Barak Chian 2015

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Đây là paper nghiên cứu về vấn đề short-termism, vấn đề này đang rất được ưa chuộng, xin lỗi, thật ra paper này nghiên cứu về truyền dẫn chính sách tiền tệ giữa Canada và Mỹ mới đúng.

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    Economic Modelling 46 (2015) 1126

    Contents lists available at ScienceDirect

    Economic M

    e lsand direct effects of other countries on Canada are likely to be small.We will discuss this issue further in Section 3. Second, data for many(developing) countries is not very reliable. Also, for many countries

    hypothesis (Crowder, 1997, and Crowder and Hoffman, 1996) andlong run interest rate rule (Assenmacher-Wesche and Pesaran, 2009,and Dees et al., 2007b).on which the GVAR is founded, we develop a two-country model com-prising a structural cointegrated VARX* for Canada and a structuralcointegrated VAR for the US. This decision is based on the followingreasons. First, the Canadian economy is dominated by the US economy

    estimate a range of possible values for that coefcoefcient lies in the range [1.4,2.0] for the US anfor Canada though it is not signicantly different fmodel. These results are consistent with bothPesaran et al. (2004) and Dees et al. (2007a), DdPS. The GVAR modelis constructed from country-specic vector error correction models inwhich domestic and foreign variables interact contemporaneously. Inthis paper, however, instead of modeling a large set of countries

    between the US and Canadian outputs. An interesting result is that theinterest rate differential between the US and Canada is a major factorin driving the Canadian macro variables.

    By relaxing the coefcient of ination in the Fisher equation, we alsodata is not available for more than two (or thr

    I'd like to thank M. Hashem Pesaran and an anonymoE-mail address: [email protected].

    http://dx.doi.org/10.1016/j.econmod.2014.10.0360264-9993/ 2014 Elsevier B.V. All rights reserved.y, we follow the Globaltegy which allows for asmission of shocks; see

    Fisher equation and Interest Rate Parity are maintained in the Canadianmodel. However, there is no strong empirical evidence in favor of thePurchasing Power Parity hypothesis and a convergence relationshipVector Autoregressive (GVAR) modeling strarich representation of the cross-country trancatches a cold. Because of strong eCanada and the US, Canada is very likethe US even more seriously than thethe extent of US monetary policy spiCanadian policy makers. Policy makersrole and relevance of different cross-These are the issues we will address in

    In order to model the Canadian ees, the rest of the worldic connections betweeninuenced by events inthe world. In particular,is a central question foro interested to know thetransmission channels.per.

    In the two-country model, which is called a VECX* model, Canada ismodeled as a small open economy and the US, treated as rest of theworld for Canada, is modeled as a closed economy. Each countrymodel is estimated using the Structural Cointegrating VAR approach.This approach tries to reconcile the economic theory and the statisticalfeatures of the data inwhich, restrictions needed to identify cointegratingrelations are provided by economic theory; for more details, see Pesaranand Shin (2002) and Pesaran et al. (2000).

    Our study shows that the Term Structure and a modied Fisherequation are maintained in the US model, and, the Term Structure,1. IntroductionTransmission of US monetary policy into tstructural cointegration analysis

    S. Mahdi BarakchianGraduate School of Management and Economics, Sharif University of Technology, Tehran, Iran

    a b s t r a c ta r t i c l e i n f o

    Article history:Accepted 20 October 2014Available online xxxx

    Keywords:Macroeconomic modelingLong-run structural VARMonetary policy shockInternational transmission

    This paper estimates a two-Using persistence prole anain theUSmodel, and, the Termodel. Then we use the modThe results show that the resimilar to the responses of thshock, output falls quickly ajumps and then gradually deOur results show that intereare transmitted into the Can

    j ourna l homepage: www.ee) decades.

    us referee for their comments.Canadian economy: A

    ntry model comprising structural cointegrated models of Canada and the US.s, we nd that the Term Structure and amodied Fisher equation aremaintainedtructure, Fisher equation and Interest Rate Parity aremaintained in the Canadiano examine the transmission of US monetary policy into the Canadian economy.nses of the Canadian macro variables to the US monetary policy shock are veryS macro variables to the same shock: after a contractionary US monetary policyhows a U-shaped response, ination falls with a delay, short-term interest ratees and long-term interest rate increases for one year and then gradually declines.te-path-through is the major mechanism by which US monetary policy shocksn economy.

    2014 Elsevier B.V. All rights reserved.

    odelling

    ev ie r .com/ locate /ecmodThenwe examine the transmission of USmonetary policy shocks intothe Canadian economy using impulse response analyses conducted forthe VECX* model. In order to make a comparison, we also use a singleequation model to estimate the responses of the macroeconomic vari-ables to the US monetary policy shock series constructed by Romer

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  • 12 S. Mahdi Barakchian / Economic Modelling 46 (2015) 1126and Romer (2004), who use a narrative approach based on the minutesof the FOMCmeetings to construct a series of USmonetary policy shocks.

    The results of the impulse response analysis show that the responsesof the Canadian macro variables to the US monetary policy shock aresimilar to the responses of the US macro variables to the same shock:after a contractionary US monetary policy shock, output falls quicklyand shows a U-shaped response, ination falls with a delay and nallyconverges to the initial equlibrium, short-term interest rate jumps andthen gradually declines and long-term interest rate increases for oneyear and then gradually declines. Our results also show that increasingthe number of lags in the VAR alleviates the price puzzle.

    The major contributions of the paper are threefold. First, wehave spent much time on constructing the USCanada two countrymodel using the GVAR modeling strategy, and paid much attention toevery detail of the model such as selecting the variables, lags, andcointegration ranks, specications of the long run relations, etc. Thiswell-constructed model enables us to answer the questions that thepaper is aimed to address: What are the short run and long run impactsof USmonetary policy onCanadianmonetary policy?HowdoesUSmon-etary policy affect Canadian output and prices? Is US monetary policytransmitted into the Canadian economy through the expenditure-switching-effect mechanism or the interest-rate-path-through mecha-nism? To our knowledge, this two-country model is new for Canadaand no other paper has yet investigated the impacts of US monetarypolicy on the Canadian economy as detailed as this paper. Of course,the two-country model is a powerful tool to conduct policy analysis forissues other than those analyzed in the paper. Second, there is a disputein the literature regarding the impacts of US monetary policy on theCanadian economy. We provide compelling evidences that interest rate-path-through is the most important mechanism by which US monetarypolicy shocks are transmitted into the Canadian economy. Specically,our estimations show that as soon as the Fed raises the US short terminterest rate by 100 basis points, the Bank of Canada follows the US byraising the Canadian short term interest rate by 62 basis points. In addi-tion, the Canadian short term interest rate converges to the US shortterm interest rate in the long run reasonably fast. Third, using awild boot-strap method to produce critical values for the overidentication testdeveloped for cointegration restrictions, when there is heteroskedasticityin error terms, is another contribution of the paper.

    The remainder of the paper is organized as follows. Section 2 reviewsthe literature on cross-country transmission of US monetary policy.Section 3 describes the two-country VECX* model. Section 4 presentsthe empirical results. Section 5 examines the transmission of US mone-tary policy shocks to the Canadian economy using impulse responsefunctions. The last section concludes.

    2. International transmission of US monetary policy

    Does a monetary expansion in the US lead to a recession or a boomin other countries? From a theoretical point of view, there is not aconclusive answer to this question. MundellFlemingDurnbush(MFD) model predicts that in the context of a oating exchange rateregime, an expansionary USmonetary shock leads to a fall in the foreignoutput. This is due to the expenditure switching effect. Based on thistheory, an expansionary US monetary shock leads to a devaluation ofthe US currency. Since prices are assumed to be sticky, or even xed inthe short run, the relative prices of US products will be decreased.Hence, US products become more competitive and this will lead to animprovement in the trade balance. As a result, the US output riseswhile the foreign output falls. So expansionary US monetary policy hasa beggar-thy-neighbour effect. Since for the foreign country, importsare cheaper now and therefore there is a substitution towards imports,the depreciation of exchange rate leads to a fall in the foreign price level.

    In the MFD model it is usually assumed that foreign interest rate isexogenously set and therefore is invariant to the US monetary policy.

    But if foreign monetary authority adjusts its monetary policy inresponse to the US Fed's policy, then an expansionary shock to the USmonetary policy will induce foreign consumption and investmentwhich in turn has a positive effect on foreign output. In a similar mech-anism, an expansionary shock to the US monetary policy may lead to afall not only in the US interest rate but in the foreign (long term real)interest rate through, for example, no arbitrage condition. Then adrop in the interest rates will induce world aggregate demand, whichincreases the demands for both US and foreign goods, which in turnleads to an increase in foreign output. This mechanism is supposed tohold for the US monetary policy because of the dominant role of theUS in the world economy.

    The inuential work of Eichenbaum and Evans (1995) is one of therst papers using the Structural VAR methodology to assess the effectof US monetary policy shock on foreign variables. Their results showthat a contractionary US monetary sock leads to persistent, signicantappreciations in US nominal and real exchange rates. This shock alsoleads to a rise in US and foreign interest rates but the rate of increasein foreign interest rates is smaller such that the spread between foreignand US interest rates falls. Therefore, they conclude that there is asignicant departure from uncovered interest parity in the short runfollowing a US monetary shock.

    Kim and Roubini (2000) show that following a US monetary policycontraction, exchange rates appreciate, foreign interest rates generallyrise, foreign prices increase in short term then converge to the initialequilibrium, and foreign outputs rise rst and then fall in long term.

    Faust et al. (2003) nd qualitatively similar results to Kim andRoubini (2000) when studying the effects of US monetary policy onGermany and the UK. However, counter to Kim and Roubini (2000),the predominant response to a US monetary contraction is a foreignoutput decline.

