Working Paper 98-2
Appendix, Tables, and Figures

Asian Competitive Devaluations

© Institute for International Economics.

 

Appendix A: Algebraic Description of the Model

The model used in this paper is an extension of de Melo and Tarr's basic general equilibrium trade model (1992) to a multi-country setting. We apply the Whalley (1985) approach to endogenize all regions (including the rest of the world), incorporate the macroeconomic specifications from Devarrajan, Lewis and Robinson (1990), and include an international shipping sector similar to the GTAP model (Hertel, 1997). However, in this application, the commonly used Leontief supply-side technology (cf. deMelo and Tarr, 1992) is replaced by a more flexible CES production function, which allows substitution between value-added and aggregate inputs in the upper-level of the production tree. On the demand-side, the standard LES demand system has been extended to an Extended Linear Expenditure System (ELES) system, allowing scope for endogenous household saving decisions in the model. Because duality approach is used throughout the specification, the model is relatively simple and transparent in structure. This Appendix provides a detailed description of the 21-region, 20-sector model for world production and trade used in this analysis.

 

Notation

Region name: USA (the United States), CAN (Canada), AUS (Australia), NZL (New Zealand), WEU (15 members of European Union), JPN (Japan), TWN (Taiwan), HKG (Hong Kong), CHN (China), KOR (Korea), SGN (Singapore), IDN (Indonesia), MYS (Malaysia), PHL (Phillipines), THA (Thailand), MEX (Mexico), CHL (Chile), EIT (Economies in Transition), SAS (South Asia), LTN (Other Latin American Countries), and ROW (rest of the world).

Sector name: ARG(agriculture, 9 detailed sectors), FOOD (processed food), MINES (mineral and energy products), ENRGY (energy), TEXT (Textile), CLOTH (wearing Apparel), LMNF (other light manufacture), INTER (manufactured intermediates), TRANS (transport equipment), MACH (other machinery), HOSC (tradable Serices), and SEVR (services).

Factor name: LND (arable land), NLB (unskilled labor), SLB (skilled labor), CAP (capital).

Subscripts and Set Definition:

• Regions are defined in set R and indexed by r or s. r, s R = {USA, CAN, AUS, NZL, WEU, JPN, TWN, HKG, CHN, KOR, SGN, IDN, MYS, PHL, THA, MEX, CHL, EIT, SAS, LTN, ROW.};

• Sectors are defined in set I and indexed by I or j. I, j I = {AGR, FOOD, MINES, ENRGY, TEXT, CLOTH, LMNF, INTER, TRANS, MACH, HOSC, SEVR, INVST};

• Agricultural sectors are defined as a subset of I: IAG(I) = {AGR};

• Primary factors are defined in set F and indexed by f. f F = {LND, ULB, SLB, CAP}; Conventions: Uppercase English letters indicate variables. A variable with a bar on top is usually set exogenously. Greek letters or lowercase English letters refer to parameters, which need to be calibrated or supplied from exogenous sources. When multiple subscripts of a variable or parameter come from the same set, the first one represents the region or sector supplying the goods; the next one represents the region or sector purchasing the goods.

 

Price Equations

Table A.1 list price equations in the model. Equations 1 and 2 define the relationship between border (world) prices and internal prices, while equations 3, 4, 6 , 7, and 8 define price indices for aggregate imported goods, Arminton goods, composite value-added, and the firm's output with and without production taxes, respectively. In equations 3, 4, 6, and 7, the price indices are the unit cost functions, while in equation 8 they are unit revenue functions, all of which are dual to the corresponding unit quantity aggregator functions. For example, equation 7 is the result of cost minimization by the representative firm in each sector with respect to its aggregate factor and inputs, subject to a CES production function. Since CES functions are used as the building blocks of the basic model, and this quantity aggregator function is homogeneous of degree one, the total costs can be written as total quantity multiplied by unit cost (Varian, 1984, p28). This implies that the average cost, under cost minimization, is independent of the number of units produced or purchased. Thus, the unit cost function also stands for the price of the composed commodity. Equation 5 defines the unit price for aggregate inputs, which is the IO coefficient weighted sum of all the value of its contents. Equation 9 states the domestic consumer price is the Arminton goods price plus sales taxes. Equation 10 specifies an economy-wide consumer price index, which is used as price of household savings. Equation 11 defines the numeraire in the model.

 

Table A.1: Price Equations

 

Supply Equations

Equation 12 and 13 specify the demand functions for aggregate factor and intermediate inputs, while equation 14 gives demand functions of each primary factor (Table A.2). They equal unit demand function multiplied by the quantities of total output, and the unit demand functions are obtained by taking partial derivatives of the unit cost functions (equation 6 and 7) with respect to the relevant factor prices, according to Shephard's lemma. Equations 15-18 are the domestic and export supply functions corresponding to the constant elasticity of transformation (CET) function commonly used in today's CGE models. They are derived from revenue maximization, subject to the CET function, in a way similar to the derivation of factor demand functions. Equation 19 aggregates exports by the representative firm in each region, which implies that producers only differentiate output sold in domestic and foreign markets, but do not differentiate exports by destination (foreign markets are perfect substitutes). Equations 15-18 can be partially or entirely turn off in the model, in such case, PD_ir = PE_ir = P_ir will be enforced and exports and domestic sales become perfect substitutes in the model.

