large” for exporting i since exports are insensitive to P E i .

The import supply M i can be derived from the elasticity of import supply β i :

P W i in Equation (19) is the pre-tariff foreign price index of commodity i imported by the domestic economy (Table 1), and it is the price perceived by foreign suppliers (not represented explicitly in the single country framework). The import supply M i is therefore:

In Equation (20), import supply M i will go up when P W i increases, and for a given P M S T A R i , the pre-tariff domestic price index of imported commodity i , an appreciation in domestic currency (i.e., E R decreases) will increase P W i and consequently raises M i for any β i > 0 . In addition, when β i → ∞ , the domestic economy is “small” as an importer of i since if it is willing to pay a slightly higher price than the world price, there will be a huge increase in import supply relative to the original import level M 0 . Alternatively, when β i is small, the domestic economy is “large” because even it is willing to pay a significant premium over the world price, the import supply will not increase much relative to the original import level M 0 . In the extreme case β i → 0 , the import supply remains at M 0 regardless of any premium paid.

To parameterize α i and β i , we follow [28] and build a 2-region CGE that has the domestic economy and the rest of the world, with structure and parameterization mirroring those in CSAVE, except for settings of region and international trade. The goal is to derive α i and β i by shocking the relevant price variables, as illustrated in Equations (21) and (22):

We aggregate GTAP dataset into 30 sectors, and find that in general, Bangladesh is a price taker of various commodities in international trade, especially in terms of imports (Table 7). Note that when deriving elasticities, for some sectors there are no exports or imports in the base year data, and in that case the export demand or import supply elasticities cannot be simulated. In the modeling exercise, each missing elasticity will be assigned the value of zero. Indeed, the [2] aggregation commonly used in CGE modeling implies that sectors without exports or imports in the base year will continue to exhibit zero trade flows in subsequent simulations. Therefore, assigning values to missing elasticities does not affect the results. For numerical reasons, import supply elasticities that are higher than 100 will be represented by 100.

For the export market of commodity i , besides the export demand (Equation (18)), the export supply of each commodity i is determined by the zero-profit condition (Condition (1)) for a joint production technology that differentiates and distributes the producer’s output between export and domestic sales for profit maximization.

Likewise, for the import market of commodity i , in addition to the import supply (Equation (20)), the import demand is the derived demand of the representative consumer’s utility maximization problem—the level of import demand is dependent on the zero-profit condition for the “production” of Armington good, which aggregates imported and domestic products, and the Armington good demand is in turn determined by the zero-profit condition for the “production” of utility. The import and export markets as well as trade balance closure setting will determine E R , the price of foreign exchange (i.e., nominal exchange rate), which will be discussed in Section 2.5.

Table 7. Simulated export demand and import supply elasticities.

In CSAVE, constant elasticity of substitution (CES) functions ([3]) is used to model the production technologies and consumer utility. While the output of utility function is the welfare level (a.k.a. utility), the output for each production technology is a composite that includes domestic sales and exports—the distribution of them is modeled by a constant elasticity of transformation (CET) function ([24]). To provide an example for a production technology with a CES input and CET output, let us consider a technology that uses two inputs—labor F L and capital F k —to produce domestic sales Q D and exports Q E . Using the calibrated share form ([26]) and normalizing prices and quantities at the calibration point to unity, the CES production function for the composite good Q is:

where γ m is the base year (i.e., the calibration point) cost share of the primary factor F m ( m = L ; K ), and ρ is the parameter that relates to the elasticity of substitution between the two primary factors, denoted by σ , in the following equation:

In Equation (24), P l and P k are the rental prices for labor and capital, respectively. Let us denote the dual of the production function as C ( P l , P k , Q ) , which is the cost function for producing Q :

A positive substitution elasticity holds if and only if ρ < 1 . When ρ → 0 the CES function becomes Cobb-Douglas. Other special cases include: 1) perfect substitution between inputs ( ρ → 1 ); and 2) Leontief, i.e., no substitution possibility between inputs ( ρ → − ∞ ).

On the output side, the composite good Q is transformed into Q D and Q E according to the CET function:

where θ n is the base year value share of commodity n ( n = D ; E ) and v is the parameter that is associated with the elasticity of transformation τ between domestic sales and exports:

In Equation (27), P E and P D are prices for exports and domestic sales, respectively. Let us denote the dual of the transformation function as R ( P E , P D , Q ) , which is the revenue function for a given level of composite Q :

Likewise, a positive transformation elasticity holds if and only if v > 1 . When v → 1 , there is a perfect transformation possibility between outputs, and when v → ∞ , there is no transformation possibility between outputs.

The optimal levels of exports and domestic sales are determined by their respective zero-profit conditions. Taking the level of exports as an example, the marginal cost for the production of exported good is:

Based on Equations (25) and (26), we have:

Since v = 1 / τ + 1 (Equation (28)), M C E can be written as:

Therefore, the marginal cost for producing the exported good is an increasing function of its level Q E , a decreasing function of composite Q , and an increasing function of the price for each input m . To determine Q E , one can use the corresponding zero-profit condition (Condition (1)) based on Equation (32). Figures 2-4 illustrate the structures of production technologies and the representative consumer’s preferences.

