Aem Article

Aquaculture Economics & Management, 9:113–139, 2005 Copyright # 2005 IAAEM ISSN: 1365-7305 DOI: 10.1080/13657300590961555

DISAGGREGATED ANALYSIS OF FISH SUPPLY, DEMAND, AND TRADE IN ASIA: BASELINE MODEL AND ESTIMATION STRATEGY

Madan M. Dey, Roehlano M. Briones, and Mahfuzzudin Ahmed & WorldFish Center, Penang, Malaysia

& Quantitative modeling of fish supply, demand and trade is a useful tool for analyzing recent structural changes, such as the rapid development of aquaculture. Existing models are, however, limited by their use of highly aggregated fish categories and assumed (rather than estimated) elasticities. This paper outlines an estimation strategy and a multiproduct equilibrium model for disaggregated analysis of fish supply, demand, and trade. The model is composed of a producer, consumer and trade core, and is specified to accommodate special features of the fish sector. The estimation and modeling strategy also address common data problems, such as heterogeneity of fish types, diversity of production categories, and so forth. The model has been applied to nine major fish producers in developing Asia. Keywords impact analysis, quantitative projection, multiproduct model

INTRODUCTION Recent decades have witnessed a major transformation in global demand for and supply of fish. Per capita fish consumption has nearly doubled from 8 kg in 1950 to about 16 kg in 1999 (FAO, 2001). In developing countries, the most dramatic response to rising demand has been the expansion of aquaculture, which has emerged as the fastest-growing food sector from the 1980 s onward. Developing countries are now major global suppliers of fish, with their fish exports on an uptrend in contrast to their falling traditional crop exports (Ahmed et al., 2003). Underlying this transformation are structural factors such as technological change and policy reform. New technologies in grow-out and hatchery operations have combined with genetic improvement of fish to drive productivity growth in aquaculture. Trade liberalization has also opened up bigger markets for consumption and production of fish. Meanwhile, Address correspondence to Madan M. Dey, WorldFish Center, P.O. Box 500 GPO 10670 Penang, Malaysia. E-mail: [email protected]

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pressures on aquatic resources, due in part to increased fishing efficiency, have threatened the sustainability of capture production, leading to new institutions and policies for managing fisheries. There is, however, little quantitative information about the impact of these structural developments on prices, production, and earnings in the fish sector. Several food sector models have been developed to study the impact of technology and policy changes on agriculture (e.g., Evenson et al., 1993; Huang & Chen, 1999). Unfortunately, the fish sector is absent in such models. For example, the Food and Agriculture Organization’s (FAO) world food model (Bruinsma, 2004) excludes fish. This omission, common in supply demand, analysis (Williams, 1999), is unfortunate given the significant contribution of fish to nutrient intake and livelihoods of the poor worldwide (Pinstrup-Andersen & Pandya-Lorch, 1999). Quantitative modeling of fish supply, demand, imports, and exports would greatly facilitate understanding of the impacts of technological change in aquaculture and capture fisheries, as well as of demand shifts and policy reforms. A noteworthy exception to the omission of fish in quantitative modeling is the extended IMPACT model (International Model for Policy Analysis of Agricultural Commodities and Trade), the outcome of collaboration between the International Food Policy Research Institute (IFPRI) and the WorldFish Center (Delgado et al., 2003). Further modeling work is nevertheless warranted for two reasons. First, the extended IMPACT model uses synthetic (rather than estimated) elasticities to characterize supply and demand for fish. Second, it defines fish types in terms of broad aggregates; in reality fish is a highly heterogeneous commodity (Westlund, 1995; Smith et al., 1998; Dey, 2000). On the demand side, consumer preferences in developing countries vary widely across fish types, as consumption is normally in terms of fresh whole fish or fish parts rather than fish fillet. For example, within the category ‘‘common carp,’’ prices can range from USD 0.65=kg in India to USD 1.07=kg in China (based on 1995 data reported in Dey et al., 2002). On the supply side, fish is produced from various production systems or categories (i.e., capture versus culture). Analysis for disaggregated fish types would clearly be more useful in many applications, such as allocation of resources for investment and research; comparison of policy options based on likely impacts; and determining market prospects within the fish sector over the medium and long term. The WorldFish Center has constructed a disaggregated supply and demand model of the fish sector to address these concerns. This paper presents the structural version of the model as well as the estimation strategy for specifying its parameters. The model has been applied to nine major fish producing countries in developing Asia, in collaboration with national researchers.1 Other related papers in this journal issue report some of the

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results of this exercise. Dey et al. (2005) discuss the consumption data used in the nine countries. Garcia et al. (2005) discuss the application of the estimation strategy on demand for fish in the Philippines. Finally, Rodriguez et al. (2005) present the country model and projections for the Philippines.

OVERVIEW OF THE MODEL The model aims to analyze the impact of technology and policy on the fish sector. The basic approach towards impact analysis is outlined in Figure 1.

FIGURE 1 Basic framework for fish sector modeling.

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The first step is to conduct a background analysis on technologies and policies affecting the fish sector, that will identify shock variables for impact analysis. The next step is to develop a baseline model of demand and supply. The third step is the numerical specification of the baseline model, involving estimation of parameters, as well as calibration of prices and quantities based on benchmark data. The system is then solved by imposing simultaneous equilibrium across markets. Impact analysis is conducted by altering shock variables in the baseline model, followed by an examination of the resulting changes in equilibrium values. The changes can be disaggregated by species group, production category, region (i.e., urban and rural) and economic class (i.e., consumers, producers, factor suppliers, or income group). The multiproduct model for each country is graphically represented by a network of supply and demand curves (Figure 2). The model is divided into producer, consumer and trade cores (Sadoulet and de Janvry, 1994). The producer core represents domestic supply, which can be differentiated by production category (e.g., freshwater aquaculture, brackishwater aquaculture, inland capture, marine capture, and so forth). The model incorporates supply shifters, to represent shocks on technology, policy, and other supply conditions. Meanwhile, the consumer core deals with household demand equations, estimated by commodity and region. Demand shifters represent demographic changes in terms of population growth, growth of per capita incomes, and urbanization. Finally, the trade core incorporates imports and exports. The imports are related to

FIGURE 2 General framework for demand and supply in the fish sector model.

