What Horizon for Targeting Inflation?

Akram, Q. Farooq Working Paper What Horizon for Targeting Inflation? Working Paper, No. 2007/13 Provided in Cooperation with: Norges Bank, Oslo Suggested Citation: Akram, Q. Farooq (2007) : What Horizon for Targeting Inflation?, Working Paper, No. 2007/13, ISBN 978-82-7553-414-7, Norges Bank, Oslo, https://hdl.handle.net/11250/2498260 This Version is available at: https://hdl.handle.net/10419/209889 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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Hensikten er blant annet at forfatteren kan motta kommentarer fra kolleger og andre interesserte. Synspunkter og konklusjoner i arbeidene står for forfatternes regning. What horizon for targeting inflation? Q. Farooq Akram∗ Research Department, Norges Bank December 7, 2007 Abstract We investigate optimal horizons for targeting inflation in response to different shocks and their properties under alternative preferences of an inflation-targeting central bank. Our analysis is based on a well specified macroeconometric model of Norway, but we examine how alternative specifications of its key equations would affect our results. We find that the optimal horizon is highly shock-specific, precluding general conclusions for demand and supply shocks. An extension of the horizon with concern for output and/or interest rate fluctuations beyond some shock-specific level proves counterproductive. The size of a given shock does not affect the horizon unless the central bank cares about interest rate volatility, while its sign does not matter unless the model is non-linear. The optimal horizon in response to a combination of shocks cannot be derived from those for each of the shocks, as different shocks may amplify or modify the effects of each other. In this case, however, sources of shocks as well as their sizes and signs become relevant, leading to complex dynamics of inflation and output. Successful inflation targeting in such cases may require a complex interest rate response. The optimal horizon generally increases with the degree of persistence in a shock and decreases with the strength of stabilisation mechanisms in the model. Keywords: Monetary policy, Inflation targeting, Horizon. JEL Codes: C53, E31, E52. ∗The views expressed in this paper are those of the author and should not be interpreted as reflecting those of Norges Bank (the central bank of Norway). I am grateful to several colleagues especially Bjørn Naug and seminar participants at Norges Bank for useful comments. Address: Research Department, Norges Bank; Bankplassen 2, P.O. Box 1179 Sentrum, 0107 Oslo, Norway; Tel: +47 22316692; Fax: +47 22424062; faroo[email protected]. 1 1 Introduction The horizon for achieving the inflation target is a key element in the design of monetary policy under an inflation-targeting regime. The horizon determines the monetary policy response to shocks. It is especially important for deriving an interest rate path consistent with the preferred inflation path towards its target; a small but increasing number of central banks publicly announce such interest rate paths. Moreover, communication of the horizon is crucial for anchoring inflation expectations at the target in the medium run and the accountability of monetary policy authorities. Inflation-targeting central banks tend to adopt short rather than long horizons, partly to avoid compromising their credibility as inflation targeters. Many inflation-targeting central banks have either preannounced a fixed horizon of 1 or 2 years or a variable horizon of 1–3 years; see Roger and Stone (2005). Some central banks including Norges Bank, however, refrain from quantifying the horizon and state that they will seek to bring inflation close the target in the ‘medium run’, which is commonly understood to extend not too far in the future. Choice of a fixed relatively short horizon or range is often based on estimated time lags from interest rate changes to their main effects on inflation. The relevant literature, however, suggests that the horizon should also depend on the nature of shocks and their properties, particularly size and persistence. It also suggests that the horizon should depend on the extent to which the central bank pursues other policy objectives in addition to the inflation target; see Svensson (1997) and Ball (1999). It is often argued that the optimal policy horizon becomes longer the greater the weight is placed on secondary objectives like smoothing output and/or interest rate fluctuations in the authorities’ objective function. It follows that, due to differences in preferences for output stabilisation, the optimal horizon in response to a shock may vary across economies even if they become exposed to the same shock. The small number of existing empirical studies do not seem to be particularly helpful in pinpointing the optimal horizons in response to different shocks and preferences for output stabilisation. So far, mostly relatively small VAR models and systems of equations for aggregate demand, aggregate supply, and (occasionally) the exchange rate have been used to derive the optimal horizons in the face of demand and supply shocks; see e.g. Batini and Nelson (2001) and Smets (2003). A drawback of using such highly aggregate models is that one can only derive optimal horizons for a few aggregate shocks. A disaggregate model allowing for different kinds of demand and supply shocks is required to estimate the corresponding optimal horizons, since the trade-off between inflation and output volatility may differ across shocks. Hence, if the optimal horizon is shock-dependent, and there are large costs associated with deviating from the optimal horizons, as suggested by e.g. Smets (2003), it may prove costly to infer the optimal horizons corresponding to various types of demand and supply shocks from those for the aggregate demand and supply 2 shocks. Second, optimal horizons corresponding to different shocks have been shown to be highly modeldependent; see e.g. Batini and Nelson (2001) for evidence based on the UK data. Therefore, one may argue that optimal horizons in response to different shocks should be derived from credible empirical models. Third, optimal horizons suggested by some studies also seem rather long to be reconciled with horizons actually communicated by inflation-targeting central banks; see Roger and Stone (2005). In e.g. Smets (2003), where the evidence is based on the Euro-area data, the optimal horizon (in the face of shock to prices) ranges from a few years to infinity depending on assumed concern for output and interest rate fluctuations. Finally, one may also question the realism of a monotonic increase in optimal horizons with concern for e.g. output fluctuations. When disturbed by a shock, an economy may be able to adjust and reach its equilibrium over time through several built-in stabilisation mechanisms. Intuitively, the adjustment period should not exceed the life spans of different forms of rigidities, especially those of nominal rigidities. An active monetary policy may help the economy reach its equilibrium at a faster pace than on its own through appropriate changes in nominal interest rates. One may therefore not expect optimal horizons to exceed the life spans of different rigidities. Otherwise, monetary policy would be prolonging the economic disequilibrium caused by shocks beyond their own ”life spans” which can seem inconsistent with strong preferences for output stabilisation. The evidence of a monotonic increase in the optimal horizons beyond reasonable time spans could be an artefact of models employed with weak if any stabilisation mechanisms besides that of monetary policy itself. We investigate the optimal policy horizons and their properties in the face of different shocks using an econometrically well specified model of the Norwegian economy based on quarterly data.1 We assume that the central bank is a flexible inflation targeter, such as Norges Bank; see Norges Bank (2007). Specifically, it