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The e¤ects of the monetary policy stance on the transmission
mechanism
Ana Beatriz Galvaoy
Queen Mary University of London
Massimiliano Marcellino
European University Institute, Bocconi University and CEPR
July 2012
Abstract
This paper contributes to the literature on changes in the transmission mechanism of mone-
tary policy by introducing a model whose parameter evolution explicitly depends on the stance
of monetary policy. The model, a structural break endogenous threshold VAR, also captures
changes in the variance of shocks, and allows for a break in the parameters at an estimated time.
We show that the transmission is asymmetric depending on the extention of the deviation of
the actual policy rate from the one required by the Taylor (1993) rule. When the policy stance
is tight - actual rate is higher than the one implied by the Taylor rule -, contractionary shocks
have stronger negative e¤ects on output and prices.
Keywords: threhold models, time-varying models, great moderation, monetary policy trans-
mission, asymmetries.
JEL classi…cation: E52, C51.
yCorresponding author: Dr. Ana Beatriz Galvao. Queen Mary University of London, Department of Economics,
Mile End Road, E1 4NS, London, UK. Phone: ++44-20-78828825. email: a.ferreira@qmul.ac.uk.
1 Introduction
Changes in the monetary policy transmission and also in the size of monetary policy shocks are
well documented (see Boivin, Kiley, Mishkin (2011) for a survey) and are often considered as an
explanation for the reduction in the volatility of key US macroeconomic aggregates, known as the
"great moderation". In econometric terms, changes in conditional means have been modelled by
means of VAR models in early contributions (e.g. Cogley and Sargent (2005), Sims and Zha (2006))
and of small scale DSGE models in more recent contributions (e.g., Justiniano and Primiceri (2008),
Benati and Surico (2009), Inoue and Rossi (2011), Davig and Doh (2009), Bianchi (2009)). The
pattern of time variation in the mean is captured either by slowly evolving parameters, typically
modelled as random walks with small innovation variance, e.g. Cogley and Sargent (2005), or by
abruptly changing parameters whose evolution is determined by an unobservable Markov chain, e.g.,
the Markov switching speci…cation of Sims and Zha (2006), Davig and Doh (2009), Bianchi (2009).
Time variation in the variance is typically modelled by means of a stochastic volatility speci…cation
both in VARs (Sims and Zha, 2006) and DSGE models (Fernandez-Villaverde, Guerron-Quintana,
Rubio-Ramirez, 2010).
In contrast to the previous literature that assumes that parameters vary with unobserved
processes, we make the latter depend on a combination of endogenous observed variables and
estimated thresholds, while also allowing for an estimated time break. The resulting model is called
structural break endogenous threshold vector autoregressive (SB-ET-VAR), and it is also designed
to capture changes in the variance of shocks. We discuss speci…cation and estimation of this model,
and its use for the computation of impulse response functions. We then …t an SB-ET-VAR to
output, prices and the policy rate, using the deviations of the observed policy rate from the one
implied by the policy rule prescribed by Taylor (1993) as the transition variable. When deviations
lie outside an estimated range (de…ned by estimated threshold values), the policy stance of the
estimated regime is identi…ed as either tight or loose. We thus obtain an endogenous measure of
the stance of monetary policy (see Cecchetti et al. (2007) for an example of the use of Taylor-rule
1
deviations in a similar context).
Boivin et al (2011) show that the e¤ect of a 25-basis-point increase in policy rate on output
and prices is smaller and more persistent after 1984. They use a DSGE model to establish that the
change in the period after 1984 is explained by a central bank that is more reactive to output and
in‡ation. We take a step further on understanding the evolution of monetary policy transmission
by using a model that allows for recurrent changes in the transmission of policy shocks depending
on the monetary policy stance within a subsample de…ned by an estimated break. We show that
the identi…cation of tight and loose regimes based on the extent of the deviation of the observed
policy rate from the one prescribed by the Taylor rule is statistically di¤erent before and after the
break, and that output and policy shocks are statistically larger before the estimated 1985 break.
All these results agree with the Boivin et al (2011) evidence that central bank preferences and
policy shocks have changed. The estimated break date, 1985Q1, is compatible with the timing of
the identi…ed change in central bank credibility measures computed as in Demertzis et al. (2012)
and Laxton and Diaye (2002). Both credibility measures are based on the fact that long-term
in‡ation expectations should be anchored at the implicit or explicit in‡ation target of the central
bank, when the latter is credible.
Our main empirical contribution is to provide evidence of recurrent changes in the monetary
policy transmission within each subsample, triggered by how far the fed rate is from the one implied
by the Taylor (1993) rule at the impact of the shock. In particular, the dynamic response of output
and prices to policy shocks is weaker when the monetary stance is loose (current rate too low in
comparison with the one implied by the Taylor (1993) rule), and it is signi…cantly negative if the
stance is tight even in the period after 1985.
Our VAR speci…cation is able to capture asymmetries in the response to policy shocks, as in
Weise (1999) and Ravn and Sola (2004). However, instead of checking for asymmetries in the
dynamic responses to policy shocks depending on the business cycle phases (see, e.g, Lo and Piger
(2005)) or the degree of in‡ationary pressure (as also suggested by Davig and Leeper (2008)), we
look for asymmetries that depend on the size/sign of deviations of the current fed rate from the
2
one implied by the linear Taylor rule. This choice of observed transition variable combines linearly
three endogenous variables, instead of considering only one variable at a time as Weise (1999).
Our approach is also compatible with the evidence of asymmetries in the Taylor rule preference
parameters depending on economic conditions as argued by Cuckierman and Muscatelli (2008).1
We use our estimated model in a set of counterfactual experiments to compare the relative
importance of switches in the autoregressive parameters to changes in the volatilities of shocks.
Changes in the autoregressive parameters, or in the dynamic transmission, could be related to
‘good policy’, while changes in the volatility of output shocks, or the size of the shocks, are nor-
mally related to ‘good luck’. We …nd that if the parameters of the tight regime were kept during
both subsamples, but the shocks were taken as observed, the volatilities of output growth and the
level of in‡ation would have been smaller. If pre-85 parameters were used for the post-85 subsam-
ple, keeping observed shocks, we would have had higher output growth and in‡ation levels and
volatilities than observed. As a consequence, both changes in the transmission and the volatility of
the shocks are required to explain the observed changes, in disagreement with Sims and Zha (2006)
support of volatility changes only, but in agreement with Boivin et al (2011).
The rest of the paper is organized as follows. Section 2 discusses the speci…cation and estimation
of the SB-ET-VAR, and the method to compute impulse response functions and their standard
errors. Section 3 presents empirical results on model speci…cation, estimation, andthe chronology
of regimes. Section 4 illustrates the changing propagation of monetary shocks depending on the
monetary policy stance before and after the estimated break. Section 5 contains counterfactual
analyses and discusses their implications for the debate on the sources of the great moderation.
Section 6 summarizes and concludes.
1Our model includes an equation for the policy rate with own lags, output and prices on the right-hand side,
similar to a reduced-form Taylor rule, and their parameters may change with the monetary policy stance, which is
related with economic conditions.
3
2 The Model
This section describes our endogenous threshold VAR model and how to compute impulse response
functions from this model; shows how to introduce additional exogenous breaks in the speci…cation;
and discusses how to determine the number of regimes and the transition variable.
2.1 Endogenous Threshold VARs
2.1.1 Speci…cation and estimation
The model employed in this paper is a modi…cation of Tsay’s (1998) Threshold VAR. The main
characteristic of the model in comparison with Markov-Switching speci…cations is that the variable
that triggers regime switching is observed. This feature makes the cause of regime changes easier
to establish.
The threshold VAR speci…cation of Tsay (1998) is a multivariate version of Self-Exciting Thresh-
old Models (Tong, 1990). As a consequence, the variable that triggers the regime switching is one
of the endogenous variables in the VAR. In contrast, our Endogenous Threshold Vector Autore-
gressive Model (ET-VAR) employs a combination of endogenous variables as transition variable.
The combination of endogenous variables is computed using known (not estimated) weights, while
the thresholds that de…ne when the transition variable triggers regime changes are estimated.
Let us group the (endogenous) variables of interest observed at time t into the m � 1 vector
yt, and label the transition variable as xt. Recall that xt contains a combination of endogenous
variables. The ET-VAR is:
yt =
8>>>>><>>>>>:
�
(1)
0 +
Pp
i=1 �
(1)
i yt�i + "
(1)
t if xt�1 � c1
�
(2)
0 +
Pp
i=1 �
(2)
i yt�i + "
(2)
t if c1 < xt�1 � c2
�
(3)
0 +
Pp
i=1 �
(3)
i yt�i + "
(3)
t if xt�1 > c2
; (1)
where �(r)0 is an m � 1 vector of intercepts for regime r (r = 1; 2; 3), �(r)i is an m � m matrix
of coe¢ cients of lag i (i = 1; :::; p), and c1 and c2 are (unknown) threshold values. Each regime
has a speci…c full variance-covariance matrix, that is, E("(r)t "
(r)0
t ) = �
(r), and we suppose that
4
"
(r)
t � N(0;�(r)).
If the threshold values were known, the observations of the transition variable xt combined with
the threshold values could be used to split the sample of yt and (yt�1;:::; yt�p) into subsamples (for
t = p+ 1; :::; T ). Hence, the usual least squares formulae could be applied to obtain the estimates
of the coe¢ cient matrices and of the variance-covariance matrices, which are also equivalent to the
maximum likelihood estimates of this reduced form model. However, the thresholds have also to be
estimated. Following Galvão (2006), we use conditional maximum likelihood since it is an adequate