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the nondomestic supply made available to a domestic market, and the exports are related to the nondomestic market destination for domestically produced goods. Model closure is found at the simultaneous intersection of supply and demand in each market. Incorporating all the core components, equilibrium for every fish type may be stated as QSF þ QM ¼ QDF þ QX

ð1Þ

where QSF is quantity supplied, QM is quantity imported, QDF is quantity demanded and QX is quantity exported. If the demand and supply shifters (e.g., population growth, technical progress) are associated with time periods, then the exercise can be extended to project supply and demand over time—that is, repeated comparative statics is interpreted in dynamic terms, a common treatment in the literature. As with other models in this mode (e.g., IMPACT, FAO’s world food model), the projections are not treated as ‘‘forecasts’’ of actual supply and demand on a year-to-year basis. Rather, they pertain to fundamental trends in production and consumption, therefore indicating the likely patterns of change in the fish sector over the medium and long term.

ESTIMATION STRATEGY: THE PRODUCER CORE The technology of a specific production category is summarized by the set of feasible ‘‘netputs,’’ i.e., a vector of quantities of net outputs (positive netput) and net inputs (negative netput). Netput supply therefore consists of positive output supply and negative input demand. The netput supply response to price is premised on profit maximization subject to market prices and technology. Estimation is undertaken here using the ‘‘dual’’ approach, which is becoming the preferred method when sufficient price data are available ( Jensen, 2003). It is particularly appropriate for multioutput, joint input production, e.g., Squires (1987), Kirkley and Strand (1988), and others have applied it to capture fisheries. It is noteworthy that this approach has yet to be applied to aquaculture, despite the widespread practice of polyculture, which is likely to fall under the case of joint input production. We adopt the convenient method of estimation based on the normalized quadratic profit function, which is widely used in cases of joint agricultural production (e.g., Shumway et al., 1987; Ball et al., 1997). Given the netput vector, identify one element as a numeraire, with price pnum and quantity QNUM. Let A be a set of non-numeraire netputs, and COND be a set of

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conditioning variables; let i; j 2 A, and k; l 2 COND. The stochastic version of the normalized quadratic profit function may be written as: 1XX aij PEih PEjh 2 i i j k XX X XX 1 þ aik PEih vkh þ akl0 vkh vlh þ eih PEi þ e h 2 i i k k l

ph ¼ a0 þ

X

ai PEih þ

X

a0k vkh þ

ð2Þ

Here p is normalized profit evaluated at the optimum. PEih is the normalized price of the ith netput, defined as PPih =pnum, where PPih is the producer price. The a’s and a’s are the unknown parameters to be estimated, while vkh is the kth conditioning variable, and the e’s are error terms. Denote the quantity of netput supply by QAih. Then by the envelope theorem, the netput supplies are the price derivatives of the profit function: QAih ¼ ai þ

X j

aij PEjh þ

X

aik vkh þ eih

ð3Þ

k

Note that if QAi < 0 then netput i is an input. Supply response to price change, expressed in own- and cross-price elasticities, can be readily computed from (3). To derive the supply of the numeraire, multiply the expression in (2) by pnum to obtain nominal profit; differentiating by pnum yields: QNUM h ¼ a0 þ

X k

a0k vkh


1XX 1XX 0 h h aij PEih PEjh þ a v v þ e h ð4Þ 2 i j 2 k l kl k l

The parameters of equations (3) and (4) are estimated by the appropriate systems approach. For capture fisheries, the use of time series data (or time series pooled with cross section) introduces stock dynamics, leading to intertemporal dependence of catch (i.e., current catch affected by previous catches). A simple approach would be to introduce a biomass indicator, or better yet its instrumented version, where available, as a conditioning variable. The derivation of the supply functions from a profit function entails certain restrictions on the former. A profit function is homogenous of degree one in prices, and should have equal cross-price derivatives; hence, the supply parameters must conform to a homogeneity and symmetry restriction.2 Homogeneity is already incorporated by normalization, while symmetry can be implemented by imposing aij ¼ aji during estimation.

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In the baseline model, it is assumed that technology and policy can be modeled as a proportional and factor-neutral shift in quantity. For a given supply function, this may be represented as a distinction between actual and effective prices. Alston et al. (1995) give the following example: let output be measured in kg per ha, and technological progress raises yield by 10%. Effective price per hectare therefore rises by 10% (though actual price per kg is constant). The normalized price, in effective form, is computed as: PEi ¼

PPi ki pnum  knum

where ki is the proportional change of output of supply fish type i due to technological progress or policy shift, and knum is the expansion for a numeraire fish type. The effective price method is fairly flexible in representing a variety of changing supply conditions. For instance, in marine capture fisheries, an alternative way to model a declining fish stock would be to reduce the k of the corresponding fish type.

ESTIMATION STRATEGY: THE CONSUMER CORE Consumption response to price change is summarized by household demand, which is premised on utility maximization. To specify this demand for fish types, Dey (2000) outlines a procedure that addresses the common estimation problems. The first problem is estimating disaggregated types of fish demand, while maintaining highly aggregated categories for nonfish goods. Theoretically, this requires that the underlying utility function be separable according to these aggregates. Under separability, optimization may be interpreted as a multistage procedure. Consider a three-stage budgeting framework, as diagrammed in the following utility tree (Fig. 3), which assumes that fish is separable from other animal protein sources. In Stage 1, total spending is divided into two aggregates, food and nonfood, measured by the total expenditure on each. In Stage 2, food is disaggregated into more specific food aggregates, namely, fish, meat, chicken, vegetables, and cereal, each of which is measured by the corresponding expenditures. Finally, in stage 3, fish expenditure is disaggregated into its major types.3 Estimation therefore proceeds in stages. For each stage j, let vjh be an error term, and Zj the set of household characteristics relevant to stage j, i.e., for i 2 Zj, zjih is the variable corresponding to the ith household characteristic. Moreover, at each stage j, Zj contains region dummies (e.g., an urban dummy). The estimating equation for Stage 1

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FIGURE 3 Utility tree.

may be written as: ln FDEX h ¼ b0 þ b1 ln PFD h þ b2 ln pfdn h þ b3 ln yh X þ b4 ðln y h Þ2 þ b0i z1i þ v1h

ð5Þ

i2z1

Here ln denotes the natural logarithm; FDEXh, the per capita household food expenditure; PFDh, a price index for the food aggregate; pfdnh, a price index of the nonfood aggregate; and yh, the per capita household expenditure.4 As (5) is an outcome of a utility maximization problem, it must observe homogeneity of degree zero in prices and income. In logarithmic derivative form, the restriction may be stated as: b1 þ b2 þ b3 þ 2b4 in y h ¼ 0: This restriction is evaluated at the sample mean. In estimating the remaining stages, the natural approach would be to include purchases of food and fish in the right-hand side as regressors. This raises the second major problem, which is simultaneity, given that such purchasing decisions are endogenous. To address this, the predicted rather than actual value is used as a regressor. This instrumental variable approach

