Economic policy. Monetary policy (part 2)

1 Modern monetary policy Economic policy. Monetary policy (part 2) Ragnar Nymoen University of Oslo, Department of Economics As we have seen, increasing degree of capital mobility reduces the scope for monetary policy in a fixed exchange rate regime. Highlighted by B&W use of the term impossible trilogy. At the same time, many governments experienced reduced fiscal independence. Other developments have also (as we have seen) reduced the belief in fiscal policy. Two (opposite) responses to this: November 18, 2003 Adopt floating exchange rate, in order to re-install monetary policy independence Adopt a so called hard peg to do away with all monetary policy. 1 2 2 Target choice: Consequence for output stability Hard pegs: Monetary union; Adopt another countries currency, a currency board is an example of formal arrangement of this type. In the following,we discuss the choice of floating exchange rate with the whole range of fixed exchange rate regimes, from hard pegs to flexible exchange rate regimes with target zones. A main issue is how a specific choice of monetary target affects the strive to reach the ultimate targets of economic policy, for example output stabilization (at a high level of employment). In modern monetary policy the choice is between a price level or inflation target (the two be not have very different in practical in times of moderate inflation, see below) and a fixed exchange rate. A first analysis of can be done is the AS/AD diagram, and the conclusions are: Price stability target reduces the impact of demand shocks Exchange rate stability target reduces the impact of supply side shock. [Graph.] 3 4

A positive demand shock leads to i % and σ % inthecaseofacleanfloat. Both effects reduce the expansionary effect relative to the fixed exchange rate regime. Hence, even if a short run rise in π above the target is tolerated (flexible inflation targeting, see below) the effect on Y is less with a price/inflation target than with an exchange rate target. A negative supply shock has a larger effect on Y with a fixedthanwitha floating exchange rate. However, if there is a strict inflation target, then the AD float curve contracts so much that the decline in Y is larger than in the fixed exchange rate case. The analysis shows that the choice of target presumes an analysis of which shock is the important or typical one. Answer is likely to depend on structure of the economy, whether it is in line with, or out of step with, international business cycles etc. Obviously, cannot switch target variable too often. However also conceivable that the reaction function, i.e., how the central bank uses its instrument to attain its target, should depend on a wider analysis, and on several variables, not only on the observed or forecasted deviation from a single target. Example: Suppose wage claims of are because of high electricity prices (living costs). Increase interest rates despite loss of competitiveness in exposed sector? 5 6 3 Strict vs flexibile monetary policy FIX FLOAT Modern monetary policy can be characterized along other several dimensions than the fix vs float distinction: How simple/complex is the reaction function? How ambitious is the (central) target? Is there a target zone? How wide is it? Depending on answer, monetary policy is more or less strict/flexible. STRICT Hard pegs Strict monetary targets Low target examples: Monetary union Narrow band Currency board Short horizon Simple reaction function flexible fixed flexible inflation targeting FLEXIBLE Wide target zone (> 4%) Allow E outside zone Reaction function: -contingent - multivariate Wide band π-forecast is target 2 3 year horizon Reaction function -multivariate Table 2: A typology of monetary policy regimes 7 8

4 Flexible exchange rate targeting Attributes 1. Wide target zone (> 4%) 2. Allow exchange rate E outside zone 3. Reaction function: -contingent - multivariate Focus on domestic real economy when E inside zone. When outside priority to E-target. Instrument mix: Use reserves when E hits boundaries bounds. Use interest rate when outside. But then may need to build credibility slowly, not overnight. This regime probably not an option for countries with high system risk. 9 [Graph, adapted from OEM]. One motivation for a wide target zone is to engineer uncertainty about depreciation/appreciation within the zone. Conversely, if E changes too little and too seldom, then the expected rate of depreciation may become uniformly zero with the result that UIP holds with i = i. A wide target zone, if successful, in a way serves the same purpose as a Tobin tax: it creates some room for monetary policy manoeuvre, in spite of capital market deregulation. Part discussion: Many central banks intervene inside zone hope to avoid to rise the interest of new investors? Speculation: When is the degree of capital mobility highest, inside or outside the target-zone? 10.0000 Inflasjonsendring.000 Appresiering av valutakurs 5 Flexible inflation targeting The defining dimension of flexibility in this case is forward looking interest rate setting. The longer time horizon, the more flexible is interest rate targeting. In real economies, the first dynamic multipliers of inflation with the respect to the rate of interest. Hence, with a short horizon a certain change in π can only be achieved with large interest rate movements. A longer time horizon allows instrument use to be based on to the larger interim multipliers. The multipliers are necessary based on a model of the transmission mechanism -.0005 -.0010 -.0015 -.0020 -.0025 -.0030 Vekstrate i fastlandsbnp.000 -.001 -.002 -.003 -.004 -.005 -.006 -.007 -.008 -.004 -.008 -.012 -.016 -.020 -.024 Endring i ledighetsrate.004.003.002.001.000 -.001 Figure 1: Norway: empirical multipliers of 1 pp interest rate increase on annual rate of inflation, nominal exchange rate, GDP growth rate, and rate of unemployment. 11 12