estimation method when the �(r) may di¤er across regimes. Hence, estimates of the unknown
thresholds are obtained as:
c^1; c^2 = min
c1�C1
c2�C2
�
T1
2
log j�^(1)(c1; c2)j+ T2
2
log j�^(2)(c1; c2)j+ T3
2
log j�^(3)(c1; c2)j
�
; (2)
where j�^(r)j is the determinant of the estimated variance-covariance matrix computed as �^(r) =
1=Tr
PTr
t=1 "^
(r)
t "^
(r)0
t , and Tr is the number of observations in each regime. The variance-covariance
matrix is computed for each combination of threshold values in a grid, �^(r) (c1; c2), since if the
threshold is known, least squares formulae can be used to estimate the coe¢ cient matrices. The
grid of threshold values is built based on restrictions on the minimum proportion of observations
in each regime (Hansen, 2000). In the case of a model with three regimes, the value of one of the
thresholds a¤ects the grid of values available for the second threshold, so there is a large number
of possible combinations that satisfy the restrictions on a given proportion of observations in each
regime. In this paper, we use the approach described by Hansen (1999), called "one-step-at-time",
to reduce the computational burden.2
Given the estimated thresholds, the remaining parameter estimates are obtained using standard
OLS formulae. Note that this analysis is conditional on the choice of the transition variable, xt,
and of the lag length, p. We will discuss their selection in the last subsection.
2The one-step-at-time approach estimates …rst one threshold, then conditional on this value, a second threshold
is estimated. Then using the second estimated threshold, a new threshold is estimated. And …nally, this procedure
is repeated one more time conditional on the new threshold computed in the previous step to deliver the estimates
of both thresholds.
5
2.1.2 Impulse Response Functions for Endogenous Threshold VARs.
An implication of the ET-VAR is that the responses to shocks are regime dependent. More precisely,
the transmission of the shock relies on �(r)i , i = 1; :::; p, and the impact of the shock on �
(r), following
eq. (1). In addition, the dynamic response to the shock can trigger a change in regime. We will
now provide details on the required procedure for the computation of the response functions and
their standard errors when changes in regime may occur as response to shocks.
To start with, let us suppose that each regime de…nes separate subsamples, as in the case
of structural break models, such as Boivin and Giannoni (2006). We could then use a Cholesky
decomposition conditional on the regime to identify the regime-speci…c structural shocks, v(r)t :
v
(r)
t =
�
A(r)
��1
"
(r)
t ; (3)
where �(r) = A(r)�(r)A(r)
0
, A(r) is a lower triangular matrix with ones on the main diagonal, and
�(r) is a diagonal matrix whose elements, �(r), are the variances of the structural shocks v(r)t . The
dynamic response to a one-unit structural shock is:
fr;j;s =
�yt+s
�v
(r)
j;t
= 	(r)s a
(r)
j ; (4)
where j = 1; :::;m, s indicates the response horizon (s = 1; :::; h), a(r)j is the j
th column of
A(r)(Hamilton, 1994, p. 92 and 323), and 	(r)s is the proper matrix in the MA(1) representa-
tion obtained by inverting the V AR(p) conditional on being in the regime r.
When computing the response as described, the implicit assumption is that the response to
a shock does not generate regime changes. However, this assumption is unrealistic because the
transition variable is a combination of endogenous variables a¤ected by the shock. For example, a
shock v(r)j;t impacting the system in regime 1, that is, xt � c1, could generate an e¤ect such that
xt+s�1 > c1 (so that the system switches to regime 2 in period t + s) or even xt+s�1 > c2 (switch
to regime 3). Moreover, whether or not the switch takes place depends not only on the impact
and dynamic response to the shock, but also on the current and past values of the endogenous
variables (since there is dependence on the past trough the VAR dynamics). Hence, contrary to the
6
standard linear case, the history preceding the shock matters to determine its e¤ects, and has to
be considered for the computation of the dynamic responses. Finally, the realizations of the future
shocks are also relevant, since they can also cause a regime change.
Our preferred computation of dynamic responses takes into account all points described above.
We make use of the concept of generalized responses introduced by Koop, Pesaran and Potter
(1996). The response to a one-unit shockhitting in t+ 1 is:
gr;j;s = E
�
yt+sj
(r)t ; v(r)j;t+1 = a(r)j
�
� E
�
yt+sj
(r)t
�
; (5)
where 
(r)t is a matrix containing the set of histories associated with the regime r at the impact
of the shock. More precisely, let us de…ne Wt = (yt; :::; yt�p+1), and 
t = ((W1; :::;WT )0). We
then partition the matrix 
t so that 
(r)
t has the rows of 
t that correspond to regime r. Hence,
(r)
t has dimension Tr � p. The assumption that v(r)j;t+1 = a(r)j implies that the impact of the shock
computed with gr;j;s=1 is the same as in the case of fr;j;s=1.
The response function described in (5) is computed conditional on a speci…c regime history at
the time of the shock with no restrictions on regime switches, and averaging out the e¤ects of future
shocks, which a¤ect similarly both conditional means. The cost is that the conditional means in
(5) cannot be evaluated analytically but need to be computed by simulation, using the procedure
in Appendix A. Finally, notice that both the size and sign of the shock matters in this context,
since the response may trigger a regime change.
Another important issue to be addressed is the impact of parameter uncertainty on the impulse-
response functions. This means that we would like to assess the impact of using �^(r)i , �^
(r), c^1 and
c^2 obtained by conditional maximum likelihood when computing gr;j;s. The normal distribution
is a good approximation for that of �^(r)i and �^
(r), provided that the threshold e¤ect vanishes
asymptotically, but the distribution of the threshold estimates is non-standard (Hansen, 2000).
Therefore, we use the bootstrap to compute 100(1 � �)% con…dence intervals for the thresholds,
the elements of the �(r) matrix, and the dynamic responses. The boostrap procedure is described
in Appendix B.
7
2.2 Endogenous Threshold VARs with a Break
There is by now strong statistical evidence of breaks in the monetary policy transmission mechanism
(e.g., Boivin et al, 2011), and in the variance of the shocks (Sims and Zha, 2006). Hence, it may be
necessary to add additional breaks in the speci…cation of our ET-VAR, in order to capture possible
parameter changes that are not explained by the monetary policy stance.
Therefore, following Galvão (2006), we introduce a Structural Break-Endogenous Threshold-
VAR model (SB-ET-VAR). In this model, the break date is estimated rather than exogenously
assumed, since the break date is uncertain and depends on the model for which the break date is
computed. The break a¤ects the dynamics of each regime and how regimes switching is triggered.
To simplify the notation, assume that Yt�1 = (1; yt�1; :::; yt�p) and z(r) = (�
(r)0
0 ;�
(r)
1 ; :::;�
(r)
p )
such that the ET-VAR can be written as:
yt =
h
(z(1)0Yt�1 + "
(1)
t )I (xt�1 � c1)
i
+
h
(z(2)0Yt�1 + "
(2)
t )I((xt�1 > c1) (xt�1 � c2))
i
+
h
(z(3)0Yt�1 + "
(3)
t )I (xt�1 > c2)
i
;
where I(:) is an indicator function that is equal to one if the inequality is true. The inclusion of a
break in the model, which yields our SB-ET-VAR speci…cation, implies that:
yt =
8><>:
h
(z(1)0Yt�1 + "
(1)
t )I (xt�1 � c1)
i
+
h
(z(2)0Yt�1 + "
(2)
t )I((xt�1 > c1) (xt�1 � c2))
i
+
h
(z(3)0Yt�1 + "
(3)
t )I (xt�1 > c2)
i
9>=>; I(t � b)+
(6)8><>:
h
(z(4)0Yt�1 + "
(4)
t )I (xt�1 � c3)
i
+
h
(z(5)0Yt�1 + "
(5)
t )I((xt�1 > c3) (xt�1 � c4))
i
+
h
(z(6)0Yt�1 + "
(6)
t )I (xt�1 > c4)
i
9>=>; I(t > b):
The SB-ET-VAR is an ET-VAR in each of the two subsamples de…ned by the break date, b.
The values of the thresholds before the break are di¤erent from the values after the break. Hence,
the regimes de…ned by the thresholds c1 and c2 may repeat until t � b. When t > b, the threshold
values are c3 and c4. The autoregressive coe¢ cients F (r) and the variance-covariance matrix �(r)
may di¤er for r = 1; :::; 6.
8
Galvão (2006) provides Monte Carlo evidence that supports joint estimation of the thresholds
and the break date by conditional maximum likelihood, when there are large changes in the variance
of the shocks across regimes. For each possible value of b in a grid, the sample is split and an ET-
VAR is estimated in each resulting subsample, by solving the grid minimization problem de…ned
by (2), using the sequential approach to de…ne the threshold grids. The grid of b (b�(bL; bU )) has to
be de…ned such that there is a reasonable number of observations in each regime for the ET-VAR
to be estimated. Formalizing:
b^; c^1; c^2; c^3; c^4 = min
bL�b�bU
c1�C1
c2�C2
c3�C3
c4�C4
264 T12 log j�^(1)(c1; c2)j+ T22 log j�^(2)(c1; c2)j+ T32 log j�^(3)(c1; c2)j
T4
2 log j�^(4)(c3; c4)j+ T52 log j�^(5)(c3; c4)j+ T62 log j�^(6)(c3; c4)j
375 : (7)
Finally, when computing impulse responses and con…dence intervals for SB-ET-VAR models,
we apply the procedures described in the Appendix for each subsample separately.
2.3 Choosing the Number of Regimes and Transition Variables
The vast literature on choosing the number of thresholds and break dates relies on test statistics
with non-standard distributions (e.g., Andrews (1993), Hansen (1996)), or on sequential procedures
associated with asymptotic bounds (e.g., Altissimo and Corradi (2002), Gonzalo and Pitarakis
(2002)). These methods are typically applied to univariate models, but they can be extended
to multivariate models estimated by conditional least squares when changes in the variance of
the disturbances across regimes are not important. In our application, changes in the variance-
covariance matrix across regimes are potentially relevant, and the estimation procedure in (7) takes
them into explicit account. As a consequence, the use of testing procedures based on the full sample
sum of squared errors may be misleading.
An alternative simple approach is to use information criteria based on a penalised likelihood
function, where the penalty depends on the number of estimated parameters, to compare speci…-
cations that di¤er for the assumed number of breaks and regimes. The same method can be also
adopted for the selection of the transition variable, among the members of a pre-speci…ed set.
9
We consider only the parameters in z(r) when computing the penalty function, as in Altissimo
and Corradi (2002) and Gonzalo and Pitarakis (2002), and we compute the likelihood as described in
equations (2) and (7). Therefore, the inclusion of a further regime in the model requires the estima-
tion ofm(mp+1) additional parameters. The penalty function can be 2K=T (AIC), 2 log(log(K))=T
(HQC) or log(K)=T (SIC), where K is number of estimated parameters. Altissimo and Corradi
