# インフレーション・ターゲッティング

Lars E.O. Svensson

NBER Working Paper No. 16654

December 2010

要旨

インフレーション・ターゲッティングは、インフレーションの数値目標を公表し、金融政策の実施においてインフレ予想に大きな役割を担わせ (そのためフォアキャスト・ターゲッティングとも呼ばれている)、高度な透明性と説明責任 (transparency and accountablity) を特徴に持つ金融政策の戦略である。インフレーション・ターゲッティングは1990年にニュージーランドで導入され、インフレーションと実質経済の両方を安定させる方法として大きく成功し、2010年現在、約 25 の先進国と新興国で採用されている。この章では、この政策の歴史やマクロ経済効果、理論的なこと、その実例、そしてこの政策の将来について論じていこう。

## 1. イントロダクション

インフレーション・ターゲッティングは金融政策上の戦略で、1990年にニュージーランドで導入され、インフレーションと実質経済の両方を安定させるのに大きく貢献した。2010年現在、約 25 の先進工業国と非工業国で採用されている。この政策の特徴は (1) インフレーションの数値目標を公表すること、(2) (市場が)予想するインフレーションに重きをおいて金融政策を実施すること (そのためフォアキャスト・ターゲッティングとも呼ばれる)、(3) 透明性が高く説明責任もしっかりしていることだ (Svensson(2006))。制度的な枠組みという点でいうと、インフレーション・ターゲッティングは中央銀行の (1) 政策目標としての物価の安定 (a mandate for price stability *1) 、(2) 独立性 (independence) 、(3) 説明責任 (accountability) という 3つと深く関わっている。とはいえ、ノルウェイの Norges Bank のように (事実上は独立性がしっかりしているのかもしれないけれど) 公には独立性を認められていなくても、とても上手にインフレーション・ターゲッティングを実施している中央銀行もある。

### 1.1 インフレーション・ターゲッティングの数値目標を公表するということ

先進国のインフレ目標として典型的な値は 2% 近辺で、インフレの指標には年間の消費者物価指数 (CPI) もしくはコア CPI が使われている。目標とする数字は、ニュージーランドのように 1～3% と幅があることもあれば、カナダのように 2% に ・1% の幅や許容範囲が設けられていることもある。スウェーデンやイギリスではこの目標値は 2% だし、ノルウェイでは 2.5% だ。このように幅が明示されない場合もある。インフレ目標の設定のしかたには違いがあるけれど、政策を実行する上で、それが問題になることはないらしい。中央銀行が幅のあるインフレ目標を使っているなら、その範囲のまんなかをめざすだろうから。目標として設定された範囲の両はじは、通常は "柔軟な境界" だと解釈される。これはインフレ率がその境界を越えたからといって、別の政策が発動するわけではないという意味。境界のすぐ外側のインフレ率は、境界のすぐ内側のインフレ率と大差ないと考えられているということである。そして、新興国や開発途上国で使われている目標値は、2% より数パーセント高くなっていることが多い。

実務上のインフレーション・ターゲッティングは、 "厳格な" ものではまったくなく "柔軟な" ものだ。 インフレーション・ターゲッティングを採用している中央銀行 (ここでいう "中央銀行" とは金融当局のことである) は、目標値周辺にインフレを維持しようとするだけでなく、実質経済の安定もある程度重視するという意味で

1 4 5 6 Table 2.1: Approximate adoption dates of inflation targeting Country Date Country Date New Zealand 1990 q1 Korea 2001 m1 Canada 1991 m2 Mexico 2001 m1 United Kingdom 1992 m10 Iceland 2001 m3 Sweden 1993 m1 Norway 2001 m3 Finland 1993 m2 Hungary 2001 m6 Australia 1993 m4 Peru 2002 m1 Spain 1995 m1 Philippines 2002 m1 Israel 1997 m6 Guatemala 2005 m1 Czech Republic 1997 m12 Slovakia 2005 m1 Poland 1998 m10 Indonesia 2005 m7 Brazil 1999 m6 Romania 2005 m8 Chile 1999 m9 Turkey 2006 m1 Colombia 1999 m9 Serbia 2006 m9 South Africa 2000 m2 Ghana 2007 m5 Thailand 2000 m5 Source: Roger (2009) 7 8 Figure 2.1: Average inflation in inflation targeting and non-inflation targeting OECD-countries. Percent per year Source: EcoWin. 18 18 Non-targeters 16 16 Inflation targeters 14 14 12 12 10 10 8 8 6 6 4 4 2 2 0 0 -2 -2 60 64 68 72 76 8 0 84 88 92 9 6 00 04 08 12 9 Figure 2.2: Average inflation in inflation targeting and non-inflation-targeting emerging economies. Percent per year. Source: Ecowin. 90 90 80 80 Non-targeters 70 70 Inflation targeters 60 60 50 50 40 40 30 30 20 20 10 10 0 0 80 82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 There is relatively robust empirical evidence that an explicit numerical target for inflation an- chors and stabilizes inflation expectations (Johnson (2002), Levin, Natalucci, and Piger (2004), G◯rkaynak, Levin, and Swanson (2006), Batini and Laxton (2007), G◯rkaynak, Levin, Marder, and Swanson (2007), and Ravenna (2008)). In particular, G◯rkaynak, Levin, and Swanson (2006) compare the behavior of daily bond yield data in the U.K. and Sweden (both inflation targeters) to that in the U.S. (a non-inflation targeter). They use the difference between far-ahead forward rates on nominal and inflation-indexed bonds as a measure of compensation for expected inflation and inflation risk at long horizons. For the U.S., they find that forward inflation compensation exhibits highly significant responses to economic news. For the U.K., they find a level of sensitivity similar to that in the U.S. prior to the Bank of England gaining independence in 1997, but a striking absence of such sensitivity since the central bank became independent. For Sweden, they find that forward inflation compensation has been insensitive to economic news over the whole period for which they have data. These findings support the view that a well-known and credible inflation target helps to anchor the private sector's long-run inflation expectations. Recently, International Monetary Fund (2008) considered which monetary-policy frameworks had been most successful in anchoring inflation expectations in the wake of the oil and food price shocks in 2007, and found that "in emerging economies, inflation targeting seems to have recently been more effective than alternative monetary-policy frameworks in anchoring expectations." Table 2.2 reports the percentage-point response of expected headline inflation 1, 3, 5 and 6--10 years ahead to a 1 percentage-point change in actual inflation for emerging-market economies. In inflation-targeting emerging economies, the response of expected headline inflation 1, 3, and 5 years ahead is zero, whereas it is positive for non-inflation targeters. 10 Table 2.2: Changes in expected inflation in response to changes in actual inflation in emerging-market economies. 1 year 3 years 5 years 6-10 years Inflation targeters 000 000 000 0024 Non-inflation targeters 023 012 007 000 Note: Expected inflation 1, 3, 5, and 6--10 years ahead; percentage- point responses to a 1 percentage point change in actual inflation. Source: International Monetary Fund (2008, figure 3.12) Skeptics of inflation targeting worry that the regime is too focused on inflation and that attempts to control inflation will generate instability in the real economy and possibly also lower growth (see, for instance, Friedman and Kuttner (1996), Friedman (2002), and Cecchetti and Ehrmann (2002)). Figure 2.3 shows the average output growth and volatility before and after the adoption of inflation targeting for inflation-targeting countries in OECD and for a group of emerging-market economies.13 It also gives the output performance for the non-inflation targeting (NT) countries in OECD and for the NT countries in the group of emerging-market economies. For the NT countries, the threshold years are 1998 for the OECD countries and 2001 for the emerging-markets economies. The panels give no basis for the pessimistic claim that inflation targeting adversely affects growth or average growth volatility. 11 a. OECD: Average growth b. OECD: Growth volatility 6 3 4 2 2 1 0 0 Non-targeters Targeters Non-targeters Targeters d. Emerging markets: Growth volatility c. Emerging markets: Average growth 8 6 6 4 4 2 2 0 0 Non-targeters Targeters Non-targeters Targeters 12 13 14 ∈ ∈ ∈ +1 = + + +1 (3.1) +1| 0 15 +1 = 11 + 12 + 1 + +1 (3.2) ∈ ∈ 11 12 1 = (3.3) 21 22 2 = -1 (+1| - 21 - 2 ) (3.4) 22 16 - = ( +1| - ) + ( - ) + ・ (3.5) - = (+1| - +1| ) - ( - +1| - ) ・ ・ ・ (3.6) +1 = + +1 (3.7) +1 = + +1 ・ ・ (3.8) - 1 +1 = ・ ( + +1 ) ・ (3.9) Equation (3.5) is the Phillips curve (aggregate-supply relation), where denotes inflation, is the inflation target, is a discount factor, denotes output, denotes potential output, - ・ ・ is the output gap, and is a so-called cost-push shock.22 Equation (3.6) is the aggregate-demand relation, where denotes the policy rate and the neutral real rate. Equations (3.7)-(3.9) give ・ the dynamics of the cost-push shock, potential output, and the neutral rate. The neutral rate and potential output satisfy 1 = ・ (・ - ) ・ +1| This equation is satisfied by (3.8) and (3.9). The vector of predetermined variables is ( )0 , and the vector of forward-looking variables is ( ). This example is special ・・ in that all predetermined variables are exogenous variables and there are no endogenous predeter- mined variables. It is straightforward to rewrite the equations (3.5)-(3.9) on the form (3.1) and thereby identify the matrices , , , and . Let be an -vector of target variables, measured as the gap to an -vector of target levels. This is not restrictive, as long as we keep the target levels time invariant. If we would like to examine the consequences of different target levels, we can instead let refer to the absolute level of the target variables and replace by - everywhere below. We assume that the target variables can be written as a linear function of the predetermined, forward-looking, and instrument variables, = [ ] (3.10) 17 Let the quadratic intertemporal loss function in period be the sum of expected discounted future period losses, X + E (3.11) =0 where 0 1 denotes a discount factor, denotes the period loss and is given by 0 (3.12) and is a symmetric positive semidefinite matrix containing the weights on the individual target variables. As an example, under flexible inflation targeting with no interest-rate smoothing, the period loss function can be written as the standard quadratic loss function, = ( - )2 + ( - )2 ・ (3.13) where denotes the inflation target, the output gap is used as a measure of resource utilization around a normal level, and the relative weight on output-gap stabilization, , is positive under flexible inflation targeting. The target variables are here the inflation gap, - , the gap between inflation and the inflation target , and the output gap, - , the gap between output and ・ potential output, so the vector of target variables satisfies ( - - )0 . Then the matrix ・ is a diagonal matrix with the diagonal (1 ). The optimization is here under the assumption that commitment in a timeless perspective is possible. The case of optimization under discretion is discussed in section 3.8.24 The optimization results in a set of first-order conditions which, combined with the model equations (3.1), results in a system of difference equations (see S‡derlind (1999) and Svensson (2009b)). The system of difference equations can be solved with several alternative algorithms, for instance, those developed by Klein (2000) and Sims (2002) (see Svensson (2005) and Svensson (2009b) for details of the derivation and application of the Klein algorithm).25 Under the assumption of optimization under commitment in a timeless perspective, the solution 24 See Woodford (2010b) for a detailed discussion of optimization under commitment, commitment in a timeless perspective, and discretion. 25 The system of difference equations can also be solved with the so-called AIM algorithm of Anderson and Moore (1983) and Anderson and Moore (1985) (see Anderson (2010) for a recent formulation). Whereas the Klein algorithm is easy to apply directly to the system of difference equations, the AIM algorithm requires some rewriting of the difference equations. Previously, the AIM algorithm have appeared to be significantly faster for large systems (see Anderson (2000) for a comparison between AIM and other algorithms), but a new Matlab function, ordqz, makes the Klein algorithm much faster. The appendix of Adolfson, Las・en, Lind・, and Svensson (2009) discusses the relation between the Klein and AIM algorithms and shows how the system of difference equations can be rewritten to fit the AIM algorithm. 18 and intertemporal equilibrium can be described by the following difference equation, ∈ ∈ ∈ ∈ = (3.14) -1 -1 ∈ ∈ ∈ +1 = + +1 (3.15) -1 0 ∈ ~ = (3.16) -1 for 0, where ∈ 0 ~ and 0 and -1 are given. The Klein algorithm returns the matrices and . The submatrix in (3.14) represents the optimal policy function, the optimal instrument rule, ∈ = (3.17) -1 The matrices and depend on , , , , , and , but they are independent of . That they are independent of demonstrates certainty equivalence (the certainty equivalence that holds when the model is linear, the loss function is quadratic, and the shocks and the uncertainty are additive); only probability means of current and future variables are needed to determine optimal policy (and the optimal projections to be discussed in section 3.3). The -vector -1 consists of the Lagrange multipliers of the lower block of (3.20), the block determining the projection of the forward-looking variables.26 Instead of a solution under optimal policy, we can consider a solution under a given arbitrary instrument rule that satisfies ∈ ∈ = [ ] (3.18) for 0, where the ・ ( + ) matrix [ ] is a given (linear) instrument rule and partitioned conformably with and . If 0, the instrument rule is an explicit instrument rule; if 6= 0, the instrument rule is an implicit instrument rule. In the latter case, the instrument rule is actually an equilibrium condition, in the sense that the policy rate in period and the forward-looking variables in period are then simultaneously determined.27 If the instrument rule is combined with (3.1), the resulting system of difference equations can be solved for a solution (3.14)-(3.16), except that there is no vector of Lagrange multipliers . In that case the matrices and depend on , , and , but not on . 26 Adolfson, Las・en, Lind・, and Svensson (2009) discusses how the initial value for -1 can be chosen. 27 See Svensson (2003b) and Svensson and Woodford (2005) for more discussion of explicit and implicit instrument rules. 19 The model (3.1) can also be solved for a given targeting rule, a linear combination of leads and lags of the target variables projection (Giannoni and Woodford (2003), Svensson and Woodford (2005)), X E + = 0 (3.19) =- where denotes the largest lag, denotes the largest lead in the targeting rule, and for = - - +1 are ・ matrices (we need as many rows in (3.19) as the number of instruments). As shown by Giannoni and Woodford (2003) and Giannoni and Woodford (2010), the first-order conditions for an optimum can be written in the form (3.19) after elimination of the Lagrange multipliers. Targeting rules are further discussed in section 3.6. How could optimal policy or policy with a given instrument rule be implemented? The standard theory of optimal monetary policy is not very explicit on this point. One interpretation of the above analysis would be that the central bank once and for all calculates the optimal instrument rule in (3.17), alternatively picks a given instrument rule in (3.18), and then publishes the instrument rule and makes a public commitment to use it to set its policy rate forever. The private sector then believes in the commitment to the instrument rule, combines it with the model in (3.1), calculates the corresponding rational-expectations equilibrium, and makes its decisions accordingly. The resulting equilibrium is then the equilibrium described by the equations (3.14)-(3.16) (for the given instrument rule (3.18), without the Lagrange multipliers). However, this is not the way monetary policy is implemented by any real-word central bank. No central bank announces a specific instrument rule and commits to follow it forever. For one thing, the optimal instrument rule would depend on a long list of predetermined variables (not to speak of the Lagrange multipliers), and the optimal instrument rule would be much too complicated to be communicated. Any simple given instrument rule, such as a Taylor rule, would be too simple and imperfect for the central bank to stick with it (see Svensson (2003b)). In the real world, an inflation-targeting central bank instead announces the current level of the policy rate, gives some indication of future policy rates or even publishes a full policy-rate forecast, and usually also publishes a forecast of inflation and the real economy. The private sector then responds to this information, and the actual equilibrium results. This is the kind of monetary policy and its implementation that I try to model next. In particular, forecasts and projections of the policy rate, inflation, and the real economy take center stage. 20 3.2. The projection model and the feasible set of projections Let {+ } denote a projection (a conditional mean forecast) in period for any vector of =0 variables , where + denotes the mean forecast of the realization of the vector in period + conditional on information available in period . We refer to as the horizon of the forecast + . The projection model for the projections ( ) in period uses that the projection of the zero-mean i.i.d. shocks is zero, + = 0 for 1. It can then be written as ∈ ∈ + +1 + = + + (3.20) + +1 + + = + + (3.21) + for 0, where = | (3.22) where | is the estimate of predetermined variables in period conditional on information available in the beginning of period . The introduction of this notation here allows the realistic possibility that the central bank has imperfect information about the current state of the economy and, for instance, as in Svensson and Woodford (2005) estimates the current state of the economy with the help of a Kalman filter, a case that is further discussed in section 3.9.1. Thus, " " and "|" in subindices refer to projections (forecasting) and estimates ("nowcasting" and "backcasting") in the beginning of period , respectively. The feasible set of projections for given | , denoted T (| ), is the set of projections ( ) that satisfy (3.20)-(3.22). We call T (| ) the set of feasible projections in period . It is conditional on the estimates of the matrices , , , and and the estimate of the current realization of the predetermined variables | . 3.3. Optimal policy choice The policy problem in period is to determine the optimal projection in period . The optimal ^^^ projection is the projection ( ^ ) that minimizes the intertemporal forecast loss function, X L( ) = + (3.23) =0 where the period forecast loss, + , is specified as + = + 0 + (3.24) 21 for 0. The minimization is subject to the projection being in the feasible set of projections for given | , T (| ).28 For the standard quadratic loss function (3.13), the corresponding period forecast loss function is + = ( + - )2 + (+ - + )2 ・ (3.25) where + and + - + are the forecast in period of inflation and the output gap, respec- ・ tively, in period + . When the policy problem is formulated in terms of projections, we can allow 0 1, since the above infinite sum in (3.23) will normally converge also for = 1. Again, the optimization is done under commitment in a timeless perspective (Woodford (2003), Woodford (2010b)). The intertemporal loss function (3.23) with the period forecast loss function (3.24) introduces a preference ordering over projections of the target variables, . We can express this preference ordering as the modified intertemporal loss function, X 1 1 L( ) + 0 ( - -1 ) + + + 0 ( - -1 ) 0 (3.26) -1 -1 =0 where the modification is the added term 1 0 ( - -1 ). In that term, -1 is as mentioned -1 the vector of Lagrange multipliers for the equations for the forward-looking variables from the optimization problem in period -1, is the projection of the vector of forward-looking variables in period that satisfies the projection model (3.20) and the initial condition (3.22), and -1 is the optimal projection in period - 1 of the vector of forward-looking variables in period (-1 is predetermined in period and normalizes the added term and makes it zero in case the projection coincides with the projection -1 but does not affect the choice of optimal policy). As discussed in Svensson and Woodford (2005), the added term and the dependence on the Lagrange multiplier -1 ensure that the minimization of (3.26), under either discretion or commitment, results in the optimal policy under commitment in a timeless perspective.29 The optimal policy choice, which results in the optimal policy projection, can now be formal- ized as choosing in the set of feasible projections in period so as to minimize the modified 28 It follows from the certainty-equivalence theorem that the minimization of the expected value of discounted future losses, E + 0 + in (3.11), results in the same optimal instrument rule in period as the minimiza- =0 0 0 tion of the intertemporal forecast loss function, =0 + + = =0 (E + ) (E + ) in (3.23). The expected value of discounted future losses will exceed the intertemporal forecast loss function by the term 0 =0 [E (+ - E + ) (+ - E + )] due to the forecast errors + - E + , but the effect of policy on those forecasts errors and that term can be disregarded under certainty equivalence. 