Monetary policy and news shocks: are Taylor rules forward-looking?

3.1 Data

Estimation was performed using quarterly data on output gap, inflation, and nominal interest rates. Inflation is measured as the quarterly change in the GDP Implicit Price Deflator. The output gap is the log difference of the GDP and potential GDP estimated by the Congressional Budget Office. Lastly, the nominal interest rate is represented by quarterly levels of the federal funds rate. All data used were taken from the St. Louis Federal Reserve Economic Data website (FRED2 database) and cover the time period from 1954Q2 to 2011Q2. In the next section, we also conduct a robustness check that excludes the earliest data in the sample, as well as the latest one associated with the Great Recession, and only covers 1960Q1–2007Q4, which is a time sample frequently used by other authors.

3.2 Priors

Priors for the estimated parameters are summarized in Table 1. Their values for the degree of price inflation indexation, interest smoothing parameter, and Calvo price stickiness follow a beta distribution with means of 0.7, 0.7, and 0.5, respectively, and standard deviation of 0.2 following Milani and Treadwell (2012). The prior for the degree of habit persistence has a mean of 0.5 and a standard deviation of 0.16. Although slightly lower than the value used in other studies, this prior mean is consistent with previously estimated posterior means for this parameter, as in, among others, Smets and Wouters (2007). Importantly, this shape of the prior distribution prevents posterior peaks from being trapped at the upper corner of the respective estimation intervals set between 0 and 1. The autoregressive coefficients in consumption Euler equation, the NKPC, and the Taylor rule take Normal distributions centered at 0.5 and with standard deviations of 0.15. The magnitude for the response to inflation and the output gap in the Taylor rule also take Normal distributions centered at 1.5, and 0.5, with the latter value slightly higher than in Milani and Treadwell (2012).

Our approach to modeling the forward-looking component of the Taylor rule conduct follows Gabriel, Levine, and Spencer (2009) and is very close to Bache, Roisland, and Torsten (2011). Using single-equation GMM estimates of the forward-looking Taylor rule, Gabriel, Levine, and Spencer (2009) find that the value of ξ is in the 0.60–0.98 range (depending on the measure of real activity and the estimation technique being used) in the post-war data. Bache, Roisland, and Torsten (2011) report estimates of about 0.4–0.5 using maximum likelihood methods and more recent data. To capture these possibilities, we assign a fairly diffuse prior for this parameter that follows the beta distribution with a mean of 0.6 and a standard deviation of 0.12, yielding a prior probability interval consistent with the range of values previously estimated in the literature.

We follow Schmitt-Grohe and Uribe (2012) and Milani and Rajbhandari (2012) in our treatment of the priors for the standard deviations of anticipated and unanticipated shocks in two important directions. First, we assign the priors for the standard deviations of the unanticipated and anticipated innovations to follow the gamma distribution. Although the inverse gamma distributions are commonly used as priors for standard deviations, as is well known, their use may push the estimates of shocks’ standard deviations away from zero. Our use of the gamma distribution, on the other hand, assigns a positive probability that the standard deviations of anticipated innovations could take a value of zero, thus capturing the possibility that news shocks play an insignificant role in the dynamics of the model. Second, we assume that 75% of the variance of observed disturbances is driven by the unanticipated component. More specifically, if σ_q is the standard deviation of the observed shock ε^q where q=[y, p, r], the variance of its concurrent component σ_c,q is given by:

σc,q2=wσq2

and its news components by:

σn,q2=(1−w)σq2,

where the weight of the unanticipated component is set to w=0.75. Variances of individual news shocks at different horizons h can be constructed using:

σh,q2=1Nσn,q2,

where N is the number of news shocks at different horizons. These assumptions on the priors give limited scope to the anticipated shocks. Hence our priors need to be overwhelmed by the data to find a significant role for them.

3.3 Theoretical impulse responses

In this subsection, we investigate whether the addition of the forward-looking interest rate term has a significant impact on the transmission of exogenous shocks. We begin our analysis by studying theoretical impulse responses with all parameter values set at their prior means in Table 1 except for ξ. We set that parameter to 0, 0.3, 0.6, or 0.69, keeping these values below the prior for ρ of 0.7, since Levine, McAdam, and Pearlman (2007) show that determinacy requires that ξ<ρ. We perform this exercise in the specification with all three types of long-run news shocks, as it provides the most comprehensive insight into the effect of different one-standard-deviation shocks under the alternative values for ξ.^[8]

