Topic 6: Financial Integration and Interest Rate Parity Part 1: Backround on interest rate parity conditions

Transcription

1 Topic 6: Financial Inegraion and Ineres Rae Pariy Par : Backround on ineres rae pariy condiions In his lecure we sudy some puzzles in inernaional financial markes, regarding he relaionship beween ineres raes and exchange raes.

2 Consider a simple ineremporal model: Asses: M home money B home nominal ineres bearing asses, a rae i B foreign nominal ineres bearing asse, a rae i F forward conrac: purchase one uni of foreign currency nex period in exchange for f unis of home currency (f known in period ) e (spo) exchange rae (home currency per foreign) Household problem M Max E U C, 0 P s.. PY i B e i B e f F M PC B e B M 2

3 FOCS: (lambda for lagrange muliplier on budge consrain.) () Home bonds: E i E e i e (2) Foreign bonds: (3) Forward exchange: E e f 0 Or Ee fe Consumpion (lambda): U P ' c, Now combine various equaions o draw conclusions 3

4 Covered ineres rae pariy (CIP): combine (), (2) and (3): e i i f i i Logic: suppose did no hold: e f or e i i, hen: ) borrow euro in Frankfur a rae i 2) conver euro in spo exchange rae o e dollars 3) receive gross reurn e i dollars a end of year 4) conver back o e i / feuros, and repay loan of +i euros wih guaraneed profie lef over. This is an arbirage opporuniy. Demand for forward conracs would rise, and f would rise, resoring condiion. Empirical evidence suppors his condiion; seems i is how banks se heir forward raes. f 4

5 Someimes see his wrien as an approximaion in logs: e f i i ln e ln f ln i ln i i i Terminology: Forward premium: lnf -ln e 5

6 Uncovered ineres rae pariy (UIP): use (2) and (): e i i E e U' P c, E U' P c, Can be rewrien: e i i i ', ', ' U c U c U c, e EeE cov e, E i P P P E e RP where U' c, U' c, RP cov e, E P P - Noe ha his is no a riskless arbirage opporuniy; risk premium is a wedge beween reurns. - Inerpre a posiive risk premium: foreign currency has high value (e high) in bad saes (U high); foreign currency asses good hedge and can offer lower i. 6

7 7 Marke efficiency condiion: rewrie (3):,, ' ' c c P U E P U e E f Can be rewrien as for UIP above c c RP e E P U E P U e e E f,, ' ', cov Quesion: is he forward rae a good predicor of he expeced fuure spo exchange rae?

8 Par 2. Empirical lieraure Early Tess of Ineres pariy and marke efficiency Framework: The earlies ess of forward efficiency regressed he fuure spo rae on he forward rae in logs: e a a 0 f Tesed if a 0 =0 and a =. Null hypohesis is ha he forward rae provides an unbiased forecas of he fuure spo exchange rae. Noe he equaion esed here replaces he expeced value of e + in he original condiion wih he acual fuure value, due o lack of daa on expecaions. 8

9 Anoher problem is nonsaionariy of exchange rae. Mos researchers subsequenly have esed he equaion wih e subraced on each side: e e a a f e 0 Relaed es: Since covered ineres pariy holds well, replace he righ erm wih he ineres rae differenial. We hen have a es of uncovered ineres pariy: e e a a i i 0 If he risk premium assumed o be consan, i would appear in he a 0 erm, making i deviae from he hypohesized value of zero, bu no affec he a erm. So he researchers focused on hypohesis ha a =. 9

10 Resuls: Froo (990 JEPerspecives:) Summarize he lieraure of 75 papers on he subjec. The average esimae of a over 75 papers is -0.88, only a few find a >0, and none find a >. Conclusions: In general, papers rejec he hypohesis ha a =, and mos find ha i is acually negaive. This means ha a counry s currency is expeced o appreciae in fuure periods when is ineres rae is high. Raher han offseing a high ineres rae, fuure appreciaion makes i even more profiable o buy a currency. How can his be consisen wih marke equilibrium? How can we explain his finding? 0

11 Time-varying risk premia - If he risk premium varies over ime, we could wrie he equaion from before: e e a0 a f e RP - Where RP and e ogeher are he error erm in he regression. So he error erm includes a componen ha may be correlaed wih regressors, biasing esimae of a. - To solve his problem, some researchers have used ARCH models of he risk premium.(domowiz-hakkio 995 JIE). - They propose a separae regression for he risk premium iself as a funcion of he ineres rae differenial. - Bu resuls were no encouraging. I appears ha he risk premium no a simple funcion of ineres rae differenial.