29 This added term is closely related to the recursive saddlepoint method of Marcet and Marimon (1998), see Svensson (2009b) and Woodford (2010b) for more discussion. 22 intertemporal loss function, that is, to solve the problem 1 minimize L( ) + 0 ( - -1 ) subject to ( ) T (| ) (3.27) -1 The set of feasible projections T (| ) is obviously very large and contains infinitely many different policy projections. The presentation of the alternative policy projections generated by alternative policy-rate paths (for instance, as described in Las・en and Svensson (2010)), can be seen as an attempt to narrow down the set of infinite alternative feasible policy projections to a finite number of alternatives for the policymaker to choose between. For a given linear projection model and a given modified quadratic intertemporal loss function, it is possible to compute the optimal policy projection exactly. By varying the parameters of the modified intertemporal loss function it is possible to generate alternative policy projections. Generating alternative policy projections in that way has the advantage that the policy projections are on the efficient frontier, to be specified below. However, the policymaker may still prefer to see a few representative alternative policy projections constructed with alternative policy-rate paths that are not constructed as optimal policy projections. The methods to construct policy projections for alternative anticipated policy-rate paths presented in Las・en and Svensson (2010) is one way to do this. As discussed in Svensson and Woodford (2005) and Giannoni and Woodford (2003), commitment in a timeless perspective can alternatively be implemented by imposing the constraint ∈ | = (3.28) -1 instead of adding the extra term to the period loss function. Let T (| -1 ) denote the subset of the feasible set of projections that satisfy (3.28) for given | and -1 and call this the restricted feasible set of projections. Then the optimal policy projection is also the solution to the problem minimize L( ) subject to ( ) T (| -1 ) (3.29) 3.4. The forecast Taylor curve The optimal policy projection, the restricted set of feasible projections, and the efficient restricted set of projections can be illustrated using a modified Taylor curve, a forecast Taylor curve. Whereas the original Taylor curve involves unconditional variances (to be precise, standard deviations in figure 1 of Taylor (1979)) of ex post outcomes, the forecast Taylor curve involves the discounted sum of squared inflation-gap and output-gap forecasts ex ante (see Svensson (2010a) for applications 23 Figure 3.1: Forecast Taylor curve (y yt ,t ) 2 t ,t 0 T ( X t|t , t 1 ) P L(Y t ) const. 0 ( *)2 t ,t 0 of forecast Taylor curves to policy evaluation). With the loss function (3.25), the intertemporal forecast loss function can be written X X 2 (+ - + )2 L( ) = ( + - ) + ・ =0 =0 P P ( + - )2 and (+ - + )2 the sum of Let us call the discounted sums =0 =0 ・ squared inflation gaps and output gaps, respectively (keeping in mind that we actually mean inflation-gap and output-gap forecasts). We can now illustrate the restricted set of feasible projec- tions, T (| -1 ), in the space of sum of squared inflation and output gaps. In figure 3.1, the sum of squared inflation gaps is plotted along the horizontal axis and the sum of squared output gaps is plotted along the vertical axis. The restricted set of feasible projections is the set on and above the curve through the point P. The efficient restricted set of feasible projections, the efficient frontier of the restricted set of feasible projections, is given by the boundary, the curve through the point P. In the figure, we can also illustrate isoloss lines of the intertemporal forecast loss function as negatively sloped lines with the slope 1. An isoloss line closer to the origin corresponds to a lower loss. The optimal policy projection is given by the tangency point P between the efficient frontier and an isoloss line, the policy projection in the restricted set of feasible projections that gives the lowest intertemporal loss. The efficient frontier consists of the projections in the set of restricted feasible projections that are efficient, in the sense that there is no other projection in the restricted feasible set that has a 24 lower sum of squared inflation gaps without having a higher sum of squared output gaps. Obviously, the optimal policy projection is in the efficient set. Section 4.3 and 4.4 show applications of these ideas in practical policy. 3.5. Optimal policy projections Under the assumption of optimization under commitment in a timeless perspective, the optimal policy projection can be described by the following difference equation, ∈ ∈ ∈ ^ + ^ + = (3.30) ^+ + -1 ∈ ∈ ^ ^ + +1 + = (3.31) + + -1 ∈ ^ + ^+ = ~ (3.32) + -1 ^ ~ for 0, where = | and -1 = -1 . The matrices , , and are the same as above. Alternative optimal projections can be constructed by varying the weights in the matrix and the discount factor . The use of alternative optimal projections has the advantage that the projections considered are efficient in the sense of minimizing an intertemporal loss function. That is, each projection is such that it is not possible to reduce the discounted sum of squared future projected deviations of a target variable from its target level without increasing the discounted sum of squared such future projected deviations of another target variable (this assumes that the positive symmetric semidefinite matrix is diagonal). In figure 3.1, the efficient subset of the set of feasible projections, the efficient frontier of the set of feasible projections, is given by the negatively sloped curve through the point P. There are obvious advantages to restricting policy choices to be among efficient alternatives. Projections constructed with an arbitrary instrument rule (or with arbitrary deviations from an optimal instrument rule) are generally not efficient in this sense. That is, they correspond to points in the interior of the feasible set of projections, points north-east of the curve through point P in figure 3.1. Projections can obviously also be constructed for a given instrument rule, ∈ ∈ + + + = [ ] + + The resulting projection will satisfy equations such as (3.30)-(3.32), although without any Lagrange multipliers, where the matrices and depend on , , and . For arbitrary instrument rules, the projections will not be efficient. 25 3.6. Targeting rules As discussed in Svensson (2003b) and Svensson (2005), the monetary-policy decision process makes the current instrument-rate decision a very complex policy function of the large amounts of data and judgment that have entered into the process. I believe that it is not very helpful to summarize this policy function as a simple instrument rule such as a Taylor rule. Furthermore, the resulting complex policy function is a reduced form, which depends on the central-bank objectives, its view of the transmission mechanism of monetary policy, and the judgment it has exercised. It is the endogenous complex result of a complex process. In no way is this policy function structural, in the sense of being invariant to the central bank's view of the transmission mechanism and private-sector behavior, or the amount of information and judgmental adjustments. Still, much current literature treats monetary policy as characterized by a given instrument rule that is essentially structural and invariant to changes in the model of the economy. Realizing that the policy function is a reduced form is a first step in a sensible theory of monetary policy. But, fortunately, this complex reduced-form policy function need not be made explicit. It is actually not needed in the modern monetary-policy process. There is a convenient, more robust representation of monetary policy, namely in the form of a targeting rule, as discussed in some detail in Svensson and Woodford (2005) and Svensson (2003b) and earlier in more general terms in Svensson (1999a). An optimal targeting rule is a first- order condition for optimal monetary policy. It corresponds to the standard efficiency condition of equality between the marginal rates of substitution and the marginal rates of transformation between the target variables, the former given by the monetary-policy loss function, the latter given by the transmission mechanism of monetary policy. An optimal targeting rule is invariant to everything else in the model, including additive judgment and the stochastic properties of additive shocks. Thus, it is a compact and robust representation of monetary policy, much more robust than the optimal policy function. A simple targeting rule can potentially be a practical representation of robust monetary policy, a robust monetary policy that performs reasonably well under different circumstances. Giannoni and Woodford (2003) and Giannoni and Woodford (2010) provide general derivations of optimal targeting rules/target criteria, and they are further discussed in Woodford (2007), Woodford (2010a), and Woodford (2010b).30 31 30 Walsh (2004) shows a case of equivalence between targeting rules and robust control. 31 Previously, Bank of England and the Riksbank assumed a constant interest rate underlying its inflation forecasts, with the implication that a constant-interest-rate inflation forecasts that overshoots (undershoots) the inflation target at some horizon such as two years indicates that the policy rate needs to increased (decreased). This is a far-from- optimal targeting rule that has now been abandoned, as discussed in section 4.2. 26 In this framework, a given targeting rule would have the form X ++ = 0 =- for 0. In the simplest New Keynesian model with the Phillips curve (3.5) and the loss function (3.13), the optimal targeting rule has the projection form + - + [(+ - + ) - (+ -1 - + -1 )] = 0 ・ ・ (3.33) for 0 (Svensson and Woodford (2005)). Optimal targeting rules remain a practical way of representing optimal monetary policy in the small models usually applied for academic monetary-policy analysis. However, for the larger and higher-dimensional operational macromodels used by many central banks in constructing projec- tions, the optimal targeting rule becomes more complex and arguably less practical as a represen- tation of optimal monetary policy. Optimal policy projections, the projections corresponding to optimal policy under commitment in a timeless perspective, can however easily be derived directly with simple numerical methods, without reference to any optimal targeting rule. For practical opti- mal monetary policy, policymakers actually need not know the optimal targeting rule. Even less do they need to know any policy function. They only need to ponder the graphs of the projections of the target variables that are generated in the policy process and choose the projections of the target variables and the policy rate that look best relative to the central bank's objectives, as illustrated in section 4.3. 3.7. Implementation and equilibrium determination ^ The policy decision can be characterized by (^ ), the optimal projection of the policy rate and the target variables. The policy decision also determines the Lagrange multipliers to be used in the loss function and policy decision in period + 1. How can we model how the policy is implemented and how the (rational-expectations) equi- ^ librium is determined? The central bank announces (or somehow communicates) ^ and (and possibly more details of its optimal projection) and sets the current policy rate in line with the policy-rate path, = ^ . Let us assume that the central-bank projections are credible and hence believed by the private sector. In particular, assume that private-sector expectations of next period's forward-looking variables are equal to the central bank's forecast and are rational and equal to E +1 . The forward-looking 27 variables and the target variables in period are then determined by Eq. (3.4), given and E +1 , and (3.10), given , , and . The next period's predetermined variables +1 are then determined next period by (3.2), given , and next period's shocks +1 . Then next ^ period's policy decision then determines ^+1 and +1 , given +1|+1 and +1 . This way a rational-expectations equilibrium is implemented. Is the equilibrium determinate? As discussed in Svensson and Woodford (2005), this may require an out-of-equilibrium commitment which may be explicit or implicit.32 That is, the central bank commits to deviate from ^ if the economy deviates from the optimal projection.33 For instance, if realized inflation exceeds the inflation projection , the central-bank may set a higher policy ^ rate according to = ^ + ( - ) ^ where 0. In the example discussed in Svensson and Woodford (2005), the Taylor Principle of 1 ensures determinacy. Another example of an out-of-equilibrium commitment in that example is = ^ + { - + [( - ) - (-1 - -1 )]} ・ ・ (3.34) where - + [( - ) - (-1 - -1 )] = 0 ・ ・ is the optimal targeting rule, the first-order condition for optimal policy, in the standard New Keynesian model with the Phillips curve (3.5) and the loss function (3.13). Here, the out-of- equilibrium commitment (3.34) implies that any positive deviation from the optimal targeting rule (in the sense of too high inflation or too high output) would result in a higher policy rate. A sufficiently high value of , usually not very different from unity, ensures determinacy. Importantly, in this setup the object of choice of the central bank and what is communicated to the private sector is , the policy-rate path, not the policy function, (although there is a one- to-one correspondence between the optimal policy-rate path and the optimal policy function).34 32 For instance, in the standard New Keynesian model, the predetermined variables are exogenous. If the central bank implements policy by letting the policy rate respond to the predetermined variables only, the policy rate will be exogenous. Then, by the arguments of Sargent and Wallace (1975), the equilibrium may be indeterminate. 33 In Svensson and Woodford (2005) the precise timing of these operations is made explicit so as to avoid any simultaneity problems. 34 There is a one-to-one correspondence between the optimal policy-rate path and the optimal policy function ~ ~ = (for which the policy instrument responds to the predetermined variables ( 0 )0 ), but there is a 0 -1 continuum of implicit instrument rules (for which the policy instrument responds also to forward-looking variables) ~ consistent with the optimal policy. For instance, the implicit instrument rule = ( - ) + is consistent ~ with the optimal policy for any value of the scalar , since in equilibrium = . However, the determinacy properties (the eigenvalue configuration) may of course depend on . 28 3.8. Optimization under discretion and the discretion equilibrium The previous discussion is under the assumption that commitment in a timeless perspective is possible. Under optimization under discretion, the central bank minimizes the intertemporal loss function (3.11) in period , taking into account that it will reoptimize again in period + 1 (and that this reoptimization is anticipated by the private sector). Oudiz and Sachs (1985) derive an iterative algorithm for the solution of this problem (with the unnecessary simplification of = ), which is further discussed in Backus and Driffill (1986), Currie and Levine (1993), and S‡derlind (1999). This algorithm is briefly described here.35 Since the loss function is quadratic and the constraints are linear, it follows that the solution will be linear and the minimized intertemporal loss will be quadratic. Reoptimization in period + 1 subject to (3.1) and given +1 will result in the policy rate +1 , the forward-looking variables +1 , and the minimized intertemporal loss in period + 1 satisfying +1 = +1 +1 (3.35) +1 = +1 +1 (3.36) P +1+ = +1 +1 +1 + +1 0 E+1 (3.37) =0 where the matrices +1 , +1 , and +1 and the scalar +1 are determined by the decision problem in period + 1. These matrices and the scalar are assumed to be known in period ; only +1 and +1 will matter for the decision problem in period . By taking expectations of (3.36) and using (3.2), we have +1| = +1 +1| = +1 (11 + 12 + 1 ) (3.38) Using (3.38) in the lower block of (3.1) and solving for results in ・ ・ = + (3.39) where ・ (22 - +1 12 )-1 (+1 11 - 21 ) (3.40) ・ (22 - +1 12 )-1 (+1 1 - 2 ) (3.41) (we assume that 22 - +1 12 is nonsingular). Using (3.39) in the upper block of (3.1) then gives ~ ~ +1 = + + +1 (3.42) 35 See Svensson (2009b) for more details of this algorithm. 29 where ~ ・ 11 + 12 (3.43) ~ ・ 1 + 12 (3.44) The optimization problem in period is now to minimize 0 + E (+1 +1 +1 + +1 ) subject to (3.42). The problem has been transformed to a standard linear-quadratic regulator problem without forward-looking variables, albeit with time-varying parameters. The solution will satisfy36 = = 0 + + E (+1 +1 +1 + +1 ) 0 where and must satisfy ・ ・ = + (3.45) Equation (3.40)-(3.45) define a mapping from (+1 +1 ) to ( ), which also determines . The solution to the problem is a fixed point ( ) of the mapping and a corresponding . It can be obtained as the limit of ( ) when -. Thus, the solution and the discretion equilibrium is ∈ ∈ = ~~ +1 = ( + ) + +1 + +1 = ~ ~~ ~~ for 0, where ( ) is the limit of ( ) when - . We note that, by (3.45), and will satisfy ・・ = + (3.46) ・・ ・ where ( ) is the limit of ( ) when - . The matrices and depend on , , , , , and , but they are independent of . This demonstrates the certainty equivalence of the discretionary equilibrium. 36 Svensson (2009b) provides details. 