Combining sign and long run parametric restrictions in a weak instrument case: Monetary policy and exchange rates. This Version: June 13, 2017.

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1 Combining sign and long run parameric resricions in a weak insrumen case: Moneary policy and exchange raes. This Version: June 3, 27. Absrac In a SVAR for four small open economies, sign resricions ogeher wih parameric resricions are used o separae he shocks using he insrumenal variable (IV) mehod of Ouliaris and Pagan (26). The long run resricion we uilise is ha he moneary policy shock has a zero long run effec on he real exchange rae. Because here is a weak insrumen problem associaed wih he long run resricion, he IV mehod breaks down. This paper develops a procedure in conjuncion wih heir signs mehod which circumvens his problem. When his procedure is implemened, we find ha none of he acceped responses for Canada and very few (less han 4 percen) for Ausralia and New Zealand show an exchange rae puzzle, while for he Unied Kingdom i is subsanially more (2 percen). In Ausralia, Canada and New Zealand, here is a sysemaic moneary policy response o a real exchange rae shock bu no in he Unied Kingdom. Key Words: sign resricions, long run parameric resricions, weak insrumens, long run and conemporaneous impac marices, exchange rae puzzles, moneary policy reacion JEL Classificaion: C32, C36, C5, F4 Lance A. Fisher Deparmen of Economics, Macquarie Universiy, Sydney, Ausralia, 29. Tel: lance.fisher@mq.edu.au Corresponding auhor Hyeon seung Huh School of Economics Yonsei Universiy 5 Yonsei ro, Seodaemun gu, Seoul, Republic of Korea, Tel: hshuh@yonsei.ac.kr

2 . Inroducion Combining sign and long run parameric resricions in a weak insrumen case: Moneary policy and exchange raes. In a recen conribuion, Ouliaris and Pagan (26) show how o implemen sign and parameric resricions in a srucural equaion sysem. The complee sysem of equaions can be esimaed by maximum likelihood mehods or by insrumenal variable (IV) mehods, which may be easier o use in some sofware packages. In he case of a long run parameric resricion, he IV approach may break down due o he problem of a weak insrumen, which occurs when he correlaion beween he variable and is insrumen is very low so ha he variable s coefficien is imprecisely esimaed. The consequence is ha he long run parameric resricion may no be eviden in he acceped responses from he esimaed model, even hough he long run resricion is par of he srucural model by design. In his paper, we firs show ha his occurs in a SVAR for four small open economies: Ausralia, Canada, New Zealand and he Unied Kingdom. The moneary policy shock is idenified by boh sign resricions and a zero long run parameric resricion. The parameric resricion is ha he moneary policy shock has a zero long run effec on he real exchange rae. This resricion is buil ino he specificaion of he SVAR and shows up in he srucural equaion for he real exchange rae where he conemporaneous change (and no he conemporaneous level) of he ineres rae appears as a righ hand side variable. The insrumen for he conemporaneous change in he ineres rae is he lagged level of he ineres rae. This insrumen is weak because he ineres rae is a highly persisen variable so ha is lagged level has low correlaion wih is firs difference. As a consequence, a large number of he exchange rae responses o he moneary policy shock in he sign resricions mehodology do no converge o zero as required by he long run parameric resricion so he IV approach breaks down. This paper develops an alernaive mehod which avoids he weak insrumen problem. In his mehod, he srucural equaion for he real exchange rae has he level of he conemporaneous ineres rae as a righ hand side variable and an esimae of is coefficien is derived from an expression ha enforces he long run zero resricion. This expression is obained from he relaionship beween he long run impac marices of he srucural and reduced form shocks and involves he conemporaneous srucural impac marix in he Ouliaris and Pagan sign resricions framework. An esimae for his ineres rae coefficien is obained from he expression on each draw in sign resricions. Using his mehod, we find ha he response of he real exchange rae o 2

