North American Journal of Economics and Finance 25 (2013) 40– 59

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North American Journal ofEconomics and Finance

Impact of China’s currency valuation and labourcost on the US in a trade and exchange ratemodel�

Keshab Bhattaraia,1, Sushanta Mallickb,∗

a University of Hull, Business School, Cottingham Road, Hull HU6 7RX, UKb Queen Mary University of London, School of Business and Management, Mile End Road, London E1 4NS,UK

a r t i c l e i n f o

Article history:Received 9 April 2012Received in revised form 27 February 2013Accepted 6 March 2013

JEL classification:P45P51

Keywords:Comparative advantageGrowthExchange rateChinaUS

a b s t r a c t

Ricardian dynamic general equilibrium analyses show that underfree trade arrangements a low income country with lower wagecost and large endowment of labour has comparative advantagein trade. Efficiency gains from this enhance economic growth andwelfare of households simultaneously in both low income andadvanced economies. Theoretical predictions are empirically val-idated here with structural VAR analysis based on quarterly dataover the time period 1995:1 to 2009:1 on China’s relative wagecost, interest rate differential, real effective exchange rate (REER),relative GDP and the US current account balance. It is shown howthe relative prices of labour, capital and the currency affect the eco-nomic activity in China and current account balance in the US. Withfree capital inflows and outflows and restrictions on labour mobil-ity, comparative advantage of China and the trade deficit of theUS will both be minimised if China allows real appreciation of theYuan and complete adjustment in prices. Higher production costand prices in China could reduce welfare of Chinese householdsand the trade imbalance of the US, while higher relative GDP ofChina lowers the current account balance for the US.

© 2013 Elsevier Inc. All rights reserved.

� The authors are grateful to the two anonymous reviewers for their very useful comments, which helped improve the paperconsiderably. We also acknowledge the comments on an earlier version of the paper by the discussant, Keunsuk Chung, andparticipants at the CES session during the ASSA Annual Meetings, 7–9 January, 2011.

∗ Corresponding author. Tel.: +44 20 7882 7447; fax: +44 20 7882 3615.E-mail addresses: K.R.Bhattarai@hull.ac.uk (K. Bhattarai), s.k.mallick@qmul.ac.uk (S. Mallick).URL: http://webspace.qmul.ac.uk/skmallick/ (S. Mallick).

1 Tel.: +44 1482463207; fax: +44 1482463484.

1062-9408/$ – see front matter © 2013 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.najef.2013.03.001

K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59 41

1. Introduction

International economic landscape has changed dramatically after the comparative advantage inproducing goods and the direction of trade changed significantly in the recent years. Interest hasincreased in understanding the new economic links between advanced economies and the emergingeconomies such as China that were able to grow at a reasonable space even during the financial crisesand recessions of 2008/09. With a large current account surplus and apparently appreciating exchangerate, how do policies in China influence more advanced economies such as the US, have become thefocus of attention in the recent studies (see Corden, 2009; Xu, 2011). Large current account surplusof China impacts not only on the real effective exchange rate with its trading partners but also on theworld real interest rate and the international relative prices of traded commodities and thereby on thecurrent account deficit of the US. How do the relative prices set in this way affect the relative demandbetween China and the US and thereby create trade imbalances between the two countries, is an issuethis paper aims to explore using a dynamic trade model supported by empirical analysis.

The Chinese Yuan continues to remain under valued and a large body of the literature concentrateson studying the relation between exchange rate movements and the trade balance (see Bahmani-Oskooee & Ratha, 2010). According to WTO’s current trade profile, US imports more than three timesfrom China than it exports to China; nearly 17 percent of US total imports originate from China whereasonly 5.6 percent of US exports go to China. Absolute price differentials and relative price volatilityincrease with exchange rate volatility (Imbs, Mumtaz, Ravn, & Rey, 2010). Granville, Mallick, and Zeng(2011) explore price and exchange rate linkages between China and the G3 (US, Euro-area and Japan),showing that the price effect in China possibly due to lower cost is found to dominate the exchangerate effect on the US import prices. This suggests that we need to evaluate the relative impacts ofexchange rate and production costs on the external balance in the US using a general equilibriumtrade model with a monetary structure. The monetary linkage has been emphasised in these twogroups of economies in the literature (see, for example, Cargill & Parker, 2004).

In order to address these underlying linkages of trade flows between two countries, we develop aneoclassical dynamic general equilibrium model based on the major developments in the literature.2

We show that under free trade arrangements a low income country with lower wage cost and largeendowment of labour has comparative advantage in trade, which improves welfare in both low incomeand advanced economies.

Theoretical predictions are empirically supported via a structural VAR analysis based on quarterlydata over the time period 1995:1 to 2009:1 using China’s relative wage cost, interest rate differential,real effective exchange rate (REER), relative GDP and the US current account balance. To understandthe dynamics of trade and exchange rate between China and the US, a structural vector error correctionmodel (VECM) is formulated as suggested in Fry and Pagan (2011) in order to derive long-run estimates,impulse responses and variance decompositions. It is shown how the relative prices of labour, capitaland the currency affect the economic activity in China and current account balance in the US. With freecapital flows and restrictions on labour mobility, comparative advantage of China and the trade deficitof the US will both be minimised if China allows real appreciation of the Yuan and complete adjustmentin prices. Higher production cost and prices in China will reduce welfare of Chinese households andthe trade imbalance of the US.

The rest of the paper is organized as follows. Section 2 presents the dynamic model of trade followedby analytical results in Section 3, and data, estimation methodology and empirical results in Section4, variance decomposition analysis in Section 5 and conclusions and the policy implications in Section6.

2 Namely international finance model of Mundell (1957), benefits of free and liberal trade in Meade (1978), scale, productdifferentian and pattern of trade in Krugman (1980), interaction among technology, geography and trade of Markusen andSvensson (1985), Eaton (1987) and Eaton and Kortum (2002), determinant of real exchange rate of Neary (1988), globalisationand location aspects in trade modeling in Krugman and Venables (1995) and Norman and Venables (1995), product differenti-ation and union negotiations of Naylor (2000), stochastic dynamic general equilibrium trade model of Melitz (2003), collapseof trade finance of Ahn, Amity, and Weinstein (2011) and cross border market segmentation and markup theory of Gopinath,Gourinchas, Hsieh, and Li (2011).