30 3.8.1. The projection model, the feasible set of projections, and the optimal policy projection Under discretion, the projection model for the projections ( ) can be written ~ ~ + +1 = + + + (3.47) ・ ・ + = + + + (3.48) + + = + (3.49) + for 0, where = | (3.50) The feasible set of projections for given | , T (| ) is then the set of projections that satisfy (3.47)-(3.50). The optimal policy projection is then the solution to the problem minimize L( ) subject to ( ) T (| ) Policy under discretion is here modeled as assuming that in each period + , private-sector expectations in period + of the forward-looking variables and the policy rate in period + + 1, + +1| and + +1| , are determined by its belief that the central bank will reoptimize in period + + 1.37 This means that the private-sector expectations of the forward-looking variables and the policy rate satisfy ∈ + +1| = + +1|+ + +1| where + +1|+ , the private-sector expectations in period + of the predetermined variables in period + + 1 is given by ~ ~ + +1|+ = + |+ + + In particular, private-sector expectations in period of the forward-looking variables and the policy rate in period + 1 satisfy ∈ +1| ~ ~ = +1| = (| + ) (3.51) +1| The central bank's forecast in period of the forward-looking variables in period + 1 depends on its forecast for both its policy rate in period + 1, +1 , according to ・ ・ ・~ ~ ・ +1 = +1 + +1 = (| + ) + +1 37 Recall that private-sector rational expectations are denoted by a vertical bar in the subindex + |, whereas central-bank projections are denoted by a comma in the subindex + . 31 If the central bank's forecast of its policy rate is consistent with its reoptimization in period + 1, it will satisfy ~ ~ +1 = +1 = (| + ) and be equal to the private-sector expectations of the policy rate, +1| . Then the central bank's forecast of the forward-looking variables, +1 , will be equal to the private-sector expectations, +1| , since ・ ・ ・ ・ ~ ~ +1 = +1 + +1 = +1 + +1 = +1 = (| + ) = +1| where we have used (3.46). Thus, the specification of the projection model under discretion, (3.47)-(3.50), implies that the central bank considers alternative policy-rate paths and associated forecasts for the predetermined and forward-looking variables, taking into account that those forecasts would not be credible and de- viate from private-sector expectations. The private-sector expectations are here consistently equal to the optimal policy projection under discretion. In contrast, the specification of the projection model under commitment, (3.20)-(3.22), implies that the central bank considers alternative policy- rate paths and associated forecasts for the predetermined and forward-looking variables under the assumption that these alternative forecasts are credible. 3.8.2. Degrees of commitment Commitment and discretion raise intriguing issues. Which is the more realistic description of actual monetary-policy decisions is not obvious. In Bergo (2007), the then Deputy Governor of Norges Bank provides a fascinating discussion of how Norges Bank tries to implement optimal policy under commitment. My own view so far has been that central-bank staff should propose to policymakers policy alternatives that are consistent with commitment in a timeless perspective, in the hope that policymakers would restrict their choices to those alternatives. This is the view underlying Adolfson, Las・en, Lind・, and Svensson (2009), for instance. How different the outcomes under commitment and discretion will depend on many things and how relevant these differences are for policymaking is an empirical issue that to my knowledge has not been resolved.38 An interesting idea is to consider not only the extremes of commitment and discretion but also a continuum in between. Schaumburg and Tambalotti (2007) present a simple framework for 38 Furthermore, as discussed by Dennis (2008), the relative performance of commitment in a timeless perspective and discretion is an intriguing issue and depends on circumstances and how policy performance is evaluated. See Woodford (2010b) for more discussion of commitment, commitment in a timeless perspective, and discretion. 32 analyzing monetary policy in such a continuum, what they call quasi-commitment, between the extremes of commitment and discretion. Quasi-commitment is characterized by a given probability of a central bank reneging from a commitment. That probability can be interpreted as a measure of the lack of credibility of the central bank's policy, and they examine the welfare effects of a marginal increase in credibility. The main finding in their simple framework is that most of the welfare gain from increased commitment accrues at relatively low levels of credibility. The magnitude of the welfare gain is smaller when there is less inflation bias under discretion, that is, less average excess of inflation over the inflation target. 3.9. Uncertainty In this subsection, I briefly discuss two kinds of uncertainty, namely uncertainty about an im- perfectly observed state of the economy and uncertainty about the model and the transmission mechanism of monetary policy. 3.9.1. Uncertainty about the state of the economy It is a truism that monetary policy operates under considerable uncertainty about the state of the economy and the size and nature of the disturbances that hit the economy. This is a particular problem for forecast targeting, under which the central bank, in order to set its interest-rate in- strument, needs to construct conditional forecasts of future inflation, conditional on alternative interest-rate paths and the bank's best estimate of the current state of the economy and the likely future development of important exogenous variables. Often, different indicators provide conflicting information on developments in the economy. In order to be successful, a central bank then needs to put the appropriate weights on different information and draw the most efficient inference. In the case of a purely backward-looking model (of the evolution of the bank's target variables and the indicators), the principles for efficient estimation and signal extraction are well known. But in the more realistic case where important indicator variables are forward-looking variables, the problem of efficient signal-extraction is inherently more complicated. In the case where there are no forward-looking variables, it is well known that a linear model with a quadratic loss function and a partially observable state of the economy (partial information) is characterized by certainty equivalence. That is, the optimal policy is the same as if the state of the economy were fully observable (full information), except that one responds to an efficient estimate of the state vector rather than to its actual value. Furthermore, a separation principle 33 applies, according to which the selection of the optimal policy (the optimization problem) and the estimation of the current state of the economy (the estimation or signal-extraction problem) can be treated as separate problems. In particular, the observable variables will be predetermined and the innovations in the observable variables (the difference between the current realization and previous prediction of each of the observable variables) contain all new information. The optimal weights to be placed on the innovations in the various observable variables in one's estimate of the state vector at each point in time are provided by a standard Kalman filter (see, for instance, Chow (1973), Kalchbrenner and Tinsley (1975), and LeRoy and Waud (1977)). The case without forward-looking variables is, however, very restrictive. In the real world, many important indicator variables for central banks are forward-looking variables, variables that depend on private-sector expectations of the future developments in the economy and future policy. Central banks routinely watch variables that are inherently forward-looking, like exchange rates, bond rates and other asset prices, as well as measures of private-sector inflation expectations, industry order-flows, confidence measures, and the like. Forward-looking variables complicate the estimation or signal-extraction problem significantly. They depend, by definition, on private-sector expectations of future endogenous variables and of current and future policy actions. However, these expectations in turn depend on an estimate of the current state of the economy, and that estimate in turn depends, to some extent, on observations of the current forward-looking variables. This circularity presents a considerable challenge for the estimation problem in the presence of forward-looking variables. Pearlman, Currie, and Levine (1986) showed in a linear (non-optimizing) model with forward-looking variables and partial symmetric information that the solution can be expressed in terms of a Kalman filter, although the solution is much more complex than in the purely backward-looking case. Pearlman (1992) later used this solution in an optimizing model to demonstrate that certainty equivalence and the separation principle apply under both discretion and commitment in the presence of forward-looking variables and symmetric partial information. Svensson and Woodford (2003) extended this previous work on partial information with forward- looking variables by providing simpler derivations of the optimal weights on the observable variables, and clarifying how the updating equations can be modified to handle the circularity mentioned above.39 They also provided a simple example, in the standard New Keynesian model, that clarifies several issues raised by Orphanides (2003). He has argued, for instance, with reference to real-time 39 Gerali and Lippi (2008) provide a toolkit of Matlab routines that applies the algorithms of Svensson and Woodford (2005). 34 U.S. data from the 1970s, that it is better that monetary policy disregards uncertain data about the output gap and responds to current inflation only. The findings in Svensson and Woodford (2003) are different and in line with the conventional wisdom. First, they found that the monetary-policy response to the optimal estimates of the current output gap is the same as under certainty, that is, that certainty equivalence applies. Second, the optimal weights put on the noisy observations, the indicators, used in constructing the optimal estimate of the output gap depends on the degree of uncertainty. For instance, when the degree of noise in an indicator of potential output is large, the optimal weight on that indicator becomes small.40 3.9.2. Uncertainty about the model and the transmission mechanism Recognizing the uncertain environment that policymakers face, recent research has considered broader forms of uncertainty for which certainty equivalence no longer applies. While this may have important implications, in practice the design of policy becomes much more difficult outside the classical linear-quadratic framework. One of the conclusions of the Onatski and Williams (2003) study of model uncertainty is that, for progress to be made, the structure of the model uncertainty has to be explicitly modeled. In line with this, Svensson and Williams (2007b) develop a very explicit but still relatively general form of model uncertainty that remains quite tractable. They use a so-called Markov jump-linear- quadratic (MJLQ) model, where model uncertainty takes the form of different "modes" (or regimes) that follow a Markov process. The approach allows the user to move beyond the classical linear- quadratic world with additive shocks, yet remains close enough to the linear-quadratic framework that the analysis is transparent. Optimal and other monetary policies are examined in an extended linear-quadratic setup, extended in a way to capture model uncertainty. The forms of model uncer- tainty the framework encompasses include: simple i.i.d. model deviations; serially correlated model deviations; estimable regime-switching models; more complex structural uncertainty about very different models, for instance, backward- and forward-looking models; time-varying central-bank judgment・information, knowledge, and views outside the scope of a particular model (Svensson (2005))・about the state of model uncertainty; and so forth. Moreover, the methods also apply to other linear models with changes of regime which may capture boom/bust cycles, productiv- ity slowdowns and accelerations, switches in monetary and/or fiscal policy regimes, and so forth. 40 Svensson and Woodford (2004) derive an equlibrium with optimal monetary policy in a general linear-quadratic model with asymmetric information, where then central bank has less information than the private sector. Aoki (2006) provides an application to the standard New Keynesian model with a particular assumption about the central bank's information set. See Woodford (2010b) for more discussion of the case of asymmetric information. 35 With algorithms for finding the optimal policy as well as solutions for arbitrary policy functions it is possible to compute and plot consistent distribution forecasts・fan charts・of target variables and instruments. The methods hence extend certainty equivalence and "mean forecast targeting," where only the mean of future variables matter (Svensson (2005)), to more general certainty non- equivalence and "distribution forecast targeting," where the whole probability distribution of future variables matter (Svensson (2003b)). Certain aspects of the MJLQ approach have been known in economics since the classic works of Aoki (1967) and Chow (1973), who allowed for multiplicative uncertainty in a linear-quadratic framework. The insight of those papers, when adapted to the MJLQ setting, is that in MJLQ models the value function for the optimal policy design problem remains quadratic in the state, but now with weights that depend on the mode. MJLQ models have also been widely studied in the control-theory literature for the special case when there are no forward-looking variables (see Costa and Fragoso (1995), Costa, Fragoso, and Marques (2005), do Val, Geromel, and Costa (1998), and the references therein). More recently, Zampolli (2006) uses an MJLQ model to examine monetary policy under shifts between regimes with and without an asset-market bubble, although still in a model without forward-looking variables. Blake and Zampolli (2005) provide an extension of the MJLQ model to include forward-looking variables, although with less generality than in Svensson and Williams (2007b) and with the analysis and the algorithms restricted to observable modes and discretion equilibria. The MJLQ approach is also closely related to the Markov regime-switching models which have been widely used in empirical work. These methods first gained prominence with Hamilton (1989) which started a burgeoning line of research. Models of this type have been used to study a host of empirical phenomena, with many developments and techniques summarized in Kim and Nelson (1999). More recently, the implications of Markov switching in rational expectations models of monetary policy have been studied by Davig and Leeper (2007) and Farmer, Waggoner, and Zha (2009). These papers focus on (and debate) the conditions for uniqueness or indeterminacy of equilibria in forward-looking models, taking as given a specified policy rule. Relative to this previous literature, Svensson and Williams (2007b) provides a more general ap- proach for solving for the optimal policy in MJLQ models that include forward-looking variables. This extension is key for policy analysis under rational expectations, but the forward-looking vari- ables make the model nonrecursive. The recursive saddlepoint method of Marcet and Marimon (1998) can then be applied to express the model in a convenient recursive way, and an algorithm 36 for determining the optimal policy and value functions can be derived. The more general case where modes are unobservable and decision makers infer from their ob- servations the probability of being in a particular mode is much more difficult to solve. The optimal filter is nonlinear, which destroys the tractability of the MJLQ approach.41 Additionally, as in most Bayesian learning problems, the optimal policy will also include an experimentation component. Thus, solving for the optimal decision rules will be a more complex numerical task. Due to the curse of dimensionality, it is only feasible in models with a relatively small number of state vari- ables and modes. Confronted with these difficulties, the literature has focused on approximations such as linearization or adaptive control.42 Svensson and Williams (2007a) develops algorithms to solve numerically for the optimal policy in these cases.43 Due to the curse of dimensionality, the Bayesian optimal policy (BOP) is only feasible in relatively small models. Confronted with these difficulties, Svensson and Williams (2007a) also considers adaptive optimal policy (AOP).44 In this case, the policymaker in each period does update the probability distribution of the current mode in a Bayesian way, but the optimal policy is computed each period under the assumption that the policymaker will not learn in the future from observations. In the MJLQ setting, the AOP is signif- icantly easier to compute, and in many cases provides a good approximation to the BOP. Moreover, the AOP analysis is of some interest in its own right, as it is closely related to specifications of adaptive learning which have been widely studied in macroeconomics (see Evans and Honkapohja (2001) for an overview). Further, the AOP specification rules out the experimentation which some may view as objectionable in a policy context. 41 The optimal nonlinear filter is well-known, and it is a key component of the estimation methods as well (Hamilton (1989) and Kim and Nelson (1999)). 42 In the first case, restricting attention to (sub-optimal) linear filters preserves the tractability of the linear- quadratic framework. See Costa, Fragoso, and Marques (2005) for a brief discussion and references. In adaptive control, agents do not take into account the informational role of their decisions. See do Val, Geromel, and Costa (1998) for an application of an adaptive control MJLQ problem in economics. In a different setting, Cogley, Colacito, and Sargent (2007) have recently studied how well adaptive procedures approximate the optimal policies. 43 In addition to the classic literature (on such problems as a monopolist learning its demand curve), Wieland (2000), Wieland (2006) and Beck and Wieland (2002) have recently examined Bayesian optimal policy and optimal experimentation in a context similar to ours but without forward-looking variables. Eijffinger, Schaling, and Tesfase- lassie (2006) examine passive and active learning in a simple model with a forward-looking element in the form of a long interest rate in the aggregate-demand equation. Ellison and Valla (2001) and Cogley, Colacito, and Sargent (2007) study situations like ours but where the expectational component is as in the Lucas-supply curve (-1 , for example) rather than our forward-looking case ( +1 , for example). Ellison (2006) analyzes active and passive learning in a New Keynesian model with uncertainty about the slope of the Phillips curve. 44 Optimal policy under no learning, adaptive optimal policy, and Bayesian optimal policy have in the literature also been referred to as myopia, passive learning, and active learning, respectively. 