Monetary policy and exchange rates: Further evidence using a new method for implementing sign restrictions

Journal of Macroeconomics 49 (2016) 177–191

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Monetary policy and exchange rates: Further evidence using a new method for implementing sign restrictions Lance A. Fisher a, Hyeon-seung Huh b,∗ a b

Department of Economics, Macquarie University, NSW, 2109, Australia School of Economics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul, Republic of Korea, 03722

a r t i c l e

i n f o

Article history: Received 18 January 2016 Revised 20 May 2016 Accepted 23 July 2016 Available online 28 July 2016 JEL classification: C32 E52 F31 F41 Keywords: Structural VARs Sign restrictions Instrumental variables Exchange rate puzzles

a b s t r a c t This paper estimates SVARs for four small and three large economies. Sign restrictions are used to identify all the shocks in the SVARs, while being agnostic about the sign of the response of the real exchange rate to a relative monetary policy shock. The large number of sets of impulse responses to be judged by sign restrictions for either retention or rejection is generated by a newly proposed method which utilizes instrumental variable estimation. The responses show an absence of an exchange rate puzzle in each economy. The peak appreciation following a contractionary monetary policy shock occurs with at most a one quarter delay in the small countries and, for the United States, on impact. For the Euro region and Japan, the peak appreciation is in the long run. There is considerable model uncertainty in the responses. © 2016 Elsevier Inc. All rights reserved.

1. Introduction Standard macroeconomic theory predicts that an unexpected tightening in monetary policy will lead to an immediate appreciation of the currency followed by depreciation (the ‘overshooting hypothesis’ of Dornbusch (1976)). In many VAR studies, however, following a monetary policy shock which raises the interest rate, the real exchange rate is found to either depreciate on impact or, if it appreciates, it does so for a prolonged period, which can be up to several years. In the literature, the former is referred to as the ‘exchange rate puzzle’ and the later as the ‘delayed overshooting puzzle’, or, as the ‘forward discount puzzle’, because delayed overshooting is inconsistent with uncovered interest rate parity (UIP). The studies which report these puzzles have typically placed recursive zero restrictions on the contemporaneous relationships between the variables in the VAR (see, for example, Sims (1992), Grilli and Roubini (1995, 1996) for non-US G7 countries, and Eichenbaum and Evans (1995) for the US). These puzzles were found to be less apparent or to even disappear in SVARs identified by non-recursive contemporaneous zero restrictions or long-run zero restrictions, which allow for a simultaneous contemporaneous interaction between monetary policy and the exchange rate (for the former, see Kim and Roubini (20 0 0) for non-US G7 countries, and for the latter, Bjørnland (2009) for four small open economies). An alternative to the use of parametric restrictions for identification is sign restrictions on the impulse responses. This method, which ∗

Corresponding author. E-mail addresses: lance.fi[email protected] (L.A. Fisher), [email protected] (H.-s. Huh).

http://dx.doi.org/10.1016/j.jmacro.2016.07.003 0164-0704/© 2016 Elsevier Inc. All rights reserved.

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L.A. Fisher, H.-s. Huh / Journal of Macroeconomics 49 (2016) 177–191

has become increasingly popular, avoids the use of strong restrictions on the values of the contemporaneous or long-run responses to the shocks. This approach was introduced by Faust (1998), Canova and De Nicoló (2002) and Uhlig (2005) to identify monetary policy shocks and generalized by Peersman (2005) to identify the full set of shocks in a SVAR. Using a signs approach, Faust and Rogers (2003), could not find robust evidence for the timing of the peak appreciation of the US exchange rate following a tightening of monetary policy but did find robust evidence for significant deviations from UIP. Scholl and Uhlig (2008) utilize Uhlig (2005) signs method and find robust evidence for delayed overshooting of the US exchange rate and for a sizable forward discount puzzle. Both studies identify only one shock in the SVAR, the monetary policy shock, and leave the other shocks unidentified. The difficulty with this approach is that the sign restrictions to identify the monetary policy shock may also be satisfied by other shocks in the system so the monetary policy shock may not be uniquely identified. This problem can occur when some of the shocks in the system are not identified and it was raised by Fry and Pagan (2011) who refer to it as the multiple shocks problem. Jääskelä and Jennings (2010) estimate a SVAR with actual Australian data and find no evidence for an exchange rate puzzle. They remark, however, that there is one unidentified shock in the SVAR on which they impose no sign restrictions and it can generate responses similar to those from the shocks which have been identified by sign restrictions (i.e. the multiple shocks problem).1 Farrant and Peersman (2006) avoid the multiple shocks problem by identifying all the shocks in their open economy SVAR by sign restrictions. Bjørnland and Halvorsen (2014) also avoid the multiple shocks problem by combining a sign restriction with contemporaneous zero restrictions to identify all the shocks. In both studies, the impact response of the exchange rate to a contractionary monetary policy shock is sign constrained to appreciate thereby ruling out an exchange rate puzzle.2 In this paper, SVARs are estimated for four small open economies, Australia, Canada, New Zealand and the United Kingdom, and for three large economies, the Euro region, Japan and the United States.3 The SVARs are specified in terms of relative variables so that, for example, the GDP variable is the GDP of an economy relative to a trade weighted average of the GDP’s of its major trading partners. Setting up the SVARs in terms of relative variables allows the economic activity of a country or region to influence, and to be influenced by, the economic activity of its major trading partners. We find that this specification of the SVAR is preferable even for the small economies, where it is often assumed that the small economy can have no economic impact on its trading partners. The shocks in the SVARs are identified by sign restrictions and they are sufficient to identify all the shocks, so our analysis is not susceptible to the multiple shocks problem. The sign restrictions identify the shocks without restricting the response of the real exchange rate to the monetary policy shock i.e. the identification is agnostic about the exchange rate response to a monetary policy shock so exchange rate puzzles can emerge. However, they do restrict the sign of the interest rate response (i.e. the monetary policy response) to an exchange rate shock. In this paper, we use a new method, proposed by Ouliaris and Pagan (2016), to generate the sets of impulse responses which are to be judged against the sign restrictions. This new method involves estimating the SVAR by the method of instrumental variables, once the unidentified coefficients are assigned values in order to achieve exact identification. The assigned values of the coefficients are randomly generated. For each set of randomly generated coefficients, the SVAR is estimated and the impulse responses are obtained. The computational demands of this new method are similar to a commonly used method, discussed in Fry and Pagan (2011), which is based on the use of rotation matrices. While we think that this new method is possibly more transparent than the one discussed in Fry and Pagan, being based on instrumental variable estimation of the equations of the SVAR for each set of generated coefficients, we leave that judgement to the reader.4 For the small economies, there does not appear to be an exchange rate puzzle. Following a contractionary monetary policy shock, the peak appreciation of the real exchange rate occurs on impact for Canada and New Zealand, and one quarter after impact for Australia and the United Kingdom. The real exchange rate depreciates smoothly from peak appreciation. It depreciates to a long-run depreciated value for Canada and New Zealand, to a long-run appreciated value for Australia, and returns to its initial value for the United Kingdom, based on the median response. There does not appear to be an exchange rate puzzle for the large economies either. However, for the Euro region and Japan, the appreciation appears to be persistent and sustained while, for the United States, the exchange rate depreciates smoothly after peak appreciation. Apart from New

1 Jääskelä and Jennings (2011) undertake a controlled experiment to evaluate SVAR models of monetary policy and the exchange rate. They simulate data from a small open economy DSGE model calibrated for Australia. They find that a sign restricted SVAR, estimated with the simulated data and which leaves the response of the exchange rate to a monetary policy shock unrestricted, produces impulse responses that match those reasonably well from the DSGE model. In particular, the real exchange rate appreciates on impact in response to a contractionary monetary policy shock in the DSGE model and in the SVAR estimated with simulated data. However, they show that when sign restrictions are imposed only to identify the monetary policy shock, leaving the other shocks unidentified, there is an exchange rate puzzle in the SVAR estimated with simulated data. In Jääskelä and Jennings (2010), they also estimate the SVAR with actual Australian data and find results consistent with those from the simulated data. 2 The concern of the Bjørnland and Halvorsen (2014) study is on how monetary policy (the short term interest rate) responds to an exchange rate shock. In order to identify the monetary policy and exchange rate shocks from one another in their SVAR, and keep the response of the interest rate to the exchange rate shock unrestricted, they need to sign restrict the exchange rate response to the monetary policy shock. 3 The Euro region refers to the eighteen countries which have adopted the euro currency. The countries are: Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Latvia, Luxembourg, Malta, Netherlands, Portugal, Slovak Republic, Slovenia, and Spain. 4 This new method can easily accommodate the case of where both parametric and sign restrictions are used to identify the structural shocks. We do not draw on this feature as the sign restrictions by themselves are sufficient to identify all the shocks in our models. Note that this new method, like the method discussed in Fry and Pagan (2011), does not assume parameter uncertainty so that it is non-Bayesian.