(2002) suggest the HQC penalty to choose the number of regimes in a threshold model, while
Gonzalo and Pitarakis (2002) suggest SIC. For comparison, we will compute all the three criteria,
and use them also for the selection of the transition variable xt, which does not a¤ect the penalty
function but the value of the likelihood.
3 Model speci…cation and estimation results
3.1 Choice of Transition Variable and Taylor rule deviations
Cechetti et al (2007) employ changes in the sign and size of the deviations from the Taylor rule as
a measure of changes in the stance of the monetary policy. They then use the time series of the
deviations from the Taylor rule to assess whether changes in monetary policy can explain the great
moderation in a group of countries. We use a similar measure as transition variable. Speci…cally,
we de…ne the deviations from the Taylor rule as:
xt = 1 + 1:5(pt � pt�4) + 0:5(GDPt �GDPt�4)� it: (8)
The parameters are …xed based on the policy rule proposed by Taylor (1993).3 Taylor (1993) results
suggest that we should observe small xt values in the 1987-1992 period, whileCechetti et al (2007)
indicate large deviations before entering the great moderation period. Given the thresholds c1 and
3Note, however, that Taylor (1993) suggested the rule using output deviations from a linear trend, instead of
annual growth as in equation (8). Because a constant growth rate may not be adequate to detrend output over a long
sample, as we do, and the problems arising from using …ltering methods in real time (as explained by Orphanides
(2001)), we consider the use of annual growth as a good proxy for a measure of current economic activity, see also
Van Norden (1995).
10
c2, with c1 < c2, when xt�1 � c1 the implied regime represents a tight policy stance, since the actual
interest rate is higher than that implied by the Taylor (1993) rule. On the contrary, if xt�1 > c2,
we have a loose stance since the interest rate implied by the Taylor (1993) rule is larger than the
actual rate. Note that by using xt�1 as the transition variable, the policy stance depends on past
monetary policy it�1 and current economic conditions [(pt�1�pt�5) and (GDPt�1�GDPt�5)] since
in real-time it is unlikely that both GDPt and pt are available.
This modelling choice di¤ers from the usual approach of adding Markov-switching to allow for
monetary policy changes in DSGE models (as, e.g., Davig and Doh (2009) and Bianchi (2009)).
Researchers working with DSGE models generally allow the central bank reaction parameters to
change, while using a latent variable to capture regime switches. Another alternative is to let
the target in‡ation to change over time (Ireland, 2007; Levin and Taylor, 2010). In this paper
instead we allow for the dynamic transmission and the size of the shocks to change explicity with
the observed monetary policy stance. Sizeable deviations in (8) - relevant to classify policy stances
(tight and loose) - can result from changes in the systematic (parameters) or nonsystematic (shocks)
components, and we cannot disentangle the two e¤ects. However, this is not problematic since our
focus in on assessing how the same policy decision - an increase in the policy rate by 25 basis points
- a¤ects di¤erently future output and prices depending on the current monetary policy stance,
also allowing for regime shifts depending on the response of the endogenous variables (economic
conditions and policy rate) to the monetary shock.
Using equation (8) as transition variable, we compare the full sample VAR, the VAR with
estimated breaks (SB-VAR), the ET-VAR model (eq. 1), and the SB-ET-VAR model (eq. 6).
When de…ning the grid to estimate the models with thresholds and breaks, we set restrictions
based on the minimum proportion of observations in each regime in a given subsample.4 Table 1
4Speci…cally, we require at least 30% of observations in each regime. In the case of an SB-ET-VAR model, this
restriction applies separately for each subsample. Other papers in the literature normally set the proportion equal
to 10 or 15%. However, because of the relative short sample size and the impact that parameter estimates have on
impulse responses, we prefer to consider at least 30% of observations in each regime.
11
reports information criteria for all these alternative speci…cations, including speci…cations with two
instead of three regimes.
Table 1 suggests that the ET-VAR with three regimes has a better penalised …t than the VAR,
that is, there is evidence of endogenous regime switches when using the Taylor rule as transition
variable. However, the VAR speci…cation with a break in the thresholds (the SB-ET-VAR model
with six regimes) yields the lowest AIC. In addition, in comparison with the SB-VAR model,
the SB-ET-VAR model also shows improvement in …t, implying that endogenous switches and a
break are both required to …t the dynamic responses. Information criteria with heavier penalties,
such as HQC and SIC, support the SB-VAR. However, the latter information criteria are more
adequate to choose the number of regimes for forecasting rather than for structural analysis. In
the case of forecasting the selection of a parsimonious model is often an advantage, while it can be
a disadvantage for structural analyses like ours, since it can distort estimated dynamic responses.
The use of deviations from the Taylor rule as transition variable has not been considered before,
but the literature provides evidence of monetary policy asymmetries when employing output growth
(Weise, 1999) and in‡ation (Davig and Leeper, 2008). As a consequence, we added to Table 1
information criteria to evaluate the …t of ET-VAR and SB-ET-VAR based on alternative transition
variables. We evaluate output growth (xt = GDPt �GDPt�4), in‡ation (xt = pt � pt�4), and the
ex-post real interest rate (xt = it � (pt � pt�4)) as transition variables. The ex-post real interest
rate is a measure of deviations from a policy rule that depends only on in‡ation.
The results indicate that models with in‡ation as transition variable, in particularly ET-VAR(3)
and ST-ET-VAR(6), …t better than models with deviations from the Taylor rule as transition vari-
able. The improved …t mainly arises from allowing for regime-dependent variances. An evaluation
of output responses to a 25-basis-point shock computed using in‡ation as transition variable sug-
gests no asymmetries in the …rst subsample and only limited asymmetries in the second subsample.5
Since the main purpose of this paper is to identify asymmetric responses of output and prices to
monetary policy shocks as a …rst step to understand the impacts of good luck and good policy
5Results available on request.
12
in explaining the great moderation, we prefer to use the SB-ET-VAR(6) model with Taylor rule
deviations as transition variable, which generates sizable asymmetries in the transmission of policy
shocks within subsamples and across subsamples, as we will see in detail in the next Section.
A …nal interesting issue to consider is whether our approach manages to capture the het-
eroscedasticity usually found in the residuals of similar VAR models (Primiceri, 2006). We test
for remaining conditional heteroscedasticity by regressing the squared residuals from the SB-ET-
VAR (eq. 6) on dummies representing changes in the variance for each regime, and on lagged
squared residuals. Under the null hypothesis of no remaining heteroscedasticity, an F-test for the
non-signi…cance of the coe¢ cients of the lagged squared residuals should not reject. The results
presented in Table 2 suggest no evidence of remaining heteroscedasticity in the output and price
equations . There is instead some evidence of heteroscedasticity in the interest rate equation, but a
split sample analysis reveals that this is a characteristic of the pre-1985 period only. Based on this
analysis, we can conclude that our SB-ET-VAR with Taylor rule deviations as transition variables
captures su¢ ciently well changes in the variances of the shocks a¤ecting the three variables under
analysis.
3.2 A Chronology of the US Monetary Policy Stance
In this subsection we discuss the estimates of the thresholds and of the break date resulting from
the SB-ET-VAR, and the implied chronology of policy stance regimes.
The break date estimate is 1985Q1. This point in time comes after a prolonged period of tight
monetary policy stance (as we will discuss shortly), which can have increased the credibility of the
central bank. Based on credibility of monetary policy measures computed based on both Laxton
Diaye (2002) and Demertzis et al. (2012), we can show a major increase in the credibility after
1985Q1.6 We are aware of the existence of several other possible explanations for the break in 1985,
such as learning by the policy makers, faster globalization, improvements in inventory management,changes in the target level of in‡ation, changes in the Taylor rule itself, etc. As mentioned, we do
6Results are not shown to save space, but are available on request.
13
not want to investigate this issue further since we want to focus on the consequences of changes in
the policy stance, and therefore we estimate the break as a function of a time trend. However, we
believe that our proposed credibility based explanation for the identi…ed break in 1985 is sensible
and in line with the response functions that we will compute later on. In particular, a more
credible central bank that implements a restrictive policy should incur lower output losses and be
more successful in …ghting in‡ation, see e.g. Goodfriend and King (2005), which is exactly what
we …nd on average after 1985.
Table 3A presents the estimated thresholds and their 90% con…dence intervals computed by
bootstrap for each subsample based on the estimated 1985Q1 break. As common in this type of
models, the thresholds are rather imprecisely estimated. However, the lower threshold in the …rst
subsample (c^1 = 1:68) falls outside the 90% interval for the lower threshold in the second subsample
(c^3 = 0:18), and for the upper threshold in the …rst subsample (c^2 = 3:91). The estimated threshold
values imply that the criterion to identify a tight monetary policy stance after the break is more
stringent than before the break. They also suggest that positive deviations from the Taylor rule
are more likely before than after the break.
Finally, the resulting chronology of regimes is plotted in Figure 1. The plot in the lower panel
also includes the chronology of the chairmen of the Federal Reserve Bank during the period, since
the literature frequently correlates them with changes in the central bank preferences (see, for
example, Fernandez-Villaverde et al, 2010), which may partially explain why the current interest
rate deviates from the rule set by Taylor (1993). Taylor (1993) suggests that his rule …ts well data
in the 87-92 period. Our estimated thresholds and break also support this evidence since the model