37 3.10. Judgment Throughout the monetary-policy decision process in central banks, a considerable amount of judg- ment is applied to assumptions and projections. Projections and monetary-policy decisions cannot rely on models and simple observable data alone. All models are drastic simplifications of the economy, and data give a very imperfect view of the state of the economy. Therefore, judgmental adjustments in both the use of models and the interpretation of their results・adjustments due to information, knowledge, and views outside the scope of any particular model・are a necessary and essential component in modern monetary policy. Any existing model is always an approximation of the true model of the economy, and monetary-policy makers always find it necessary to make some judgmental adjustments to the results of any given model. Such judgmental adjustments could refer to future fiscal policy, productivity, consumption, investment, international trade, foreign-exchange and other risk premia, raw-material prices, private-sector expectations, and so forth. One way to represent central-bank judgment is as the central-bank's conditional mean estimate of arbitrary multidimensional stochastic "deviations"・"add factors"・to the model equations, as in Reifschneider, Stockton, and Wilcox (1997) and Svensson (2005). The deviations represent additional determinants・determinants outside the model・of the variables in the economy, the difference between the actual value of a variable and the value predicted by the model. It can be interpreted as model perturbations, as in the literature on robust control.45 Svensson (2005) discusses optimal monetary policy, taking judgment into account, in backward- and forward-looking models. Svensson and Tetlow (2005) show how central-bank judgment can be extracted according to the method of Optimal Policy Projections (OPP). This method provides advice on optimal monetary policy while taking policymakers' judgment into account. Svensson and Tetlow (2005) demonstrate the usefulness of OPP with a few example projections for two Greenbook forecasts and the FRB/US model. An early version of the method was developed by Robert Tetlow for a mostly backward-looking variant of the Federal Reserve Board's FRB/US model. The resulting projections have been referred to at the Federal Reserve Board as "policymaker perfect-foresight projections"・somewhat misleadingly. A description and application of the method is given in Federal Reserve Board (2002), the Federal Reserve Board's Bluebook for the FOMC meeting on May 2, 2002. Section 4.3 gives another example of the application of judgment, from the Riksbank's policy 45 See, for instance, Hansen and Sargent (2008). However, that literature deals with the more complex case when the model perturbations are endogenous and chosen by nature to correspond to a worst-case scenario. 38 decision on February 2009. In the middle of the recent financial crisis and rapidly deteriorating economic situation, the Riksbank posted forecasts quite different from the forecasts generated by the Riksbank's models. 4. Practice In this section on the practice of inflation targeting, I first discuss some development of practical inflation targeting since its introduction in New Zealand in 1990. Then I make some brief comments on the publication of policy-rate paths and describe the recent practice of two inflation-targeting central banks that I know more about; the Riksbank, which is ranked as one of the world's most transparent central banks, and Norges Bank, which has been a pioneer in applying explicit optimal monetary policy as an input in its policy decision. Finally I also comment on the issue of what preconditions are appropriate for emerging-market economies that consider inflation targeting. 4.1. Some developments of inflation targeting Inflation targeting was introduced in New Zealand in 1990.46 The Reserve Bank of New Zealand was the first central bank in the world to implement such a monetary policy setup, so it could not rely on the experience of other inflation-targeting central banks. Likewise, it had little experience in constructing inflation projections. During the 1990s, the Bank gradually established credibility and anchored inflation expectations on the inflation target. The Bank also accumulated an increased understanding of the transmission mechanism of monetary policy and increased confidence in its ability to fulfil the inflation target. This allowed the Bank some more degrees of freedom, and a gradual move towards more flexible and medium-term inflation targeting was to a large extent a natural consequence. It is possible that a shorter horizon and somewhat higher weight on inflation stabilization in the beginning may have contributed to establishing initial credibility. Initially, the Bank had a rather rudimentary view of the transmission mechanism and mostly emphasized the direct exchange rate channel to CPI inflation.47 The Bank also had a rather short policy horizon of 2--4 quarters within which it would attempt to meet the inflation target (see the Bank's Briefing of October 1996, Reserve Bank of New Zealand (1996)). The Bank's view of the transmission mechanism evolved gradually over the years to emphasize other channels 46 See Svensson (2001) and, in particular, Singleton, Hawke, and Grimes (2006) for the developments of inflation targeting in New Zealand. 47 See Svensson (2000) and Svensson (2001) for a discussion of the channels of the transmission mechanism of monetary policy. 39 of transmission, especially the aggregate-demand channel. The Monetary Policy Statement of December 1995, for instance, contains a box with a brief and preliminary discussion of the concept of potential output, which is so central in modern views of the transmission mechanism. With the introduction of the Forecasting and Policy System (FPS) in 1997 (Black, Cassino, Drew, Hansen et al. (1997)), which built on Bank of Canada's then state-of-the-art Quarterly Projection Model (QPM) (Poloz, Rose, and Tetlow (1994)), the Bank had developed a fully-fledged modern view of the transmission mechanism in an open economy in line with best international practice. With the introduction of the FPS, the Bank started to publish an interest-rate forecast in 1997, much earlier than any other inflation-targeting central bank. Parallel to these developments, the Bank lengthened its policy horizon and took a more flexible interpretation of the inflation target. Indeed, in its Briefing of November 1999, Reserve Bank of New Zealand (1999), the Bank completely subscribes to the idea of flexible inflation targeting: "Our conclusion, on the whole, has been to adopt a more medium-term approach, which attaches more weight to the desirability of stabilising output, interest rates and the exchange rate, while still aiming to keep inflation within the target range." The Bank mentioned some steps taken in this direction that include: ・ "The widening of the inflation target range, from 0 to 2 percent to 0 to 3 percent..." ・ "A lengthening of the horizon at which policy responses to inflation pressures are directed, from 6 to 12 months to something more like 12 to 24 months. This means that, provided the medium-term inflation outlook is in line with the target, near-term shifts in the price level are more likely to be accepted without policy reaction." ・ "Some de-emphasis of the edges of the target range as hard and precise thresholds..." ・ "The shift from an MCI target to a cash interest rate instrument for implementing monetary policy. This change has lessened the need for frequent intervention in the financial markets, and has resulted in more interest rate stability."48 48 From June 1997 to March 1999, the Reserve Bank used a so-called Monetary Conditions Index (MCI) both as an indicator and as an instrument in implementing monetary policy. The real MCI was constructed by combining the 90-day real interest rate with the real exchange rate (expressed in terms of a trade-weighted index, the TWI), with a weight of 0.5 on the exchange rate. (Using the nominal interest rate and exchange rate results in the nominal MCI.) The MCI was supposed to measure the overall stance of monetary policy: the degree to which monetary policy is deemed to resist either inflationary or deflationary tendencies. However, from the complexity of the transmission mechanism, with different channels, different lags and different strengths of the effects, it is apparent that a simple summary index like the MCI will be unreliable. For instance, the relative effect of interest rate and exchange rate 40 Regarding the policy horizon, inflation targeting has sometimes been associated with a fixed horizon, such as two years, within which the inflation target should be achieved. However, as is now generally understood, under optimal stabilization of inflation and the real economy there is no such fixed horizon at which inflation goes to target or resource utilization goes to normal. The horizon at which the inflation forecast is close to the target and/or the resource-utilization forecast is close to normal depends on the initial situation of the economy, the initial deviation of inflation and resource utilization from target and normal and the nature and size of the estimated shocks to the economy (Faust and Henderson (2004), Giavazzi and Mishkin (2006), Smets (2003)). In line with this, many or even most inflation-targeting central banks have more or less ceased to refer to a fixed horizon and instead refer to the "medium term."49 With the linear models of the transmission mechanism that are standard for central banks, reasonable equilibrium and optimal paths for inflation and resource utilization approach the target and a normal level asymptotically, including the case when the policy rate is an estimated empirical function of observable variables. More precisely, the resulting equilibrium forecasts on period of such models for the inflation and output gaps in period + , + - and + - + , ・ changes on output and inflation varies with the channel, the time horizon, and how persistent these changes are expected to be by households and firms. Thus, there is no reason to believe that the relative weight on the exchange rate, taken to be 0.5 by the Reserve Bank, is stable. In line with this, attempts to estimate the relative weights have resulted in different and very uncertain estimates. The numerous problems of the MCI are discussed in Stevens (1998). In my review of monetary policy 1990-2000 in New Zealand (Svensson (2001)), one of my conclusions was that the uncritical use of the MCI had contributed to too tight policy in 1997/98 during the Asian crisis. In March 1999, the Reserve Bank abandoned this unusual way of implementing monetary policy and instead moved to a completely conventional implementation, by setting the Official Cash Rate (OCR). With regard to the operational framework and how monetary policy was managed in pursuit of the inflation target, my overall conclusion was that "the period (mid 1997 to March 1999) when the Reserve Bank used a Monetary Conditions Index (MCI) to implement monetary policy represents a significant deviation from best international practice. This has now been remedied, and monetary policy in New Zealand is currently entirely consistent with the best international practice of flexible inflation targeting, with a medium-term inflation target that avoids unnecessary variability in output, interest rates and the exchange rate. Only some marginal improvements, mostly of a technical nature, are recommended." 49 The Policy Target Agreement for the Reserve Bank of New Zealand (Reserve Bank of New Zealand (2007)) states that "the policy target shall be to keep future CPI inflation outcomes between 1 and 3 per cent on average over the medium term." The Bank of England (Bank of England (2007)) states that "the MPC's aim is to set interest rates so that inflation can be brought back to target within a reasonable time period without creating undue instability in the economy." The Reserve Bank of Australia states (Reserve Bank of Australia (2008)) "[m]onetary policy aims to achieve this [a target for consumer price inflation of 2-3 per cent per annum] over the medium term." Norges Bank states in its Monetary Policy Report that "Norges Bank sets the interest rate with a view to stabilising inflation close to the target in the medium term." In contrast, the Bank of Canada (Bank of Canada (2006)) mentions a more specific target time horizon: "[T]he present policy of bringing inflation back to the 2 per cent target within six to eight quarters (18 to 24 months) is still appropriate generally, although specific occasions may arise in which a somewhat shorter or longer time horizon might be appropriate." At the time of writing (March 2010) the Riksbank mostly uses the phrase "in a couple of years," but some documents (hopefully not for very long) still use the phrase "within two years." 41 respectively, are all of the basic form P + - = 1 |1 | |2 | =1 P + - + = ・ =1 where and are constants determined by the initial state of the economy, for = 1 denote eigenvalues with modulus below unity, and = 0 1 denotes the forecast horizon. This means that the inflation-gap and the output-gap forecast for a particular forecast horizon are a linear combination of terms that approach zero exponentially and asymptotically. There is hence no particular horizon at which the forecast for the inflation or output gap is zero. Generally, a lower (higher) relative weight () on output-gap stabilization implies that the inflation gap (the output gap) goes to zero faster (slower) (Svensson (1997)). Furthermore, for any given horizon, the size of the inflation or output gap depends on the initial inflation and output gap. Because of this, half-time, meaning the horizon at which the gap has been reduced to a half of the initial gap, is a more appropriate concept than a fixed horizon for describing the convergence of the forecast to the long-term mean values.50 4.2. Publishing an interest-rate path As mentioned, inflation targeting is characterized by a high degree of transparency. Typically, an inflation-targeting central bank publishes a regular monetary-policy report which includes the bank's forecast of inflation and other variables, a summary of its analysis behind the forecasts, and the motivation for its policy decisions. Some inflation-targeting central banks also provide some information on, or even forecasts of, its likely future policy decisions. Indeed, a current much-debated issue concerning the further development of inflation targeting is the appropriate assumption about the policy-rate path that underlies the forecasts of inflation and other target variables and the information provided about future policy actions. Tradition- ally, inflation-targeting central banks have assumed a constant interest rate underlying its inflation forecasts, with the implication that a constant-interest-rate inflation forecast that overshoots (un- dershoots) the inflation target at some horizon such as two years indicates that the policy rate needs to increased (decreased) (Jansson and Vredin (2003), Vickers (1998)). Increasingly, central banks have become aware of a number of serious problems with the assumption of constant interest rates. A possible definition of half-time, , is the solution to the equation |1 | = 12, where 1 is the eigenvalue 50 with the largest modulus, so = - ln 2 ln |1 |. 42 These problems include that the assumption may often be unrealistic and therefore imply biased forecasts, imply either explosive or indeterminate behavior of standard models of the transmission mechanism of monetary policy, and at closer scrutiny be shown to combine inconsistent inputs in the forecasting process (such as some inputs such as asset prices that are conditional on market expectations of future interest rates rather than constant interest rates) and therefore produce in- consistent and difficult-to-interpret forecasts (Leitemo (2003), Woodford (2005))). Some central banks have moved to a policy-rate assumption equal to market expectations at some recent date of future interest rates, as they can be extracted from the yield curve. This reduces the number of problems mentioned above but does not eliminate them. For instance, the central bank may have a view about the appropriate future interest-rate path that differs from the market's view. A few central banks (notably the Reserve Bank of New Zealand already in 1997, Norges Bank in 2005, the Riksbank in 2007, and the Czech National Bank in 2008) have moved to deciding on and announcing a policy-rate path; this approach solves all the above problems, is the most consistent way of implementing inflation targeting, and provides the best information for the private sector. The practice of deciding on and announcing optimal policy-rate paths is now likely to be gradu- ally adopted by other central banks in other countries, in spite of being considered more or less impossible, or even dangerous, only a few years ago (Svensson (2007), Woodford (2005), Woodford (2007), Svensson (2009c)).51 4.3. The Riksbank In January 1993, the Riksbank announced an inflation target of 2 percent for the CPI, with a tolerance interval of ・1 percent, to apply from 1995. (The tolerance interval was considered unnecessary and abolished in June 2010.) In 1999, the Riksbank became independent, and a six-member executive board was appointed. The board members are individually accountable with one vote each and the Governor has the tie-braking vote. There are normally six monetary-policy meetings per year. After a meeting the policy decision and a Monetary Policy Report or Update are released the next morning. Since February 2007, the Riksbank publishes not only a forecast of inflation and the real economy but also a policy-rate path in its report/update. Minutes from the policy meeting are published about two weeks after the meeting. Since June 2007, the minutes are attributed. Since April 2009, the votes and any dissents are published in the press release the 51 Gosselin, Lotz, and Wyplosz (2008) provide a theoretical analysis of transparency and opaqueness about the central bank's policy-rate path. 43 Figure 4.1: Policy options for the Riksbank, July 2009 a. Alternative repo-rate paths c. CPIF Percent, quarterly averages Annual percentage change 5.0 4.0 Main Low High Main Low High 4.0 3.0 3.0 2.0 2.0 1.0 1.0 0.0 -1.0 0.0 08 09 10 11 12 08 09 10 11 12 d. Output gap b. Mean squared gaps Percent 15.0 1.0 High Main 0.0 10.0 Output -1.0 Main Low High Low -2.0 5.0 -3.0 -4.0 0.0 0.10 -5.0 0.00 0.02 0.04 0.06 0.08 08 09 10 11 12 CPIF day after the meeting and not only in the minutes two weeks later. The Riksbank ranks as one of the most transparent central banks in the world (Dincer and Eichengreen (2009), Eijffinger and Geraats (2006)). The Riksbank has announced that it conducts flexible inflation targeting and aims at stabilizing both inflation around the inflation target and resource utilization