    Kim (2001) shows that an expansionary US monetary shock has apositive spillover effect over the non-US G-6 output. He argues thatthis positive spillover occurs through the capital market mechanismby reducing the world interest rate rather than through trade mecha-nism suggested by the MFD model. But the size of the positive effecton foreign output is smaller than on US output. There is no signicanteffect of US monetary policy on foreign price level. He also shows thatthere is not a strong evidence in favor of the endogeneity of non-USmonetary authorities reaction to the US monetary policy. This resultis in contrast to studies like Bluedorn and Bowdler (2011) andScrimgeour (2010), who show that a positive innovation to the FederalFunds rate increases foreign short term interest rate, and they interpretthat as a sign that non-US monetary authorities follow the Fed'smonetary policy.

    Holman and Neumann (2002) do not nd evidence to support theclaim that Canadian monetary policy follows US monetary policy.They show that US money can explain only a small fraction of thevariation in Canadianmoney. The exchange rate appreciates inmediumterm following an expansionary US monetary shock which can beinterpreted as the exchange rate puzzle. The effect of an expansionaryUSmonetary shock on Canadian output is positive in the long run but ismixed in the short run.

    Bluedorn and Bowdler (2011) examine the effects of US Monetarypolicy shocks on the other G-7 countries. Using the Romer andRomer's (2004)monetary policy shock series, theynd that direct inter-est rate linkages are an important channel in international businesscycle propagation. An increase in the US interest rate raises foreigninterest rates at short horizon but reduces it at long horizon. They alsond that after a contractionary US monetary shock foreign countriesexperience a recession and foreign prices fall, in some cases immediatelyand in others with one or two years delay.

    Scrimgeour (2010), studying the effects of US monetary policy onoutput of four countries in the Americas, nds that foreign output fallssignicantly after a contractionary US monetary policy shock and theresponse of foreign output is generally similar to the response of US

    output. He therefore concludes that the results are inconsistent with

  • expenditure-switching theory and he argues that this is perhaps dueto the fact that foreign monetary authorities tend to follow the Fed'spolicy.

    show that including long term interest rate contributes substantiallyto the forecast accuracy of output growth and ination for Canada andthe US.

    In order to prevent having quadratic trends in the level of thevariables in the models of the US and Canada, deterministics aretreated according to case IV, as described in Pesaran et al. (2000),in which, intercepts are unrestricted, but the trend coefcients arerestricted to lie in the cointegrating space. Hence, the US model can bewritten as

    xt xt1 t1 Xp1

    i1i x

    ti a0 ut ; 1

    where xt is a m* 1 vector of endogenous variables. When the rank ofthe matrix * is r* b m*, * can be decomposed as

    0, where

    * is a m* r* matrix of loading coefcients and * is a m* r* matrixof cointegrating vectors.

    3.2. Model for Canada

    Weestimate a cointegratedVARX*model for Canada over the period1958Q12004Q2, where the endogenous variables, xt, are Canadianshort term interest rate (rts), Canadian long term interest rate (rtl),

    13S. Mahdi Barakchian / Economic Modelling 46 (2015) 1126In summary, there is not a consensus among empirical studiesregarding the effects of the international transmission of US monetarypolicy shocks. However, majority of the studies support the interestrate-path-through as the major channel of cross-country monetarypolicy transmission rather than the expenditure switching effect,and therefore their results are more consistent with a prosper-thy-neighbour effect as opposed to a beggar-thy-neighbour effect.

    3. Outline of the two-country model

    The high dominance of the US economy over the Canadian economymeans that the US essentially serves the role of rest of the world toCanada. This fact simplies the specication of foreign variables in aCanadian model and most of the macroeconometric models developedfor Canada, e.g. NAOMI, M1-VECM, etc., include US variables as foreignvariables (see Ct et al., 2003). As Ct et al. (2003) indicate, sinceshocks from Canada have little impact on theUS it is generally acknowl-edged that US variables can be assumed exogenous with respect to theCanadian economy; see also Cushman and Zha (1997). This strategy hasalso been adopted by other papers, e.g. Canova (2005) and Mackowiak(2007), which study the effects of the US economy on other small openeconomies.

    This is also consistent with the literature on the US economy;Majority of studies,model theUS as a closed economy; see, for example,Anderson et al. (2002), Bernanke and Mihov (1998), Christiano et al.(1996,1999) and Sims and Zha (2006) inter alia. This is the line whichwill be followed in this research; we develop a two-country VECX*model comprising the US which is modeled as a closed economy andCanada which is modeled as a small open economy.

    To construct the two-country model, rst a cointegrated VAR for theUS and a cointegrated VARX* for Canada are estimated. As noted earlier,we use economic theory to provide restrictions needed to identifycointegrating relations. The over-identifying restrictions implied bythe long-run theory relations are tested, and if not rejected, are thenembodied in the model. The result is a cointegrating VAR such that thelong-run relations are its steady-state solutions. Then the Canadianand US models are combined to form a complete system, called aVECX* model.

    The structure of the two-countrymodel enables us to considermanydifferent channels of transmission of shocks from the US to Canada.These channels range from nancial markets, e.g. through cross-country correlations of long term interest rates, to technology diffusion,e.g. through output convergence relation.

    3.1. Model for the US

    We estimate a cointegrated VAR for the US over the period 1958Q12004Q2, where the variables, xt, are US short term interest rate (r ts ),US long term interest rate rlt

    , US ination (pt), US income per capita

    (yt), and oil price (ot).1 All variables are treated as endogenous in the USmodel. Long term interest rate is added to allow for the yield curverelationship since macroeconomic variables and the yield curve aremutually interdependent. Not only macro variables affect the yieldcurve (Diebold et al., 2006), but the yield curve can also help to explainchanges inmacro variables like output (Estrella andMishkin, 1998). Ourstudy provides more support regarding the latter and it shows that theerror correction term corresponding to the yield curve has a signicantnegative effect on output growth. In addition, Pesaran et al. (2009)

    1 See the Appendix A for more details on the description of the time series.Canadian ination (pt), Canadian income per capita (yt), and Canadianreal exchange rate (etr). etr is computed as etr = et pt + pt, where etis the (log) Canadian currency per US dollar.2 For estimation, theforeign variables, xt, are treated as weakly exogenous with respect tothe parameters of the Canadian model. The model for Canada can bewritten as

    xt zt1 t1 xt Xp1i1izti a0 ut ; 2

    where xt is am 1 vector of endogenous variables, xt is am* 1 vector

    of exogenous variables and zt is a em 1vector, wherez0t x0t ;x0t 0 andem mm . When there are r cointegrating relations, within xt orbetween xt and xt, then can be decomposed as = , where is a m r matrix of loading coefcients and is a em r matrix ofcointegrating vectors.

    2 In contrast to theVECMs developed for Canada in the literature (e.g. Hendry, 1995; Ar-mour et al., 1996; Engert and Hendry, 1998; Adam and Hendry, 2000; Kasumovich, 1996,money measures are not included in our VECX* model. The rationale behind our decisionis based on the three following reasons.

    (i) In recent years, most of the models developed for monetary policy analysis as-sume thatmoney only plays a passive role. In otherwords, they assume thatmon-ey is supplied passively by the central and commercial banks to meet rms' andhouseholds' demand and, therefore, itmay be ignored; see e.g.McCallumandNel-son (1999) and Rotemberg and Woodford (1997). It has also been argued thatmeasures of past ination, economic activity and interest rates contain a greatdeal of information embedded in monetary aggregates; see e.g. Gal (2006) andWoodford (2006), and also the papers presented at the 4th ECB ConferenceThe role of money: money and monetary policy in the twenty rst century.

    (ii) The relationship betweenmoney and other economic variables in Canada has notbeen stable over time. This observation can be partly explained by the institution-al changes and nancial innovations that have occurred in Canada, particularlyafter the 1980s, and also the improvement in electronicnancial services. As a re-sult, the ofcial measure of money, M1, does not measure the appropriate mea-sure of narrow money over time; see e.g. Adam and Hendry (2000) and Aubryand Nott (2000).

    (iii) For most of the past four decades, monetary aggregates have played no specialrole in conducting monetary policy by the Federal Reserve; for more detailssee e.g. Bernanke and Mihov (1998) and Kahn and Benolkin (2007). It has alsobeen shown that monetary aggregates have negligible prediction power for US

    ination; see, for example, Hale and Jord (2007) andKahnand Benolkin (2007).

  • Although IRP is written here in terms of long term interest rate,it could be written alternatively in terms of short term interestrate. When building a structural cointegrating VECM for each country,these long run relations will be incorporated into an otherwise unre-

    14 S. Mahdi Barakchian / Economic Modelling 46 (2015) 11263.3. The VECX* model

    The models of Canada and the US are combined to form a completeeconometric model, a VECX* in which, all variables will be endogenous.The VAR representation of the VECX* model can be written as

    zt Xpi1izti a bt Hvt ; 3

    where

    zt xtxt

    ;1 I e e1;i eiei1; i 2;; p1;p ep1;

    a a0

    a0 a0 ;b

    ; e 0mm 0mm

    ;

    ei i 0mmi i 0mm

    ;H Im 0mm Im

    ; vt u

    t

    ut

    The covariance matrix = E(vtv t) can be freely estimated by theem em matrix ^ tv^t v^

    0t=T , when no restriction is imposed on the

    covariance matrix. This VECX* model has 10 endogenous variables,r + r* cointegrating relations, and 10-(r + r*) stochastic trends.This model allows for a large degree of interdependence through twodifferent channels. First, through the direct effects of xt variables;shocks to the US have considerable impacts on Canada. Second, through

    the covariances between errors, ^ , which are expected to be smallrelative to the direct xt effects.