42 K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59

2. Two country dynamic model of trade and exchange rate

Traditional Ricardian, Hecksher–Ohlin, Stopler–Samuelson trade theories suggest that the patternof trade is dominated by factor endowments, trade is beneficial for all trading partners and factor pricestend to equalise across the globe with free and liberal trade (Bhagwati, 1964). Generally economistssince Ricardo have argued for removing tariff barriers to enhance welfare of all trading nations fromspecialisation according to the comparative advantage in production. As Johsnon (1951–52) stated,“countries with high tariffs may stand to gain, within limits, from a unilateral reduction in tariff barriersand maximum revenue will always be higher than the optimal tariff that raises welfare on trading nations.”Mundell (1957) explained implications on price equalisation process from trade on capital flows withor without free or restricted mobility of factors of production or trade protections given the size andscale of industries of the trading nations. In a comparative static general equilibrium analysis, Millerand Spencer (1977) had shown benefits to the UK of joining the European Union following Balassa’s(1967) analysis on stages of integration in EU in the form of the customs union, a common market, aneconomic union and eventually a political union. Meade (1978) had felt a need for an elaborate dynamicmodel to capture the complex interactions among countries when he stated, “perhaps a mysteriousdynamic model operated inconspicuously in some back room by control experts for silent information ofthe authorities concerned might be useful; and in any case in the real world it would be desirable for thedifferent authorities at least to communicate their plans to each other so that, by what one hopes would bea convergent process of mutual accommodation, some account could be taken of their interaction.”

Equipped with a sharper and more focused analytical structure, Krugman (1980) pioneered incor-poration of imperfect competition in trade models in which scale economies, increasing returns andlarger domestic markets for exported products not only influence the patterns of intra-industry tradebut also determines the number of firms in the industry. It makes Frenkel and Mussa (1981) believe thatno macroeconomic policies can succeed unless it takes account of interlinkages created by patterns andstructures of trade and relative prices of commodities. While the trade generated technical spilloversfrom the R&D investment of the profit maximising firms driving economic growth as in Grosssmanand Helpman (1990), the globalisation and agglomorations may cause a relative decline in incomes ofcountries in peripheries despite a fall in the cost of transportation (Krugman & Venables, 1995). Tradein goods alone does not equalise factor prices as claimed in Stopler–Samuelson theorems (Norman &Venables, 1995). With the endogenous growth models, Ventura (1997) and Turnovsky (1997) illus-trate how the patterns and benefits of trade relate to scale economies, innovations and productivitythan traditional factor endowments. Union preferences matter both in one or two way trade withproduct differentiation (Naylor, 2000). Analysis of Ricardian absolute and comparative advantage andgeographic barrier to trade requires solutions of structural equations derived from a general equilib-rium model as in Eaton (1987) or Eaton and Kortum (2002) who apply their model to estimate gainsfrom trade, technology diffusion and tariff reductions. In a two country stochastic general equilib-rium model of trade and macroeconomic dynamics with monopolistic competition and heterogenousfirms, Melitz (2003) illustrates how producer entry, product introduction and economic fluctuationsare associated and connected to trade flows and changes in traded varieties across countries. WithS-shpaped correlations between various leads and lags of GDP and trade flows, he reproduces styl-ized facts on countercyclicality of trade patterns analogous to those in the international real businesscycle models. Country size and trade policy matter in the division of gains between larger and smallercountries in the global trade (Bhattarai & Whalley, 2006).

Taking intuitive lessons from above theoretical developments regarding impact of factor priceson real exchange rates and growth rate of trading nations, we propose a dynamic two country openeconomy model of trade to ascertain factors that determine mutual gains from free trade and causeflows of capital when trade does not balance. Then we test the model with empirical evidences onrelative GDP, wages, interest rate, real exchange rates and trade balances of the US and China toexplain recent developments and to speculate what might happen to them in the future. Each countryconsumes goods produced at home and produced in the partner country and uses labour along withcapital in production. Domestic and foreign wage, interest rates and relative prices are determinedby the optimality conditions when economic activities of two countries are connected through thereal exchange rate. Those optimal conditions which are subject to shocks of technological progress,

K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59 43

preferences and policy from time to time will cause a deviation from the optimal equilibrium as capitalis mobile across countries but not the labour.

Our model consists of a home country i and a foreign country j. The utility function of a represen-tative household in country i contains goods produced at home (Ci,t), imported from abroad (Mi,t) andleisure (li,t). Government uses taxes on consumption (tci,t), imported goods (tmi,t) and labour income(twi,t) to provide for public consumption (Gi,t). With the Cobb–Douglas utility function and the sub-jective discount factor (0 < �i < 1), the intertemporal problem of the representative household in homecountry i can be stated as:

maxUi0 =

∞∑t=0

�ti (C˛i

i,tMˇii,t l

�ii,t) (1)

subject to its intertemporal budget constraint:[∑∞t=0Pi,t(1 + tci)Ci,t + Pj,t(1 + tmi)Mi,t + wj,t(1 − twi)li,t

]≤

[∑∞t=0wi,t(1 − twi)Li,t + rj,t(1 − tki)Ki,t

] (2)

where share parameters, each between zero and one (0 < ˛i, ˇi, � i < 1), sum up to one (˛i + ˇi + � i = 1).Shocks to the preferences in this model occur either with changes in the subjective discount factor�i or in share parameters ˛i, ˇi and � i. The representative households in the foreign contry j solvessimilar intertemporal problem.

A representative firm in home country i maximises profit (�i,t) in a similar way supplying output(Yi,t) with labour (LSi,t) and capital inputs (Ki,t) as in Eaton (1987) and Grosssman and Helpman (1990):

max �i,t = Pi,tYi,t − ri,tKi,t − wi,tLSi,t (3)

subject to the technology and accumulation constraints:

Yi,t = Ai,tK�ti,t L(1−�t )

i,t (4)

Ii,t = Ki,t − (1 − ı)Ki,t−1 (5)

Random productivity shocks Ai,t with costant mean Ai and variance �2i

influence output of firms.Investment (Ii,t) net of depreciation (ıKi,t−1) contributes to the accumulation of capital stock.

