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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 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. Vote by July. 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% pub Bel lic a Co ngo Camb rus , De odi a m. Re p. Ind ia Sou Ukrai th A ne fr Vie ica tn B u am lga ria C Ban h gla ina Phi desh lipp Ind ines one si a Ru Ita ssi an Thail ly Fed a era nd Ho tion ng Ko Hung a ng, Ch ry i Fin na lan Fra d nc Un ited Swed e en Ki Ko ngdom rea ,R ep Jap . a Sau Kuw n di A ait rab Ven Zam ia ez u bia Co ela, R ngo B , Re p. Kyr 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? The theoretical justification for the Rogoff-Frankel regression model • The Rogoff-Frankel regression model RER i f ( GDPpci ) i Theoretical 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 Justification • Country i's trade balance (net exports) is a function of its overvaluation or undervaluation. X i a(RER i -RER*) • 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. Theoretical 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 Justification • Globally, all trade deficits and surpluses shall be cancelled out. Summarize all countries trade, and note that it must be globally balanced: . n X n i a (RER i RER*) 0 i RER i i i n RER* Theoretical Justification • The equilibrium real exchange rate RER* is determined by 1 RER*= RER i n i Theoretical 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 • Let si be country i's share of the global trade. • The net exports volume of country i will be affected by si. • X as (RER -RER*) i i i n n n i i i • X i asi (RER i RER*) a si (RER i RER*) 0 With different GDP sizes • n s RER i i • Because • RER* n i n RER* si s n i i 1 , so, s RER i i i i • Hence the equilibrium RER is trade share weighted average of RERs of all trading countries. With the Balassa-Samuelson effect • RER*=f ( GDPpc) • there are m income-per-capita groups in the world. There is only one country in each incomeper-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: X (e* ) 0 j 1,..., m j j With the Balassa-Samuelson effect • PjT the price of tradable goods of country j • PjNT the price of the non tradable goods of country j. • k is the share of the tradable in the GDP. • T NT Pj kPj (1 k ) Pj With the Balassa-Samuelson effect • The law of one price, or the principle of purchasing power parity, only applies to the tradable. The equilibrium exchange rate is: • • e*j P T PjT PT the price of the tradables of the numeraire country * numerair e PT T 1 P With the Balassa-Samuelson effect • equilibrium real exchange rate of a country at income group j is: RER j * e*j P Pj e*j kP T e*j (1 k ) P NT kP (1 k ) P T j NT j ke*j P T (1 k )e*j P NT ke*j P T (1 k ) PjNT • Hence the equilibrium real exchange rate RER* is a function of the price of nontradable of the country. With the Balassa-Samuelson effect • The B-S effect implies the nontradable price in poor countries is lower, • P NT g (GDPpc ) j j • with • g '(GDPpc) 0 With the Balassa-Samuelson effect • Hence, RER j * ke*j P T e*j (1 k ) P NT ke*j P T (1 k ) g (GDPpc j ) • RER * (GDPpc) f (GDPpc) • and f’ < 0 The Balassa-Samuelson effect • Let country ij denote country i in income-percapita 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: • X ij a (RER ij -RER j *) 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: • m nj X j i ij 0 The Balassa-Samuelson effect • m nj X ij m nj j i a (RER ij RER j *) 0 j i m nj m nj m j i j i j • RER ij RER* j n j RER* j The Balassa-Samuelson effect • Then the following is true, the above equation is true: • 1 RER* j nj nj RER i ij j 1,..., m • 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. 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 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 groups • X i a(RER i - RER i *) • RER* E (RER i ) f ( ,GDPpc) • where is the parameter(s). • X i a(RER i - RER i *) a[RER i - f ( ,GDPpci )] Trading across income groups • The condition of balance of the global trade X a[RER - f ( ,GDPpc )] 0 n n i i • n [RER i i i i - f ( ,GDPpci )] 0 i Trading 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 groups • The regression model is • • RER i f ( ,GDPpci ) i Suppose that the regression method is a nonlinear least square or maximum likelihood estimation. Then it implies to minimize with respect to the parameters: • min 2 [RER f ( ,GDPpc )] i i i Trading across income groups • If the specification is Chang 2006: RER* f ( ,GDPpc) c (a b GDPpc)1 Trading across income groups • The first order condition of nonlinear least square regression is, • 2 [RER f ( ,GDPpc )] i i i 2 {[RER i f ( ,GDPpci )] f ( ,GDPpc i )} i 0 Trading across income groups • The first-order-condition with parameter c in the regression estimation will lead to f ( ,GDPpci ) 1 c Trading across income groups • Then, • 1 2 [RER c ( a b GDPpc ) ] i i c i 2 1 {[RER c ( a b GDPpc ) ] i i i 2 1 [RER c ( a b GDPpc ) ]1 i i i 0 f ( ,GDPpci )} c Trading 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 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 , each 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. 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.