Gene Hsin Chang Department of Economics, the University of Toledo, Toledo, USA © March 2007 Estimation of the Undervaluation of the Chinese Currency by

Gene Hsin ChangDepartment of Economics, the University of Tole

do, Toledo, USA

©

March 2007

Estimation of the Undervaluation of the Chinese Currency by a Non-linear Model

BackgroundBackground

Senate Bill: Senate Bill:

by Charles Schumer (D., N.Y.) and Lindsey Graby Charles Schumer (D., N.Y.) and Lindsey Graham (R., S.C.)ham (R., S.C.)

Currency manipulation by China.Currency manipulation by China.

If no RMB revaluation, imports from China can bIf no RMB revaluation, imports from China can be subject to 27.5% tariff. e subject to 27.5% tariff.

Vote by July. Vote by July.

BackgroundBackground

House China Currency Act: House China Currency Act:

by Congressmen Duncan Hunter (R., Calif.) and Tim Ryby Congressmen Duncan Hunter (R., Calif.) and Tim Ryan (D., Ohio)an (D., Ohio)

Currency manipulation as a "prohibited export subsidy" bCurrency manipulation as a "prohibited export subsidy" by China, under Article VI of the GATT.y China, under Article VI of the GATT.

If no RMB revaluation, trigger an antidumping or counterIf no RMB revaluation, trigger an antidumping or countervailing duty. Prohibition of importation of Chinese defevailing duty. Prohibition of importation of Chinese defense productsnse products

US Trade with China US Trade with China (million dollars)(million dollars)

0

50,000

100,000

150,000

200,000

250,000

Total

Deficit

Estimates of Undervaluation of Estimates of Undervaluation of RMBRMB

Jeffrey Frankel (2004): Using Rogoff model and Jeffrey Frankel (2004): Using Rogoff model and found that yuan is 42% undervaluedfound that yuan is 42% undervalued

Lardy and Goldstein (2003): 15%-25% Lardy and Goldstein (2003): 15%-25% undervalued. No formal model provided.undervalued. No formal model provided.

Gene Chang: Linear regression model: 19.2% Gene Chang: Linear regression model: 19.2% undervaluedundervalued

Gene Chang and Shao (2004): linear model with Gene Chang and Shao (2004): linear model with control of heteroskedasticity: 22.5% control of heteroskedasticity: 22.5% undervalued.undervalued.

Estimates of Undervaluation of Estimates of Undervaluation of RMBRMB

Zhang and Pan (2004): 15-22% Zhang and Pan (2004): 15-22% undervalued.undervalued.

Steve Hanke and Michael Connoly (2004 Steve Hanke and Michael Connoly (2004 WSJ): No undervaluation WSJ): No undervaluation

Ronald McKinnon: No revaluation, at most Ronald McKinnon: No revaluation, at most 1%. 1%.

Robert Mundell: No need for revaluation Robert Mundell: No need for revaluation for RMBfor RMB

Approaches to estimate Equilibrium Approaches to estimate Equilibrium Value of YuanValue of Yuan

Determination in the short-run: Supply Determination in the short-run: Supply and demand for the foreign exchangesand demand for the foreign exchanges

Estimating supply and demand for the Estimating supply and demand for the foreign exchanges, including trade foreign exchanges, including trade balance and current account balance.balance and current account balance.


Determination in the long-runDetermination in the long-run

Absolute purchasing power parityAbsolute purchasing power parity

Real Exchange Rate (RER)Real Exchange Rate (RER)

RER = (E X PRER = (E X PChinaChina) / P) / PU.S.U.S.

If absolute PPP holds, RER = 1If absolute PPP holds, RER = 1

Data are available now for abs PPPData are available now for abs PPP


Determination in the long-runDetermination in the long-runPurchasing power parityPurchasing power parity

E = PE = PU.S.U.S. / P / PChinaChina

Relative purchasing power parityRelative purchasing power parity% depreciation in E% depreciation in E

= inflation U.S. – inflation China= inflation U.S. – inflation ChinaProblems with using relative PPP to Problems with using relative PPP to estimate equilibrium value of yuanestimate equilibrium value of yuan

Real Exchange Rate of CountriesReal Exchange Rate of Countries

Estimation of Equilibrium Value Estimation of Equilibrium Value of Yuanof Yuan

Why is RER greater than 1 for poor Why is RER greater than 1 for poor countries?countries?