Government receives revenue (Ri,t) from taxes on consumption and imports as well as in labourand capital income and spends on public services (Gi,t) as:

Ri,t = tciPi,tCi,t + tmiPj,tMi,t + twiwj,tLSi,t + tkiriKi,t ≷ Gi,t (6)

Markets for goods clear but can be segmented across borders (Gopinath et al., 2011):

Yi,t = Ci,t + Ii,t + Xi,t − Mi,t + Gi,t (7)

Labour market clears at national level as in Markusen and Svensson (1985):

Li,t = LSi,t + li,t (8)

The foreign country j has similar specification of technology and labour markets.There can be twodifferent ways of trade balance. First one where trade is balanced period by period in the sense thatvalue of exports and imports are the same for country i as:

Pi,tXi,t = Pj,tMi,t (9)

Trade is financed by the flow of credits which is subject to trade-finance shocks as in Ahn et al.(2011):

(Si,t − Ii,t) + (Xi,t − Mi,t) = 0 (10)

Another way to make trade balanced intertemporally (in the present value terms) is:∞∑

�t(Pi,tXi,t − Pj,tMi,t) =∞∑

�t(TBi,t) =∞∑

�t(�Fi,t) = 0 (11)

44 K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59

Imbalances result in the accumulation of foreign assets temporarily but should disappear in the longrun though this may last far long into the future. A country with trade surplus (TBi,t > 0) accumulatesforeign assets (Ft) and one with deficit (TBi,t < 0) builds its stock of foreign debt. The dynamics of foreignasset accumulation is driven by the real interest rate as:

Fi,t+1 = Fi,t(1 + ri,t) + �Fi,t (12)

Stocks of these assets increase options available to an economy in investment (Ii,t) or adoption of anew technology (Ai,t) which determine growth of output and welfare of households in it. Depletion ofthese assets persistently can influence the confidence of consumers and producers, lower growth rateand can cause financial and economic crisis.

Current price of commodity in country i is linked to the future price and the interest rate throughan inter-temporal arbitrage condition as:

Pi,t = Pi,t+1

1 + ri,t(13)

Bilateral real exchange rate for country i is expressed in ratios of domestic and foreign prices forcountries i and j respectively as:

Ei,t = Pi,t

Pj,t(14)

A competitive equilibrium in this two country trade model is given by the sequence of prices {Pi,t,Pj,t} interest rates, {ri,t, rj,t} wage rates {wi,t, wj,t}, the real exchange rates, {Ei,t, Ej,t} such that givenpublic policies that include taxes in consumption {tci,t, tcj,t} labour income {twi,t, twj,t} and capitalincome {tri,t, trj,t} and imports tariffs {tmi,t, tmj,t} the allocations of consumption, imports, leisure,

{Ci,t, Mj,t, li,t, Cj,t, Mi,t, lj,t} that maximise the lifetime utility of households Ui0 and Uj

0 in home and theforeign countries. The choices of labour and capital inputs {LSi,t, Kj,t, Ki,t, LSj,t} that maximise profitof firms and the government expenditures {Gi,t, Gj,t} compatible with government revenue, {Ri,t, Rj,t}and exports {Xi,t, Xj,t} are compatible with imports {Mi,t, Mj,t} in both countries. Market mechanisminfluences allocations of resources in both countries through the real exchange rate that depends onrelative prices.

The infinite horizon problem is reduced to finite horizon by fixing the terminal period T to the fardistance in the future. Similarly the labour endowments {Li,t, Lj,t} grow exogenously. Policy shocks tothese economies occur through tax instruments {tci,t, tcj,t, twi,t, twj,t, tri,t, trj,t} and tariffs {tmi,t, tmj,t}that are determined by the policy makers considering national and international circumstances. Themodel parameters ˛i, ˇi, � i and �i are estimated from the data.

3. Analytical results of optimisation

Since the infinite horizon problem is analytically intractable, the model is solved using the first orderintertemporal optimisation conditions for any two time intervals as these optimality should hold forany other periods. First order conditions for households with respect to consumption, imports, leisureand shadow prices for t and t + 1 periods are:

Ci,t : ˛i�t(C˛i−1

t Mˇit l�i

t ) = �tPi,t(1 + tci) (15)

Ci,t+1 : ˛i�t+1(C˛i−1

t+1 Mˇit+1l�i

t+1) = �t+1Pi,t+1(1 + tci) (16)

Mi,t : ˇi�t(C˛i

t Mˇi−1t l�i

t ) = �tPj,t(1 + tmi) (17)

Mi,t+1 : ˇi�t+1(C˛i

t+1Mˇi−1t+1 l�i

t+1) = �t+1Pj,t+1(1 + tmi) (18)

li,t : �i�ti (C˛i

t Mˇit l�i−1

t ) = �twi,t(1 − twi) (19)

li,t+1 : �i�t+1i

(C˛it+1Mˇi

t+1l�i−1t+1 ) = �t+1wi,t+1(1 − twi) (20)

K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59 45

�i,t : Pi,t(1 + tci)Ci,t + Pj,t(1 + tmi)Mi,t + wj,t(1 − twi)li,t

= wi,t(1 − twi)Li,t + rj,t(1 − tki)Ki,t

(21)

�i,t+1 : Pi,t+1(1 + tci)Ci,t+1 + Pj,t+1(1 + tmi)Mi,t+1 + wj,t+1(1 − twi)li,t+1

= wi,t+1(1 − twi)Li,t+1 + rj,t+1(1 − tki)Ki,t+1

(22)

The above first order conditions result in the Euler equations as follows:

Ci,t

Ci,t+1:

1�

(Ci,t

Ci,t+1

)(˛i−1)(Mi,t

Mi,t+1

)ˇi(

li,tli,t+1

)�i

= Pi,t

Pj,t(23)

Mi,t

Mi,t+1:

1�i

(Ci,t

Ci,t+1

)˛i(

Mi,t

Mi,t+1

)(ˇi−1)(li,t

li,t+1

)�i

= Pj,t

Pj,t(24)

Mi,t

Mi,t+1:

1�i

(Ci,t

Ci,t+1

)˛i(

Mi,t

Mi,t+1

)(ˇi−1)(li,t

li,t+1

)�i

= wj,t

wi,t+1(25)

Ci,t+1

Mi,t+1:

˛i

ˇi

(Mi,t+1

Ci,t+1

)= Pi,t+1(1 + tci)

Pj,t+1(1 + tmi)(26)

li,t+1

Mi,t+1:

˛i

�i

(li,t+1

Ci,t+1

)= Pi,t+1(1 + tci)

wi,t+1(1 − twi)(27)

Mi,t+1

li,t+1:

ˇi

�i

(li,t+1

Mi,t+1

)= Pj,t+1(1 + tmi)

wi,t+1(1 − twi)(28)

Similarly the first order conditions for firms are:

�i,t = Pi,tYi,t − ri,tKi,t − wi,tLSi,t (29)

Ki,t : �i,tPi,tK�t−1i,t L(1−�t )

i,t = ri,t or�i,tPi,tYi,t

Ki,t= ri,t (30)

Kj,t : �j,tPj,tK�t−1j,t L(1−�t )

j,t = rj,t or�j,tPj,tYj,t

Kj,t= rj,t (31)

Li,t : (1 − �i,t)Pi,tK�ti,t L−�t

i,t = wi,t or(1 − �i,t)Pi,tYi,t

Li,t= wi,t (32)

Lj,t : (1 − �j,t)Pj,tK�tj,t

L−�tj,t

= wj,t or(1−�i,t )Pj,tYj,t

Lj,t= wj,t

Initial capital stocks and the terminal investment conditions for country i and j are:

Ki,0 and Kj,0 (33)

Ii,t = (gi + ıi)Ki,T−1; Ij,t = (gj + ıj)Kj,T−1 (34)

Whether the wage rates and the interest rates are same or differ from one country to another dependpartly upon the marginal productivity and mobility of factors and partly on the tariff rates acrosscountries as mentioned in the literature above. If labour and capital are perfectly mobile then ratiosof marginal productivities across two countries in equilibrium are same as the ratios of rental ratesand wage rates as:

�j,tPj,tYj,t

�i,tPi,tYi,t

Ki,t

Kj,t= rj,t

ri,t(35)

(1 − �j,t)Pj,tYj,t

(1 − �i,t)Pi,tYi,t

Li,t

Lj,t= wj,t

wi,t(36)

46 K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59

Table 1Theoretical predictions from dynamic two country trade model.