12 Eichenbaum and Evans (QJE 995): Moivaion - This paper documens he failure of UIP condiional on moneary policy shocks. Shocks are idenified here in a vecor auoregression (VAR). - I also provides evidence regarding he disagreemen beween Mussa and Sockman regarding wheher moneary or real shocks drove exchange raes. 2

13 Mehodology: - Use a simple VAR. Included in he vecor of variables is a variable represening policy. - Apply a Cholesky decomposiion, in which ordering of variables maers: variables, X, preceding i are observed conemporaneously. - Define policy shock as he innovaion o he policy variable (nonborrowed reserve raio) ha is orhogonal o he conemporaneous values of he observed variables. 3

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19 Daa: - Daa on bilaeral exchange raes of five counries wih he US dollar. Monhly daa, saring in Five variables in firs sysem esimaed: ) US-IP: indusrial producion (oupu) 2) US-CPI: price level 3) NBR/TR, non-borrowed reserve raio o oal reserves, measures degree of liquidiy 4) Gap in 3-mo T-bils: foreign-home, 5) exchange rae (firs nominal and hen real) - Measure moneary policy acion as a change in nonborrowed reserves no explained as a response o changes in conemporaneous price or oupu. 9

20 Resuls: Show figure : impulse responses o NBR/TR shock ) A U.S. moneary conracion leads o a rise in iniial period in U.S. ineres rae rel o foreign (fall in R for R US ). 2) Appreciaes real and nominal exchange raes for U.S. 3) Exchange rae effec reaches maximal afer 2-3 years. This delayed overshooing is inconsisen wih UIP; reflecs wrong sign in UIP ess above. (Discuss Overshooing) 4) Plo also he excess reurn on holding dollar asses: reurn from dollar appreciaion plus higher ineres rae. 5) Tables a and b: Rejec ha he maximal impac happens in iniial period. 6) Variance decomp: moneary shocks accoun for 8-43% of exchange rae volailiy. 20

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22 Real exchange rae: (Table a) 22

23 nominal exchange rae (able b) 23

24 Overshooing - Suppose U.S. moneary conracion raises US ineres rae relaive o foreign rae. - According o UIP, if people are sill willing o hold foreign asses despie he lower ineres rae, hey mus expec o be compensaed by appreciaion in value of he foreign currency over ime ( e $/ rising over ime). - Now consider role of PPP, which seems o hold in long run: A fall in U.S. money supply should make he dollar more valuable ( e $/ lower) in fuure han iniially. - If we pu hese wo conclusions ogeher, we ge he following ype of pah for he exchange rae following a U.S. moneary conracion: 24

25 e e 3 e 2 ime - The exchange rae falls on impac, bu i overshoos is long run level. This is so i can gradually move upward in subsequen periods, and sill end up lower han iniially. - This is one characerizaion of he Overshooing heory of Dornbusch. 25

26 Conclusions: - Rejec UIP; insead see delayed overshooing - Moneary shocks are imporan, bu hey explain \less han half of exchange rae flucuaions Criiques: Wha do you hink abou he idenificaion scheme for idenifying moneary policy shocks? Quesion: do you see a way o make money from he finding of his paper? 26

27 Par 3: Some heoreical explanaions: 3a. Benigno e. al (202 NBER Macro Annual) Main idea: Wan o explain why a fall in i predics a currency depreciaion, raher han appreciaion as required by ineres rae pariy. Mus be a large fall in RP. i i E e e RP 27

28 28 A simple way o view his is in erms of heory presened earlier in lecure. Recall a general expression for he risk premium:,, ' ' c c P U E P U e E RP Recall also ha under a model wih perfec risk sharing, we have seen: P U e P U c ' c ', So we have: P C E P C E RP

29 Rewrie his using: log EX Elog X varlog X Assume ha he shocks are log normally disribued, hen: (lower case leers represen logs, overbars are means) log RP p p c c 2 2 var var 2 p var c 2 cov p, c 2 2 p var c 2 cov p, c Under symmery and perfec risk sharing: RP p p 2 cp cp 2 where: ( p ), and ( c p ) p var 2 cp cov, 29

