CAPITAL FLOWS, TERMS OF TRADE, AND REAL EXCHANGE RATE FLUCTUATIONS

Transcription

1 CAPITAL FLOWS, TERMS OF TRADE, AND REAL EXCHANGE RATE FLUCTUATIONS After financial openings, like that in Spain and Mexico in the late 1980s, large capital inflows have been accompanied by substantial appreciations in the real exchange rate. Previous work has shown that, to capture the timing of capital inflows and the changes in the relative prices of nontraded goods, frictions in factor markets are important. The model here stresses the role of the imperfect substitutability between domestic and foreign traded goods in determining the terms of trade, whose movements are major components of real exchange rate fluctuations.

2 This is preliminary work based on Capital Flows and Real Exchange Rate Fluctuations Following Spain s Entry into the European Community, with Gonzalo Fernandez de Cordoba. Tradability of Goods and Real Exchange Rate Fluctuations with Caroline M. Betts

3 units: REAL EXCHANGE RATE RER NER P ger P esp pesetas deutsche marks deutsche marks/german basket pesetas/spanish basket Spanish basket German basket

4 Suppose PT esp NER P T ger (law of one price) RER N P T esp P ger P ger/p T ger T P ger P esp P esp /P T esp RER N is the part of the real exchange rate explained by the relative price of nontraded goods.

5 REAL EXCHANGE RATE - DATA RER RERp year

6 What is left over in RER is the part explained by the terms of trade. Notice that TRADED Agriculture and Industry RER T NER P T ger T P esp RER RER T RER N NONTRADED Construction and Services

7 MODELING CAPITAL FLOWS INTO SPAIN Y j AN j 1 K j y j Ak j r j Ak j 1 y esp 21, 875 y ger 27, 879 k esp 45, 528 k ger 73, 618 y esp y ger k esp k ger 1986

8 Let in data y esp y ger y esp y ger Differences in capital per worker explain 63 percent of differences in output per worker between Spain and Germany.

9 HOW LARGE SHOULD CAPITAL FLOWS BE? Calibrate A esp y esp /k esp A ger y ger /k ger Equate marginal products A esp k 1 esp A ger k 1 ger k ger 73, 618 implies k esp 64,030 Spanish capital stock would have to increase by 18,502, which is 85 percent of Spanish GDP, 41 percent of Spanish capital stock. r ger implies r esp 0.088

10 Simple Model Consumers max t 0 t c Tt 1 c Nt / subject to c Tt p t c Nt a t 1 w t l 1 r t a t a t A where a t q t 1 k t b t.

11 Feasibility condtions c Nt z Nt A N k N 1 Nt l 1 Nt k Tt k Nt k t l Tt l Nt l k t 1 1 k t Gz 1 Nt z Tt c Tt z TNt b t 1 A T k T 1 Tt l T Tt 1 r t b t

12 Calibration y N k N l N y T k T l T x z T z N k/y / k/y c N /c T 1 1 c N /c T / 1 r r A ale k 1 ale

13 Labor adjustment frictions l Nt 1 l Nt l Tt 1 l Tt 1 (In the simulacions, )

14 Capital adjustment frictions x Nt 1 x Tt 1 Gz 1 Nt z Tt k Nt 1 x Nt 1 /k Tt k Nt 1 k Nt k Tt 1 x Tt 1 /k Tt k Tt 1 k Tt x/k 0, x/k 0,, 1 x/k 1 x/k 1 /, 0 1 (In the simulaciones 0.9.)

15 MODEL WITH ARMINGTON AGGREGATOR Consumers subject to max t c Tt 1 c Nt t 0 1 / p Tt c Tt p Nt c Nt a t 1 w t l 1 r t a t T t where a t A a t q t 1 k t b t

16 Feasibility-Equilibrium Conditions Domestically produced traded good x Dt x Ft A D k D 1 Dt l D Dt Armington aggregator c Tt z Tt M x Dt 1 m t 1/ Nontraded good c Nt z Nt A N k N 1 Nt l N Nt Balance of payments Investment m t b t 1 p Dt x Ft 1 r t b t k t 1 1 k t Gz 1 Tt z Nt

