The large US-China trade imbalance is a common cause for concern and regularly blamed on the undervaluation of the RMB. We estimate a simple model of the trade balance and simulate the long-run effects on the trade balance of RMB revaluations in the range of 10-50%. We find that improvements in the trade balance following plausible revaluations are likely to be modest.

Lei He

Nicolaas Groenewold

English

Research Papers in Economics

The US-China Trade Imbalance: Will Revaluing the RMB Help (Much)? 
 
by 
 
Nicolaas Groenewold* 
and 
Lei He 
Economics Program, 
University of Western Australia, 
Crawley, WA 6009 
Australia 
 
 
Abstract: The large US-China trade imbalance is a common cause for concern and 
regularly blamed on the undervaluation of the RMB.  We estimate a simple model of the 
trade balance and simulate the long-run effects on the trade balance of RMB revaluations 
in the range of 10-50%.  We find that improvements in the trade balance following 
plausible revaluations are likely to be modest. 
 
 
 
 
 
 
*Corresponding Author; e-mail address: nic.groenewold@uwa.edu.au 2
1. Introduction 
Bilateral trade flows between China and the US have expanded considerably over the 
past two decades but the increasingly unbalanced nature of this trade has caused 
considerable concern in American political circles. It has been widely argued that the 
imbalance is largely the result of the supposed undervaluation of the renminbi (RMB) 
which has been effectively pegged against the US dollar, giving Chinese manufacturers 
an “unfair advantage”.
 1 
 
The aim of this paper is not to resolve the question of whether the Chinese RMB is 
indeed misaligned, nor if it is, to evaluate the extent of such misalignment, nor even to 
consider whether bilateral trade deficits are a legitimate matter for concern. Rather, we 
take others’ estimates of the undervaluation and assess the likely impact on the Chins-US 
trade balance of the re-alignment of the RMB US dollar exchange rate.  We argue that 
this is an interesting exercise both as a contribution to the debate about how serious the 
supposed misalignment is and also in light of the likely future movement of China to a 
more market-oriented exchange rate which should see any undervaluation disappear.  We 
find that even large changes in the real exchange rate are likely to have modest effects on 
the trade deficit. 
 
 
 
2. The model 
The model we estimate is a reduced-form equation for the trade balance between China 
and the US derived from a simple two-country model of trade based on work of Rose and 
Yellen (1989).  The fact that both countries have important trading relationship with third 
countries is likely to introduce important specification bias into the empirical model 
                                                 
1 For its part, the US has long alleged that the RMB is undervalued by as much as 40%; see for example 
Testimony of Franklin J. Vargo before the House Committee on International Relations, United States 
Congress (2003).  It is reported that China’s foreign exchange reserve topped $853.7 billion US at the end 
of February 2006; see People’s Daily Online (2006).  
  3
based on only two countries and we therefore extend the two-country model to account 
for the possible importance of a third country (the “rest of the world”). 
 
Denoting demands for imports by country i from country j by Dij, supply of exports by 
country i to country j by Sij,  corresponding import prices relative to domestic prices by 
mij, export prices relative to domestic prices by xij, and real exchange rates by qij where, 
in each case, i, j = u, c, w (denoting the US, China and the rest of the world), we can 
write the three-country version of the Rose and Yellen (1989) model as: 
(1)  Duc = Duc(muc, muw, Yu) = Duc(quc.xcu, quw.xwu, Yu) 
(2)  Duw = Duw(muc, muw, Yu) = Duw(quc.xcu, quw.xwu, Yu) 
(3)   Dcu = Dcu(mcu, mcw, Yc) = Dcu(xuc/quc, qcw.xwc, Yc) 
(4)  Dcw = Dcw(mcu, mcw, Yc) = Dcw(xuc/quc, qcw.xwc, Yc) 
(5)  Suc = Suc(xuc, xuw) 
(6)  Suw = Suw(xuc, xuw) 
(7)  Scu = Scu(xcu, xcw) 
(8)   Scw = Scw(xcu, xcw) 
(9)  Dij = Sji,   i,j=c,u,w (i≠j) 
In each case the second equality in (1) to (4) follows from: 
 m ij = qij.xji  and qij = 1/qji.  
The model consists of 12 equations which allow us to solve for the Dij, the Sij  and the xij 
in terms of the qij  and Yu and Yc.  The US-China trade balance is defined as the ratio of 
US exports to imports which has the advantages that the measure is unit-free and that its 
magnitude is independent of scale effects (Brada et al., 1993).  
 
