Bilateral multifactor CES general equilibrium with state-replicating Armington elasticities
aa r X i v : . [ q -f i n . E C ] J u l Bilateral multifactor CES general equilibrium withstate-replicating Armington elasticities
Jiyoung Kim · Satoshi Nakano · KazuhikoNishimura
July 21, 2017
Abstract
We measure elasticity of substitution between foreign and domesticcommodities by two-point calibration such that the Armington aggregator canreplicate the two temporally distant observations of market shares and prices.Along with the sectoral multifactor CES elasticities which we estimate by regres-sion using a set of disaggregated linked input–output observations, we integratedomestic production of two countries, namely, Japan and the Republic of Korea,with bilateral trade models and construct a bilateral general equilibrium model.Finally, we make an assessment of a tariff elimination scheme between the twocountries.
Keywords
State-replicating elasticities · Two-point calibration · Linked input–output tables · Bilateral general equilibrium
JEL Codes
C54, C68, F17, F47, N75
Recently, Kim et al (2017) established a general equilibrium framework compris-ing multifactor CES production functions with estimated elasticities for each ofthe industrial sectors; each elasticity is measured by the slope of the regressionline between the growths of factor shares and factor prices, which are observedin a set of linked input–output tables. The present study is intended to extend
This material is based upon work supported by JSPS Grant No. 16K00687.J. KimInstitute of Developing Economies, Chiba 261-8545, JapanE-mail: jiyoung [email protected]. NakanoThe Japan Institute for Labour Policy and Training, Tokyo 177-8502, JapanE-mail: [email protected]. Nishimura (cid:0)
Faculty of Economics, Nihon Fukushi University, Tokai 477-0031, JapanE-mail: [email protected] Jiyoung Kim et al. this framework in such a way as to incorporate substitution between domestic andimported commodities (i.e., Armington elasticity) and to endogenize the interna-tional trades for all commodities traded between two countries, namely, Japan andthe Republic of Korea.Armington elasticity is an essential component in trade policy analyses. Pre-vious work concerning economic assessment of trade liberalization schemes (e.g.,Harrison et al, 1997; Nakajima, 2002; Urata and Kiyota, 2003; Park, 2004) haveused computable general equilibrium (CGE) models based on the Global TradeAnalysis Project (GTAP) database. While these models make use of empirically es-timated elasticities, the estimates of the elasticities between the aggregated factors,which are essentially based upon time series analyses, tend to show smaller elastic-ities than anticipated (McDaniel and Balistreri, 2002). Notwithstanding, Arming-ton elasticities can be large in light of the indifferences between goods of the sameclassification but from different countries. Moreover, previous CGE models are cal-ibrated at a single state (i.e., one-point calibration) to incorporate regionalities,except for the elasticity parameters, which are usually given a priori.From another perspective, Saito (2004) was concerned with the separability offoreign commodities i.e., the distinction between inter- and intra-group Armingtonelasticities. The inter-group elasticity is the elasticity of substitution between abasket of domestic commodities and that of imports as a whole, whereas the intra-group elasticity is the elasticity of substitution between a basket of imports fromone foreign country and that from another. The estimates of inter-group elasticitieswere larger for intermediate input sectors, whereas the intra-group elasticities weresignificantly lower. In the same vein, Feenstra et al (2014) studied the elasticityof substitution between domestic and foreign goods (i.e., macro elasticity), andbetween varieties of foreign goods (i.e., micro elasticity) and essentially found theopposite: the micro elasticity was significantly larger than the macro elasticity.Our approach differs from those of the previous studies in two aspects. First,all elasticities are measured based upon published statistics, i.e., linked input–output tables for Japan and for Korea and the UN Comtrade database, and arenot adopted from elsewhere. Second, we construct a model that completely repli-cates two temporally distant state observations rather than conducting a timeseries analysis to measure elasticities between aggregated factor inputs, as we areinterested in a shorter term and a sector-wide policy implication such as regard-ing tariff liberalization. The state-replicating Armington elasticities are measuredby two-point calibration. That is, we measure elasticity that agrees with the twoobserved domestic–foreign shares in both physical and monetary terms. Moreover,the elasticities are measured in a two-stage nested structure as illustrated in Fig.1. Specifically, we evaluate the compound price of each factor input w Ci , in termsof domestic and foreign factor input prices ( w Di , w Fi ) that are observable, viaCES aggregation whose macro elasticity replicates the observed domestic-foreignmarket shares. We then calibrate the micro elasticity by using w Fi and the partnercountry’s domestic price w D ′ i in order that the observed partner-ROW marketshares are replicated. In this way and based upon 2000–2005 linked input–outputtables for Japan and Korea, we construct a multi-sectoral (395 for Japan and 350for Korea) general equilibrium model with endogenized bilateral trades, in contrastto the previous studies with limited variety of industrial sectors. ilateral multifactor CES general equilibrium 3 Fig. 1
Nested structure of macro and micro Armington elasticities. A foreign commodity priceis given by aggregating the partner country’s and the rest of the world’s (ROW’s) commodityprices. The compound commodity price is given by aggregating the domestic and foreigncommodities’ prices. Finally, the domestic price is given by a multifactor CES aggregator (i.e.,unit cost function).