3 he moneary policy shock converges o zero on each draw, as required by he long run resricion. We repor he resuls from his esimaed SVAR as i circumvens he weak insrumen problem. The SVAR consiss of he five variables ha were uilised by Bjørnland (29) o invesigae he relaionship beween moneary policy and he real exchange rae in several small economies. The srucural shocks in Bjørnland s model were idenified by recursive zero resricions on heir conemporaneous impacs and by he resricion ha he moneary policy shock has a zero long run effec on he real exchange rae. In Bjørnland s model, he imposiion of he long run resricion means ha i is no necessary o resric he conemporaneous response of he exchange rae o a moneary policy shock nor he conemporaneous response of he ineres rae o an exchange rae shock. Tha is he case in our model where i is no necessary o sign resric hese responses and ha is he advanage of uilising he long run resricion. The advanage of uilising sign resricions is ha a range of response oucomes can be esablished from he ses of acceped responses. Because each acceped response o a shock is equally valid under sign resricions, i is he range of acceped responses o he shock which is of ineres. Full parameric idenificaion of he shocks as in Bjørnland s model, produces a single se of impulse response funcions. The main empirical findings of he paper are as follows. Firs, in response o a moneary policy shock which raises he ineres rae, all of he acceped responses for Canada and nearly all for Ausralia and New Zealand show an impac appreciaion. Very few of he responses for Ausralia and New Zealand (less han 3 and 4 percen, respecively), and none for Canada, show an exchange rae puzzle, which is said o occur if here is a depreciaion on impac (e.g. Eichenbaum and Evans (995), Kim and Roubini (2), Scholl and Uhlig (28)). For he Unied Kingdom, however, 2 percen of he acceped responses show an exchange rae puzzle. Second, in response o an exchange rae shock ha depreciaes he currency, all of he acceped responses for Canada and New Zealand, and 94 percen of hem for Ausralia, show a rise in he ineres rae on impac while for he Unied Kingdom, one fifh show a fall in he ineres rae. The moneary auhoriy in Ausralia, Canada and New Zealand appears o respond sysemaically o an exchange rae shock bu ha does no appear o be he case for he Unied Kingdom where one fifh of he impac responses have he ineres rae moving in he couner direcion. The paper has he following srucure. Secion 2 describes he srucural model and how he zero long run resricion is imposed on i. Secion 3 applies he Ouliaris and Pagan (26) sign resricions mehod o he SVAR and describes he IV esimaion of he model on each draw. Secion 4 presens he sign resricions ha are applied o he impulse responses. Secion 5 shows ha here is a weak insrumen problem in he SVARs. Secion 6 develops he procedure which is used o circumven he 3

4 weak insrumen problem in he framework of he sign resricion mehodology of Ouliaris and Pagan (26). This procedure is used o generae he resuls which are repored in Secion 7. Lasly, Secion 8 concludes. 2. The srucural model Following Bjørnland (29), he variables ha ener he srucural model are a counry s log real GDP ( y ), inflaion ( ), he ineres rae ( i ), he rade weighed foreign ineres rae * ( ), i and he firs difference of he log of he rade weighed real exchange rae ( q ). Inflaion is he change in he consumer price index from he same quarer of he previous year, measured as percen per annum. The domesic ineres rae is he 3 monh rae in percen per annum and he foreign ineres rae is a rade weighed average of he 3 monh raes for he counry s major rading parners, in percen per annum. The real exchange rae is defined as he number of domesic goods per uni of he foreign good so ha a decrease in is value represens a real appreciaion of he domesic counry s real exchange rae. The log of he real exchange rae is reaed as he only I() variable in he sysem and hus appears in firs difference form. We follow Bjørnland, whose SVAR reflecs he model se up of Svensson (997), and rea he log of real GDP as saionary abou a deerminisic ime rend. Daa on he five variables is aken from Fisher and Huh (26) for four small open economies; Ausralia, Canada, New Zealand and he Unied Kingdom. The daa is quarerly for he period 994:Q o 24:Q. The foreign ineres rae shock (denoed FI) is idenified under four conemporaneous zero resricions. The oher orhogonal shocks in he srucural model are obained by imposing a longrun parameric resricion ogeher wih sign resricions o separae he shocks as eiher an aggregae supply (AS), an aggregae demand (AD), a moneary policy (MP) or a real exchange rae (RX) shock. The parameric resricion is ha he moneary policy shock has a zero long run effec on he real exchange rae. We wrie he srucural equaions wih one lag (i.e. for a SVAR()) and wih no deerminisic erms, alhough in he acual esimaion, each equaion has wo lags, a consan, a ime rend following Bjørnland, and, for one counry, a dummy variable; generalisaion of he discussion below o his case is sraighforward. The srucural model is: i a y a a i a q a i a y a a i a q () * * y a i a a i a q a i a y a a i a q (2) * * a i a y a i a q a i a y a a i a q (3) * *