17 Foreign demand x Ft D 1 Ft p Dt 1 1 Factor markets k Dt k Nt k t, l Dt l Nt l Transfer of tariff revenue T t Dt m t

18 Profit maximization w t p Dt A D 1 D k Dt /l Dt D p Nt A N 1 N k Nt /l Nt N 1 r t p Dt A D D l Dt /k Dt 1 D 1 qt /q t 1 p Nt A N N l Nt /k Nt 1 N 1 qt q t 1 p Tt q t G z Nt /z Tt 1 p Nt q t 1 G z Tt /z Nt

19 where x Dt 1 1 M 1 ptt /p Dt 1 1 ctt z Tt m t M 1 ptt / 1 Dt 1 1 ctt z Tt p Tt 1/M pdt Dt 1 1

20 LABOR ADJUSTMENT FRICTIONS l Dt 1 l Dt l Nt 1 l Nt 1 If constraint binds, labor in traded goods sector receives a different wage, w Dt, than the wage of labor in the nontraded goods sector, w Nt. (In simulations, )

21 CAPITAL ADJUSTMENT FRICTIONS i Dt 1 i Nt 1 Gz 1 Tt z Nt k Dt 1 i Dt 1 /k Dt k Dt 1 k Dt k Nt 1 i Nt 1 /k Nt k Nt 1 k Nt i/k 0, i/k 0,, 1 i/k 1 i/k 1 /, 0 1 Adjusting the sector specific capital stock rapidly is costly. (In simulations 0. 9.)

22 TRADE BALANCE Data Model year

23 REAL EXCHANGE RATE - MODEL RER RERp year

24 REAL EXCHANGE RATE Bilateral real exchange rate between the United States and country i: RER = NER ius, ius, P us P i NER ius, : nominal exchange rate country i currency units per U.S. dollar P j: price deflator or index for the basket of goods consumed or produced in country j, j = us, i.

25 Decompose T T T P us Pi P us T RERius, = NERius, / P T RER = RER RER i P i P us where P RER NER P T T us ius, = ius, T i N ius, ius, ius, is the real exchange rate of traded goods the component that measures deviations from the law of one price and RER P P = (, ) (, ) T T N i us ius, / T N T N Pi Pi Pi Pus Pus Pus is the (bilateral) relative price of nontraded (to traded) goods.

26 TRADED Agriculture, Mining and Petroleum, and Manufacturing NONTRADED Construction and Services

27 Mexico-U.S. real exchange rate rer log(rer) rern year

28 MODELING CAPITAL FLOWS INTO MEXICO Y = AK N α 1 j j j y j = Ak α y mex = 16,373, y us = 36,859 (1989) 1 r α Ak α = δ j r = 0.13, r = 0.05( ) mex us j j Let α = 0.30, δ = 0.05 α y mex k mex rus + δ = = yus kus rmex + δ α 1 α

29 y y mex us = = while, in the data, y y mex us = Difference in capital per worker explains 30 percent of difference in output per worker.

30 We can calibrate different productivity parameters A mex and A us: k j A = j α y r = j j + δ y j k α j k = 27, 288, A = mex mex k = 110,577, A = us Productivity in the United States is 48 percent higher than in Mexico. us

31 Notice that k k mex us 27, 288 = = 110, while, in the Summers-Heston data set, k k mex us 21,985 = = 59, This would imply a much smaller difference in real interest rates: rmex + δ kus / yus = = = r + δ k / y us mex mex r = 0.05, δ = 0.05 imply r = 0.07 us mex

32 HOW LARGE SHOULD CAPITAL FLOWS BE? Equate returns on capital marginal products α A k δ = αa k δ α 1 α 1 mex mex us us N k + N k = N 27, N 110,577 mex mex us us mex us N = 27,302,000, N = 121,863,000. mex Free capital flows result in k mex = 56,019, k us = 98,027. Mexican capital stock would have to increase by 28,731, which is 175 percent of Mexican GDP, 105 percent of Mexican capital stock. us

33 MODEL Consumers subject to where ρ ρ max t c Tt ( 1 c Nt ) 1 β ε ε / ρ t= t + 0 nt n t ( ) p c p c a w r a T a A Tt Tt + Nt Nt + t+ 1 = t t + 1+ t t + t t at = qt 1kt + bt, k, b given. 0 0 Here t is working-age population and n = pop adult-equivalent population. t t t is

34 Production functions Domestically produced traded good D 1 D ydt = min ztdt / atd, zndt / and, AD k α α Dt Dt Nontraded good Investment good Armington aggregator y z a z a A k α α N 1 N Nt = min TNt / TN, NNt / NN, N Nt Nt i = Gz z γ 1 γ t TIt NIt 1 ζ ζ Tt = µ Dt + ( 1 µ ζ ) t y M x m.