is assumed that the central bank decides on an interest rate path that minimizes variability in deviations from the inflation target and the variability in the output gap, while ensuring that inflation will reach its target in the foreseeable future. The primacy of achieving the inflation target in the ’medium run’ while accepting short-run deviations from the inflation target to promote output stability seems consistent with the practice of many inflation targeting central banks; see e.g. Tuladhar (2005), Smets (2003), Meyer (2004), Blinder (2006) and Giavazzi and Mishkin (2006). That is, such central banks seem to accommodate concern for output stabilisation by choosing 1The model used is a version of the model presented in B˚ardsen et al. (2003,2005) which is documented in Akram and Eitrheim (2006). The model is part of the suite of models maintained by Norges Bank. A number of researchers have called for monetary policy analysis using models that are actually used in policy making institutions rather than simplified models used for illustrations; cf. Goodhart (2001). Our use of this macroeconometric model is partly motivated by this call. 3 an appropriate horizon for achieving an implicit or explicit inflation target. Accordingly, one may define the optimal target horizon as the time at which it is least costly, for a given loss function, to bring inflation back to target after a shock; cf. Batini and Nelson (2001). To derive optimal horizons within such a monetary policy framework using the econometric model, we employ the procedure suggested in Akram (2007). This procedure seems to characterise the actual process of deriving interest rate and inflation rate paths quite well and makes it easy to conduct such analyses when employing macroeconometric models, irrespective of their size. This procedure focuses on the optimal policy horizon, which is defined as the time at which it is least costly to bring the nominal policy rate back to its neutral rate. In practice and in the model used, the optimal policy horizon is closely linked to the optimal target horizon, as defined above.2 The model employed is more extensive than the models used in most of the previous studies. It therefore enables us to investigate optimal horizons associated with several kinds of demand and supply shocks. In addition, the quarterly base of our model makes it possible to derive the optimal horizons more precisely than models based on annual data. Such precision is important if there are relatively large costs associated with deviating from an optimal horizon. Our model also pertains to a relatively more open economy than e.g. the UK and the Euro area, which are the subjects of two notable studies Batini and Nelson (2001) and Smets (2003), respectively. If the exchange rate channel plays a relatively stronger role in our model, the optimal policy horizons for different shocks are likely to be shorter than those reported by these studies. Moreover, our model has more built-in stabilisation mechanisms than models used in much of the previous work on the topic. Ours is an equilibrium-correction model characterising dynamic adjustment of endogenous variables to their long-run equilibrium paths. This feature may also contribute to relatively shorter horizons. On the other hand, our model does not have forwardlooking features. This may contribute to relatively longer horizons than implied by models with forward-looking features. We use the model to investigate several issues in addition to those studied earlier. We investigate effects of the source, size, sign and persistence of single as well as combined shocks on the optimal policy horizon. The investigation also shed lights on how concern for output stabilisation and/or interest rate volatility affects optimal policy horizons. Moreover, we illustrate the model dependence of the optimal horizons by altering key equations of the model rather than limiting such an exercise to changes in specific parameters, as in previous studies. This exercise highlights the role of adjustment mechanisms in the model and their influence on optimal policy horizons. Our analysis brings forth the important role of the transmission lags of shocks relative to those of monetary policy. The horizon is often chosen on the basis of transmission lags from a 2Monetary Policy Reports of e.g. Norges Bank and Sveriges Riksbank typically show that forecasts of inflation and policy interest rates converge with the target inflation and some level of the neutral interest rate, respectively, at about the same time. 4 monetary policy shock to the economy, while transmission lags from shocks to the economy are often neglected. Our study suggests that both kinds of lags must be viewed in relation to each other, to better synchronise stabilising effects of monetary policy to destabilising effects of shocks. Our results regarding optimal horizons for transitory shocks are consistent with those usually communicated by central banks while those for relatively persistent shocks call for substantially longer horizons than 3–4 years. It appears that evidence of relatively long (optimal) horizons reported by some previous studies can be reproduced if we weaken or switch off the equilibriumcorrection features of our model. Our results do not support a generally positive relationship between optimal horizons and the degree of concern for output stability. Specifically, optimal horizons becomes invariant to concern for output stability above some shock-specific degrees. Finally, our results support the view that monetary policy need not always prove to be stabilising; cf. Friedman (1961). The intuition behind this result is that when there are numerous shocks with different signs and sizes, their combined effects on the economy can be relatively complex. In such cases, a rather simple monetary policy response, e.g. a contractionary or expansionary monetary policy followed by a gradual return to a neutral monetary policy stance, can prove counterproductive, as it can turn out to e.g. amplify the effects of the shocks in some periods. Such a policy response can also be unnecessary if the effects of different shocks outweigh each other. Accordingly, we find that monetary policy turns out to be counterproductive in a non-negligible number of cases, and warrants a lot of information and fine-tuning to get the response right. This is consistent with Friedman’s argument that monetary policy in the face of e.g. ”long and variable lags” can prove to be destabilising. The paper is organised as follows. Section 2characterizes the monetary policy framework. Section 3sets out a stylised version of the macroeconometric model. Sections 4–7present our results and analysis while Section 8concludes. The appendix includes data definitions and alternative wage and price systems. 2 Monetary policy objectives and the interest rate rule To devise an optimal response to an observable shock that occurs at time τ, we assume that a forward-looking central bank minimises the following loss function with respect to an interest rate path iτ,iτ+1,iτ+2,..iτ+H−1,iτ+H,iτ+H+1,...: Lτ=V(πt−π∗) + λV (yt),(1) subject to the constraint that the conditional mean of inflation in period τ+His close to its constant target rate, π∗: Eτπτ+H≈π∗.