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Zealand and the Euro region, there is some support for UIP. There is considerable uncertainty associated with these results because the spread of accepted impulse responses to the monetary policy shock is wide, judging by the 16th and 84th percentile responses. Moreover, recent research shows that summary measures, like percentile responses, depend on the method used to generate responses in sign restrictions. The paper is organized as follows. Section 2 describes the specification of the SVARs. Section 3 presents the sign restrictions on the impulse response functions which are used to identify all the shocks in the SVARs. Section 4 describes the method of Ouliaris and Pagan (2016) to generate the impulse responses and shows how they are judged with reference to the sign restrictions. Section 5 presents the key empirical results. Section 6 discusses UIP, conditional on the monetary policy shock, and presents results. Section 7 concludes. The appendix gives a detailed account of the data. 2. Specification of the SVARs Both domestic and foreign variables enter the SVAR for each country or region. The domestic variables are the log of real GDP (ytd ), inflation (πtd ), a short-term interest rate (itd ), and the log of the real exchange rate (qt ). The real exchange rate is defined as the number of ‘home’ goods per unit of the ‘foreign’ good so that a decrease in its value represents a real appreciation of the ‘home’ (i.e. domestic) currency. The foreign variables are a trade weighted average of the real GDPs, inflation, and the short-term interest rates of an economy’s major trading partners. These variables are denoted as f f log foreign GDP (yt ) (i.e. the log of the trade weighted GDP), foreign inflation (πt ) and the foreign short-term interest rate

(itf ). The appendix describes the construction of the trade weights to form these variables, and provides precise definitions

of all the variables and where the data is sourced. f f f The SVARs comprise relative real GDP (ytd − yt ), relative inflation (πtd − πt ),the relative interest rate (itd − it ) and the real exchange rate. We denote the relative variables as yt , π t and it , respectively. The SVAR for each country (excluding deterministic terms) has the form:

yt = a012 πt + a013 it + a014 qt + {lags o f these} + ε1,t

(1)

πt = a021 yt + a023 it + a024 qt + {lags o f these} + ε2,t

(2)

it = a031 yt + a032 πt + a034 qt + {lags o f these} + ε3,t

(3)

qt = a041 yt + a042 πt + a043 it + {lags o f these} + ε4,t

(4)

As relative GDP and the real exchange rate are I(1) variables, they enter the SVAR in first differenced form. The other variables are all I(0) and enter in levels. The specification of the SVAR in terms of relative variables allows for a two-way interaction between a country’s economic activity and that of its major trading partners. However, there are other specifications of the SVAR we could consider. For example, we could treat the large economies as closed so that their trading partners have no economic impact on them and we could treat the small economies as small enough not to have an economic impact on their trading partners. While we consider these later, the preferred SVAR is in terms of relative variables which permit the domestic economy to be influenced by, and to influence, the economic activity of its major trading partners.5 At this juncture, the system of Eqs. (1) to (4) cannot be estimated as each equation is the same, apart from the normalisation of the dependent variable. Once enough parametric restrictions are imposed on the contemporaneous interactions among the variables to achieve exact identification, the system can then be estimated by the method of instrumental variables, first introduced into the SVAR literature by Shapiro and Watson (1988). Fisher, Huh and Pagan (2015), estimate a variation of Peersman (2005) SVAR, which contains both I(1) and I(0) variables (as does the SVAR here), using instrumental variables. Ouliaris and Pagan (2016) utilize the instrumental variable approach to develop a method for generating the large sets of impulse responses that are used in the sign restrictions methodology. Before turning to their method, which is utilized in this paper, we present the sign restrictions against which the impulses responses are judged for retention in the sign restrictions methodology. 3. Sign restrictions on the impulse responses In this section, we present the sign restrictions for a structural shock (εi,t , i = 1, . . . , 4 ) to be either an aggregate supply (AS) shock, or an aggregate demand (AD) shock, or a monetary policy (MP) shock or a real exchange rate shock (RX). The AS, AD and MP shocks are relative shocks. That is to say, an AS shock alters the level of aggregate supply in an economy in relation to that of its major trading partners, and similarly for an AD shock. An MP shock alters the interest rate differential between an economy and its major trading partners, while an RX shock moves an economy’s real trade-weighted exchange 5 Other studies in international macroeconomics which have used relative variables include Clarida and Galí (1994), Prasad (1999), Fisher and Huh (2002), and Huh and Kwon (2015).

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L.A. Fisher, H.-s. Huh / Journal of Macroeconomics 49 (2016) 177–191 Table 1 Shock\Variable AS AD MP RX

GDP

Inflation

Interest Rate

Real Exchange Rate

≥ ≥ ≤ ≥

≤ ≥ ≤ ≥

UR ≥0 ≥0 ≥0

UR ≤0 UR ≥0

0 0 0 0

0 0 0 0

Notes: AS denotes an aggregate supply shock, AD an aggregate demand shock, MP a monetary policy shock and RX a real exchange rate shock. AS, AD and MP are relative shocks with respect to a country’s major trading partners. The designation  ≥  indicates a non-negative response so that the variable does not fall in response to the shock while  ≤  indicates a non-positive response so that the variable does not rise in response to the shock. UR denotes an unrestricted response of the variable to the shock. The sign restrictions are imposed on the impact response and on the response for the following quarter. Table 1A Shock\Variable MP RX

GDP

Inflation

Interest Rate

Real Exchange Rate

≤0 ≥0

≤0 ≥0

≥0 UR

≤0 ≥0

Notes: See the notes to Table 1.

rate (a relative price). The sign restrictions we employ to separate the AS, AD, and MP shocks from each other are standard, and have been utilized by Farrant and Peersman (2006), Finlay and Jääskelä (2014), and Jääskelä and Jennings (2010, 2011), among others. Following the conventional approach adopted in the aforementioned studies, the sign restrictions on the monetary policy shock rule out an output or price puzzle, i.e. in response to a contractionary monetary policy shock, GDP and inflation cannot rise.6 The full set of sign restrictions is shown in Table 1. They are applied for two quarters, on impact and for the subsequent quarter. Responses which are left unrestricted are designated as “UR”. The sign restrictions in the table are sufficient to separate uniquely all of the structural shocks so that our analysis is not susceptible to the multiple shocks problem whereby an unidentified shock could satisfy the restrictions for a sign restricted shock and be conflated with it. It is not necessary to restrict the real exchange rate response to the monetary policy shock, nor the interest rate and real exchange rate response to the aggregate supply shock. Because our identification is agnostic about the response of the real exchange rate to a monetary policy shock, it allows us to see whether the sign restrictions on the other variables are sufficient to give rise to impulse responses that do not show exchange rate puzzles. Jääskelä and Jennings (2010, 2011) leave the effect of the AS, AD and MP shocks on the real exchange rate unrestricted in their SVAR so that puzzles in the response of the real exchange rate to a monetary policy shock can emerge. They leave one shock unidentified and remark that this may mean their results are susceptible to the multiple shocks problem. To identify the exchange rate shock from other shocks in our model, it is necessary to impose sign restrictions on the responses of all the variables to it. Specifically, in response to an exchange rate shock which does not appreciate the domestic currency, we impose the restriction that the interest rate cannot fall. This means that our analysis restricts the direction, though not the strength, of the interest rate response (i.e. the monetary policy response) to an exchange rate shock. This allows us to separate the monetary policy shock from the real exchange rate shock. Suppose that in response to a shock we observe that GDP and inflation do not fall, the interest rate does not rise and the real exchange rate does not appreciate over the next two quarters. By the sign restrictions in Table 1, this shock can only be a monetary policy shock that does not cause the interest rate to rise.7 The SVAR of Bjørnland and Halvorsen (2014) is agnostic about the interest rate response to an exchange rate shock but it imposes the restriction that the exchange rate appreciates on impact following a monetary policy shock which raises the interest rate. In our context, this alternate identification would change the last two rows of Table 1 to Table 1A. Suppose, as before, that in response to a shock we observe that GDP and inflation do not fall, the interest rate does not rise and the real exchange rate does not appreciate over the next two quarters. Under this alternate identification, this shock can either be a monetary policy shock that does not cause the interest rate to rise or an exchange rate shock that does not appreciate the currency. This is an example of where this identification cannot separate a monetary policy shock from an exchange rate shock.

6 It has been suggested that the price puzzle may not in fact be a puzzle. A monetary policy shock which raises interest rates could increase inflation owing to increased working capital or inventory costs. See, for example, Barth and Ramey (2001). We follow convention and classify rises in output and inflation in response to a contractionary monetary policy shock as “puzzles” and rule them out. 7 This can be seen when the MP row in Table 1 is multiplied through by -1 (i.e. the weak inequalities are reversed for the case of a monetary policy shock which does not cause the interest rate to rise).