Table A.2: Factor Demand and Export Supply Equations

 

Trade and Final demand Equations

Trade and final demand equations are shown in Table A.3. Equation 20 is the consumer demand function, which is the Extended Linear Expenditure System derived from maximizing a Stone-Geary utility function subject to household disposable income, which is specified in equation 31. Equation 21 defines household supernumerary income, which is disposal income less total expenditure on the subsistence minima. Equations 22 and 23 give government and investment demands. Equations 24-26 are demand functions for domestic goods, for aggregate imported goods, and for imported goods by source, respectively. They describe the cost-minimizing choice of domestic and import purchases, as well as import sources. They are derived from corresponding cost functions according to Shephard's lemma in a way similar to the derivation of factor demand functions (taking partial derivatives of the cost function with respect to the relevant component prices). Because of the linear homogeneity of the CES function, the cost function that is dual to the commodity aggregator can be represented by its unit cost function (equations 3 and 4) multiplied by total quantity demanded.

 

Table A.3: Trade and Final Demand Equations

 

International Shipping Equations

Table A.4 lists the equations describe international shipping industry in the model. Equations 27 and 28 describe the supply side of the international shipping industry. Equation 27 states that at equilibrium, the returns from shipping activity must cover its cost. Like other industries in the model, it also earns zero profit. Equation 28 describes the demand for each region's service sector exports to the international shipping industry, which is generated by the assumed Cobb-Douglas technology in this industry. The next two equations (29 and 30), refer to the demand side of the international shipping industry. The demand for shipping services associated with commodity i in region r is generated by a fixed proportion input requirement (Leontief) coefficient trs_isr, which is routine/commodity specific (equation 29). In equilibrium, the total demand of shipping service must equal its total supply (equation 30).

 

Table A.4: International Shipping Equations

 

Income and Saving Equations

Table A.5 summarizes all income and saving equations in the model. Equations 31 and 32 define household disposal income and savings. Equations 33-37 determine government revenue from production taxes, consumption taxes, tariffs and export taxes (its negative equals a subsidy), respectively, while equations 38-39 define government transfer to household and the balance of trade (foreign savings) in each region.

 

Table A.5: Income and Saving Equations

 

General Equilibrium Conditions

Equations define general equilibrium conditions are given in Table A.6. Equations 40-43 are system constraints that the model economy must satisfy. For every sector in each region, the supply of the composite goods must equal total demand (equation 40), which is the sum of household consumption (C_ir), government purchases (GC_ir), investment (ID_ir) and the firm's intermediate demand. Similarly, the demand for each factor in every region must equal the exogenously fixed supply (equation 41). In this dual formulation, output in each region is determined by demand. Sectoral equilibrium is determined in equation 42, unit output price equals average cost, which is also the zero profit condition. Equation 43 describes the macroeconomic equilibrium identity in each region, which is also the budget constraint for the investor. Since all agents in each region (households, government, investor, and firms) satisfy their respective budget constraints, it is well known that the sum of the excess demand for all goods is zero; that is, Walras's law holds for each region. Therefore, there is a functional dependence among the equations of the model. One equation is redundant in each region and thus can be dropped.

 

Table A.6: General Equilibrium Conditions

 

Welfare Measure

We measure the change in welfare induced by trade liberalization by the Hicksian equivalent variation (EV), with changes in government consumption and investment spending valued according to private household's preference.

There are 2,431 equations and 2,480 variables in the static version of the model. Since the 28 factor endowment variables (FS_r) are usually set exogenously, three additional sets of variables have to be set exogenously as macro closures in order to make the model fully determinate. They are chosen from following variables: (1) government spending or gross investment (GSP_r or INV_r), (2) balance of trade or exchange rate (BOT_r or ER_r), (3) government savings or transfer (GSAV_r or GTRANS_r).

The model is implemented in GAMS (Brooke, et. al. 1988). The computer code and related data files are available from the authors upon request. Definitions of variables and parameters are list in tables A.7 and A.8.

 

Table A.7: Definitions of Variables

 

Table A.8: Definitions of Parameters

 

Table 1: Stock Markets and Exchange Rates Selected Asian Countries

 

Table 2: China's Nominal and Real Effective Exchange Rate

 

Table 3: Change of Bilateral Trade Matrix (Current Price with Productivity Shock)

 

Table 4: Asian Competitive Devaluation on US Trade and Production

 

Table 5: USTR Scrutiny of Foreign Trade and Investment Barriers

	Pages in Foreign Trade Barriers	Share of Total Pages	Ratio of Page Shares to Export Share
Australia	9	3.1	1.5
China	19	6.6	3.4
Hong Kong	0	0.0	0.0
India	9	3.1	6.5
Indonesia	7	2.4	4.2
Japan	41	14.2	1.3
Korea	14	4.9	1.3
Malaysia	5	1.7	1.2
New Zealand	3	1.0	3.4
Philippines	7	2.4	3.0
Singapore	3	1.0	0.4
Taiwan	13	4.5	1.3
Thailand	7	2.4	2.4
Memorandum: Asia, total	137	47.6	1.6

Source: United States Trade Representative, 1995 National Trade Estimate Report on Foreign Trade Barriers.