5 i a i a y a a q a i a y a a i a q (4) * * q a i a y a a i a i a y a a i a q (5) * * We rea he foreign ineres rae as exogenous in he equaions for GDP, inflaion, he ineres rae and he real exchange rae by imposing he exclusion resricions a5 on Eq. () which becomes: a2, a3, a4 and i a i a y a a i a q (6) * * These resricions isolae as he foreign ineres rae shock and can be shown o imply ha he oher shocks, i.e. he AS, AD, MP and RX shocks, do no have a conemporaneous effec on he foreign ineres rae (see Fn. 4 below). Following Fisher, Huh and Pagan (26), he long run zero parameric resricion is imposed by using he mehod of Shapiro and Wason (988) of replacing Eq. (5) wih: q a i a y a a i a i a y a a q (7) * * This follows because he long run resricion is a 54 a54, and imposing i on Eq. (5) produces Eq. (7), where he conemporaneous change in he ineres rae and no is level now appears as a righhand side variable. The orhogonal shock in Eq. (4),, 4 will have a zero long run effec on he real exchange rae. I is he only candidae for he moneary policy shock and i is subjec o sign resricions as are he oher shocks, apar from he foreign ineres rae shock which is isolaed by he conemporaneous resricions alone. 3. Generaing impulse responses for sign resricions In his secion, we describe he Ouliaris and Pagan (26) mehod for generaing he large ses of impulse response funcions o be judged agains he sign resricions. Consider he srucural sysem given by Eqs. (6), (2), (3), (4) and (7). Define he marix of conemporaneous coefficiens on he variables as: a a a a a4 a42 a43 a45 a5 a52 a53 a54 A a a a a (8) 5

6 where he above a coefficien indicaes ha a value is assigned o i. In heir procedure, he value assigned o each of hese coefficiens is generaed as follows: a a a ( ) ( ) ( ) a abs abs 2 abs 3 a ( ) ( ) abs 4 abs 5 (9) where abs denoes absolue value and he, i,,5 are drawn from a uniform probabiliy i densiy funcion over (,). For a given draw of he five i coefficiens, he insrumenal variable esimaion of he sysem proceeds in he following seps: (i) * Esimae Eq. (6) by regressing i on he firs lag of he variables and compue ˆ. (ii) Esimae Eq. (2) by regressing y a a i a q on * i and he firs lag of he variables using ˆ as he insrumen for * i and compue ˆ 2. (iii) Esimae Eq. (3) by regressing a i a q on he remaining righ hand side variables using ˆ as he insrumen for ˆ. 3 ˆ * i and 2 as he insrumen for y. Compue (iv) Esimae Eq. (7) by regressing q on he remaining righ hand side variables by using ˆ as he insrumen for i *, ˆ2 as he insrumen for, and i as he insrumen for i. Compue ˆ 5. y ˆ 3 as he insrumen for (v) Esimae Eq. (4) by regressing i on he variables using ˆ, ˆ 2, ˆ3 ˆ and 5 as he insrumens for i y, *, and q, respecively. Compue ˆ 4. Having esimaed he sysem, he nex sep is o expand erms involving he firs difference of he real exchange rae (and he ineres rae in Eq. 7) so ha all variables in he esimaed sysem appear in levels. The full se of impulse responses o one sandard error orhogonal shocks are calculaed and judged for eiher reenion or rejecion by he sign resricions. The process is hen repeaed for anoher draw of he i parameers. Once a predeermined number of ses of responses are acceped by he sign resricions, no furher draws are made and he process ends. 4. Sign resricions on he impulse responses The sign resricions o be applied o he impulse responses are shown in Table where " " indicaes a non negaive response (i.e. he variable does no fall in response o he shock), " " 6

7 indicaes a non posiive response (i.e. he variable does no rise in response o he shock) and UR indicaes an unresriced response. They are applied o he responses which occur on impac and in he subsequen quarer. No sign resricions are applied o he responses o he foreign ineres rae shock since i is isolaed by he conemporaneous zero resricions alone. The only candidae for he moneary policy shock is 4 as i is he only shock which is resriced o have a zero long run impac on he real exchange rae. This is indicaed as LR= in Table. However, for i o be a moneary policy shock, is responses mus saisfy he sign resricions shown in he able, which rule ou price and oupu puzzles. The sign resricions along wih he long run parameric resricion uniquely separae he AS, AD, MP and RX shocks. I is no necessary o sign resric he conemporaneous response of he exchange rae o he moneary policy shock so an exchange rae puzzle can emerge, nor he conemporaneous ineres rae response o he exchange rae shock. In he absence of he long run parameric resricion, i would be necessary o impose a furher sign resricion o separae he MP shock from he RX shock. For example, Fisher and Huh (26) impose he resricion ha he ineres rae canno fall in response o an RX shock which depreciaes he domesic currency, while Bjørnland and Halvorsen (24) require he exchange rae o appreciae following a posiive moneary policy shock (i.e. hey rule ou an exchange rae puzzle). On a successful draw, here are 3!=6 possible aribuions ha can be given o he se of srucural shocks (, 2, 3, 4, 5), since and 4 can only be he foreign ineres rae (FI) shock and he moneary policy shock, respecively. They are: (FI, AS, AD, MP, RX), (FI, AS, RX, MP, AD), (FI, AD, AS, MP, RX), (FI, AD, RX, MP, AS), (FI, RX, AS, MP, AD) and (FI, RX, AD, MP, AS). A draw is successful if he se of impulse responses o all he shocks saisfy he sign resricions for one of hese aribuions. If hey do no saisfy he sign resricions for any of hese aribuions, he draw is unsuccessful and all he impulse responses are discarded. In sign resricions, he acceped responses are arranged ino ascending order a each horizon and summary measures are hen calculaed. In his paper, we will focus on he maximum and minimum response a each horizon, which provides he range of acceped responses. Following he lieraure, we also repor he median, 6h and 84h percenile responses and he mid range response, calculaed as he sum of he maximum and minimum responses divided by wo. While repored, hese summary measures are no necessarily discussed as we focus specifically on he range of The sign resricions mehodology was inroduced by Faus (998), Canova and De Nicoló (22) and Uhlig(25). Scholl and Uhlig (28) is an applicaion of Uhlig s (25) approach o moneary policy and exchange raes. 7