Thus, the equation of interest is: 
 
                                  +    +      –    –   + 
(10)  TBuc = TBuc (quc, quw, qcw, Yu, Yc)      
where the indicated signs follow from standard restrictions on the demand and supply 
functions (1) to (8).  Log-linearising and adding a random error term, we obtain the 
following estimating model:   4
(11)  lnTB uct = α1 + α2 (lnYut) + α3 ln(Yct) + α4 ln(quct) + α5 ln(quwt) + α6 ln(qcwt) + εt    
 
3. The data 
Quarterly data were used for the period to 1987(1) to 2003(4). Quarterly observations, 
seasonally adjusted where relevant, for all variables except Yc and quc were obtained from 
the IMF’s International Financial Statistics and Direction of Trade Statistics.  Quarterly 
real GDP data for China are not available until 1999(1) so that annual data were 
interpolated using the regression approach.
2  The real exchange rate was based on annual 
Chinese CPI data interpolated using a moving average approach. The real exchange rates 
for the US and China with respect to the rest of the world were measured by real effective 
exchange rate indexes for each country. Finally, data for bilateral trade between the 
China and the US are problematic.
3 There are major discrepancies between trade flows 
reported by China and by the US but the consensus is that US figures are more reliable 
that the Chinese ones and we therefore used the US-derived figures for the trade balance. 
 
4. The results 
4.1 Estimated trade-balance equations 
Following Shirvani and Wilbratte (1977), we begin by estimating equation (11) using 
OLS.  The resulting estimates are shown in Table 1.  A trend is included to allow direct 
comparison to estimates based on cointegration analysis reported below. 
[Table 1 near here] 
All variables have their predicted signs and, with the exception of qcw and Yc, they are 
significant at 1%. In particular, the real exchange rate’s coefficient displays the 
hypothesised sign and is significant.    
 
Before using these estimates to draw conclusions regarding the effects of an RMB 
revaluation on the trade balance between the US and China, however, we need to 
consider the stationarity of the variables.  Except for TB, all variables were found to be 
I(1) irrespective of the lag length and the presence or absence of a trend.  TB was found 
                                                 
2 Cf  Chow and Lin (1976),  Bahmani-Oskooee (1986) and Brada et al. (1993). 
3 See Feenstra et al.(1999) and Fung and Lau (2001, 2003).    5
to have a significant trend and when lags were chosen to eliminate autocorrelation, was 
found to be clearly non-stationary.  We therefore proceeded to test for cointegration and, 
using the Johansen procedure, we found evidence for a single cointegrating relationship.  
The cointegrating regression estimated using the Phillips-Hansen FMOLS estimator is 
reported in the second set of results in Table 1.  It is clearly similar to the OLS results; in 
particular, the coefficient of the real exchange rate is significant and of similar magnitude.  
A third estimate is given by the cointegrating vector estimated by the Johansen procedure 
which is also reported in Table 1.  Again, the results are similar, particularly the estimate 
of the coefficient of the real exchange rate which is significant and almost the same 
magnitude as that estimated by FMOLS.   
 
We can, therefore, be confident that there is a significant long-run effect of the real 
exchange rate on the trade balance and that the magnitude is in the range 0.83 to 1.1.  We 
now explore the implications of these estimated coefficients for the response of the trade 
balance to a change in the exchange rate.   
 