Table 6: Correlations, 1984-93

	Attention	Action
TARIFF	0.10c	-0.01
STNDTAR	-0.09	-0.07
XRESID	0.10c	-0.01
INVRESID	-0.00	0.04
GDP	0.63a	0.49a
GDPGROWTH	-0.03	-0.01
TBAL	-0.67a	-0.33a
EXPORT	0.57a	0.40a
FDI	0.43a	0.39a
IIT	0.12b	0.10c

Note: Superscripts a, b, and c indicate 1, 5, and 10 percent significant level, respectively.

Definitions: GDP = gross domestic product (millions of dollars); GDPGrowth = growth rate of GDP; TRADEBAL = bilateral trade balance (millions of dollars); IIT = index of intra-industry trade; EXPORT = U.S. bilateral exports (millions of dollars); INFEXP = U.S. intra-firm exports (millions of dollars); TARIFF = trade-weighted average tariff; STDTARIFF = standard deviation of TARIFF.

Source: Noland, 1997b, Table 3.

Table 7: Bilateral Trade Conflict

	7.1	7.2	7.3
SAMPLE	N=28, 1993	N=360, 1984-93	N=360, 1984-93
DEPENDENT VARIABLE	Attention	Attention	Action
CONSTANT	5.63 (2.46)b	__	__
GDP	3.44E-6 (1.38)	0.01 (3.65)a	-0.00 (-0.29)
GDPGROWTH	0.32 (1.42)	4.56 (2.04)b	1.83 (0.83)
TRADEBAL	-2.74E-4 (-1.89)c	-0.30 (-4.60)a	-0.02 (-0.61)
IIT	-6.99 (1.98)b	2.09 (1.58)	2.32 (2.83)a
EXPORT	3.92E-4 (2.52)b	-0.08 (1.56)	0.02 (0.63)
INFEXP	-7.41E-4 (-1.84)c	__	__
FDI	-2.31E-5 (-0.27)	0.07 (2.29)b	-1.54 (-0.09)
TARIFF	-0.08 (-0.64)	1.20 (0.25)	1.89 (4.01)a
STD TARIFF	2.15 (-0.62)	-3.55 (-0.09)	4.57 (2.83)a
R2	0.90	0.21
Log likelihood			-117.02
Cases correct (percentage)			0.88

Note: Superscript a indicates significance at the 1 percent level, b the 5 percent level, and c the 10 percent level.

Definitions: See Table 6.

Sources: (7.1): Noland, 1996, Table 11; (7.2): Noland, 1997b, Table 4; (7.3): Noland, 1997b, Table 5.

Table 8: Determinants of Success

	8.1	8.2
DEPENDENT VARIABLE	Case A Success Rate	Case B Success Rate
CONSTANT	-0.19 (-0.80)	-0.65 (-1.60)
LEXPRAT	0.29 (3.97)a	0.47 (3.14)a
LIMPRAT	-0.38 (-4.45)a	-0.37 (-2.25)b
LFDIRAT	0.10 (3.04)a	0.04 (0.65)
LGDP	0.02 (0.82)	0.06 (1.31)
LGDPCAP	0.06 (2.36)b	0.16 (3.35)a
TRADEBAL	0.01 (2.57)b	0.01 (1.93)c
TARIFF	0.00 (0.04)	-0.01 (-1.99)c
STDTARIFF	-0.00 (-1.88)c	0.01 (1.09)
R2	.68	.63

Note: Superscript a indicates significance at the 1 percent level, b at the 5 percent level, and c at the 10 percent level.

Definitions: LEXPRAT = log of exports to U.S. as share of partner country income; LIMPRAT = log of imports from the U.S. as share of partner country income; LDIRAT = log of U.S. FDI in partner country income; LGDP = log of GDP; LGDPCAP = log of per capita GDP; for all other definitions, see Table 6.

Source: Noland, 1997b, Table 10.

 

Table 9: Impact on US Trade Relations

	ATTENTION (actual)	ATTENTION (projected, EXP9)	PROBABILITY OF ACTION	PROBABILITY OF ACTION (projected, EXP9)
China	19	20	0.91	0.92
Indonesia	7	9	0.08	0.09
Japan	41	46	0.94	0.96
Korea	14	17	0.45	0.51
Malaysia	5	6	0.41	0.44
Philippines	7	8	0.26	0.27
Singapore	3	3	0.00	0.00
Taiwan	13	14	0.20	0.24
Thailand	7	9	0.12	0.13
TOTAL	116	132

 

Figure 1:

Working Paper 98-2
Appendix, Tables, and Figures

Asian Competitive Devaluations

© Institute for International Economics.

 

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