Figure 1 demonstrates the theoretical impulse responses of endogenous variables to surprise and anticipated demand shocks. The key intuition about the effect of higher values of ξ may be gleaned from comparing the effects of surprise and news shocks at shorter horizons versus those of the news shocks at longer horizons. The immediate effect of ξ increases is that the central bank tempers its interest rate response to current output gap and inflation, allowing their equilibrium values to increase. Given the persistence in inflation and output gap, that means somewhat higher values of these variables in the future, which, through the forward-looking interest rate terms has a positive effect on the interest rate. This explains why both output gap and inflation are more sensitive to surprise and news shocks with h=4 under higher values of ξ. For the interest rate, the immediate effect dominates the forward-looking one for surprise shocks and the converse is true for news shocks. As the news shock horizon increases, the effect of the forward-looking term becomes more and more dominant, so much so that for h=12 output gap and inflation decrease in response to a positive anticipated demand shock as soon as it becomes known. In general, all three variables become more sensitive to demand shocks and hence more volatile, as the value of ξ and the the news shock horizon increase.^[9]

Figure 1:

Theoretical impulse responses to demand shocks: solid black line – ξ=0; dashed blue line – ξ=0.3; punctuated green line – ξ=0.6; solid red line with circles – ξ=0.69.

Figure 2 provides similar analysis for the endogenous variable responses to supply shocks. The intuition is similar to the one conveyed by Figure 1 for demand shocks with the main difference being that output gap dynamics due to the different supply shocks remain largely unaffected by changes in the value of ξ. Again, the immediate response of the interest rate rate to inflationary pressure decreases as ξ increases, which allows the pressures to build up going forward and brings about a stronger secondary response due to the forward-looking interest rate term in the monetary policy rule. As a result, the volatility of inflation and interest rate increase markedly at higher levels of ξ.

Figure 2:

Theoretical impulse responses to supply shocks: solid black line – ξ=0; dashed blue line – ξ=0.3; punctuated green line – ξ=0.6; solid red line with circles – ξ=0.69.

Finally, Figure 3 describes the effect of different types of monetary shocks. A contractionary monetary surprise shock generates decreases in inflation and output gap that, given their inertial behavior, persist into the future. Anticipation of the future recession through the forward-looking interest rate term makes then central bank reduce the interest rates by larger amounts for higher values of ξ, eventually making output gap and inflation overshoot into the positive territory on the way to their adjustment to the steady state. Similar intuition holds for news shocks except that anticipation of a future recession driven by a contractionary monetary shock is so strong that the equilibrium interest rate actually falls and briefly ventures into the positive territory when the anticipated shock materializes h time period ahead. The strength of these dynamics increases with anticipation horizon h and the central bank’s forecast horizon ξ.

Figure 3:

Theoretical impulse responses to monetary shocks: solid black line – ξ=0; dashed blue line – ξ=0.3; punctuated green line – ξ=0.6; solid red line with circles – ξ=0.69.

In sum, the presence of news shocks in the empirical model clearly has far-reaching implications for identifying our main parameter of interest, ξ. As ξ increases, endogenous variable responses generally become stronger, although this effect is more pronounced for demand and monetary shocks and less so for supply shocks. This volatility increases with the news anticipation horizon, h, and may imply that variables move in the opposite direction of the one given by the shock, due to the model’s endogenous mechanism, as is the case for the equilibrium interest rate in response to monetary news shocks. These results are likely to set up a horse race between the forward-looking term in the Taylor rule and anticipated shocks, especially monetary news, since the strong presence of both is likely to generate implausible dynamics.

4.1 Parameter estimates

Table 2 reports the posterior mean estimates along with the 95% posterior probability intervals (PPI) of the more parsimonious specifications with respect to the structure of news shocks that provide the closest functional form fit with available parameter estimates in models that do not feature anticipated shocks. We refer to the preferred specification with the forward-looking interest term in the Taylor rule and the long-run identification of the monetary news shocks as “FTR+MN”. For all of the specifications that we have estimated, we have calculated the Bayes factor, taking “FTR+MN” as the baseline model.^[10] Panel A of Table 2 focuses on the parameter estimates of ξ and the standard deviations of the monetary news shocks.

The first two columns feature estimation results from specifications where only the monetary shock has a news component under the forward-looking (“FTR+MN”) or standard (“STR+MN”) Taylor rule. While the introduction of the forward-looking term yields a dramatic increase in the marginal likelihood, the estimated value of ξ in the latter specification is quite low at only 0.251 with a posterior probability interval that contains a value close to zero: [0.112, 0.396]. This suggests that the forecast targeting is only one month, which is barely frequent enough to bridge the gap between at most half of the Federal Open Market Committee (FOMC) meetings. Importantly, the standard deviations of the monetary news shocks are quite large, especially at the 8-quarter anticipation horizon when they are larger than the standard deviations of monetary surprises. This suggests an economically significant role for the anticipated shocks to interest rates.

