ESPACIOS DE PESCA

Figure 4.3 visualizes the p-values for the usual two-sided t-tests when estimating equation (4.7). One array consists of (max(h) + 1) × (max(k) + 1) = 81 tiles. The conventional row- and column order of a matrix is changed here. Along the x-axis, the horizon of the inflation forecasts, h, ascends from 0 quarters (the nowcast) to 8 (the policy horizon), and along the y-axis, real output growth forecast horizon k ascends from 0 to 8 quarters out. White [light gray, dark gray] tiles imply significance of the estimate at the 1% [5%, 10%] level, and black tiles imply an insignificant estimate. That is, the tile in a bottom left corner corresponds to the marginal significance level of a coefficient estimate when the regression model is estimated on a combination of nowcast data. The tile in a right upper corner consequently implies a combination of forecasts for the policy horizon, and so on. For instance, in the lower right panel for αππ, the white tile at (h = 0, k = 0) implies that an estimate of the coefficient αππ is significantly different from zero at the 1% level, when the rule is estimated on inflation data for h = 0 and real output growth data for k = 0. It is significantly different from zero at the 10% level, when the rule is estimated on inflation data for h = 0 and real output growth data for k = 8, as indicated by the dark gray tile. Finally, the p-value exceeds 0.10 for the combination h = 8 and k = 0, rendering this estimate insignificant. As indicated by the shading, the MPC interest rate decisions respond to forecasts for output growth for up to one and a half years ahead. Longer-term forecasts, i.e. horizons k = 6, 7, 8, are not taken into account. Conversely, the responses to the inflation gap vanish for h = 0, . . . , 6, whereas for

h = 7, 8 they seem to provide the relevant information content required to set interest rates in response to forecasts. The arrays for the estimates of α_ππ and α_yy, though, are more mixed. The significance pattern, however, remains intact, with short-term output growth uncertainty forecasts and inflation uncertainty forecasts at the policy horizon mattering, as indicated by white tiles.

Combining inflation forecasts for h = 7, 8 and real output growth forecasts for k = 1, 2, 3 yields the most promising specifications in terms of the log-likelihood, as Table 4.2, comprising the best results from estimating equation (4.7), selected by their log-likelihood, shows. The findings on the horizon choice of the MPC reverify the results of Goodhart (2005), who similarly detects diminishing estimates for inflation at shorter horizons and for output growth at farther horizons. The results based on inflation forecasts for h = 7 have an even higher log-likelihood than for the policy horizon h = 8. This can be interpreted as support to the argument of Bhattacharjee and Holly (2010), who state that two-years ahead forecasts are less informative since they are adjusted to meet the inflation target in a policy-consistent manner, while the forecast deviations from target for one period earlier are less subject to judgement but yield more information content on which to base interest rate decisions.

The immediate implication of the results in Table 4.2 is that the MPC is very forward- looking with respect to inflation, but considers the very near term with respect to output growth. In terms of the log-likelihood, the horizon combination (h = 7, k = 2) yields the best description of monetary policy for the period 1997Q4 to 2009Q4. The autoregressive parameter, however, reflects quite inertial interest rates, with ˆρ = 0.99.13 The MPC seems to have a strong desire to smooth interest rates, with only little additional information from the forecasts utilized, given the degree of forward-looking implied by this horizon combination. Hence, the reaction to a change in forecast inflation seven quarters ahead is relatively weak, implied by ˆαπ = 0.68, significant at the 5% level. Hence, this estimate does not satisfy the principle proposed by Taylor (1993), according to which the coefficient should exceed unity, implying an overproportional reaction of interest rates to a change in inflation to stabilize the economy. What is highly significant is the fairly weak reaction to a change in output growth, as reflected by ˆαy = 0.20. The findings of the optimal degree of forward-looking implied by (h = 7, k = 2) partly contradict the results of the theoretical literature on optimal monetary policy rules, for instance, by Svensson (2001) and by Giannoni and Woodford (2003), where optimal policy should, rather, depend on forecasts for the current period or the very near term. Levin et al. (2003) come to similar conclusions. Their benchmark rule for US data, however, depends on the current output gap forecast and the one-year-ahead inflation gap forecast, with interest rates being very persistent. Longer horizons are advocated by Batini and Nelson (2001), who provide UK data VAR evidence that the optimal feedback horizon of monetary policy is between two and four years.

13

Throughout this study, I stick to the notational convention using hat characters to denote estimates of coefficients.

Figure 4.3: Visualized marginal significance levels for coefficient estimates when varying the forecast horizons in equation (4.7)

απ 0 1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 0 αy 0 1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 0 αππ 0 1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 0 αyy 0 1 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 0

Note: X-axes show forecast horizons h and Y -axes forecast horizons k. White [light gray, dark gray] tiles

imply significance of the estimate at the 1% [5%, 10%] level, and black tiles imply an insignificant estimate.