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4. Generating impulse responses for sign restrictions Fry and Pagan (2011) describe a popular approach for generating the large sets of impulse responses which are used in sign restrictions. The approach starts with an initial set of shocks which are uncorrelated and which have zero mean and unit variance. One way to get these is to estimate a recursive VAR which imposes n(n − 1 )/2 zero restrictions on the contemporaneous interactions among the n variables and to standardize the estimated structural shocks. The initial standardized shocks are re-combined to form a new set of shocks, which are also uncorrelated with mean zero and unit variance, from which a another set of impulse responses are obtained and judged against the signs. Those that satisfy the sign restrictions are retained. The process is repeated a large number of times. Fry and Pagan describe two transformations (Givens and Householder) that can be used to re-combine the initial shocks to form the new set of orthogonal shocks. Jääskelä and Jennings (2011), for example, apply the Givens transformation. Ouliaris and Pagan (2016) name this approach SRR, sign restrictions (SR) by re-combination (R). Ouliaris and Pagan (2016) propose a new approach. It recognizes that once n(n − 1 )/2coefficients on the contemporaneous variables in a VAR are assigned some values, the remaining coefficients can be estimated and the impulse responses found. By varying the values of the assigned coefficients in a random way, a large set of impulse responses can be generated. They name this method SRC, sign restrictions (SR) with generated coefficients (C) i.e. by randomly generating the values of the assigned coefficients. The SRR and SRC methods are differentiated solely on how they generate the impulses responses; they judge the responses against the sign restrictions in the same way. The SRC method is implemented as follows. Begin with Eq. (1) and assign values to the coefficients a012 , a013 and a014 , and regress yt − a012 πt − a013 it − a014 qt on the remaining variables to obtainεˆ1t .Then assign values to the coefficients a023 and a024 in Eq. (2), regress πt − a023 it − a024 qt on the other variables using εˆ1t as the instrument for yt , and obtain εˆ2t . Similarly, assign a value to the coefficient a034 ,regress it − a034 qt on the remaining variables using εˆ1t and εˆ2t as instruments for yt and π t , respectively, and obtain εˆ3t .Finally, estimate Eq. (4) using as instruments εˆ1t , εˆ2t and εˆ3t ,to obtain εˆ4t .8 To generate the widest possible range of impulse responses to be judged by the sign restrictions, the values of the assigned coefficients should fall on the interval (−∞, ∞ ). This is accomplished by generating the values of the coefficients as:

a012 (θ1 ) = a024 (θ5 ) =

θ5

θ1

1 − abs(θ1 )

1−abs (θ5 )

,

, a034 (θ6 ) =

a013 (θ2 ) = θ6

1−abs (θ6 )

θ2

1 − abs(θ2 )

,

a014 (θ3 ) =

θ3

1 − abs(θ3 )

,

a023 (θ4 ) =

θ4

1 − abs(θ4 )

,

, where abs denotes absolute value, and θ i , i = 1, . . . , 6, are drawn from a uniform

(-1,1) probability density function. For each draw of θi , i = 1, . . . , 6, we obtain values of the assigned coefficients, and then estimate the structural equations, as described above. The estimated equations are then expressed in terms of the levels of all the variables and from the levels specification we calculate the impulse response functions to one-standard error shocks. If the set of impulse responses satisfy the sign restrictions, they are retained. If not, they are discarded. We then estimate the equations of the model with another draw of the six θ  s, re-parameterize the estimated equations to levels, calculate the impulses responses and judge them against the sign restrictions. The process is repeated many times.9 Some care needs to be exercised in determining whether a set of impulses responses should be retained or not. In our models, there are 4!=24 possible attributions that can be given to the set of structural shocks (ɛ1t , ɛ2t , ɛ3t , ɛ4t ) . The first structural shock can be any one of an AS, AD, MP and RX shock. Conditional on it being one of these, the second structural shock can be any one of the remaining three and so on. For example, a successful draw has the responses from the first structural shock satisfying the sign restrictions, say, for the AD shock, the second for the AS shock, the third for the RX shock and the fourth for the MP shock. Another successful draw may have the responses satisfying the sign restrictions in the order AD-AS-MP-RX. The impulse responses to the MP shock are the responses to ɛ4t and to ɛ3t in the two successful draws. A draw is unsuccessful if the responses from the set of structural shocks (ɛ1t , ɛ2t , ɛ3t , ɛ4t ) do not satisfy the sign restrictions for any one of the 24 (=4!) possible combinations of AS, AD, MP and RX shocks, in which case all of the responses are discarded. The standard practice in the literature to summarize the large number of accepted responses is to report the median impulse response. This involves ordering the accepted responses at each horizon into ascending order and selecting the 50th percentile response. Fry and Pagan (2011) argue that the median response (and, for that matter, any percentile response) is subject to a multiple models problem. The median response of a variable at horizon h comes from a specific model, which is derived under a particular draw of the six generated SVAR coefficients. There is no reason to expect the median response in the variable at horizon h+j nor the median response of other variables at horizon h to come from the same model i.e. from the same draw of the six generated SVAR coefficients. 8 In each of these regressions, the lagged variables are their own instruments. Instead of instrumental variable (IV) estimation, one could estimate the system of equations, given the values of the six assigned coefficients, using Maximum Likelihood (ML) estimation, where the likelihood is constructed so that the shocks are orthogonal. Because the system of equations is exactly identified, estimation by IV and ML produce identical estimates of the non-assigned (i.e. estimable) coefficients. 9 In our application, the number of repetitions (or draws) is terminated when 10 0 0 sets of impulse responses are retained or, if that is not reached, at 10 0,0 0 0 draws.

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To address this problem, Fry and Pagan propose a criterion to find a single SVAR whose impulse responses are as close to the median responses as possible. These are the median target responses. The SVAR which produces the median target responses is characterized by a particular draw of the six assigned (i.e. generated) coefficients, so the median target responses correspond to those from a single model.10 There is no guarantee, however, that the median target responses will fall between the 16th and 84th percentiles, which are commonly reported. It should be stressed that it is misleading to treat the region covering the 16th to the 84th percentile responses as a confidence region, because it does not reflect sampling uncertainty. Rather, it reflects the spread of equally valid accepted responses as the model (not the sample) varies. We follow the literature and report the median, median target, and 16th and 84th percentiles, of the accepted impulse responses. However, there is a problem with these statistics. While they summarize the distribution of accepted impulse responses, the distribution itself depends on how the impulse response functions are generated. Changing the method of generation changes the median and other statistics that summarize the distribution of accepted impulse responses because the distribution itself changes. This result is due to Baumeister and Hamilton (2015), who critique Bayesian methods for summarising the range of impulse responses. This result applies to all of the various methods employed to generate impulse response functions in sign restrictions.11 Specifically, in the SRC method we utilize, the distribution of the accepted impulses responses will depend on the how the assigned coefficients (i.e. how the six a0i j s )are generated. For example, had they instead been drawn directly from a uniform distribution defined over some part of the positive real number line, the resulting summary statistics for the impulse responses may well be quite different.12 The distribution of accepted responses may also depend on which six a0i j coefficients are selected to have generated values. In our SVAR, relative output is ordered first so there are three generated coefficients in its structural equation, relative inflation is second so its equation has two generated coefficients and the relative interest rate is third so its equation has only one, and the real exchange rate equation has none as the exchange rate is ordered last. This is only one selection of the set of generated coefficients from 24 possible recursive SVARs.13 The Baumeister and Hamilton (2015) findings mean that it is difficult to draw inferences from the summary statistics for the accepted impulses responses. Accordingly, the interpretations we make of what the median, median target and percentile responses show should be viewed with their findings firmly in mind; that the values of these statistics are method generation dependent. 5. Empirical results The SVARs are estimated with quarterly data for the sample 1994:Q1 to 2014:Q1.14 In each equation of the SVARs, there is a constant and a time trend. The lag length of the SVAR for each country was selected on the basis of the AIC criteria. It selected two lags for Australia, Canada, the United Kingdom and one lag for New Zealand and, for the large economies, one lag for the Euro region and two lags for Japan and the United States. Fig. 1 shows the responses of the variables to the shocks for the four small economies, and Fig. 2 for the three large economies. In each graph, there is a shaded region, where the lower bound is the 16th percentile response and the upper bound the 84th percentile response, to give an indication of the spread of accepted impulse responses. Also shown are the median and median target impulse responses to the shocks to give an indication of central tendency. Recall that the shocks are all one-standard error in size and that the sign restrictions are applied to the impact and one quarter horizon response.15 5.1. Responses to a monetary policy shock In response to a contractionary monetary policy shock, relative GDP and inflation fall on impact and over the next quarter, as required by the sign restrictions. Relative GDP would then be expected to revert. We know that inflation will revert 10 The criterion finds the draw of the six coefficients which minimises the distance between the accepted impulse responses and the median impulses responses for all of the shocks. The median target responses are those responses produced by that draw of the six coefficients. 11 Stock and Watson (2016) provide a two variable example that demonstrates analytically the results in Baumeister and Hamilton (2015). Their two variable example is similar, though simplified, to that in Baumeister and Hamilton, and they essentially use the SRR method (with Givens) to generate the impulse response functions. 12 An example is provided by Ouliaris and Pagan (2016). 13 We also generated the results across all 24 recursive orderings for each country/region and found that the success rates and the summary statistics for the accepted impulses responses did not change noticeably. This may not be too surprising since the method, for a given selection of the set of generated coefficients, produces a wide range of impulse responses, and many of these responses may coincide with those that come from SVARs for other selections of the set of generated coefficients. 14 The ADF test did not reject the null of a unit root in the relative GDP series of each economy, nor did it reject the null of a unit root in the real exchange rate of each economy. The test did reject the null of a unit root in relative inflation and the relative interest rate for each economy. These results support the specification of the estimated SVARs. 15 For Australia, Canada and New Zealand, 10 0 0 sets of impulse responses were retained in 68,931, 36,745, and 29,185 draws, respectively. This produced a success rate of 1.451% for Australia, 2.721% for Canada and 3.426% for New Zealand. For the United Kingdom, 621 from 10 0,0 0 0 draws were retained, producing a success rate of 0.621%. The SVAR which gave the median target responses corresponded to successful draw 821 for Australia, 269 for Canada, 605 for New Zealand and 455 for the United Kingdom. For the Euro region, Japan and the United States, 10 0 0 sets of impulse responses were retained in 31,472, 72,825 and 14,982 draws, respectively, giving a success rate of 3.177% for the Euro region, 1.373% for Japan and 6.675% for the United States. The SVAR which gave the median target responses corresponded to successful draw 962 for the Euro region, 480 for Japan, and 996 for the United States.