identi…es the middle regime (small deviations from the Taylor rule) for the largest part of the 87-92
period. In terms of identi…cation of the monetary policy stance before the 1985 break, the tight
stance (regime 1, xt�1 < c^1) is mainly identi…ed in the 1980-84 period, with some shorter episodes
in the ’60s, while the period of loose stance (regime 3, xt�1 > c^2) is largely associated with the 70’s.
After the 1985 break, it is harder to associate regimes with time periods, since the regime-switching
is more frequent among all three regimes. However, the loose monetary stance (regime 6, xt�1 >
14
c^4) is mainly associated with the 2002-2006 period.
Figure 1 shows that for a given chairman, normally associated with a speci…c policy strategy and
preferences regarding output and in‡ation deviations, the policy stance can vary. The policy stance
may vary during a given chairmanship because deviations from the Taylor rule may be explained
not only by central bank preferences, but also by shocks to economic conditions and past policy
decisions. However the evidence in Figure 1 suggests that a chairman service period may have a
predominant policy stance. For example, regime 3 (loose) is prevalent in the Burns-Miller period,
while regimes 1 and 4 (both refer to tight policy stances) de…ne the Volcker period. In contrast, the
period of Greenspan service as a chairman covers all monetary policy stances with no predominant
regime, though the stance was clearly loose in the …nal part of his mandate (in line with Taylor
(2007)).
3.3 Time-varying Volatility
The SB-ET-VAR can also measure shifts in the variances of the structural shocks. Of interest
is to check how much the variance of the shocks has changed, and whether the changes are only
related to the break in 1985 or also to the di¤erent regimes associated with policy stances. Table
3B presents the standard deviations of the output, prices and monetary policy shocks (elements of
the �^(r) matrix) for each regime within a subsample and their 90% con…dence intervals computed
by bootstrap as described in Appendix B.
The results indicate that the standard deviation of output and policy shocks in the outer regimes
(loose and tight) are statistically lower after the break in comparison with equivalent regimes before
the break. We investigate in Section 5 whether this initial evidence of good luck (reduction in
the volatility of output and policy shocks) can explain the observed changes in the endogenous
variables. The shocks’volatilities do not generally di¤er across regimes within the same subsample.
An exception is found by comparing the standard deviation of policy shocks in the …rst subsample:
the volatility during the neutral regime is statistically lower than the one in the outer regimes.
Since the outer regimes are more frequent during the 1970-1985 period and the inner regime is
15
frequent in the 1960-1970 period, this could be an evidence that surprising changes in the policy
rate were more important during the Burns-Miller and Volcker chairmenships (see Figure 1) than
during Martin’s chair service.
4 The transmission of monetary policy and the policy stance
We now discuss how the e¤ects of monetary policy have changed over periods and depending on the
stance, according to our estimated SB-ET-VAR model. In the previous section, we have detected
substantial changes in the average size of the shocks that, due to the nonlinearity of the model, could
by themselves determine also changes in their transmission (see, e.g., Ravn and Sola (2004)). For
example, a large shock can trigger more easily switches in regimes than a smaller shock. However, as
argued by Boivin et al (2011), from an economic point of view it is more interesting and informative
to focus on changes in the transmission of a monetary policy shock of a …xed size. Hence, Figures
2-3 present the dynamic response to a 25 basis point increase in the interest rate at time t of output
(Figure 2) and prices (Figure 3).7
The responses (black line) are computed as described in equation (5) using v(r)j;t+1 = (0; 0; :25)
0 ,
that is, they are the average response over all histories from a speci…c regime allowing for regime-
switching over the horizon of up to 20 quarters. All six regimes identi…ed in the estimated SB-ET-
VAR are represented in the …gures. We recall that regimes 1 and 4 describe tight monetary stance
before and after the 1985 break, while regimes 3 and 6 are associated with loose monetary policy.
The plots also include 68% and 90% con…dence intervals computed by the bootstrap procedure
described in Appendix B, and the responses computed without allowing for regime switching as a
consequence of the shocks (eq. 4).
We use Figures 2 and 3 to answer two main questions. First, is there any statistical evidence
in favour of signi…cant di¤erences in the transmission of shocks depending on the policy stance?
7We only present results for positive shocks. Preliminary results with the chosen model indicate no signi…cant
asymmetries in the dynamic responses from the sign of the shocks even when comparing increases with decreases of
100 basis points.
16
Second, are there any changes in the transmission of shocks that can be associated with an im-
provement of monetary policy after the 1985 break?
With reference to the …rst question, Figures 2 and 3 present evidence that the transmission of
monetary policy shocks is indeed a¤ected by the monetary policy stance. After 1985, the monetary
policy has a negative e¤ect on output and prices only in the tight regime using 90% con…dence
bands. By using 68% con…dence bands, we …nd negative e¤ects on output also in themiddle regime.
Before 1985, there is a stronger negative e¤ect on prices at long horizons in the tight regime (reg
1) in comparison with the loose regime (reg3); and a stronger e¤ect on the output response after 8
quarters in the middle regime in comparison with the outer regimes.
About the second question, we also …nd some support for "good policy" as a driver of the
great moderation. In particular, as mentioned before, Figure 1 illustrates that the early ’80s were
characterized by a long period of tight policy that likely re-established the credibility of the central
bank, magnifying the e¤ects of the continued tight policy after 1985 and up to about 1987 (again
see Figure 1). Speci…cally, the e¤ects on prices and output of a policy shock with a tight stance at
the impact (regimes 1 and 4) are rather di¤erent. Before 1985, it takes 10 quarters to …nd evidence
of a negative e¤ect on prices, while this happens already after 1 quarter after 1985 (Figure 3). The
transmission on output also changes. The negative e¤ect on output is faster before 1985 than after
1985, although the marginal e¤ect after 8 quarters (around -.3) is similar. Similar changes in the
reaction of output and prices before and after 1985 are observed for the middle regimes (regimes 2
and 5), where the actual interest rate is close to that required by the Taylor rule.
In comparison with studies reviewed by Boivin et al (2011), our model allows us to shift the
focus from changes in the transmission of monetary policy shocks caused by changes of the chair-
man of the Federal Reserve Bank to changes caused by the monetary policy stance. Recall that
the chronology described in Figure 1 indicates that the stance may vary during the period of a
chairman service. The evidence provided in Figures 2 and 3 supports the claim that output and
prices dynamic responses from a 25-basis point unexpected change in the policy rate change with
the monetary policy stance, measured by deviations from the Taylor (1993) rule with respect to
17
estimated thresholds.
Finally, it is worth commenting on the responses that do not allow for a regime switch triggered
by the dynamic transmission of the shock (the dashed lines in Figures 2 and 3). In a few cases, in
particular during the loose regimes 3 and 6, they can be signi…cantly di¤erent from the responses
that we have commented so far. Hence, in order to avoid biased results, it is important to allow for
the shock to trigger a change in regime rather than simply conditioning the responses on a given
regime.
To conclude and summarize, using our SB-ET-VAR model, this Section has highlighted changes
in the transmission of monetary policy shocks to output and in‡ation, related to a di¤erent mon-
etary policy stance. With …xed size shocks, there are statistically signi…cant di¤erences in shock
transmission across regimes only after 1985.
5 Counterfactual analysis
The previous Sections have shown that the contemporaneous and dynamic relationships across
output, prices and interest rates are quite di¤erent before and after 1985 and depending on how far
the observed policy rate is from the one implied by the Taylor rule, describing periods of tight and
loose policy stance. In this Section we speculate on what would have happened if a single regime
was in place over the entire sample period, or if the coe¢ cients of a given regime did not change
before and after 1985. The …rst type of experiment could shed light, for example, on what would
have happened if the interest rate was always kept close to the value implied by the Taylor rule,
that is, a "good policy story". The second type of experiment would provide additional information
about the role of the structural break in 1985, likely associated with the regained credibility of the
central bank.
Of course this kind of counterfactual analysis is open to a wide range of criticisms. Therefore,
we do not want to provide any strong policy advice based on the results. We just think of these
experiments as another useful way to analyze the properties of our SB-ET-VAR model, and to get
18
information on the relative role of good policy and good luck in determining the lower volatility of
output and the lower level and volatility of in‡ation after 1985.
Let us start with counterfactuals based on a single regime. From the computational point of
view, we use the estimated coe¢ cients for a given policy stance before and after 1985 (e.g., regimes
1 and 4 in the case of tight policy stance), the actual values for output, prices and interest rate in
1960Q1 and 1985Q1 as starting values, and then solve the model forward …rst for 1960Q2-1985Q1
and then for 1985Q2-2009Q1, adding in each period the estimated SB-ET-VAR residuals. In this
way we obtain generated time series for the three variables, conditional on being always in a speci…c
monetary policy stance. In Figure 4 we report the resulting series for output, prices and interest
rate using estimates of the middle regime (small deviations from Taylor rule) for the entire period,
together with the actual time series.
According to the upper panel of Figure 4, if the interest rate had followed closely the Taylor rule,
the volatility of output would have increased during the 1960-1984 period, yielding in particular