The remainder of the paper is organized as follows. In the next section, weintroduce the basics of the two-point calibration of the CES elasticity parameters,i.e., macro and micro Armington elasticities, and the multifactor CES elastic-ity estimation by regression. In Section 3, we apply these protocols using linkedinput–output tables for Japan and for Korea and the UN Comtrade database. InSection 4, we integrate domestic and trade models to construct a bilateral generalequilibrium model for welfare analysis of trade liberalization. Section 5 providesconcluding remarks. i is omitted) can be evaluated by a CES aggregator offoreign and domestic commodity prices as follows: w C = (cid:18) α (cid:16) w D (cid:17) − ε + (1 − α ) (cid:16) w F (cid:17) − ε (cid:19) − ε ≡ U (cid:16) w D , w F (cid:17) (1)where w C is the composite price of a commodity in the concerned country, w F isthe price of the imported foreign product (including tariff), and w D is the priceof the domestic commodity. Here, the share parameter α ∈ (0 ,
1) and the macroArmington elasticity ε are subject to estimation.According to Shephard’s lemma, we can obtain the cost share by taking deriva-tives as follows: s D = ∂w C ∂w D w D w C = α (cid:18) w D w C (cid:19) − ε s F = ∂w C ∂w F w F w C = (1 − α ) (cid:18) w F w C (cid:19) − ε (2) Jiyoung Kim et al. where s D and s F denote the market shares of the domestic and imported com-modities, respectively. One may verify that s D + s F = 1 by taking (1) into account.Below we show that ε can be measured by two-point calibration using two tem-porally distant market share observations, namely, the reference market shares( s D< , s F< ) and the current market shares ( s D> , s F> ), with the price changes in thedomestic ( w D< , w D> ) and imported commodities ( w F< , w F> ). Now, according to (2),the identities s D< = α (cid:18) w D< w C< (cid:19) − ε s F< = (1 − α ) (cid:18) w F< w C< (cid:19) − ε (3)must hold at the reference state and the identities s D> = α (cid:18) w D> w C> (cid:19) − ε s F> = (1 − α ) (cid:18) w F> w C> (cid:19) − ε (4)must hold at the current state. By virtue of (3) and (4), ε can be solved (two-statecalibrated) as follows: ε = 1 − ln s D> /s D< − ln s F> /s F< ln w D> /w D< − ln w F> /w F< = 1 − ∆ ln s D − ∆ ln s F ∆ ln w D − ∆ ln w F (5)where ∆ is the difference operator, i.e., current value minus reference value. Also,we may solve for the share parameter α as follows: α − α = s D< s F< (cid:18) w F< w D< (cid:19) (1 − ε ) = s D> s F> (cid:18) w F> w D> (cid:19) (1 − ε ) (6)In this way, we obtain the macro Armington aggregator (1) that replicates boththe reference and current states specified by (3) and (4), respectively. We also notethat the compound price w C will be evaluated assuming (1) and thus it is shownin brackets in Fig. 1.2.2 Micro AggregatorLet us indicate the partner country by P and the ROW by R . Assume that theaggregated foreign import product price w F (whose commodity index i is omitted)can be expressed as a CES aggregator function of price of commodity importedfrom the partner country w P and that from the ROW w R , as follows: w F = (cid:18) β (cid:16) w P (cid:17) − η + (1 − β ) (cid:16) w R (cid:17) − η (cid:19) − η ≡ V (cid:16) w P , w R (cid:17) (7)where β ∈ (0 ,
1) is the share parameter and η is the micro Armington elasticity,both of which are subject to estimation. Note that w R must be evaluated assuming(7) with the calibrated parameters, while w F and w P are statistically observable. As we will be discussing later, the price of the commodity from the partner country w P will be measured by using the partner country’s domestic price w D ′ , the relative import barrierfactor with respect to the partner country µ , and the currency exchange factor ν , i.e., w P = νµw D ′ .ilateral multifactor CES general equilibrium 5 Hence, the parameters are calibrated according to the two-state observation of thepartner country’s market share within the commodity’s fraction of imports, i.e.,( s P< , s P> ). Notice that s P< + s R< = 1 and s P> + s R> = 1 by definition.The following identities must hold at the reference state, according to Shep-hard’s lemma applied to (7): s P< = β (cid:18) w P< w F< (cid:19) − η s R< = (1 − β ) (cid:18) w R< w F< (cid:19) − η (8)Likewise, the following identities must hold at the current state: s P> = β (cid:18) w P> w F> (cid:19) − η s R> = (1 − β ) (cid:18) w R> w F> (cid:19) − η (9)By virtue of (8 left) and (9 left), η can be solved (two-state calibrated) as follows: η = 1 − ln s P> /s P< ln w P> /w P< − ln w F> /w F< = 1 − ∆ ln s P ∆ ln w P − ∆ ln w F (10)Also, we may solve for β as follows: β = s P< (cid:18) w F< w P< (cid:19) − η = s P> (cid:18) w F> w P> (cid:19) − η (11)Hence, we have the micro Armington aggregator (7) that replicates both the ref-erence and current states. Also note that w R will be evaluated by (7): w R = (cid:0) w F (cid:1) − η − β (cid:0) w P (cid:1) − η − β ! − η . The in-bound price of the product imported from the partner country w P isevaluated by the domestic price at the partner country w D ′ and the barrier factor µ under the currency exchange factor ν . The barrier factor µ captures variusfactors such as insurance, freight, miscellaneous tax, and tariff factors. For furtherconvenience, we may decompose µ into the tariff factor 1 + τ , where τ representsthe tariff rate, and other factors which we denote by ρ , as follows: w P = νµw D ′ = ν (1 + τ ) ρw D ′ (12)As we monitor ν and µ for the two states, w P can be evaluated accordingly, i.e., w P< = ν < · µ < · w D ′ < w P> = ν > · µ > · w D ′ > (13) Jiyoung Kim et al. j (index omitted) is assumed to be carried out under aconstant returns multifactor CES (constant elasticity of substitution) whose unitcost function can be described in the following form: w D = t − n X i =0 λ i (cid:16) w Ci (cid:17) − σ ! − σ (14)where λ i ∈ (0 ,
1) and σ are the share parameter for the i th input and the multi-factor CES elasticity of substitution, respectively, while t denotes the productivitylevel. While w D is observable, w Ci depends on (1) via w D and w F , which arestatistically observable, and the calibrated parameters α and ε .We note below that σ and t can be estimated by regression, for each indus-trial sector. The cost share of the i th input s i may be represented according toShephard’s lemma by differentiating (14) as follows: s i = ∂w D ∂w Ci w Ci w D = λ i t − (cid:18) w Ci w D (cid:19) − σ (15)By taking the logarithm of both sides, we haveln s i = ln λ i − (1 − σ ) ln t + (1 − σ ) (cid:16) ln w Ci − ln w D (cid:17) (16)Thus, the difference in (16) between two temporally distant states, i.e., referenceand current, is given by the following formula: ∆ ln s i = − (1 − σ ) ∆ ln t + (1 − σ ) (cid:16) ∆ ln w Ci − ∆ ln w D (cid:17) (17)Note, if σ and t are estimated by the slope and the intercept of (17), λ i will bedetermined by (15). ε j on two stateobservations using (5), we standardize all prices at the current state and evaluatethe reference state prices by the current-standardized price index (the inflator ),which we denote by q . Specifically, we use the following terms for calibrating theparameters: (cid:16) w D< , w D> (cid:17) = (cid:16) q D , (cid:17) (cid:16) w F< , w F> (cid:17) = (cid:16) q F , (cid:17) ilateral multifactor CES general equilibrium 7 The parameters of the macro aggregator are thus evaluated by the following for-mulae, based on (5) and (6): α = s D> ε = 1 + ∆ ln s D − ∆ ln s F ln q D − ln q F In order to evaluate micro elasticities, we need reference and current obser-vations of the partner country and the ROW market shares ( s P< , s P> ) within theforeign factor inputs. To this end, we use the 6-digit HS trade data of the UNComtrade database (Comtrade, 2017), spanning 6,376 goods, converted into thelinked input–output sector classification in order to obtain the market share ofthe partner country with respect to that of the ROW in two periods (2000 and2005). Further, in order to calibrate the parameters of the micro aggregators, weneed to specify the in-bound prices of the partner country’s commodities as notedin (13). That is, we need the inflator q P , while q F is observable in the linkedinput–output tables. (cid:16) w F< , w F> (cid:17) = (cid:16) q F , (cid:17) (cid:16) w P< , w P> (cid:17) = (cid:16) q P , (cid:17) Therefore, we use the exchange rate that properly scales the two countries’ priceindexes. Specifically, (13) must be replaced by the following identities: q P = ν < · µ < · q D ′ ν > · µ > · ν < µ < = ( ν < /ν > )( µ < /µ > ), according to (18), we may use currentstandardized index numbers for reference currency exchange factor ν < as well asfor the reference barrier factor µ < . In this way, we evaluate the in-bound partnercountry’s commodity inflator q P by way of an inflator of the commodity producedinside the partner country q D ′ . Then, according to (10) and (11), the parametersof micro aggregator are determined by the following equations: β = s P> η = 1 − ∆ ln s P ln q F − ln q P In Fig. 2, we display the two-point calibrated macro and micro Armingtonelasticities of 395 sectors for Japan. Note that the sectors are ordered accordingto Colin Clark’s Three-sector theory, namely, j = 1–27 are primary, j = 28–294are secondary, and j = 295–395 are tertiary sectors. The figure shows the recipro-cals since the calibrated elasticities were very large and diverse. Overall, we havevery large macro Armington elasticities, meaning that the domestic and importedcommodities are (almost complete) substitutes, while some of the imported com-modities of the primary sectors show some extent of complementarity. On the otherhand, Japan’s micro Armington elasticities relative to Korean products are rela-tively