The Balassa-Samuelson hypothesisThe Balassa-Samuelson hypothesis

The Bhagwati-Kravis-Lipsey hypothesisThe Bhagwati-Kravis-Lipsey hypothesis

RER is a function of per capita income RER is a function of per capita income levellevel

Estimation of Equilibrium Value Estimation of Equilibrium Value of Yuan: Model Specificationof Yuan: Model Specification

Model with control of the income level:Model with control of the income level:

RER = f (GDP per capita)RER = f (GDP per capita)

Data for RERData for RER

Linear or Rogoff log linearLinear or Rogoff log linear

(ln) RER = a + b X (ln) GDP per (ln) RER = a + b X (ln) GDP per capitacapita

Control heteroskedasticityControl heteroskedasticity

Estimation of Equilibrium Value Estimation of Equilibrium Value of Yuan: Simple OLSof Yuan: Simple OLS

Using the world sample to obtain the Using the world sample to obtain the estimates and the prediction equationestimates and the prediction equation

CoefficientsCoefficients Standard Standard errorerror

t -statisticst -statistics

InterceptIntercept 4.28039 4.28039 0.15922 0.15922 26.88387 26.88387

GDP p.c.GDP p.c. -0.13386 -0.13386 0.01320 0.01320 -10.14495 -10.14495

Simple Linear Model: OLSSimple Linear Model: OLS

The Rogoff ModelThe Rogoff Model

ln RER = a + b ln GDPpcln RER = a + b ln GDPpc + + εε

CoefficientsCoefficients aa bb

0.687420.68742 -0.38561-0.38561

Sum of Squared Errors of the log RER Sum of Squared Errors of the log RER values:values: 11.10511.105

Sum of Squared Errors of the true values*:Sum of Squared Errors of the true values*:856.44856.44

1RER ( GDPpc )i i ic a b

The Rogoff SpecificatgionThe Rogoff Specificatgion

The New Non-linear ModelThe New Non-linear Model

The new modelThe new model

Non-linear regression equationNon-linear regression equation

RER = c + (a + b GDPpc)RER = c + (a + b GDPpc)-1 -1 + + εε

1RER ( GDPpc )i i ic a b


Regression resultsRegression results

Observations:160 Observations:160

Sum of squared errors: 299.0869Sum of squared errors: 299.0869

Estimated coefficientsEstimated coefficients

a: 0.18903852a: 0.18903852

b: 0.023503552b: 0.023503552

c: 0.010 c: 0.010


RMB Undervaluation EstimationRMB Undervaluation EstimationNon-linear ModelNon-linear Model

YearYear GDP pc GDP pc 20012001

RER RER actualactual

RER RER predictedpredicted

ValuationValuation P-value**P-value**

19781978 662662 2.002.00 4.904.90 59.2%59.2% 0.0840.084

19851985 12481248 3.263.26 4.594.59 28.9%28.9% 0.1870.187

19861986 13711371 4.134.13 4.534.53 8.9%8.9% 0.2990.299

19871987 15021502 4.154.15 4.474.47 7.2%7.2% 0.4060.406

19911991 16921692 4.444.44 4.384.38 -1.4%-1.4% 0.3840.384

19941994 23942394 4.834.83 4.094.09 -18.1%-18.1% 0.2630.263

19951995 26562656 4.284.28 3.993.99 -7.4%-7.4% 0.3720.372

19961996 28762876 4.094.09 3.913.91 -4.8%-4.8% 0.4240.424

RMB Undervaluation EstimationRMB Undervaluation Estimationby Non-linear Modelby Non-linear Model

