Results for Dynamic Identification Selection

As discussed before, method 1, while informative, is silent about possible shifts in the nature of policy shocks underlying trend inflation. To address this, we now report identification selection results based on the regime switching procedure discussed in Section 3.3.1.2, i.e., method 2. Recall such an approach introduces a multinomial

discrete state variable, kt ∈ {1, 2, 3}, which selects one of the three best-fit models

under method 1 (MR1, MR2, MR3)at each pointt = 1, ...,T. Moreover, recall under

method 2 each model corresponds to a particular regime described by the identified

monetary policy shock to trend inflation.35

Figure 3.2 reports the posterior probabilities (Pr(kt =i|Y)fori =1, 2, 3 and t =

1, ...,T) for an inflation target adjustment, inflation gap stabilization and output gap

stabilization regime.36 _{To a certain extent, our results in this section corroborate our}

34_{We initialize the random walk representation of}

π_t∗with a diffuse prior given byπ₀∗∼ U(2, 6). 35_{Recall regimes are informative about a specific systematic monetary policy shock underlying trend}

inflation in addition to non-policy shocks.

36_{Posterior regime probabilities are constructed by calculating the frequency each realization ofk} t∈

§3.5 Evaluation 85

Table 3.4: Variance decomposition results for policy and non-policy shocks shocks (posterior medians) to trend inflation for all models under identification selection method 1

Model Policy Shock

Great Inflation Great Moderation

MR1 31.74% 48.87% MR2 8.33% 18.50% MR3 28.31% 49.81% MR4 10.22% 13.82% MR5 9.39% 9.13% MR6 9.19% 7.02%

Model Non-Policy Shock

Great Inflation Great Moderation

MR1 69.26% 51.23% MR2 91.67% 81.50% MR3 71.69% 50.19% MR4 89.78% 86.18% MR5 90.61% 90.77% MR6 90.81% 92.98%

Note: Results based on the sample period from 1967Q1 through 2007Q4 and allowing for a break in the variance of measurement and state innovations at 1984Q1. Results in bold denote the best-fit model ranked according to the four selection criteria in Table 3.3.

Figure 3.1: Estimated sequence of systematic monetary policy shocks (posterior me-

dians) and implied structural policy parameter for MR1. The best-fit model under

identification selection method 1. The structural policy parameter below is recov-

ered by feeding the identified policy shock to the random walk representation ofπ_t∗.

Shaded regions denote recession periods as recorded by the NBER.

1970 1975 1980 1985 1990 1995 2000 2005 −1.5 −1 −0.5 0 0.5 1 1.5

Inflation target adjustment shock: v_π* ,t 1970 1975 1980 1985 1990 1995 2000 2005 0 1 2 3 4 5 6

Implied inflation target: π*_t = π*_t−1 + v_π* ,t

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findings from method 1. Inflation target adjustment shocks still stand out as the key policy driver of trend inflation. Specifically, the posterior probability associated with such shocks is around 70% and close to 100% at the start of the sample and throughout the Great Moderation, respectively. Nevertheless, method 2 suggests a more nuanced picture in terms of policy contributions to trend inflation during the transition from the Great Inflation to the Great Moderation. In particular, the period from 1975 to 1984 is marked by an alternation between inflation gap and output gap stabilization shocks as the main systematic monetary policy influences behind trend inflation.

To assess what such shocks entail for the dynamics of structural policy parame- ters, as in the last section, we feed the sequence of shocks,{vπ∗,t, vω1,t, vω2,t}

T t=1 (see

Figure 3.3), obtained from MCMC algorithm 2 into the implied random walk rep-

resentation of each structural policy parameter, π∗_t, ω1,t andω2,t, accordingly. The

resulting time series (posterior medians) are shown in Figure 3.4.37

Overall, our results are broadly aligned with previous studies such as Orphanides [2001], Boivin [2006], Kim and Nelson [2006] and Coibion and Gorodnichenko [2011]. In particular, we find that monetary policy reaction to expected output gap move- ments declined around the mid 1970s. This was accompanied by an upward trend in policy emphasis to react to expected deviations of inflation from its target. Further- more, similar to Coibion and Gorodnichenko [2011] we find that the Taylor principle,

captured here as 1+ωt > 1, is satisfied throughout the sample period. For the im-

plied inflation target, we observe a steady decline from around 4% to 2.5% around 1987.