35 Market clearing Domestically produced traded good Composite traded good Nontraded good Investment good Factor markets xdt + xft = ydt ctt + ztit + ztdt + ztnt = ytt cnt + znit + zndt + znnt = ynt ( δ ) k k i t 1 1 = + t t kdt + knt = kt, Dt + Nt = t

36 Balance of payments ( ) m b p x r b t + t+ 1 = Dt Ft + 1+ t t Foreign demand ( 1 τ ) 1 1 xft = D Ft p ζ + Dt Transfer of tariff revenue T = τ m t Dt t

37 Profit maximization Domestically produced traded good αd wt = ( pdt atdptt andpnt)( 1 α D) AD( kdt / Dt) 1 α D ( ) α ( ) ( δ) 1 + r = p a p a p A / k + 1 q / q t Dt TD Tt ND Nt D D Dt Dt t t 1 Nontraded good α N wt = ( pnt atnptt annpnt)( 1 α N) AN ( knt / Nt) 1 α N ( ) α ( ) ( δ) 1 + r = p a p a p A / k + 1 q / q t Nt TN Tt NN Nt N N Nt Nt t t 1

38 Investment good Armington aggregator where ( / ) 1 γ γ ( 1 γ ) ( / ) p = q G z z Tt t NIt TIt p = q G z z Nt t TIt NIt 1 ζ ζ y Tt pdt = ptt µ M x Dt 1 ζ ζ y Tt 1+ τ Dt = ptt ( 1 µ ) M m t 1 ζ 1 p = M p ζ 1 ζ ( 1/ ) µ ( 1 µ ) 1 ζ ( 1 τ ) Tt Dt Dt γ ζ 1 ζ ( 1 ζ ) ζ

39 CAPITAL ADJUSTMENT FRICTIONS i + i Gz z γ 1 γ Dt Nt Tt Nt ( ) ( δ ) ( ) ( δ ) k + 1 φ i / k k + 1 k k + 1 φ i / k k + 1 k Dt Dt Dt Dt Dt Dt Dt Dt Dt Dt φ '( i/ k) > 0, φ ''( i/ k) < 0, φ( δ) = δ, φ '( δ ) = 1 ( ( i / k) 1 ( i / k) η ( 1 ) /, 0 1 ) η φ = δ η δ η < η Adjusting the sector specific capital stock rapidly is costly. Capital in the traded goods sector has a different price, q Dt, than capital in the nontraded goods sector, q Nt. (In simulations η = 0.9.)

40 LABOR ADJUSTMENT FRICTIONS Dt λ Dt λ Nt There is a limit to how fast sector specific labor can adjust. Labor in the traded goods sector receives a different wage, w Dt, than labor in the nontraded goods sector, w Nt. (In simulations λ = 1.03.) Nt 1 1

41 Input-Output Matrix for Mexico 1989 (percent of GDP) traded nontraded C+ G I X total traded nontraded w ( r+ δ ) k w + ( r+δ ) k m τ m total

42 Principal Ingredients in Numerical Experiments Demographic differences Differences in initial real interest rates Financial liberalization Trade liberalization

43 SUDDEN STOP! bt = bt-1 + b, t = T,..., T + N Domestic interest rate is endogenously determined, although interest payments on foreign debt bt are made at international interest rate.

44 Real GDP Y = p y p z p z t Dt Dt Tt TDt Nt NDt p y p z p z + τ m Nt Dt Tt TNt Nt NNt Dt t Real Investment Real capital stock I = p z + p z t Tt TIt Nt NIt 0 0 K = + 1 (1- δ ) K + I t t t Total factor productivity TFP t = K Y t α ( ) 1 t α Dt + Nt

45 Base Case: Trade Balance 4 2 data percent GDP model year

46 Sudden Stop: Trade Balance 4 2 data percent GDP model year

47 Sudden Stop: Real Exchange Rate index (1989=100) model data year

48 Sudden Stop: Real Exchange Rate index (1989=100) RERN 80 RER year

49 Data: Gross Output by Sector 200 index (1988=100) traded nontraded year

50 Sudden Stop: Gross Output by Sector index (1988=100) nontraded traded year