small, meaning that the Korean-made commodities are somehow differentfrom those of the rest of the importing countries, for Japan. In Fig. 3, we displaythe two-point calibrated macro and micro Armington elasticities of 350 sectors forKorea. In this case, sectors are primary for j = 1–28, secondary for j = 29–282,and tertiary for j = 283–350. The figure shows the reciprocals since the calibratedelasticities were very large. Overall, Korea’s macro and micro Armington elastic-ities are both smaller than those of Japan. This means that Korean industriesperceive foreign-made inputs to be somehow different from Korean-made inputs. Subsequent analysis will be confined to traded goods (products) while excluding services,due to data availability. Jiyoung Kim et al. − − − I n v e r s e M a c r o E l a s t i c i t y − − − I n v e r s e M i c r o E l a s t i c i t y Fig. 2
Inverse macro Armington elasticity ε − j for Japan (left) and inverse micro Armingtonelasticity η − j for Japan against Korea (right). − − I n v e r s e M a c r o E l a s t i c i t y − − I n v e r s e M i c r o E l a s t i c i t y Fig. 3
Inverse macro Armington elasticity ε − j for Korea (left) and inverse micro Armingtonelasticity η − j for Korea against Japan (right). ∆ ln w Ci between current and reference states in advance, using the macro aggregator (1)whose parameters are measured via the two-point calibration method presentedpreviously. The reference and current compound prices evaluated with respect tothe price indexes (inflators) used for domestic and foreign commodities are asfollows: (cid:16) w C< , w C> (cid:17) = (cid:16) q C , (cid:17) q C = (cid:18) λ (cid:16) q D (cid:17) − ε + (1 − λ ) (cid:16) q F (cid:17) − ε (cid:19) − ε Using these values, we estimate σ via (17). Specifically, 1 − σ is estimated by theslope of the following linear regression equation: ∆ ln s i = − (1 − σ ) ∆ ln t + (1 − σ ) (cid:16) ln q D − ln q Ci (cid:17) + u i (19)where s i is the cost share of input i for the concerned industrial sector whosereference and current values are both available in a set of linked input–output ilateral multifactor CES general equilibrium 9 − s i g m a − s i g m a Fig. 4
Multifactor CES elasticities σ j estimated for Japan. s i g m a s i g m a Fig. 5
Multifactor CES elasticities σ j estimated for Korea. tables and u i is the disturbance term. Further, note that growth of productivity,i.e., ∆ ln t , is estimable from the intercept of the regression line, although thatanalysis is beyond the purpose of this study.We must note that linked input–output tables do not provide price indexes forthe primary input (comprising labor and capital), which we aggregate as a singleinput in this study. To address this, we use the quality-adjusted price indexesof labor and capital compiled by JIP (2015) for Japan and by KIP (2015) forKorea for the corresponding periods in order to inflate the value added observedin nominal values. In Fig. 4, we report the estimated multifactor CES elasticities σ for all sectors (left) with the corresponding statistical significances (right) forJapan. Fig. 5 is the equivalent figure for Korea. Further, we shall note that theaverage of the estimated elasticities (ignoring statistical significance) is 1.46 forJapan and 1.53 for Korea, and these values are almost identical to those estimatedby using q Di instead of q Ci in regression equation (19) as reported in Kim et al(2017). Notice that an input–output coefficient of input i for output j represents the cost share offactor i for industry j .0 Jiyoung Kim et al. λ i at the current state where the productivity isstandardized at unity t = 1, according to (15): λ i = a i (20)Here, a i is the current state input–output coefficient (i.e., cost share) of input i for the industry (output) concerned, and thus, P ni =0 a i = 1. We may express thesystem of unit cost functions (14) as w D = (cid:16) a ( w C ) − σ + a ( w C ) − σ + · · · + a n ( w Cn ) − σ (cid:17) − σ w D = (cid:16) a ( w C ) − σ + a ( w C ) − σ + · · · + a n ( w Cn ) − σ (cid:17) − σ ... w Dn = (cid:16) a n ( w C ) − σ n + a n ( w C ) − σ n + · · · + a nn ( w Cn ) − σ n (cid:17) − σn or more concisely as w D = H (cid:16) w C , w C (cid:17) (21)The model for both countries according to the multifactor CES aggregator(14), the macro aggregator (1), and the micro aggregator (7), can be expressed asfollows, where J and K indicate Japan and Korea, respectively: w DJ = H J (cid:16) w CJ (cid:17) w DK = H K (cid:16) w CK (cid:17) (22) w CJ = U J (cid:16) w DJ , w FJ (cid:17) w CK = U K (cid:16) w DK , w FK (cid:17) (23) w FJ = V J (cid:16) w PJ (cid:17) w FK = V K (cid:16) w PK (cid:17) (24)Note that we eliminate w C from the multifactor CES aggregator since it is fixedas constant and w R from the micro aggregators as we assume that ROW importprices are invariable (under the small-country assumption).In order to close (integrate) the model, we must introduce a weighted converterthat connects the foreign sector with the domestic sector classifications in termsof 6-digit HS transactions. Specifically, a sector-HS converter z jk that assigns asectoral commodity j to an HS item k has the following form: z jk = x jk P k ∈ j x jk ilateral multifactor CES general equilibrium 11 T a r i ff R a t e ( % ) T a r i ff R a t e ( % ) Fig. 6