8 acceped responses, which encompass hese summary measures in any case. We noe ha all of hese responses (including he maximum and minimum responses) a a given horizon and across horizons are almos cerainly from differen models i.e. hey are from impulse responses ha are generaed from differen draws of he i parameers. 2 In sign resricions, i is he range of acceped responses o a shock which is of ineres because all of he acceped responses are equally valid as hey are observaionally equivalen. Accordingly, we focus on he range of acceped responses o he MP and RX shocks in his paper and, in paricular, on wo saisics; he maximum and minimum response a each horizon. However, Baumeiser and Hamilon (25) have shown ha saisics which summarise he acceped responses, like he median or some oher percenile response or, for ha maer, he maximum or minimum response, are no unique because hey depend on he mehod which generaes he acceped responses; in our case, on he mehod used o generae he a ij coefficiens. In a simulaed demand and supply model, Ouliaris and Pagan (26) show ha he maximum and minimum of impulse responses are less affeced by he generaion mehod han he median of he impulse responses and conclude ha I is really he range of responses ha one can ge which is of ulimae ineres (Ouliaris and Pagan, 26, p. 62). 5. The weak insrumen problem We generaed he ses of impulse responses using he procedure of Secion 3 and judged each se for eiher accepance or rejecion by he sign resricions. Fig. repors he summary measures of he responses of he real exchange rae o he moneary policy shock from he, acceped responses o all he shocks for he case of Canada. I is clear ha many of he acceped responses of he real exchange rae o he MP shock do no converge o zero since he summary measures do no show a zero response a long horizons. The maximum response converges o a long run depreciaion of 4 percen while he minimum response converges o a long run appreciaion of around.5 percen. 3 Alhough he SVAR is designed so ha he long run response of he real exchange rae o he MP shock will be zero, ha does no show up in a large number of he acceped responses for Canada, nor is i eviden in he acceped responses of he oher hree counries. Alhough hese are 2 We also repor, hough again no necessarily discuss, he median arge and mid range arge responses which are calculaed using he meric suggesed by Fry and Pagan (2). This meric finds he paricular draw of he parameers ha minimises he disance beween he acceped impulse responses and he summary i responses (i.e. eiher he median or mid range responses) for all of he shocks. The summary arge responses are he responses produced by his paricular draw of he parameers i.e. he median arge and mid range arge responses come from a single model corresponding o his draw. 3 Recall ha a decrease in he real exchange rae (a negaive response) corresponds o a real appreciaion while an increase (a posiive response) corresponds o a real depreciaion. 8

9 no shown in Fig., he long run responses range from.5percen for Ausralia and he Unied Kingdom and from 2 o somewha more han 3 percen for New Zealand. The reason why he long run resricion is no eviden in he acceped responses for each counry is due o he use of a weak insrumen in he esimaion of Eq. (7). Fry and Pagan (25) show ha he lagged level of a variable will be a weak insrumen for is conemporaneous firs difference when he variable iself is highly persisen. Specifically, hey show ha if he firs order auocorrelaion coefficien of a variable ( X ) is in excess of.82 in a sample of observaions, he correlaion beween he insrumen ( X ) and he variable i is insrumening ( X ) will be less han.3 in absolue value, so he insrumen is weak. In he esimaion of Eq. (7), i is used as he insrumen for i bu he ineres rae is a highly persisen variable rendering he insrumen weak. Table 2 shows ha he ineres rae in each counry is a highly persisen variable (he firs order auocorrelaion coefficiens are all above.9) and he correlaion beween he firs difference and lagged level of he ineres rae is very low for each counry. The sronges correlaion is only.5, which is for Canada, while he weakes correlaion is.3, which is for he counry wih he mos persisen ineres rae, namely, he Unied Kingdom. For each counry, he weak insrumen problem arises in he esimaion of Eq. (7), wih he consequence ha he coefficien a 54 is imprecisely esimaed on each draw. This shows up wih he failure of he long run resricion o be eviden in many of he acceped responses. We now provide a mehod o obain a precise esimae of he coefficien insrumen problem. 6. A mehod ha circumvens he weak insrumen problem a 54 on each draw, which avoids he weak To begin, he reduced form VAR is z Bz e, where e are he VAR errors. The mehod begins from he relaionship beween he long run impac marix of he srucural shocks and of he VAR errors. I is: C() A B() () where C () is he long run impac marix of he srucural shocks, B () is he long run impac marix of he VAR errors and A is given by Eq. (8). The elemen in he fifh row and fourh column of C () is se o zero (i.e. c54 ) by he resricion ha 4 (i.e. he MP shock) has a zero long 9