(2) 5 V(·) is a variance function while π−π∗denotes the inflation gap, ydenotes the output gap and λ indicates the degree of concern for fluctuations in the output gap relative to that for fluctuations in inflation; tis a period indicator. The loss function is a reformulation of a quadratic loss function assuming that the discount factor is close to one. Eτis an expectation operator conditional on the information at time τ. We use Hto represent the policy horizon, which we define as the number of periods of appropriate length, here quarters, during which the policy interest rate will deviate from its neutral value and stimulate or cool off the economy. Hcan take on any discrete value from zero onwards. Thus, the precise policy horizon, when measured as the number of periods, would be H+ 1, because H ≥0. The target horizon, i.e. the number of periods inflation will deviate from target, will generally be linked and be close to the policy horizon, but the exact relationship will be shock- and modeldependent, as shown in Section 4.2.1.3Inflation will typically converge asymptotically to its target rate in the wake of a shock in a dynamic model. Hence, imposing an exact target horizon is generally not meaningful.4We assume that when the policy interest rate has almost converged with its reference value in period H, the inflation target will be largely achieved. This seems to be consistent with published future paths of interest rates and inflation, as noted earlier. Also, our approach would not lead to overly gross approximations of the optimal target horizons, in comparison with those based on alternative suggestions in the literature; cf. Batini and Nelson (2001).5 We envision that in the face of a shock, the central bank derives a set of interest rate paths, each of them satisfying the constraint (2) for different policy horizons, i.e. Hvalues. Then, from this set of interest rate paths, it selects and implements the interest rate path, and the corresponding policy horizon, that would minimise the loss function (1). However, there can be numerous interest rate paths that satisfy the constraint (2) for every possible value of H. By only considering interest rate paths that adhere to some reasonable pattern, however, the set of relevant interest rate paths can be limited to the number of policy horizons (H 3In several studies, including Batini and Nelson (2001), policy horizon is equated with target horizon, as defined here. 4Beside its simplicity, the procedure allows us to achieve price stability asymptotically rather than exactly at a particular horizon. The latter is apparently an unrealistic feature of e.g. Smets (2003) who models the price stability constraint as an exact forward-looking constraint on either inflation or the price level at a particular horizon. Imposing an exact constraint at a particular horizon also gives rise to unattractive interest rate volatility at that horizon. 5Batini and Nelson (2001) suggest two operational definition of an optimal target horizon: an absolute and a relative horizon concept. They define an absolute horizon as the number of periods ahead at which inflation has returned permanently to within a specific target range, i.e. of ±0.1 percentage point, following a shock today. The relative horizon concept is based on what fraction of a shock’s effect policy has succeeded in eliminating. They define the relative horizon as the number of periods ahead at which 90% of the peak effect of the shock on inflation has been extinguished. In contrast to the relative horizon, the absolute horizon depends on the size of the shock. Another way to define target horizon is to associate it with the time period when inflation ”first touches-down” at its target rate in the wake of a (positive) shock. We essentially define policy and target horizons as relative horizons. We use the relative concept for the interest rate as well as the inflation rate, while specifying the convergence criteria explicitly for only the interest rate. The extent of convergence of inflation with its target rate at the policy horizon will depend on the convergence criteria for the interest rate, but varies across shocks. 6 4 Shock properties and policy horizons In this section, we first investigate variation in the policy horizon across different kinds of shocks in detail and demonstrate that there may exist a close relationship between optimal policy horizons and optimal target horizons. Thereafter, we investigate possible effects on optimal policy horizons of size, sign and persistence of shocks. Our empirical analysis is based on the following assumptions, unless otherwise stated. The monetary policy response to a shock is characterised by (3). Values of %Hfor different policy horizons are obtained from %H=δ1/(H+1), where we set δat say 0.1 to define convergence of interest rates with the neutral interest rate i0. That is, we would consider an interest rate deviation from i0 eliminated when the deviation is not more than 1/10 of the initial deviation from i0. Alternative values of δdo not bring about substantially different results. Estimates of the horizon-specific response coefficients βε,H for a given shock can be obtained from its formula: (1 −%H)βε/(1 −φ), for different degrees of persistence in the shock and interest rates, φand %H, respectively. Finally, values of the loss function (4) are based on λequal to 0.5. Implications of alternative values of λ are discussed in Section 6. 4.1 Demand and supply shocks 4.1.1 Monetary policy response to transitory demand and supply shocks In the following, we present our estimates of βε,H and %Hpertaining to transitory demand and supply shocks, respectively, for different policy horizons in the range 0–20 quarters. Here, the transitory demand shock refers to an increase in the residual in the aggregate demand equation (εy) such that growth in aggregate demand initially increases by one percentage point over a year. The transitory supply shock refers to an increase in the residual in the (consumer) price equation (εcpi) such that price inflation increases by one percentage point over a year. The left and the middle frames of Figure 1display values of the response coefficient for the (transitory, φ= 0) demand shock and the supply shock, respectively. The horizontal axes present policy horizons. The right frame of Figure 1depicts the degree of interest rate smoothing %H implied by the different policy horizons. Before analysing the results for each of the two shocks, we make the following general observations. First, an increase in the policy horizon reduces the required initial interest rate response to a shock, but raises the degree of interest rate smoothing, ceteris paribus; see Figure 1. For example, the required initial interest rate response declines substantially if the policy horizon is increased from 0 to 8 quarters. This must, however, be accompanied by an increase in interest rate smoothing, %H, from 0.1 to 0.77 (right frame). And second, an increase in the policy horizon from a low level leads to a larger reduction in the response coefficient than an increase in the policy horizon from 13 0 3 6 9 12 15 18 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 βy,H 0 3 6 9 12 15 18 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 βcpi,H 0 3 6 9 12 15 18 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 ρ× H Figure 1: Left: Initial interest rate responses to the demand shock (in percentage points) implied by different policy horizons (horizontal axes), βy,H . Middle: Initial interest rate responses to the supply shock (in percentage points) implied by different policy horizons, βcpi,H. Right: Interest rate smoothing, %H, associated with different policy horizons. a relatively high level. This is due to the concave relationship between the degree of interest rate smoothing and the policy horizon, since %H=δ1/(H+1), which in turn leads to a convex relationship of geometric form between the response coefficient and the policy horizon. A linear relationship between the degree of interest rate smoothing and the policy horizon would have implied a linear relationship between the response coefficient and the policy horizon. However, the results presented would not have changed qualitatively. Notably, the response coefficients in the face of the demand shock and the supply shock are comparable to typical response coefficients in simple Taylor rules, especially when the horizon is around 3 quarters. Then, the response coefficient in response to the demand shock is about 1.5, while that in response to the supply shock is 0.5. At this horizon or higher, the implied degree of interest rate smoothing is also comparable to that found on many data sets; see e.g. Brian and Wieland (2000). The right frame shows that the degree of interest rate smoothing is close to 0.6 for horizons around 3 quarters. Figure 2displays interest rate paths over time suggested by the policy rule (3) in response to a supply shock for three different policy horizons: 3, 6 and 12 quarters. The policy rule has been specified by reading the corresponding values of the response coefficients and the degree of interest rate smoothing from Figure 1. 