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has been implemented by Pashardes (1993), Balisacan (1994), and others. Here, it is implemented in Stages 2 and 3. The estimating equation for Stage 2 is: X h2i ln pfnih þ h3 ln FDEX h FEX h ¼ h0 þ h1 ln PF h þ i2FN h 2

þ h4ðln FDEX Þ þ

X

h0i z2hi þ v2h

ð6Þ

i2z2

Here FEXh is spending for fish, PFh is a price index of fish, pfni is the ith nonfish food price and FDEX h is the predicted value of FDEX h from Stage 1. In estimating (6) a homogeneity restriction is imposed of the following form: X h2i þ h3 þ 2h4 ln FDEX h ¼ 0 h1 þ i2FN

It is likely that sample data for estimating (6) would contain zero values for fish expenditure. As fish is an important part of the Asian diet, this is probably due to measurement error, as the recall method used in household surveys may fail to capture actual consumption patterns if fish is purchased infrequently. Due to this censoring problem, (6) is more appropriately estimated by Tobit regression. Estimation of Stage 3 is based on the Almost Ideal Demand System (AIDS), originally proposed by Deaton and Muellbauer (1980). Among the class of flexible functional forms, AIDS permits exact aggregation of individual consumer demands into market demand. Denote the set of fish types on the demand side as DF. For i 2 DF, the following states the quadratic version of the AIDS (Blundell et al., 1993):
 X FEX h h h cij ln PCj þ c1i  ln SHi ¼ c0 þ STONE h j2DF

2 X FEX h þ c2i ln þ c0i z3hi þ v3h ð7Þ STONE h k2Z3 Here SHih is the expenditure share of fish type i in total fish expenditure, and PCj is the consumer price of fish type j. Instrumenting for FEX h (yielding FEX h ) deals with both endogeneity and censoring of fish expenditure. STONEh, an approximation of the AIDS price index, is computed as: X ln STONE h ¼ SHih ln PCih ð8Þ i2DF

In estimating (7), censoring is again an issue, given the high probability of observing zero purchases for certain fish types. Unlike in Stage 2, this

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case of censoring may be attributed to household choice (rather than measurement error).5 The standard censored regression techniques are complicated by the fact that (7) is a system of equations, often requiring estimation by maximum likelihood techniques. To deal with this, Heien and Wessels (1990) suggest a Heckman procedure, which treats unobserved fish consumption as analogous to the sample selection problem. The Heckman procedure corrects for selection bias by running a probit regression to obtain PRih , the predicted probability that household h consumes fish type i. Regressors are the prices, nominal fish spending and demographic variables of (7). An inverse Mill’s ratio imrih is then computed as follows: imrih

 ¼

/ðPRih Þ=UðPRih Þ; /ðPRih Þ=ð1
UðPRih ÞÞ

h consumes i; h does not consume i:

ð9Þ

Here / and H are, respectively, the density and cumulative density functions of the normal distribution (evaluated at the sample mean and variance). Equation (7) may therefore be rewritten as:
 X FEX h h h cij ln PCj þ c1i ln SHi ¼ c0 þ STONE h j2DF

2 X FEX h þ c3i imrih þ c0i z3hi þ v3h : ð10Þ þ c2i ln h STONE k2z3 Utility maximization requires that parameters of (10) comply with several restrictions, namely, homogeneity of degree zero in prices, symmetry of the Slutsky matrix and the adding up restriction (budget shares sum to 1). These restrictions are expressed as follows: X

cij ¼ 0;

i; j 2 DF

ðHomogeneityÞ

j

cij ¼ cji ; X i

~c0i ¼ 1;

c1i c1j ¼ ; i; j 2 DF c2i c2j X X c1i ¼ c2i ¼ 0; i

ðSymmetryÞ i 2 DF

ð11Þ

ðAdding upÞ

i¼1

The ratios in the symmetry restriction hold owing to the quadratic form of (10), as in Blundell et al. (1993). The foregoing restrictions are imposed during estimation. Own- and cross-price, as well as income elasticities can be computed upon estimation of (10). For i; j 2 DF, let ehij be the own- and cross-price elasticities, ghiy the income elasticity of fish type i, ghif be the elasticity of fish

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type i to fish expenditure to food expenditure, ghy the elasticity of food expenditure to income, and kij the Kronecker delta, where kij ¼ 1 if i ¼ j and kij ¼ 0 otherwise. The elasticities of fish demand with respect to fish prices are: ehij

¼

cij SHih

h

h


½c1i þ 2c2i ln ðFEX =P Þ

SH hj SH hi


kij

ð12Þ

The other elasticities are similarly calculated: Fish type to fish expenditure ghif ¼

c1i 2c2i lnðFEX h =p h Þ þ þ1 SH i SH hi

Fish type to income ghiy ¼ ghif ghfd ghy Fish expenditure to income ghfd ¼ ðh3 þ 2h4 ln FDEX h ÞPRFD h Food expenditure to income ghy ¼ b3 þ 2b4 ln yh Here, PRFDh is the probability that fish is consumed, and may be estimated from the sample proportion.6 THE TRADE CORE Ideally, the trade core should model trade elasticities in a flexible manner, while accommodating the probable unavailability of an extended time series on trade by disaggregated fish type. One such parsimonious formulation is the Armington approach (1969), commonly adopted in applied general equilibrium models. The main problem of the trade core is to isolate the domestic from the foreign component on both market demand and market supply. In the Armington approach, the foreign and domestic versions of a good are first combined into a foreign-domestic aggregate, which is the object of consumption or production. The foreign and domestic versions are deemed imperfect substitutes. Flexibility is gained by specifying the aggregating equation as a constant elasticity of substitution (CES) function for the demand side, and as a constant elasticity of

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transformation (CET) function for the supply side. Given foreign and domestic prices, imports (exports) can be determined by optimization, conditional on the total quantity demanded (supplied). Let F be the set of fish types common to both supply and demand categories. Denote market demand and supply aggregates as QSFi and QDFi, respectively. Let FM be the set of imported types, FX the set of exported types, while FMN and FXN, respectively, denote nonimported and nonexported fish types. (The set FM \ FX is the set of fish types for which there is intra-industry trade; the set of nontraded fish types is FMN \ FXN .) Consider the case of imports: for i 2 F, let QHMi be the total demand for the domestic component, and QMi the total demand for imports. The combination of QHMi and QMi into the import-domestic aggregate is described by:
1

