#### DCGE Model Specification

Country-level CGE models have been used to examine a range of external and policy changes in developing countries (see, for example, Bautista et al., 2001; Lay et al., 2008; and Jensen and Tarp, 2005). Below we describe the Bangladesh DCGE model.^{7} Consumers and producers in the model are treated as individual economic agents. Under a Stone–Geary function, consumers maximize utility subject to a budget constraint. This generates a linear expenditure system (LES) of demand functions:

- (1)

where *C* is consumption of good *i* in region *j*, *γ* is a minimum subsistence level, *β* is the marginal budget share, *P* is the market price of each good, *Y* is total household income, and *s* and *td* are savings and direct tax rates, respectively. Similarly, producers maximize profits subject to given input and output prices. Assuming constant returns to scale, a constant elasticity of substitution (CES) function determines production:

- (2)

where *X* is output quantity of sector *i*, *α* is a shift parameter reflecting total factor productivity (TFP), *L* and *K* are labor and capital demand, and *δ* is a share parameter. The elasticity of factor substitution is a transformation of *ρ* (i.e. *σ* = 1/(1 + *ρ*)). Maximizing profits subject to equation (2) and rearranging the first order condition gives a system of factor demand equations:

- (3)

where *W* is the area-specific labor wage, and *R* is the sector/area-specific capital rental rate. For ease of exposition, we do not show intermediate demand in the equations. The producer price *PX* is the sum of factor payments per unit of output:

- (4)

Products are traded in national markets, implying a single market-clearing price *P* for each good. Inadequate internal trade data necessitates this assumption. Output from each area is combined into a composite national good *Q* using a CES function:

- (5)

Equation (5) permits imperfect substitution between goods from different regions. Relative producer prices are determined by the following first order condition, derived from minimizing the composite supply price of each good:

- (6)

where *ti* is the indirect tax rate applied to domestic sales.

For ease of exposition, the variables and equations governing international trade are not shown. However, our model permits two-way trade by assuming imperfect substitution between domestic and foreign goods (see Armington, 1969). More specifically, a constant elasticity of transformation (CET) function determines exports, and a CES function determines imports.^{8} World prices are fixed under the small country assumption. The current account balance is held constant (in foreign currency units) by allowing the real exchange rate to adjust (i.e. a price index of tradable to nontradable goods).

Assuming that all factors in an area are owned by households in that area, total income *Y* is

- (7)

where *h* is transfer payments from the government (e.g. social grants).

The government is a separate agent with revenues and expenditures, but without any behavioral functions. Total revenue is the summation of direct and indirect taxes, as shown on the left-hand side of the following equation:

- (8)

Revenues are used to purchase goods and make transfers (i.e. recurrent spending) and to save (i.e. finance public capital investment). This is shown on the right-hand side of equation (8). Our macroeconomic closure rule assumes that public consumption spending is equal to base-year quantities *qg* multiplied by an exogenous adjustment factor *A*. The fiscal balance *B* adjusts to ensure total revenues equal total expenditures in equilibrium.

There is also no behavioral function determining investment demand for each good. We assume a savings-driven closure, i.e. total investment adjusts to match the level of savings in the economy. As shown below, a national savings pool finances investment:

- (9)

where *qi* is base-year investment quantities multiplied by an endogenous adjustment factor *I*.

We assume that labor is fully employed. As such, total labor supply *LS* in each region is fixed and, in equilibrium, must equal the sum of all sector labor demands:

- (10)

Unlike labor, which is mobile across sectors, capital is both sector- and region-specific. Capital demand *K* in each sector and region are fixed (see equation (3)). The rental rate *R* adjusts so that the sector/region-specific profit rate equates capital demand and supply in each sector.

Finally, product market equilibrium requires that the composite supply of each good *Q* equals total private and public consumption and investment demand:

- (11)

Market prices *P* adjust to maintain equilibrium. Together, the above 11 equations simultaneously solve for the values of 11 endogenous variables (i.e., *C*, *X*, *L*, *R*, *Q*, *PX*, *Y*, *B*, *I*, *W*, and *P*). The national consumer price index (CPI) is selected as a numéraire.

#### Recursive Dynamics

Our model is recursive dynamic; i.e. it consists of distinct within- and between-period components. The above equations specify the within-period component. Between-periods, certain exogenous variables are updated based on either externally determined trends or previous period results. Exogenous trends include labor supply growth rates (i.e. *LS* in equation (10)) and rates of technical change (i.e. *α* in equation (2)).

Although not shown in equations (1)–(11), each variable has a time subscript associated with it. Sector-level capital accumulation rates are determined endogenously based on investment levels from the previous period. The quantity of new capital *N* depends on the total value of investment and the capital price *PK* (i.e. a composite price index derived from investment demand shares *qi*). New capital is allocated across sectors/regions after applying a national depreciation rate *υ* and according to a capital allocation factor *SK* (0 < *SK* < 1).