    3.4. Economic theory of the long-run

    The long-run equilibrium relations can be derived from differenttheoretical approaches to macroeconometric modeling. Garratt et al.(2003a and 2006, Ch. 4) use stock-ow equilibria, arbitrage conditionsand long-run solvency requirements. Dees et al. (2007b), DHPS, extendsthe analysis of Garratt et al. to the cases where the long term interestrate and equity prices are included in the model. Alternatively, Gal andMonacelli (2005) derive the long run relations using inter-temporaloptimization conditions in a New-Keynesian DSGE model. Despite thedifferences between the two approaches, they yield similar long runrelations; for more details, see Garratt et al. (2006, Ch. 4), and Pesaranand Smith (2006).

    In our two-country model, the US is modeled as a closed economy.Hence, in light of the above-mentioned literature, two possible within-country long run relations suggested by economic theory to hold inthe US model are the Term Structure (TS) and Fisher equation:

    TS : rst rlt b1 1;t ; 4

    Fisher : rst pt b2 2;t ; 5

    where i,t, i= 1, 2, is a mean zero stationary process.But, Canada is modeled as a small open economy. Therefore, in

    addition to the Term structure and Fisher equations, three possiblecross-country long run relations are also suggested by economic theoryto hold in the model of Canada, i.e. Interest Rate Parity (IRP), OutputConvergence (OC), and Purchasing Power Parity (PPP):

    IRP : rltrlt b3 3;t ; 6

    OC : ytyt b4 4;t ; 7

    PPP : e p p b : 8t t t 5 5;tstricted VAR model.There is a sizable literature examining the validity of the above-

    mentioned long run relations for the US and Canada. Studies likeBradley and Lumpkin (1992), Campbell and Shiller (1987), Choi andWohar (1991), Engle and Granger (1987), Hall et al. (1992) andZhang (1993) nd a cointegrating relation between the yields of theUS bonds with different maturities which supports the Term Structurerelation for theUS. Boothe (1991) and Siklos andWohar (1996) providemixed support for existence of such a cointegrating relation for bothCanada and theUS: in Siklos andWohar (1996) the one-for-one relationbetween the yields is generally accepted whereas in Boothe (1991) thecoefcient in the cointegrating relation is signicantly different from1. Several studies have found a one-for-one cointegrating relationshipbetween Canadian and US interest rates which justies IRP; see, forexample, Boothe (1991) and Engert and Hendry (1998). But, theevidence in support of PPP condition between Canada and the US israther weak; see, for instance, Johnson (1990), Turtle and Abeysebera(1996) and Flynn and Boucher (1993).3 Similarly, the time series evi-dence has not been supportive of the output convergence hypothesis,i.e. a one-for-one cointegrating relation between these two countries'real income per capita; see for example, Bernard and Durlauf (1995).4

    The Fisher equation will be discussed in more detail in Section 4.3.

    4. Empirical results

    Tables 7 to 10 in Appendix A show the results of the AugmentedDickeyFuller (ADF) and PhillipsPerron (PP) tests for the levelsand rst differences of the variables. These tests are calculated over1958Q12004Q2. The results suggest that the null hypothesis that ert ; r

    st ;

    rlt ; yt ; rst ; r

    lt ; y

    t and pt

    o contain a unit root cannot be rejected when theunit root tests are applied to the level of the variables but is rejectedwhen the tests are applied to the rst difference of the variables.

    The ADF test results for pt and pt are ambiguous. The unit roothypothesis is rejected for low orders of augmentation when applied tothe rst differences of pt and pt, but it is not rejected for higher orderof augmentation. The PP test results for pt are doubtful too. The unitroot hypothesis is rejected for larger Bartlett windows used in thecomputation of the PP statistics when applied to the rst differencesof pt, but it is not rejected for smaller windows. The Fisher equationimplies that the orders of integration of ination and interest rate arethe same. Although in economic literature, ination and interest rateare usually supposed to be I(0) but regarding the results of unit roottests for interest rate, which show that rts and rts are I(1), and theambiguous results for pt and pt, which show that pt and pt areon the border of being I(1)/I(0), we decide to treat pt and pt asI(1) series. Treating rts, rts , pt and pt as I(1) variables enables us torepresent the statistical properties of the series and at the same timeto consider the Fisher equation as a long-run relation in our model.In view of the above results, from now on we assume that all the tenvariables in the VECX* model are I(1).

    4.1. Lag order selection

    Table 1 shows that the SIC selects 1 lag for both Canada and the US,whereas the AIC favors 2 lags for Canada and 3 lags for the US. Actuallythere is a trade off here; on the one hand, choosing low order of VAR

    3 Most of the studies examining whether PPP holds between countries have been criti-cized for suffering from the size distortion bias arising from heteroskedasticity. Recently,Su et al. (2014) have found that evenwhen this problem is taken into account using awildbootstrap method, still there is a strong evidence against PPP.4 In all the studies noted in this section, the long-run relations are treated individually.

  • leaves the residuals to be serially correlated. But on the other hand,choosing high order of VAR implies a large number of parameters tobe estimated. In practice, two lags generally provide sufcient dynamicsin themodel and it is seldom the case that a well-speciedmodel needsmore than two lags; see Juselius (2007, p. 72) and Garratt et al. (2006,

    weakly exogenous variables, m*, minus the number of cointegrationrelations among the exogenous variables, r*. Hence, we report twosets of critical values in Table 2, CV5 and CV3 which assume thepresence of ve (m* = 5) and three (m* r* = 3) exogenousI(1) variables, respectively. Based on CV5, the trace test indicates r =3 and the maximal eigenvalue test indicates r = 1. Based on CV3, thetrace test rejects even r=4 in favor of r=5 but themaximal eigenvaluetest indicates r = 3.

    Economic theory suggests ve long run relations, i.e. PPP, IRP, OC,Fisher and TS, to hold in the model of Canada. However, we need rst

    the US and Canada over the period 19551986 only when the sampleis split according to exchange rate regime. Atkins and Coe (2002) use

    Table 1Lag order selection criteria.

    US Canada

    Lag order AIC SIC AIC SIC

    1 3542.5 3486.2 7504.1 7310.92 3572.0 3475.4 7517.7 7163.53 3581.2 3444.3 7501.3 6986.04 3571.0 3393.8 7479.3 6803.0

    Notes: AIC is the Akaike information criterion and SIC the Schwarz information criterion.The information criteria are computed using 186 observations from 1958Q1 to 2004Q2.Intercept and trend are included in the estimations. Considering the nature of quarterlydata and the number of observations in each sample, we set the maximum lag order at 4.

    15S. Mahdi Barakchian / Economic Modelling 46 (2015) 1126Ch. 9). We will proceed from here with the lag length of two for bothmodels and leave a further discussion on lag order selection (and itsconsequences for impulse response functions) to Section 5.1.

    4.2. Cointegration rank

    Table 2 presents the results of the trace and maximal eigenvaluestatistics with the critical values. Both the maximal eigenvalue andtrace tests favor r* = 2 for the US model. As we argued in Section 4,macroeconomic theory also suggests that two long run relations,i.e. the Term Structure and Fisher relations, hold in the US model.Fig. 1 shows that the persistence proles of the Term Structure and(modied) Fisher equation in the US model are very well behaved andthey quickly converge to zero after a system-wide shock. Therefore, itseems that r* = 2 is appropriate for the US model.

    The results of the cointegration rank tests for themodel of Canada isnot as straightforward. The cointegration rank tests in a VECM withweakly exogenous I(1) variables have been analyzed in both Harboet al. (1998) and Pesaran et al. (2000). In both of these studies, it isassumed that the weakly exogenous variables, xt, are not cointegratedamong themselves. Based on this assumption the critical values aresimulated where the number of weakly exogenous variables is m* (m*is the dimension of xt). However, as we just showed, this assumptiondoes not hold in the model of Canada because two cointegrating rela-tions exist among the ve variables in xt. For this case, the cointegrationtest needs to be modied. But no formal statistical analysis has been yetdeveloped for this. Assenmacher-Wesche and Pesaran (2009) suggestthat in this case the effective number of weakly exogenous variablesused in the cointegration rank test should be equal to the number of

    Table 2Cointegration rank tests.

    US Rank Trace CV -max CV

    0 149.5 82.8 87.0 35.0

    1 62.5 59.1 29.1 29.12 33.4 39.3 17.2 23.13 16.1 23.0 12.0 17.14 4.1 10.5 4.1 10.5

    Canada Rank Trace CV5 CV3 -max CV5 CV3

    0 168.4 135.7 114.7 53.4 49.5 43.91 115.0 102.4 85.5 39.6 43.6 38.02 75.3 72.3 59.3 32.0 37.2 31.83 43.2 46.1 37.0 24.1 30.5 25.24 19.1 23.1 18.1 19.1 23.1 18.1

    Note: The sample period is 1958Q1 to 2004Q2. CV5 (CV3) denotes the 90% critical valuethat assumes the presence ofve (three) exogenous I(1) variables. The order of theunder-lying VAR is 2 and the model contains unrestricted intercept and restricted trendcoefcients.the ARDL technique and nd results consistent with the one-for-oneFisher equation for the US and Canada over the period 1953:011999:12. In a recent study, Everaert (2014) shows that the impact ofination on the nominal interest rate is not signicantly different fromone in the sample of OECD countries (including the US and Canada)which supports for the Fisher effect, when controlling for anunobservednon-stationary common factor in estimating the Fisher equation.

    DHPS show that the estimate of the ination coefcient in the Fisherequation for theUS is 2.06whereas for Canada is not signicantly differ-ent from 1. They interpret the value of the ination coefcient as theimportance of the ination term in the central bank feedback rule andargue that the coefcient should be greater than one if the centralbank wants to ensure that the real interest rates move in the rightdirection to stabilize output, in accordance with the Taylor principle.The modied Fisher equation is then called a long run interest raterule (Assenmacher-Wesche and Pesaran, 2009).