4.2 The effect of a revaluation on the trade balance 
There are three preliminary matters.  First, the real exchange rate appears in the equations 
while a revaluation directly affects only the nominal rate.  We can use the coefficient of 
the real exchange rate only if we can assume that the price levels are largely unaffected 
by the revaluation.  Himarios (1989) found this to be a reasonable approximation in his 
work and we proceed under this assumption.
4 
   
Second, the assumed revaluation of the RMB.  On the basis of estimates in existing work
5 
it appears that a broad consensus is that the RMB is undervalued by something in the 
range of 10-50%. 
 
                                                 
4 Note that if the assumption is violated the effects of the revaluation are likely to be smaller to the extent 
that subsequent price changes offset the revaluation, an effect which will strengthen our general 
conclusions. 
 
5 See Chang and Shao (2004) and Coudert and Couharde (2005).  6
Third, the method of computing the effect on the trade balance.  Our estimated coefficient 
gives us an elasticity for the trade balance in ratio form with respect to the exchange rate.  
Thus our model allows us to predict ΔTB/TB = ΔD/D –ΔX/X while for the change in the 
dollar value of the trade balance we need ΔX and ΔD separately.  We compute our effects 
under three alternative identification assumptions: that ΔD/D=0, that ΔX/X=0 and the 
ΔD/D=-ΔX/X and apply the percentage changes to the final quarter’s trade balance. The 
results are in Table 2. 
[Table 2 near here] 
The results show clearly that the improvement in the trade balance would be very modest 
unless there were a very large revaluation – even with a 50% revaluation, the trade deficit 
would fall by only about 37% under the assumption of equi-proportionate import and 
export contributions.  At more realistic revaluations of, say, 10-20%, the change in the 
trade balance would be marginal, certainly not of the order that one might expect from 
the political rhetoric. 
 
7. Conclusions 
This paper has estimated the effect on the US-Chian trade balance of a revaluation of the  
RMB, supposedly undervalued.  We present a range of computations but likely changes 
in the value of the RMB are not predicted to make much inroad into the trade imbalance 
between the US and China – a 10% revaluation is likely to improve the trade balance by 
less than 10%.  7
References 
Bahmani-Oskooee, M. 1986, ‘Determinants of International Trade Flows: The Case of 
Developing Countries’, Journal of Development Economics, vol.20, pp. 107-123. 
 
Brada, J., Kutan, A. and Zhou, S. 1993, ‘China’s Exchange Rate and the Balance of 
Trade’, Economics of Planning, vol.26, pp. 229-242. 
 
Chang, G.H. and Shao, Q. 2004, ‘How Much Is the Chinese Currency Undervalued? A 
Quantitative Estimation’, China Economic Review, vol.15, pp. 366-371. 
 
Chow, G.C. and Lin, A. 1976, ‘Best Linear Unbiased Estimation of Missing Observations 
in an  Economic Time Series’, Journal of the American Statistical Association, vol.71, 
pp. 719-21. 
 
Coudert, V. and Couharde, C. 2005, ‘Real Equilibrium Exchange Rate in China: Is the 
Renminbi Undervalued?’  CEPII Research Center: Working Paper No. 2005-01. 
http://www.cepii.fr/anglaisgraph/workpap/pdf/2005/wp05-01.pdf 
 
Feenstra, R.C. et al. 1999, ‘Discrepancies in International Data: An Application to China-
Hong Kong Entrepot Trade’, American Economic Review, May, vol.89, pp.338-343. 
 
Fung, K.C and Lau, L.J. 2001, ‘New Estimates of the United States-China Bilateral Trade 
Balances’, Journal of the Japanese and International Economies, vol.15, pp. 102-130. 
 
Fung, K.C and Lau, L.J. 2003, ‘Adjusted Estimates of United States – China Bilateral 
Trade Balances: 1995-2002’, Journal of Asian Economics, vol.14, pp.489-496. 
 
