Chapter 3: Dynamic Macroeconomic Approaches to the Balance of Payments and the Exchange Rate

Transcription

1 Advanced International Macroeconomics and Finance Chapter 3: Dynamic Macroeconomic Approaches to the Balance of Payments and the Exchange Rate Miguel Leon-Ledesma and Alexander Mihailov

2 Plan of talk introduction 1. The rational expectations revolution 2. Flexible-price stock approach under perfect foresight: the monetary model 1. the monetary approach to BoP (peg) 2. the monetary approach to NER (float) the monetary model 3. Sticky-price models under perfect foresight: Dornbusch (1976) motivation for the model key elements and assumptions model equilibrium and transition paths key result: exchange-rate overshooting 4. Empirics of the NER and the random walk hypothesis wrap-up 2

3 Aims and learning outcomes aims to distinguish, summarise and interpret the key macroeconomic approaches to BoP and NER dynamics under perfect foresight to present and discuss the mechanics and implications of two of the most influential models in international macroeconomics learning outcomes contrast and compare flow and stock-flow BoP/NER models derive and interpret the automatic (Humean) price-specie-flow mechanism of BoP adjustment the monetary model under peg vs. float the exchange rate as an asset price the fundamentals vs. the bubbles solution for the exchange rate the Dornbusch model equilibrium and transition paths in continuous time and the effects of monetary expansion 3

4 Expectations and economic behaviour behaviour of economic agents is based on expectations concerning future levels or evolution of relevant variables or processes this fact differentiates social from natural sciences as acknowledged by Evans and Honkapohja (2001): Modern economic theory recognises that the central difference between economics and natural sciences lies in the forward-looking decisions made by economic agents. (p. 5) expectations influence the time path of the macroeconomy and vice versa so this profound two-sided relationship is a challenge to modellers economic theories attributing a major role to expectations can be first seen in Thornton (1802) and Cheysson (1887) 4

5 Basic analytical taxonomy of modelling expectations in economics perfect foresight: implicit in classical economics, explicit in early RE models endowing agents with superhuman powers: Marshall static (naïve, no-change) expectations: Cagan (1956) adaptive expectations: p e e t p t 1 Muth (1961) rational expectations as an equilibrium concept the actual stochastic process that a variable follows depends on the forecast rules used by economic agents the optimal choice of the forecast rule by each agent is, in turn, conditional on the choices of others in effect, RE equilibrium imposes the consistency condition that each agent's choice is a best response to the choices by others e e p t1 Ep t1 t or p t1 E t p t1 p e t p t p e t p t 1 e p t 1 p t 1 5

6 The rational expectations revolution Muth (1961) on rational expectations Rational Expectations and the Theory of Price Movements, Econometrica 29 (3, July) introduces (to the economics profession) the concept of rational expectations (RE) and the (minimum) necessary mathematics to implement it RE imply that agents forecast in a way that is internally consistent with the model generating the variable(s) whose future behaviour they try to predict agents are rational in the sense that they incorporate all available relevant information (in their information set) and do not make systematic errors in their predictions the rational expectations revolution (in economics) 6

7 Classical price-specie-flow mechanism classical theory of BoP (that is, CA or TB) adjustment builds on Hume (1752): automatic price-specie-flow mechanism if BoP (CA or TB) surplus, TB > 0 inflow of specie (= gold = money, under the gold standard) QTM valid (under flex-price full-employment): M t V= P t Y => price level relative price of exports from surplus country => demand for exports by nonresidents relative price of imports to surplus country => demand for imports by residents initial BoP (trade) surplus tends to => equilibrium restored: TB = 0 if BoP (CA or TB) deficit, TB < 0: inverse causation applies origins of the monetary approach to BoP can be traced back here 7

8 Monetary approach: assumptions 1. LOP in goods market (individual level) => PPP (aggregate level) 2. UIP in asset (bond) market 3. flexible prices: not fixed, as in the flow approaches to BoP we studied earlier 4. focus on conditions for stock equilibrium in money market 5. stable money demand function 6. production at the level of full employment => real income fixed 7. SOE 8

9 Monetary approach to BoP: set-up 1. (credible) peg => money supply is endogenous(ly determined) m t s 1 d t ir t EIR t EMB t 2. money demand arises from transactions motive m t d p t y t t t t iid 0, 2 3. PPP: goods market equilibrium p t s p t 4. UIP with static expectations (since peg): capital market equilibrium t t 5. money market equilibrium EMS t EMB t MS t MB t DC t IR t E t S t1 S t S const for any t (hence ln E ts t1 S t ln 1 0) 1 d t ir t p t y t t t s p t t 9