QDFi ¼ ðd1m  QDHi
qmi þ d2mQM
qmi Þqmi

ð13Þ

The parameter qmi is a transformation of the elasticity of substitution rmi , i.e., qmi ¼ ðrmi
1Þ=rmi . The expenditure constraint is PARMi  QDFi ¼ PPi  QHMi þ pmi  QMi ;

ð14Þ

where PARMi is the price of the import-domestic aggregate; PPi is the producer price of fish type i, and pmi is the fixed world price of the imported fish type (the open economy assumption). The use of the producer price implies that aggregation occurs between production and consumption, hence, the unit cost of the domestic component is the price paid to the producer. Minimizing the right-hand side of (14), subject to fixed QDFi in (13), implies the following conditional demands:
 PARMi rmi rmi QHMi ¼ d1m   QDFi ð15Þ PPi QMi ¼ d2m rmi 




PARMi pmi

rmi  QDFi

ð16Þ

(For a detailed derivation, see Horridge et al., 1993). Given PPi, pmi and QDTi, equations (14)–(16) are used to solve for PARMi, QHMi, and QMi. The parameters of the foregoing may be obtained by calibration from benchmark data.7 Consider the case of exports: for fish type i, let QHXi represent the domestic component (for domestic consumption) and and QXi the foreign

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component or export. The export-domestic aggregate equation is given by 1

QSFi ¼ ðd1x  QHXiqxi þ d2x  QX qxi Þqxi

ð17Þ

Again qxi is a reexpression of the constant elasticity of transformation rxi . By a similar derivation, the trade core equations for exports are given by: PARXi  QSFi ¼ PPi  QHXi þ pxi  QXi ; QHXi ¼ d1x

QXi ¼ d2x

rxi

rxi




PPi  PARXi


pxi  PARXi

ð18Þ

rxi  QSFi

ð19Þ

rxi  QSFi

ð20Þ

where PARXi is the price of the export-domestic aggregate and pxi is the world price of exports. As in the previous case, the parameters may be specified by calibration. MATCHING THE FISH TYPES IN THE PRODUCER AND CONSUMER CORES The foregoing discussion assumes that the fish types in the supply, demand, and trade cores are identical. However, differences in the classification of fish-types on the demand and supply sides are likely to arise, given differences in fish-type definitions adopted in data collection. This section attempts to match these categories for the producer and consumer cores of the baseline model. By data construction, fish types in the trade core are defined in terms of the final, matched-fish types. Denote the set of fish types for supply as SF, and that for demand as DF. For i 2 SF and j 2 DF , sets FSj and FDi, such that FSj are the supply fish types matched to j, and FDi are the demand fish types matched to i. Figure 4 illustrates this correspondence. Clearly FSDF1 contains SF1, SF2, which can be relabeled F 1, F 2. Meanwhile DFSF3contains DF2, DF3, which can be relabeled F 3, F 4. Finally, FSDF4 ¼ SF4, and FSSF4 ¼ DF4, hence, the corresponding singletons are relabeled F 5. To summarize, the set F ¼ {F 1, F 2, F 2, F 4, F 5} ¼ {SF1, SF2, DF2, DF3, SF4} (one can replace SF4 by DF4). DF1 is referred to as a demand composite, i.e., if FS contains more than one element, then j is a demand composite. Similarly, SF3 is termed a supply composite. In general, to identify the final fish types contained in F, simply pick out the most disaggregated types, that is: if SF j contains more than one element, then SF j  F ; and if SF j is a singleton containing i, and DFi

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FIGURE 4 An example of correspondence between supply and demand fish types.

is a singleton containing j, then i 2 F . The following restrictions are also imposed—h 2 DF , i 6¼ h; FSi \ FSh ¼ Ø; and h 2 SF ; i 6¼ h; FDj \ FDh ¼ Ø– that is, each element of either SF or DF is matched to exactly one element of F. Disaggregation of composites follows the same Armington procedure discussed under the trade core. Suppose the following functional relation holds for demand fish type i, and j 2 DF i : !qd
1 i X QDTi ¼ ddj QDFj
qdi ð21Þ j

Here QDFj is the unknown quantity demanded for fish type j, while QDTi is obtained elsewhere in the model. The parameter qdi is the transform of rdi , the constant elasticity of substitution between component types of composite i. Equation (13) implies that QDFj is divided into an imported and a domestic component. Expenditures on the demand composite must therefore observe the following identity: X PARMj  QDFj : ð22Þ PDi  QDTi ¼ j

Here PDi is the price of the demand composite. Minimizing P PARMj  QDFj subject to fixed QDTi yields the first-order condition: QDFj ¼

ddjrdi




PDi  PARMj

rdi  QDTi :

ð23Þ

This condition, along with (22), can determine the unknown QDFj’s and PDi.

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Similarly, in the case of a supply composite i and j 2 DF i , with obvious notation, the constant elasticity of transformation function is

QSTi ¼

X

!qs1 dsQSFjqsi

i

ð24Þ

j

Disaggregation of the supply composite into the component fish types occurs in the production stage, prior to international trade. Hence, the expenditure constraint is:8 X PSi  QSTi ¼ PPj  QSFj : ð25Þ j

Likewise, the first-order conditions are:
rdi PPj rdi QSFj ¼ ddj  QDTi PSi

ð26Þ

Calculation of QDFj and PSi is straightforward.