Besides, the power sector in CSAVE includes 9 subsectors (Figure 5). Following [15], we make renewables (wind and solar) perfect substitutes to other forms of generation, while considering the value factor adjustment proposed by [21]. The adjustment considers the observation that higher market shares of renewables in total electricity generation increase the “profit-adjusted levelized costs of electricity (PLCOE)” for renewables (Figure 5), i.e., the generation costs of renewables are higher as their market shares get larger. The cost function structure for power sector aggregation is also presented in Figure 5.

Figure 2. Cost function for a non-power sector.

Figure 3. Cost function for a power subsector.

Figure 4. Expenditure function.

Figure 5. Cost function for aggregating power subsectors.

Closures of a CGE model specify the rules for how markets are cleared or macro balances (receipts equal payments) are achieved ([31]). Each closure involves a decision about what variable can be adjusted to reestablish an equilibrium after the model receives a shock ([9]). Key closures of CSAVE include those for: 1) labor market; 2) trade balance; 3) macroeconomics; and 4) government expenditure.

The labor market closure of our model considers the circumstance where the economy is in full employment—wage rate is flexible and can be adjusted upward or downward to equalize labor supply and demand². In our model, labor supply level is fixed within a given period. Therefore, the wage rate is fully determined by labor demand, which can be derived from producers’ cost minimization problems using the Shephard’s Lemma ([30]).

CSAVE allows modelers to choose different settings for trade balance closure for comparison purposes or to better represent the country-specific characteristic. To illustrate this, let us denote the net capital outflow of the domestic economy by F , which is just the difference between the values of exports and imports, and denote the received foreign transfer by F T D :

To model the flexible exchange rate setting, the net capital outflow is fixed within a given period, and can be either fixed or updated across periods. The price of foreign exchange (i.e., nominal exchange rate) E R in Equation (33) is therefore endogenous, and as all other prices, it is measured relative to the price of utility, the numeraire of the model (See Section 2.1). Alternatively, when the price of foreign exchange is fixed, E R is constant and other prices are adjusted to meet the relevant market clearing conditions. In this case, the net capital outflow F in Equation (33) becomes endogenous. Throughout the study, we consider the flexible exchange rate setting where within a period, the net capital outflow remains constant, but over time it will be updated proportional to previous period’s gross domestic product (GDP) level.

In CSAVE, the representative consumer allocates the income between consumption and savings to maximize his utility, and savings provide fund for investment, i.e., investment is driven by savings, i.e., the more the economy saves, the higher investment it achieves. The investment beyond the depreciation level eventually expands the production capacity of the following period. The setting constitutes the model’s macroeconomics closure.

For the government expenditure closure, we assume the “quantities” of government purchases from various sectoral outputs are fixed within a given time period, i.e., v a f m 0 i ,   "   g " in Equation (11) remains a constant vector in that period. However, over time those quantities are updated proportional to the GDP of the economy. Besides, the standard setting of CSAVE assumes that tax revenues are recycled in a lump-sum fashion back to the representative consumer. Nevertheless, with some revisions, other settings can be incorporated into modeling exercises. We will provide some examples with different tax revenue recycling assumptions later.

The SAM of CSAVE comes from the input-output dataset presented in GTAP-power version 11 ([7]). In the database, the input-output table for Bangladesh was contributed by the Bangladesh Planning Commission ([1]), and the Bangladesh data and those for other countries were adjusted and recompiled to ensure global consistencies in trade flows for the base year of 2017. The data are key inputs in parameterizing preference and various technologies in general (see Section 2.2 for details).

Another data required in calibrating technologies and preference are elasticities of substitution between inputs and elasticities of transformation between outputs (see Section 2.4 for details). These elasticities are mostly sourced from existing studies (Table 8), except for the elasticities of transformation between outputs for domestic sale and those for exports, which are often unavailable for existing research.

To overcome this, [20] assume that for each commodity type, the transformation elasticity is proportional to the substitution elasticity between imported good and the indigenous product sold domestically. We adopt the strategy and calibrate transformation elasticities e t a d x such that they are half the levels for the corresponding substitution elasticities e s u b d m . The calibration ensures that CSAVE captures the average trend of Bangladesh’s historical foreign exchange rate evolution (Figure 6). Besides, with lower transformation elasticities, it is harder for the domestic economy in diverting production resources to increase exports, which provide foreign exchange in supporting for the purchase of imports. In this case, there will be a higher extent of devaluation in domestic currency (Figure 6).

Another critical task for building CSAVE is calibrating the growth path for GDP under the reference scenario. In this study, the simulated reference GDP growth for Bangladesh up to 2030 is calibrated to IMF World Economic Outlook ([18]). For years beyond 2030, the growth is assumed to decrease exponentially to 3% in 2050. To match the given GDP growth path, following [6], for each period, the total factor productivity (TFP) of the economy is endogenously solved first. The solution for TFP is saved and used to parameterize the model for subsequent simulations, and it remains exogenous across scenarios. While the solved TFP path allows the model to reproduce the targeted GDP growth path under the reference scenario, in general, the GDP growth as well as other economic variables will deviate from the reference levels under a policy run³.

Table 8. Substitution and transformation elasticities of CSAVE.

Figure 6. Foreign exchange price index under different transformation elasticity levels.