    5 In Fig. 5 we only report the persistence proles of PPP and OC. The results for the per-sistence proles of the other long run relations are almost identical to Fig. 1.We also inves-tigate the properties of the persistence proles where r= 4 (5models; TS, Fisher, IRP andone of PPP orOC are imposed on the Canadianmodel) and r=1 (5models; each of the theTS, Fisher, IRP, PPP and OC is imposed separately on the Canadian model). In all thesecases, the persistence proles of PPP andOC are almost identical to Fig. 5 and they are verypersistent.6 Since the real exchange rate shows a small trend over part of the period 1958Q1

    2004Q2,we also examined the PPPwhere co-trending is not imposed on the cointegratingrelation. The persistence prole of the PPP was still persistent although the convergenceto investigate the properties of these long run relations using persis-tence prole analysis. We impose all the ve long run relations (r =5) on the model of Canada and then combine the Canadian modelwith the US model, where TS and (modied) Fisher equation areimposed on the USmodel, to obtain a complete VECX* model. Needlessto say thatweneed a completemodel to derive persistence proles. Thisanalysis shows that the persistence proles of the Canadian TermStructure, Canadian Fisher equation and Interest Rate Parity die outfast whereas the persistence proles of the Purchasing Power Parityand Output Convergence are very persistent (see Fig. 5 in AppendixA).5,6 Based on these observations we believe that r = 3 where theTerm Structure, Interest Rate Parity and Fisher equation are imposedon the model of Canada is the most appropriate. In Section 4 belowwe will test the over-identifying restrictions implied by these threelong run relations. The result that Canada has three cointegratingrelations is consistent with the results of other studies such as DdPS.

    4.3. Fisher equation

    The empirical evidence on the long run Fisher parity is mixed. Usingthe Johansen technique, Dutt and Ghosh (1995) nd no evidence of theFisher parity over the post-war period (1960Q11993Q4) for Canada.Using the EngleGranger technique, Atkins (1989) nds evidence infavor of a long run relation between ination and the nominal interestrate for the US over the period 19531981. MacDonald and Murphy(1989) use the same technique and nd such a long run relation fortowards zero was faster.

  • 16 S. Mahdi Barakchian / Economic Modelling 46 (2015) 1126Canada TS

    00.20.40.60.8

    11.21.41.61.8

    Canada Fisher

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    US TS

    1.21.41.61.8

    0 4 8 12 16 20 24 28 32 36

    0 4 8 12 16 20 24 28 32 36Another interpretation for the modied Fisher relationship isprovided by the tax-adjusted Fisher hypothesis; see, for example,Crowder and Hoffman (1996) and Crowder (1997). When nominalinterest income is taxed, the after-tax Fisher effect implies that nominalinterest rate will adjust by more than one-for-one with movements inination. Using the Johansen technique, Crowder and Hoffman (1996)estimate the coefcient to be about 1.4 for the US over the period1952Q11991Q4 in a bivariate system. Crowder (1997) uses the samemethodology and estimates the coefcient to be between 1.51 and1.89 for Canada over the period 1960Q11991Q4. Atkins and Coe's(2002) results do not support the tax-adjusted Fisher effect for Canadaand provide mixed evidence for the US over the period 1953:011999:12.

    We follow the above literature and relax the coefcient of inationin the Fisher equation to see if it is signicantly different from 1 in themodels of the US and Canada. The modied Fisher equation can bewritten as

    rstpt b20 2;t : 9

    The estimates of * and , namely the coefcient of ination inthe Fisher equations of the US and Canadian models, are 1:9536

    0:5068 and

    1:71460:8239

    , respectively (standard errors are in parenthesis). These esti-

    mates are obtained where TS and modied Fisher are imposed on theUSmodel and TS, IRP andmodied Fisher are imposed on the Canadian

    00.20.40.60.8

    1

    0 8 12 16 20 24 28 32 36

    Notes: The solid line is the persistence profile generathe 90% confidence bands derived from 500 iteration

    4

    Fig. 1. Persistence proles of the effect of a system-wide shock to the cointegrating relations. Notlines are the 90% condence bands derived from 500 iterations of the wild bootstrap procedurCanada IRP

    00.20.40.60.8

    11.21.41.6

    US Modified Fisher

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    0 4 8 12 16 20 24 28 32 36

    0 4 8 12 16 20 24 28 32 36model. It is clear that the coefcient of ination is signicantly largerthan 1 for the US and not signicantly different from 1 for Canada.

    We examine the sensitivity of the results to the lag structureadopted for our VAR models. We consider the lag orders between 1and 8 for both the US and Canadian models and estimate * and foreach lag order. The results, reported in Table 3, show that * liesbetween 1.4 and 2.0 and lies between 1.4 and 2.2. The coefcient inthe Canadian model is never signicantly different from 1 whereas itis signicantly larger than 1 in the US model for most of the lagstructures.

    Based on the DHPS' interpretation, it seems that the Fed has over-reacted to ination persistently, so that the US interest rate has beenraised more than ination in the long run whereas the over-reactionperhaps is not as profound in the case of the Bank of Canada. But towhat extent the Fed's reaction to ination has been stronger than thatof the Bank of Canada is an issue for further research. The estimatespresented here clearly show a lack of precision.

    We proceed with the results obtained for our model with two lags:The modied Fisher equation with * = 1.9536 is imposed on the USmodel and the Fisher equation, with one-for-one relation betweeninterest rate and ination, is imposed on the Canadian model.

    4.4. Over-identifying restriction test

    Based on the results obtained in the previous sections, we imposethe Term Structure and the modied Fisher equation on the US modeland the Term Structure, Interest Rate Parity and Fisher equation on

    ted from the VECX* model and the dashed lines ares of the wild bootstrap procedure.

    es: The solid line is thepersistence prole generated from theVECX*model and thedashede.

  • 0000

    0000

    17S. Mahdi Barakchian / Economic Modelling 46 (2015) 1126US short term interest rate

    0

    0.0005

    0.001

    0.0015

    0.002

    0.0025

    US inflation

    0.00180.002

    0 4 8 12 16 20 24 28the Canadian model. This amounts to 7 and 24 over-identifying restric-tions for the models of the US and Canada, respectively. The LikelihoodRatio (LR) statistic for over-identifying restrictions is reported inTable 5. The LR test is asymptotically distributed by 2(q), where q isthe number of over-identifying restrictions (Pesaran and Shin, 2002).However, in small samples, this test tends to over-reject (Garratt et al.,2003). Therefore, we use bootstrap method to generate the criticalvalues.

    4.4.1. HeteroskedasticitySeveral studies have recently suggested that over the past two

    decades, i.e. the so-called great moderation period, the variances ofthe shocks driving macroeconomic and nancial time series havechanged and, in particular, have shown a general decline; see, for

    00.00020.00040.00060.00080.001

    0.00120.00140.0016

    Canadian short term interest rate

    0

    0.0005

    0.001

    0.0015

    0.002

    0.0025

    0000

    0000

    Canadian inflation

    -0.0005

    0

    0.0005

    0.001

    0.0015

    0.002

    0 4 8 12 16 20 24 28

    0 4 8 12 16 20 24 28

    0 4 8 12 16 20 24 28

    Notes: The solid line is the impulse responses genethe 90% confidence bands derived from 500 iteratio

    Fig. 2. Impulse responses to a USmonetary policy shock obtained from the VECX*modelwith twthe dashed lines are the 90% condence bands derived from 500 iterations of the wild bootstraUS long term interest rate

    0.0002.0004.0006.00080.001.0012.0014.0016.0018

    US output0.004

    0 4 8 12 16 20 24 28instance, Busetti and Taylor (2003), Kim and Nelson (1999) and Koopand Potter (2000). Cavaliere et al. (2010) argue that in the context oftime-varying volatility the wild bootstrap scheme is required ratherthan the standard residual resampling bootstrap scheme proposed inthe literature (for instance, in Li and Maddala, 1996). That is becausethe wild bootstrap replicates the pattern of heteroskedasticity presentin the original shocks.

    When we examine the residuals of the error correction equations ofthe US and Canadian models, we observe that the residuals of the outputequations in both countries showa clear decline in volatility over the pasttwo decades. Apart from the changes in volatility due to the great mod-eration, some other changes in volatility of the residuals can also beidentied. For example, the volatility of the residuals of the oil priceequation markedly increases from the early 1970s (rst oil price shock),

    -0.012

    -0.01

    -0.008

    -0.006

    -0.004

    -0.002

    0

    0.002

    Canadian long term interest rate

    0.0002.0004.0006.00080.001.0012.0014.0016.0018

    Canadian output

    -0.008

    -0.006

    -0.004

    -0.002

    0

    0.002

    0.004

    0 4 8 12 16 20 24 28

    0 4 8 12 16 20 24 28

    0 4 8 12 16 20 24 28

    rated from the VECX* model and the dashed lines arens of the wild bootstrap procedure.

    o lags. Notes: The solid line is the impulse responses generated from theVECX*model andp procedure.

  • 18 S. Mahdi Barakchian / Economic Modelling 46 (2015) 1126US short term interest rate

    -0.001

    -0.0005

    0

    0.0005

    0.001

    0.0015

    0.002

    US inflation0.0015

    0 4 8 12 16 20 24 28and the volatility of the residuals of the US short and long term interestrates rises over the period 19781982 (the Volcker shock period).

    Table 4 presents the results of heteroskedasticity test for theresiduals of the error correction equations. The null hypothesis ofhomoskedasticity is rejected for ve equations at 1% and for twoequations at 10% signicance levels.

    Therefore, we employ the wild bootstrap procedure with the boot-strap residuals generated according to the technique proposed inCavaliere et al. (2010). See Appendix A for a description of the bootstrapprocedure.

    To our knowledge, no one has yet investigated the statistical proper-ties of the wild bootstrap scheme for the over-identifying restrictionstest. The wild bootstrap has not also been used in any empirical studyto compute the critical values of the over-identifying restrictions test.