SUMMARY AND CLOSURE OF THE BASELINE MODEL This section consolidates the previous discussions on the core equations, links them using closure conditions and discusses the application for impact analysis. The reader is referred to the Annex for a summary statement of the variables and equations of the baseline model. First to be defined are the sets. In addition to the supply, demand, and matched fish types, an additional distinction has been made between SFF (fish types that are produced in fresh form) and SFFN (processed fish types). For the producer core, the set K for production categories is introduced, along with the netput vector Ak. The sets SFk and AFNk distinguish the outputs from the inputs in each production category. Note that SFk is defined only for members of SFF, i.e., each k in K produces only fresh fish. KSi identifies the production categories that contribute to a particular (fresh) fish type; for example, tilapia may be sourced from aquaculture as well as inland capture. Meanwhile, for the consumer core, the set of regions R has been defined, e.g., R ¼ {urban, rural }. As discussed previously, the sets FSi , i 2 SF match the elements of F with those SF, while the sets FDi match the elements of F with those of DF. The variables are divided into endogenous and exogenous categories, with each category listed alphabetically. Endogenous variables and set

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names are in uppercase, while exogenous variables are in lowercase. The exception is that producer and effective prices (denoted by PP and PE respectively, with subscripts) are all in uppercase. These variables are all defined for the average unit within the associated domain, hence the h superscript has been dropped. Under the producer core, (P1) defines effective prices from the producer prices. Equation (P2) copies the producer prices from the supply composites to those of the component fish types. Equation (P3) is the netput supply equation, with aijk identical to the estimated parameters in equation (3). Some conditioning variables (such as location dummies) may have to be collapsed in the course of computing the category average, hence the intercept term and the list of conditioning variables would have to be derived from their counterparts in (3). Equations (P5) and (P6) represent two levels of aggregation across supply units. The first is across units within a category k; the second is across production categories in K. Note under the netput convention, (P6) subtracts out fish types that appear as input demand in some production categories. Equation (P7) expresses the per unit contribution (under Leontieff technology) from each fresh fish type to the processed fish types. The conversion ratio fi allows for the change in per unit weight due to processing. Finally, (P8) states the remaining total supply of fresh fish, net of contribution to processed fish. Under the consumer core, the Stages 1, 2, and 3 equations, i.e., (C1), (C2), and (C3), are separately stated for each region. Equations (C4) to (C9) endogenize the aggregate prices of fish and food, as a consequence of endogenous adjustments in prices and quantities of individual fish types. Finally, (C10) and (C11) introduce aggregation across consumers, first within the region, then at the country level. As for the trade core, (T1) and (T2) initialize the absence of imports and exports for the FMN and FXN categories, respectively. Equation (T3) then allows calculation of the prices of the import-domestic aggregates; (T4) calculates the domestic demand component; and (T5) the import component. Similarly, equations (T6) to (T8) calculate the price of the export-domestic aggregate, domestic supply component and exports. Matching of demand and supply is accomplished in equations (M1) to (M6). The first two equations pertain to quantity demanded for the fish types, while the next two pertain to quantity supplied. Each pair contains an initialization for the noncomposite fish types, followed by a first-order condition for the fish type components of a composite type. The last pair of equations calculates the composite prices. Incidentally, the composite supply price from (M6) replaces the producer price in equation (14), which accounts for (T3) in the trade core.

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Model closure is imposed in (E1) and (E2). The first is essentially a restatement of equation (1). Another modification of (1) in (E1) is absence of a vector of prices p common to supply and demand. Rather, prices are computed separately for the supply and demand sides of the market. This accounts for (E2), which links the prices faced by producer with those faced by consumers. NUMERICAL IMPLEMENTATION To construct a numerical version of the model, a baseline data set was assembled consistent with equilibrium conditions for the endogenous variables. That is, actual data on the endogenous variables of the model (i.e., prices, quantities, and expenditures) for a given base year were assumed to represent the model equilibrium. Data for exogenous variables, such as income and population, were also incorporated. Initial values for exogenous variables, as well as the intercept terms in the producer and consumer cores, must all be calibrated to fit the baseline data. Coefficients in the supply and demand equations were parametrized based on the estimated elasticities. Intercept terms can then be calibrated, consistent with these coefficients and the baseline data. Calibration and model solution were implemented using the Generalized Algebraic Modeling Solver (GAMS) program. The base-year solution of the model replicates the baseline data set; impact analysis and market projections were then obtained by finding the model solutions under alternative values of the exogenous variables. Among the major types of shocks exogenous to the model are: . technological change, movements in resource stocks and supply-side policy reforms in the fish sector; . changes in the prices of fish inputs; . growth of per capita income; . price changes for nonfish consumer items; . population growth in urban and rural areas; . improved marketing efficiency of fish (decline in the marketing margin); and . changes in world prices of fish exports and imports. Exogenous variable trends can be obtained from time series data, other models (e.g., IMPACT), literature review, and expert judgment. Impact analysis is conducted by evaluating the computed changes in equilibrium prices and quantities. These changes can be disaggregated by fish type, production category, and consumption region. One can therefore gauge the welfare impact on consumers (through changes in retail

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price and per capita consumption) as well as producers (through changes in producer price and production level). With additional information (say, from household survey data), these changes in consumption patterns may be disaggregated by income group. The analysis may even be extended to examine welfare impact based on changes in consumer and producer surplus. CONCLUDING REMARKS This paper discusses the need for and an approach to disaggregated, empirically based analysis of fish demand and supply. The approach consists of the formulation and estimation of a baseline model of the fish sector where commodities are defined over major fish types by country. The strategy outlined here addresses several modeling challenges, such as the diversity of production methods, the presence of cross-price effects from other goods, measurement error and censoring. Foreign trade is modeled in a practical but flexible manner to accommodate data constraints. Model closure also adjusts for the likely disparities in fish groupings when combining supply, demand, and trade in calculating model equilibrium. Nine major fish-producing countries in developing Asia have applied the entire framework, from estimation to projection. In addition to the papers found in this journal issue, other papers reporting on the final results are in process. The framework presented here is arguably a rigorous, yet practical, tool for disaggregated analysis of the impact of structural change. ACKNOWLEDGMENTS The authors gratefully acknowledge the helpful comments of U-Primo E. Rodriguez and two anonymous referees. The usual disclaimer applies. The work reported herein was partially funded by the Asian Development Bank (ADB) under the ‘Strategies and Options for Increasing and Sustaining Fisheries and Aquaculture Production to Benefit Poorer Households in Asia’ Project (ADB RETA 5945). This is WorldFish Center contribution No. 1739. NOTES 1. The countries are: Bangladesh, China, India, Indonesia, Malaysia, Philippines, Thailand, Sri Lanka, and Vietnam. 2. A profit function should also be convex in prices. Implementing the corresponding restriction is possible (e.g., Lang, 2001); however, the procedure is highly technical and lacking in intuitive appeal.