YearYear GDP pc GDP pc 20012001

RER RER actualactual

RER RER predictedpredicted

ValuationValuation P-value**P-value**

19981998 33153315 4.274.27 3.763.76 -13.7%-13.7% 0.4370.437

19991999 35063506 4.414.41 3.693.69 -19.5%-19.5% 0.4090.409

20002000 37563756 4.464.46 3.623.62 -23.5%-23.5% 0.3570.357

20012001 40204020 4.534.53 3.543.54 -28.0%-28.0% 0.3190.319

20022002 43054305 4.594.59 3.463.46 -32.7%-32.7% 0.3040.304

20032003 46474647 4.554.55 3.363.36 -35.3%-35.3% 0.2780.278

20042004 49994999 4.324.32 3.273.27 -32.0%-32.0% 0.2860.286

2005*2005* 54625462 3.963.96 3.163.16 -25.3%-25.3% 0.3150.315

Fittings of Different ModelsFittings of Different Models

0

200

400

600

800

1000

Sum of SquareErrors

Sum of SquareErrors

856.4 539.9 299.1

Rogoff OLS Non-linear

Comparison of various modelsComparison of various models

YearYear OLSOLS HeteroHetero RogoffRogoff Non-linearNon-linear

19781978 52.3%52.3% 51.3%51.3% 6.2%6.2% 59.2%59.2%

19801980 48.7%48.7% 44.9%44.9% -2.8%-2.8% 55.8%55.8%

19811981 42.3%42.3% 40.2%40.2% -16.2%-16.2% 50.1%50.1%

19841984 30.5%30.5% 33.8%33.8% -45.6%-45.6% 38.7%38.7%

19861986 20.7%20.7% 19.7%19.7% -70.2%-70.2% 28.9%28.9%

19871987 -0.7%-0.7% -8.9%-8.9% -118.8%-118.8% 8.9%8.9%

19901990 -2.5%-2.5% -5.0%-5.0% -126.2%-126.2% 6.0%6.0%

19921992 -16.3%-16.3% -19.7%-19.7% -162.4%-162.4% -9.3%-9.3%

19931993 -32.2%-32.2% -35.2%-35.2% -201.7%-201.7% -26.1%-26.1%

Comparison of various modelsComparison of various modelsYearYear OLSOLS HeteroHetero RogoffRogoff Non-linearNon-linear

19941994 -21.9%-21.9% -24.3%-24.3% -181.0%-181.0% -18.1%-18.1%

19951995 -9.1%-9.1% -12.6%-12.6% -153.6%-153.6% -7.4%-7.4%

19981998 -11.3%-11.3% -8.9%-8.9% -162.4%-162.4% -13.7%-13.7%

19991999 -15.8%-15.8% -14.3%-14.3% -173.9%-173.9% -19.5%-19.5%

20002000 -18.2%-18.2% -18.4%-18.4% -180.2%-180.2% -23.5%-23.5%

20012001 -21.0%-21.0% -20.1%-20.1% -187.5%-187.5% -28.0%-28.0%

20022002 -23.8%-23.8% -23.2%-23.2% -194.6%-194.6% -32.7%-32.7%

20032003 -24.4%-24.4% -22.5%-22.5% -196.0%-196.0% -35.3%-35.3%

20042004 -19.6%-19.6% -19.2%-19.2% -184.4%-184.4% -32.0%-32.0%

2005*2005* -11.5%-11.5% -164.6%-164.6% -25.3%-25.3%

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

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The theoretical justification for the The theoretical justification for the Rogoff-Frankel regression modelRogoff-Frankel regression model

Why is the regression mean (predicted linWhy is the regression mean (predicted line)) serves as the equilibrium exchange rate)) serves as the equilibrium exchange rate?e?

Why does the error term (residual) measurWhy does the error term (residual) measure the magnitude of the under or over valuae the magnitude of the under or over valuation?tion?