10 run effec on he real exchange rae. We esimae he VAR and obain esimaes of he VAR errors e ˆ and an esimae of B (). We seek o find an expression for a By Eq. (), he inner produc of he fifh row of C () wih. 54 he fifh column of A is equal o he elemen in he fifh row and fifh column of B (). This equaion can be wrien as: c b a c a c () Similarly, he inner produc of he fifh row of C () wih he fourh column of A is equal o elemen b 54 and his equaion can be wrien as: a ( / c )( b a c a c ) (2) Subsiue Eq. () ino Eq. (2) o obain: a ( b a c a c ) ( ) b55 a25c52 a35c53 (3) As indicaed earlier, we can obain esimaes for he elemens in B() so we have an esimae for b 54 and b 55 o use in Eq. (3). We also have values for he generaed coefficiens, he on each draw. Then we can esimae a ij in Eq. (3), a 54 from Eq. (3) once esimaes of c 52 and c 53 are found. Denoe he elemens of A ij as a. I follows from Eq. () ha: a a a a a a a c c b b b b b a a We need o find esimaes of he elemens in he second and hird columns of a A (4) on each draw, in order o find esimaes of c 52 and c. 53 Recall ha we esimae Eq. (6) of he srucural model firs as in Sep (i) and obain ˆ. We hen esimae Eqs. (2) and (3) as in Seps (ii) and (iii) and obain he esimaed srucural shocks, ˆ 2 and

11 ˆ. By he relaionship beween he reduced form (VAR) errors and he srucural shocks, given by 3 e A i follows ha:, e a, a a a a, i,2,3,4,5. (5) i2 i i3 i4 i5 i 2 i i and e a, a a a a, i,2,3,4,5. (6) i3 i i2 i4 i5 i 3 i i Because he srucural shocks are orhogonal, i is uncorrelaed wih 2 and i is uncorrelaed wih. 3 We can obain a consisen esimae of he coefficiens in he second column of A by an ˆ OLS regression of e ˆi on 2 for i,2,3,4,5, respecively, and similarly for he coefficiens in he hird column of A ˆ by an OLS regression of e ˆi on 3 for i,2,3,4,5, respecively. 4 We hen obain an esimae of c 52 and c 53 from Eq. (4), which are used in Eq. (3) o form he esimae of a which is denoed a ˆ., We hen esimae Eq. (5) by regressing q aˆ54i on he righ hand side variables using ˆ as he insrumen for i *, ˆ2 as he insrumen for y, and ˆ 3 as he insrumen for, and compue ˆ 5. Finally, we esimae Eq. (4) by regressing i on he variables using ˆ, ˆ 2, ˆ3 ˆ and 5 as he insrumens for i y, *, and q, respecively, and compue ˆ 4. We close his secion by noing ha he expression for a 54 in Eq. (3) can be specialised o he case of full parameric idenificaion of he shocks, which would comprise a furher five conemporaneous zero recursive resricions, bringing he oal number of parameric resricions (including he long run resricion) o en. The furher conemporaneous resricions are ha a, a, a and a 35 are all zero. In his case, he expression in Eq. (3) reduces o a ( b / b ), which is analogous o he expression derived as Eq. (9) in Fry and Pagan (25, p. ) and o he expression implied by he long run resricion in Gospodinov (2, p. 4), and in Gospodinov, Maynard and Pesaveno (2, p. 459). a, 23 4 We noe ha he esimaes for resricions imply 2 a, a, 2 3 a, a, a and a in hese regressions will be close o zero because he exclusion a and 4 4 a and 5 a. a on he foreign ineres rae equaion can be shown o 5