Pi,t Pj,t wi,t wj,t ri,t rj,t Yi,t Yj,t Li,t Lj,t Ki,t Kj,t �i,t �j,t Ei,t Ci,t Mi,t

Ei,t + − − + − + + − − + − + + − 1 − +Yi,t + − − + + − 1 + + − + − − + + − +ri,t − + + − 1 + + − + − − + + − − + −wi,t − + 1 + + − + − − + + − − + − + −Ci,t − + + − + − − + + − + − − + − 1 +Mi,t + − − + − + + − − + − + + − + + 1

These conditions give us the equilibrium real exchange rate in terms of relative prices of commodi-ties between two countries, which further relate to marginal productivies of labour and capital, rentalrates and ratio of imports to domestic consumption as follows:

Ei,t = Pi,t

Pj,t= �i,tYi,t

�j,tYj,t

Kj,t

Ki,t

rj,t

ri,t= (1 − �i,t)Yi,t

(1 − �j,t)Yj,t

Lj,t

Li,t

wj,t

wi,t= ˛i

ˇi

Mi,t

Ci,t

(1 + tmi)(1 + tci)

(37)

These theoretical derivations, similar to those in Bhattarai (2011), show interdepedence of theexchange rates, relative output, relative wages, relative interest rate, consumption taxes and tariffrates between two trading nations.

It is possible to make theoretical predictions using the derivations of the dynamic two countrytrade model as presented in Table 1.

Exchange rate (Ei,t) rises when the domestic goods are sold at higher price than comparable foreigngoods, (∂Ei,t ↑ if ∂Pi,t > ∂Pj,t). Term of trade is in favour of the home country. Higher domestic wage ratemakes home country less competitive causing a fall in the exchange rate but it rises when wage rateincreases in the foreign country, (∂Ei,t ↓ if ∂wi,t > ∂wj,t). Similar arguments apply to the interest rate.Higher domestic interest rate pushes exchange rate up by raising the the cost of capital at home buthigher interest rate abroad makes the foreign country less competitive and raises the value of homecurrency (∂Ei,t ↓ if ∂ri,t > ∂rj,t). Increase in labour and capital at home lowers the price of commodityand hence puts downward pressure on the exchange rate but these are sensitive to productivity oflabour and capital inputs, (∂Ei,t ↑ if ∂Li,t > ∂Lj,tor ∂Ki,t > ∂Kj,t).

Similar arguments can be made to other model variables including the GDP (Yi,t), wage rate(wi,t),interest rate (ri,t), consumption (Ci,t), and imports (Mi,t) as illustrated in Table 1.

The model solutions can differ remarkably when two countries differ in productivites of capital(�i,t, �j,t) or interest rates (ri,t, rj,t) or the wage rates (wi,t, wj,t) or in the stock of capital (Ki,t, Kj,t)or endowments of labour (Li,t, Lj,t) or in tariffs and tax rates (tmi,t, tcj,t) or in the preferences andtechnologies (�i, ˛i, ˇi) . Cooperation in policies of home and foreign countries can result in mutuallybeneficial inflows and outflows or the retaliation could result in the collapse of trade as seen in 2008–09recession when international demand or supply shocks had reduced global trade by up to 14 percent.How such structural features of the real exchange rates underpin the patterns of the nominal exchangerates is well explained in the studies of Mundell (1957), Meade (1978), Miller and Spencer (1977),Eaton (1987), Neary (1988), Baldwin (1992), Taylor (1995), and Eaton and Kortum (2002) or Dekle,Eaton, and Kortum (2007). In short, the long run equilibrium real exchange rate is a consequence ofthe balancing forces of the demand and supply for home and foreign products.

4. Empirical analysis on trade and exchange rate

We examine time series data for China and the US on wages, interest rates, exchange rates, GDP,current account balance and the US trade decifit to find empirical evidence on above theoretical anal-ysis. A structural VAR model estimated in line of Sim (1980) and Bernanke (1986) with restrictionsappropriate to theoretical derivations (see Fry & Pagan, 2011 for an uptodate review on this). We limitour analysis to five variables that include relative wage between China and the US (rwcu), interest ratedifferential between China and the US (irdcu), Chinese real effective exchange rate (reer), GDP of Chinarelative to that of the US (rycu) and the current account balance (CABu) determining the ordering ofthese variables in the SVAR as explained in Rafiq and Mallick (2008). In a nutshell we try to show how

K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59 47

Fig. 1. Plot of time series used in the VAR.

the relative prices of labour, capital and the currency affect the economic activities in China and tradebalance in the US. The time series of these data are presented in Fig. 1.

When the Chinese economy has been growing rapidly, the exchange rate being fixed leads us touse China’s real exchange rate (reerc,t) rather than the nominal exchange rate. By doing so, we are also

48 K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59

capturing the relative price effect. China’s unit labour cost (ULC) is measured as total wage bill overreal output (nominal output divided by CPI (1985 = 100)). Then relative wage (rwcu,t) is calculated bydividing ULC-China over ULC-US. Relative GDP (rycu,t) on the other hand has been defined as ChineseGDP in dollar terms over US GDP. We calculate interest rate differential (irdcu,t) as the differencebetween Chinese average inter-bank rate and US 3-month Tbill rate. Current account balance (CABu,t)for the US is used as the percentage of US nominal GDP. With these five variables, we formulate afirst-order structural VAR of the following form:

⎡⎢⎢⎢⎢⎢⎣

b11 b12 b13 b14 b15

b21 b22 b23 b24 b25

b31 b32 b33 b34 b35

b41 b42 b43 b44 b45

b51 b52 b53 b54 b55

⎤⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎣

rwcu,t

irdcu,t

reerc,t

rycu,t

CABu,t

⎤⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎣

b10

b20

b30

b40

b50

⎤⎥⎥⎥⎥⎥⎦

+

⎡⎢⎢⎢⎢⎢⎣

�11 �12 �13 �14 �15

�21 �22 �23 �24 �25

�31 �32 �33 �34 �35

�41 �42 �43 �44 �45

�51 �52 �53 �54 �55

⎤⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎣

rwcu,t−1

irdcu,t−1

reerc,t−1

rycu,t−1

CABu,t−1

⎤⎥⎥⎥⎥⎥⎦

+

⎡⎢⎢⎢⎢⎢⎣

εwt

εrt

εet

εyt

εcat

⎤⎥⎥⎥⎥⎥⎦

(38)

where matrix notations can be employed for more compact representation.