higher growth during the recoveries following the recessions of 1974 and 1981-82, and during the
period 1978-79. The rationale for this positive growth result is the much lower interest rates
resulting from the lower panel of Figure 4 around 1974 and 1981-82. But there is a cost: the much
higher and persistent in‡ation during 1979-1984, see the middle panel of Figure 4. Interestingly,
the interest rate spike in 1979-80 is compatible with a normal (Taylor rule based) policy stance, the
di¤erence is with the subsequent behaviour of the interest rate, which was kept at an higher level
than that required by the Taylor rule (indeed the post 1980 period is identi…ed as a tight stance,
see Figure 1).
It is also important to mention that the decrease in in‡ation after 1985 resulting from Figure
4 is mostly due to the re-initialization of the simulated series (based on the actual 1985Q1 value
of in‡ation) and to the new set of parameters characterizing the middle regime. In other words,
without these changes, in‡ation would have remained at a higher level for a longer period. Hence,
the parameter break in 1985 played an important role and good policy by itself (broadly following
a Taylor rule) does not seem su¢ cient to lower in‡ation and the volatility of output.
19
Looking at the post 1985 period in Figure 4, a policy rate that closely follows the one implied
by the Taylor rule would have implied on average slightly lower interest rates over the 1995-2003
period, but higher ones afterwards (again in line with the timing of the regimes in Figure 1).
Overall, there would have been slightly positive average e¤ects on output, and no costs in terms of
higher in‡ation.
Given the important consequences of the 1985 break emerging from the …rst type of counter-
factual, we now consider an experiment that let us better assess its role. From the computational
point of view, we use the estimated coe¢ cients for the three regimes before 1985 (including the
estimated thresholds) for the entire sample period, actual values for output, prices and interest
rate in 1985Q1, and then solve the model forward for the period 1985Q2-2009Q1, adding in each
period the estimated SB-ET-VAR residuals. In this way we obtain generated time series for the
three variables, conditional on the pre-1985 parameters but on the post-1985 shocks. The resulting
series for output, prices and interest rate are reported in Figure 5.
If the Great Moderation, that is, the reduction in the volatilityof output and in‡ation (and
other variables), was purely due to "good luck", namely to smaller shocks, it should emerge from
Figure 5, since the simulated values are based on the post-1985 shocks, whose variance is indeed
smaller than in the pre-1985 period (see Figure 4). Instead, both the levels and the volatility of
output and in‡ation are fairly close to the pre-1985 values, actually even higher.
The …nal exercise we consider is a mixture of the …rst two cases. Speci…cally, we use the pre-1985
parameters coming from the tight policy stance only, to simulate data for the post-1985 period,
conditional on the post-1985 SB-ET-VAR residuals. The goal is to understand whether a tight
policy stance enforced over the entire post-1985 period, combined with the smaller post-85 shocks,
could have reduced the volatility of output and the level and volatility of in‡ation, in the absence
of the parameter changes that took place around 1985. The results are reported in Figure 6.
A comparison of Figures 5 and 6 shows that a tight monetary policy stance is indeed helpful
in reducing the volatility of output and the level of in‡ation, but it is de…nitely not su¢ cient to
replicate the actual behaviour, of growth, in‡ation, and the interest rate.
20
Overall, the lesson from this Section is that a policy stance that keeps the interest rate close
to the Taylor-rule implied rate is helpful in reducing growth volatility and the level of in‡ation.
However, this is not su¢ cient to explain what happened to the US growth and in‡ation after 1985.
The reduction in the volatility of the shocks is also not a su¢ cient explanation, according to our
model, since using the pre-85 VAR parameters with the post-85 shocks still generates substantial
growth volatility and in‡ation after 1985. What is needed is a more general change in the VAR
parameters, namely, in the contemporaneous and dynamic transmission of the shocks. This could
be related to the increased credibility of monetary policy, or to other factors, whose investigation
is beyond the scope of the present paper.
6 Conclusions
In this paper we analyze the speci…cation and estimation of a structural break endogenous threshold
VAR model (SB-ET-VAR), and consider its use to compute impulse response functions. We also
contribute to the literature on the changing transmission mechanism of monetary policy by using
a model whose parameter evolution explicitly depends on the monetary policy stance.
Empirically, we model prices, aggregate output, and the policy interest rate with an SB-ET-
VAR, whose parameters are subject to a structural break at an estimated date and to periodic
changes related to how close or far the interest rate is from the level prescribed by the Taylor rule.
The resulting model, with a break in the …rst quarter of 1985 and three regimes in each of the
subperiods identi…ed by the break date, …ts the data well in comparison with alternatives with
fewer regimes and di¤erent transition variables. In addition, we …nd evidence that the volatility of
output and policy shocks changes across subsamples for equivalent regimes, and that policy shocks
during the 1960-70 period are generally smaller than during the 1970-85 period.
The model generates responses of output and prices to 25-basis points monetary policy shocks
that change not only before and after 1985 but also according to the monetary policy stance.
Restrictive monetary policy has stronger negative e¤ects on output before 1985, but takes time to
21
reduce prices, even when the monetary stance is tight. After 1985, the e¤ects on output and prices
are only signi…cantly negative when the current policy stance is tight, and the negative e¤ect on
prices is faster.
A set of counterfactual experiments con…rms that good monetary policy is helpful to reduce the
level of in‡ation, and also the volatility of output growth. However, the extent of the reduction is
not su¢ cient to explain what happened to the US growth and in‡ation after 1985. The reduction in
the volatility of the shocks is also not a su¢ cient explanation, according to our model, since using
the pre-85 VAR parameters with the post-85 shocks still generates substantial growth volatility and
in‡ation after 1985. Therefore, we conclude that both good policy and good luck were relevant to
explain part of the reduction in the level and volatility of in‡ation and growth
Finally, our evidence of asymmetries in the transmission policy shocks depending on how far
the actual policy rate is from the one implied by the Taylor (1993) rule is also a contribution to
the literature that has found asymmetries depending on business cycle phases and the degree of
in‡ationary pressure (as Weise (1999) for example). This new evidence of asymmetric transmission
of monetary policy could also inspire research developments in structural modelling in the same
way that Davig and Leeper (2008) proposed changes in DSGE models as response to the evidence
of asymmetric transmission depending on in‡ation levels.
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A Computation of Impulse Response Functions
In this Appendix, we describe how we compute both conditional means required for the computation
of gr;j;s (eq. 5). Based on the estimates of �
(r)
i and of the thresholds, we can draw an s�m matrix
from each N(0;�(r)) (for r = 1; 2; 3) such that sequences of y�t+1; :::; y�t+s can be computed using
one row of 
(r)t as initial value. The gr;j;s will be the di¤erence between two average sequences of
y�t+1; :::; y�t+s: one with v
(r)
j;t+1 = a
(r)
j and the other with v
(r)
j;t+1 = 0. By using the same draws from
each N(0;�(r)) to compute both conditional means, we guarantee that the only di¤erence between
them is the e¤ect of the structural shock at t+ 1. Note also that the gr;j;s is the average across all
vector of histories in 
(r)t . This means that if Tr = 50 and we draw 1000 times from N(0;�
(r)), the
gr;j;s is computed using the average across 50 � 1000 replications.
26
B Con…dence intervals for the Parameters and Impulse Response
Functions
Let us label bgr;j;s the impulse response function based on the conditional maximum likelihood
estimates �^(r)i , �^
(r), c^1 and c^2. As described by Canova (2007, p. 134), a typical issue in applying
the bootstrap to compute con…dence intervals for impulse responses obtained from linear models
is that the bootstrapped distributions are not scale invariant, implying that standard error bands
may not include the point estimates. In addition, VAR estimates using small samples are severely
downward biased. Unfortunately, techniques of bias correction such as those described in Kilian
(1998) cannot be applied since the uncertainty in the ET-VAR parameters depends strongly on
the uncertainty about the threshold estimation, while the empirical distribution of the threshold
estimates may be quite asymmetric (Kapetanios, 2000).
Our bootstrap approach attempts to solve some of these issues. The …rst step is to draw with
replacement sequences of length T � p from all "(r)t (r = 1; 2; 3), and use the estimates �^(r)i , �^(r),
c^1 and c^2 and initial values of yt (t = 1; :::; p) to generate bootstrapped sequences of y��p+1; :::; y��T .
For each of these sequences, conditional maximum likelihood is applied to obtain estimates of
all the parameters, that is, �^��(r)i , �^
��(r), c^��1 and c^��2 . Using these parameters and the speci…c
bootstrapped sequence, we compute g��r;j;s using the simulation procedure described previously. By
repeating the bootstrapped procedure B times, an empirical distribution for the gr;j;s is obtained.
Using the B values of g��r;j;s, we compute �grf��r:j:s = 1=B
PB
b=1 g
��
r;j;s;b and the empirical quan-
tiles q�=2g��r:j:s and q
(1��=2)
g��r:j:s
for 100(1 � �)% con…dence intervals. Using the empirical quantiles and
the empirical mean of the impulse response function, the range of the 100(1 � �)% con…dence
intervals is computed, that is, rLO = abs(q
�=2
g��r:j:s
� �g��r:j:s) and rUP = abs(q
(1��=2)
g��r:j:s
� �g��r:j:s). As a
result, centred con…dence intervals, but potentially asymmetric and skewed, can be computed as
fbgr;j;s � rLO; bgr;j;s + rUP g. We emphasize that these intervals consider uncertainty on both coe¢ -
cient and threshold estimates.
Using the B values of �^��(r), c^��1 and c^��2 , we compute empirical quantiles to de…ne the range
27
of con…dence intervals for the estimates of the standard deviations of the shock (elements of �^(r))
and thresholds.
28
29 
 