Himarios, D. 1989, ‘Do Devaluations Improve the Trade Balance? The Evidence 
Revisited’, Economic Inquiry, vol.27, pp. 143-165. 
  8
People’s Daily Online, 2006, ‘China Expected To Have The World's Largest Forex 
Reserves’. 
 http://english.people.com.cn/200603/29/eng20060329_254418.html  [03/29/2006] 
 
Rose, A.K. and Yellen, J.L. 1989, ‘Is there a J-Curve?’, Journal of Monetary Economics, 
vol. 24, pp.53-68. 
 
United States Congress, 2003, ‘U.S-China Ties: Reassessing the Economic Relationship 
– Hearing Before The Committee on International Relations House of Representatives’,  
Serial No. 108-70. http://www.house.gov/international—relations  9
Table 1: Regression Results 
 OLS  FMOLS  Cointegration 
Variable coefficient  p-value  coefficient p-value coefficient p-value 
CONST 48.8203 0.000 73.5661 0.000  NA  NA 
TREND 0.0562 0.004 0.0941 0.000  0.0837  0.002 
Yu  -5.9689 0.000 -8.7017 0.000  -6.2032  0.009 
Yc  0.0632 0.614 0.0134 0.916 -0.5056  0.015 
quw  0.7986 0.099 0.7817 0.112  0.1995  0.757 
qcw  -0.4303 0.120 -0.6464 0.021  -0.5967  0.106 
quc  0.8298 0.003 1.0767 0.000  1.0774  0.011 
R
2 0.8745  NA  NA 
DWS 1.5185  NA  NA 
Note: the p-values for the OLS and FMOLS regressions are derived from a t-test while those for the 
cointegrating regression are derived from a Chi-squared test for the exclusion of the variable from the 
cointegrating vector.  The intercept is omitted from the cointegrating regression since the VECM was 
specified with unrestricted intercepts so that the intercept for the cointegrating vector is not separately 
identified.  Values for R
2 and the Durbin-Watson statistics (DWS) are not available for the FMOLS and 
cointegration estimates. 
 
   10
Table 2: Increases in the US-China trade balance for various real appreciations of the RMB 
  OLS elasticity = 0.8298  FMOLS elasticity = 1.0767  Cointegration elasticity = 1.0776 
Δquc/quc  ΔD = 0  ΔX = 0 
ΔX/X = 
-ΔD/D  ΔD = 0  ΔX = 0 
ΔX/X = 
-ΔD/D  ΔD = 0  ΔX = 0 
ΔX/X = 
-ΔD/D 
0.05 254  1581 918 329 2052  1191 329 2054 1192
0.10 507  3163 1835 658 4104  2381 659 4107 2383
0.20 1015 6326 3670 1316 8208 4762 1317 8215 4766
0.30 1522 9488 5505 1975 12312 7143 1976 12322 7149
0.50 2536  15814 9175 3291 20519  11905 3294 20536 11915
Note: Numbers in the body of the table are increases in the US-China balance of trade compared to the value for 2003(4)  
when exports were 6113 billion USD, imports were 38115 billion USD and the trade deficit was 32002 billion USD. 
 

Adjusted Estimates of United States – China Bilateral Trade Balances: 1995-2002’,

Best Linear Unbiased Estimation of Missing Observations in an Economic Time Series’,

China Expected To Have The World's Largest Forex Reserves’. http://english.people.com.cn/200603/29/eng20060329_254418.html [03/29/2006]

China’s Exchange Rate and the Balance of Trade’,

Determinants of International Trade Flows: The Case of Developing Countries’,

Do Devaluations Improve the Trade Balance? The Evidence Revisited’,

How Much Is the Chinese Currency Undervalued? A Quantitative Estimation’,

New Estimates of the United States-China Bilateral Trade Balances’,

Real Equilibrium Exchange Rate in China: Is the Renminbi Undervalued?’ CEPII Research Center: Working Paper No.

U.S-China Ties: Reassessing the Economic Relationship – Hearing Before The

The US-China Trade Imbalance: Will Revaluing the RMB Help (Much)?

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The US-China Trade Imbalance: Will Revaluing the RMB Help (Much)?

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