14 0 3 6 9 12 15 18 0.5 1.0 1.5 2.0 2.5 (i − i0)|H=3; εcpi (i − i0)|H=6; εcpi (i − i0)|H=12; εcpi Figure 2: Interest rate paths over time (in quarters) implied by three different policy horizons in the face of the supply shock. The three interest rate paths are associated with the policy horizons of 3, 6 and 12 quarters, respectively. The interest rates are measured as deviation from the reference interest rate, i.e. the neutral rate, in percentage points. 4.1.2 Optimal policy horizons Figure 3sets out the economic performance conditional on different horizons in the face of the demand and supply shocks. The economic performance associated with every policy horizon is measured by the standard deviations of the output gap and inflation. We present values of the loss functions under different policy horizons relative to their value under the optimal policy horizon (H∗) for a given shock (ε); see equation (5) for the definition. As expected, there is no conflict between the objectives of price stabilisation and output stabilisation in the case of the demand shock; see Figure 3, left panel. Moreover, it appears that both objectives can be promoted by reducing the policy horizon. Hence, a policy horizon of zero appears as the most efficient one. The values of the relative loss functions are zero, i.e. at their optimal level, for H= 0. This finding is consistent with the bulk of studies suggesting that demand shocks should be counteracted as aggressively as possible, since inflation can be stabilised jointly with output. Figure 3also presents the economic performance of (optimal and suboptimal) policies employed in response to the supply shock. The right panel of the figure shows that there is a trade-off between price and output stabilisation for different ranges of policy horizons. Specifically, there is a trade-off in the range of 0 to 6 quarters. Policy horizons that are longer than 6 quarters appear inefficient 15 .20 .22 .24 .26 .28 .30 .040 .045 .050 ← H=0 s_inf × s_y .15 .20 .25 .30 .35 .40 .32 .34 .36 H=0 ↓ s_inf × s_y 0 3 6 9 12 15 0 25 50 75 100 ∆L(H, y) ×H 0 3 6 9 12 15 0 5 10 15 20 25 ∆L(H, cpi) ×H Figure 3: Top: Performance of the policy rules associated with different policy horizons in the face of the demand shock (left-hand side) and the supply shock (right-hand side), respectively. The policy rules are associated with policy horizons (Hs) in the range of 0-15 quarters. We only indicate the performance of the interest rate rule defined by H =0, while that of the interest rate rule defined by H = 1 is depicted next to it and so on. Bottom: plots of the values of the relative loss function (in %), ∆L(.),against different policy horizons in the case of the demand shock (left-hand side) and the supply shock (right-hand side). The policy horizon is optimal when ∆L(.)= 0. as both price and output stabilisation can be improved by shortening the policy horizon. The optimal policy horizon is 3 quarters in the case of the supply shock. It also appears that there are substantial costs associated with choosing a suboptimal policy horizon. The costs of deviating from the optimal horizon are larger in the case of the demand shock than the supply shock. Second, the increase in the costs seem to decline with the policy horizon. The case of the supply shock also suggests that the costs of deviating from the optimal horizon are asymmetrically distributed around the optimal. Specifically, the costs of choosing a longer than optimal horizon seem to be lower than those from choosing a shorter than optimal horizon. This asymmetry is because of the concave relationship between the degree of interest rate smoothing and the policy horizon, and not due to any asymmetry in the loss function. Nevertheless, the evidence is apparently consistent with that presented in Smets (2003). 4.2 Different kinds of demand shocks The above section suggests that one should offset effects of a demand shock as soon as possible and adopt a relatively aggressive response. However, in the following we show that relatively 16 0 3 6 9 12 15 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 βe,H 0 3 6 9 12 15 0.05 0.10 0.15 0.20 0.25 βhp,H Figure 4: Left: Initial interest rate responses to the nominal exchange rate shock (in percentage points) implied by different policy horizons (horizontal axes), βe,H . Right: Left: Initial interest rate responses to the house price shock (in percentage points) implied by different policy horizons, βhp,H. aggregated models may provide a distorted view of the appropriate horizon in the case of different demand shocks. This is because different demand shocks affect the economy with different lags. Hence, if one offsets the effects of all shocks that are commonly classified as demand shocks with a rather short horizon, monetary policy may prove inefficient and even counterproductive. In the following, we show that optimal policy horizons may vary considerably across shocks even when they are of the same type. We consider the cases of an exchange rate shock and a house price shock which in our model can be interpreted as demand shocks. Similar results can be obtained for the case of different supply shocks such as productivity shocks or wage growth shocks. Figure 4shows the response coefficients associated with the different horizons in response to an exchange rate shock and a house price shock. In the latter case, the response coefficients are relatively smaller in comparison with those in the case of the exchange rate shock. This is because the inflationary effects of a house price shock are considerably smaller than those of an exchange rate shock, as noted in Section 3.1. As noted above, the lags from the house price shock to output and inflation are also longer than those in the case of the exchange rate shock. This is reflected in the corresponding optimal policy horizons. The effects of the exchange rate shock are actually comparable to those of the supply shock. Figure 5depicts the efficiency frontiers for different horizons. It appears that the optimal 17 .060 .065 .070 .075 .080 .085 .090 .020 .025 .030 .035 .040 H=0 ↓ s_inf × s_y .015 .020 .025 .030 .035 .005 .008 .011 H=0 → s_inf × s_y 0 3 6 9 12 15 20 40 60 ∆L(e, H) ×H 0 3 6 9 12 15 100 300 500 700 ∆L(hp, H) ×H Figure 5: Top: Performance of the policy rules associated with different policy horizons in the face of the exchange rate shock (left-hand side) and the house price shock (right-hand side), respectively. The policy rules are associated with policy horizons (Hs) in the range of 0-15 quarters. See Figure 3for more details. horizons in the case of both the exchange rate shock and the house price shock are longer than in the case of the shock to the aggregate demand equation. In particular, the optimal horizon in the latter case is about 12/13 quarters, which is even longer than in the case of the supply shock considered above. In these two examples, the optimal policy horizons are close to or longer than that for the supply shock. 4.2.1 Optimal target horizons Below, we present some examples suggesting that there is a close relationship between the optimal policy horizon and the target horizon. Hence, the optimal policy horizon can be considered a close indicator of the optimal target horizon. In general, the relationship between policy and target horizons is shock- and model-dependent. In a dynamic model, the target horizon is likely to be somewhat longer than the policy horizon as the effects of monetary policy stimulus may remain effective for some time after interest rates have converged to their neutral rate. The optimal target horizon associated with a shock can be defined as the time it takes for inflation to almost converge with its target rate after the shock under the corresponding optimal interest rate rule, as defined by the optimal policy horizon associated with the shock. We would consider inflation to be converged with its target rate when it first ’touches’ its target after the 18 shock. Even though it can display complicated dynamics after the first ’touch’, we would consider that to be largely dependent on the dynamic properties of the model.13. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 −0.005 0.000 0.005 0.010 Inflationt |εcpi; H* = 3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 −0.0005 0.0000 0.0005 0.0010 Inflationt |εe; H* = 3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 −0.0005 0.0000 0.0005 0.0010 Inflationt |εy; H* = 0 Figure 6: Convergence of inflation to its target rate in response to different shocks under the corresponding optimal policy rules, which are represented by the optimal policy horizons H ∗. Optimal target horizons are suggested by the first ’touch down’ of inflation to its target rate, indicated by zero on the vertical axes. The horizontal axes indicate the time periods in quarters. To obtain the precise target horizons in the case of different shock, we simulate the model under corresponding optimal interest rate rules defined by the associated optimal policy horizons. Figures 6.a–c show the optimal target horizons in the case of the supply shock, exchange rate shock and the aggregate demand shock, respectively. Obviously, inflation converges gradually to its target rate after the first ”touch down”. Nevertheless, it appears that the first ’touch downs’ are remarkably close to the optimal policy horizons. In particular, in the case of the supply shock, the optimal policy horizon is equal to the optimal target horizon, i.e. 3 quarters. In the case of the exchange rate shock, the optimal target horizon exceeds the policy horizon by just one quarter, and is equal to 4 quarters. In the case of the aggregate demand shock, the optimal target horizon is approximately equal to the optimal policy horizon. We note that the optimal target horizon is about 1/2 of a quarter in this case, while the 13There are also alternative definitions of optimal target horizons, e.g. the relative measure, which are influenced by the pattern of convergence to the target in the aftermath of a shock. This measure appears, however, to be influenced too much by properties such as the size of the shock and the dynamic properties of a given model. For example, the relative measure implies optimal target horizons that would also depend on the size of the shock and suggests that the horizon is short in the case of small shocks but long in the case of large shocks. Moreover, convergence becomes too lengthy in the case of all shocks in a dynamic model. Thus, differences between optimal target horizons become less pronounced. Hence, such measures seem not only to overestimate the optimal target horizons in general, but also underplay differences in them across shocks. 19 .2 .3 .4 .5 .6 .04 .06 .08 .10 s_inf ×s_y; εy = 2pp s_inf ×s_y; εy = 1pp .2 .3 .4 .5 .6 .7 .8 .3 .4 .5 .6 .7 s_inf ×s_y; εcpi = 2pp s_inf ×s_y; εcpi = 1pp 0 3 6 9 12 15 25 50 75 100 125 ∆L(y, H); εy = − 2pp ∆L(y, H); εy = − 1pp ∆L(y, H); εy = + 1pp ∆L(y, H); εy = + 2pp 0 3 6 9 12 15 10 20 30 ∆L(cpi, H); εcpi = − 2pp ∆L(cpi, H); εcpi = − 1pp ∆L(cpi, H); εcpi = + 1pp ∆L(cpi, H); εcpi = + 2pp Figure 7: Performance of the policy rules associated with different policy horizons in the face of demand shocks of different sizes and signs (left-hand side) and that of different sizes and signs of the supply shock (right-hand side), respectively; see Figure 3for more details. 1pp and 2pp denote shocks implying 1 and 2 percentage points direct initial changes in the variable of interest, e.g. output growth or inflation, respectively. The results for shocks implying -1pp and -2pp changes in the graphs at the top are left out since their results were identical to those for shock sizes 1pp and 2pp. optimal policy horizon is equal to zero, i.e. contemporaneously with the shock. In contrast to the case of the supply shock and the exchange rate shock, inflation displays quite complex dynamics after the first touch down before it settles down to the inflation target. In the former cases, inflation converges relatively smoothly towards the target over the 5-year period (20 quarters). These three shocks also illustrate that if we had defined the optimal target horizon as the time it would take before inflation settles down to its target, there would not be much difference in optimal target horizons across different shocks. 4.3 Size and sign of shocks The sign of a given shock is not expected to have an effect on the optimal policy horizon when the model is linear and the loss function is quadratic. Figure 7confirms this intuitive result. It shows that the optimal policy horizon is the same irrespective of the signs of the shocks. Figure 7also shows that the size of a shock does not affect the optimal policy horizon. This is because only the location of the efficiency frontier changes when we vary the size of the shock, while its shape remains the same. The left panel shows that the optimal policy horizon remains 20 0 3 6 9 12 15 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 f(H*)|εy 0 3 6 9 12 15 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 f(H*)|εcpi Figure 8: Distribution of the optimal policy horizon in the case of demand shocks of different sizes and signs is presented on the left-hand side and that in the case of supply shocks of different sizes and signs is presented on the right-hand side. Value of ”1” on the vertical axis suggest that 100% of the shocks of a given kind have optimal horizon at the level indicated on the horizontal axis (in quarters). 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 ∆L(H; εcpi = +1pp); χ= .05 ∆L(H; εcpi = +2pp); χ= .05 Figure 9: Plots of the values of the relative loss function ( ∆L(.)) (in %) at different policy horizons in the case of supply shocks of different sizes. The loss function has been modified to incorporate concern for interest rate volatility which is measured by χand its value has been set to 0.05. The policy horizon is optimal when ∆L(.)= 0. zero in the case of demand shocks while it remains 3 quarters in the case of supply shocks, when λis 0.5. This is further confirmed by Figure 8, which reports the optimal horizons in the face of numerous demand and supply shocks of different sizes and signs. It shows that all of the demand shocks have an optimal policy horizon equal to zero while all of the supply shocks have an optimal policy horizon equal to 3 quarters. 21 In our approach, the optimal policy horizon seeks to synchronise the effects of the shock with those of the monetary policy response as much as possible. The degree of synchronisation is independent of the size of the shock in our linear model. Thus, a counteraction of the effects of a shock only requires a rescaling of the monetary policy response in accordance with the size of the shock. The optimal policy horizon therefore remains invariant to the size of the shock. However, the required interest rate changes can be particularly large in the face of relatively large shocks. Thus, if we had allowed for a concern for interest rate volatility in the loss function, the optimal policy horizon would have increased with the size of the shock. For example, Figure 9shows that the optimal horizon increases by one quarter, from 4 to 5 quarters, when the size of the shock is increased from 1pp to 2 pp, under the assumption that the central bank is averse to interest rate volatility. This is defined as variance of ∆rand the degree of aversion, represented by χ, is set at 0.05. In the benchmark case, where χis zero, the optimal policy horizon is 3 quarters. Higher degrees of aversion (χ) are expected to bring about a larger extension in the optimal policy horizon when the shock size is increased. Figure 7also suggests that if the shock is correctly identified, the costs of choosing the wrong horizon are independent of the size and signs of the shocks if the central bank only cares about output stability. This is mainly because the monetary policy response is otherwise attuned to the shock. However, when the economy is exposed to a combination of shocks, their signs as well as sizes influence the optimal policy horizons. The results for combinations of shocks are presented in Section 5. 