    -0.0015

    -0.001

    -0.0005

    0

    0.0005

    0.001

    Canadian short term interest rate

    -0.001

    -0.0005

    0

    0.0005

    0.001

    0.0015

    0.002

    Canadian inflation

    -0.0015

    -0.001

    -0.0005

    0

    0.0005

    0.001

    0.0015

    0 4 8 12 16 20 24 28

    0 4 8 12 16 20 24 28

    0 4 8 12 16 20 24 28

    Notes: The solid line is the impulse responses generthe 90% confidence bands derived from 500 iteratio

    Fig. 3. Impulse responses to aUSmonetary policy shockobtained from theVECX*modelwith eigthe dashed lines are the 90% condence bands derived from 500 iterations of the wild bootstraUS long term interest rate

    -0.0006-0.0004-0.0002

    00.0002

    0.00040.00060.00080.001

    US output0.004

    0 4 8 12 16 20 24 28Hence, in order to compare between the results of the standard andwild bootstrap schemes,we present the CVs generated by both schemesin Table 5.

    The CVs here are generatedwith 1000 replications. The results showthat the wild bootstrap generates wider condence intervals than thestandard bootstrap: the over-identifying restrictions of the US modelare not rejected at 1% signicance level using the wild bootstrap butare rejected using the standard bootstrap; the over-identifying restric-tions of the Canadian model are not rejected at 10% and 5% signicancelevels when the wild and standard bootstraps are used, respectively.Due to the heteroskedasticity present in the residuals, we use theCVs generated by the wild bootstrap and conclude that the over-identifying restrictions are not rejected in the models of Canada andthe US, i.e. the Term Structure and modied Fisher equation are

    -0.008

    -0.006

    -0.004

    -0.002

    0

    0.002

    Canadian long term interest rate

    -0.0006

    -0.0004

    -0.0002

    0

    0.0002

    0.0004

    0.0006

    0.0008

    0.001

    Canadian output

    -0.008

    -0.006

    -0.004

    -0.002

    0

    0.002

    0.004

    0 4 8 12 16 20 24 28

    0 4 8 12 16 20 24 28

    0 4 8 12 16 20 24 28

    ated from the VECX* model and the dashed lines arens of the wild bootstrap procedure.

    ht lags. Notes: The solid line is the impulse responses generated from theVECX*model andp procedure.

  • 19S. Mahdi Barakchian / Economic Modelling 46 (2015) 1126US short term interest rate

    -1.5

    -1

    -0.5

    0

    0.5

    1

    1.5

    2

    US inflation0.003

    0 12 24 36 48 60 72 84maintained in themodel of the US and the Term structure, Fisher equa-tion and Interest Rate Parity are maintained in the model of Canada.

    Fig. 1 shows that the persistence proles of all ve long run relationsin the VECX* model die out very fast after a system-wide shock hitsthe cointegrating relations. The half life of the shocks ranges from onlyone quarter for the US modied Fisher equation to six quarters for theCanadian Term Structure relation. This conrms that the theoreticlong run relations are empirically valid.

    4.5. Error Correction Equations of the Canadian Model

    The estimates of the reduced form error correction equations of theCanadian model with a number of diagnostic statistics are reported in

    -0.004

    -0.003

    -0.002

    -0.001

    0

    0.001

    0.002

    Canadian short term interest rate

    -2

    -1.5

    -1

    -0.5

    0

    0.5

    1

    1.5

    2

    Canadian inflation

    -0.004

    -0.003

    -0.002

    -0.001

    0

    0.001

    0.002

    0.003

    0 12 24 36 48 60 72 84

    0 12 24 36 48 60 72 84

    0 12 24 36 48 60 72 84

    Notes: The solid line is the impulse responses generated from90% confidence bands produced by Monte Carlo methods (50Romer (2004, footnote 17).

    Fig. 4. Impulse responses to the Romer& Romer shock obtained from a single equationmodel. Nthe dashed lines are the 90% condence bands produced by Monte Carlo methods (500 replicaUS long term interest rate

    -1.5

    -1

    -0.5

    0

    0.5

    1

    US output0.03

    0 12 24 36 48 60 72 84Table 6. The adjusted R2 of the different equations (except the realexchange rate) is quite reasonable; it ranges from 0.34 for the outputto 0.75 for the long term interest rate. Overall, the diagnostic testsindicate that the model performs well; The test for functional form isrejected for none of the equations and the test for serial correlation isrejected only for the ination equation. The test for normality, however,is rejected for all equations except for the short term interest rate. Theerror correction equations reveal some interesting results:

    First, the only three variables which are signicant (at 10% level) inthe real exchange rate equation are the IRP term, and the Canadianand US short term interest rates. The coefcients of these variablesshow that raising Canadian interest rate relative to US interest ratewill appreciate the Canadian currency (in real terms), as to be expected.

    -0.06-0.05-0.04-0.03-0.02-0.01

    00.010.02

    Canadian long term interest rate

    -1-0.8-0.6-0.4-0.2

    00.20.40.60.8

    1

    Canadian output

    -0.07

    -0.06

    -0.05

    -0.04

    -0.03

    -0.02

    -0.01

    0

    0.01

    0 12 24 36 48 60 72 84

    0 12 24 36 48 60 72 84

    0 12 24 36 48 60 72 84

    the single equation model and the dashed lines are the0 replications) following the methodology in Romer and

    otes: The solid line is the impulse responses generated from the single equationmodel andtions) following the methodology in Romer and Romer (2004, footnote 17).

  • Canada OC

    11.21.41.6

    Canada PPP

    00.20.40.60.8

    11.21.41.6

    0 4 8 12 16 20 24 28 32 36

    eration

    Notdur

    20 S. Mahdi Barakchian / Economic Modelling 46 (2015) 1126Second, the effect of oil price changes in all equations is very smalland mostly insignicant. Its effect on output is signicantly positive,though very small. This observation is consistent with other studieswhichnd oil price level to be almost neutral for the Canadian economy(see Bashar et al., 2013, and IMF, 2005).

    Third, in the output equation, the TS term is signicant (at 5% level).It shows that raising short term interest rate relative to long terminterest rate has a considerable signicant negative effect on outputwhich is consistent with studies like Estrella and Mishkin (1998).

    Fourth, in all the equations, the analogous US variable (at time t) ishighly signicant (at 1% level). The sign of the coefcient of the USvariable is positive and its size is considerable. In particular, the coef-cient of rlt in the equation of the Canadian long term interest rate(rtl), is 0.875,which shows that 1% increase in theUS long term interestrate raises the Canadian long term interest rate by 0.9% within thequarter. This result demonstrates the strong and quick effect of the USeconomy's uctuations on the Canadian economy.

    Fifth, the IRP error correction term, ^3;t1, enters signicantly in allequations except the ination equation. The sign of ^3;t1 in all theseequations is economicallymeaningful. This interesting result underlinesthe fact that the US monetary policy drives the Canadian economy viainterest rate path-through mechanism.

    Sixth, in the short term interest rate equation, only ^3;t1 and rts

    are signicant at 5% signicance level.7 Therefore, we can present theshort term interest rate equation as:

    rst 0:2130:093

    ^3;t1 0:6220:091

    rst u2t : 10

    This equation shows that the Canadianmonetary policy is extremelyinuenced by theUSmonetary policy. Based on this equation, as soon asthe Fed raises the US short term interest rate by 100 basis points, the

    00.20.40.60.8

    0 4 8 12 16 20 24 28 32 36

    Notes: The solid line is the persistence profile genthe 90% confidence bands derived from 500 iterat

    Fig. 5. Persistence proles of the effect of a system-wide shock to the cointegrating relations.lines are the 90% condence bands derived from 500 iterations of the wild bootstrap proceBank of Canada follows the US by raising the Canadian short terminterest rate by 62 basis points. Moreover, the signicance of ^3;t1ensures that the Canadian short term interest rate converges to the USshort term interest rate in the long run reasonably fast. When we dropthe US interest rates from the VARX* model of Canada, the adjusted R2

    drops from 0.58 to 0.30 for the Canadian short term interest rate equa-tion (It drops dramatically from 0.75 to 0.14 for the Canadian long terminterest rate.) This again emphasizes the inimitable role of USmonetarypolicy in shaping Canadian monetary policy.

    As it is clear from Eq. (10) and also from the strong correlationbetween the Canadian and US short term interest rates, the Bank of

    7 The coefcient of the exchange rate in the interest rate equation is insignicant. Al-though the exchange rate is an important part of the transmission mechanism in shapingmonetary policy, measuring the response of themonetary policy tool to the exchange rateis problematic. This is due to the simultaneous response of the exchange rate tomonetarypolicy changes. See, for example, Demir (2014) on how to identify the exchange rate's ef-fect on monetary policy using high-frequency data.Canada's strategy generally involves moving its interest rate in linewith US interest rate. This strategy has been at the center of debatesamong Canadian policy makers. For example, in one of the sessions ofthe Standing Committee of Finance in the Parliament of Canada atMay 16, 2000, members of the parliament challenged Governor of theBank of Canada for his monetary policy:8

    This afternoon, the American federal bank, in view of the overheatingin the U.S., is getting ready to raise the American interest rate by abouthalf a point. What does the Bank of Canada plan to do? Does it simplyintend to increase the Canadian interest rates by half a point too, theway it usually does, because, in my opinion, the Canadian monetarypolicy is not autonomous.

    [Yvan Loubier, MP]

    In Canada, you must always look at what is happening in the U.S.because this country is our biggest partner for foreign trade. whenthe federal reserve increases its interest rates, this is a very importantpiece of information for us. Sometimes we follow the U.S., sometimeswe decide not to follow.