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3. Note that the aggregation would change if separability fails to hold, e.g., if fish is not separable from meat and chicken, then an animal protein aggregate would appear in Stage 2, which may be disaggregated into meat, chicken, and individual fish types in Stage 3. 4. The price indices are in Stone form, as in equation (8). In case a nonfood price index is unavailable, we may use per capita nonfood spending as a proxy. This proxy should preferably be instrumented to avoid the simultaneity problem. 5. It may also be due to seasonality of some fish types, in which case seasonal dummies should be inserted in the Stage 3 regression. 6. It can be shown that the Heckman correction can be ignored in calculating elasticities. However, the Tobit correction should be incorporated in the elasticity of fish expenditure. See Greene (2001). 7. In either imports or exports, the value of the sigma-terms is specified within a plausible range, from which the delta-terms are calibrated. 8. In practice, producer prices are available only for the supply fish types; hence, a method must be devised to proceed from PPi for i 2 SF to PPj for DFi, The simplest assumption to make for the component prices (adopted here) would be to impose PPi for all the PPj’s, i.e., assuming an identical marginal cost structure in transforming composite i into outputs j. Due to this difficulty, it is preferable to adopt as few supply composites as possible in assembling the benchmark data set.

REFERENCES Ahmed, M., Rab, M. & Dey, M.M. (2003) Changing structure of fish supply, demand, and trade in developing countries: issues and needs. In: Fisheries in the Global Economy. Proceedings of the Biennial Conference of the International Institute on Fisheries Economics and Trade (IIFET) 2002. Alston, J., Norton, G. & Pardey, P. (1995) Science Under Scarcity: Principles and Practice for Agricultural Research Evaluation and Priority Setting. Cornell University Press, Ithaca. Armington, P. (1969) A theory of demand for products distinguished by place of production. IMF Staff Papers, 16, 159–178. Balisacan, A. (1994) Demand for food in the Philippines: response to price and income changes. Paper presented at the Third Workshop on Projections and Policy Implications of Medium and Long Term Rice Supply and Demand, International Rice Research Institute, 24 January 1994. Ball, E., Bureau, J.-F., Eakin, K. & Somwaru, A. (1997) Cap reform: modeling supply response subject to the land set-aside. Agricultural Economics, 17, 277–288. Blundell, R., Pashardes, P. & Weber, G. (1993) What do we learn about consumer demand patterns from micro data?. American Economic Review, 83, 570–597. Bruinsma, J. (2004) World Agriculture: Towards 2015=2030. ed. Food and Agriculture Organization, Rome. Deaton, A. & Muellbauer, J. (1980) An almost ideal demand system. American Economic Review, 70, 312–326. Delgado, C., Wada, N., Rosegrant, M., Meijer, S. & Ahmed, M. (2003) Fish to 2020: Supply and Demand in Changing Global Markets. International Food Policy Research Institute, Washington, and WorldFish Center, Penang. Dey, M.M., Rab, A., Paraguas, F., Piumsombun, S., Bhatta, R., Alam, F. & Ahmed, M. (2005) Fish consumption and food security: a disaggregated analysis by types of fish and classes of consumers in selected Asian countries. Aquaculture Economics and Management (this issue). Dey, M. M., Paraguas, F. & Alam, M. (2003) Cross-country synthesis. In: Production, Accessibility, Marketing, and Consumption Patterns of Freshwater Aquaculture Products in Asia FAO Fisheries Circular, 973. Food and Agriculture Organization, Rome. Dey, M.M. (2000) Analysis of demand for fish in Bangladesh. Aquaculture Economics and Management, 4, 63–79. Evenson, R., Quisumbing, A. & Bantilan, M.C. (1993) Population, technology, and rural poverty in the Philippines: rural income implications from a simple CGE impact multiplier model. Perspectives on Philippine Poverty. University of the Philippines Press, Quezon City, and Council on Southeast Asian Studies, Yale University.

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(Food and Agriculture Organization) (2001) FishStat hhttp:==www.fao.org=fi=statist= fisoft=FISHPLUS.aspi, downloaded January 2004. Garcia, Y., Dey, M.M. & Navarez, S. (2005) Demand for fish in the Philippines: a disaggregated analysis. Aquaculture Economics and Management (this issue). Greene, W. (2001) Econometric Analysis. 4th ed. Prentice-Hall, New Jersey. Heien, D. & Wessells, C. (1990) Demand systems estimation with microdata: a censored regression approach. Journal of Business & Economic Statistics, 8, 365–371. Horridge, J., Parmenter, B. & Pearson, K. (1993) ORANI-F: a general equilibrium model of the Australian economy. Economic and Financial Computing 3(2), 71–140. Huang, J. & Chen, C. (1999) Effects of trade liberalization on agriculture in China: commodity aspects. Working Paper No. 43. Regional Coordination Center for Coarse Grains, Pulses, Roots and Tuber Crops in the Humid Tropics of Asia and the Pacific, Bogor, Indonesia. Jensen, C. (2003) Applications of dual theory in fisheries: a survey. Marine Resource Economics, 17, 309– 334. Kirkley, J. & Strand, I. (1988) The technology and management of multi-species fisheries. Applied Economics, 20, 1279–1292. Lang, G. (2001) Global warming in German agriculture: impact estimations using a restricted profit function. Environmental and Resource Economics, 19(1), 97–112. Pashardes, P. (1993) Bias in estimating the almost ideal demand system with the Stone index approximation. Economic Journal, 103, 908–915. Pinstrup-Andersen, P. & Pandya-Lorch, R. (1999) Achieving food security for all: key policy issues for developing countries. Fisheries Policy Research in Developing Countries: Issues, Priorities and Needs (eds. M. Ahmed, C. Delgado, S. Sverdrup-Jensen & R.V. Santos), pp 13–20. International Center for Living Aquatic Resources Management (ICLARM) Conference Proceedings 60. Rodriguez, U-P., Garcia, Y. & Navarez, S. (2005) Modeling fisheries supply and demand in the Philippines. Aquaculture Economics and Management (this tissue). Sadoulet, E. & de Janvry, A. (1994) Quantitative Development Policy Analysis. Johns Hopkins University Press, Baltimore. Shumway, R., Jegasothy, K. & Alexander, W. (1987) Production interrelationships in Sri Lankan peasant agriculture. Australian Journal of Agricultural Economics, 31, 16–28. Smith, P., Griffiths, G. & Ruello, N. (1998) Price formation in the Sydney fish market. Research Report 98.8. Australian Bureau of Agricultural and Resource Economics, Canberra. Squires, D. (1987) Long-run profit functions for multiproduct firms. American Journal of Agricultural Economics, 69, 558–569. Westlund, L. (1995) Apparent historical consumption and future demand for fish and fishery products: exploratory calculation. Paper presented at the International Conference on the Sustainable Contribution of Fisheries to Food Security, Kyoto, Japan, 4–9 December 1995. Williams, M. (1999) Factoring fish into food security: policy issues. Fisheries Policy Research in Developing Countries: Issues, Priorities and Needs (eds. M. Ahmed, C. Delgado, S. Sverdrup-Jensen & R.V. Santos), pp 13–20. International Center for Living Aquatic Resources Management (ICLARM) Conference Proceedings 60. FAO