around a normal level. Figure 4.1 shows some policy options for the Riksbank at the policy meeting in July 2009. Panel a shows three alternative repo-rate paths (the repo rate is the Riksbank's policy rate), named Main, Low, and High. Panel c shows the corresponding forecasts for CPIF inflation (the CPI calculated with a fixed interest rate regarding housing costs) for the three repo-rate paths. Panel d shows corresponding output-gap forecasts for the three repo-rate paths. Panel b, finally, shows the tradeoff between the mean squared gaps for the inflation- and output-gap forecasts. The mean squared gap for the inflation- and output-gap forecast is the sum of the squared gaps over the forecast horizon divided by the number of periods within the forecast horizon.52 The point marked Main shows, for the Main repo-rate path, the mean squared gap for the inflation- and output-gap forecasts along the horizontal and vertical axis, respectively. The points marked Low and High show the 52 Mean squared gaps were introduced in Svensson (2010a). They appeared in the Riksbank's Monetary Pol- icy Report the first time in October 2009. The mean squared gap for the inflation- and output-gap forecasts are 2 2 =0 ( + - ) ( + 1) and =0 (+ - + ) ( + 1), respectively, where is the forecast horizon. ・ 44 corresponding mean squared gaps for the Low and High repo-rate paths. The almost horizontal line shows an isoloss line corresponding to equal weight on inflation and output-gap stabilization ( = 1). (The line is almost horizontal because the scales of the axes are so different.) We see that the High repo-rate path is dominated by the Main and Low repo-rate path. The majority of the board voted in favor of the Main alternative. Thanks to the high level of transparency of the Riksbank, the attributed minutes from the meeting (available in English on the Riksbank's web page, www.riksbank.com) reveal a lively debate about the decision, including whether a zero repo-rate was a feasible alternative or not. (I dissented in favor of the Low alternative.) Figure 4.2 shows an example of how judgment is applied to result in a different forecast than the model one. The four panels a-d show the forecast of the repo-rate, CPIF, GDP growth, and the output gap at the policy meeting in February 2009. The dash-dotted curves show the forecast from the Riksbank's DSGE model Ramses (Adolfson, Laseen, Lind・, and Villani (2007), Adolfson, Laseen, Lind・, and Villani (2008)) when an estimated policy function is applied. The dashed curve shows the forecast from the Riksbank's Bayesian VAR model BVAR. The dotted curves, finally, shows the Riksbank's forecast of the four variables as presented in the Monetary Policy Report. Taking into the account the severe financial crisis and the rapidly deteriorating economic situation, the Riksbank lowered the repo-rate by 100 basis points to 1 percent, much lower than the repo-rate paths suggested by the models, and still had a more pessimistic view of GDP growth and the output gap than the models. 4.4. Norges Bank Norway adopted an inflation target of 2.5 percent for monetary policy in March 2001. Norges Bank focuses on an index for core inflation. It is explicit about being a flexible inflation targeter and in explaining what that means: "Norges Bank operates a flexible inflation targeting regime, so that weight is given to both variability in inflation and variability in output and employment" (Norges Bank (2009)). Thus, Norges Bank can be seen as attempting to stabilize both the inflation gap and the output gap, which is consistent with minimizing a conventional intertemporal quadratic loss function. The policy rate is set by the Bank's executive board. Decisions concerning the policy rate are normally taken at the executive board's monetary-policy meeting every sixth week. At three of these meetings, normally in March, June and October/November, Norges Bank publishes its Monetary Policy Report with an explicit instrument-rate path and corresponding projections of 45 Figure 4.2: The application of judgment by the Riksbank, February 2009. a. Repo rate b. CPIF Percent Annual percentage change 5 7 Outcome Outcome 4 BVAR BVAR 5 Ramses Ramses 3 Riksbank Riksbank 3 2 1 1 0 -1 03 04 05 06 07 08 09 10 11 12 03 04 05 06 07 08 09 10 11 12 c. GDP growth d. Output gap Annual percentage change Percent 7 4 Outcome 5 BVAR 2 Ramses 3 Riksbank 0 Outcome 1 BVAR -2 Ramses -1 Riksbank -3 -4 03 04 05 06 07 08 09 10 11 12 03 04 05 06 07 08 09 10 11 12 CPI inflation, a measure of core inflation, the output gap, and the policy rate. The uncertainty of the forecast is illustrated with probability distributions (uncertainty intervals), as in figure 4.3 from the policy meeting in January 2008 (Bank of England and the Riksbank, for instance, also illustrate the uncertainty with the help of uncertainty intervals). The main scenario is the mean of the probability distributions. It is normally assumed that the distribution is symmetric. Officially, Norges Bank started to publish its own policy-rate forecast in the Inflation Report of November 2005. However, already in the Inflation Report of March 2005, it published graphs of alternative policy-rate paths and corresponding inflation and output-gap forecasts. These are reproduced in figure 4.4, panels a, c, and d. In panel b, I have computed and plotted the corre- sponding mean squared gaps for the three alternatives. The two negatively sloped lines show an isoloss line for = 1 and = 03 (the latter is the steeper line). The bank chose the Main alterna- tive. Norges Bank is the only central bank that has announced that it applies a specific when it computes optimal policy in its macroeconomic model. Bergo (2007) and Holmsen, Qvigstad, and R・island (2007) report that optimal policy with = 03 has replicated policy projections published by Norges Bank (with a discount factor of 099 and a weight on interest-rate smoothing of 02). Disregarding interest-rate smoothing, panel b shows that the Main alternative is marginally better then the High alternative for = 03 46 Figure 4.3: Main scenario and uncertainty intervals, Norges Bank, January 2008 5 5 9 9 Output gap Key policy rate 8 8 4 4 7 7 3 3 6 6 5 5 2 2 4 4 1 1 3 3 0 0 2 2 1 1 -1 -1 0 0 -2 -2 2005 2006 2007 2008 2009 2010 2005 2006 2007 2008 2009 2010 4 4 5 5 Underlying inflation (CPI- Inflation (CPI) ATE) 4 4 3 3 3 3 2 2 2 2 1 1 1 1 0 0 0 0 -1 -1 2005 2006 2007 2008 2009 2010 2005 2006 2007 2008 2009 2010 The decision process starts with the staff producing optimal policy projections under commit- ment.53 Although optimal policy projections with the medium-sized DSGE-model NEMO (Brubakk and Sveen (2009)) is used as an input in the decision process, weight is also put on simple interest- rate rules, such as the Taylor rule. Judgements are then added to the model-based projections. The projections are then discussed by the board which might ask for additional adjustments based on their judgments. Norges Bank has also published a set of criteria that it uses when judging between different instrument-rate paths. The first two criteria can be understood as verbal forms of optimality conditions. The other three provide for interest-rate smoothing, robustness and cross-checking. The criteria also work as an agenda for the internal discussions, see Holmsen, Qvigstad, R・island, and Solberg-Johansen (2008). Like many other central banks, Norges Bank indicates how it will react should certain dis- turbances occur by presenting alternative scenarios in the Monetary Policy Report. The exact specification of the shocks in the illustrations differs over time. The shifts are specified such that, if shocks of the same type and size occur, the alternative instrument-rate path is the Bank's best estimate of how it would react in such a situation. The shifts are consistent with the main scenario 53 The staff normally use commitment in a timeless perspective as the main normative benchmark, but they have also considered alternatives such as the quasi-commitment in Schaumburg and Tambalotti (2007) (see section 3.8.2). 47 Figure 4.4: Policy options for Norges Bank, March 2005 a. Alternative interest rate paths c. CPI-ATE Percent, quarterly averages Annual percentage change 8.0 8.0 3.0 3.0 Main Low High Main Low High 6.0 6.0 2.0 2.0 4.0 4.0 1.0 1.0 2.0 2.0 0.0 0.0 0.0 0.0 02 03 04 05 06 07 08 02 03 04 05 06 07 08 d. Output gap b. Mean squared gaps Percent 4.0 4.0 2.0 Main Low High Low 1.5 Output 2.0 2.0 1.0 Main 0.5 0.0 0.0 High 0.0 2.0 -2.0 -2.0 0.0 0.5 1.0 1.5 02 03 04 05 06 07 08 CPIF in the sense that they are based on the same loss function guiding the response of the central bank. The Monetary Policy Report includes an account of the disturbances that have led to a change in the instrument-rate forecast from the previous report. This "interest-rate account" is a model- based illustration of how the change in the policy-rate forecast from the previous report can be decomposed by different exogenous shocks to the model. The illustration shows how changes in the assessment of international and domestic economic variables as well as changes in the shock processes have affected the policy-rate path. The interest-rate account serves as a tool for commu- nicating commitment. When the central bank commits to a reaction pattern under commitment, a change in the instrument-rate forecast should reflect economic news and not re-optimization of monetary policy. With an interest-rate account, the public is better able to check whether the central bank responds to news only or whether it re-optimizes. 4.5. Preconditions for inflation targeting in emerging-market economies An oft-heard objection to inflation targeting (at least before Batini and Laxton (2007)) is that it is costly in terms of institutional and technical requirements, making the framework unsuitable for some emerging-market economies. A detailed exposition of this point was made in Eichengreen, Masson, Savastano, and Sharma (1999), who argued that technical capabilities and central bank 48 autonomy were severely lacking in most emerging-market economies (including several that sub- sequently adopted inflation targeting).54 Such countries, the argument goes, would be better off sticking with a "conventional" policy framework, such as an exchange-rate peg or money-growth targeting. The preconditions include (International Monetary Fund (2005, chapt. 4) and Ba- tini and Laxton (2007)) institutional independence of the central bank; a well-developed technical infrastructure in terms of forecasting, modeling and data availability; an economy with fully dereg- ulated prices, not overly sensitive to commodity prices and exchange rates, and with minimal dollarization; and a healthy financial system with sound banks and well-developed capital markets. To assess the role of preconditions for the adoption of inflation targeting, Batini and Laxton (2007) administered a survey to 21 inflation-targeting central banks and 10 non-targeting central banks in emerging-market countries. The version of the survey given to inflation-targeting central banks focused on how policy was formulated, implemented, and communicated and how various as- pects of central banking practice had changed before and during the adoption of targeting. Survey responses were cross-checked with independent primary and secondary sources and in many cases augmented with "hard" economic data. The evidence indicates that no inflation targeter had all the preconditions in place before adopting inflation targeting. Furthermore, their evidence suggests that it does not appear to be necessary for emerging-market countries to meet a stringent set of institutional, technical, and economic preconditions before successfully adopting inflation target- ing. Instead, the feasibility and success of targeting appears to depend more on the authorities' commitment and ability to plan and drive institutional change after introducing targeting. Con- sequently, policy advice to countries that are interested in adopting targeting could usefully focus on the institutional and technical goals central banks should strive for during and after adopting targeting in order to maximize its potential benefits. In a study of the experiences of Brazil, Chile, the Czech Republic, Indonesia, South Africa, and Turkey, de Mello (2008) concludes that many of the preconditions associated with inflation targeting had not been fulfilled when these countries adopted inflation targeting. Nevertheless, he finds that "these deficiencies have not undermined the implementation of inflation targeting where policy efforts have been focused on addressing them" (p. 10). In an extensive survey, Freedman and ・tker-Robe (2009) describe the experiences of a number 54 Others who stressed the conceptual relevance of "preconditions" include Agenor (2000); Schaechter, Stone, and Zelmer (2000); Carare, Schaechter, Stone, and Zelmer (2002); Khan (2003); and the May 2001 World Economic Outlook. See also Masson, Savastano, and Sharma (1997). More neutral or benign views on the conceptual relevance of "preconditions" can instead be found in Truman (2003); Jonas and Mishkin (2003); Debelle (2001); and Amato and Gerlach (2002). 49 of countries with the introduction and implementation of inflation targeting regimes, and discuss how they fared in meeting the various conditions that some have argued are needed in advance of introducing inflation targeting. They find that the country experiences are not supportive of the view that countries have to satisfy a long list of preconditions before adopting inflation targeting but that some elements were important in making the inflation-targeting framework more feasible and less challenging: (i) price stability as the overriding monetary policy goal; (ii) absence of fis- cal dominance; (iii) central bank instrument independence; (iv) broad domestic consensus on the prominence of the inflation target; (v) some basic understanding of the transmission mechanism, and a reasonable capacity to affect short-term interest rates; and (vi) reasonably well-functioning financial system and markets. They suggest that these elements could perhaps be viewed as the conditions conducive to the introduction of a successful inflation-targeting framework. In particu- lar, they conclude: "There is no single most effective path toward adoption of inflation targeting. It would certainly be a mistake to think that all the conditions for a successful implementation of inflation targeting need to be in place before the framework could be launched. As country experi- ences show, in many countries that now have successful inflation targeting, some of the conditions were not in place at the outset, but the authorities worked over time to establish them, and also learned by doing. It would similarly be a mistake, however, to think that all the conventional con- ditions would arrive spontaneously. The central banks have to initiate the process and make their best effort to establish the true conditions and work with the government toward that objective" (p. 19--20). 5. Future This section discusses two potential future issues for inflation targeting -- whether it would be ad- vantageous to move on to price-level targeting and whether inflation targeting needs to be modified in the light of the recent financial crisis and deep recession. 5.1. Price-level targeting A possible future issue is whether flexible inflation targeting should eventually be transformed into flexible price-level targeting. Inflation targeting as practised implies that past deviations of inflation from target are not undone. This introduces a unit root in the price level and makes the price level not trend-stationary, that is, nonstationary even after the removal of a deterministic trend. That is, 50 the conditional variance of the future price level increases without bound with the horizon. In spite of this, inflation targeting with a low inflation rate is referred to as "price stability'. An alternative monetary-policy regime would be "price-level targeting', where the objective is to stabilize the price level around a price-level target.55 That price-level target need not be constant but could follow a deterministic path corresponding to a steady inflation of two percent, for instance. Stability of the price level around such a price-level target would imply that the price level becomes trend- stationary, that is, the conditional variance of the price level becomes constant and independent of the horizon. One benefit of this compared with inflation targeting is that long-run uncertainty about the price level is smaller. Another benefit is that, if the price level falls below a credible price-level target, inflation expectations would rise and reduce the real interest rate even if the nominal interest rate is unchanged. The reduced real interest rate would stimulate the economy and bring the price level back to the target. Thus, price-level targeting may imply some automatic stabilization. This may be highly desirable, especially in situations when the zero lower bound on nominal interest rates is binding, the nominal interest rate cannot be further reduced, and the economy is in a liquidity trap, as has been the case for several years in Japan (and during the recent deep recession in several other countries). Whether price-level targeting would have any negative effects on the real economy remains a topic for current debate and research (Svensson (2002)). Recently several central banks, especially Bank of Canada, have shown new interest in price-level targeting and several reviews of new and old research have been published, for instance, Ambler (2009), Amano, Carter, and Coletti (2009), Deutsche Bundesbank (2010), and Kahn (2009). 5.2. Inflation targeting and financial stability: Lessons from the financial crisis56 At the time of writing (April 2010), the world economy was beginning to recover from the financial crisis and the resulting deep recession of the global economy, and there is a lively debate about what caused the crisis and how the risks of future crises can be reduced. Some blame loose monetary policy for laying the foundation for the crisis, and there is also a lively debate about the future of monetary policy and its relation to financial stability. In this section I discuss the lessons for inflation targeting after the crisis. My view is that the crisis was not caused by monetary policy but mainly by regulatory and supervisory failures in combination with some special circumstances, 55 See Berg and Jonung (1999) for a discussion of the good experience of price-level targeting in Sweden during the Great Depression. 56 This section builds on Svensson (2009a) and Svensson (2010b). I thank Hanna Armelius, Charles Bean, Claes Berg, Alan Blinder, Stephen Cecchetti, Hans Dellmo, Chuck Freedman, Charles Goodhart, Bj‡rn Lagerwall, Lars Nyberg, Irma Rosenberg, Hyun Shin, Frank Smets, and Staffan Viotti for discussions of these issues. 