- (12)

- (13)

where *SK* specifies how much investment is directed towards each sector/region and so sums to one. Following Dervis et al. (1982), *SK* is defined as follows:

- (14)

where *SP* is a sector/region's current share in aggregate profits, *R* is a sector/region's profit rate, and *AR* is the average profit rate. New capital is allocated in proportion to each sector/region's share in aggregate capital income, adjusted by its profit rate relative to the average profit rate. Sectors/regions with above-average profit rates receive a greater share of investible funds than their share in aggregate profits. The term *ϕ* is an investment mobility parameter.^{9} This allocation procedure is known as a “putty–clay” specification, since new capital is mobile, but installed capital is not.

#### Climate Impact Channels

Three climate impact channels are captured in the DCGE model. The first is changes in crop productivity. As shown below, TFP (*α*) in each sector/region grows at a long-term rate *γ*:

- (15)

The crop models estimate annual crop yield deviations from maximum potential yields. The first parameter *ω* varies around a base year value of one depending on the randomly selected year from the climate data series (0 < *ω* < ∞).^{10} The second parameter *ν* is caused by water-logging (0 < *ν* ≤ 1). These yield adjustment factors compound each other, and when their product is less than one, yields fall below long-term trends. Agricultural land cannot be reallocated between crops within each season, although consumers can substitute between aus, aman and boro rice crops.^{11} Yields return to trend levels if weather conditions permit (i.e. no lasting effects).

The second channel is the additional economic losses incurred during extreme weather events. Although not shown in the above equations, the model separates labor and agricultural land within each region. Equation (16) governs the expansion of regional land supply *NS*, which equals the sum of sector land demands within each period:

- (16)

Four lasting impacts occur when a major flood year is drawn from the climate data series (over and above temporary yield deviations). First, agricultural land expansion is normally set at the long-term rate *ϕ*, but ceases during major flood years (i.e. *ϕ* = 0 in affected regions). It returns to trend in subsequent years. Secondly, historical data indicates that the harvested land area of aus and aman rice falls during major flood years owing to prolonged water inundation. Accordingly, the parameter *ε*, which is normally equal to one, declines based on the land losses observed in historical production data during major flood years. Thirdly, long-term improvements in agricultural productivity stop during flood years (i.e. *γ* = 0 in affected regions—see equation (15)). Finally, infrastructure is damaged during major flood years. The annual capital depreciation rate *υ* in equation (13) is increased from 0.05 to 0.075 in flood years and to 0.10 in severe flood years (i.e. 1988/89 and 1998/98). This is assumed to only affect agro-processing and trade and transport services, given that they are more likely to be rural-based.

The third impact channel is the rising sea level caused by climate change. Section 2 discussed the estimated land losses for 15 and 27 cm scenarios. We assume these correspond to the 2030s and 2050s periods, respectively. Land losses are permanently imposed on the DCGE model. We gradually reduce *λ* (0 ≤ *λ* ≤ 1) from its base value of one, to levels that reflect the predicted land area reductions in coastal regions from IWM and CEGIS (2007). Sea level rises are only imposed in the climate change scenarios, although the impacts are assumed to be the same for all GCM/SRES pairings.

In summary, the model captures three climate-related impact channels: (1) climate-induced yield deviations from the crop models; (2) reduced land and capital supplies and factor productivity during major flood years; and (3) declining agricultural land availability due to rising sea levels. The model also simulates increased frequency of major flooding owing to climate change. The return periods for the 1988 and 1998 floods are reduced by one-third. More specifically, the 1988 and 1998 floods were 1-in-33 and 1-in-50 year events, respectively (based on river discharges). The frequency of these floods in the sample used to randomly generate future weather sequences is increased to 1-in-25 and 1-in-33, respectively. This only occurs in the climate change scenarios.

#### Model Calibration

The model is calibrated to a detailed 2005 social accounting matrix (SAM) (Dorosh and Thurlow, 2008). The SAM identifies 36 sectors in the 16 agro-climate regions (17 sectors in agriculture, 14 in industry and 5 in services). Base-year production quantities and yields are calibrated to the Agricultural Sample Survey (Bangladesh Bureau of Statistics, 2005a). Substitution elasticities for the production and trade functions are based on cross-country estimates from Dimaranan (2006).

Using the Household Income and Expenditure Survey (BBS, 2005b), labor markets in each region are segmented by education groups: no schooling; primary schooling; secondary schooling; and tertiary educated. Farm land and agricultural sectors are divided by region and, within each region, into marginal (<0.5 ha), small-scale (0.5–2.5 ha) and large-scale farms (>2.5 ha). Households within each region are divided into farm and non-farm groups, and farm households are divided into landowners and landless farm workers (according to the household head's occupation). Landowning farm households are separated into marginal, small and large-scale farmers. Non-farm households are split into four groups depending on the education-level of the household head. The DCGE model is therefore a very detailed representation of the Bangladesh economy, particularly of the country's agricultural sector.