Tariff rates τ for Japan against Korea (left) and for Korea against Japan (right). where x jk represents the amount of import of HS item k that belongs to sector j .As we represent Japan’s sector-HS converter by matrix z J and Korea’s sector-HSconverter by z K , Korea’s 350 sectors can be converted into Japan’s 395 sectorsby z K z ⊺ J , and likewise Japan’s sectors can be converted into Korea’s by z J z ⊺ K ,where ⊺ indicates transposition. Thereupon, we introduce the following identities,according to (12): w PJ = w DK z K z ⊺ J h ν J i h µ J i w PK = w DJ z J z ⊺ K h ν K i h µ K i (25)where angle brackets indicate diagonalization. Additionally, we know that νµ = 1from (18) at the current state. Hence, we know that the equilibrium solution tothe bilateral integrated price system (22)–(25) at the current state is unity for all,i.e., w DJ = w CJ = w FJ = w PJ = in terms of Japan’s sectors and w DK = w CK = w FK = w PK = in terms of Korea’s sectors.4.2 Tariff EliminationWe first calculate the equilibrium price when all tariffs that levied against thepartner country’s commodities in both countries were eliminated. For the purposewe specify the tariff rates levied at the current state and thus we used the UNCTADTrade Analysis Information System (TRAINS, 2017) database. Specifically, weused the tariff rates evaluated by way of customs duties-imported values thatwere converted into ratios and distributed over the linked input–output productclassifications. In Fig. 6 we display the estimated tariff rates levied against thepartner country’s commodities for all sectoral commodities, for both countries.Note that “Refined sake” (59.0%) and “Beef cattle” (22.5%) were among the highertariff rate commodities in Japan against Korea, whereas “Vegetables” (53.6%) and“Fruits” (37.4%) were among the higher tariff rate commodities in Korea againstJapan.Let us now consider what happens if the tariff between the two countires wereentirely eliminated over the current state. In that event the ex ante barrier factor µ ∗ will equal ρ instead of ρ (1 + τ ), in regard to (12). Thus, because νµ = 1 at Here, we are assuming the exchange factor ν to be constant.2 Jiyoung Kim et al. the current state according to (18), µ ∗ must be evaluated as follows: νµ ∗ = νρ = νµ τ = 11 + τ ≡ θ and hence, we must modify (25) when evaluating tariff-eliminated bilateral generalequilibrium prices, as follows: w PJ = w DK z K z ⊺ J h θ J i w PK = w DJ z J z ⊺ K h θ K i (26)Hereafter let us denote by π the tariff-eliminated bilateral general equilibriumprices. That is, π = (cid:16) π DJ , π CJ , π FJ , π PJ , π DK , π CK , π FK , π PK (cid:17) More specifically π is the fix point of the mapping G : R n J + n K ) → R n J + n K ) which comprises of the functions (22–24) and (26) i.e., π = G ( π ) (27)Note that G is a concave and monotone increasing mapping because CES aggre-gators H , U and V are all concave functions, and linear functions (26) are alsoconcave (although not strictly concave). Thus, G becomes a contraction mappingand we may solve (27) for the fixed point by recursive means (see e.g., Kennan,2001; Krasnosel’ski˘ı, 1964) from arbitrary initial guess such as i.e., π = lim k →∞ G k ( ) = G ( · · · G ( G ( G ( ))) · · · )4.3 Prospective AnalysisSince we know by the Shephard’s lemma that the factor input can be obtainedby differentiating the unit cost function, inputs in physical units per physicalunit output for all sectors, or the physical input–output coefficient matrix, can beobtained as the gradient of (21) i.e., ∇ w D = ∂H ( w C ,w C ) ∂w C ∂H ( w C ,w C ) ∂w C · · · ∂H n ( w C ,w C ) ∂w C ∂H ( w C ,w C ) ∂w C ∂H ( w C ,w C ) ∂w C · · · ∂H n ( w C ,w C ) ∂w C ... ... . . . ... ∂H ( w C ,w C ) ∂w Cn ∂H ( w C ,w C ) ∂w Cn · · · ∂H n ( w C ,w C ) ∂w Cn = (cid:20) ∇ H (cid:0) w C , w C (cid:1) ∇ H (cid:0) w C , w C (cid:1) (cid:21) where ∇ H is an n row vector, while ∇ H is an n × n matrix. For later conve-nience, let us use the following terms to indicate monetary input–output coefficientmatrices for current and posterior (with tariff elimination) states.1 ∇ H ( , h i − ≡ a π C ∇ H (cid:0) π C , π C (cid:1) (cid:10) π C (cid:11) − ≡ ˜a h i ∇ H ( , h i − ≡ A (cid:10) π C (cid:11) ∇ H (cid:0) π C , π C (cid:1) (cid:10) π C (cid:11) − ≡ ˜A The dimension of the sectors are n J = 395 for Japan and n K = 350 for Korea.ilateral multifactor CES general equilibrium 13 Note that we set π C = 1 as we take the primary input i = 0, which