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APPENDIX: BASELINE MODEL VARIABLES AND EQUATIONS Definitions Sets Set name

Definition

Relations

Ak AFNk DCOM DCOMN

netput vector, production category k, k 2 K nonfish inputs in production category k, k 2 K demand composites among demand fish types noncomposites among demand fish types

DF F FDi

demand fish types fish types fish types contained in demand fish type i, i 2 DF

FM FMN FSi

fish types, imported fish types, not imported fish types contained in supply fish type i, i 2 SF

FM  F FM [ FMN ¼ F FSi  F S FSi ¼ F

FX FXN K KSi R SCOM SCOMN

fish types, exported fish types, not exported production categories production categories with netput as fish type i, i 2 SFF region supply composites among supply fish types noncomposites among supply fish types

FX  F FX [ FXN ¼ F

SF SFk SFF SFFN CONDk

supply fish types supply fish types in production category k, k 2 K supply fish types produced as fresh fish supply fish types produced as nonfresh fish (i.e., processed) types of conditioning variables, k 2 K

FDFN

food types, nonfish

AFNk  Ak DCOM  DF DCOMN  F DCOMN  DF F \ DF ¼ DCOMN F \ DF ¼ DCOMN FD Si F FSi ¼ F i

i

S

Ki ¼ K

i

SCOM  SF SCOMN  F SCOMN  SF SCOMN  SF S SFk ¼ SFF k SFF  SF SFFN  SF Ak ¼ CONDk [ AFNk [ Vk

Endogenous variables Variable

Definition

FDEXi FEXi PAGFNi PARMi PARXi PCij

food expenditure, per capita in region i fish expenditure, per capita in region i price index, aggregate nonfish food, in region i price of import-domestic aggregate, fish type i price of export-domestic aggregate, fish type i Consumer price, fish type i, region j

PDi PEik

demand price, with aggregation (where applicable) normalized effective price, netput element i, in production category k

PFDi PFi

aggregate price, food, in region i aggregate price, fish, in region i

Domain i i i i i i j i i

2R 2R 2R 2F 2F 2 DF 2R 2 DF 2 Ak

k2K i2R i2R

(Continued)

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APPENDIX Continued Variable

Definition

PPi PPik PSi QAik

producer price, fish type i producer price, supply fish type i, in production category k supply price, with aggregation (where applicable) quantity of netput, element i in netput vector, for production category k

QSCATi QDFi QDTi QDTij

quantity quantity quantity quantity

QHMi QHXi QMi QNUMi QSFi QSik

domestic component of import-domestic aggregate domestic component of export-domestic aggregate imports of fish type i quantity of numeraire netput, production category i quantity supplied, fish type i quantity supplied, supply fish type i, total in production category k

QSTi QXi SHFi SHij

quantity supplied, total for supply fish type i exports of fish type i average share of fish in food expenditure share in fish expenditure, fish type i, per capita in region j

STONEi

Stone price index (in logs), fish, per capita in region i

Domain i 2 SF i 2 SF i 2 SFk k2K

supplied, total, across categories, prior to processing demanded, fish type i demanded, total, fish type i demanded, total, fish type i, in region

Exogenous variables kik technology index, netput vector element i, in production category k knumk convi firmsk marij

technology index, numeraire input in production category k conversion ratio from supply to demand, fish type i (includes processing and statistical discrepancy) number of supply units in kth category mark-up between consumer and demand price, fish type i, in region j

pfdni pmi pxi pfdni pnumk popi pfnij

aggregate price, nonfood goods, in region i import price of fish type i, imported fish type export price of fish type i, exported fish type aggregate price, nonfood goods, in region i price of numeraire, production category k population in region i price of nonfish food item i, in region j

PPik

prices of nonfish input i in production category k

shfnij

share of nonfish food item i, in region j, in food expenditure

vik

value of conditioning variable i, in production category k, averaged within k

yj

household income, per capita in region j

i2F i 2 DF ji 2 DF j 2R i2F i2F i2F i2K i2F i 2 SF j 2K i 2 SF i 2 FX i2R i 2 DF j 2R i2R i 2 Ak k2K k2K i 2 SF k2K i2F j 2R i2R i 2 FM i 2 FX i2R k2K i2R i 2 FDFN j 2R i 2 AFNk k2K i2Z j 2R i 2 SF k2K j 2R (Continued)

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Analysis of Fish Supply, Demand, and Trade in Asia APPENDIX Continued Parameters Parameter

Definition

aijk

supply coefficient, of netput element i, for netput element j, in production category k

aik

supply coefficient, of conditioning variable i, in production category k

aik

intercept term of supply, of netput element i, for production category k

a0k /ij

intercept term of numeraire netput, in production category k per unit contribution of supply fish type i, fresh, to one unit of processed fish type j

fi

conversion ratio from preprocessed to processed form, for processed fish type i Stage 1 equation, coefficient i intercept term, Stage 1 equation, for region i intercept term, Stage 2 equation coefficient of fish price (logs), Stage 2 equation coefficient of nonfish food price i, Stage 2 equation

Domain i 2 Ak k2K i 2 SF k2K i 2 SF k 2 Kk 2 K

bi b0i hi h1 h2ij h3 h4 b20i cij

coefficient of expenditure term, Stage 2 equation coefficient of quadratic term, Stage 2 equation intercept term, Stage 2 equation, for region i Stage 1 coefficient, of fish type i, for the price of fish type j (in logs)

c0ij

intercept term, Stage 1 equation for fish type i, in region j

c1i c2i rmi

Stage 1 coefficient for expenditure term, fish type i Stage 1 coefficient for quadratic term, fish type i elasticity of substitution, domestically produced and imported versions, fish type i elasticity of transformation, domestically consumed and exported versions, fish type i elasticity of substitution between components in demand fish type for disaggregation elasticity of transformation between components in supply fish type, for disaggregation parameter for rmi parameter for rxi parameter for rdi parameter for rsi parameter for domestic production, fish type i, i an imported fish type parameter for imports, fish type i, i an imported fish type

rxi rdi rsi &mi &xi &di &si dm1i dm2i

i 2 SFF j 2 SFFN i 2 SFFN i ¼ 1, 2, 3, 4 i2R i2R i 2 DF j 2R

i2R i 2 DF j i j i i i

2R 2 DF 2R 2R 2F 2 FM

i 2 FX i 2 DCOM i 2 SCOM i i i i i

2 FM 2 FX 2 DCOM 2 SCOM 2 FM

i 2 FM (Continued)