L.A. Fisher, H.-s. Huh / Journal of Macroeconomics 49 (2016) 177–191

AS GDP

AD 0.2

0.6

0.8

-0.0

0.5

1.0

0.6

0.8

0.4

0.6

0.2

0.4

0.0

-0.2

10

15

20

25

MED

30

35

16%

0.5

-0.1

0.4

-0.2

0.3

-0.3

0.2

-0.4

0.1

-0.5

0.0

-0.6

-0.1

-0.7

-1.2 5

10

15

20

25

MED

30

35

16%

5

10

MED-T

15

20

25

MED

30

35

16%

84%

0

5

10

MED-T

0.30

0.15

0.25

15

20

25

MED

30

0.00

-0.10

-0.05 0

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

2

5

10

MED-T

15

20

25

MED

30 16%

-1

-2.5

-3.5

-3

-4.0 0

5

10

MED-T

15

20

25

MED

30

35

16%

16%

0 84%

0 84%

5

10

MED-T

15

20

25

MED

30 16%

10

15

20

25

MED

30

35

16%

84%

0.0

-0.2 5

10

15

20

25

MED

30

35

16%

0 84%

5

10

MED-T

15

20

25

MED

30

35

16%

84%

0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 5

10

MED-T

35

5 MED-T

-0.1

15

20

25

MED

30

35

16%

0 84%

0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -4.0

-3.0 -2

35

0.1

84%

-1.5 -2.0

30

0.2

0

-1.0

0

MED

MED-T

35

-0.5

1

25

0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 -0.10

0.05

-0.05

20

0.3

0

0.10

0.00

15

0.4

84%

0.15

0.05

10

MED-T

35

16%

0.20

0.10

5

0.05 -0.00 -0.05 -0.10 -0.15 -0.20 -0.25 -0.30 -0.35 -0.40

84%

0.20

0.0 0

-0.2 0

0.1

-1.0

MED-T

-0.0

0.2

-0.8

84%

0.6

0.3

-0.6

0

0.1

0.4

-0.4

-0.2 5 MED-T

REX

RX

1.0

1.2

0

INT

MP

1.4

0.2

INF

183

5

10

MED-T

15

20

25

MED

30

35

16%

84%

2.5 2.0 1.5 1.0 0.5 0.0 -0.5 0

84%

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

5

10

MED-T

15

20

25

MED

30

35

16%

84%

(a) Australia

AS GDP

-0.0

0.6

0.6

-0.1

0.5

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

-0.5

0.0

0.1

0.0

-0.6

-0.1

5

10

MED-T

15

20

25

MED

30

35

16%

84%

10

MED-T

15

20

25

MED

30

35

16%

84%

0.05

0.25

-0.00

MED

30

35

16%

84%

MED-T

15

20

25

MED

30

35

16%

0.00

MED-T

MED

16%

0 84%

MED-T

15

20

25

MED

30

35

16%

0 84%

5

10

MED-T

15

20

25

MED

30

35

16%

15

20

25

MED

30

35

16%

0 84%

-1.0

-2.25

-1.5

MED-T

MED

25

30 16%

35

0 84%

5 MED-T

10

15 MED

20

25

30 16%

35

15

20

25

MED

30

35

16%

84%

1.5 1.0 0.5 0.0 0

84%

10

2.0

0.0

-2.00

5 MED-T

2.5

-1.5

84%

0.00 10

0.5

-1.0

35

0.05

5

1.0

-0.5

30 16%

0.10

1.5

-1.75

25

-0.05 MED-T

-0.5

20

0.15

-0.75

-1.50

15 MED

0.20

84%

-1.25

10

0.25

1.0

20

84%

0.30

1.5

15

35

0.35

0

-1.00

5 MED-T

3.0

10

30 16%

0.00 10

2.0

5

25

-0.05 5

-0.50

0

20

0.10

-0.25

0.0

15 MED

0.15

2.0

0.5

10

0.20

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05

-0.05 35

5 MED-T

0.30

84%

0.05

30

0 84%

0.35

0

0.10

25

16%

0.05

10

0.15

20

35

-0.25 5

0.20

15

MED

30

-0.20

0.25

10

25

-0.15

0.30

5

20

0.25

0.35

0

15

-0.10

0

0.06 0.04 0.02 0.00 -0.02 -0.04 -0.06 -0.08 -0.10 -0.12

10

-0.05

-0.05 25

5 MED-T

0.30

0.00 20

0.1

0

0.05

MED-T

REX

5

0.10

15

0.2

-0.4

0.15

10

0.3

-0.3

0.20

5

0.4

-0.2

0

0.05 -0.00 -0.05 -0.10 -0.15 -0.20 -0.25 -0.30 -0.35 -0.40 0

INT

RX

0.7

0.7

0

INF

MP

AD

0.8

5 MED-T

10

15 MED

20

25

30 16%

35

0 84%

5 MED-T

10

15 MED

20

25

30 16%

35 84%

(b) Canada Fig. 1. Responses to shocks.

to its initial level because it is an I(0) variable. However, relative GDP may move to a level other than its initial level because the shock to the structural equation for the relative interest rate (an I(0) variable) can have a permanent effect on the I(1) variables (GDP and the real exchange rate), given the way our SVAR is setup.16 However, we would expect to see some reversion in the response of GDP for the shock to be confidently seen as a monetary policy shock.

16 The SVAR is setup to allow shocks to the structural equations for the I(0) variables to have potentially permanent effects on the I(1) variables. See Fisher, Huh and Pagan (2015).