is not producedindustrially, as the num´eraire good. Also, a and A are the current state (observed)value-added and input–output coefficients, respectively.Below is the commodity balance in monetary terms: x = Ax + y + e − m (28)where, x denotes domestic output, y denotes domestic final demand, e denotesexport, m denotes import, all in column vectors of monetary terms, while Ax represents the intermediate demand. Here, we may recall that we have obtainedthe current state foreign share of a commodity s F> = 1 − α , by the amount ofimport m (i.e., an element of m whose index is omitted) and the domestic totaldemand, i.e., m = (1 − α ) y + n X j =1 a j x j For further conveniece let us define s = s F> = 1 − α and endogenize import withrespect to the domestic total demand as follows: m = h s i [ Ax + y ]Further, we may recall that the import from the partner country m P can bereplicated by the current share of the partner country’s commodity s P> , which wehereafter denote s P for convenience, as follows: m P = (cid:10) s P (cid:11) m = (cid:10) s P (cid:11) h s i [ Ax + y ]Displayed below is the commodity balance of the posterior state:˜ x = ˜ A ˜ x + ˜ y + (cid:16) e W + ˜ e P (cid:17) − (cid:16) ˜ m W + ˜ m P (cid:17) (29)The posterior state values are distinguished by tildes. We assume that importsand exports are subject to change due to tariff elimination, except for the exportsto the ROW. Notice that imports from the partner and the ROW are assumed tobe proportional to the total domestic demands in the following manner:˜ m P = (cid:10) ˜ s P (cid:11) h ˜ s i h ˜ A ˜ x + ˜ y i = ˜ e P ′ ˜ m W = (cid:2) I − (cid:10) s P (cid:11)(cid:3) h s i h ˜ A ˜ x + ˜ y i (30)As indicated above, the export against the partner country is determined by theimport from the partner’s partner country. The import coefficients are determinedby (2) and (9) as follows:˜ s = (1 − α ) (cid:18) π F π C (cid:19) − ε ˜ s P = β (cid:18) π P π F (cid:19) − η Here, a prime is used to indicate the partner country’s export against its partner country.4 Jiyoung Kim et al. F i na l D e m and [ B J PY ] − − E x t e r na l I npu t [ B J PY ] Fig. 7
Maximized increment of current-proportioned final demand ˜ y − y (left) and the cor-responding redistribution of the external inputs ˜ a ˜ x − a x (right) for Japan. The posterior value added (external inputs) total can be evaluated by the importendogenized model in regard to the posterior commodity balance equation (29): ˜ a ˜ x = ˜ a h I − (cid:2) I − (cid:10) s ∗ (cid:11)(cid:3) ˜ A i − h(cid:2) I − (cid:10) s ∗ (cid:11)(cid:3) ˜ y + e W + ˜ e P i (31)where, the import coefficient s ∗ is specified as follows, according to (30): h s ∗ i = (cid:10) ˜ s P (cid:11) h ˜ s i + (cid:2) I − (cid:10) s P (cid:11)(cid:3) h s i We assume an economy to maximize its final demand given the external inputstotal, and to this end the compensation of increased exports against the partnercountry can be spent for whatever commodity demanded. We incorporate suchexternal inputs into the domestic production in such a way that the externalinputs (value added) total is fortified. In particular, we are to find a scalar δ of the following problem that maximizes the total ex ante value of the current-proportioned final demand i.e., ˜ y = (cid:10) π D (cid:11) y δ , given the ex ante total value added(31), which is limited to the sum of the locally existing primary factor ℓ (= a x ),and the compensation of exports against the partner country, i.e.,max δ ˜ y = (cid:10) π D (cid:11) y δ s.t. ˜ a ˜ x ≤ ℓ + (cid:0) ˜ e P − e P (cid:1) (32)Note that the solution of (32) determines the posterior total domestic demandsand thus the imports from the partner country which, in turn, determines thecompesation of exports against the partner’s partner country via (30) that mustenter into the constraint of the parter country’s problem. In other words, (32)must be solved recurrsively for both countries under the condition given by thepartner country.Figs. 7 and 8 illustrate the increments of maximized current-proportioned finaldemand i.e., ˜ y − y and the corresponding redistribution of the external inputsi.e., ˜ a ˜ x − a x for Japan and Korea, respectively, under the tariff elimination This model is otherwise called the Chenery–Moses type or the competitive import model. It may be more natural to incorporate export compensation into imports; but this optionwas not adopted on the ground that imports are endoginized with respect to domestic finaldemand alone as specified in (30).ilateral multifactor CES general equilibrium 15 F i na l D e m and [ BK R W ] − E x t e r na l I npu t [ BK R W ] Fig. 8
Maximized increment of current-proportioned final demand ˜ y − y (left) and the cor-responding redistribution of the external inputs ˜ a ˜ x − a x (right) for Korea. Table 1
Prospective analysis of tariff elimination between Japan and Korea.