4.4 Persistent shocks In the following we analyse effects of persistence in shocks on the optimal policy horizons. For simplicity, we assume that a shock (to an equation in the model) follows an AR(1) process with degree of persistence denoted by φ: ετ=φετ−1+υτ(14) We shock the model conditional on a specific φvalue and then implement the rule (3) for different H-values, to derive the optimal policy horizon. The interest rate rule (3) implies that the interest rate response increases in a non-linear fashion with the degree of persistence. In the following, we present the results for the demand and supply shocks with different degrees of persistence. The estimated response coefficient at different H-values for these shocks can be learned from Figures 10 and 11, and then adjusted for different degrees of persistence to obtain implementable rules. For comparison, we also plot the results in the case of the transitory shocks presented in Figure 10. 22 0 3 6 9 12 15 0 25 50 75 100 ∆L(y, H); λ= 0 ∆L(y, H); λ= .5 ∆L(y, H); λ= 1 ∆L(y, H); λ= 2 0 3 6 9 12 15 0 25 50 75 100 ∆L(e, H); λ= 0 ∆L(e, H); λ= .5 ∆L(e, H); λ= 1 ∆L(e, H); λ= 2 0 3 6 9 12 15 0 25 50 75 100 ∆L(hp, H); λ= 0 ∆L(hp, H); λ= .5 ∆L(hp, H); λ= 1 ∆L(hp, H); λ= 2 0 3 6 9 12 15 0 25 50 75 100 ∆L(cpi, H); λ= 0 ∆L(cpi, H); λ= .5 ∆L(cpi, H); λ= 1 ∆L(cpi, H); λ= 2 Figure 15: Top: plots of the values of the relative loss function, ∆L(.)in %, defined by different λ values against different policy horizons in the cases of the demand shock (left-hand side) and that of the nominal exchange rate shock (right-hand side). Bottom: plots of the values of the relative loss function defined by different λvalues against different policy horizons in the cases of the house price shock (left-hand side) and those of the supply shock (right-hand side); see Figure 3for more details. There seems to be a strongly concave relationship between the optimal horizon and lambda (λ); see Figure 15. This shows that the optimal policy horizon increases abruptly from zero to 3 when lambda increases from 0 to 0.5. Thereafter, however, the optimal horizon increases only up to 5 even when lambda becomes 2 or even higher. This is because, increasing the horizon beyond 5 quarters would be inefficient; see Figures 3and 5. Thus, no matter how much one cares about output, one will not adopt a horizon, and the associated interest rate path, that can be improved on. In particular, the monetary policy rule suggests that choosing a too long horizon can imply a too large reduction of the response coefficient (βε,H ) causing a violation of the so-called Taylorprinciple. That is, the nominal interest rate can turn out to increase by less than the increase in inflation which could cause a fall in the real interest rate and thereby contribute to instability. This may explain why the optimal policy horizon does not increase with lambda beyond some shock-specific level. The case for the different demand shocks is notable; see Figure 15. It appears that the optimal horizon is largely invariant to lambda for different kinds of demand shocks. The crucial difference is between the case of strict and flexible inflation targeting, i.e. between the case of λ= 0 and λ >0. In the former case, a relatively long horizon is suggested in the case of the aggregate demand 29 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 ∆L(H; εcpi = +1pp); χ= 0 ∆L(H; εcpi = +1pp); χ= .05 ∆L(H; εcpi = +1pp); χ= .10 Figure 16: Plots of the relative loss function defined by different χvalues against different policy horizons in the case of the the supply shock. The policy horizon is optimal when ∆L(.)= 0 and the relative loss is measured in %. and the house price shocks, while a relatively short horizon is suggested in the case of the exchange rate shock. Output is affected before inflation in the case of a direct shock to aggregate demand and house prices. Therefore, concern for output stabilisation λ > 0, would lead one to choose a short horizon, while no concern for output stabilisation would lead one to choose a relatively longer horizon. In the latter case, one is only concerned about price stability, and hence there is no need to reign in the inflationary effects of the shocks before they appear. The opposite is the case when there is a shock to the exchange rate and to the cpi directly. In these cases, inflation is affected before output. Hence, a concern for output stabilisation would lead one to choose a relatively longer horizon, while concern for price stability alone would lead one to offset the inflationary effects of the shocks as soon as possible. 6.2 Concern for interest rate volatility Figure 16 shows that an increase in concern for interest rate volatility, represented by χ, raises the optimal policy horizon. However, there seems to be a concave relationship between χand the optimal policy horizon. The figure shows that if χis 0.05, instead of zero in the benchmark case, the optimal policy horizon becomes 4 quarters, and if it is 0.1, the optimal policy horizon becomes 8 quarters. The value of χequal to 0.1 is commonly assumed in the literature, see e.g. Smets (2003) and Taylor (1999). A closer examination suggests that there is not a linear relationship between χand optimal policy horizon, conditional on a given value of λ. For example, a further doubling of χfrom 0.1 to 0.2 would not increase the optimal policy horizon from 8 to 16 quarters. Figure 16 shows that if χis 0.5, the optimal policy horizon becomes 15 quarters. 30 7 Model properties and policy horizons We demonstrate the strong model-dependence of optimal policy horizons by replacing the wage and price systems of the macroeconometric model with alternative equations and exposing the model to a supply shock as defined above.15 The following investigation particularly underscores the importance of equilibrium-correcting properties of models for the implied optimal policy horizons. It also suggests possible costs of deriving optimal policy horizons using models that turn out to be invalid. The incumbent wage and price system (in the macroeconometric model) is a VECM of wages and consumer prices which is derived in the light of open economy models of imperfect competition in product markets and a wage-bargaining framework. This is sequentially replaced by two systems of Phillips curves for prices and wages. In the first system, the Phillips curves are data consistent, but downward sloping even in the long run. In the second system, the Phillips curves for wage and price inflation are restricted to be vertical in the long run through homogeneity restrictions. The apparently small differences between the two systems of Phillips curves in their parameter estimates are especially useful in demonstrating the model-dependency of optimal policy horizons (and of monetary policy). The three systems of wages and prices are presented in Appendix C, while their economic and statistical properties are discussed in detail in Akram and Nymoen (2006). The difference between the three versions of the macroeconometric model essentially consists of differences in restrictions on the overall equilibrium-correction behaviour. The version with the wage-price VECM has more equilibrium-correction mechanisms than the version with the downward-sloping Phillips curve which in turn is more equilibrium-correcting than the version with a vertical Phillips curve system. In the following, we denote the version of the macroeconometric model with the VECM as ECM, that with the unrestricted Phillips curves as