184

L.A. Fisher, H.-s. Huh / Journal of Macroeconomics 49 (2016) 177–191

AS

AD -0.0

1.0

1.4

-0.2

0.8

1.2

-0.4

1.0

0.4

0.2 5

10

MED-T

15

20

25

MED

30

35

16%

-1.2 0

84%

0.5

-0.0

0.4

-0.1

5

10

MED-T

0.1

15

20

25

MED

30

35

16%

84%

0.1

-0.4 -0.5

0.0

-0.6

-0.1 0

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

0.30 0.25

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

0.10 0.05 -0.00 -0.05 -0.10 -0.15 -0.20 -0.25 -0.30 -0.35

0.2

-0.3

0.0 0

0.3

-0.2

0.2

-1.0

0.4 0

0.4

-0.8

0.6

-0.2

0.6

-0.6

0.8

0.2 0.0

INF

RX

1.6

0.8 0.6

GDP

MP

1.0

5

10

MED-T

15

20

25

MED

30

35

16%

5

10

MED-T

15

20

25

MED

30

35

16%

84%

0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 0

84%

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

5

10

MED-T

0.25

0.5

0.5

0.20

0.4

0.4

0.15

0.3

0.3

0.10

0.2

0.2

0.05

0.1

0.00

0.0

0.0

-0.05

-0.1

-0.1

15

20

25

MED

30

35

16%

84%

0.20 0.15 0.10

INT

0.05 -0.05 -0.10 0

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

5

10

MED-T

3

-1.0

2

-1.5

15

20

25

MED

30

35

16%

0 84%

-2.5 0

-3.0

-1

-3.5

-2

-4.0 0

5

10

MED-T

15

20

MED

25

30

35

16%

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5

-2.0

1

REX

0.1

0.00

0 84%

5

10

MED-T

15

20

MED

25

30

35

16%

5

10

MED-T

15

20

25

MED

30

35

16%

84%

2.25 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0.00 0

84%

5

10

MED-T

15

20

MED

25

30

35

16%

0 84%

5

10

MED-T

15

20

MED

25

30

35

16%

84%

(c) New Zealand

AS

AD

0.9

GDP

0.40

0.8

0.5

0.1

0.35

0.4

-0.0

0.30

0.7 0.6

0.3

0.5

0.2

0.4

0.1 5

10

MED-T

15

20

25

MED

30

35

16%

-0.2 -0.3 -0.4 -0.5 0

5

10

MED-T

15

20

25

MED

30 16%

10

15

20

25

MED

30

35

16%

84%

0.100 0.075 0.050 0.025 0.000 -0.025 0

5

10

MED-T

15

20

25

MED

30 16%

25

MED

30

35

16%

0 84%

-0.25 5

10

15

20

25

MED

30

35

16%

0 84%

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

10

MED-T

15

20

25

MED

30

0.25

0.25

0.20

0.20

0.15

0.15

0.10

16%

0.00

0.00

-0.05 0

84%

-0.75

5

10

MED-T

15

20

25

MED

30

35

16%

0.5

REX

0.0

-1.50

0.0

-1.75

-0.5

-2.00

-0.5

-1.0

-2.25 -1.0

-1.5

-2.50

-1.5

-2.75 0

5 MED-T

10

15 MED

20

25

30 16%

35

-2.0 0

84%

5 MED-T

10

15 MED

20

25

30 16%

35

0 84%

20

25

30

35

16%

84%

10

15

20

25

MED

30

35

16%

84%

5

10

MED-T

15

20

25

MED

30

35

16%

84%

1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

-1.25 0.5

5

0 84%

1.0

-1.00

15 MED

0.05

0.05 35

10

MED-T

0.30

0.10

5

5 MED-T

0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 -0.02 -0.04

-0.20

84%

1.0

20

-0.15

0

1.5

MED-T

15

-0.10

MED-T

35

10

-0.05

0.225 0.200 0.175 0.150 0.125 0.100 0.075 0.050 0.025 0.000

0.125

5

-0.00

84%

0.150

0.00 0

0.05

0

0.175

0.05

-0.5 5 MED-T

35

0.10

-0.4

0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 -0.10 -0.15

-0.1

0.15

-0.3

84%

-0.0

0.20

-0.2

0

0.1

0.25

-0.1

0.0 0

INT

RX

0.2

0.3

INF

MP

0.6

5 MED-T

10

15 MED

20

25

30 16%

35

0 84%

5 MED-T

10

15 MED

20

25

30 16%

35 84%

(d) United Kingdom Fig. 1. Continued

Fig. 1 shows the responses for the small economies. For Australia and New Zealand, the median and median target responses show that relative GDP reverts to a long run level somewhat below its level prior to the contractionary monetary policy shock. However, the 85th percentile responses suggest complete reversion of relative GDP to its original level. For the United Kingdom, the median and median target responses suggest complete reversion of GDP to its level prior to the shock. Canada is somewhat of an exception. There is reversion in the median response but only for the quarter after impact, after which the response converges to a level nearly unchanged from the level of impact. There is little evidence of a price

L.A. Fisher, H.-s. Huh / Journal of Macroeconomics 49 (2016) 177–191

AS

AD

1.2

MP

1.25

0.4

1.00

0.2

1.0 0.8 0.6

1.6 1.4 1.2

-0.2 0.50

0.2 0.0 -0.4 0

5

10

15

MED-T

20

25

MED

30

-0.6

0.00

-0.8 0

84%

5

10

15

MED-T

20

25

MED

30

35

-0.00

0.25

-0.00

-0.30

0.00 0

5

10

15

MED-T

20

25

MED

30

35

25

30

35

0

16%

84%

-0.25 -0.30

84%

5

10

15

MED-T

20

25

MED

30

35

0

16%

84%

5

10

15

MED-T

0.10

0.30

0.30

0.08

0.25

0.25

0.06

0.20

0.20

0.04

0.15

0.15

0.02

0.10

0.10

0.00

0.05

0.05

-0.02

0.00

0.00

5

10

15

MED-T

20

25

MED

30

35

16%

84%

0.225 0.200 0.175 0.150 0.125 0.100 0.075 0.050 0.025 0.000

-0.20

0

16%

20

-0.15

0.10 0.05

15 MED

-0.10

0.15

-0.25

10

-0.05

0.20

-0.20

5 MED-T

0.05

-0.15

0.2

84%

0.30

-0.10

0.4 0

16%

0.05

-0.05

0.8 0.6

0.25

35

16%

1.0

-0.4

-0.2

INF

RX 1.8

-0.0

0.75

0.4

GDP

185

20

25

MED

30

35

0

16%

84%

5

10

15

MED-T

20

25

MED

30

35

16%

84%

0.200 0.175 0.150

INT

0.100 0.075 0.050

0

5

10

15

MED-T

20

25

MED

30

35

0

16%

84%

1.0

5

10

15

MED-T

20

25

MED

30

35

0.5 0.0

-1.0 -1.5 -2.0 -2.5 0

5

10

15

MED-T

20

25

MED

30

35 84%

0.000

84%

5

10

15

MED-T

20

25

MED

30

35

0

16%

84%

5

10

15

MED-T

20

25

MED

30

3

1

2

0

1

-1

0

-2

-1

-3

-2

35

10

15

20

25

MED

30

35

16%

84%

-3 0

16%

5 MED-T

2

-4 0

16%

0.025 0

16%

0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -4.0 -4.5

-0.5

REX

0.125

84%

5

10

15

MED-T

20

25

MED

30

35

0

16%

84%

5

10

15

MED-T

20

25

MED

30

35

16%

84%

(a) Euro

AS

AD

2.00

1.2

1.75

1.0

MP

0.8

1.50

0.6

GDP

1.25

0.4

1.00

0.2

0.75

0.0 0

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

0.1 -0.1 -0.2 -0.3

INF

-0.4 -0.5 -0.6 -0.7 0

5

10

MED-T

15

20

25

MED

30

15

20

25

MED

30

35

16%

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

84%

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

0.05 -0.00 -0.05 -0.10 -0.15 -0.20 -0.25 -0.30 -0.35 -0.40 0

84%

5

10

MED-T

15

20

25

MED

30

35

16%

0.0

5

10

15

20

25

MED

30

35

16%

0 84%

0.35 0.30

-0.025

0.10

0.20

0.25

-0.02 0

5

10

MED-T

15

20

25

MED

30

35

16%

84%

2.5 2.0

5

10

15 MED

20

25

30 16%

35

MED

30

35

16%

84%

MED-T

15

20

25

MED

30

35

16%

0 84%

-0.5

1.5

-1.0

-4.0

-2.5

0.0

-4.5

-3.0

-0.5

-5.0

-3.5

-1.0

20

25

30 16%

35

0 84%

10

15

20

25

MED

30

35

16%

84%

0.5

-2.0

15

84%

1.0

-1.5

MED

5 MED-T

-2.5

10

35

0.00 10

2.0

5

30 16%

0.05

5

2.5

MED-T

25

-0.05 0

0.0

0 84%

25

0.5

-3.5

MED-T

20

-2.0

-3.0

0

15

-1.5

1.0

0.0

10

MED-T

1.5

0.5

5

20

0.10

-0.05 0

15 MED

0.15

0.10

0.00

10

0.20

0.15

0.00

5 MED-T

0.25

-0.125

84%

-0.2

0.30

0.02

35

0.1

0.12

0.05

30 16%

-0.1

0.14

0.04

25

0.2

MED-T

-0.100

20

0.3

0.025

-0.075

15 MED

0.4

0

0.06

10

0.5

84%

0.08

5 MED-T

-0.000

-0.150

REX

10

MED-T

35

16%

-0.050

INT

5

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05

-0.0

RX

0.25 0.00 -0.25 -0.50 -0.75 -1.00 -1.25 -1.50 -1.75 -2.00

5 MED-T

10

15 MED

20

25

30 16%

35

0 84%

5 MED-T

10

15 MED

20

25

30 16%

35 84%

(b) Japan Fig. 2. Responses to shocks.