10 Monetary approach to BoP: key result ir t s p t y t t t 1 d t m t d it is clear from key equation above that if SOE experiences any of positive income growth declining interest rates rising prices demand for nominal money balances will grow if it is not satisfied by an accommodating increase of domestic credit, the public will obtain the additional money it desires to hold by selling goods and/or assets abroad, thus running a(n overall) BoP surplus, i.e. an increase in international reserves (they get paid in FC which they exchange for HC) if it is more than satisfied by central bank domestic credit expansion that exceeds it, the public will eliminate the excess supply of money (it does not wish to hold) by spending or investing it abroad and thus running a(n overall) BoP deficit, i.e. a decrease in international reserves (they pay FC) hence, money supply in the monetary model under peg is endogenous, that is, determined by the above equation 10

11 Flexible-price models under perfect foresight Cagan (1956) on hyperinflation The Monetary Dynamics of Hyperinflation, in Friedman, Milton (ed.), Studies in the Quantity Theory of Money, Chicago University Press empirical closed-economy model to study hyperinflation in 7 countries argued that during a hyperinflation expected inflation swamps all other influences on money demand => specified the MDF in a simple way real money balances depend only on expected inflation and not on real income and interest rates as in the conventional (IS-LM) MDF adaptive forecasting: expected future inflation depends on lagged inflation the (flexible NER) monetary model Cagan model: extended to open economy with the conventional MDF assuming perfect foresight (as an extreme form of rational expectations) and underpinned with some basic (but ad-hoc) macro-theory to read more: Obstfeld and Rogoff (1996), chapter 8 11

12 Monetary approach to NER: set-up 1. float => also called the monetary model (of NER) => money supply exogenous(ly chosen), to equilibrate money markets in H and F: m t p t supply of real balances in H y t t demand for real balances in H 2. PPP: goods market equilibrium 3. usual UIP: capital market equilibrium 4. definition of NER fundamentals 5. substituting (in PPP) and solving m t p t supply of real balances in F s t p t p t y t t demand for real balances in F t t E t s t1 s t f t m t m t y t y t 1 s t 1 f t E 1 t s t1 1 12

13 Monetary approach to NER: key result general forward-looking (RE) solution no-bubbles solution (TVC) 0 1 rational bubbles b t 1 b 1 t 1 t k s t t iid N0, 2 s t s t b t interpretation: monetary model is a useful first approximation in providing intuition about NER dynamics (asset price); RER? k 1 j E t f tj 1 k1 E t s tk1 1 lim 1 k E t s tk 0 s t 1 lim 1 k E t s tk lim 1 k E t s tk k k 0 j0 k 1 j E t f tj j0 lim 1 k E t b tk b t 0 k b t 13

14 Sticky-price models under perfect foresight Dornbusch (1976): perhaps the best known OEM example Expectations and Exchange Rate Dynamics, Journal of Political Economy 84 (December) extension of the (Keynesian) static Mundell-Fleming model we studied in Chapter 2 to a dynamic setting under perfect foresight very influential model => Mundell-Fleming-Dornbusch tradition/paradigm among academic circles involved with open-economy macro among policy makers at national and international institutions summary of technical approach ad-hoc (not optimising!) model, assuming explicit functional forms (not deriving them from microfoundations!) written in continuous time (but can be translated to a discrete version: see Obstfeld-Rogoff textbook, section 9.2) all variables (except interest rates) in logarithms: z ln Z for any Z 14

15 Dornbusch (1976): motivation for model stylised facts to explain observed large exchange rate volatility after the demise of Bretton-Woods much higher than that of underlying fundamentals needed to be consistent with rational expectations formation effects of a monetary expansion in the short run, an immediate domestic currency depreciation => monetary expansion seems to account for fluctuations in the exchange rate and ToT during the adjustment process, rising prices may be accompanied by an appreciation => the trend behaviour of exchange rates and the cyclical behaviour of exchange rates and prices stand potentially in contrast during the adjustment process, there is also a direct effect of the exchange rate on domestic inflation => the exchange rate as a critical channel for the transmission of monetary policy to AD for domestic output differential speed of adjustment of asset vs goods markets which was becoming an interesting novel topic for research 15

16 Dornbusch (1976): general assumptions 1. SOE => the world (nominal) interest rate is given in the world asset market ι* the world price of SOE s imports is given in the world goods market p* 2. domestic output is an imperfect substitute for imports => demand for H (SOE) and F (RoW) output will be affected by their relative price, s + p* p in logs (from PPP-based RER, SP*/P, in levels) 3. (NB!) differential adjustment speed of markets goods markets adjust slow relative to asset (including exchange rate) markets, which adjust instantaneously 4. (NB!) consistent expectations (formation) formation of (rational) expectations is consistent with perfect foresight, i.e., the strongest, extreme form of RE 16