Xt =

⎡⎢⎢⎢⎢⎢⎢⎣

rwcu,t

irdcu,t

reerc,t

rycu,t

CABu,t

⎤⎥⎥⎥⎥⎥⎥⎦

; Xt−1 =

⎡⎢⎢⎢⎢⎢⎢⎣

rwcu,t−1

irdcu,t−1

reerc,t−1

rycu,t−1

CABu,t−1

⎤⎥⎥⎥⎥⎥⎥⎦

; εt =

⎡⎢⎢⎢⎢⎢⎢⎣

εwt

εrt

εet

εyt

εcat

⎤⎥⎥⎥⎥⎥⎥⎦

(39)

Thus the path of Xit is affected by both contemporaneous and lagged effects of Xjt as measured by � 0and � 1 and its own past values. Consider

Xt = B−1�0 + B−1�1Xt−1 + B−1εt (40)

B−1 =

⎡⎢⎢⎣

b11 b12 b13 b14 b15b21 b22 b23 b24 b25b31 b32 b33 b34 b35b41 b42 b43 b44 b45b51 b52 b53 b54 b55

⎤⎥⎥⎦

−1

; �0 =

⎡⎢⎢⎣

b10b20b30b40b50

⎤⎥⎥⎦; �1 =

⎡⎢⎢⎣

�11 �12 �13 �14 �15�21 �22 �23 �24 �25�31 �32 �33 �34 �35�41 �42 �43 �44 �45�51 �52 �53 �54 �55

⎤⎥⎥⎦ .

The reduced form of this VAR system is then given by:

Xt = A0 + A1Xt−1 + et (41)

where A0 = B−1� 0, A1 = B−1� 1, et = B−1εt.Reduced form is estimated with the available data; then structural shocks are retrieved using

et = B−1εt. This requires estimation of the variance covariance matrix of the error term:

∑=

⎡⎢⎢⎢⎢⎢⎢⎣

�11 �12 �13 �14 �15

�21 �22 �23 �24 �25

�31 �32 �33 �34 �35

�41 �42 �43 �44 �45

�51 �52 �53 �54 �55

⎤⎥⎥⎥⎥⎥⎥⎦

(42)

where �ij = 1T

∑Tt=1eije′ij.

K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59 49

Table 2Single equation-based unit root tests.

ADF(t˛c) ADF(t˛ct) DF-GLS KPSS

rw −1.2141 −2.3522 −0.2223 0.7786**ird −3.2789* −3.4218 −1.8574 0.4262reer −2.2832 −2.2567 −0.5861 0.1648ry −0.9719 −2.8950 −1.2533 0.8048**cab −1.3608 0.8982 −0.8782 0.7548**

Notes:1. ADF(t˛c) and ADF(t˛ct) are the test statistics on the lagged variable in the Augmented Dickey–Fuller test regression withconstant, and constant and time trend respectively. DF-GLS and KPSS tests are known as Dickey–Fuller test with GLS detrending,and the Kwiatkowski, Phillips, Schmidt, and Shin test respectively. The KPSS test differs from other unit root tests in the sensethat the time series is assumed to be stationary under the null.2. * and ** denote rejection of the null at 5% and 1% level of significance respectively. The asymptotic 5% critical values are:ADF test: −2.9176 (with constant); −3.4970 (with constant and trend); DF-GLS: −1.9472 (with constant); KPSS: 0.4630 (withconstant).

VAR is a-theoretic model. In order to understand the long-run dynamics, we perform impulseresponse shock analysis, as the results from impulse responses are more informative than the esti-mated VAR regression coefficients (see Stock & Watson, 2001). It is customary to impose restrictionson coefficients based on prior economic theory. These restrictions can be on parameters, variancecovariance matrices or symmetry.

⎡⎢⎢⎢⎢⎢⎢⎣

a11 0 0 0 0

a21 a22 0 0 0

a31 a32 a33 0 0

a41 a42 a43 a44 0

a51 a52 a53 a54 a55

⎤⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎣

rwcu,t

irdcu,t

reerc,t

rycu,t

CABu,t

⎤⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎣

εwt

εrt

εet

εyt

εcat

⎤⎥⎥⎥⎥⎥⎥⎦

(43)

Quarterly observations from 1995-Q1 to 2009-Q1 are used to estimate the model with two optimallags. All the data have been gathered from Datastream and the variables are plotted in Fig. 1. Sincethere is evidence of a structural break around 1994Q1 in China (see for example Baak, 2008), oursample in this paper starts from 1995Q1. Furthermore there is unavailability of quarterly data for thevariables involved in this paper prior to 1995Q1.

The time series properties are examined by undertaking unit-root tests which are shown in Table 2.The standard Augmented Dickey–Fuller unit root tests for relative wage (rw), relative GDP (ry) andCAB do not reject the unit root null hypothesis at 5% level of significance, while KPSS test for ird andreer – which outperform the ADF tests – indicate the presence of stationarity. All the tests suggest thatthree variables are I(1), while two variables are I(0). Given the mixed properties of the time series, it isimportant to test for cointegration before undertaking further analysis. We carried out cointegrationtests to see if the variables are cointegrated.

Using Johansen’s cointegration tests, we found the existence of two cointegrating vectors andhence we formulated a vector error correction model (VECM) and examined the impact of each of thefive shocks on all the endogenous variables in the system. We assume relative wage to be a purelyexogenous shock, as the included variables may not contemporaneously influence the labour marketactivity. In China, interest rates have not been an important monetary policy tool (see Mehrotra, 2007).So we consider China’s interest rate differential with the US to reflect the relative price of capital andChinese REER shocks as a standard indicator of changes in external competitiveness of China as inMarquez and Schindler (2007) who find that a 10 percent real appreciation of the renminbi lowersthe share of aggregate Chinese exports by nearly one percentage point.

50 K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59

4.1. Impulse response analysis

The VAR is formulated with the following ordering: relative wage, interest rate differential, ChineseREER, relative GDP, and US current account balance. Shocks are extracted by applying a recursiveidentification structure with the above ordering to a vector error correction model.