5.1 Forecast based interest rate setting Forecast properties are closely linked to the assumptions we make about the forecasting situation. One possible classification, is: A The forecast model coincides with actual inflation in the econometric sense. The parameters of the model are known and true constants over the forecasting period. B As under A, but the parameters have to be estimated. C As under B, but we cannot expect the parameters to remain constant over the forecasting period structural changes are likely to occur somewhere in the system. D We do not know how well the forecasting model corresponds to the inflation mechanism in the forecast period. 13 A is a very idealized description of the assumptions of macroeconomic forecasting. Nevertheless, there is still the incumbency of inherent uncertainty even under A. Situation B represents the situation most econometric textbooks conjures up, The properties of situation A will still hold even though the inherent uncertainty will increase. The theory of inflation targeting also seems stuck with B. In real life we of course do not know what kind of shocks that will hit the economy, or the policy makers during, the forecasting period, which is the focus of situation C. Structural breaks and regime changes are the most important source of forecast failure. Situation D finally leads us to a realistic situation, namely one of uncertainty and professional discord regarding what kind of model best representing reality. This opens up the whole field of model building as well as the controversies regarding econometric specification, so we will leave that subject here. 14 A later section looks at the sources and implications of systematic forecast errors. In order to illustrate the principles, assume the following model of the transmission mechanism π t = δ + απ t 1 + β i t + ε t, t =1, 2, 3..., T, (1) 1 <α<1,β <0, Thinkofthetimeperiodasoneyear. Overthesampleperiod1, 2, 3..., T the model is econometrically well specified, and, since we are at level A, the parameters δ, α and β are assumed to be known, thus neglecting estimation uncertainty. The forecast period is T +1,T +2,...,T + H. An inflation targeting central bank has its focus on the 2 periods ahead forecast, i.e., ˆπ T +2 T and sets the interest rate in period T +1 in order to make that forecast equal to the inflation target π. For the subsequent periods the interest rate is kept constant, i.e. i T +2 T = i T +3 T =... = i T +1 T.Basedonthis,thetwofirst forecasts are: ˆπ T +1 T = δ + απ T + β i T +1 T 15 and ˆπ T +2 T = δ(1 + α)+α 2 π T + βα i T +1 Setting ˆπ T +2 T = π shows that at the time of preparing the forecast, the period T + 1 interest rate is set to: δ(1 + α) i T +1 T = i T αβ The resulting forecasts are given below, + 1 αβ (π α 2 π T ), (2) Instrument use: Inflation forecast: i T +1 T ˆπ T +1 T = δ α + 1 α π 0 ˆπ T +2 T = π 0 ˆπ T +3 T = δ + E[π t ]+α(π E[π t ]).... 0 ˆπ T +h T = E[π t ]= δ 1 α where E denotes the mathematical expectation. 16

E[π t ] is the long-run mean of π t. As the forecast horizon increases, the conditional forecast converges to the marginal expectation: ˆπ T +h T δ 1 α = E[π t], when H, 1 <α<1. (3) which is also the (asymptotic) steady state solution based on (1). This always holds, even though the forecast for the first period ahead is very model dependent, the long run forecast is more objective. 4 p Start of sample for estimation of mean 0.10 0.05 1965 1970 1975 1980 1985 1990 1995 2000 0.050 mean 4 p 0.025 0.000-0.025 Clearly, since any conditional forecast converge to the long run mean of inflation, and hence the equilibrium rate of inflation, it is quite helpful for the legitimacy of inflation targeting that this equilibrium value is not too far from the target. 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 20 Figure 2: Actual inflation rate in Norway for the period 1966(1)-2002(2). Estimation of the univariate model of the rate of inflation is based on a sample that starts in 1984(1). The lower part of the figure shows the estimated marginal expectation of the inflation rate, i.e., the equilibrium rate of inflation. 17 18 5.2 Forecast error variance (The prediction interval) Define the forecast errors (for the period T forecasting round) as e T +h T = π T +h ˆπ T +h T.Itcanbeshownthat Var[e T +h T ]= σ2 (1 α 2h ) (1 α 2, ) h =1, 2,...,H (4) 1 α<1, where σ 2 is the variance of ε t. Hence for e T +2 T we have Var[e T +2 T ] = σ 2 (1 + α 2 )andforasufficiently long horizon Var[e T +H T ] σ2 (1 α 2 which is ) the (marginal) variance of the rate of inflation. Hence, despite forward looking interest rate setting, the forecast error variance increases with the horizon, and the unconditional variance may be a useful measure of the limit of forecastability. Hence, we define the limit of inflation forecastability horizon H α as where α is 0.05, 0.01, etc. The value of H α depends on the dynamics of the forecasting system. Implicit in the choice of a 2-3 years horizon for inflation targeting is that H α < 2.5 say. Var[e T +Hα T ] > (1 α)var[e T +H] (5) 19 20