The significant estimates of coefficients α_ππ and α_yy, which capture the interest rate reactions in response to a change in forecast uncertainty, are remarkable. In particular for the tuple (h = 7, k = 2), the high value of ˆαππ = 3.51 is significant at the 1% level and implies a very aggressive reaction by the MPC when forecast inflation in almost two years ahead becomes very uncertain. The positive sign of the estimate is particularly sensible bearing in mind that the BoE seeks to have two-year-ahead inflation back on target. Any uncertainty about achieving this target results in increased efforts to finally succeed.

A hint that these clear-cut results are not obvious comes again from the Inflation Report of November 2000, p.67. If forecast uncertainty proxies the uncertainty “about the current conjuncture or the impact of any policy change, both of which tend to encourage more cautious decisions”, then a reading of this report’s box would lead one to expect a negative value of αππ.

However, the significantly positive value found is not overly surprising and corresponds to the idea of “preventing particularly costly outcomes”, as Ben Bernanke (2007) puts it.14

14_{The speech “Monetary Policy under Uncertainty” is available on the Board of Governors of the Federal}

Table 4.2: Selected OLS estimation results for equation (4.7) - Accounting for forecast uncertainty (h, k) c ρ απ αy αππ αyy ` (7, 1) -0.03 0.98∗∗∗ _0.82∗∗ _0.20∗∗∗ _3.70∗∗∗ _−0.95∗∗∗ _-7.71 (0.24) (0.05) (0.33) (0.05) (0.90) (0.14) (7, 2) -0.08 0.99∗∗∗ 0.68∗∗ 0.20∗∗∗ 3.51∗∗∗ −0.75∗∗∗ _-5.97 (0.18) (0.04) (0.34) (0.07) (0.80) (0.07) (7, 3) 0.19 0.95∗∗∗ _0.70∗ _0.16∗ _3.18∗∗∗ _−0.51∗∗∗ _-10.49 (0.26) (0.05) (0.41) (0.09) (1.07) (0.08) (8, 1) -0.20 1.00∗∗∗ 1.04∗∗∗ 0.24∗∗∗ 0.98 −0.70∗∗∗ _-13.64 (0.23) (0.05) (0.26) (0.04) (0.94) (0.17) (8, 2) −0.46∗∗∗ _1.05∗∗∗ _0.71∗∗ _0.27∗∗∗ _1.64∗∗∗ _−0.68∗∗∗ _-10.61 (0.17) (0.04) (0.28) (0.06) (0.54) (0.07) (8, 3) −0.35∗∗∗ _1.04∗∗∗ _0.72∗ _0.23∗∗ _1.95∗∗∗ _−0.55∗∗∗ _-12.48 (0.13) (0.03) (0.39) (0.10) (0.70) (0.06)

Note: Bank of England data spans from 1997Q4 to 2009Q4 (49 observations). Figures in parentheses

are Newey-West (1987) standard errors where the bandwidth parameter is chosen based on the procedure proposed by Andrews (1991). Asterisks [∗,∗∗,∗∗∗ ] correspond to the marginal significance level of the coefficient estimates of [10%, 5%, 1%].

When the MPC forecasts that two-year-ahead inflation will be off target, it will change interest rates today. If forecast uncertainty becomes larger and confidence bands widen so to give a certain probability to values that are even more off target, the MPC will increase efforts to ultimately meet its two-year-ahead objective. Such aggressive behavior is in line with the robust control theory of Hansen and Sargent (2008). In the context of a New-Keynesian model, Soederstroem (2002) finds on p.126 that “when the central bank attaches some weight to stabilizing output in addition to inflation”, uncertainty about inflation (persistence) increases the policy response, while “uncertainty about other parameters, in contrast, always dampens the policy response”.

That finding is supported by the highly significant coefficient estimate ˆαyy = −0.75 for (h = 7, k = 2). Forecast uncertainty of output growth can be considered as a proxy for uncertainty about the current state of the economy. If forecast uncertainty is high such that positive point estimates are surrounded by confidence bands that reach well into negative territory, the MPC might be better off with a cautious interest rate change, as suggested by the Inflation Report of November 2000. The motivation could be to avoid the danger of having changed interest rates too much when output growth indeed materializes below zero. The cautious MPC dampens its response to a change in forecast output growth when the forecast standard deviation of output growth increases, in favor of the attenuation principle of Brainard (1967). Another explanation for the dampened response could be based on a certain

trade-off between forecast uncertainty and data uncertainty the MPC might have. Estimates of current real GDP are subject to forecast uncertainty, as early releases of GDP are subject to revisions. Any change in forecast uncertainty also affects the forecast uncertainty/data uncertainty trade-off. As the reliability of forecast output growth deteriorates with increasing forecast uncertainty, and the relative reliability of reported data thus improves, the response of interest rates to a change in forecast output growth becomes muted.