PCM, and the restricted Phillips curve implying vertical Phillips curve as PCMr. Figure 17 suggests that three model versions imply substantially different monetary policy responses to the supply shock. The figure depicts the interest rate paths defined by selected policy horizons in the face of a supply shock. Figure 18, left panel, sets out the economic performance of the policies in the face of the supply shock suggested by the three models. The economic performance associated with every policy horizon is measured by the standard deviations of the output gap and inflation. The right panel presents values of the loss function under different policy horizons relative to their value under the optimal policy horizon (H∗) for a given model version (M), where M=ECM,PCM,PCMr. Figure 18, right panel, presents the economic performance of (optimal and suboptimal) policies employed in response to the supply shock. The left panel of the figure shows that there is a trade-off 15It can be demonstrated that the optimal policy horizon in the case of a demand shock remains invariant to the alterations of the wage and price systems discussed here. This is because the interaction of the wage and price system with the demand side remains largely unaltered. 31 0 3 6 9 12 15 18 1 2 3 4 5 6 7 8 9(i − i0)|H=3; ECM (i − i0)|H=3; PCM (i − i0)|H=3; PCMr 0 3 6 9 12 15 18 1 2 3 4 5 (i − i0)|H=6; ECM (i − i0)|H=6; PCM (i − i0)|H=6; PCMr 0 3 6 9 12 15 18 1 2 3 (i − i0)|H=12; ECM (i − i0)|H=12; PCM (i − i0)|H=12; PCMr Figure 17: Interest rate paths over time suggested by three versions of the model in the face of the supply shock. The three frames shows interest rate paths associated with the policy horizons of 3, 6 and 12 quarters, respectively. The interest rates are measured as deviation from the reference interest rate in percentage points, while the horizontal axes depict periods in quarters. between price and output stabilisation for different ranges of policy horizons. We note that in the case of ECM and PCM there is a trade-off in the range of 0 to 6 and 8 quarters. Policy horizons that are longer than 8 quarters appear inefficient as both price and output stabilisation can be improved by shortening the policy horizon. The opposite is the case for PCMr. In this case, the trade-off curve is associated with policy horizons that are longer than 6 quarters, while policy horizons shorter than 6 seem inefficient. Figure 18, right panel, shows that the three models recommend substantially different policy horizons. Even though the efficiency frontiers for ECM and PCM are defined by almost the same policy horizon, the optimal horizon is 3 quarters conditional on ECM, but 6 quarters in the case of PCM. In the case of PCMr the policy horizon is 11 quarters. (An increase in the value of λfrom 0.5 would have increased the optimal policy horizons in all three models.) The large differences in the monetary policy response represented by the optimal policy horizons across the three model versions can be mainly ascribed to the associated wage and price systems, specifically to differences in the autoregressive coefficients across the three systems and to the effect of the unemployment term. The systems of Phillips curves, (27) and (28), which have relatively stronger autoregressive effects than the wage-price VECM, (26), effectively make the transitory supply shock a more persistent one than the VECM. The larger the persistence, the more lasting 32 .002 .003 .004 .0027 .0030 .0033 .0036 H=0 ↓ std_inf × std_y; ECM 0 2 4 6 8 10 12 0 10 20 30 40 ∆L(H; ECM) ×H .003 .004 .005 .006 .007 .008 .0036 .0039 .0042 .0045 std_inf × std_y; PCM 0 2 4 6 8 10 12 0 50 100 150 H*= 3 ∆L(H; PCM) ×H .005 .010 .015 .020 .002 .004 .006 .008 H=0 ↓ H=0 → std_inf × std_y; PCMr 0 2 4 6 8 10 12 0 500 1000 1500 H*= 6 H*= 11 ∆L(H; PCMr) ×H Figure 18: Economic performance and optimal policy suggested by three versions of the model in the face of the supply shock. Left column: Standard deviations of inflation gap and output gap (horizontal axis) associated with different (policy) horizon-specific rules in response to the supply shock. The standard deviations are plotted for rules associated with policy horizons (H) in the range of 0–12 quarters, where that for H= 0 is indicated. Right column: Values of the relative loss function (in %), defined by equation (5), at the different policy horizons (horizontal axis). the inflationary effects. From above, we know that the optimal policy horizon increases with the degree of persistence. Specifically, the degree of persistence implied by the lagged and contemporaneous terms of wages and prices in the vertical Phillips curves system (28) is higher than that implied by the Phillips curve system (27), which in itself implies higher persistence than equilibrium correction system (26). Consequently, the inflationary effects of the transitory supply shock are more lasting in the case of PCMr than in the case of PCM, which in itself implies more lasting effects than ECM. Accordingly, the optimal policy horizon is longer in the case of PCMr than in the case of PCM and relatively low in the case of ECM. This analysis also sheds light on the costs of choosing a suboptimal policy horizon when the ’true’ model is unknown. It appears that such costs depend on the model selected. For example, if we wrongly assume that H∗= 3, the loss would be much higher if PCMr turns out to be the true model rather than PCM. 33 8 Conclusions We find that optimal policy horizons, and consequently optimal target horizons, hereafter ‘the horizon(s)’ are highly shock-specific and vary substantially with properties of shocks and a central banks’s preferences for output stabilisation and smooth interest rate paths. When an inflationtargeting central bank cares about output stabilisation, the horizon depends on the shock type and its persistence, while its size and sign do not matter. The horizon is extremely short in response to an aggregate demand shock and implies an aggressive interest rate response to immediately eliminate deviations from the inflation target. In this case, there is no trade-off between inflation and output stabilisation. However, in the case of an aggregate supply shock, i.e. a direct shock to inflation, the horizon is relatively longer as there is a trade-off between inflation and output stabilisation in the short and medium run. In this case, the horizon increases with preferences for output stabilisation in a strongly concave fashion, up to some shock-specific level, though. Policy horizons beyond some shock-specific level amplify both inflation and output fluctuations and are therefore not chosen, irrespective of the strength of preferences for output stabilisation. However, the result of a short optimal horizon in response to an aggregate demand shock and a relatively long one in response to an aggregate supply shock does not generalise to other kinds of demand and supply shocks. For example, we find that the horizon in the case of a shock to house prices, which can also be interpreted as a demand shock, is substantially longer than that for the aggregate supply shock. This is because the horizon generally depends on lags from effects of shocks and interest rates on inflation, additionally on output and/or interest rates under flexible inflation targeting. The horizon contributes to synchronising the effects of interest rate changes on inflation with those of shocks to maximise their offsetting effects. Thus, if the effects of a particular shock on inflation (and other target variables) emerge gradually and/or are distributed over many periods, relatively long (optimal) horizons will be preferred since they would, by extending the duration of a non-neutral monetary policy stance, make policy more effective in offsetting the effects of the shock than relatively short horizons. A relatively short horizon would be preferred in the opposite case. Accordingly, the horizon generally increases with the persistence of a shock, since the effects of a persistent shock