1. Estimation of the Undervaluation of the Chinese Currency
by a Non-linear Model
Gene Hsin Chang
Department of Economics, the University of Toledo, Toledo, USA
March 2007

2. Background The U.S. Senate Bill:
by Charles Schumer (D., N.Y.) and Lindsey Graham (R., S.C.)
Currency manipulation by China.
If no RMB revaluation, imports from China can be subject to 27.5% tariff.
Congress is currently taking a hard line against China’s exchange rate policy, which de facto pegs its currency, the yuan, to the U.S. dollar. Senators Charles Schumer and Lindsey Graham are sponsoring a bill pressing China to revalue the yuan, while in the House, Representatives Duncan Hunter and Tim Ryan are sponsoring an act that will penalize China if the yuan is not revalued.

3. Background House China Currency Act:
by Congressmen Duncan Hunter (R., Calif.) and Tim Ryan (D., Ohio)
Currency manipulation as a "prohibited export subsidy" by China, under Article VI of the GATT.
If no RMB revaluation, trigger an antidumping or countervailing duty. Prohibition of importation of Chinese defense products
Congress is currently taking a hard line against China’s exchange rate policy, which de facto pegs its currency, the yuan, to the U.S. dollar. Senators Charles Schumer and Lindsey Graham are sponsoring a bill pressing China to revalue the yuan, while in the House, Representatives Duncan Hunter and Tim Ryan are sponsoring an act that will penalize China if the yuan is not revalued.

4. US Trade with China (million dollars)

5. Estimates of Undervaluation of RMB
Jeffrey Frankel (2004): Using Rogoff model and found that yuan is 42% undervalued
Lardy and Goldstein (2003): 15%-25% undervalued. No formal model provided.
Gene Chang: Linear regression model: 19.2% undervalued
Gene Chang and Shao (2004): linear model with control of heteroskedasticity: 22.5% undervalued.

6. Estimates of Undervaluation of RMB
Zhang and Pan (2004): 15-22% undervalued.
Steve Hanke and Michael Connoly (2004 WSJ): No undervaluation
Ronald McKinnon: No revaluation, at most 1%.
Robert Mundell: No need for revaluation for RMB

7. Approaches to estimate Equilibrium Value of Yuan
Determination in the short-run: Supply and demand for the foreign exchanges
Estimating supply and demand for the foreign exchanges, including trade balance and current account balance.

8. Approaches to estimate Equilibrium Value of Yuan
Determination in the long-run
Absolute purchasing power parity
Real Exchange Rate (RER)
RER = (E X PChina) / PU.S.
If absolute PPP holds, RER = 1
Data are available now for abs PPP

9. Approaches to estimate Equilibrium Value of Yuan
Determination in the long-run
Purchasing power parity
E = PU.S. / PChina
Relative purchasing power parity
% depreciation in E
= inflation U.S. – inflation China
Problems with using relative PPP to estimate equilibrium value of yuan

10. Real Exchange Rate of Countries

11. Estimation of Equilibrium Value of Yuan
Why is RER greater than 1 for poor countries?
The Balassa-Samuelson hypothesis
The Bhagwati-Kravis-Lipsey hypothesis
RER is a function of per capita income level

12. Estimation of Equilibrium Value of Yuan: Model Specification
Model with control of the income level:
RER = f (GDP per capita)
Data for RER
Linear or Rogoff log linear
(ln) RER = a + b X (ln) GDP per capita
Control heteroskedasticity

13. Estimation of Equilibrium Value of Yuan: Simple OLS
Using the world sample to obtain the estimates and the prediction equation 
Coefficients
Standard error
t -statistics
Intercept
GDP p.c.