⎡⎢⎢⎢⎢⎢⎢⎣

rwc,t

irdc,t

reerc,t

ryu,t

CABu,t

⎤⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎢⎣

rwc,t

irdc,t

reerc,t

ryu,t

CABu,t

⎤⎥⎥⎥⎥⎥⎥⎥⎦

+∞∑

i=0

⎡⎢⎢⎢⎢⎢⎢⎣

a11 a12 a13 a14 a15

a21 a22 a23 a24 a25

a31 a32 a33 a34 a35

a41 a42 a43 a44 a45

a51 a52 a53 a54 a55

⎤⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎣

e1t−i

e2t−i

e3t−i

e4t−i

e5t−i

⎤⎥⎥⎥⎥⎥⎥⎦

(44)

Errors of the reduced form equations are related to the structural parameters as:

⎡⎢⎢⎢⎢⎢⎢⎣

e1t

e2t

e3t

e4t

e5t

⎤⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎣

b11 b12 b13 b14 b15

b21 b22 b23 b24 b25

b31 b32 b33 b34 b35

b41 b42 b43 b44 b45

b51 b52 b53 b54 b55

⎤⎥⎥⎥⎥⎥⎥⎦

−1 ⎡⎢⎢⎢⎢⎢⎢⎣

εwt

εrt

εet

εyt

εcat

⎤⎥⎥⎥⎥⎥⎥⎦

(45)

Introducing more simplifying assumptions:⎡⎢⎢⎢⎢⎢⎢⎣

rwc,t

irdc,t

reerc,t

ryu,t

CABu,t

⎤⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎢⎣

rwc,t

irdc,t

reerc,t

ryu,t

CABu,t

⎤⎥⎥⎥⎥⎥⎥⎥⎦

+∞∑

i=0

⎡⎢⎢⎢⎢⎢⎢⎣

�11 �12 �13 �14 �15

�21 �22 �23 �24 �25

�31 �32 �33 �34 �35

�41 �42 �43 �44 �45

�51 �52 �53 �54 �55

⎤⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎣

εwt

εrt

εet

εyt

εcat

⎤⎥⎥⎥⎥⎥⎥⎦

(46)

where �i =

⎡⎢⎢⎣

a11 a12 a13 a14 a15a21 a22 a23 a24 a25a31 a32 a33 a34 a35a41 a42 a43 a44 a45a51 a52 a53 a54 a55

⎤⎥⎥⎦

⎡⎢⎢⎣

b11 b12 b13 b14 b15b21 b22 b23 b24 b25b31 b32 b33 b34 b35b41 b42 b43 b44 b45b51 b52 b53 b54 b55

⎤⎥⎥⎦

−1

.

�i,j(n) are impulse response coefficients for equation n. More compactly this can be represented as:

xt = +∞∑

i=0

�i(i)�t−i (47)

Given the higher US imports (more than three times the amount they export), incurring a hugeoverall trade deficit, there is a growing pressure on China to raise the value of its currency, particularlyfrom the US. This concern can be assessed via a structural VEC exercise whether the deficit is due torelative domestic demand or relative prices (real exchange rate). We have therefore used relative GDPand REER as a relative price variable. The impulse responses of REER shocks on relative GDP showthat REER appreciation harms Chinese exports thereby helping US GDP increase faster than ChineseGDP, leading to a decline in relative GDP between the two countries. This suggests that Chinese yuanreal appreciation is required to ensure sustainability, as relative GDP shocks only lead to short-runappreciation in REER (see Fig. 4). Xu (2008) reports a statistically significant long-run relationshipbetween the RMB/dollar exchange rate and the US trade deficit with China, suggesting a need forChina to adjust its exchange rate policy to help reduce the ever mounting US trade deficit.

K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59 51

Fig. 2. IRFs for relative wage shocks.

Impulse responses for the empirical model, calculated with Jmulti software, are presented inFigs. 2–6. Both long-run and short-run effects are summarised in Tables 3 and 4 respectively. China’sREER responds positively to shocks in all the four variables in the short-run, except the relativewage shock to which the REER responds negatively, which can happen via price adjustment by Chi-nese exporters (given fixed nominal exchange rate) on the back of lower profit mark-up in order to

Table 3Estimated matrix of long-run impact.

Shocks in −→ rw ird reer ry cab

rw 0.5387* −0.3595 −0.7420* 0.9380 −0.1203ird 0.3064 1.2237* 0.3780 −0.6904 0.1899reer −0.8826* 0.1650 0.5077 −0.4475 0.2744*ry 0.0505 0.0432 −0.1436* 0.2028 0.0410cab −0.0204 0.0637* −0.0447 0.0772 0.0466*

Notes: * and ** denote rejection of the null at 5% and 1% level of significance respectively.

Table 4Estimated matrix of short-run effects.

Shocks in −→ rw ird reer ry cab

rw 0.8837* 0.0000 0.0000 0.0000 0.0000ird 0.0547 0.6074* 0.0000 0.0000 0.0000reer −0.4894* 0.0895 1.5268* 0.0000 0.0000ry 0.0019 0.0104 −0.0133 0.0766* 0.0000cab −0.0074 0.0225* 0.0031 −0.0304* 0.0669*

Notes: * and ** denote rejection of the null at 5% and 1% level of significance respectively.

52 K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59

Fig. 3. IRFs for shocks in interest rate differential.

Fig. 4. IRFs for Chinese REER shocks.

K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59 53

Fig. 5. IRFs of relative GDP shocks.

Fig. 6. IRFs for shocks in US current account balance.

54 K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59

Fig. 7. Impulse responses of REER shocks with reordering of variables.

maintain its market share in the US. Under an unanticipated RMB real appreciation, the impulseresponses suggest that Chinese GDP declines more than the US GDP. To prevent such outcome, itis likely that Chinese exporters could change their export prices via adjusting profit margins in orderto offset the impact of real currency appreciation (see Bergin & Feenstra, 2009; Witte, 2009).

As an important international competitiveness indicator, REER can provide a reliable gauge of pricecompetitiveness about the relative profitability of Chinese traded goods. The results in Fig. 4 implythat there could be loss in competitiveness due to RMB appreciation, leading to a decline in ChineseGDP relative to the US. On the other hand, following a shock to relative GDP as in Fig. 5, relative wagein China increases, thus lowering China’s trade competitiveness and thus helping improve US currentaccount balance. Thus lower production cost remains the key to China’s trade competitiveness withthe US. From Fig. 6, it is clear that US current account balance can improve if it is accompanied byChina’s REER appreciation and an increase in China’s relative wage.