We next report the results for the more traditional specifications that do not feature news shocks at all. The model with the forward-looking term (“FTR+NoN”) has a posterior mean value for ξ of 0.641, which is in line with the previously reported results. This estimate suggests a forecast horizon of close to two quarters, with a confidence interval of 1–4.5 quarters, which is economically significant and matches the forecast horizons used in non-Calvo forward-looking rules by Clarida, Gali, and Gertler (2000), Orphanides and Wieland (2008), and Mavroeidis (2010) among others. However, the likelihood associated with this model is lower than that of “FTR+MN”. It is also lower that the likelihood of the model without news shocks and the standard Taylor rule (“STR+NoN”). Collectively, these results suggest that the forward-looking interest rate term is at best economically unimportant.

Panel B of Table 2 reports the remainder of the structural parameters in these four specifications. We find that the estimated parameters take values consistent with previous estimations of similar models, such as Dennis (2009) and Milani and Treadwell (2012). One possible exception is the high estimate of θp, which exceeds the values reported in Smets and Wouters (2007), among a large number of others.^[11] However, depending on the specific sample, model, or estimation technique, similar results have been obtained earlier as well; see Rabanal and Rubio-Ramirez (2005), Cho and Moreno (2006), or Boivin and Giannoni (2006). While the elevated estimate of θp is in line with these studies, there are two potential reasons for its being towards the high end of all available estimates in the literature. First, our sample includes the Great Recession, which is likely to increase the estimated degree of price stickiness; see Hirose and Inoue (2015) for an illustration. Second, the introduction of news shocks typically leads to a substantial increase in the value of this parameter, as documented by Milani and Treadwell (2012), Milani and Rajbhandari (2012), or Hirose and Kurozumi (2012). Therefore, this parameter is expected to be considerably higher than in DSGE models that do not feature news shocks or whose samples do not include the zero-interest-rate environment.

Table 3 imposes alternative news shock structures on the model, with each specification having a positive value of ξ. The column labeled “FTR+SRN” imposes the short-run identification on the structure of news shocks allowing their anticipation horizons to vary between 1 and 4 quarters. The standard deviations of demand and supply news shocks at the 4-quarter horizon are particularly large and are about the same in magnitude as their surprise counterparts. The standard deviation of the anticipated monetary shock at the 2-quarter horizon is larger than its surprise counterpart, while the estimated value of ξ plummets to 0.257. The column labeled “FTR+LRN” reports the results for the specification with the long-run identification of all three types of news shocks. Monetary and demand news shocks at the 4-quarter anticipation horizon and supply news shock at the 12-quarter anticipation horizon are almost as large or larger than their surprise counterparts. The estimated value of ξ falls further to 0.185. We note, however, the marginal likelihoods of the specifications that feature all three types of news shocks remain below the baseline “FTR+MN” specification. The last two columns in Table 3 summarize estimation results from specifications where the news component features only in the demand shock (“FTR+DN”) or the supply shock (“FTR+SN”). These specifications produce relatively high estimates of ξ that are well in line with the previous literature. However, their marginal likelihoods are much lower than in the FTR+MN specification, the mean estimates of the news components’ standard deviations are smaller than their surprise counterparts, and the lower bounds of the posterior probability intervals are close to zero. Therefore, these checks confirm our main finding that the model with monetary news and low, economically insignificant ξ best fits the data.

4.2 Empirical impulse responses

We next compare impulse response functions (IRFs) in models where ξ≥0 (dashed mean IRF, filled 95% confidence interval) and models where it is set to zero (solid mean IRF, cross-hatched 95% confidence interval). Figure 4 compares models designated “FTR+NoN” and “STR+NoN” for the parameter values presented in Table 2 to assess the impact of this term in models without news shocks. Sets of IRF confidence intervals from both models overlap closely for all shocks and response variables, as mean responses from one model are well within the confidence intervals from the other model. One possible exception is the output gap response to the supply shock where the mean response from “FTR+NoN” follows the upper branch of the confidence interval for “STR+NoN.” But this seems to be primarily driven by the fact that the confidence interval for the former model is considerably wider than for the latter.

Figure 4:

Impulse responses for models without news shocks: blue dashed line with shaded 95% confidence interval – model with ξ>0; solid black line with cross-hatched 95% confidence intervals – model with ξ=0.