14. Simple Linear Model: OLS

15. The Rogoff Model ln RER = a + b ln GDPpc + ε Coefficients a b
Sum of Squared Errors of the log RER values:
Sum of Squared Errors of the true values*:

16. The Rogoff Specificatgion

17. The New Non-linear Model
The new model
Non-linear regression equation
RER = c + (a + b GDPpc)-1 + ε

18. The New Non-linear Model
Regression results
Observations:160  
Sum of squared errors:
Estimated coefficients
a:  b:
c: 0.010  

19. The New Non-linear Model

20. RMB Undervaluation Estimation Non-linear Model
Year
GDP pc 2001
RER actual
RER predicted
Valuation
P-value**
1978
662
2.00
4.90
59.2%
0.084
1985
1248
3.26
4.59
28.9%
0.187
1986
1371
4.13
4.53
8.9%
0.299
1987
1502
4.15
4.47
7.2%
0.406
1991
1692
4.44
4.38
-1.4%
0.384
1994
2394
4.83
4.09
-18.1%
0.263
1995
2656
4.28
3.99
-7.4%
0.372
1996
2876
3.91
-4.8%
0.424

21. RMB Undervaluation Estimation by Non-linear Model
Year
GDP pc 2001
RER actual
RER predicted
Valuation
P-value**
1998
3315
4.27
3.76
-13.7%
0.437
1999
3506
4.41
3.69
-19.5%
0.409
2000
3756
4.46
3.62
-23.5%
0.357
2001
4020
4.53
3.54
-28.0%
0.319
2002
4305
4.59
3.46
-32.7%
0.304
2003
4647
4.55
3.36
-35.3%
0.278
2004
4999
4.32
3.27
-32.0%
0.286
2005*
5462
3.96
3.16
-25.3%
0.315

22. Fittings of Different Models

23. Comparison of various models
Year
OLS
Hetero
Rogoff
Non-linear
1978
52.3%
51.3%
6.2%
59.2%
1980
48.7%
44.9%
-2.8%
55.8%
1981
42.3%
40.2%
-16.2%
50.1%
1984
30.5%
33.8%
-45.6%
38.7%
1986
20.7%
19.7%
-70.2%
28.9%
1987
-0.7%
-8.9%
-118.8%
8.9%
1990
-2.5%
-5.0%
-126.2%
6.0%
1992
-16.3%
-19.7%
-162.4%
-9.3%
1993
-32.2%
-35.2%
-201.7%
-26.1%

24. Comparison of various models
Year
OLS
Hetero
Rogoff
Non-linear
1994
-21.9%
-24.3%
-181.0%
-18.1%
1995
-9.1%
-12.6%
-153.6%
-7.4%
1998
-11.3%
-8.9%
-162.4%
-13.7%
1999
-15.8%
-14.3%
-173.9%
-19.5%
2000
-18.2%
-18.4%
-180.2%
-23.5%
2001
-21.0%
-20.1%
-187.5%
-28.0%
2002
-23.8%
-23.2%
-194.6%
-32.7%
2003
-24.4%
-22.5%
-196.0%
-35.3%
2004
-19.6%
-19.2%
-184.4%
-32.0%
2005*
-11.5%
-164.6%
-25.3%

25. Under/over-valuation of currencies (2001) by hetero-controlled linear model

26. The theoretical justification for the Rogoff-Frankel regression model
Why is the regression mean (predicted line)) serves as the equilibrium exchange rate?
Why does the error term (residual) measure the magnitude of the under or over valuation?

27. Summary
The long run equilibrium value of RMB provides the best information about the trend of the valuation of RMB.
Absolute PPP with control of the Balassa-Samuelson effect is the best approximation available for the long-run equilibrium value of a currency.
The suggested non-linear model provides better fitting for the data than previous models.

28. Concluding Remarks
RMB is undervalued by 25.5% in 2005, hence the revaluation pressure continuously presents.
RMB has revalued substantially in real term in 2005 by a nominal revaluation and a higher inflation rate (10.46%) in the GDP deflator.

29. Concluding Remarks
The magnitude of undervaluation will diminish in near future due to: (1) revaluation of the nominal exchange rate of RMB, and (2) a higher inflation rate in China than that in U.S.
The undervaluation will intensify as China is growing rapidly.
The net result depends on the relative magnitudes of the two opposite forces. But RMB revaluation represents the general trend, which is in response to the market pressure.