puzzle, when the sign restrictions are no longer in effect, except possibly for New Zealand. Fig. 2 shows the responses for the large economies. For the Euro region, the median target response shows that relative GDP reverts to close to its level before the shock and the median response also shows reversion. The spread of equally valid responses between the 16th and 84th percentile responses is wide and enclose the zero axis at medium and long horizons. For Japan, the median and median target responses revert after impact and the 84th percentile response suggests complete reversion as it coincides with the zero axis at medium and long horizons. The United States is somewhat of an exception, among the large economies. Relative GDP falls for six quarters following the monetary policy shock and then reverts somewhat to a permanently lower level, which even for the 84th percentile response is quite below the initial level. There is little evidence of a price puzzle

186

L.A. Fisher, H.-s. Huh / Journal of Macroeconomics 49 (2016) 177–191

AS

AD

0.6

MP

0.8

0.5

0.2

-0.3

0.4

0.2

-0.4

0.2

-0.5 0.0

0.1 0.0 5

10

MED-T

15

20

25

MED

30

35

16%

84%

-0.0 -0.1

5

10

MED-T

15

20

25

MED

30

35

16%

84%

0.05

0.30

-0.00

0.25

-0.05

0.10

-0.4 -0.5 5

10

MED-T

15

20

25

MED

30 16%

-0.05 -0.10 -0.15 -0.20 0

5

10

MED-T

15

20

25

MED

30

10

MED-T

35

16%

15

20

25

MED

30

35

0.0 -0.5 -1.0 -1.5 0

5 MED-T

10

15 MED

20

25

30 16%

35

16%

5

10

MED-T

15

20

25

MED

30

35

16%

84%

0.20

0.05 0.00

84%

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

5

10

MED-T

15

20

25

MED

30

35

16%

84%

0.35 0.30 0.25

0.1

0.20

0.0

0.15 0.10

-0.1

0.05

-0.2 5

10

MED-T

15

20

25

MED

30

35

16%

0.00 0

84%

5

10

MED-T

15

20

25

MED

30

35

16%

0 84%

1.5

0.5 0.0 -0.5 -1.0 -1.5 5 MED-T

10

15 MED

20

25

30 16%

35

0 84%

5

10

MED-T

15

20

25

MED

30

35

16%

84%

2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2

1.0

0 84%

0 84%

0.25

0

-0.4 -0.6 -0.8 -1.0 -1.2 -1.4 -1.6 -1.8 -2.0 -2.2

0.5

16%

0.2

0

1.0

35

0.3

84%

1.5

MED

30

-0.30 5

0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -0.05

0.05

25

0.10

-0.25

84%

-0.00

20

0.15

0.00 0

0.10

15

-0.15 -0.20

35

10

-0.10

0.05 -0.05 0

5 MED-T

0.35

0.15

-0.3

-0.2 0

0.20

-0.2

REX

-0.7 0

0.1

0.0

-0.6

-0.2 0

INT

0.6

-0.2 0.4

0.3

INF

0.8

-0.1

0.6

0.4

GDP

RX

-0.0

5

10

MED-T

15 MED

20

25

30 16%

35

0 84%

5 MED-T

10

15 MED

20

25

30 16%

35 84%

(c) United States Fig. 2. Continued

in any of the large economies. As there is evidence of reversion of relative GDP in all the countries (admittedly to varying degrees) in response to the monetary policy shock, and little evidence for price puzzles, the identification of the shock as a monetary policy shock seems credible. Fig. 1 shows that there does not appear to be an exchange rate puzzle in the small open economies. The median and median target responses show that the real exchange rate (which is not sign restricted) appreciates on impact in response to a monetary policy shock which raises the relative interest rate, although for Canada, the impact appreciation is small. The peak appreciation occurs on impact of the monetary policy shock for Canada and New Zealand, and with a one quarter delay for Australia and the United Kingdom.17 There is, however, considerable model uncertainty as the region between the 16th and 84th percentile responses covers the zero axis for each country at medium and long horizons, and for Canada at all horizons. For Australia, the median and median-target responses suggest that real exchange rate depreciates from peak appreciation to a long-run appreciated value of the currency. However, for Canada, New Zealand and the United Kingdom, they suggest depreciation from peak appreciation to either the currency’s initial value or to a long-run depreciated value. Convergence to the currency’s long-run value takes around three years for Australia, two years for New Zealand and the United Kingdom, and one year for Canada. In our SVARs, the monetary policy shock can have a long-run effect on the real exchange rate while Bjørnland (2009) combined contemporaneous recursive zero restrictions with the restriction that the monetary policy shock has a zero long-run effect on the real exchange rate.18 She found no evidence of an exchange rate puzzle for Australia, Canada and New Zealand, consistent with our evidence for these countries. Fig. 2 shows that there does not appear to be an exchange rate puzzle either for the large economies. The median and median target responses show that the real exchange rate appreciates on impact following a monetary policy shock which raises the interest rate differential between the large economy and its trading partners. For the Euro region, they show that the real exchange rate appreciates further after impact and converges slowly to a long-run appreciated value considerably higher than the impact appreciation. For Japan, they show a slight depreciation for a few quarters following the impact appreciation and then the exchange rate appreciates to a long-run level, close to the level of the impact appreciation. For the United States, the median response shows that the peak appreciation occurs on impact and then the exchange rate depreciates to its level before the relative monetary policy shock. The median target response, however, coincides closely with the 16th percentile response, and shows that the peak appreciation occurs one quarter after impact after which the exchange rate depreciates to a long-run appreciated value. There is considerable model uncertainty as the region between

17 Liu (2010) estimates a slightly more complex SVAR for Australia that includes the terms of trade and finds evidence for a peak appreciation at around 1 year following a contractionary monetary policy shock. 18 The application of the long-run restriction reduced the number of zero contemporaneous restrictions by one so that in her SVAR the interest rate and the exchange rate can respond contemporaneously to both monetary policy and exchange rate shocks.

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the 16th and 84th percentile exchange rate responses is wide, and for the Euro region and the United States, the region covers the zero axis at all horizons, and for Japan, at short horizons. 5.2. Responses to an exchange rate shock Fig. 1 shows that in response to an exchange rate shock that depreciates the real value of a small country’s currency, the interest rate differential between it and its trading partners increases on impact, in line with the sign restrictions. The rise in the relative interest rate on impact appears large, and although there is considerable model uncertainty, the 16th percentile impact response is quite above the zero response for each country.19 Relative inflation and GDP increase on impact in accordance with the sign restrictions. These responses are consistent with the notion that the domestic monetary authority, following an unexpected depreciation, raises the policy rate to curb future anticipated inflation. The results suggest that GDP rises to a permanently higher level following the exchange rate shock, except possibly for Canada, where the 16th percentile response coincides with the zero axis at medium and long horizons. Fig. 2 shows that the relative interest rate increases on impact in the large economies following an exchange rate shock, and that judging by the size of the region between the 16th and 84th percentile impact responses, the increases can be sizable.20 Relative inflation and GDP also increase on impact. Relative GDP appears to increase to a permanently higher level for the Euro region and Japan, judging by the spread of equally valid responses, shown as the region between the 16th and 84th percentile responses. However, for the United States, relative GDP could just as well return to its initial level as that region encompasses the zero axis. 5.3. Responses to AS and AD shocks An implication of some fairly standard models, e.g. the model of Clarida and Gali (1994), is for the real exchange rate to depreciate in the long-run following an AS shock. For the small economies, the median and median target responses of the exchange rate to a relative AS shock show this, and among them, the long-run depreciation appears to be noticeably smaller for Australia. However, there is considerable model uncertainty surrounding the exchange rate response with the United Kingdom being the only country where the region between the 16th and 84th percentile responses does not cover the zero axis at median and long horizons. There appears to be a small impact appreciation of the exchange rate in each small country following the relative AS shock while the impact response of the interest rate varies among them (recall that these responses are not sign constrained). In response to the relative AD shock, the median and median target responses show that the real exchange rate of each small country appreciates over all horizons. For Japan and the United States, the median and median target responses show a long-run depreciation in response to the relative AS shock while for the Euro region they show a slight long-run appreciation. There is considerable model uncertainty in the direction of this response for the Euro region and the United States. The impact response of the interest rate and the real exchange rate varies across the large economies to the relative AS shock. Finally, the real exchange rates of the large economies appreciate over all horizons in response to a relative AD shock, on the basis of the median target and all percentile responses shown. 5.4. Sensitivity analysis For the small economies, the SVAR could be specified so that the foreign variables are exogenous with respect to the domestic variables. In this specification, the structural equation for domestic GDP, for example, would be

ytd = a012 πtd + a013 itd + a014 qt + a015 ytf + a016 πtf + a017 itf + {l ags o f al l } + ε1t

(5)

The change in domestic GDP is conditioned on the contemporaneous values of the foreign variables and depends also on their lags. The other equations in the SVAR, namely, for domestic inflation, the domestic interest rate, and the real exchange rate are similarly formulated. In this SVAR, the domestic variables do not affect the foreign variables, while the foreign variables (both contemporaneous and lagged) can affect the domestic variables. This unidirectional channel is often applied to small open economies and can be thought of as a small country assumption. We estimated this SVAR for each small country using the lag length selected by the AIC criteria, which was two in each case. For each small country, the median and median target responses showed an appreciation of the country’s real exchange rate on impact following a contractionary monetary policy shock. The peak appreciation occurred on impact for New Zealand and the United Kingdom and with a one quarter delay for Australia and Canada. There did not appear to be an exchange rate puzzle here. However, the median and median target responses of GDP to the contractionary monetary policy shock appeared somewhat puzzling in this model. For Canada and the United Kingdom, GDP fell on impact and, rather than reverting, continued to fall over subsequent horizons before levelling out at a permanently lower level. A similar pattern was 19 In the figures, the real exchange rate shock is a one-standard error shock (in percent). When it is normalized to be a 1% shock, the median response shows that the relative interest rate rise on impact is around 25 basis points for Australia, 5 basis points for Canada, 35 basis points for New Zealand and 20 basis points for the United Kingdom. 20 Using the median response, the rise in the relative interest rate on impact following a 1% shock in the real exchange rate is around 35 basis points for the Euro region, 20 basis points for Japan and 15 basis points for the United States.