12 We now presen he resuls for he srucural model esimaed his way. 7. Resuls As indicaed earlier, each equaion of he SVAR has a consan and a ime rend and he sample is 994:Q o 24:Q. In addiion, a dummy variable is included in each equaion for Ausralia o accoun for he impac of he Goods and Services Tax (GST) ha was inroduced in 2:Q3. 5 In he acual esimaion, he lag lengh of he SVAR was seleced by he AIC crierion and i seleced wo lags for every counry. The economeric procedure coninues o draw unil, ses of impulse responses are reained i.e. ha saisfy he sign resricions. Recall ha he iniial shocks are onesandard error in size and ha he sign resricions are applied o he impac and subsequen quarer responses. The success raes (he, accepances divided by he number of draws ha were required o obain hem) are.7% for Ausralia,.258% for Canada,.2% for New Zealand and.3% for he Unied Kingdom. Our discussion will focus on he responses o he moneary policy and real exchange rae shocks from amongs he acceped responses o all of he shocks. While we repor several summary response measures in he figures, we will focus on he maximum and minimum response a each horizon as hey provide he range of acceped responses. As indicaed earlier, he maximum response a each horizon will likely come from a differen model i.e. from a differen draw of he five i coefficiens, and ha is similarly he case for he minimum response a each horizon. 7.. Responses o he moneary policy shock Fig. 2 shows he responses of he domesic variables o a moneary policy shock which raises he ineres rae. For Ausralia, 97.6% of he acceped responses show an appreciaion of he real exchange rae on impac o he MP shock. For Canada, % of responses show an impac appreciaion and for New Zealand i is 96.%, while for he Unied Kingdom i is only 8%. There is no evidence of an exchange rae puzzle for Canada and i arises very infrequenly in he acceped responses for Ausralia and New Zealand. The Unied Kingdom is he excepion where one fifh of he acceped responses show an exchange rae puzzle. However, he median and mid range responses (and heir associaed arge responses) all show an impac appreciaion for he Unied Kingdom. The absence of an exchange rae puzzle in Canada, and is near absence in Ausralia and New Zealand, is a srong resul, given ha he SVAR is agnosic abou wheher or no here is an 5 The GST had he effec of raising he consumer price index o a higher level from 2:Q3. As inflaion is calculaed as he percenage change in he level of he consumer price index from he same quarer of he previous year, his will affec he inflaion measure for 2:Q3, 2:Q4, 2:Q and 2:Q2. Accordingly, he dummy variable akes he value one for each of hese quarers and he value zero oherwise. 2

13 exchange rae puzzle i.e. he SVAR does no sign resric he response of he real exchange rae o he MP shock. A long horizons, all of he acceped exchange rae responses for each counry converge o zero under our mehod as required by he long run parameric resricion. Bjørnland (29) idenified he shocks in her SVAR by parameric resricions alone, which were comprised of zero recursive conemporaneous resricions and he zero long run resricion we uilize. In her SVAR, which is also agnosic abou an exchange rae puzzle, he real exchange rae appreciaed on impac in Ausralia, Canada and New Zealand, following a posiive moneary policy shock (he Unied Kingdom was no included in her sudy). An advanage of combining sign resricions wih he long run parameric resricion is ha a range can be esablished from he acceped responses, all of which are equally valid. For Ausralia, he impac responses range from a negligible depreciaion (less han hree percen of responses show ha) o an appreciaion of around.6 percen. For Canada, he impac responses range from an appreciaion of.25 percen o slighly more han percen. For New Zealand, he range is for a depreciaion of.5 percen (hough less han four percen of responses show a depreciaion) o an appreciaion of.5 percen. The range is similar for he Unied Kingdom, alhough he proporion of responses showing an impac depreciaion is much larger a 2 percen. Noe, i can clearly be seen in Fig. 2 ha he acceped responses saisfy he sign resricions o he MP shock: oupu and inflaion fall and he ineres rises, in he curren and subsequen quarer. A long horizons, he responses of GDP, inflaion and he ineres rae converge o zero because hey are reaed as I() variables Responses o he real exchange rae shock Fig. 3 shows he responses of he domesic variables o an exchange rae shock which depreciaes he real value of he domesic currency. Recall ha he responses of he ineres rae are no sign resriced o his shock. For Canada and New Zealand, all of he ineres rae responses are posiive on impac in response o his shock, and for Ausralia, 93.9% of hem are. The Unied Kingdom is again he excepion wih only 78.9% of responses showing an increase in he ineres rae on impac. For Canada and New Zealand, he moneary auhoriies respond sysemaically o an exchange rae shock ha depreciaes he currency by increasing he domesic ineres rae on impac. This is almos always he case for Ausralia as well. For Canada he ineres rae increases by beween. and.3 percenage poins and for New Zealand he increase ranges from near zero o.3 percenage poins. For Ausralia, he increase can be up o nearly.8 percenage poins. In he case of he Unied Kingdom, i is less cerain ha he moneary auhoriy responds sysemaically o an exchange rae shock as abou one fifh of acceped responses have he ineres rae moving in he couner direcion on impac. 3