Estimated structural shocks do tend to capture the turning points. For robustness check, wereordered the variables with US current account balance ordered first, followed by relative GDP, REER,interest rate differential and relative wage, in order to check the responses of US current account bal-ance and Chinese relative GDP, but the results remain robust. We present below in Fig. 7 the responsesdue to shocks in REER – a key policy shock that we are interested in examining in this paper. We findthat as Chinese currency appreciates, its relative GDP declines, which leads to a current account sur-plus in the US. It appears that relative price effects dominate the relative demand effect. When Chinesereal exchange rate appreciates, it leads to an improvement in US current account balance. Thus theundervalued Chinese currency is one of the reasons why the deficit in the US current account persists.This is in line with the results in Bahmani-Oskooee and Wang (2007) and Xu (2008) at the industrylevel that the real yuan-dollar rate has indeed played a significant role in the trade balance betweenChina and the US.

K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59 55

Table 5Variance decompositions (k = 20).

Shocks in ↓ rw ird reer ry cab

rw 0.19 0.05 0.55 0.02 0.04ird 0.08 0.64 0.02 0.02 0.20reer 0.24 0.06 0.21 0.29 0.16ry 0.47 0.22 0.16 0.65 0.49cab 0.02 0.02 0.06 0.02 0.12

5. Variance decomposition

Let us start from the reduced form:

Xt = A0 + A1Xt−1 + et (48)

from successive iteration this reduces to

EtXt+n = (I + A1 + A21 + A3

1 + ...... + An−11 )A0 + An

1Xt + et (49)

Forecast error is given by

(et+n + A1et+n−1 + A21et+n−2 + ...... + An−1

1 et+1)A0 + An1Xt (50)

Xt+n − EtXt+n =n−1∑i=0

�i(i)�t+n−i (51)

Taking only one equationwt+n − Etwt+n = �11(0)�wt+n + �11(1)�wt+n−1 + ... + �11(n − 1)�wt+1 + �12(0)�rt+n +

�12(1)�rt+n−1 + ... + �12(n − 1)�rt+1+�12(0)�et+n + �12(1)�et+n−1 + . . . + �12(n − 1)�et+1+�12(0)�yt+n + �12(1)�yt+n−1 + . . . + �12(n − 1)�yt+1+�12(0)�cat+n + �12(1)�cat+n−1 + . . . + �12(n − 1)�cat+1Variance of n-step ahead forecast error is

�(n)2w = �2

w[�11(0) + �11(1) + ... + �11(n − 1)] + �2r [�12(0) + �12(1) + ... + �12(n − 1)]+

�2e [�12(0) + �12(1) + ... + �12(n − 1)] + �2

y [�12(0) + �12(1) + ... + �12(n − 1)]+�2

CA[�12(0) + �12(1) + ... + �12(n − 1)]

(52)

Variance decomposition in terms of variances of shocks �wt, �rt, �et, �yt and �cat.

�(n)2w = �2

w[�11(0) + �11(1) + ... + �11(n − 1)]

�(n)2w

+ �2r [�12(0) + �12(1) + ... + �12(n − 1)]

�(n)2w

+

�2e [�12(0) + �12(1) + ... + �12(n − 1)]

�(n)2w

+ �2y [�12(0) + �12(1) + ... + �12(n − 1)]

�(n)2w

+

�2CA[�12(0) + �12(1) + ... + �12(n − 1)]

�(n)2w

(53)

Thus the variance decomposition is finding the proportion of variance explained by a variable’sown shock (�wt) versus the variance explained by shock to the other variables �rt, �et, �ytand �cat.The variance decomposition for the empirical model in the long-run is presented in Table 5 for k = 20quarters following the shock. However, in the short-run (not reported in the table), nearly 75% of thevariation in US current account balance is explained by its own shocks, which declined to 12% in thelong-run as in the table. As nearly 25% of the variation in US current account balance is explainedtogether by interest rate differential (11%), REER (5%), relative GDP (6%) and China’s wage cost (3%),

56 K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59

Fig. 8. IRFs from over-identified SVAR.

this could suggest that China’s exchange rate appreciation might not solve the enlarging US cur-rent account deficits in the short-run. But in the long run, relative GDP explains a bigger proportionof the current account balance to the extent of 49%, reducing the impact of its own innovations to12%. From the earlier long-run and short-run parameter estimates, higher relative GDP of China doeshave a significant effect on lowering current account balance, and from this variance decompositionresults, we can conclude that higher relative GDP of China explains lowering US current balance in thelong-run. As shown in Fig. 2 earlier, following a relative wage shock on the other hand, relative GDPdeclines with either loss of income for the low-wage country or the rise in income for the high-wagecountry.

To further validate this result, a 6-variable VAR has been formulated by adding US import price asanother variable in the VAR, following an over-identified SVAR strategy (Sims-Zha) and impose therestrictions in the matrix below:⎡

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

1 a12 0 0 a15 0

0 1 a23 0 a25 0

a31 a32 1 a34 a35 a36

a41 0 a43 1 0 a46

a51 a52 0 0 1 a56

0 0 a63 a64 0 a66

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

The technique draws a set of posterior samples from the VAR coefficients and computes impulseresponses for each sample. These samples are then summarized to compute MC-based estimates ofthe responses using the error band methods in Sims and Zha (1999). The confidence bands are drawnby taking draws from the posterior distribution and identifying the shocks. The bands are modelledas the 16 and 84 percentile quantities for the response, which if the distribution is normal, thesequantiles would correspond to a one standard deviation band as recommended by Sims and Zha

K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59 57

(1999).3 These responses further help pinpoint the effects of different shocks, consistent with the ear-lier results from recursive factorisation (see Fig. 8). The results further pinpoint how China’s heavilymanaged exchange rate contributes to its huge trade surplus with the United States. The fixed pegcurrency regime of China could act as a form of “exchange rate protection”, alongside China’s com-parative advantage coming from lower relative wage cost, which remain central to any explanation ofglobal imbalances. With import prices as an additional variable in an over-identified SVAR, we showthat higher import price shock (4th column, Fig. 8) could immediately worsen US current account bal-ance if China’s fixed peg is replaced, but it will help improve the US external balance in the mediumrun.