We repeat this exercise in the models that feature monetary news shocks, “FTR+MN” and “STR+MN”, with parameter values again taken from Table 2. Figure 5 reveals a large overlap between the two sets of confidence intervals. Again, in one case, the output gap response to the demand surprise shock, the mean response from the “FTR+MN” model appears to closely match the upper branch of the confidence interval from the “STR+MN” model, but in all other cases, mean IRFs are very close to each other. To economize on space, we show the IRFs to the monetary news shock only at horizon h=8.^[12] Recall that Table 2 suggests that monetary news has the largest economic significance at this horizon. Again, confidence intervals from models with and without the forward-looking interest rate term overlap quite closely, although in this case, the former specification delivers wider confidence intervals. We, therefore, conclude that the presence of the forward-looking interest rate term in the Taylor rule does not have important implications for the dynamic transmission of stochastic shocks in the class of models employed in this paper.

Figure 5:

Impulse responses for models with news shocks: blue dashed line with shaded 95% confidence interval – model with ξ>0; solid black line with cross-hatched 95% confidence intervals – model with ξ=0.

5.1 Zero lower bound on the nominal interest rate

Since our sample includes the Great Recession, it is important to address the possible impact of the zero lower bound (ZLB) on the nominal interest rate on the structural parameter estimates. On one had, Fernandez-Villaverde et al. (2012), Gali (2011), and Gali, Smets, and Wouters (2011) argue that the presence of the ZLB may introduce bias into the estimation procedure of a DSGE model. On the other, Hirose and Inoue (2015) provide evidence from a simulation experiment in the context of a model very similar to ours that shows that it is unlikely that the ZLB will bias estimated parameters or affect the shape of impulse response functions. Without taking a stance in this important debate, we re-estimate the specifications in Tables 2 and 3 using the data from the 1960Q1–2007Q4 subsample. We find that our results hold without major changes to our conclusions and, if anything, bolster the case against the economic significance of the forward-looking term in the Taylor rule specification. To economize on space, Table 4 reports the estimated value of ξ and the marginal likelihoods for all eight specifications. All other parameter estimates are very close to the values reported in Tables 2 and 3. The majority of the estimated values of ξ are slightly lower than in their full-sample counterparts and, of all eight specifications, the marginal likelihood is the highest in cases where ξ is set to 0. Models where the estimates of ξ are the highest and in line with previously reported results (“FTR+SN” and “FTR+DN”) continue to have the lowest marginal likelihoods.

5.2 Alternative specifications of the Fed’s forward-looking behavior

While the Calvo-type Taylor rule (3) provides a parsimonious summary of the central bank’s responding to forecasts of the future macroeconomic activity, that parsimony comes at a cost in terms of imposing assumptions on the nature of forecast horizons, the weights on which decline geometrically. It may be possible that in practice, the Fed uses a specification closer to the one where the nominal interest rate responds to the future values of output gap and inflation at a particular horizon, as in the specification of Clarida, Galí, and Gertler (2000).

The general specification takes the following form:

This equation nests several special cases:

1. ξ=0, α=0: standard Taylor rule (STR);

2. ξ>0, α=0: Calvo-type forward-looking rule (FTR);

3. ξ=0, α>0: non-Calvo-type forward-looking rule of Orphanides and Wieland (2008);^[13]

4. ξ>0, α>0: generalized forward-looking rule (GFR).

To understand the effect of introducing monetary news shocks on the estimated Taylor rule, we first estimate the most general specification, treating ξ and α as estimated parameters. Our prior for α is quite diffuse, given by the beta distribution with a mean of 0.7 and the standard deviation of 0.2. We conduct our estimation exercise using two values for the leads of output gap and inflation targets: k=1, 4. While the setting with k=1 is standard benchmark, e.g. Clarida, Galí, and Gertler (2000) or Mavroeidis (2010), many authors have argued that the Fed’s target horizon stretches farther out, at about one year; Orphanides (2003) and Nikolsko-Rzhevskyy (2011) provide such evidence for the Fed’s policy conduct in the United States. The presence of a weight on current and future inflation is also similar to the averaging of future target values at different horizons, as in Campbell et al. (2012), without imposing equal weights due to averaging.

Panel A of Table 5 presents estimates of (9) with “NoN” designating models with no news shocks, “LRMN” designating the long-run structure of monetary news shocks, and k describing the leads for inflation and output gap targets in the rule. Our main result holds: the introduction of monetary news shocks leads to a fall in the estimated value of ξ in half towards the values from the baseline specification. Similarly, the estimated value of α that describes the weight placed on the future values of inflation and output gap falls with the introduction of monetary news and is indistinguishable from 0 in the “LRMN, k=4” case.

Since our baseline results correspond to the case of α=0 and its value is not well identified in most specifications, we also explore the possibility of restricting the value of α to 1. Panel B of Table 5 has the corresponding set of estimates. Again, the introduction of monetary news shocks leads to a pronounced decline in the estimated values of ξ to levels consistent with our baseline results. We, therefore, conclude that our robustness checks confirm the quantitative unimportance of the forward-looking interest rate term in the Calvo-type Taylor rule.