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observed for Australia and New Zealand, although GDP reverted somewhat at medium term horizons before converging to a permanently lower level. In addition, the success rate for retained impulse responses was substantially lower for Australia, New Zealand and the United Kingdom, and somewhat lower for Canada, under this specification.21 Given the higher success rates and more intuitive responses of GDP to the monetary policy shock in the relative SVAR, it was selected as the preferred model for the small economies. The large economies can potentially influence the economic activity of their trading partners in the SVAR. An alternative approach is to shut down this channel and model the large economies as if they were closed. In that case the domestic variables of a large economy would enter the SVAR simply as themselves with no relativity to the foreign variables which are absent. When SVARs of this type were estimated, there emerged exchange rate and price puzzles. For the Euro region, the median response of the exchange rate to a contractionary monetary policy shock showed a very slight appreciation on impact followed by a very slight depreciation at medium and long horizons. Essentially, the response was not that discernible from zero at all horizons. However, the median target response showed an appreciation at all horizons. For Japan, both the median and median target responses showed that the real exchange rate depreciated (not appreciated) on impact and continued to depreciate for the next four quarters as it converged to a new long-run depreciated value. For the United States, there was no exchange rate puzzle but a price puzzle emerged after four quarters (when the sign restrictions were not in effect) as inflation rose. There was considerable model uncertainty in the response of the exchange rate to the monetary policy shock for each large country as the region between the 16th and 84th percentile responses covered the zero axis at all horizons. In view of these results, the preferred model for the large economies, as for the small economies, is the one formulated in terms of the relative variables. We now investigate whether the results for the relative SVARs are sensitive to the choice of the number of quarters over which the sign restrictions are applied to the impulse responses. Recall that they were applied for two quarters, the quarter of impact and the following one. When applied to the quarter of impact only, the median and median target responses and the region between the 16th and 84th percentile responses changed little. However, for Canada there was now a very slight impact depreciation, and for the United States, an almost indiscernible impact appreciation, shown by the median and median target responses in response to the monetary policy shock. Also a slight price puzzle emerged in the median and median target responses for inflation in the United States. These quantitative changes were all very slight. When the sign restrictions were applied to the quarter of impact and to the subsequent three quarters, there was practically no change in the median target and all the percentile responses. We conclude that our results are robust to whether the sign restrictions are applied for one, two or four quarters, bearing in mind that all our results are subject to the critique of Baumeister and Hamilton (2015). 6. Conditional uncovered interest rate parity (UIP) We now turn to the question of whether UIP holds in each economy, conditional on the monetary policy shock. To f establish notation, let idj and i j be the response of the domestic and foreign interest rate, and sj the response of the nominal exchange rate, j quarters hence, to the monetary policy shock. Consider the following trading strategy. An investor borrows foreign currency, exchanges it for one unit of domestic currency, and with it buys domestic bonds with a term to maturity of one period, then exchanges the interest return from the bond back to foreign currency one period later. (Here a period is a quarter). The excess return on domestic bonds from this strategy is

ψ j = idj − i jf − (s j+1 − s j )

(6)

where the one period change in the nominal exchange rate is expressed as percent per annum, to be compatible with the measure for interest rates. An appreciation of the domestic currency adds to the return from a higher domestic interest rate relative to the foreign interest rate. The excess return ψ j is ex-post and is conditional on the monetary policy shock. Now the relationship between the real f

and nominal exchange rate is given by q j = s j + p j − pdj , where pf and pd are the foreign and domestic price levels and q is the real exchange rate as before. Substitute this expression into (6) and collect terms to arrive at the excess return at horizon j, conditional on the monetary policy shock at time zero22 f d ψ j = idj − i jf − (q j+1 − q j ) − (π j+1 − π j+1 )

(7)

In terms of the notation of the SVAR, this expression is

ψ j = i j − q j+1 − π j+1

(8)

Under conditional UIP

E0 ψ j = 0, 21

∀ j≥0

(9)

The success rates here were: 0.104% for Australia, 2.677% for Canada, 0.102% for New Zealand and 0.521% for the United Kingdom. In the empirics, the one period change in the real exchange rate is measured as percent per quarter. Consequently, it must be multiplied by 4 to put it on an annual percentage basis to be consistent with relative inflation and interest rates which also appear in eq. (8). 22

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Australia

Canada 0.5

3 2

0.0

1

-0.5

0

-1.0

-1

-1.5

-2

-2.0 -2.5

-3 0

5

10

15

20

MED-T

25

MED

16%

30

0

35

5

10

15

MED-T

84%

New Zealand

20

25

MED

30

16%

35

84%

United Kingdom

0.5

2.0 1.5

0.0

1.0 -0.5 0.5 -1.0 0.0 -1.5

-0.5

-2.0

-1.0 0

5

10

15

MED-T

20

25

MED

16%

30

35

0

5

84%

10

15

MED-T

20 MED

25 16%

30

35

84%

Fig. 3. Conditional excess returns for the small economies (percent).

Euro

Japan

1.2

1.5

1.0

1.0

0.8

0.5

0.6

0.0

0.4 -0.5 0.2 -1.0

0.0

-1.5

-0.2

-2.0

-0.4 -0.6

-2.5 0

5

10

15

MED-T

20 MED

25 16%

30

35

84%

0

5

10

15

MED-T

20 MED

25 16%

30

35

84%

United States 1.00 0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 -1.00 -1.25 0

5

10 MED-T

15

20 MED

25 16%

30

35

84%

Fig. 4. Conditional excess returns for the large economies (percent).

where E0 is the expectation, conditional on the realizations of the variables at the time of the monetary policy shock. Eq. (9) says that the excess return, expected to prevail at the time of the monetary policy shock and at all future horizons, is zero under UIP. Basically, UIP says that the expected gain from the domestic interest rate rising above the foreign interest rate following an unexpected tightening of domestic monetary policy is offset by a nominal depreciation of the domestic currency. We report estimates of the response function, eq. (8), corresponding to both the median and median target responses to the monetary policy shock for the small economies in Fig. 3 and for the large economies in Fig. 4. We also show the region