are distributed over more periods than those of a less persistent or transitory shock. Furthermore, even a strict inflation-targeting central bank may prefer a long horizon when the inflationary effects of a shock emerge gradually. The horizon increases with the size of a shock when the central bank also cares about interest rate fluctuations. A longer horizon moderates required interest rate movements. The increase in the horizon with the size of the shock depends on the degree of concern for interest rate fluctuations. An extension of the horizon beyond some shock-specific level can, however, prove counterproductive and hence not undertaken, as in the case of strong concern for output fluctuations. The horizon 34 does not depend on the sign of a given shock as the model is linear. However, our results for the case when the central bank faces a combination of several shocks differ somewhat from the above-noted results for individual shocks. In contrast to the latter case, the sizes and signs of different shocks also influence the horizon, even in the absence of preferences for smooth interest rates and despite using a linear model. This is because shocks may outweigh or amplify the effects of each other. Therefore, the horizon associated with a combination of shocks may not be just a convex combination of the horizons suggested by the different shocks individually. Moreover, combined shocks may contribute to a complex dynamic behaviour of inflation and output, warranting a quite complex monetary policy response to achieve stabilising effects. In a substantial number of such cases, monetary policy as modelled has even turned out to be destabilising, calling for complex interest rate paths to achieve desirable effects in the face of combined shocks. Our investigation of the model-dependence of the horizons suggests that they fall with the strength of equilibrium-correcting mechanisms in a model, ceteris paribus. When such mechanisms are weak, effects of shocks tend to be distributed over more periods than when the mechanisms are strong. Thus, relatively long horizons are preferred when the mechanisms are weak, and vice versa. This analysis sheds light on relatively long optimal horizons found previously. Our estimates of the horizons and the associated optimal target horizons in the case of transitory shocks are close to those typically announced by inflation-targeting central banks. Such horizons may be rather short in the face of relatively persistent shocks, however. It also appears that there may be substantial costs associated with adhering to a fixed policy horizon, irrespective of shock type and its properties. Such losses imply substantial gains from a precise derivation of the horizons in response to different shocks as well as from timely identification of shocks and their properties. Moreover, the non-negligible number of cases with combined shocks where monetary policy has turned out to be destabilising is a useful reminder of Friedman’s argument that active monetary policy is demanding. References Akram, Q. F. 2007. Designing monetary policy using econometric models. Working Paper forthcoming, Norges Bank. Akram, Q. F. and Ø. Eitrheim. 2006. Flexible inflation targeting and financial stability: Is it enough to stabilise inflation and output? Working Paper 2006/7, Norges Bank. Forthcoming Journal of Banking & Finance. Akram, Q. F. and R. Nymoen. 2006. Model selection for monetary policy analysis–How important is empirical validity? Working Paper 2006/13, Norges Bank. 35 Ball, L. 1999. Aggregated Demand and Long-Run Unemployment. Brookings Papers on Economics Activity 1999(2): 189–250. With discussion. B˚ardsen, G. 2005. Stylized dynamic model representations. Mimeo. B˚ardsen, G., Ø. Eitrheim, E. S. Jansen and R. Nymoen. 2005. 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A Impulse responses Figures 19–23 display the response of the key variables inflation (Inf) and output (y) to transitory partial increases in the nominal interest rate (i), aggregate demand (y), consumer prices (cpi), the nominal exchange rate (e) and house prices (hp). The results are invariant to the choice of simulation horizon because the model is (log) linear. 1995 1996 1997 1998 1999 2000 2001 −0.15 −0.10 −0.05 0.00 0.05 Inf_i 1995 1996 1997 1998 1999 2000 2001 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 y_i Figure 19: Responses to a one percentage point (pp) higher short-term interest rate over the period 1995q1–1995q4. Here and elsewhere, solid lines depict deviations from the baseline simulations. ”Inf i” and ”y i” represent the impulse responses of inflation and output gaps, respectively, to the change in interest rate. 37 1995 1996 1997 1998 1999 2000 2001 0.00 0.05 0.10 0.15 0.20 Inf_y 1995 1996 1997 1998 1999 2000 2001 0.0 0.5 1.0 y_y Figure 20: Responses to a transitory shock that induces a 1 pp increase in output growth in 1995. 1995 1996 1997 1998 1999 2000 2001 0.0 0.5 1.0 Inf_cpi 1995 1996 1997 1998 1999 2000 2001 −0.25 0.00 0.25 y_cpi Figure 21: Responses to a transitory shock that increases CPI-inflation by 1 pp in 1995. 1995 1996 1997 1998 1999 2000 2001 0.0 0.5 1.0 Inf_e 1995 1996 1997 1998 1999 2000 2001 0.0 0.5 1.0 1.5 2.0 y_e Figure 22: Responses to a transitory shock that induces a 10% depreciation of the nominal exchange rate in 1995. 1995 1996 1997 1998 1999 2000 2001 0.05 0.10 Inf_hp 1995 1996 1997 1998 1999 2000 2001 0.00 0.25 0.50 0.75 y_hp Figure 23: Responses to a transitory shock that induces a 10% increase in house prices in 1995. 38 45 Research Department, 57 p 2006/10 Q. Farooq Akram, Yakov Ben-Haim and Øyvind Eitrheim Managing uncertainty through robust-satisficing monetary policy Research Department, 33 p 2006/11 Gisle James Natvik: Government spending and the Taylor pinciple Research Department, 41 p 2006/12 Kjell Bjørn Nordal: Banks’ optimal implementation strategies for a risk sensitive regulatory capital rule: a real options and signalling approach Research Department, 36 p 2006/13 Q. Farooq Akram and Ragnar Nymoen Model selection for monetary policy analysis – importance of empirical validity Research Department, 37 p 2007/1 Steinar Holden and Fredrik Wulfsberg Are real wages rigid downwards? Research Department, 44 p 2007/2 Dagfinn Rime, Lucio Sarno and Elvira Sojli Exchange rate forecasting, order flow and macroeconomic information Research Department, 43 p 2007/3 Lorán Chollete, Randi Næs and Johannes A. Skjeltorp What captures liquidity risk? A comparison of trade and order based liquidity factors Research Department, 45 p 2007/4 Moshe Kim, Eirik Gaard Kristiansen and Bent Vale Life-cycle patterns of interest rate markups in small firm finance Research Department, 42 p 2007/5 Francesco Furlanetto and Martin Seneca Rule-of-thumb consumers, productivity and hours Research Department, 41 p 2007/6 Yakov Ben-Haim, Q. Farooq Akram and Øyvind Eitrheim Monetary policy under uncertainty: Min-max vs robust-satisficing strategies Research Department, 28 p 2007/7 Carl Andreas Claussen and Øistein Røisland Aggregating judgments on dependent variables: an (im)possibility result Research Department, 17 p 2007/8 Randi Næs, Johannes Skjeltorp og Bernt Arne Ødegaard Hvilke faktorer driver kursutviklingen på Oslo Børs? Forskningsavdelingen, 68 s 2007/9 Knut Are Astveit and Tørres G. Trovik Nowcasting Norwegian GDP: The role of asset prices in a small open economy Research Department, 29 p 2007/10 Hilde C. Bjørnland, Kai Leitemo and Junior Maih Estimating the natural rates in a simple new Keynesian framework Economics Department, 33 p 2007/11 Randi Næs and Bernt Arne Ødegaard Liquidity and asset pricing: Evidence on the role of investor holding period Research Department, 31 p 2007/12 Ida Wolden Bache Assessing estimates of the exchange rate pass-through Research Department, 60 p 2007/13 Q. Farooq Akram What horizon for targeting inflation? Research Department, 45 p Q. Farooq Akram: What horizon for targeting inflation? Working Paper 2007/13 KEY WORDS: Monetary policy Inflation targeting Horizon - 43901