    [Gordon Thiessen, Governor of the Bank of Canada]

    In the debate about the independence of Canadian policy, most of theexperts agree that, if the U.S. Federal Reserve raises its short-term inter-est rates by half a point, or 50 basis points, it is quite possible, indeedalmost certain, that the Bank of Canada will keep step by deciding onan increase of 25 or 50 basis points. This is a trend that has beenobserved for several years and it raises the entire question of theindependence of Canada's monetary policy in relation to U.S. monetarypolicy.9

    ed from the VECX* model and the dashed lines ares of the wild bootstrap procedure.

    es: The solid line is thepersistence prole generated from theVECX*model and thedashede.[Richard Marceau, MP]

    As we see in the next section, the impulse response functionsalso provide support for interest-rate-path-through mechanism viapresenting the time prole of the response of the Canadian monetaryauthority to US monetary policy shock.

    8 See the website of the parliament of Canada at http://www2.parl.gc.ca/HousePublications/Publication.aspx?DocId=1040348.&Language = E&Mode = 1&Parl = 36&Ses = 2.9 As another example, John Crow (2002, pp. 152153), Governor of the Bank of Canada

    19871994, discusses this strategy in the case of the Canadian response to the Volker dis-ination: At the start of the 1980s, the Bank's monetary policy was to all intents forced byevents outside our borders - namely, the great America disination led by the Federal Reserve'sPaul Volcker. Confronted itself with the fallout from the U.S. decision to confront ination,the Bank of Canada decided to try to hang on to the U.S. dollar exchange value for our currency.This meant, in practice, at least matching U.S. rate increases.

  • Fig. 2 shows that a contractionary US monetary policy shock is

    Table 3Estimate of the coefcient of ination in the Fisher equation.

    Lag order

    1 2 4 6 8

    US (*) 1:64180:3772

    1:95360:5068

    1:80550:5893

    1:42430:2901

    1:56090:3265

    Canada () 1:44900:4805

    1:71460:8239

    1:52200:9294

    2:20031:7938

    1:63120:6089

    Note: The US cointegrated model is estimated with two long run relations (TS andmodied Fisher) and the Canadian cointegrated model is estimated with three long runrelations (TS, modied Fisher and IRP). Critical value for a one tailed t test at 5%signicance level is 1.645. * denotes signicance at 5% level. The sample period is1958Q1 to 2004Q2.

    Table 5Long run over-identifying restrictions test.

    # LR statistic Bootstrap scheme CV 90% CV 95% CV 99%

    US 7 33.65 Standard 21.27 24.57 31.68

    21S. Mahdi Barakchian / Economic Modelling 46 (2015) 11265. Impulse Response Functions (IRF)

    The literature of the identication of US monetary policy shocksis founded on the idea that US monetary policy instruments are notexogenous with respect to other US macro variables and therefore cannot be used directly to estimate the effects of monetary policy onmacro variables. This logic can be extended to the case of cross-country effects of US monetary policy. Although in reality the USmonetary policy instrument (US short-term interest rate) may notrespond directly to movements in the Canadian economy but the USand Canadian economies may be affected by common shocks. In thiscase there is an endogenous component in the US monetary policyinstrument with respect to Canadian macroeconomic variables and itcannot be used as an exogenous variable to estimate the effects of USmonetary policy on the Canadian economy. Therefore, we need todecompose the US monetary policy instrument into systematic andshock components and use the shock component, as an exogenousvariable with respect to the Canadian macroeconomic variables, toestimate the effects of US monetary policy on the Canadian economy.

    It is widely accepted that the Fed does not generally target exchangerates or foreign variables directly; see for example Meulendyke (1998).Therefore, in order to identify US monetary policy shock, we assumethat the US short term interest rate is not adjusted in response toidiosyncratic foreign shocks. This is similar to the assumption adoptedby studies like Scrimgeour (2010). This assumption implies that if ameasure of monetary shock is exogenous to US variables, it is alsoexogenous to Canadian variables. This assumption justies the useof the US monetary policy shock identied in our closed US model toestimate the effects of the US shock on Canadian variables.

    Christiano et al. (1999) show that to identify the effects of monetarypolicy shocks on other variables in an exactly-identied short runstructure, only specifying the place of monetary policy variable in thevector of variables is crucial and the position of the other variablesrelative to each other is not important. Hence, the IRFs are invariant tothe ordering of the Canadian variables in the VECX* model, so long asthe contemporaneous correlations of these variables are left unrestricted.In summary, we only need to identify a short-run structure for the USvariables.Table 4Heteroskedasticity test.

    US rts rtl pt yt pto

    0.366 17.798*** 9.802*** 3.489* 19.351***

    Canada etr rts rtl pt yt

    0.540 3.647* 8.592*** 10.139*** 0.832

    Notes: The US cointegrated model is estimated with two long run relations (TS andmodied Fisher) and the Canadian cointegrated model is estimated with three long runrelations (TS, Fisher and IRP). * ,** and *** denote signicance at the 10, 5, and 1% levels.Critical values of 2(1) for 10, 5 and 1% signicance levels are 2.706, 3.841 and 6.635,respectively. The sample period is 1958Q1 to 2004Q2.associated with a signicant quick rise in the US ination and shortterm interest rate which is followed by a moderate decline. Theresponse of the US ination and short term interest rate remain signi-cantly positive over the horizon of 30 quarters. This is the well-knownprice puzzle which will be investigated further in the next section.The US long term interest rate gradually increases and the US outputrst rises, though not signicantly, and then falls. The response of theUS output becomes negative (though not signicant) after threequarters and it becomes signicantly negative after one year and ahalf. The gures show that the IRFs of the Canadian variables are verysimilar to the IRFs of the US variables. However, although the Canadianination rises in response to a contractionary USmonetary policy shock,but the shape of the response is different from that of the US ination.Besides, the negative response of the Canadian output never becomessignicant.

    5.1. Sensitivity of the Impulse Response Functions to the Lag Structure

    The presence of the price puzzle in the IRFs indicates that either theUS monetary policy shock derived from the model is not sufcientlypurged of the endogenous movements of interest rate originated fromresponse to conditions of the economy, or the model does not allowthe monetary shock to be passed on completely into the economy, ora combination of both of them. There are several factors which canexplain either of the above possibilities. One factor, for example, is theomitted variables problem. If the variables which will be consideredWe adopt an structure which is similar to the recursive orderingsuggested by Christiano et al. (1996,1999) to identify US monetarypolicy shock in the closed US cointegrated VAR model. Based on thisstructure, macro variables respond to the shock only with a lag whereasnancial variables respond instantaneously. Also, monetary authorityreacts to oil price, as an information variable of inationary expectations,contemporaneously. Therefore the variables in the US model areordered as: output, ination, oil price, short term interest rate and longterm interest rate. See Appendix A for the derivation of the IRF for theVECX* model.10

    Wild 25.57 30.39 43.16Canada 24 61.42 Standard 59.32 64.29 73.46

    Wild 63.82 69.30 80.90

    Note: The US cointegrated model is estimated with two long run relations (TS andmodied Fisher) and the Canadian cointegrated model is estimated with three long runrelations (TS, Fisher and IRP). The critical values are simulated using both the standardand wild bootstrap schemes. The sample period is 1958Q1 to 2004Q2. # denotes thenumber of over-identifying restrictions.by the Fed when settingmonetary policy is not included in the reactionfunction, it will bias the shocks and consequently the IRFs; see, forexample, Christiano et al. (1999), and Sims and Zha (2006), for therole of commodity prices in resolving the price puzzle. Similarly, ifthe variables which are critical in transmitting monetary policy intothe economy are not included in themodel, it will create another sourceof bias for the IRFs. But, in this sectionwewould like to focus on anotherfactor which could explain the price puzzle observed and that is thechoice of lag order.

    10 All the estimations, construction of the VECX* model, and generation of the persis-tence proles and impulse response functions were done using the GAUSS software.

  • VARs with the lag orders selected by the SIC perform better in short-run forecasting. It is well known that the SIC generally underestimatesthe lag order of a VAR in small samples and therefore selects a moreparsimonious model.

    However, when it comes to impulse response functions the storychanges dramatically. Using a Monte Carlo experiment, Kilian (2001)shows that the effects of overtting and undertting a VAR are stronglyasymmetric for impulse response functions and the costs associated

    shock reaches its maximum impact on output after 2 years; the US

    22 S. Mahdi Barakchian / Economic Modelling 46 (2015) 1126Table 6Error correction equations of the Canadian model.

    Equation etr rts rtl 2pt yt

    ^1;t1 0:2170:592 0:0030:040 0:041

    0:016 0:199

    0:112 0:462

    0:194

    ^2;t1 0:3310:284 0:031

    0:019 0:008

    0:008 0:171

    0:054 0:037

    0:093

    ^3;t1 2:513

    1:367 0:213

    0:093 0:113

    0:037 0:193

    0:259 1:110

    0:447 et 1r 0:043

    0:077 0:0090:005

    0:0010:002

    0:0330:015

    0:0190:025

    rt 1s 3:0281:233

    0:0780:084

    0:1150:034

    0:2050:234

    0:4320:403

    rt 1l 0:3372:942

    0:0460:200

    0:0730:080

    0:0960:557

    0:4180:963

    2pt 1 0:3190:388

    0:0460:026

    0:0100:011

    0:2950:074

    0:0930:127

    yt 1 0:1040:233

    0:0140:016

    0:0050:006

    0:0390:044

    0:0850:076

    rt 1s 2:6271:580

    0:1670:107

    0:0780:043

    0:4350:299

    0:4830:517

    rt 1l 2:0663:152

    0:0100:214

    0:0450:086

    0:0260:597

    1:3331:031

    2pt 1 0:1090:547

    0:0230:037

    0:0020:015

    0:2320:104

    0:2550:179

    yt 1 0:1580:238

    0:0160:016

    0:0100:006

    0:0280:045

    0:1810:078

    pt 1o 0:0000:015

    0:0010:001

    0:0010:000

    0:0050:003

    0:0040:005

    rts 1:6291:339

    0:6220:091

    0:0040:037

    0:2160:254

    0:1130:438

    rlt 2:4601:992 0:2620:135

    0:8750:054

    0:1950:377

    1:0470:652

    2pt 0:2910:520

    0:0420:035

    0:0150:014

    0:4680:099

    0:1440:170

    yt 0:2820:215

    0:0200:015

    0:0000:006

    0:0900:041

    0:3350:070

    pto 0:0190:014

    0:0020:001

    0:0010:000

    0:0000:003

    0:0100:005

    R2 0.039 0.576 0.753 0.338 0.341It is well know that the lag order selected for a VAR model canaffect the dynamic properties of impulse responses and can even changethe interpretation of impulse response estimates of a VAR; seee.g. Hamilton and Herrera (2004) and Kilian (2001). Faced with aproblem similar to ours, Bluedorn and Bowdler (2011) nd that theprice responses depend crucially on the number of lags of themonetarypolicy shock included in the model: by increasing the number ofmonthly policy shock lags from 6 to 48, the price puzzle disappearswhile preserving many of the other impulse responses.