Taken together, these results indicate that systematic monetary policy contribu- tion to bring down trend inflation between the late 1970s and early 1980s can be mapped to an increase in the degree of policy activism towards expected inflation relative to the output gap outlook. During the Great Moderation, when inflation expectations were less unhinged, monetary policy adjustments to its target inflation rate and trend inflation appeared to be better aligned.

Lastly, one should not expect the dynamics of the structural policy parameters reported in Figure 3.4 to mimic exactly the dynamics observed in other studies of TVP policy rules where all coefficients are driven by orthogonal innovations (e.g., Boivin [2006], Kim and Nelson [2006] and Coibion and Gorodnichenko [2011]). As discussed in Section 3.4.2, within our exercise if a particular shock is not a key driver of trend inflation then it does not enter the likelihood function (i.e., it is not up-

{1, 2, 3}occurs given all MCMC draws from algorithm 2 in Section 3.4.2.1.

37_{As in Section 3.5.3, we initialize random walk representations of structural policy parameters with}

a diffuse prior. More precisely, we adopt the following initial conditionsπ∗₀ ∼ U(2, 6) and ωi,0 ∼ U(0, 2)fori=1, 2.

dated). As a result, such shock is simply sampled from its prior density which has zero mean and median. This is reflected in Figure 3.4, which shows that parame- ters become virtually time invariant when their corresponding policy shock regime probabilities in Figure 3.2 are low. With that in mind, the fact that our results are qualitatively comparable with the ones obtained from studies adopting considerably different modeling frameworks is reassuring.

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Figure 3.2: Posterior probabilities (posterior medians) for each type of systematic monetary policy shock driving trend inflation under method 2: regime switching between the three best-fit identification strategies under method 1. Shaded regions denote recession periods as recorded by the NBER.

1970 1975 1980 1985 1990 1995 2000 2005 0 20 40 60 80 100 (%)

Inflation Target Adjustment Inflation Gap Stabilization Shock Output Gap Stabilization Shock

Figure 3.3: Estimated sequence of systematic monetary policy shocks (posterior me- dians) to trend inflation under identification selection method 2: regime switching between the three best-fit identification strategies under method 1. Shaded regions denote recession periods as recorded by the NBER.

1970 1975 1980 1985 1990 1995 2000 2005

−0.5 0 0.5

Output gap stabilization shock: v_ω 2,t

1970 1975 1980 1985 1990 1995 2000 2005

−0.5 0 0.5

Inflation gap stabilization shock: v_ω 1,t

1970 1975 1980 1985 1990 1995 2000 2005

−0.5 0 0.5

Inflation target adjustment shock: v_π* ,t

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Figure 3.4: Implied time varying structural policy parameters (posterior medians) under identification selection method 2: regime switching between the three best-fit identification strategies under method 1. Structural policy parameters are recovered by feeding the estimated sequences of shocks in Figure 3.3 to the corresponding

random walk representation of π∗_t, ω1,t and ω2,t. Shaded regions denote recession

periods as recorded by the NBER.

1970 1975 1980 1985 1990 1995 2000 2005 0 2 4 6 8

Implied inflation target: π_t* = π_t−1* + v_π* ,t 1970 1975 1980 1985 1990 1995 2000 2005 0.5 1 1.5 2 2.5 3 3.5

Reaction to expected inflation gap: 1+ω

1,t such that ω1,t = ω1,t−1 + vω 1,t 1970 1975 1980 1985 1990 1995 2000 2005 −0.5 0 0.5 1 1.5 2

Reaction to expected output gap: ω

2,t = ω2,t−1 + vω 2,t