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obtained by substituting the 16th and 84th percentile responses into eq. (8) to give an indication of the spread of excess returns that come from the equally valid responses. For each small country following the monetary policy shock, excess returns deviate from zero (i.e. from UIP) on impact and for several quarters thereafter, based on the returns from the median and median target responses. The deviations are largest (in absolute value) either on impact or in the following two quarters. Apart from these deviations, the results tend to favour UIP in the small economies with the exception of New Zealand. In New Zealand, the negative excess returns are quite persistent and gradually decline from around –1.2 percent to zero percent by 10 quarters. In Australia, Canada and the United Kingdom, the excess returns (in absolute value) are much smaller than in New Zealand after the impact and subsequent two quarters. Turning to the large economies, for the Euro region, excess returns are positive and small, and very gradually converge to zero, based on the median and median target responses This persistence in excess returns is not consistent with UIP. For Japan, the largest excess return (in absolute value) of about 1 percent occurs three quarters after impact. Apart from this deviation, the results for Japan tend to favour UIP. For the United States, the excess return on impact is close to zero based on the median response measure and around 0.75 percent based on the median target response measure. Thereafter excess returns are small for either based measure. The evidence for the United States is the most supportive of UIP. 7. Conclusion This paper provides further evidence of the effect of relative monetary policy shocks on the real exchange rate of four small economies and three large economies. Sign restrictions are used to identify all the shocks in the SVARs so that our analysis is not susceptible to the multiple shocks problem. Exchange rate puzzles can emerge in the SVARs because the sign of the response of the real exchange rate to a relative monetary policy shock is not restricted. We do restrict the sign of the response of all the variables to a real exchange rate shock; in particular, the interest rate cannot fall for two quarters in response to a depreciating real exchange rate shock. The large number of sets of impulse response functions required for the sign restrictions method are generated by the newly proposed procedure of Ouliaris and Pagan (2016). This generation method, like all the other methods of generating impulse responses in sign restrictions, will influence the distribution of accepted impulse responses, and the statistics (e.g. the median response) that summarize them. This makes inference in sign restrictions difficult and our findings should be viewed with this limitation in mind. Moreover, there is considerable model uncertainty in our results as the region covering the 16th to the 84th percentile responses is wide, and covers the zero axis, in many cases. On the basis of the median and median target responses, an exchange rate puzzle does not emerge in either of the small or large economies. However, for some economies, other puzzles emerge. For the Euro region, the impact appreciation is small following a shock that tightens relative monetary policy but the real exchange rate continues to appreciate over subsequent horizons until converging to a much higher long-run level. Also, for the Euro region and New Zealand, the evidence does not favour UIP. On balance though, our findings are in line with many of the predictions of standard open economy models. Acknowledgments We thank Adrian Pagan for detailed remarks, and Geoffrey Kingston and Helmut Lütkepohl for helpful discussion. We also thank two anonymous referees of the journal for constructive comments that improved the paper. Any errors or omissions are our own. The first author thanks the Australian Research Council (Grant DP120102239) for financial support and the School of Economics at Yonsei University for its hospitality. The second author thanks the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2015S1A5A2A01010187) for funding. Appendix Quarterly data for real GDP, inflation and the short-term interest rate for a country were obtained from the OECD’s Main Economic Indicators (MEI) database. (The Euro region is treated as a country). Real GDP for a country is a volume estimate, measured in millions of the national currency, and is seasonally adjusted. Inflation is the change in a country’s consumer price index from the same quarter of the previous year, measured as percent per annum. The interest rate is the 3-month rate, measured as percent per annum and is the average of the monthly figures for the quarter. The real exchange rate is calculated on the basis of a country’s trade weights and is obtained from the Bank for International Settlements (BIS). It is constructed so that a decrease in its value represents a real appreciation of the home, i.e. domestic currency. The OECD MEI database also provides real GDP series for a country in US dollar terms and these are used to construct the trade-weighted average of foreign real GDP’s for a country (the GDP components are unit consistent). We also constructed the trade-weighted average of foreign inflation and foreign short-term interest rates for a country (also in consistent units, percent per annum). The table below shows the trade weights, averaged over the period 1993–2014 and sourced from the BIS, which were used to construct foreign GDP, foreign inflation and the foreign interest rate for the small countries (Australia, Canada, New Zealand and the United Kingdom) and for the large countries (the Euro region, Japan and the United States). The trade weights are the share of a country’s world trade with a major trading partner (Table A1).

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Table A1 Country

Australia Canada N.Z. U.K. Euro Japan U.S.

Major trading partner Australia

Canada

China

Euro

Japan

U.K.

U.S.

Total

− − 0.23 − − − −

− − − − − − 0.17

0.11 0.06 0.10 0.05 0.09 0.18 0.12

0.17 0.08 0.13 0.51 − 0.16 0.18

0.15 0.05 0.14 0.05 0.09 − 0.13

0.05 0.02 − − 0.16 0.03 0.04

0.19 0.67 0.15 0.13 0.18 0.24 −

0.67 0.88 0.75 0.74 0.52 0.61 0.64

Source: Bank for International Settlements (http://www.bis.org/statistics/eer/index.htm)

The table shows, for example, that exports to and imports from Australia represented 23% of New Zealand’s trade with the world. In calculating the foreign variables we used the normalized trade weights which sum to one. For this example, the normalized trade weight is 0.23/0.75, or 30.67%, which says that Australia accounts for 30.67% of New Zealand’s trade with the world. References Barth, M.J., Ramey, V.A.Bernanke, B.S., Rogoff, K. (Eds.), 2001. The cost channel of monetary transmission. NBER Macroecon. Annu. 2001 16, 199–240. Baumeister, C., Hamilton, J.D., 2015. Sign restrictions, structural vector autoregressions, and useful prior information. Econometrica 83 (5), 1963–1999. Bjørnland, H.C., 2009. Monetary policy and exchange rate overshooting: dornbusch was right after all. J. Int. Econ. 79 (1), 64–77. Bjørnland, H.C., Halvorsen, J.I., 2014. How does monetary policy respond to exchange rate movements? New international evidence. Oxford Bulletin Econ. Statis. 76 (2), 208–232. Canova, F., De Nicoló, G., 2002. Monetary disturbances matter for business fluctuations in the G-7. J. Monet. Econ. 49 (6), 1131–1159. Clarida, R., Galí, J., 1994. Sources of real exchange rate fluctuations: how important are nominal shocks? Carnegie–Rochester Conf. Series Public Policy 41, 1–56. Dornbusch, R., 1976. Expectations and exchange rate dynamics. J. Polit. Econ. 84 (6), 1161–1176. Eichenbaum, M., Evans, C.L., 1995. Some empirical evidence on the effects of shocks to monetary policy on exchange rates. Quart. J. Econ. 110 (4), 975–1009. Farrant, K., Peersman, G., 2006. Is the exchange rate a shock absorber or a source of shocks? New empirical evidence. J. Money Credit Bank 38 (4), 939–961. Faust, J., 1998. The robustness of identified VAR conclusions about money. Carnegie–Rochester Conf. Series Public Policy 49, 207–244. Faust, J., Rogers, J.H., 2003. Monetary policy’s role in exchange rate behaviour. J. Monet. Econ. 50 (7), 1403–1424. Finlay, R., Jääskelä, J., 2014. Credit supply shocks and the global financial crisis in three small open economies. J. Macroecon. 40, 270–276. Fisher, L., Huh, H-S., 2002. Real exchange rates, trade balances and nominal shocks: evidence for the G-7. J. Int. Money Financ. 21 (4), 497–518. Fisher, L.A., Huh, H-S., Pagan, A.R., 2015. Econometric methods for modelling systems with a mixture of I(1) and I(0) variables. J. Appl. Econ. doi:10.1002/ jae.2459, Published online 7 April. Fry, R., Pagan, A.R., 2011. Sign restrictions in structural vector autoregressions: a critical review. J. Econ. Literature 49 (4), 938–960. Grilli, V., Roubini, N., 1995. Liquidity and exchange rates: puzzling evidence from the G-7 countries. Mimeo (Yale University, New Haven, CT) March. Grilli, V., Roubini, N., 1996. Liquidity models in open economies: theory and empirical evidence. Eur. Econ. Rev. 40 (4), 847–859. Huh, H-S., Kwon, W.S., 2015. Sources of fluctuations in the real exchange rates and trade balances of the G-7: a sign restriction VAR approach. Rev. Int. Econ. 23 (4), 715–737. Jääskelä, J., Jennings, D., 2011. Monetary policy and the exchange rate: evaluation of VAR models. J. Int. Money Financ. 30 (7), 1358–1374. Jääskelä, J., Jennings, D., 2010. Monetary Policy and the Exchange Rate: Evaluation of VAR Models. Reserve Bank of Australia Research Discussion Paper, 2010-07. http://www.rba.gov.au/publications/rdp/2010/2010-07.html . Kim, S., Roubini, N., 20 0 0. Exchange rate anomalies in the industrial countries: a solution with a structural VAR approach. J. Monet. Econ. 45 (3), 561–586. Liu, P., 2010. The effects of international shocks on Australia’s business cycle. Econ. Record 86 (275), 486–503. Ouliaris, S., Pagan, A.R., 2016. A method for working with sign restrictions in structural equation modelling. Oxford Bulletin of Economics and Statistics, http://dx.doi.org/10.1111/obes.12137, Published online 29 April. Peersman, G., 2005. What caused the early millennium slowdown? Evidence based on vector autoregressions. J. Appl. Econ. 20 (2), 185–207. Prasad, E., 1999. International trade and the business cycle. Econ. J. 109 (458), 588–606. Scholl, A., Uhlig, H., 2008. New evidence on the puzzles: results from agnostic identification on monetary policy and exchange rates. J. Int. Econ. 76 (1), 1–13. Shapiro, M.D., Watson, M.W.Fischer, S. (Ed.), 1988. Sources of business cycle fluctuations. NBER Macroeconomics Annual 3, 111–148. Sims, C.A., 1992. Interpreting the macroeconomic time series facts: the effects of monetary policy. Eur. Econ. Rev. 36 (5), 975–10 0 0. Stock, J.H., Watson, M.W., 2016. Factor models and structural vector autoregressions in macroeconomics. Handbook of Macroeconomics. Uhlig, H., 2005. What are the effects of monetary policy on output? Results from an agnostic identification procedure. J. Monet. Econ. 52 (2), 381–419.