 
Figure 1: The six regimes identified by the SB-ET-VAR model. 
Note: The transition function is: =0 in regime 1, =.2 in regime 2, =.4 in regime 3, =.6 in regime 4, =.8 in regime 5, and =1 
in regime 6. 
-0.1
0.1
0.3
0.5
0.7
0.9
1.1
-8
-6
-4
-2
0
2
4
6
8
10
19
60
Q2
19
61
Q4
19
63
Q2
19
64
Q4
19
66
Q2
19
67
Q4
19
69
Q2
19
70
Q4
19
72
Q2
19
73
Q4
19
75
Q2
19
76
Q4
19
78
Q2
19
79
Q4
19
81
Q2
19
82
Q4
19
84
Q2
19
85
Q4
19
87
Q2
19
88
Q4
19
90
Q2
19
91
Q4
19
93
Q2
19
94
Q4
19
96
Q2
19
97
Q4
19
99
Q2
20
00
Q4
20
02
Q2
20
03
Q4
20
05
Q2
20
06
Q4
20
08
Q2
Deviations from the Taylor rule and Regime SwitchingTaylor rule Deviations (left) transition function (right)-0.1
0.1
0.3
0.5
0.7
0.9
1.1
19
60
Q2
19
61
Q4
19
63
Q2
19
64
Q4
19
66
Q2
19
67
Q4
19
69
Q2
19
70
Q4
19
72
Q2
19
73
Q4
19
75
Q2
19
76
Q4
19
78
Q2
19
79
Q4
19
81
Q2
19
82
Q4
19
84
Q2
19
85
Q4
19
87
Q2
19
88
Q4
19
90
Q2
19
91
Q4
19
93
Q2
19
94
Q4
19
96
Q2
19
97
Q4
19
99
Q2
20
00
Q4
20
02
Q2
20
03
Q4
20
05
Q2
20
06
Q4
20
08
Q2
Regime Switching and the Chairman of the Federal Reserve
transition function
Burns-Miller BernankeMartin Volcker
Greenspan
loose
tight
loose
tight
30 
 