14 In he sudy of Bjørnland and Halvorsen (24), an exchange rae shock which depreciaes he currency resuls in he median response of he ineres rae rising on impac in Canada and New Zealand, while for he Unied Kingdom i rises negligibly and for Ausralia i falls. They conclude ha moneary policy responds sysemaically o an exchange rae shock in Canada and New Zealand bu no in Ausralia and he Unied Kingdom. 6 In Fig. 3 he median response, and indeed he oher summary responses, all show ha he ineres rae rises on impac in response o he exchange rae shock in each counry. The summary measures on impac all lie beween he 6h and 84h percenile responses which are hemselves posiive (excep ha he 6h percenile response on impac is marginally negaive for he Unied Kingdom). Tha may sugges ha here is a sysemaic moneary policy response in each counry, excep possibly for he Unied Kingdom. However, we prefer o focus on he range of acceped responses and he proporion of responses ha have he same sign on impac. On ha basis, we conclude similarly o Bjørnland and Halvorsen (24), excep for he case of Ausralia, where we find ha 93.9% of ineres rae responses o he exchange rae shock have he same sign on impac, (posiive o a depreciaing shock), indicaing a predominanly sysemaic response of moneary policy in Ausralia Responses o he AS and AD shocks Here we provide only a brief summary of wha he acceped responses o hese shocks show. The acceped responses of he ineres rae o he AS shock range over he zero axis a he impac and subsequen horizons in each counry and hey all converge o zero since he ineres rae is reaed as an I() variable. The acceped responses of he real exchange rae o he AS shock range over he zero axis a all horizons for Ausralia, Canada and New Zealand. For he Unied Kingdom, he range is for only a depreciaion a medium and long horizons. Recall ha boh ineres rae and real exchange rae responses are no sign resriced in his case. The wide range of responses indicaes ha here is considerable model uncerainy wih respec o he direcion of movemen of he ineres rae and he real exchange rae in response o he AS shock in each counry. In response o he AD shock, he range of acceped responses shows ha he real exchange rae appreciaes over all horizons, excep in he Unied Kingdom, where he range covers he zero axis a long horizons. 8. Conclusion This paper separaes he shocks in a SVAR for four small open economies by combining sign resricions wih parameric resricions using he recenly developed framework of Ouliaris and 6 In heir SVAR, he response of he ineres rae o an exchange rae shock is no sign resriced bu he response of he exchange rae o he moneary policy shock is whereas in he SVAR of Fisher and Huh (26) i is he converse. The SVAR of he presen paper sign resrics neiher. 4

15 Pagan (26). We uilise heir IV approach and find ha he insrumen associaed wih he esimaion of he coefficien associaed wih he long run resricion is weak so ha he coefficien is imprecisely esimaed. This shows up as a serious problem because many of he real exchange rae responses o he moneary policy shock converge in he long run o values considerably away from zero, when hey should converge o zero by design of he SVAR. As a demonsraion, his was specifically shown for he case of Canada. We provide a mehod o obain a direc esimae of he coefficien associaed wih he long run resricion on each draw in he Ouliaris and Pagan framework ha avoids his problem. When his mehod is applied, he acceped responses of he real exchange rae o he MP shock all converge o zero. There are wo main findings from he SVARs. Firs, for Canada here is no evidence for an exchange rae puzzle and for Ausralia and New Zealand an exchange rae puzzle only emerges in fewer han four percen of acceped responses. The Unied Kingdom is he excepion wih weny percen of acceped responses showing an exchange rae puzzle. Second, he moneary auhoriy in Ausralia, Canada and New Zealand appears o sysemaically respond o a real exchange rae shock. For Canada and New Zealand, all of he acceped responses, and 94 percen of hem for Ausralia, show an impac rise in he ineres rae following an exchange rae shock which depreciaes he real value of he currency. The Unied Kingdom is again he excepion where i appears ha he moneary auhoriy does no respond sysemaically o an exchange rae shock as weny percen of he acceped responses have he ineres rae moving in he couner direcion on impac. 5