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APPENDIX Continued Parameters Parameter

Definition

dx1i

Domain

dx2i ddij

parameter for domestic consumption, fish type i, i an exported fish type parameter for exports, fish type i, i an exported fish type parameter for fish type j, in demand fish type i for disaggregation

dsij

parameter for fish type j, in supply fish type i for disaggregation

i 2 FX i i j i j

2 FX 2 DF 2 FDi 2 SF 2 FSi

Equations Producer core Definition of effective price ðP1Þ

PEik ¼

PPik pnumk



kik knumk

i 2 Ak ; k 2 K

Definition of producer price by fish type ðP2Þ

PPi ¼ PPjk

i 2 FSj ; j 2 SFk ; k 2 K

Netput quantity per supply unit ðP3Þ QAik ¼

aik þ

X

aijk  PEjk þ

X

j

! 

alk vlk

 kik

i; j 2 Ak ; k 2 Kl 2 CONDk

l¼1

Netput quantity, numeraire, per supply unit ðP4Þ QNUMk ¼

a0k


1XX aijk  PEik  PEjk 2 i j

!  knumk

i; j 2 Ak ; j 2 K

Total netput supply by production category ðP5Þ

QSik ¼ QAik  firmsk

i 2 SFk ; k 2 K

Total output supply, by supply fish type, pre-processed X ðP6Þ QSik i 2 SFF ; k 2 KSi QSCATi ¼ k

Conversion from fresh fish to processed fish X ðP7Þ /ij  QSCATj i 2 SFFN ; j 2 SFF QSTi ¼ fi  j

Total supply of fresh fish after conversion X ðP8Þ /ij Þ  QSCATi 2 SFF ; j 2 SFFN QSTi ¼ ð1
j

Consumer core Predicted food expenditure (Stage 1)

(Continued)

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Analysis of Fish Supply, Demand, and Trade in Asia APPENDIX Continued Equations ðC1Þ ln FDEXi ¼ b0i þ b1  ln PFDi þ b2  ln pfdni þ b3  ln yi þ b4  ðln yi Þ2

i2R

Predicted fish expenditure (Stage 2) X ðC2Þ FEXi ¼ hi þ h1  ln PFi þ h2ij  ln pfnij þ h3  ln FDEXi þ h4  ðln FDEXi Þ2

i 2 R; j 2 FDFN

j

Quadratic LA-AIDS share equation (Stage 3) X ðC3Þ SHij ¼ c0ij þ cik  ln PCij þ c1i  ðln FEXj Þ þ c2i  ðln FEXj
STONEj Þ2

i; k 2 DF ; j 2 R

k

Stone price index (in logs) X STONEi ¼ ðC4Þ SHij  ln PCij 2 DF ; j 2 R j

Aggregate price of fish ðC5Þ

PFj ¼

X

SHFi  PCij 2 DF ; j 2 R

i

Share of fish in food expenditure ðC6Þ

SHFi ¼

FEXi FDEXi

i2R

Aggregate price of food ðC7Þ

PFDi ¼ SHFi  PFi þ ð1
SHFi Þ  PAGFNi

Aggregate price of nonfish food X ðC8Þ shfnij  pfnij PAGFNij ¼

i2R

i 2 R; j 2 FDFN

j

Average quantity demanded, demand fish type i in region j ðC9Þ

QDij ¼

SHij  FEXj PCij

i 2 DF ; j 2 R

Total quantity demanded, demand fish type i in region j ðC10Þ

QDTij ¼ QDij  popj

i 2 DF ; j 2 R

Total quantity demanded, demand fish type i X ðC11Þ QDTij 2 DF ; j 2 R QDTi ¼ j

Trade core Zero entries for nonimported and nonexported fish types ðT1Þ

QMi ¼ 0;

QHMi ¼ QDFi

i 2 FMN

(Continued)

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APPENDIX Continued Equations ðT2Þ

QXi ¼ 0; QHXi ¼ QSFi

i 2 FXN

Composite price of import-domestic aggregate ðT3Þ

PSi  QHMi þ pmi  QMi QDFi

PARMi ¼

i2F

Conditional demand for domestic component of imported fish type
 PARMi rmi ðT4Þ  QDFi i 2 FM QHMi ¼ d1m rmi  PPi Conditional demand for imports
 PARMi rmi ðT5Þ  QDFi QMi ¼ d2m rmi  pmi

i 2 FM

Composite price of export-domestic aggregate ðT6Þ

PARXi ¼

PPi  QHXi þ pxi  QXi QSFi

i2F

Conditional supply of domestic component of exported fish type
 PPi rxi ðT7Þ  QSFi i 2 FX QHXi ¼ d1x rxi  PARXi Conditional supply of exports
rxi pxi QXi ¼ d2x rxi  ðT8Þ  QSFi PARXi

i 2 FX

Disaggregation of composites Equality for noncomposite demand fish types ðM1Þ

QDTi ¼ QDFj

i 2 DCOMN ; j 2 FDi

Conditional demand for components of demand composite
rdi PDi ðM2Þ  QDTi i 2 DCOM ; j 2 FDi QDFj ¼ ddjrdi  PARMj Equality for noncomposite supply fish types ðM3Þ

QSTi ¼ QSFj

i 2 SCOMN ; j 2 FSi

Conditional supplies for components of supply composite
rsi PPj QSFj ¼ dsjrsi  ðM4Þ  QSTi 2 SCOM ; j 2 FSi PSi Demand price P ðM5Þ

PDi ¼

! PARMj  QDFj

j

QDTi

i 2 DF ; j 2 FDi

(Continued)

Analysis of Fish Supply, Demand, and Trade in Asia APPENDIX Continued Equations Supply price P ðM7Þ

PSi ¼

! PPj  QSFj

j

QSTi

i 2 SF ; j 2 FSi

Model closure Equilibrium conditions ðE1Þ

QHMi ¼ QHXi

i2F

Percentage margin on price, import-domestic aggregate ðE2Þ

PCij ¼ PDi ð1 þ marij Þ i 2 DF ; j 2 R

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