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transcript
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.
Approaches to estimate Equilibrium Approaches to estimate Equilibrium Value of YuanValue of Yuan
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
Approaches to estimate Equilibrium Approaches to estimate Equilibrium Value of YuanValue of Yuan
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
The New Non-linear ModelThe New Non-linear Model
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
The New Non-linear ModelThe New Non-linear Model
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
-150.00%
-100.00%
-50.00%
0.00%
50.00%
100.00%
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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).
Theoretical JustificationTheoretical Justification
• 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
Theoretical JustificationTheoretical Justification
• 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.
Theoretical JustificationTheoretical Justification
• 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
Theoretical JustificationTheoretical Justification
• The equilibrium real exchange rate RER* is determined by
1RER*= RER i
in
Theoretical JustificationTheoretical Justification
• 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
With the Balassa-Samuelson effecWith the Balassa-Samuelson effect t
• 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
With the Balassa-Samuelson effecWith the Balassa-Samuelson effect t
• 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
With the Balassa-Samuelson effecWith the Balassa-Samuelson effect t
• 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
With the Balassa-Samuelson effecWith the Balassa-Samuelson effect t
• The B-S effect implies the nontradable price in poor countries is lower,
•
• with•
(GDPpc )NTj jP g
'(GDPpc) 0g
With the Balassa-Samuelson effecWith the Balassa-Samuelson effect t
• 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
The Balassa-Samuelson effect The Balassa-Samuelson effect
•
•
(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
The Balassa-Samuelson effect The Balassa-Samuelson effect
• 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).
Trading across income groupsTrading across income groups
•
• • 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
Trading across income groupsTrading across income groups
• 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
Trading across income groupsTrading across income groups
• 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?
Trading across income groupsTrading across income groups
• 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
Trading across income groupsTrading across income groups
• If the specification is Chang 2006:
1RER* ( ,GDPpc) ( GDPpc)f c a b
Trading across income groupsTrading across income groups
• 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
Trading across income groupsTrading across income groups
• The first-order-condition with parameter c in the regression estimation will lead to
( ,GDPpc ) 1ifc
Trading across income groupsTrading across income groups
• 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
Trading across income groupsTrading across income groups
• 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.