Japan KoreaBJPY (BKRW) BKRW (BJPY)Gross Domestic Product (GDP) 505,269 851,982 ∆ Final Demand ∆y
853 7,924 6,309 679 ∆ Import from Partner ∆m P
803 7,459 3,338 359 ∆ Export to Partner ∆e P
359 3,338 7,459 803between the two countries. Notice that BJPY stands for billion Japanese yensand BKRW for billion Korean wons. The total effects are summarized in Table1. The net benefit (in terms of gained final demand ∆y ) of tariff eliminationis about 0.17% of the current GDP (853 BJPY) for Japan, whereas it is about0.74% of the current GDP (6,309 BKRW) for Korea. As regards the redistributionof the external inputs, current-proportioned final demand maximization suggeststhat sectors such as j = 302 (House rent), j = 25 (Fisheries), j = 352 (Medicalservice (medical corporations, etc.)), and j = 329 (Information services) must bereinforced, and curtailed in sectors such as j = 65 (Other liquors), j = 75 (Woolenfabrics, hemp fabrics and other fabrics), j = 145 (Miscellaneous leather products),and j = 17 (Hogs), for Japan. On the other hand, preferable policy for Korea isto reinforce in sectors such as j = 71 (Other liquors), j = 283 (Wholesale andRetail trade), j = 19 (Pigs), and j = 18 (Beef cattle), and to curtail in sectorssuch as j = 53 (Raw sugar), j = 26 (Fishing), j = 63 (Canned or cured fruitsand vegetables), and j = 17 (Motor vehicle engines, chassis, bodies and parts), forKorea.Table 1 also displays the import change from the partner country ∆m P definedas below, which by definition equals the export change of the partner country As regards (32), the increment total of external inputs must be equal to the incrementtotal of export compensation from the partner country i.e., (˜ a ˜ x − a x ) = (˜ e P − e P ).6 Jiyoung Kim et al. Table 2
Notable net export (top 20) from Japan to Korea ∆f JK .sector/commodity BJPY BKRWFisheries 48 446Sugar 38 350Motor vehicle parts and accessories 34 321Salted, dried or smoked seafood 32 298Bottled or canned vegetables and fruits 29 272Preserved agricultural foodstuffs (other than bottled or canned) 28 258Other wearing apparel and clothing accessories 18 164Machinery and equipment for construction and mining 16 148Knitted apparel 15 136Toys and games 12 110Frozen fish and shellfish 11 103Electric audio equipment 11 99Activities not elsewhere classified 10 96Rotating electrical equipment 8 76Hot rolled steel 8 76Synthetic fibers 7 65Internal combustion engines for motor vehicles and parts 6 60Machinery for service industry 6 54Miscellaneous ceramic, stone and clay products 5 48Trucks, buses and other cars 5 44 against its partner country ∆e P ′ , or more specifically, ∆m PJ = (cid:16) ˜ m PJ − m PJ (cid:17) = ∆ m PJ = ∆e PK ∆m PK = (cid:16) ˜ m PK − m PK (cid:17) = ∆ m PK = ∆e PJ Thus, we may look into the net export ∆f against the partner country as follows: ∆e PJ − ∆m PJ = ∆m PK − ∆e PK = ∆e PJ − ∆e PK = ∆m PK − ∆m PJ ≡ ∆f JK ∆e PK − ∆m PK = ∆m PJ − ∆e PM = ∆e PK − ∆e PJ = ∆m PJ − ∆m PK ≡ ∆f KJ where naturally ∆f JK + ∆f KJ = 0. In Table 2 we display the positive entriesof the net export from Japan to Korea ∆f JK . Likewise, Table 3 is the positiveentries of the net export from Korea to Japan.We may notice from these tables that, a lot of meat (i.e., Slaughtering andmeat processing) will be exported from Korea to Japan, whereas Japan will ex-port fish (i.e., Fisheries, Frozen fish and shellfish) to Korea, under tariff elimina-tion. Other notable features are that Korea will net-export petrochemical prod-ucts (e.g., Petrochemical aromatic productss (except synthetic resin), Coal mining,crude petroleum and natrual gas, Petrochemical basic products, Petroleum refineryproducts (incl. greases), etc.) to Japan, whereas Japan will net-export mechani-cal and assembling products (e.g., Motor vehicle parts and accessories, Machineryand equipment for construction and mining, Electric audio equipment, Rotatingelectrical equipment, etc.) to Korea. The negative entries are the net import from Japan to Korea, or, the net export fromKorea to Japan.ilateral multifactor CES general equilibrium 17
Table 3