The theoretical justification The theoretical justification for the Rogoff-Frankel for the Rogoff-Frankel

regression modelregression model• The Rogoff-Frankel regression model

RER ( GDPpc )i i if

Theoretical JustificationTheoretical Justification

• Starting from a simple version• n trading countries• All are of the same economic size and at

the same development level (same GDP per capita level).


• Country i's trade balance (net exports) is a function of its overvaluation or undervaluation.

• where Xi is the next exports of country i. RER* is the equilibrium real exchange rate. RERi is the real exchange rate of country i, and a is a positive constant.

(RER -RER*)i iX a


• If the country revalues/devalues its currency back to the equilibrium level thus, then its trade is in balance Xi = 0.

• Conversely, if its trade is not balanced, its currency is not at the equilibrium level.


• Globally, all trade deficits and surpluses shall be cancelled out. Summarize all countries trade, and note that it must be globally balanced: .

(RER RER*) 0n n

i ii i

X a RER RER*i

i

n


• The equilibrium real exchange rate RER* is determined by

1RER*= RER i

in


• So, the equilibrium exchange rate is the mean of the real exchange rates.

• Further, the difference between RERi and RER*, , measures the under- or overvaluation.

With different GDP sizes With different GDP sizes

• Let si be country i's share of the global trade.

• The net exports volume of country i will be affected by si.

•

•

(RER -RER*)i i iX as

(RER RER*) (RER RER*) 0n n n

i i i i ii i i

X as a s

With different GDP sizes With different GDP sizes •

• Because , so,

•

• Hence the equilibrium RER is trade share weighted average of RERs of all trading countries.

RER RER*n n

i i ii i

s s 1

n

ii

s RER* RER

n

i ii

s

With the Balassa-Samuelson effecWith the Balassa-Samuelson effect t

•

• there are m income-per-capita groups in the world. There is only one country in each income-per-capita group:. Without loss of generality, let us assume that the income-per-capita level follows the same order, where group 1 is the poorest and group m is the richest. The nominal exchange rates of all countries are at the equilibrium levels. That is, all of them are trade balanced:

RER*= ( GDPpc)f

*( ) 0 1,...,j jX e j m


• the price of tradable goods of country j

• the price of the non tradable goods of country j.

• k is the share of the tradable in the GDP.•

TjP

NTjP

(1 )T NTj j jP kP k P


• The law of one price, or the principle of purchasing power parity, only applies to the tradable. The equilibrium exchange rate is:

•

• the price of the tradables of the numeraire country

*Tj

j T

Pe

P

TP* 1

T

numerair T

Pe

P


• equilibrium real exchange rate of a country at income group j is:

• Hence the equilibrium real exchange rate RER* is a function of the price of non-tradable of the country.

* * * * *

*

(1 ) (1 )RER *

(1 ) (1 )

T NT T NTj j j j j

j T NT T NTj j j j j

e P e kP e k P ke P k e P

P kP k P ke P k P


• The B-S effect implies the nontradable price in poor countries is lower,

•

• with•

(GDPpc )NTj jP g

'(GDPpc) 0g


• Hence,

• • and f’ < 0

* *

*

(1 )RER *

(1 ) (GDPpc )

T NTj j

j Tj j

ke P e k P

ke P k g

RER *(GDPpc) (GDPpc)f

The Balassa-Samuelson effect The Balassa-Samuelson effect • Let country ij denote country i in income-per-

capita group j. Each group j has nj countries. Drop the assumption that each country is in equilibrium, but assume all of them are of the same trade volume size, we have the net exports of country ij be determined by its real exchange rate against the equilibrium value:

• (RER -RER *)ij ij jX a

The Balassa-Samuelson effect The Balassa-Samuelson effect

• Globally, all trade deficits and surpluses shall be cancelled out. Summarize all countries trade, and note that it must be globally balanced:

• 0

jnm

ijj i

X


•

•

(RER RER *) 0j jn nm m

ij ij jj i j i

X a

RER RER* RER*j jn nm m m

ij j j jj i j i j

n

The Balassa-Samuelson effect The Balassa-Samuelson effect • Then the following is true, the above equation is

true:

•

• This shows that the equilibrium vales of the real exchange rates is the means of the real exchange rates of all countries in the same income groups.