51 such as low world real interest rates and U.S. housing policy. Ultimately, my main conclusion for monetary policy from the crisis so far is that flexible inflation targeting, applied in the right way and using all the information about financial factors that is relevant for the forecast of inflation and resource utilization at any horizon, remains the monetary policy before, during, and after the financial crisis that has the best chance to stabilize both inflation and the real economy. But a better theoretical, empirical, and operational understanding of the role of financial factors in the transmission mechanism is urgently required and needs much work, work that is already underway in academia and in central banks. As described in the previous sections, flexible inflation targeting means that monetary policy aims at stabilizing both inflation around the inflation target and resource utilization around a normal level, keeping in mind that monetary policy cannot affect the long-term level of resource utilization. Because of the time lags between monetary-policy actions and their effect on inflation and the real economy, flexible inflation targeting is more effective if it relies on forecasts of inflation and the real economy. Therefore, flexible inflation targeting can be described as "forecast targeting": the central bank chooses a policy-rate path so that the forecast of inflation and resource utilization stabilizes both inflation around the inflation target and resource utilization around a normal level or achieves a reasonable compromise between the two. The forecasts of inflation and the real economy are then conditional on the central bank's view of the transmission mechanism, an estimate of the current state of the economy and a forecast of important exogenous variables. The central bank uses all relevant information that has an impact on the forecast of inflation and the real economy. In this framework, the central bank takes financial conditions such as credit growth, asset prices, imbalances, potential asset price bubbles and so on into account only to the extent that they have an impact on the forecast of inflation and resource utilization. Inflation and resource utilization are target variables, that is, variables that the central bank tries to stabilize. Financial conditions are not target variables. Instead, they are only indicators, as they provide information to the central bank about the state of the economy, the transmission mechanism and exogenous shocks. Financial conditions then affect policy rates only to the extent that they have an impact on the forecast of inflation and resource utilization. Now, is there any reason to modify this view of monetary policy given the experience of the financial crisis so far? Let me approach this question by first asking what the causes of the financial crisis were, whether monetary policy contributed to the crisis, and whether a different monetary policy was warranted and could have prevented or reduced the size of the crisis. 52 5.2.1. Did monetary policy contribute to the crisis, and could different monetary policy have prevented the crisis? Many have claimed that excessively easy monetary policy by the Federal Reserve after 2001 helped cause a bubble in house prices in the U.S., a bubble whose inevitable bursting proved to be a major source of the financial crisis.57 However, as I see it, the crisis was mainly caused by factors that had very little to do with monetary policy and were mostly due to background macro conditions, distorted incentives in financial markets, regulatory and supervisory failures (also when central banks have been responsible for regulation and supervision), information problems, and some spe- cific circumstances, including the U.S. housing policy to support home ownership for low-income households.58 The macro conditions preceding the crisis included low world real interest rates associated with global imbalances, as well as the Great Moderation, with a long period of very stable growth and stable low inflation, which led to a systematic underestimation of risk and very low risk premia in financial markets. There were distorted incentives for commercial and investment banks to increase leverage that were made possible by lax regulation and supervision and the lack of an appropriate bank resolution regime. There were also distorted incentives to exercise less due diligence in loan origination because of securitization and to conduct regulatory arbitrage by setting up off-balance- sheet entities, which for various specific reasons ended up still effectively remaining on the balance sheet. There were also distorted incentives for traders and fund managers to take excessive risks because of myopic and asymmetric remuneration contracts. There were eventually enormous in- formation problems in assessing the risks of extremely complex asset-backed securities, and there was a huge underestimation of the potential for correlated systemic risks. None of these causes had anything to do with monetary policy, except that monetary policy may have contributed to the Great Moderation. Regarding the role of Federal Reserve monetary policy in the crisis, there are two relevant questions. First, was the low interest rate reasonable given the information available at the time? Second, could a different monetary policy with higher interest rates have prevented the crisis? The first question, whether the low interest rate was reasonable given the available information, is the 57 See, for instance, Taylor (2007). 58 See Bean (2009) for an extensive and excellent discussion of the crisis, including the credit expansion and housing boom, the macroeconomic antecedents, the distorted incentives, the information problems, the amplification and propagation of the crisis into the real economy, the policy responses, and the lessons for monetary policy and economics generally. Bank for International Settlements (2009) provides a more detailed account of the possible macro- and microeconomic causes of the crisis. 53 relevant one when evaluating monetary policy. It is more relevant to evaluate policy taking into account the information available ex ante to the policymaker rather than information ex post that was unknown to the policymaker at the time (see Svensson (2010a) on evaluating monetary policy ex ante and ex post). During the period in question, given the information available, there was a genuine and well-motivated fear of the U.S. falling into a Japanese-style deflationary liquidity trap, and the optimal policy in such a situation is a very expansionary monetary policy.59 It may be that, in retrospect, the risk of deflation was exaggerated, but there was no way to know this ex ante. Hence, I consider the expansionary policy very appropriate. Adding some ex post evaluation, one can note that it did not lead ex post to very high inflation or an overheated economy.60 The second question, whether a different monetary policy could have prevented the crisis, is relevant when assessing to what extent monetary policy can be blamed for causing the crisis, notwithstanding if it was reasonable from an ex ante perspective. The credit growth and the housing boom in the U.S. and elsewhere were very powerful. Real interest rates were low to a large extent because of global imbalances, and the global saving glut and investment shortage. I believe that somewhat higher interest rates would have made little or no difference. Empirical evidence indicates that only a small portion of house-price increases can be attributed to monetary policy.61 Bernanke (2010) shows that the recent phenomenon of a higher share of adjustable-rate mortgages was unlikely to have significantly increased the sensitivity of house prices to monetary policy. The availability of new, more exotic mortgage types mattered much more for initial mortgage payments than the level of short-term interest rates. In my view, interest rates would probably have had to be raised very high so as to cause considerable damage to the real economy in order to stop the credit growth and housing boom. That could have thrown the U.S. right into Japanese-style deflation and eventually a liquidity trap.62 Certainly, higher interest rates would have had no impact on the regulatory problems, distorted incentives and information problems mentioned above (although they could have ended the Great Moderation with a deep recession and deflation).63 59 See Svensson (2003a) for a discussion of policy options before and in a liquidity trap. 60 Bernanke (2010) shows that Fed policy rates do not seem excessively low given real-time FOMC forecasts. See also Dokko, Doyle, Kiley, Kim et al. (2009). 61 See Del Negro and Otrok (2007), Jarocinski and Smets (2008), Edge, Kiley, and Laforte (2008), and Iacoviello and Neri (2008). 62 Assenmacher-Wesche and Gerlach (2009) study the responses of residential property and equity prices, inflation and economic activity to monetary policy shocks in 17 countries in the period 1986-2007, using single-country VARs and panel VARs in which they distinguish between groups of countries depending on their financial systems. The effect of monetary policy shocks on GDP is about a third of the effect on property prices. Thus, to increase policy rates so as to lower property prices by 15 percent would result in 5 percent lower GDP. 63 Kohn (2008), after extensive discussion, concludes that there is insufficient evidence that low interest rates would have contributed much to the house-price boom and that higher interest rates would have had much dampening effect on it. 54 However, going beyond the Federal Reserve's actual monetary policy, perhaps it is possible that the emphasis on its readiness to relax monetary policy aggressively in the wake of a sharp fall in asset prices, as expressed by Greenspan (2002) for example, may have induced expectations of a floor under future asset prices and contributed to the asset-price boom, the so-called Greenspan put (Miller, Weller, and Zhang (2002)). Arguably, this is more of a communication issue than one of actual policy, and less emphasis on the readiness to clean up after a sharp fall in asset prices might have been a preferable alternative. The IMF (International Monetary Fund (2009, chapt. 3)) has investigated the role of monetary policy in causing financial crises. A large number of countries and financial crises were included in the sample. The conclusion is that "the stance of monetary policy has not generally been a good leading indicator of future house price busts. . . There is some association between loose monetary policy and house price rises in the years leading up to the current crisis in some countries, but loose monetary policy was not the main, systematic cause of the boom and consequent bust." Further- more, the overall relationship between the stance of monetary policy and house-price appreciation across countries in the years before the current crisis is statistically insignificant and economically weak, and monetary policy differences explain only about 5 percent of the variability in house price appreciation across countries.64 What conclusions can we draw so far from the financial crisis about the conduct of monetary policy and any need to modify the framework of flexible inflation targeting? One obvious conclusion is that price stability is not enough to achieve financial stability (Carney (2003), White (2006)). Good flexible inflation targeting by itself does not achieve financial stability, if anyone ever believed it would. Another conclusion is that interest-rate policy is not enough to achieve financial stability. Spe- cific policies and instruments are needed to ensure financial stability. Instruments like supervision and regulation, including appropriate bank resolution regimes, are more effective in promoting fi- nancial stability. In many countries, the responsibility for these instruments rests on authorities other than the central bank. Generally, to the extent financial instability depends on specific dis- tortions, regulation is most effective if it aims to attack these distortions as close to the source as possible. To counter the observed procyclicality of existing regulation, macro-prudential regula- tion that is contingent on the business cycle and financial indicators may need to be introduced 64 The relationship for the euro area countries is less weak, but for reasons explained by Bernanke (2010) it is potentially overstated. See also Dokko, Doyle, Kiley, Kim et al. (2009). 55 to induce better financial stability. Possible macro-prudential regulation includes variable capital, margin, and equity/loan requirements. As expressed by Bean (2009), "the best approach is likely to involve a portfolio of instruments." 5.2.2. Distinguish monetary policy and financial-stability policy More generally, what is the relation between financial stability and monetary policy? Financial stability is an important objective of economic policy. A possible definition of financial stability is a situation when the financial system can fulfil its main functions (of submitting payments, channeling saving into investment, and providing risk sharing) without disturbances that have significant social costs. I find it helpful to conceptually distinguish financial-stability policy from monetary policy. Different economic policies and policy areas, such as fiscal policy, labor market policy, structural policies to improve competition, etc., can be distinguished according to their objectives, the policy instruments that are suitable for achieving the objectives, and the authority or authorities controlling the instruments and responsible for achieving the objectives. Monetary policy in the form of flexible inflation targeting has the objective of stabilizing both inflation around the inflation target and resource utilization around a normal level. The suitable instruments are under normal circumstances the policy rate and communication, including possibly a published policy-rate path and a forecast of inflation and the real economy. In times of crisis, as we have seen during the current crisis, other more unconventional instruments can be used, such as fixed-rate lending at longer maturities, asset purchases (quantitative easing), and foreign-exchange intervention to prevent currency appreciation. The authority responsible for monetary policy is typically the central bank. The objective of financial-stability policy is maintaining or promoting financial stability. Under normal circumstances the available instruments are supervision, regulation, and financial-stability reports with analyses and leading indicators that may provide early warnings of stability threats. In times of crisis, there are instruments such as lending of last resort, variable-rate lending at longer maturities (credit policy, credit easing), special resolution regimes for financial firms in trouble, government lending guarantees, government capital injections, and so forth.65 The responsible authority or authorities vary across countries. In some countries it is the central bank, in other 65 Gertler and Kiyotaki (2010) develop a canonical framework to help organize thinking about credit market frictions and aggregate economic activity in the context of the current crisis. They use the framework to discuss how disruptions in financial intermediation can induce a crisis that affects real activity and to illustrate how various credit market interventions by the central bank and/or the Treasury of the type seen during the crisis might work to mitigate the crisis. 56 countries there is a separate financial supervisory authority, sometimes the responsibility is shared between different institutions. In Sweden, the Financial Supervisory Authority is responsible for supervision and regulation, the Riksbank is responsible for lending of last resort to solvent banks and for promoting a safe and efficient payment system, while the National Debt Office is responsible for bank guarantees and the resolution of failed banks. During times of crisis, these authorities cooperate closely with the Ministry of Finance. My point here is that financial-stability policy and monetary policy are quite different, with different objectives, instruments, and responsible authorities, the latter with considerable differences across countries. This does not mean that there is no interaction between them. Financial stability directly affects the financial markets, and financial conditions affect the transmission mechanism of monetary policy. Problems in financial markets may have a drastic effect on the real economy, as the current financial crisis has shown. Monetary policy affects asset prices and balance sheets and can thereby affect financial stability. But the fact that financial-stability policy and monetary policy are conceptually distinct, with distinct objectives and distinct suitable instruments, has to be taken into account when considering the lessons of the financial crisis for monetary policy. Thus, because the policy rate is a blunt and unsuitable instrument for achieving financial stability, it makes little sense to assign the objective of financial stability to monetary policy, although it may make sense assign that objective to the central bank, if the central bank gets control of the appropriate supervisory and regulatory instruments.66 5.2.3. Conclusions for flexible inflation targeting What are the specific conclusions for flexible inflation targeting? One important lesson from the financial crisis is that financial factors may have a very strong and deteriorating effect on the trans- mission mechanism, making standard interest-rate policy much less effective. This motivates more research on how to incorporate financial factors into the standard models of the transmission mech- anism used by central banks. A rapidly-increasing volume of such research is now being produced by academic and central-bank researchers and presented at an increasing number of conferences on financial factors and monetary policy. Important and challenging questions include how potential output and neutral real interest rates are affected by financial factors and financial distortions (Cur- dia and Woodford (2009), Walsh (2009b)), and what impact financial factors have on the general 66 Blinder (2010) discusses how much of the responsibility for financial-stability policy should rest with the central bank. 57 equilibrium effects of alternative policy-rate paths on inflation and resource utilization forecasts.67 Even with much better analytical foundations concerning the role of financial factors in the trans- mission mechanism, there will of course, as always, be considerable scope for the application of good judgment in monetary policy. Another conclusion, which is not new, is that consideration of the impact of financial factors on the forecast of inflation and resource utilization may require longer forecast horizons. Several inflation-targeting central banks (including the Bank of England, Norges Bank, and the Riksbank) have for other reasons already extended their forecast horizon from the previously common two years to three years. There is nothing that in principle prevents an inflation targeter from considering forecasts beyond a three-year horizon, but in practice there is usually little information about anything at longer horizons except the tendency to revert to the long-term average. What about "leaning against the wind" (as advocated by, for instance, Borio and White (2003) and Cecchetti, Genberg, and Wadhwani (2002)), the idea that central banks should raise the interest rate more than what appears to be warranted by inflation and resource utilization to counter rapid credit growth and rising asset prices? It has sometimes not been quite clear whether advocates of leaning against the wind mean that credit growth and asset prices should be considered targets and enter the explicit or implicit loss functions alongside inflation and resource utilization, or whether they mean that credit growth and asset prices should still be considered just indicators and are emphasized only because credit growth and asset prices may have potential negative effects on inflation and resource utilization at a longer horizon. In the latter case, leaning against the wind is a way to improve the stability of inflation and resource utilization in the longer run. Then it is completely consistent with flexible inflation targeting.68 However, in line with the previous discussion, instruments other than interest rates are likely to be much more effective in avoiding excessive credit growth and asset- price booms, and are therefore more appropriate to use as a first-best alternative. Interest rates that are high enough to have a noticeable effect on credit growth and asset prices may have strong negative effects on inflation and 67 Walsh (2009b) points out that when financial factors cause distortions, these distortions will in general introduce corresponding terms in a loss function for monetary policy that is a second-order approximation to household welfare. Curdia and Woodford (2009) present a model where the second-order welfare approximation is a standard quadratic loss function of inflation and the output gap between output and potential output, but where potential output is affected by financial factors. Then inflation and the output gap remain the target variables, with and without financial factors. The neutral rate in the model, that is, the real rate consistent with output equal to potential output, is then also affected by financial factors. 