 Regime 1: Tight Regime 2: Middle Regime 3: Loose 
 
 Regime 4: Tight Regime 5: Middle Regime 6: Loose 
 
Figure 2: Responses of output to monetary policy shocks (25 basis point shock): IRFs with 68% (dark grey) and 90% (light grey) confidence intervals. Dashed 
black line is response when regime-switching is not allowed. 
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 3 5 7 9 11 13 15 17 19
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 3 5 7 9 11 13 15 17 19
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 3 5 7 9 11 13 15 17 19
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 3 5 7 9 11 13 15 17 19
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 3 5 7 9 11 13 15 17 19
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 3 5 7 9 11 13 15 17 19
31 
 
 Regime 1: Tight Regime 2: Middle Regime 3: Loose
 
 Regime 4: Tight Regime 5: Middle Regime 6: Loose
 
Figure 3: Responses of Prices to Monetary Policy Shocks (25 basis point shock): IRFs with 68% (dark grey) and 90% (light grey) confidence intervals. Dashed 
black line is response when regime-switching is not allowed. 
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 3 5 7 9 11 13 15 17 19
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 3 5 7 9 11 13 15 17 19
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 3 5 7 9 11 13 15 17 19
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 3 5 7 9 11 13 15 17 19
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 3 5 7 9 11 13 15 17 19
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 3 5 7 9 11 13 15 17 19
32 
 
 
Figure 4. Counterfactual: Always in the middle regime (reg2 and reg5) in each subsample. Black line is 
observed data; grey line is the simulated counterfactual. 
 
-5
0
5
10
15
20
19
60
Q2
19
62
Q2
19
64
Q2
19
66
Q2
19
68
Q2
19
70
Q2
19
72
Q2
19
74
Q2
19
76
Q2
19
78
Q2
19
80
Q2
19
82
Q2
19
84
Q2
19
86
Q2
19
88
Q2
19
90
Q2
19
92
Q2
19
94
Q2
19
96
Q2
19
98
Q2
20
00
Q2
20
02
Q2
20
04
Q2
20
06
Q2
20
08
Q2
Growth
-4
-2
0
2
4
6
8
10
12
14
16
19
60
Q2
19
62
Q2
19
64
Q2
19
66
Q2
19
68
Q2
19
70
Q2
19
72
Q2
19
74
Q2
19
76
Q2
19
78
Q2
19
80
Q2
19
82
Q2
19
84
Q2
19
86
Q2
19
88
Q2
19
90
Q2
19
92
Q2
19
94
Q2
19
96
Q2
19
98
Q2
20
00
Q2
20
02
Q2
20
04
Q2
20
06
Q2
20
08
Q2
Inflation
-2
0
2
4
6
8
10
12
14
16
18
19
60
Q2
19
62
Q2
19
64
Q2
19
66
Q2
19
68
Q2
19
70
Q2
19
72
Q2
19
74
Q2
19
76
Q2
19
78
Q2
19
80
Q2
19
82
Q2
19
84
Q2
19
86
Q2
19
88
Q2
19
90
Q2
19
92
Q2
19
94
Q2
19
96
Q2
19
98
Q2
20
00
Q2
20
02
Q2
20
04
Q2
20
06
Q2
20
08
Q2
Fed Rate
33 
 