16 References Baumeiser, C., Hamilon, J.D., 25. Sign resricions, srucural vecor auoregressions, and useful prior informaion. Economerica 83(5), Bjørnland, H.C., 29. Moneary policy and exchange rae overshooing: Dornbusch was righ afer all. Journal of Inernaional Economics 79(), Bjørnland, H.C., Halvorsen, J.I., 24. How does moneary policy respond o exchange rae movemens? New inernaional evidence. Oxford Bullein of Economics and Saisics 76(2), Canova, F., De Nicoló, G., 22. Moneary disurbances maer for business flucuaions in he G 7. Journal of Moneary Economics 49(6), Eichenbaum, M., Evans, C.L., 995. Some empirical evidence on he effecs of shocks o moneary policy on exchange raes. Quarerly Journal of Economics (4), Faus J., 998. The robusness of idenified VAR conclusions abou money. Carnegie Rocheser Conference on Public Policy 49, Fisher L.A., Huh, H S., 26. Moneary policy and exchange raes: Furher evidence using a new mehod for implemening sign resricions. Journal of Macroeconomics 49, Fisher L.A., Huh, H S., Pagan, A.R., 26. Economeric mehods for modelling sysems wih a mixure of I() and I() variables. Journal of Applied Economerics 3(5), Fry R., Pagan, A.R., 25. Some issues in using VARs for macroeconomeric research. Cenre for Applied Macroeconomic Analysis, Ausralian Naional Universiy, CAMA Working Paper 9/25. Fry R., Pagan, A.R., 2. Sign resricions in srucural vecor auoregressions: A criical review. Journal of Economic Lieraure 49(4), Gospodinov, N., 2. Inference in nearly nonsaionary SVAR models wih long run idenifying resricions. Journal of Business and Economic Saisics, 28(), 2. Gospodinov, N., Maynard, A., Pesaveno, E., 2. Sensiiviy of impulse responses o small lowfrequency comovemens: Reconciling he evidence on he effecs of echnology shocks. Journal of Business and Economic Saisics, 29(4), Kim, S., Roubini, N., 2. Exchange rae anomalies in he indusrial counries: A soluion wih a srucural VAR approach. Journal of Moneary Economics 45(3), Ouliaris, S., Pagan, A.R., 26. A mehod for working wih sign resricions in srucural equaion modelling. Oxford Bullein of Economics and Saisics 78(5), Scholl, A., Uhlig, H., 28. New evidence on he puzzles: Resuls from agnosic idenificaion on moneary policy and exchange raes. Journal of Inernaional Economics 76(), 3. Shapiro, M.D., Wason, M.W., Sources of business cycle flucuaions. In: Fischer, S. (Ed.), NBER Macroeconomics Annual 988, vol. 3, pp. 48. Svensson, L.E.O., 997. Inflaion forecas argeing: implemening and monioring inflaion arges. European Economic Review 4, 46. 6

17 Uhlig, H., 25. Wha are he effecs of moneary policy on oupu? Resuls from an agnosic idenificaion procedure. Journal of Moneary Economics 52(2),

18 Table. Sign resricions Shock\Variable GDP Inflaion Ineres Rae Real Exchange Rae AS UR UR AD MP UR, LR= RX UR Noes: AS denoes an aggregae supply shock, AD an aggregae demand shock, MP a moneary policy shock and RX a real exchange rae shock. The designaion " " indicaes a non negaive response so ha he variable does no fall in response o he shock while " " indicaes a non posiive response so ha he variable does no rise in response o he shock. UR denoes an unresriced response of he variable o he shock. The sign resricions are imposed on he impac response and on he response for he following quarer. LR= is he parameric resricion ha he MP shock has a zero impac on he real exchange rae in he longrun. Table 2. The weak insrumen problem Saisic\Counry Ausralia Canada New Zealand Unied Kingdom AR() corr( i, i ) Noes: AR() is he firs order auocorrelaion coefficien of he ineres rae and corr( i, i ) is he correlaion beween he firs difference of he ineres rae and is level lagged one quarer. The sample is 994:Q 24:Q for each counry. 8

19 .25 GDP.4 INT MED MID MIN 84% MED MID MIN 84% MED-T MID-T 6% MAX MED-T MID-T 6% MAX. INF 5 REX MED MID MIN 84% MED MID MIN 84% MED-T MID-T 6% MAX MED-T MID-T 6% MAX Canada: Weak insrumen case Fig.. Response of variables o he moneary policy shock under he weak insrumen: Canada 9

20 -. GDP.25 INT INF.2 REX (a) Ausralia.3 GDP.3 INT INF.25 REX (b) Canada Fig. 2. Response of variables o moneary policy shock 2

21 . GDP.5 INT INF.5 REX (c) New Zealand.2 GDP.25 INT INF.5 REX (d) Unied Kingdom Fig. 2 (coninued). Response of variables o moneary policy shock 2

22 .5 GDP.25 INT INF 3.5 REX (a) Ausralia.6 GDP.4 INT INF 4 REX (b) Canada Fig. 3. Response of variables o real exchange rae shock 22

23 .8 GDP.5 INT INF 4 REX (c) New Zealand.7 GDP.25 INT INF 2.5 REX (d) Unied Kingdom Fig. 3 (coninued). Response of variables o real exchange rae shock 23