68 Adrian and Shin (2010a) and Adrian and Shin (2010b) argue, in a model with a risk-taking channel as in Borio and Zhu (2008), that short interest-rate movements may have considerable effects on the leverage of securities broker-dealers in the market-based financial sector outside the commercial-banking sector. However, new regulation may affect the magnitude of these affects, and the size of the market-based financial sector may end up being smaller after the crisis. In Europe, the commercial banks dominate the financial sector. 58 resource utilization, and a central bank will probably rarely have sufficient information about the likely beneficial longer-horizon effects on inflation and resource utilization for the trade-off to be worthwhile and motivated.69 In particular, if there is evidence of rapidly rising house prices and mortgage loans, and these developments are deemed to be unsustainable and a possible bubble, there are much more effective instruments than policy rates. Restrictions on loan-to-value ratios and requirements of realistic cash-flow calculations for house buyers with realistic interest rates are much more effective in putting a break on possible unsustainable developments than a rise in the policy rates. In particular, more transparency about future policy rates, in the form a policy-rate path published by the central bank, may help in providing realistic information about future interest rates. Suppose, however, that, for some reason, the appropriate and effective instruments to ensure financial stability are not available, for instance, because of serious problems with the regulatory and supervisory framework that cannot be remedied in the short run. In such a second-best situation, if there is a threat to financial stability, one may argue that, to the extent that policy rates do have an impact on financial stability, that impact should be taken into consideration when choosing the policy-rate path to best stabilize inflation and resource utilization. Such considerations could result in a lower or higher policy-rate path than otherwise, in order to trade off less effective stabilization of inflation and resource utilization for more financial stability. However, so far all of the evidence indicates that in normal times that tradeoff is very unfavorable, in the sense that the impact of policy rates on financial stability is quite small and the impact on inflation and resource utilization is significantly larger, so an optimal tradeoff would still have little impact on financial stability. A good financial-stability policy framework is necessary to ensure financial stability. Monetary policy cannot serve as a substitute. Ultimately, my main conclusion from the crisis so far is that flexible inflation targeting, applied in the right way and using all the information about financial factors that is relevant for the forecast of inflation and resource utilization at any horizon, remains the monetary policy before, during, and after the financial crisis that has the best chance to stabilize both inflation and the real economy. But a better theoretical, empirical and operational understanding of the role of financial factors in the transmission mechanism is urgently required and needs much work, work that is already 69 Kohn (2006) specifies three conditions that should be fulfilled for central banks to take "extra action" to deal with a possible asset-price bubble: "First, policymakers must be able to identify bubbles in a timely fashion with reasonable confidence. Second, a somewhat tighter monetary policy must have a high probability that it will help to check at least some of the speculative activity. And third, the expected improvement in future economic performance that would result from the curtailment of the bubble must be sufficiently great." He concludes, also in Kohn (2008) and after thorough considerations, that those conditions would rarely be met. See also Kohn (2009). 59 underway in academia and in central banks. The outcome might very well be that financial factors are considered to have a larger role in affecting the transmission mechanism and as indicators of future inflation and resource utilization. If so, central banks would end up responding more to financial indicators, in the sense of adjusting the policy rate and policy-rate path more to a given change in a financial indicator. However, this would not mean that financial factors and indicators have become independent targets besides inflation and resource utilization in the explicit or implicit central-bank loss function. Instead, it would be a matter of responding appropriately to financial indicators in order to achieve over time the best possible stabilization of inflation around the inflation target and resource utilization around a normal level. 60 References Adolfson, Malin, Stefan Laseen, Jesper Lind・, and Mattias Villani (2007), "Bayesian Estimation of an Open Economy DSGE Model with Incomplete Pass-Through," Journal of International Economics 72(2), 481--511. Adolfson, Malin, Stefan Laseen, Jesper Lind・, and Mattias Villani (2008), "Evaluating an Estimated New Keynesian Small Open Economy Model," Journal of Economic Dynamics and Control 32(8), 2690--2721. Adolfson, Malin, Stefan Las・en, Jesper Lind・, and Lars E.O. Svensson (2009), "Optimal Monetary Policy in an Operational Medium-Sized DSGE Model," working paper, www.larseosvensson.net. Adrian, Tobias, and Hyun Song Shin (2010a), "Financial Intermediaries and Monetary Economics," in Friedman, Benjamin M., and Michael Woodford (eds.), Handbook of Monetary Economics, Volume 3a and 3b, Elsevier. Adrian, Tobias, and Hyun Song Shin (2010b), "Liquidity and Leverage," Journal of Financial Intermediation 19(3), 418--437, available as Federal Reserve Bank of New York Staff Reports 328, 2007. Agenor, Pierre-Richard (2000), "Monetary Policy under Flexible Exchange Rates - An Introduction to Inflation Targeting," The World Bank Policy Research Working Paper 2511. Amano, Robert, Tom Carter, and Don Coletti (2009), "Next Step for Canadian Monetary Policy," Bank of Canada Review Spring 2009, 5--18. Amato, Jeffery D., and Stefan Gerlach (2002), "Inflation Targeting in Emerging Market and Tran- sition Economies: Lessons After a Decade," European Economic Review 46(4-5), 781--790. Ambler, Steve (2009), "Price-Level Targeting and Stabilization Policy: A Review," Bank of Canada Review Spring 2009, 19--29. Anderson, Gary S. (2000), "A Systematic Comparison of Linear Rational Expectations Model Solution Algorithms," working paper. Anderson, Gary S. (2010), "A Reliable and Computationally Efficient Algorithm for Imposing the Saddle Point Property in Dynamic Models," Journal of Economic Dynamics and Control 34(3), 472--489. 61 Anderson, Gary S., and George Moore (1983), "An Efficient Procedure for Solving Linear Perfect Foresight Models," working paper. Anderson, Gary S., and George Moore (1985), "A Linear Algebraic Procedure for Solving Linear Perfect Foresight Models," Economics Letters 17(3), 247--252. Angeriz, Alvaro, and Philip Arestis (2008), "Assessing Inflation Targeting Through Intervention Analysis," Oxford Economic Papers 60(2), 293--317. Aoki, Kosuke (2006), "Optimal Commitment Policy Under Noisy Information," Journal of Eco- nomic Dynamics and Control 30(1), 81--109. Aoki, Masanao (1967), Optimization of Stochastic Systems, Academic Press, New York. Assenmacher-Wesche, Katrin, and Stefan Gerlach (2009), "Financial Structure and the Impact of Monetary Policy on Asset Price," CFS Working Paper 2008/30. Backus, David, and John Driffill (1986), "The Consistency of Optimal Policy in Stochastic Rational Expectations Models," CEPR Discussion Paper 124. Ball, Laurence, and Niamh Sheridan (2005), "Does Inflation Targeting Matter?" in Bernanke, Ben S., and Michael Woodford (eds.), The Inflation-Targeting Debate, The University of Chicago Press, 249--276. Bank for International Settlements (2009), 79th Annual Report. Bank of Canada (2006), "Bank of Canada Releases Background Information on Renewal of the Inflation-Control Target," Press release, November 27, 2006, www.bankofcanada.ca. Bank of England (2007), "Monetary Policy Framework," www.bankofengland.co.uk. Batini, Nicoletta, and Douglas Laxton (2007), "Under What Conditions Can Inflation Targeting Be Adopted? The Experience of Emerging Markets," in Mishkin, Frederic, and Klaus Schmidt- Hebbel (eds.), Monetary Policy under Inflation Targeting, vol. 11 of Central Banking, Analysis, and Economic Policies, Central Bank of Chile, 467--506. Bean, Charles R. (2009), "The Great Moderation, the Great Panic and the Great Con- traction," Schumpeter Lecture, Annual Congress of the European Economic Association, www.bankofengland.co.uk. 62 Beck, Gunter W., and Volker Wieland (2002), "Learning and Control in a Changing Economic Environment," Journal of Economic Dynamics and Control 26(9-10), 1359--1377. Berg, Claes, and Lars Jonung (1999), "Pioneering Price Level Targeting: The Swedish Experience 1931-1937," Journal of Monetary Economics 43(3), 525--551. Bergo, Jarle (2007), "Interest Rate Projections in Theory and Practice," Speech on January 26, 2007, www.Norges-Bank.no. Bernanke, Ben S. (2010), "Monetary Policy and the Housing Bubble," Speech on January 3, 2010, www.federalreserve.gov. Bernanke, Ben S., Thomas Laubach, Frederic S. Mishkin, and Adam S. Posen (1999), Inflation Targeting: Lessons From the International Experience, Princeton University Press. Black, R., V. Cassino, A. Drew, E. Hansen, B. Hunt, D. Rose, and A. Scott (1997), "The Forecasting and Policy System: The Core Model," Reserve Bank of New Zealand Research Paper 43. Blake, Andrew P., and Fabrizio Zampolli (2005), "Time Consistent Policy in Markov Switching Models," Society for Computational Economics series Computing in Economics and Finance 134. Blinder, Alan S. (2010), "How Central Should the Central Bank Be?" Journal of Economic Liter- ature 48(1), 123--133. Borio, Claudio, and William R. White (2003), "Whither Monetary and Financial Stability? The Implications of Evolving Policy Regimes," in Monetary Policy and Uncertainty: Adapting to a Changing Economy, Federal Reserve Bank of Kansas City Jackson Hole Symposium, 131--212. Borio, Claudio, and Haibin Zhu (2008), "Capital Regulation, Risk-taking and Monetary Policy: A Missing Link in the Transmission Mechanism?" BIS Working Paper 268. Brubakk, Leif, and Tommy Sveen (2009), "NEMO, a New Macro Model for Forecasting and Mon- etary Policy Analysis," Norges Bank Economic Bulletin 80(1), 39--47. Carare, Alina, Andrea Schaechter, Mark R. Stone, and Marc Zelmer (2002), "Establishing Initial Conditions in Support of Inflation Targeting," IMF Working Paper WP/02/102. 63 Carney, Mark (2003), "Some Considerations on Using Monetary Policy to Stabilize Economic Ac- tivity," in Financial Stability and Macroeconomic Policy, Federal Reserve Bank of Kansas City Jackson Hole Symposium, 131--212. Carvalho Filho, Irineu E. (2010), "Inflation Targeting and the Crisis: An Empirical Assessment," IMF Working Paper WP/10/45. Cecchetti, Stephen, and Michael Ehrmann (2002), "Does Inflation Targeting Increase Output Volatility? An International Comparison of Policymakers Preferences and Outcomes," in Loayza, Norman, and Klaus Schmidt-Hebbel (eds.), Monetary Policy: Rules and Transmission Mecha- nisms, vol. 4 of Series on Central Banking, Analysis, and Economic Policies, Central Bank of Chile, 247--274. Cecchetti, Stephen G., Hans Genberg, and Sushil Wadhwani (2002), "Asset Prices in a Flexible Inflation Targeting Framework," in Hunter, W., G. Kaufman, and M. Pomerleano (eds.), Asset Price Bubbles: The Implications for Monetary, Regulatory and International Policies, Cam- bridge, 427--444. Chow, Gregory C (1973), "Effect of Uncertainty on Optimal Control Policies," International Eco- nomic Review 14(3), 632--645. Cogley, Timothy, Riccardo Colacito, and Thomas J. Sargent (2007), "Benefits from U.S. Monetary Policy Experimentation in the Days of Samuelson and Solow and Lucas," Journal of Money, Credit and Banking 39(s1), 67--99. Corbo, Vittorio, Oscar Landerretche, and Klaus Schmidt-Hebbel (2001), "Assessing Inflation Tar- geting after a Decade of World Experience," International Journal of Finance & Economics 6(4), 343--68. Costa, Oswaldo L.V., and Marcelo D. Fragoso (1995), "Discrete-Time LQ-Optimal Control Prob- lems for Infinite Markov Jump Parameter Systems," IEEE Transactions on Automatic Control 40(12), 2076--2088. Costa, Oswaldo L.V., Marecelo D. Fragoso, and Ricardo P. Marques (2005), Discrete-Time Markov Jump Linear Systems, Springer, London. Curdia, Vasco, and Michael Woodford (2009), "Credit Frictions and Optimal Monetary Policy," BIS Working Paper 278. 64 Currie, David, and Paul Levine (1993), Rules, Reputation and Macroeconomic Policy Coordination, Cambridge University Press, Cambridge. Davig, Troy, and Eric Leeper (2007), "Generalizing the Taylor Principle," American Economic Review 97(3), 607--635. Debelle, Guy (2001), "The Case for Inflation Targeting in East Asian Countries," in Gruen, David, and John Simon (eds.), Future Directions for Monetary Policies in East Asia, Reserve Bank of Australia. Del Negro, Marco, and Christopher Otrok (2007), "99 Luftballons: Monetary Policy and the House Price Boom across U.S. States," Journal of Monetary Economics 54(7), 1962--1985. Dennis, Richard (2008), "Timeless Perspective Policymaking: When is Discretion Superior," Fed- eral Reserve Bank of San Francisco Working Paper 2008-21. Deutsche Bundesbank (2010), "Price-Level Targeting as a Monetary Policy Strategy," Deutsche Bundesbank Monthly Report 62(1), 31--45. Dincer, Nergiz, and Barry Eichengreen (2009), "Central Bank Transparency: Causes, Consequences and Updates," NBER Working Paper 14791. Dokko, Jane, Brian Doyle, Michael T. Kiley, Jinill Kim, Shane Sherlund, Jae Sim, and Skander Van den Heuvel (2009), "Monetary Policy and the House Bubble," Federal Reserve Board Finance and Economics Discussion Series 200-49. Edge, Rochelle M., Michael T. Kiley, and Jean-Philippe Laforte (2008), "The Sources of Fluc- tuations in Residential Investment: A View from a Policy-Oriented DSGE Model of the U.S. Economy," Paper presented at the 2009 American Economic Association annual meeting, Janu- ary 3-5. Eichengreen, Barry, Paul R. Masson, Miguel A. Savastano, and Sunil Sharma (1999), "Transition Strategies and Nominal Anchors on the Road to Greater Exchange-Rate Flexibility," Princeton Essays in International Economics 213, International Economics Section, Department of Eco- nomics Princeton University. Eijffinger, Sylvester C., and Petra M. Geraats (2006), "How Transparent are Central Banks?" European Journal of Political Economy 22(1), 1--21. 65 Eijffinger, Sylvester C W, Eric Schaling, and Mewael F. Tesfaselassie (2006), "Learning About the Term Structure and Optimal Rules for Inflation Targeting," CEPR Discussion Paper 5896. Ellison, Martin (2006), "The Learning Cost of Interest Rate Reversals," Journal of Monetary Economics 53(8), 1895--1907. Ellison, Martin, and Natacha Valla (2001), "Learning, Uncertainty and Central Bank Activism in an Economy With Strategic Interactions," Journal of Monetary Economics 48(1), 153--171. Evans, George, and Seppo Honkapohja (2001), Learning and Expectations in Macroeconomics, Princeton University Press, Princeton. Fang, WenShwo, Stephen M. Miller, and ChunShen Lee (2009), "Inflation Targeting Evaluation: Short-run Costs and Long-run Irrelevance," University of Nevada, Department of Economics Working Paper 0920. Farmer, Roger E.A., Daniel F. Waggoner, and Tao Zha (2009), "Understanding Markov-Switching Rational Expectations Models," Journal of Economic Theory 144(5), 1849--1867. Faust, Jon, and Dale W. Henderson (2004), "Is inflation targeting best-practice monetary policy?" Federal Reserve Bank of St. Louis Review 86(4), 117--144. Federal Reserve Board (2002), "Monetary Policy Alternatives," The Bluebook for the FOMC Meet- ing on May 2, 2002, Federal Reserve Board. Freedman, Charles, and Douglas Laxton (2009), "Why Inflation Targeting?" IMF Working Paper wp/09/86. Freedman, Charles, and Inci ・tker-Robe (2009), "Country Experiences with the Introduction and Implementation of Inflation Targeting," IMF Working Paper wp/09/161. Friedman, Benjamin M. (2002), "The Use and Meaning of Words in Central Banking: Inflation Targeting, Credibility, and Transparency," NBER Working Paper 8972. Friedman, Benjamin M., and Kenneth N. Kuttner (1996), "A Price Target for U.S. Monetary Pol- icy? Lessons from the Experience with Money Growth Targets," Brookings Papers on Economic Activity 27(1), 77--146. 