    It is generally accepted in the literature that monetary policy takesmore than one year to be transmitted fully into the economy andempirical studies in this area usually consider between 1 to even4 years lag in their models. Romer and Romer (2004), for example,include three years lag in their VAR and four years lag in their singleequation model when estimating the response of price to monetarypolicy shock.

    Lag order selection for a VAR is a sensitive issue with serious conse-quences. Abadir et al. (1999) show that adding irrelevant variables(lags) to a nonstationary VAR increases the bias of all the estimators(this is in contrast with the theory for stationary data where addingirrelevant variables (lags) increases the variance of estimators butdoes not affect biases). They also show that as the dimension of theVAR increases the variance and hence the mean squared error of theestimators increases. Their ndings therefore favor parsimoniousmodeling.

    Consistentwith the results of Abadir et al., it is widely believed that amore parsimonious lag structure in a VAR leads to a better forecastingperformance. For example, Ltkepohl (1985, 1991) shows that the

    SC : 2(1) 0.575 1.582 .019 4.231 1.744FF : 2(1) 0.104 1.003 .951 2.911 0.206N : 2(2) 20.99 2.003 13.46 10.62 7.83HS : 2(1) 0.540 3.647 8.592 10.139 0.832

    Note: The error correction terms ^1;t1; ^2;t1 and3;t1, correspond to the Term Structure,

    Fisher equation and Interest Rate Parity, respectively. , and denote signicanceat the 10, 5, and 1% levels. SC is a test for serial correlation, FF a test for functional form, N atest for normality andHS a test for heteroscedasticity. Critical values are 3.84 for2(1) and5.99 for 2(2). The sample period is 1958Q1 to 2004Q2.ination rises rst and then falls; however, it rises signicantly only inthe rst quarter after the shock and then starts to decline; it becomesnegative after ve quarters and the negative impact on the US inationbecomes marginally signicant after about two years (between the 8thand 15th quarters); nally the US ination converges to the initialequilibrium; the US short-term interest rate jumps immediately afterthe shock and peaks in the rst quarter and then gradually falls; andthe US long-term interest rate jumps instantly after the shock, peaksafter one year and then steadily declines.

    The IRFs of the Canadian variables are similar to the IRFs of the USvariables. Actually, the responses of the Canadian short and long terminterest rates are almost identical to the responses of the US interestrates. The response of the Canadian ination is slightly weaker andslower than that of the US ination and the negative response neverbecomes signicant. But the negative effect of a contractionary USmonetary shock on the Canadian output is more persistent than onthe US output.12 The responses of the Canadian variables apparentlyconrm the interest rate-path-through mechanism as opposed to theMFD mechanism.

    5.2. Impulse Response Function using Romer and Romer (2004) Shock

    In order to assess the reliability of the IRFs simulated using theVECX*model, we also estimate another set of IRFs using Romer and Romer's(2004) monetary policy shock series. Romer and Romer (2004) employa narrative approach to construct a series of US monetary policy shocksfor the period 19691996. They estimate a reaction function in whichthe desired Fed Funds target rate, as agreed to at Federal Open MarketCommittee (FOMC) meetings, is the dependent variable and theestimates/forecasts for unemployment, real GDP growth and the changein the GDP deator, taken from the Greenbook forecasts, are theexplanatory variables.13 The error term from this reaction function isinterpreted as the monetary policy shock. Following Romer and Romer

    11 The results for the models with the other lag orders are available upon request.12 We also examinedwhether the IRFs obtained from the VECX*model is sensitive to thevalue of * and in Eq. (9). The results show that the variation of * and , where* {1, 2.0}, {1, 2.2}, has almost no effect on the IRFs in the rst year after the shockand a marginal effect after the rst year.13 The Greenbook forecasts are prepared by the Federal Reserve staff and are presentedwith undertting tend to be disproportionately larger. Kilian suggeststhat it is safer to include extra lags (even higher lag orders thansuggested by the AIC) rather than to truncate the lag order early. Insummary, it seems that the literature suggests one to select differentlag orders for different purposes: a more parsimonious lag order forshort (to medium) run forecasting whereas a less parsimonious lagorder for impulse response analysis.

    Concerned with the extra cost of undertting, we set the maximumlag at 8, andwe increase the number of lags in ourmodel between p=2to p = 8. The results show that increasing the number of lags alleviatesthe price puzzle, indeed.

    Fig. 3 presents the IRFs derived from the VECX* model with p= 8.11

    After a contractionary US monetary policy shock, US output falls veryquickly and shows the well-known U-shaped response; the monetaryto the FOMC before each meeting.

  • (2004), we estimate the effects of the US monetary shock on US andCanadian variables using a single equation framework14:

    xt a0 XIi1

    bixti XJj1

    c jst j et ;

    where x is the macro variable of interest and st is the Romer & Romershock measure. Our regression runs from 1970:01 to 2004:06.15 Thedecision to exclude any other explanatory variable from the regressionis based on the assumption that the shock is not affected by otherexplanatory variables that inuence the dependent variable. In otherwords, the shock is purely exogenous with respect to other variablesby construction. Based on this assumption, the estimates of the coef-cients of the regression equation will be unbiased. The dependentvariables, x, are monthly US and Canadian industrial production (IP),consumer price ination (CPI), treasury bill rate and 10-years govern-

    23S. Mahdi Barakchian / Economic Modelling 46 (2015) 1126ment bond rate. Following Romer andRomer (2004), the number of lagsof dependent variable, I, is set at 24, and the number of lags of the shock,J, is set at 36 (48) for IP (CPI).We set a shorter lag structure for interestrates, where I= 12 and J= 24, because nancial variables are believedto respond to shocksmore quickly. However, the shape of the responsesof the interest rates to the USmonetary shock remain virtually the samewhen different combinations of the lag structures (I,J) are considered.Following Romer and Romer, we assume that the monetary shockdoes not affect IP and CPI within the month. However, we allow theshock to impact interest rates contemporaneously. These assumptionsare consistent with the recursive structure of Christiano et al. (1996,1999).

    The responses of the level of the variables to a Romer & Romer shockof one percentage point are reported in Fig. 4. The impulse responsefunctions estimated using the Romer & Romer shock are similar to theIRFs obtained using the VECX* model with eight lags (Section 1). Aftera contractionary USmonetary policy shock, US output falls very quickly(after a small rise at the beginning) and show thewell-knownU-shapedresponse; the monetary shock reaches its maximum impact on outputafter two years; the US ination rises rst and then starts to decline;ination falls below zero after about two years and remains negativefor the rest of the horizon (the high variation of the ination's impulseresponse is due to the high volatility of monthly ination); onedifference between these IRFs and the IRFs obtained from the VECX*model is that the responses of the US and Canadian ination ratesremain signicantly negative after almost four years using the Romer& Romer shock, whereas they converge to zero in the VECX* model.This is consistent with the Romer and Romer's (2004) claim that theresponse of price to the Romer & Romer shock is stronger than theresponse to the shocks derived from the standard recursive identica-tion schemes. The US short-term interest rate jumps immediately

    14 Romer and Romer (2004) use the single equation regression method to estimate theeffects of the Romer & Romer shock on theUS economy. Scrimgeour (2010) uses the samemethod to estimate the effects of the Romer & Romer shock on four countries in theAmericas. Our exercise in this section deviates from these studies in several respects,though in essense is similar to them. First, we use an extended series of the Romer &Romer shock (our series end in 2004:06 instead of 1996:12). Second, we estimate the re-sponse of consumer price ination, and not price level, to the shock (Romer and Romer es-timate the effects on the level of PPI for nished goods and Scrimgour does not estimatethe effects of the shock on price level). Third, we estimate the responses of both shortand long term interest rates to the shock where I = 12 and J = 24 (Romer and Romerdo not estimate the effect of the shock on interest rates and Scrimgour esimates onlythe response of the short-term interest rate, where he considers I= 24 and J= 36).15 See Barakchian and Crowe (2013) on how the Romer& Romer shock is extended from1997:01 to 2004:06. Similar to Romer and Romer (2004), the regression is run from

    1970:01 with the values of st before 1969:03 are set at zero.after a contractionary US monetary shock and peaks in the rst monthafter the shock and then declines gradually; the US long-term interestrate jumps instantly after the shock, peaks after thirteen months andthen steadily declines; and both the short- and long-term interestrates converge to their equilibrium, which is around zero, after twoyears.

    Here again the impulse responses of the Canadian variablesare similar to the impulse responses of the analogous US variables.The responses of the Canadian short- and long-term interest ratesare almost identical to the responses of the US interest rates.Similar to the result obtained from the VECX* model, the negative re-sponse of the Canadian output is more persistent than that of the USoutput.

    6. Conclusion

    In this paper, following the GVARmodeling strategy we constructeda two-country VECX* model comprising a structural cointegratedVARX* for Canada and a structural cointegrated VAR for the US.We used the VECX* model to shed light on the links connecting theCanadian economy to the US economy in both short and long run.