30 Inerpreaion: - The firs brackeed erm above is a Jensen inequaliy erm. - The second brackeed erm represens how a home nominal asse acs as a hedge agains consumpion risk. - If consumpion and he price posiively correlaed, home nominal asses pay off bes in real erms (low price) in bad saes of he world (low consumpion) - So home asses are a hedge and risk premium is low. - Says ha a rise in he volailiy of money supply can lower he risk premium. 30

31 Inuiion: - In a sicky price model, a money supply rise only parly ranslaes ino a rise in price. - To he degree ha price doesn rise fully, here is a rise in demand which raises producion and consumpion. - So a rise in moneary volailiy raises he correlaion of price and consumpion. - This makes home asses more aracive as a hedge, and lowers he risk premium. - Suggess ha we sudy he effec of shocks o moneary policy volailiy insead of shocks o money supply. 3

32 Empirical: esimae a vecor auo-regression based on Eichenbaum and Evans (995) sudied above, bu include measures of volailiy o moneary policy shocks (as well as shocks o inflaion arge and GDP growh rae). Measure policy shocks: change in fuures for forecased reasury bill rae. Measure sandard deviaion of hese. Daa in VAR: ) moneary of moneary policy shocks 2) us ineres rae; 3) foreign ineres rae 4) real exchange rae 5) aggregae price index 6) aggregae oupu index 32

33 Repor response for: ) US ineres rae (FFR) 2) slope of erm premium (i-long erm i-shor erm) 3) real exchange rae 4) failure in UIP: i - i + E (s + -s ) Resuls: ) show volailiy in moneary policy (ie in crisis) 2) replicae EE(995) resul for shocks o moneary policy: rise in money supply leads o delayed overshooing depreciaion in dollar 3) show ha a rise in variance of moneary policy shocks leads o rise in UIP deviaion, excess reurn on foreign asses (dollar becomes more aracive as a hedge). 33

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35 Responses o U.S. moneary policy conracion 35

36 Responses o rise in U.S. moneary policy volailiy 36

37 3b) Benigno, Beigno and Nisico (202) Suden presenaion 37

38 Par 4 Engel (AER 206): Discusses an addiional sylized fac: High real ineres rae counries end o have currencies ha are srong in real erms. While his fac is known in he lieraure, Engel claims i conflics wih he usual explanaion of he UIP puzzle in using a ime-varying risk premium: The high ineres rae counry ends o have high expeced reurns on is shor erm asse because i has a high currency risk premium. Puzzle as summarized by Chris Telmer: Righ now he Brazilian Real (BRL) is overvalued in real erms. Brazilian real ineres raes are also high. The laer suggess more BRL appreciaion. Bu we know ha evenually PPP mus kick in, wih he BRL depreciaing. 38

39 This new fac is differen from he UIP puzzle above in ha i relaes o: o Real raher han nominal ineres and exchange rae o Level of exchange rae raher han change Bu we can show he wo condiions are linked: Firs conver nominal ineres rae and exchange raes ino real counerpars by adjusing for inflaion: UIP: i i Ee e Subrac E E Ep p Ep p sides from boh 39

40 i E i E E e p p e p p i E i E E e p p e p p So r r Eq q Where r is he real ineres rae and q is he real exchange rae. Second, rearrange and ierae forward: q r r Eq r r r r Eq R lim Eq j j 40

41 represens prospecive real Where R E r i r i i0 ineres differenials Now assume also long run PPP : lim j Eq j Then, q q R Noe his predics ha if r R hen his should imply q, ha is, a real appreciaion. For reference, we can also define a measure of he excess reurn on he foreign deposi inclusive of currency appreciaion, ha is, he deviaion from UIP: i e e i q 4

42 Empirical: ) confirm failure of UIP in real erms q q r r Recall equaion: Surprisingly, bea is >0 and ofen >. 42

43 Empirical: 2) levels equaion: q q E r i r i So bea should be >0. Esimaes suppor his. i0 43

44 Empirical: 3) cumulaive excess reurns regression So bea should be <0. Esimaes suppor his. 44

45 Explain why conradicory 45

46 i i e e 46

47 Conclude: Models ha explain UIP failure in erms of a rise in he currency risk premium when a counry s ineres rae is high for shor horizons. Canno explain why he implied risk premium swiches sign a longer horizons. This poses a new challenge o heoreical models rying o explain failure in UIP. 47