17 Dornbusch (1976): assumptions on capital mobility and NER expectations formation 1. perfect capital mobility assets denominated in domestic and foreign currency are perfect substitutes given a proper premium/discount to offset anticipated NER changes equivalently, this is (a form of) UIP: x 2. exchange-rate expectations formation expected depreciation, x > 0, of current spot NER, s, is assumed proportional (via a coefficient θ) to its discrepancy w.r.t. long-run NER, s const (for now taken as known, but later an expression which determines it will be developed): x s s Dornbusch (1976) makes the point that while expectations formation, as assumed, may appear ad hoc it will be consistent with perfect foresight (to be shown further down) 17

18 Dornbusch (1976): assumptions on money market structure and equilibrium 1. conventional money demand function a monetary model 2. money supply /stock/ exogenous(ly given, by SOE s CnBk) 3. (NB!) real income (or output, or AS) is fixed at its fullemployment level, y (initially variable output later) 4. money market equilibrium: m s m d m => money demand can be written as m p y 1 m p y => relationship linking spot and LR NER with price level p m y s s 5. stationary money supply process: long-run equilibrium would imply s s and hence, through UIP => an expression for the long-run equilibrium price level p m y 18

19 Dornbusch (1976): key equation on the relationship b/n the NER and the price level s s 1 p p solving it for p determines asset market equilibrium, to be graphically represented later as the QQ schedule: p p s s p s s interpretation of key equation: for given LR values s and p, the spot NER s can be determined as a f-n of the current price level p given the price level p, we have a domestic interest rate from MDF and an interest rate differential from UIP determined endogenously given also the LR NER s, from expected depreciation eq. there is a unique level of the spot NER s such that expected depreciation x matches the interest differential so p => (from MDF) => an incipient capital inflow => (from UIP and expected depreciation eq.) s (appreciation) to the point where the anticipated depreciation x offsets exactly the increase in 19

20 Dornbusch (1976): assumptions on goods market structure and equilibrium 1. the foreign price level normalised p ln P ln 1 0 so that the relative price of domestic goods s p p becomes 2. a special, ad-hoc demand f-n for domestic output ln D u s p y 3. a special, ad-hoc f-n for the rate of increase of the price of domestic goods: proportional to an excess demand measure p ln D ln D Y ln Y y s p u s p 1y 4. with the relevant LR assumptions p 0 and and further substituting for above from MDF, solving for s yields the LR equilibrium NER: s p 1 1 y u 20

21 Dornbusch (1976): price level and NER dynamics now the earlier price adjustment eq. can be simplified using the LR NER to substitute in it as well as UIP and expected depreciation eq. to express x s s => p p p p p recall that a 1 st -order linear homogeneous differential eq. of some f-n dz of time z(t), cz 0, has a (definite) s-n of the form dt z solving, by analogy, the price eq. above yields substituting in key NER eq.: interpretation the spot NER will converge to its LR level NER will appreciate if prices are initially below their LR level, and conversely zt z0e ct pt p p 0 p e t st s 1 p 0 p e t s s 0 s e t 21

22 Dornbusch (1976): graphical analysis of model equilibrium and transition paths F1 next the QQ schedule describes asset (here also money) market equilibrium and has a negative slope (as can be checked earlier), so it must intersect the line the p 0 schedule shows all combinations of price levels and exchange rates for which the goods market and the money market clear: can be derived from the p eq. with p 0 and the MDF: p u 0 p s m p y u s p 1y, frommdf m 1 solving for p, the slope is 0 1, hence p 0 must intersect the line too => model equilibrium => model transition paths (F1 next) y 22

23 F1 - Dornbusch model: long-run equilibrium and transition paths Source: Authors, based on Dornbusch's (1976) original Figure 1, p p 45 0 line p C p LR p B C A B p& = 0 QQ 0 s C s LR s B s 23

24 Dornbusch (1976): consistent expectations if the expectations formation process in expected depreciation eq., driven by θ, must correctly predict in compliance with perfect foresight the actual path of exchange rates, determined by ν, it must be true that hence, the consistent expectations coefficient,, is obtained as the (positive and stable) solution to the quadratic equation implied by the above expression:,,, 2 gives the rate at which Dornbusch (1976) economy will converge to longrun equilibrium along the perfect foresight path: of interest because this assumption is not arbitrary does not involve persistent prediction errors for any given price adjustment parameter π, convergence will be faster the lower the interest-rate response of money demand, λ and the higher the interest-rate response of goods demand, σ and the price elasticity of demand for domestic output, δ