 
Figure 5. Counterfactual: Using pre-1985 estimates (including threshold values) for the period after 1985 
Black line is observed data; grey line is simulated counterfactual. 
-4
-2
0
2
4
6
8
10
12
19
85
Q1
19
86
Q1
19
87
Q1
19
88
Q1
19
89
Q1
19
90
Q1
19
91
Q1
19
92
Q1
19
93
Q1
19
94
Q1
19
95
Q1
19
96
Q1
19
97
Q1
19
98
Q1
19
99
Q1
20
00
Q1
20
01
Q1
20
02
Q1
20
03
Q1
20
04
Q1
20
05
Q1
20
06
Q1
20
07
Q1
20
08
Q1
20
09
Q1
Growth
0
2
4
6
8
10
12
14
16
19
85
Q1
19
86
Q1
19
87
Q1
19
88
Q1
19
89
Q1
19
90
Q1
19
91
Q1
19
92
Q1
19
93
Q1
19
94
Q1
19
95
Q1
19
96
Q1
19
97
Q1
19
98
Q1
19
99
Q1
20
00
Q1
20
01
Q1
20
02
Q1
20
03
Q1
20
04
Q1
20
05
Q1
20
06
Q1
20
07
Q1
20
08
Q1
20
09
Q1
Inflation
0
5
10
15
20
25
30
19
85
Q1
19
86
Q1
19
87
Q1
19
88
Q1
19
89
Q1
19
90
Q1
19
91
Q1
19
92
Q1
19
93
Q1
19
94
Q1
19
95
Q1
19
96
Q1
19
97
Q1
19
98
Q1
19
99
Q1
20
00
Q1
20
01
Q1
20
02
Q1
20
03
Q1
20
04
Q1
20
05
Q1
20
06
Q1
20
07
Q1
20
08
Q1
20
09
Q1
Fed Rate
34 
 
 
Figure 6: Counterfactual: Using the tight regime estimated with data before 1985 (regime 1) during the post-
1985 period. Black line is observed data; grey line is simulated counterfactual. 
-4
-2
0
2
4
6
8
10
19
85
Q1
19
86
Q1
19
87
Q1
19
88
Q1
19
89
Q1
19
90
Q1
19
91
Q1
19
92
Q1
19
93
Q1
19
94
Q1
19
95
Q1
19
96
Q1
19
97
Q1
19
98
Q1
19
99
Q1
20
00
Q1
20
01
Q1
20
02
Q1
20
03
Q1
20
04
Q1
20
05
Q1
20
06
Q1
20
07
Q1
20
08
Q1
20
09
Q1
Growth
0
2
4
6
8
10
12
14
19
85
Q1
19
86
Q1
19
87
Q1
19
88
Q1
19
89
Q1
19
90
Q1
19
91
Q1
19
92
Q1
19
93
Q1
19
94
Q1
19
95
Q1
19
96
Q1
19
97
Q1
19
98
Q1
19
99
Q1
20
00
Q1
20
01
Q1
20
02
Q1
20
03
Q1
20
04
Q1
20
05
Q1
20
06
Q1
20
07
Q1
20
08
Q1
20
09
Q1
Inflation
0
5
10
15
20
25
30
19
85
Q1
19
86
Q1
19
87
Q1
19
88
Q1
19
89
Q1
19
90
Q1
19
91
Q1
19
92
Q1
19
93
Q1
19
94
Q1
19
95
Q1
19
96
Q1
19
97
Q1
19
98
Q1
19
99
Q1
20
00
Q1
20
01
Q1
20
02
Q1
20
03
Q1
20
04
Q1
20
05
Q1
20
06
Q1
20
07
Q1
20
08
Q1
20
09
Q1
Fed Rate
35 
 
Table 1: Measures of Fit of Different SpecificationsModel N. Regimes Lik AIC HQC SIC 
Transition Variable: Taylor Rule Deviations 
VAR 1 -537.673 5.70 5.84 6.05 
SB-VAR 2 -422.533 4.74 5.02 5.44 
ET-VAR 2 -689.114 7.46 7.75 8.16 
ET-VAR 3 -452.220 5.26 5.68 6.31 
SB-ET-VAR 4 -466.281 5.62 6.18 7.02 
SB-ET-VAR 6 -305.687 4.41 5.26 6.51 
Transition variable: output growth 
ET-VAR 2 -498.880 5.52 5.80 6.22 
ET-VAR 3 -437.806 5.11 5.53 6.17 
SB-ET-VAR 4 -427.122 5.22 5.78 6.62 
SB-ET-VAR 6 -313.113 4.48 5.33 6.59 
Transition variable: inflation 
ET-VAR 2 -595.270 6.50 6.79 7.21 
ET-VAR 3 -366.053 4.38 4.80 5.43 
SB-ET-VAR 4 -422.533 4.74 5.02 5.44 
SB-ET-VAR 6 -263.687 3.98 4.83 6.08 
Transition variable: ex-post real interest rate 
ET-VAR 2 -531.718 5.85 6.14 6.56 
ET-VAR 3 -462.904 5.37 5.79 6.42 
SB-ET-VAR 4 -480.932 5.76 6.33 7.17 
SB-ET-VAR 6 -315.813 4.51 5.36 6.62 
 
Note: All estimates are with p=2; sample period 1960Q2-2009Q1 
 
 
Table 2: Tests for remaining heteroscedasticity in the SB-ET-VAR (6 regimes). 
Test on Disturbances from: Wald [pv] 
Output equation 4.39 [.11] 
Price equation 3.99[.14] 
Fed fund equation 17.80[.01] 
Fed fund equation 
(first subsample) 
9.07[.01] 
Fed fund equation 
(second subsample) 
1.62[0.44] 
 
Note: The SB-ET-VAR uses the Taylor rule deviations as transition variable. The 
test statistics are computed with an auxiliary regression (LM) of squared residuals 
on dummies to capture regime-dependent changes and with two lags of squared 
residuals. The null hypothesis of homoscedasticity is that the coefficients on the 
lag-squared disturbances are zero. 
 
36 
 
Table 3: Estimates of Thresholds and Standard Deviations of Shocks. 
3A: Threshold Estimates. 
Before the 1985Q1 break 
 ̂ 
 ̂ 
{0.083,3.953} {1.873,5.889} 
After the 1985Q1 break 
 ̂ ̂ 
 
{-0.630,1.643} {-0.696,8.128} 
 
3B: Standard Deviations of Shocks 
Regime Classification: Output Prices Monetary Policy 
reg 1 Tight 0.647 
{0.484, 0.819} 
0.235 
{0.187, 0.289} 
0.901S 
{0.706, 1.101} 
reg 2 On Target 0.688 
{0.517, 0.866} 
0.258 
{0.191, 0.336} 
0.562R,S 
{0.163, 0.969} 
reg 3 Loose 0.851S 
{0.641,1.062} 
0.241 
{0.193,0.289} 
1.226R,S 
{0.925, 1.639} 
1985Q1 Break 
reg 4 Tight 0.374S 
{0.170,0.846} 
0.245 
{0.091,0.645} 
0.267S 
{0.185, 0.375} 
reg 5 On Target 0.520 
{0.296,0.948} 
0.210 
{0.009,0.931} 
0.310 
{0.245, 0.382} 
reg 6 Loose 0.427S 
{0.199,0.838} 
0.290 
{0.043, 0.984} 
0.284S 
{0.216, 0.366} 
 
 
Note: S indicates statistically different across subsamples for equivalent regime. R indicates 
statistically different across regime within subsample. {} describe 90% confidence-interval 
limits computed by bootstrap as described in Appendix B. Number of bootstrap replications: 
500.