66 Gerali, Andrea, and Francesco Lippi (2008), "Solving Dynamic Linear-Quadratic Problems with Forward-Looking Variables and Imperfect Information using Matlab," Toolkit manual. Gertler, Mark (2005), "Comment," in Bernanke, Ben S., and Michael Woodford (eds.), The Inflation Targeting Debate, NBER Book Series Studies in Business Cycles, University of Chicago Press, 276--281. Gertler, Mark, and Nobuhiro Kiyotaki (2010), "Financial Intermediation and Credit Policy in Business Cycle Analysis," in Friedman, Benjamin M., and Michael Woodford (eds.), Handbook of Monetary Economics, Volume 3a and 3b, Elsevier. Giannoni, Marc P., and Michael Woodford (2003), "Optimal Interest-Rate Rules: I. General The- ory," NBER Working Paper 9419. Giannoni, Marc P., and Michael Woodford (2010), "Optimal Target Criteria for Stabilization Pol- icy," NBER Working Paper 15757. Giavazzi, Francesco, and Frederic S. Mishkin (2006), "An Evaluation of Swedish Monetary Pol- icy between 1995 and 2005," Report to the Swedish Parliament, www.riksdagen.se, Sweden's Parliament. Goncalves, Carlos Eduardo S., and Alexandre Carvalho (2009), "Inflation Targeting Matters: Ev- idence from OECD Economies' Sacrifice Ratios," Journal of Money, Credit and Banking 41(1), 233--243. Gon∫alves, Carlos Eduardo S., and Jo√o M. Salles (2008), "Inflation Targeting in Emerging Economies: What Do the Data Say?" Journal of Development Economics 85(1-2), 312 -- 318. Goodhart, Charles A.E. (2010), "The Political Economy of Inflation Targets: New Zealand and the U.K." in Leeson, Robert (ed.), Canadian Policy Debates and Case Studies in Honour of David Laidler, Palgrave Macmillian, 171--214. Gosselin, Pierre, Aileen Lotz, and Charles Wyplosz (2008), "The Expected Interest Rate Path: Alignment of Expectations vs. Creative Opacity," International Journal of Central Banking 4(3), 145--185. Greenspan, Alan (2002), "Opening Remarks," in Rethinking Stabilization Policy, Federal Reserve Bank of Kansas City Jackson Hole Symposium, 1--10. 67 G◯rkaynak, Refet S., Andrew T. Levin, Andrew N. Marder, and Eric T. Swanson (2007), "Inflation Targeting and the Anchoring of Inflation Expectations in the Western Hemisphere," in Mishkin, Frederic, and Klaus Schmidt-Hebbel (eds.), Monetary Policy under Inflation Targeting, vol. 11 of Central Banking, Analysis, and Economic Policies, Central Bank of Chile, 415--465. G◯rkaynak, Refet S., Andrew T. Levin, and Eric T. Swanson (2006), "Does Inflation Targeting Anchor Long-Run Inflation Expectations? Evidence From Long-Term Bond Yields in the U.S., U.K., and Sweden," CEPR Discussion Papers 5808. Hamilton, James D (1989), "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica 57(2), 357--84. Hansen, Lars Peter, and Thomas J. Sargent (2008), Robustness, Princeton University Press. Holmsen, Amund, Jan F. Qvigstad, and ・istein R・island (2007), "Implementing and Communi- cating Optimal Monetary Policy," Norges Bank Staff Memo 2007/3. Holmsen, Amund, Jan F. Qvigstad, ・istein R・island, and Kristin Solberg-Johansen (2008), "Com- municating Monetary Policy Intentions: The Case of Norges Bank," Norges Bank Working Paper 20/2008. Hyvonen, Markus (2004), "Inflation Convergence Across Countries," Reserve Bank of Australia Research Discussion Paper 2004-04. Iacoviello, Matteo, and Stefano Neri (2008), "Housing Market Spillovers: Evidence from an Esti- mated DSGE Model," Bank of Italy Economic Working Paper 659. International Monetary Fund (2005), World Economic Outlook, September 2005. International Monetary Fund (2008), World Economic Outlook, October 2008. International Monetary Fund (2009), World Economic Outlook, October 2009. Jansson, Per, and Anders Vredin (2003), "Forecast-Based Monetary Policy: The Case of Sweden," International Finance 6(3), 349--380. Jarocinski, Marek, and Frank R. Smets (2008), "House Prices and the Stance of Monetary Policy," Federal Reserve Bank of St. Louis Review 90(4), 339--365. 68 Johnson, David R. (2002), "The effect of inflation targeting on the behavior of expected inflation: evidence from an 11 country panel," Journal of Monetary Economics 49(8), 1521--1538. Jonas, Jiri, and Frederic S. Mishkin (2003), "Inflation Targeting in Transition Countries: Experience and Prospects," NBER Working Paper 9667. Kahn, George A. (2009), "Beyond Inflation Targeting: Should Central Banks Target the Price Level?" Federal Reserve Bank of Kansas Review 3rd quarter(3), 35--64. Kalchbrenner, J.H., and P.A. Tinsley (1975), "On the Use of Optimal Control in the Design of Monetary Policy," Federal Reserve Board Special Studies Papers 76. Khan, Mohsin S. (2003), "Current Issues in the Design and Conduct of Monetary Policy," IMF Working Paper WP/03/56. Kim, Chang-Jin, and Charles R. Nelson (1999), State-Space Models with Regime Switching, MIT Press, Cambridge, MA. King, Mervyn (1994), "Monetary Policy in the UK," Fiscal Studies 15(3), 109--128. King, Mervyn (1997), "Changes in UK Monetary Policy: Rules and Discretion in Practice," Journal of Monetary Economics 39(1), 81--97. Klein, Paul (2000), "Using the Generalized Schur Form to Solve a Multivariate Linear Rational Expectations Model," Journal of Economic Dynamics and Control 24(10), 1405--1423. Kohn, Donald L. (2006), "Monetary Policy and Asset Prices," Speech on March 16, 2006, www.federalreserve.gov. Kohn, Donald L. (2008), "Monetary Policy and Asset Prices Revisited," Speech on November 19, 2008, www.federalreserve.gov. Kohn, Donald L. (2009), "Policy Challenges for the Federal Reserve," Speech on November 16, 2009, www.federalreserve.gov. Las・en, Stefan, and Lars E.O. Svensson (2010), "Anticipated Alternative Instrument-Rate Paths in Policy Simulations," working paper, www.larseosvensson.net. Leitemo, Kai (2003), "Targeting Inflation by Constant-Interest-Rate Forecasts," Journal of Money, Credit and Banking 35(4), 609--626. 69 LeRoy, Stephen F., and Roger N. Waud (1977), "Applications of the Kalman Filter in Short-Run Monetary Control," International Economic Review 18(1), 195--207. Levin, Andrew T., Fabio M. Natalucci, and Jeremy M. Piger (2004), "The Macroeconomic Effects of Inflation Targeting," Federal Reserve Bank of St. Louis Review 86(4), 51--80. Lin, Shu, and Haichun Ye (2007), "Does Inflation Targeting Really Make a Difference? Evaluating the Treatment Effect of Inflation Targeting in Seven Industrial Countries," Journal of Monetary Economics 54(8), 2521 -- 2533. Lin, Shu, and Haichun Ye (2009), "Does Inflation Targeting Make a Difference in Developing Countries?" Journal of Development Economics 89(1), 118--123. Marcet, Albert, and Ramon Marimon (1998), "Recursive Contracts," University of Pompeu Fabra Economics Working Paper 337. Masson, Paul R., Miguel A. Savastano, and Sunil Sharma (1997), "The Scope for Inflation Targeting in Developing Countries," IMF Working Paper wp/97/130. de Mello, Luiz (ed.) (2008), Monetary Policies and Inflation Targeting in Emerging Economies, OECD. Miller, Marcus H., Paul A. Weller, and Lei Zhang (2002), "Moral Hazard and the U.S. Stock Market: Analysing the Greenspan Put," Economic Journal 112, C171--C186. Mishkin, Frederic S., and Klaus Schmidt-Hebbel (2007), "Does Inflation Targeting Make a Differ- ence?" in Mishkin, Frederic, and Klaus Schmidt-Hebbel (eds.), Monetary Policy under Inflation Targeting, vol. 11 of Central Banking, Analysis, and Economic Policies, Central Bank of Chile, 291--372. Nelson, Edward (2005), "'Monetary Policy Neglect and the Great Inflation in Canada, Australia, and New Zealand," International Journal of Central Banking 1(1), 133--179. Neumann, Manfred J.M., and J◯rgen von Hagen (2002), "Does Inflation Targeting Matter?" The Federal Reserve Bank of St. Louis Review 84(4), 127--148. Norges Bank (2009), "Monetary Policy Report 2/09," . 70 Onatski, Alexei, and Noah Williams (2003), "Modeling Model Uncertainty," Journal of the Euro- pean Economic Association 1(5), 1087--1122. Orphanides, Athanasios (2003), "The Quest for Prosperity Without Inflation," Journal of Monetary Economics 50(3), 633--663. Oudiz, Gilles, and Jeffrey Sachs (1985), "International Policy Coordination in Dynamic Macroeco- nomic Models," in Buiter, William H., and Richard C. Marston (eds.), International Economic Policy Coordination, Cambridge University Press, Cambridge. Pearlman, Joseph (1992), "Reputational and Nonreputational Policies under Partial Information," Journal of Economic Dynamics and Control 16, 339--357. Pearlman, Joseph, David Currie, and Paul Levine (1986), "Rational Expectations Models with Partial Information," Economic Modelling 3(2), 90--105. Poloz, Stephen, David Rose, and Robert Tetlow (1994), "The Bank of CanadaSs new Quarterly Projection Model (QPM): An introduction," Bank of Canada Review Autumn 1994, 23--38. P・tursson, Th♭rarinn G. (2004a), "The Effects of Inflation Targeting on Macroeconomic Perfor- mance," Central Bank of Iceland Working Paper 23. P・tursson, Th♭rarinn G. (2004b), "Formulation of Inflation Targeting Around the World," Central Bank of Iceland Monetary bulletin 6(1), 57--84. P・tursson, Th♭rarinn G. (2009), "Inflation Control Around the World: Why are Some Contries More Successful Than Others?" Central Bank of Iceland Working Paper 42. Ravenna, Federico (2008), "The Impact of Inflation Targeting: Testing the Good Luck Hypothesis," working paper, ic.ucsc.edu/ fravenna/. Reifschneider, David L., David J. Stockton, and David W. Wilcox (1997), "Econometric Models and the Monetary Policy Process," Carnegie-Rochester Conference Series on Public Policy 47, 1--37. Reserve Bank of Australia (2008), "About Monetary Policy," www.rba.gov.au. Reserve Bank of New Zealand (1996), Briefing on the Reserve Bank of New Zealand, October 1996. 71 Reserve Bank of New Zealand (1999), Briefing on the Reserve Bank of New Zealand, November 1999. Reserve Bank of New Zealand (2007), "Policy Target Agreement 2007," www.rbnz.govt.nz. Roger, Scott (2009), "Inflation Targeting at 20: Achievements and Challenges," IMF Working Paper WP/09/236. Roger, Scott, and Mark Stone (2005), "On Target? The International Experience with Achieving Inflation Targets," IMF Working Paper wp/05/163. Rose, Andrew K. (2007), "A stable international monetary system emerges: Inflation targeting is Bretton Woods, reversed," Journal of International Money and Finance 26(5), 663 -- 681. Rudebusch, Glenn, and Lars E.O. Svensson (1999), "Policy Rules for Inflation Targeting," in Taylor, John B. (ed.), Monetary Policy Rules, The University of Chicago Press, 203--246. Sargent, Thomas J., and Neil Wallace (1975), "Rational Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule," Journal of Political Economy 83, 241--254. Schaechter, Andrea, Mark Richard Stone, and Mark Zelmer (2000), "Adopting Inflation Targeting: Practical Issues for Emerging Market Countries," IMF Occational Paper 202. Schaumburg, Ernst, and Andrea Tambalotti (2007), "An Investigation of the Gains from Commit- ment in Monetary Policy," Journal of Monetary Economics 54(2), 302--324. Sims, Christopher A. (2002), "Solving Linear Rational Expectations Models," Computational Eco- nomics 20(1-2), 1--20. Singleton, John, Gary Hawke, and Arthur Grimes (2006), Innovation and Independence: The Reserve Bank of New Zealand, Auckland University Press. Smets, Frank (2003), "Maintaining price stability: how long is the medium term?" Journal of Monetary Economics 50(6), 1293--1309. Stevens, Glenn R. (1998), "Pitfalls in the Use of Monetary Conditions Indexes," Reserve Bank of Australia Bulletin August 1998, 34--43. Svensson, Lars E.O. (1997), "Inflation Forecast Targeting: Implementing and Monitoring Inflation Targets," European Economic Review 41(6), 1111--1146. 72 Svensson, Lars E.O. (1999a), "Inflation Targeting as a Monetary Policy Rule," Journal of Monetary Economics 43(3), 607--654. Svensson, Lars E.O. (1999b), "Inflation Targeting: Some Extensions," Scandinavian Journal of Economics 101(3), 337--61. Svensson, Lars E.O. (1999c), "Monetary Policy Issues for the Eurosystem," Carnegie-Rochester Conferences Series on Public Policy 51, 79--136. Svensson, Lars E.O. (2000), "Open-Economy Inflation Targeting," Journal of International Eco- nomics 50(1), 155--183. Svensson, Lars E.O. (2001), "Independent Review of the Operation of Monetary Policy in New Zealand," Report to the Minister of Finance, www.larseosvensson.net. Svensson, Lars E.O. (2002), "Monetary Policy and Real Stabilization," in Rethinking Stabilization Policy, Federal Reserve Bank of Kansas City Jackson Hole Symposium, 261--312. Svensson, Lars E.O. (2003a), "Escaping from a Liquidity Trap and Deflation: The Foolproof Way and Others," Journal of Economic Perspectives 17(4), 145--166. Svensson, Lars E.O. (2003b), "What Is Wrong with Taylor Rules? Using Judgment in Monetary Policy through Targeting Rules," Journal of Economic Literature 41(2), 426--477. Svensson, Lars E.O. (2005), "Monetary Policy with Judgment: Forecast Targeting," International Journal of Central Banking 1(1), 1--54. Svensson, Lars E.O. (2007), "Optimal Inflation Targeting: Further Developments of Inflation Tar- geting," in Mishkin, Frederic, and Klaus Schmidt-Hebbel (eds.), Monetary Policy under Inflation Targeting, vol. 11 of Central Banking, Analysis, and Economic Policies, Central Bank of Chile, 187--225. Svensson, Lars E.O. (2008), "Inflation Targeting," in Durlauf, Stephen N., and Lawrence E. Blume (eds.), The New Palgrave Dictionary of Economics, 2nd edition, Palgrave Macmillan. Svensson, Lars E.O. (2009a), "Flexible Inflation Targeting: Lessons from the Financial Crisis," Speech in Amsterdam, September 21, 2009, www.riksbank.se. 73 Svensson, Lars E.O. (2009b), "Optimization under Commitment and Discretion, the Recursive Saddlepoint Method, and Targeting Rules and Instrument Rules: Lecture Notes," lecture notes, www.larseosvensson.net. Svensson, Lars E.O. (2009c), "Transparency under Flexible Inflation Targeting: Experiences and Challenges," Sveriges Riksbank Economic Review 1/2009(1), 5--44. Svensson, Lars E.O. (2009d), "What Have Economists Learned about Monetary Policy over the past 50 Years?" in Herrmann, Heinz (ed.), Monetary Policy Over Fifty Years: Experiences and Lessons, Routledge. Svensson, Lars E.O. (2010a), "Evaluating Monetary Policy," in Koenig, Evan, and Robert Leeson (eds.), From the Great Moderation to the Great Deviation: A Round-Trip Journey Based on the Work of John B. Taylor, www.larseosvensson.net. Svensson, Lars E.O. (2010b), "Inflation Targeting after the Financial Crisis," Speech in Mumbai, February 12, 2010, www.riksbank.se. Svensson, Lars E.O., Kjetil Houg, Haakon O.Aa. Solheim, and Erling Steigum (2002), "An In- dependent Review of Monetary Policy and Institutions in Norway," Norges Bank Watch 2002, www.larseosvensson.net. Svensson, Lars E.O., and Robert J. Tetlow (2005), "Optimal Policy Projections," International Journal of Central Banking 1(3), 177--207. Svensson, Lars E.O., and Noah Williams (2007a), "Bayesian and Adaptive Optimal Policy under Model Uncertainty," working paper, www.larseosvensson.net. Svensson, Lars E.O., and Noah Williams (2007b), "Monetary Policy with Model Uncertainty: Distribution Forecast Targeting," working paper, www.larseosvensson.net. Svensson, Lars E.O., and Michael Woodford (2003), "Indicator Variables for Optimal Policy," Journal of Monetary Economics 50(3), 691--720. Svensson, Lars E.O., and Michael Woodford (2004), "Indicator Variables for Optimal Policy under Asymmetric Information," Journal of Economic Dynamics and Control 28(4), 661--690. 74 Svensson, Lars E.O., and Michael Woodford (2005), "Implementing Optimal Policy through Inflation-Forecast Targeting," in Bernanke, Ben S., and Michael Woodford (eds.), The Inflation- Targeting Debate, University of Chicago Press, 19--83. S‡derlind, Paul (1999), "Solution and Estimation of RE Macromodels with Optimal Policy," Eu- ropean Economic Review 43, 813--823. Taylor, John B. (1979), "Estimation and Control of a Macroeconomic Model with Rational Expec- tations," Econometrica 47(5), 1267--1286. Taylor, John B. (2007), "Housing and Monetary Policy," in Housing, Housing Finance, and Mon- etary Policy, Federal Reserve Bank of Kansas City Jackson Hole Symposium, 463--476. Truman, Edwin M. (2003), Inflation Targeting in the World Economy, Peterson Institute for In- ternational Economics. do Val, Jo√o B.R, Jos・ C. Geromel, and Oswaldo L.V. Costa (1998), "Uncoupled Riccati Iterations for the Linear Quadratic Control Problem of Discrete-Time Markov Jump Linear Systems," IEEE Transactions on Automatic Control 43(12), 1727--1733. Vega, Marco, and Diego Winkelried (2005), "Inflation Targeting and Inflation Behavior: A Suc- cessful Story?" International Journal of Central Banking 1(3), 153--175. Vickers, John (1998), "Inflation Targeting in Practice: The U.K. Experience," Bank of England Quarterly Bulletin November 1998. Walsh, Carl (2004), "Robustly Optimal Instrument Rules and Robust Control: An Equivalence Result," Journal of Money, Credit, and Banking 36(6), 1105--1113. Walsh, Carl E. (2009a), "Inflation Targeting: What Have We Learned?" International Finance 12(2), 195--233. Walsh, Carl E. (2009b), "Using Monetary Policy to Stabilize Economic Activity," in Financial Sta- bility and Macroeconomic Policy, Federal Reserve Bank of Kansas City Jackson Hole Symposium. White, William R. (2006), "Is Price Stability Enough?" BIS Working Paper 205. Wieland, Volker (2000), "Learning by Doing and the Value of Optimal Experimentation," Journal of Economic Dynamics and Control 24(4), 501--534. 75 Wieland, Volker (2006), "Monetary Policy and Uncertainty about the Natural Unemployment Rate: Brainard-Style Conservatism versus Experimental Activism," Advances in Macroeconomics 6(1), Article 1. Woodford, Michael (2003), Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton University Press. Woodford, Michael (2005), "Central Bank Communication and Policy Effectiveness," in The Greenspan Era: Lessons for the Future, A Symposium Sponsored by the Federal Reserve Bank of Kansas City, Jackson Hole, 399--474. Woodford, Michael (2007), "The Case for Forecast Targeting as a Monetary Policy Strategy," Journal of Economic Perspectives 21(4), 3--24. Woodford, Michael (2010a), "Forecast Targeting as a Monetary Policy Strategy: Policy Rules in Practice," in Koenig, Evan, and Robert Leeson (eds.), From the Great Moderation to the Great Deviation: A Round-Trip Journey Based on the Work of John B. Taylor, To be published. Woodford, Michael (2010b), "Optimal Monetary Stabilization Policy," in Friedman, Benjamin M., and Michael Woodford (eds.), Handbook of Monetary Economics, Volume 3a and 3b, Elsevier. Zampolli, Fabrizio (2006), "Optimal Monetary Policy in a Regime-Switching Economy: The Re- sponse to Abrupt Shifts in Exchange Rate Dynamics," Bank of England Working Paper 297. 76 -- !>訳注1 : こういう訳語にするとわからないけど、mandate には選挙民から任されたという意味がある。

訳注 :