Download China Turn Into the Largest Market in the World

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
©
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.
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
US Trade with China
(million dollars)
250,000
200,000
Total
Deficit
150,000
100,000
50,000
19
85
19
87
19
89
19
91
19
93
19
95
19
97
19
99
20
01
20
03
20
05
0
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.
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
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.
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
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
Real Exchange Rate of Countries
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
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
Estimation of Equilibrium Value
of Yuan: Simple OLS
Using the world sample to obtain the
estimates and the prediction equation
Intercept
Coefficients Standard
error
4.28039
0.15922
GDP p.c. -0.13386
0.01320
t -statistics
26.88387
-10.14495
Simple Linear Model: OLS
RER i  c  (a  b GDPpci ) 1   i
The Rogoff Model
ln RER = a + b ln GDPpc + ε
Coefficients
a
b
0.68742
-0.38561
Sum of Squared Errors of the log RER
values: 11.105
Sum of Squared Errors of the true values*:
856.44
The Rogoff Specificatgion
RER i  c  (a  b GDPpci ) 1   i
The New Non-linear Model
The new model
Non-linear regression equation
RER = c + (a + b GDPpc)-1 + ε
The New Non-linear Model
Regression results
Observations:160
Sum of squared errors: 299.0869
Estimated coefficients
a: 0.18903852
b: 0.023503552
c: 0.010
The New Non-linear Model
RMB Undervaluation Estimation
Non-linear Model
Year
GDP pc
2001
RER
actual
RER
predicted
Valuation
P-value**
1978
662
1248
1371
1502
1692
2394
2656
2876
2.00
3.26
4.13
4.15
4.44
4.83
4.28
4.09
4.90
4.59
4.53
4.47
4.38
4.09
3.99
3.91
59.2%
28.9%
8.9%
7.2%
-1.4%
-18.1%
-7.4%
-4.8%
0.084
1985
1986
1987
1991
1994
1995
1996
0.187
0.299
0.406
0.384
0.263
0.372
0.424
RMB Undervaluation Estimation
by Non-linear Model
Year
GDP pc
2001
RER
actual
RER
predicted
Valuation
P-value**
1998
3315
3506
3756
4020
4305
4647
4999
5462
4.27
4.41
4.46
4.53
4.59
4.55
4.32
3.96
3.76
3.69
3.62
3.54
3.46
3.36
3.27
3.16
-13.7%
-19.5%
-23.5%
-28.0%
-32.7%
-35.3%
-32.0%
-25.3%
0.437
1999
2000
2001
2002
2003
2004
2005*
0.409
0.357
0.319
0.304
0.278
0.286
0.315
Fittings of Different Models
1000
Sum of Square
Errors
800
600
400
200
0
Sum of Square
Errors
Rogoff
OLS
Non-linear
856.4
539.9
299.1
Comparison of various models
Year
OLS
Hetero
Rogoff
Non-linear
1978
1980
1981
1984
1986
1987
1990
1992
1993
52.3%
48.7%
42.3%
30.5%
20.7%
-0.7%
-2.5%
-16.3%
-32.2%
51.3%
44.9%
40.2%
33.8%
19.7%
-8.9%
-5.0%
-19.7%
-35.2%
6.2%
-2.8%
-16.2%
-45.6%
-70.2%
-118.8%
-126.2%
-162.4%
-201.7%
59.2%
55.8%
50.1%
38.7%
28.9%
8.9%
6.0%
-9.3%
-26.1%
Comparison of various models
Year
OLS
Hetero
Rogoff
Non-linear
1994
1995
1998
1999
2000
2001
2002
2003
2004
2005*
-21.9%
-9.1%
-11.3%
-15.8%
-18.2%
-21.0%
-23.8%
-24.4%
-19.6%
-11.5%
-24.3%
-12.6%
-8.9%
-14.3%
-18.4%
-20.1%
-23.2%
-22.5%
-19.2%
-181.0%
-153.6%
-162.4%
-173.9%
-180.2%
-187.5%
-194.6%
-196.0%
-184.4%
-164.6%
-18.1%
-7.4%
-13.7%
-19.5%
-23.5%
-28.0%
-32.7%
-35.3%
-32.0%
-25.3%
gyz
Re
-50.00%
-100.00%
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Under/over-valuation of currencies (2001)
by hetero-controlled linear model
100.00%
50.00%
0.00%
-150.00%
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?
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 BalassaSamuelson 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.
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.
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.