Notable net export (top 20) from Korea to Japan ∆f KJ .sector/commodity BKRW BJPYSlaughtering and meat processing 1,966 212Woolen fabrics, hemp fabrics and other fabrics 1,360 146Other liquors 1,350 145Refined sake 647 70Miscellaneous leather products 567 61Liquid crystal element 434 47Woven fabric apparel 322 35Analytical instruments, testing machine, measuring instruments 206 22Pumps and compressors 136 15Rolled and drawn aluminum 134 14Petrochemical aromatic products (except synthetic resin) 131 14Coal mining , crude petroleum and natural gas 109 12Petrochemical basic products 106 11Sheet glass and safety glass 103 11Metal molds 84 9Leather footwear 54 6Integrated circuits 53 6Other non-ferrous metals 47 5Fruits 46 5Petroleum refinery products (incl. greases) 44 5 The highlight of this study may perhaps be the discovery of a way to calibratethe parameters of a two-input CES aggregator in order that the aggregator com-pletely replicates the observed two temporally distant shares of inputs in bothmonetary and physical terms. The elasticity parameters i.e., the Armington elas-ticities that we obtained by way of this approach (i.e., two-point calibration), werefound to be much larger than those observed in the previous studies based upontime series, implying almost complete substitutability between foreign and domes-tic commodities, which should not be too surprising. We then used the Armingtonaggregator functions to uncover the composite price index for each commodity,which is key for modeling production activities comprising many factor inputs,including imported commodities, for each industrial sector.As we are concerned with multisectoral production functions of multiple (morethan two) factor inputs, we estimated multifactor CES production elasticities bylinearly regressing the growth of commodity-wise cost shares against the relativegrowths of factor prices. We used published statistics, namely, linked input–outputtables and the UN Comtrade database, to measure all the concerned elasticities(i.e., multifactor CES production, and micro and macro Armington elasticities)for both Japan and Korea. The two multisectoral general equilibrium models forJapan and Korea were integrated by the bilateral trading models which reflect thetrade barriers between the two countries.Since the models presume constant returns in all activities and thus interactentirely in terms of unit costs and prices, we were able to simulate the bilateralgeneral equilibrium consequences of eliminating tariffs between the two countries,without (physically) quantitative consideration. The consequential social benefitsand costs of tariff elimination were estimated by the amount of linear final demand that can potentially be enhanced under the projected structure for a given totalprimary input. The result implies positive effects (in terms of total net benefit) forboth countries, while considerable structural change is expected to be inevitable.
Conflict of Interest:
The authors declare that they have no conflict of interest.
References
BOK (2009) 1995, 2000, 2005 linked input-output tables [in Korean]. Economicstatistics system, Bank of Korea, URL http://ecos.bok.or.kr
Comtrade (2017) UN Comtrade–International Trade Statistics Database. URL https://comtrade.un.org
Feenstra RC, Luck PA, Obstfeld M, Russ KN (2014) In search of the Armingtonelasticity. Working Paper 20063, National Bureau of Economic Research,DOI 10.3386/w20063Harrison GW, Rutherford TF, Tarr DG (1997) Quantifying the Uruguay round.The Economic Journal 107(444):1405–1430,DOI 10.1111/j.1468-0297.1997.tb00055.xJIP (2015) Japan Industrial Productivity Database. URL
Kennan J (2001) Uniqueness of positive fixed points for increasing concavefunctions on Rn: An elementary result. Review of Economic Dynamics4(4):893 – 899, DOI http://dx.doi.org/10.1006/redy.2001.0133Kim J, Nakano S, Nishimura K (2017) Multifactor CES general equilibrium:Models and applications. Economic Modelling 63:115 – 127,DOI 10.1016/j.econmod.2017.01.024KIP (2015) Korea Industrial Productivity Database. URL
Krasnosel’ski˘ı MA (1964) Positive Solutions of Operator Equations. Groningen,P. NoordhoffMcDaniel CA, Balistreri EJ (2002) A discussion on armington trade substitutionelasticities. Working Paper 2002-01-A, US International Trade CommissionMIAC (2011) Ministry of Internal Affaris and Communications 1995–2000–2005Linked Input-Output Tables [in Japanese]. URL