6. Conclusion

Role of real and nominal exchange rates in flows of goods and capital are evaluated theo-retically using the Ricardian comparative static and dynamic general equilibrium models. Underfree trade arrangements a low income country with lower wage cost and large endowment oflabour has comparative advantage in trade and accumulates foreign and domestic capital. Effi-ciency gains from free trade enhance economic growth and welfare of households simultaneouslyin both low income and advanced economies. Empirically a dynamic general equilibrium modelis solved, calibrated and tested with quarterly data over the time period 1995:1 to 2009:1 onChina’s relative wage cost, interest rate differential, and REER (with US import price in an overi-dentified VAR), China’s relative GDP and the US current account balance. This paper shows howthe relative prices of labour, capital and the currency affect the economic activities in China andthe trade balance in the US. Decomposition of the variance of shocks and impulse response anal-yses are used to examine the size and the speed of adjustments to shocks. Dynamic simulationsare compared with predictions and impulse response analyses from the VECM exercise to showhow shocks to China’s relative wages, REER, and relative GDP interact with the US current accountbalance.

Empirical findings support theoretical predictions that welfare of households in China can catchup to households in the US as the former develops dynamic comparative advantage and accumulatesmore capital through trade surplus to expand its production of both tradable and non-tradable prod-ucts. In the long-run, China’s interest rate and exchange rate shocks are positively related, whileChina’s REER responds negatively to US import price shocks, which can happen via price adjust-ment by Chinese exporters (given fixed nominal exchange rate) on the back of lower wage cost inorder to maintain its market share in the US. This suggests that although China’s fixed peg makesthe Renminbi undervalued, yet this creates dynamic comparative advantage for China and the ris-ing US external imbalance. Higher relative prices in China will gradually erode benefits to Chinaand can improve US trade imbalance. Aside from the fixed exchange rate policy, the real shocksin China including the low relative wages and prices, which tend to keep the country’s REER at anundervalued level, are the key determinants of persistent external imbalance of the US. While higherproduction cost and prices in China could reduce the welfare of Chinese households and the tradeimbalance of the US, higher relative GDP of China helps lower the current account balance for theUS.

3 Sims and Zha (1999) found that the impulse responses from a VAR have highly asymmetrical distributions. As a result, theuse of one or two standard error bands can give a misleading impression about the shape. Hence, Sims and Zha (1999) argue infavour of fractiles with 16 and 84 percentiles.

58 K. Bhattarai, S. Mallick / North American Journal of Economics and Finance 25 (2013) 40– 59

Appendix A. Appendix

Detailed derivation of structural coefficients:⎡⎢⎢⎢⎢⎢⎢⎣

rwcu,t

irdcu,t

reerc,t

rycu,t

CABu,t

⎤⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎣

b11 b12 b13 b14 b15

b21 b22 b23 b24 b25

b31 b32 b33 b34 b35

b41 b42 b43 b44 b45

b51 b52 b53 b54 b55

⎤⎥⎥⎥⎥⎥⎥⎦

−1 ⎡⎢⎢⎢⎢⎢⎢⎣

b10

b20

b30

b40

b50

⎤⎥⎥⎥⎥⎥⎥⎦

+

⎡⎢⎢⎢⎢⎢⎢⎣

b11 b12 b13 b14 b15

b21 b22 b23 b24 b25

b31 b32 b33 b34 b35

b41 b42 b43 b44 b45

b51 b52 b53 b54 b55

⎤⎥⎥⎥⎥⎥⎥⎦

−1

⎡⎢⎢⎢⎢⎢⎢⎣

�11 �12 �13 �14 �15

�21 �22 �23 �24 �25

�31 �32 �33 �34 �35

�41 �42 �43 �44 �45

�51 �52 �53 �54 �55

⎤⎥⎥⎥⎥⎥⎥⎦

+

(A.1)

⎡⎢⎢⎢⎢⎢⎢⎣

b11 b12 b13 b14 b15

b21 b22 b23 b24 b25

b31 b32 b33 b34 b35

b41 b42 b43 b44 b45

b51 b52 b53 b54 b55

⎤⎥⎥⎥⎥⎥⎥⎦

−1 ⎡⎢⎢⎢⎢⎢⎢⎣

εwt

εrt

εet

εyt

εcat

⎤⎥⎥⎥⎥⎥⎥⎦

(A.2)

⎡⎢⎢⎢⎢⎢⎣

a10

a20

a30

a40

a50

⎤⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎣

b11 b12 b13 b14 b15

b21 b22 b23 b24 b25

b31 b32 b33 b34 b35

b41 b42 b43 b44 b45

b51 b52 b53 b54 b55

⎤⎥⎥⎥⎥⎥⎦

−1 ⎡⎢⎢⎢⎢⎢⎣

b10

b20

b30

b40

b50

⎤⎥⎥⎥⎥⎥⎦

;

⎡⎢⎢⎢⎢⎢⎣

e1t

e2t

e3t

e4t

e5t

⎤⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎣

b11 b12 b13 b14 b15

b21 b22 b23 b24 b25

b31 b32 b33 b34 b35

b41 b42 b43 b44 b45

b51 b52 b53 b54 b55

⎤⎥⎥⎥⎥⎥⎦

−1 ⎡⎢⎢⎢⎢⎢⎣

εwt

εrt

εet

εyt

εcat

⎤⎥⎥⎥⎥⎥⎦

(A.3)

⎡⎢⎢⎢⎢⎢⎣

a11 a12 a13 a14 a15

a21 a22 a23 a24 a25

a31 a32 a33 a34 a35

a41 a42 a43 a44 a45

a51 a52 a53 a54 a55

⎤⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎣

b11 b12 b13 b14 b15

b21 b22 b23 b24 b25

b31 b32 b33 b34 b35

b41 b42 b43 b44 b45

b51 b52 b53 b54 b55

⎤⎥⎥⎥⎥⎥⎦

−1 ⎡⎢⎢⎢⎢⎢⎣

�11 �12 �13 �14 �15

�21 �22 �23 �24 �25

�31 �32 �33 �34 �35

�41 �42 �43 �44 �45

�51 �52 �53 �54 �55

⎤⎥⎥⎥⎥⎥⎦

(A.4)

⎡⎢⎢⎢⎢⎢⎣

rwc,t

irdc,t

reerc,t

ryu,t

CABu,t

⎤⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎣

rwc,t

irdc,t

reerc,t

ryu,t

CABu,t

⎤⎥⎥⎥⎥⎥⎦

+∞∑

i=0

⎡⎢⎢⎢⎢⎢⎣

a11 a12 a13 a14 a15

a21 a22 a23 a24 a25

a31 a32 a33 a34 a35

a41 a42 a43 a44 a45

a51 a52 a53 a54 a55

⎤⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎣

b11 b12 b13 b14 b15

b21 b22 b23 b24 b25

b31 b32 b33 b34 b35

b41 b42 b43 b44 b45

b51 b52 b53 b54 b55

⎤⎥⎥⎥⎥⎥⎦

−1 ⎡⎢⎢⎢⎢⎢⎣

εwt

εrt

εet

εyt

εcat

⎤⎥⎥⎥⎥⎥⎦

(A.5)

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