25 Dornbusch (1976): graphical and analytical account of NER overshooting F2 next a two-stage adjustment which implies exchange rate overshooting: a phenomenon whereby the spot exchange rate temporarily exceeds its longrun value, illustrated by the short-run equilibrium at point B in Figure 2 to better understand the key model result, let us also derive it analytically totally differentiate MDF, noting that p is instantaneously fixed and y is always fixed d dm 1 0 in the LR, an in money causes an equiproportionate in prices and the exchange rate: d s d p dm totally differentiate UIP eq. while holding constant d dm ds and use d s dm in expected depreciation eq. to obtain d s use this to eliminate d in liquidity effect eq. above and solve for ds ds 1 1 dm ds d s d s 25

26 F2 - Dornbusch model: Exchange Rate Overshooting Source: Authors, based on Dornbusch's (1976) original Figure 2, p p p LR p LR A B 45 0 line p&'= 0 2 p& = 0 B 1 Q Q QQ 0 s LR s LR s SR overshooting s 26

27 Meese and Rogoff (1983): the exchange rate disconnect puzzle earlier models imply a semi-reduced form specification s a 0 a 1 m m a 2 y y a 3 a 4 e e a 5 tb a 6 tb u ME they estimated the following VAR specification s t a 1 s t 1 a 2 s t 2...a n s t n B 1 X t 1 B 2 X t 2...B n X t n u t criteria to judge and compare forecast performance N k 1 Ftqk Atqk q0 N k MAE N k 1 Ftqk Atqk q0 N k RMSE N k 1 Ftqk Atqk2 q0 N k 27

28 T1 The Meese-Rogoff results Source: Meese and Rogoff (1983), Table 1, p. 13, slightly shortened by the authors Exchange rate Random Forward Univariate VAR Monetary Dornbusch Complete Model: walk rate AR model model eq. (41) Horizon (months) $/DM $/yen $/ trade n.a weighted n.a $ NEER

29 Explaining the Meese-Rogoff results reaction to the Meese-Rogoff results has become a subdiscipline within international macroeconomics in itself exchange rate forecasting is not only a potentially useful tool for investors seeking to gain returns from currency trading but a way of testing the validity of fundamentals-based models of exchange rate determination the way Meese and Rogoff obtain forecasts of exchange rates using fundamentals is not a proper out-of-sample forecast as they used the actual values of fundamentals instead of their forecasts this led to the appearance of true out-of-sample forecast exercises, of which Mark (1995) is perhaps the best exponent he presented evidence of long-horizon predictability based on ideas coming from the theory of integration and cointegration 29

30 T2 Long-horizon forecasts Source: Authors own calculations of Theil s U=RMSE f /RMSE RW. Money is M1 and output is GDP. Data from IMF s IFS database for 1974:1-2001:3. Country Canada Japan UK Horizon

31 Engel and West (2005): the exchange rate as a near-random walk Engel and West (2005) take a different route claim that exchange rates and fundamentals are linked in a way still broadly consistent with asset-pricing exchange rate models the exchange rate should be good predictor of future evolution of fundamentals as they reflect market participants expectations about the future stream of fundamentals to test this hypothesis they present Granger-causality tests b/n fundamentals and exchange rates for the G7 countries and for different measures of fundamentals d Δf t i Δf t i i Δs t i t i1 d i1 31

32 Exchange rate empirics: where do we stand? several facts accumulating since Meese and Rogoff 1. exchange rate models appear to beat the random walk at forecast horizons beyond one year 2. in-sample fit of exchange rate models is satisfactory 3. in periods of current and/or expected high inflation (especially for emerging markets) exchange rate models have proven extremely useful 4. exchange rates seem to contain significant information about the future evolution of fundamentals (Rossi, 2007) 5. fundamentals are good predictors of exchange rates for so-called commodity currencies pertaining to the Australian, Canadian, and New Zealand dollars (Chen and Rogoff, 2003) 6. ample evidence that news about macroeconomic fundamentals affect exchange rates in a manner that is compatible with theoretical predictions 32

33 Concluding wrap-up What have we learnt? distinguish and discuss rational expectations and perfect foresight flexible-price vs. sticky-price models of exchange rate dynamics derive and interpret the monetary approach under both peg and float derive and understand Dornbusch (1976) model equilibrium and transition paths effects of monetary expansion when and why NER overshooting occurs when and why NER overshooting needs not necessarily occur analyse the basic set-up of ad-hoc dynamic monetary OEMs Where we go next to the microfoundations of BoP and exchange rate models in particular to modelling the dynamics of the current account within the intertemporal approach to it 33