5.3 Real world forecast uncertainty So far we have assumed that forecasting and interest rate setting, thrived in a situation like A and B, where there was no misspecification within sample. and where the there were no regime shifts in the forecast period. In such a situation, systematic forecast errors would never occur, and single incidents of error larger than the 95% prediction interval would by definition be very rare. By implications, there would be little chance of policy errors and serious misjudgements in interest rate setting (r T +1 T above). However, experience tells us that economics forecasts are often systematically wrong, and that within sample model fit underestimates the true uncertainty of the forecasts. Hence, a more realistic description of the situation is C or D above. The interest rate setting captured by (2) will only be correct if the parameters α, δ and β remain stable in the forecast period. 21 Using the definition δ = δ +(1 α)µ, whereµ is the long run mean of the rate of inflation, and δ is the growth rate, the expression for i T +1 T can be re-expressed more conveniently: i T +1 T = i T δ(1 + α)+(1 α 2 )µ αβ + 1 αβ (π α 2 π T ) (6) As an illustration, assume that µ = 0.028 (corresponding to figure 2 above), and α =0.8, β = 0.1. In this case a reduction in δ by 0.0001 in the course of the first two years of the forecast period means that the i T +1 T should be 1.4% lower than was determined in the forecasting round. Modest changes in the equilibrium rate of inflation have a similar impact: Say that µ changes from 0.028 to 0.025: according to the (of course) stylized policy setting here this would entail that interest rates are 1.35% higher than necessary to achieve the target two years ahead. Changes in the long run mean of µ of this magnitude hard to detect even within sample, e.g., the graph 95% confidence interval in of ˆµ in figure 2. 22 The potential damage of deterministic shifts in the forecast period to interest rate setting have been little discussed in the inflation targeting literature, but represent a difficult challenge for inflation targets. 5.4 Robust interest rate setting The rationale for the current dictum of forward looking interest rate setting, is that the targeting of the forecasted rate of inflation speeds up the adjustment of actual inflation to the target, i.e., relative to having interest rates reacting to current or lagged inflation. However, as we have seen, there is a cost to this as the sources of forecast failure are transmitted directly into policy decisions. Moreover, a simple way of avoiding the damaging consequences of forecast failure for interest rate setting, is to let the interest rate react to lagged inflation: i T +1 T = λ(π T π ), λ>0, (7) i T +j T =0,j =2, 3,... (8) 23 With this simple rule, the conditional inflation forecast for period T +1, T +2 etc. will be influenced by the any large deviations from the target in period T, so qualitatively inflation is helped towards the target in the course of the first few quarters, also with the backward looking rule (7). For longer horizons ˆπ T +h T converges on the long run mean µ, justasintheforwardlookingcase. Figure 3 illustrates by showing a sequence of dynamic forecasts for the annual rate of inflation for the period 2002(4)-2005(2), i.e. 12 quarters. The last observation of the rate of the rate of inflation is 2002(3), which is the initial value for the forecast of 2002(4). The estimated equilibrium inflation rate of inflation (the long run mean E[π t ]), is 2.8%, which is well within a ±1 percent interval of tolerance around the target of 2.5% inflation. Hence, it is not surprising that in this example, the inflation target is reached within the eight first quarters of the forecast horizon of 12 quarters. In line with the algebra, the estimated uncertainty of the forecast increases with the length of the horizon, as shown by the fan-chart of the distribution of the forecast errors. 24

0.05 0.04 0.03 E[π t ] 0.02 0.01 0.00 2002 2003 2004 2005 2006 Figure 3: Example of dynamic forecasts of the annual rate of Norwegian inflation The first forecast period is 2002(4). The boundaries of the fan represent the 95percent prediction intervals. The dashed horizontal lines are ±2 estimated standard errors of the rate of inflation. 25