    The results show that in the long run, the (modied) Fisher equationand the Term Structure relation hold in both the US and Canadianeconomies and the Interest Rate Parity between the US and Canadais highly crucial in driving the Canadian economy. However, nostrong evidence was found to support the Purchasing Power Parityand Output Convergence relationship between the US and Canadianeconomies.

    Then we examined the transmission of US monetary policy shocksinto the Canadian economy using the VECX* model. We found that theimpulse response functions are sensitive to the lag structure. In particu-lar, with a short lag structure (p= 2), the price puzzle was pronouncedand, that increasing the lag order could alleviate the price puzzle. Theimpulse responses obtained from the VECX* model with a relativelylarge lag order (p = 8) showed that the responses of the Canadianmacro variables to the US monetary policy shock are similar to theresponses of the US macro variables to the same shock: after a contrac-tionary US monetary policy shock, output falls quickly and shows aU-shaped response, ination falls with a delay and nally convergesto the initial equilibrium, short-term interest rate jumps and thengradually declines and long-term interest rate increases for one yearand then gradually declines. The impulse responses estimated througha single-equation model using the Romer and Romer (2004) shockmeasure were similar to the impulse responses obtained using theVECX* model. Our results conrmed that interest rate-path-through isthe most important mechanism by which US monetary policy shocksare transmitted into the Canadian economy.

    Appendix A

    A.1. Denitions and sources of variables

    The data set contains quarterly observations on the US and Canada,from 1958Q1 to 2004Q2. The Canadian variables included are (log)real per capita output, yt, (log) price level, pt, the nominal quarterlyshort term interest rate, rts, the nominal quarterly long term interestrate, rtl, and (log) exchange rate, et. Specically

    yt ln GDPt=POPt ; pt ln Pt ; et ln Et ;rst 0:25ln 1 Rst=100

    ; rlt 0:25ln 1 Rlt=100

    ;

    where GDPt is real gross domestic product volume index (seasonallyadjusted and indexed at 100 in 2000), Pt is the consumer price index(seasonally adjusted and indexed at 100 in 2000), Rts is the treasury

    lbill rate (percent per annum), Rt is the 10 years bond rate (percent

  • mic Modelling 46 (2015) 1126per annum), and Et is the Canadian currency per US dollar (indexed at100 in 2000). The US variables, yt, pt, rts , rtl , are constructed usingthe same method.

    POPt is constructed as a quarterly series through linear interpolationof the annual series and then converted into an index number (indexedat 1 in 2000). The oil price variable, pto, is constructed as pto = ln(POILt),where POILt is the average price of crude oil in terms of US dollar perbarrel (indexed at 100 in 2000).

    The data were obtained from the International Financial Statistics,IMF. GDP and CPI series are seasonally adjusted using the X12-ARIMAmethod.

    The monthly series used for the single-equation regression modelare the original monthly series (seasonally adjusted series for IndustrialProduction and CPI) which were also obtained from the InternationalFinancial Statistics.

    A.2. Derivation of impulse response function

    In order to derive the formula for impulse response function, westart with the VAR representation of the VECX* model, Eq. (3):

    zt Xpi1izti a bt Hvt :

    The moving average representation of the above equation can bewritten as

    zt C L a bt Hvt 11

    where

    C L Xj0

    C jL j C 1 1L C L ;

    C L Xj0

    Cj L j; and Cj

    Xi j1

    Ci;

    C0= Im, C1=1 Im, Ci=1Ci 1+2Ci 2++pCi p, for i N 2,and Ci = 0 for i b 0. By forward cumulating of Eq. (11), one can obtainthe moving average representation of the level of variables as

    zt z0 b0t C 1 Xtj1

    Hv j C L H vtv0 ; 12

    where b0 = C(1)a+ C*(1)b.To derive the impulse response function of zt + n with respect to a

    structural shock, it, requires imposing a structure on the contempora-neous coefcientsmatrix. Aswe argued in Section 5, under our assump-tions US monetary policy shock is identied by imposing a structure onthe contemporaneous coefcients matrix of the US cointegrated VARmodel while the Canadian model is left unrestricted. So we order thevariables in the US model according to the Christiano et al.'s (1996,1999) identication scheme as: output, ination oil price, short terminterest rate and long term interest rate.

    Consider the US VAR model

    xt Xpi1i x

    ti a bt ut : 13

    Premultiply Eq. (13) by P01,

    P01x

    p

    P01x P

    01a P01bt P

    01u

    24 S. Mahdi Barakchian / Econot i ti twhere P* is the Cholesky factor of u ; it is an upper triangular matrixsuch that u P

    0P , and u cov ut . The structural shocks are

    dened as

    t P01ut

    and the identication conditions are given by (i) cov t Im , (ii)P01

    is lower triangular.Now, consider the VAR representation of the VECX* model (Eq. (3))

    and premultiply it by H1,

    H1zt Xpi1

    H1izti H1aH1bt vt : 14

    To derive the structural shocks, we premultiply Eq. (14) by

    P10 P01 0mm

    0mm Im

    " #

    to obtain

    P10 H1zt

    Xpi1

    P10 H1izti P10 H1a P10 H1bt t

    where

    t tut

    ;

    cov t cov t ;

    t

    cov t ;ut

    cov ut ;

    t

    cov ut ;ut

    with

    cov t ; t

    Im ; cov t ;ut cov P01ut ;ut P

    01u;u; cov ut ;ut u:

    Since vt = P0t, Eq. (12) can be written as

    zt z0 b0t C 1 Xtj1

    Hv j C L HP0 t0 :

    Therefore the impulse response function is given by

    sir f n; z : i 1ii

    p eCnHP0Si; i 1;;m; n 0;1;

    A.3. The bootstrap algorithm

    To produce critical values for the over-identifying restrictions LR testusing the standard bootstrap, we follow the procedure proposed inGarratt et al. (2006, Ch. 6). For the wild bootstrap, we follow the sameprocedure but instead of resampling the residuals we use the devicesuggested by Cavaliere et al. (2010) to generate the wild bootstrapresiduals:

    v^ n t v^tn;t 15

    where {n,t}t = 1T , n = 1, , N denotes a doubly independent N(0,1)scalar sequence (T is the sample size and N is the number of iterationsof the bootstrap procedure). Cavaliere et al. show that the simulatederrors preserve the pattern of heteroskedasticity present in the original

    sample.

  • The algorithm used to produce condence bounds for the persis-tence proles and impulse response functions is as follows:

    Step 1: We follow Cavaliere et al. (2010) and generate the bootstrapresiduals, v^ n t ; t 1;; T , according to the device presentedin Eq. (15).

    Step 2: Similar to the standard bootstrap procedure, as in e.g. Li andMaddala (1996), we construct the bootstrap sample zt(n), t =1,, T, recursively using the VAR representation of the VECX*model

    z n t ^1z n t1 ^2z n t2 a^ b^t H^v^ n t ; t 1;; T; 16

    where ^1; ^2; a^; b^ and are the estimates of the parametersof the model obtained from the estimation over 1958Q12004Q2, and the actual realizations are used for the initialvalues, z1,, zp.

    Step 3: Using the simulated sample zt(n), t = 1, , T, a structural

    VAR for the US are estimated for given long run relations. Theshort run parameters are re-estimated at each iteration of thebootstrap procedure. After that, we combine the Canadianand US models to create a new VECX* model and generatepersistence proles and impulse response functions from thebootstrapped VECX* model.

    Step 4: We iterate Steps 1 to 3, N times to generate N samples of thepersistence proles and impulse response functions.

    A.4. Unit root tests

    References

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    Table 7Augmented DickeyFuller unit root test for the rst differences of the variables.

    ADF(0) ADF(1) ADF(2) ADF(3) ADF(4)

    yt 2.17 1.73 2.05 2.43 2.69pto 1.59 1.26 1.25 1.23 1.22

    only include intercept. The relevant 5% critical values are 2.88 for the case with justintercept and 3.45 for the case with both intercept and trend. The sample period is1958Q1 to 2004Q2.

    25S. Mahdi Barakchian / Economic Modelling 46 (2015) 1126etr 12.42 8.52 6.06 5.30 5.77*rts 10.50 9.60* 7.23 7.17 6.04rtl 11.60 9.58 6.94 5.87 6.53*pt 4.15 3.00 2.47 2.49 1.93*2pt 19.20 13.66 9.65 10.05 9.11*yt 10.51 7.30 5.39 6.02* 5.55rts 10.80 10.97 6.42 6.33 4.59*rtl 10.36 8.78 6.39 6.28 6.77*pt 3.79 3.05 2.34 2.87* 2.672pt 17.36 14.24 8.21* 7.63 7.00yt 9.62 6.87* 6.21 6.46 5.88ptO 10.09 9.37 6.71 667 6.75*

    Table 8Augmented DickeyFuller unit root test for the levels of the variables.

    ADF(0) ADF(1) ADF(2) ADF(3) ADF(4)

    etr 1.83 1.99 2.14 2.58* 2.73rts 1.72 2.26 1.96* 2.14 1.89rtl 1.43 1.62* 1.51 1.65 1.72pt 1.13 0.63 1.06 1.40 1.35yt 1.38 1.61 1.77 2.02 1.73*rts 1.66 2.19 1.63 2.31* 2.10rtl 1.45 1.81 1.72 1.94* 1.79pt 0.44 1.12 1.46 1.99 1.51*yt 2.17 2.68 2.99* 2.98 2.63pto 1.37 1.85 1.58 1.82* 1.63

    Notes: For the rst differences, ADF regressions include an intercept and p lagged rstdifferences of dependent variable. But for the levels, ADF regressions include an intercept,a linear time trend and p lagged rst differences of dependent variable, except for rts, rtl, rts

    and r