1RER* RER 1,...,

jn

j ijij

j mn


• If each country ij adjust its RERij to the mean of RERs of its income group, then their trade is balanced as indicates.

• The country's under- or overvaluation currency can be measured by the deviation from the mean of RERs of its income group.

Trading across income groupsTrading across income groups

• Let Xi be any country, which can be at different income level (but we maintain the assumption that their volume of trade is the same, or, its net exports is only affected by its under or overvaluation of exchange rate but not the GDP size).


•

• • where is the parameter(s).

•

(RER - RER *)i i iX a

RER* (RER ) ( ,GDPpc)iE f

(RER - RER *) [RER - ( ,GDPpc )]i i i i iX a a f


• The condition of balance of the global trade

• [RER - ( ,GDPpc )] 0n

i ii

f

[RER - ( ,GDPpc )] 0n n

i i ii i

X a f


• Suppose we use the Rogoff-Frankel model to regress RERi on GDPpc, would the estimated RER be the consistent estimate of , that satisfy the condition of global trade balance?


• The regression model is

• • Suppose that the regression method is a non-

linear least square or maximum likelihood estimation. Then it implies to minimize with respect to the parameters:

•

RER ( ,GDPpc )i i if

2

i

min [RER ( ,GDPpc )]i if


• If the specification is Chang 2006:

1RER* ( ,GDPpc) ( GDPpc)f c a b


• The first order condition of nonlinear least square regression is,

• 2

i

i

[RER ( ,GDPpc )]

2 {[RER ( ,GDPpc )] ( ,GDPpc )}

0

i i

i i i

f

f f


• The first-order-condition with parameter c in the regression estimation will lead to

( ,GDPpc ) 1ifc


• Then,

• 1 2

i

1

i

1

i

[RER ( GDPpc ) ]

2 {[RER ( GDPpc ) ] ( ,GDPpc )}

2 [RER ( GDPpc ) ] 1

0

i i

i i i

i i

c a bc

c a b fc

c a b


• By using MLE or nonlinear LS, the estimates for parameters are asymptotically consistent. The estimated model servers as the equilibrium values of the exchange rates of trading countries, taking account of the Balassa-Samuelson effect.

Trading across income groupsTrading across income groups• Our model is justified by three reasons: • first, if a country adjusts its exchange rate to , its trade

is balanced as Xi = 0. • Secondly, if all countries adjust their exchanges to , ea

ch country is own trade balanced. • Finally, by using Chang's model specification or linear

specification, the global trade balance condition is always satisfied by the MLE estimates, even if each country itself has trade surplus, which is caused by an undervalued currency, or has trade deficit, which is caused by an overvalued currency.

SummarySummary

The long run equilibrium value of RMB provides The long run equilibrium value of RMB provides the best information about the trend of the the best information about the trend of the valuation of RMB.valuation of RMB.

Absolute PPP with control of the Balassa-Absolute PPP with control of the Balassa-Samuelson effect is the best approximation Samuelson effect is the best approximation available for the long-run equilibrium value of a available for the long-run equilibrium value of a currency.currency.

The suggested non-linear model provides better The suggested non-linear model provides better fitting for the data than previous models.fitting for the data than previous models.

Concluding RemarksConcluding Remarks

RMB is undervalued by 25.5% in 2005, RMB is undervalued by 25.5% in 2005, hence the revaluation pressure hence the revaluation pressure continuously presents.continuously presents.

RMB has revalued substantially in real RMB has revalued substantially in real term in 2005 by a nominal revaluation and term in 2005 by a nominal revaluation and a higher inflation rate (10.46%) in the GDP a higher inflation rate (10.46%) in the GDP deflator. deflator.

Concluding RemarksConcluding Remarks

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

Documents

Gene Hsin Chang Department of Economics, the University of Toledo, Toledo, USA © March 2007 Estimation of the Undervaluation of the Chinese Currency by