Download What is the ECB Reaction Function? A Static and

What is the ECB Reaction Function?
A Static and Dynamic Probit Analysis *
Carlo Rosa a
ABSTRACT
We examine the role of the European Central Bank (ECB) communication to identify which
macroeconomic variables guide its monetary policy decisions. Moreover, we propose a
dynamic ordered probit specification of discrete changes to model the ECB policy rate. We
find that interest rate decisions are closely tied to business and consumer surveys rather than
to the real time estimate of the output gap. Contrary to the previous literature, we show that
once the econometric model is correctly specified the ECB also reacts to inflation shocks,
especially core inflation and inflation expectations rather than realized headline inflation.
Formal model comparison based on Bayes factors provides decisive evidence that the
dynamic probit model better takes into account both the discreteness and the serial correlation
displayed by policy rates compared to a standard ordered probit specification.
Keywords: Bayesian econometrics, Markov Chain Monte Carlo, Gibbs sampling, monetary
policy rules, European Central Bank, central bank communication, dynamic ordered probit.
JEL classification: E43, E52, E58.
________________________
*
I thank seminar participants at CORE, Dutch National Bank, Einaudi Institute, London School of Economics and the Kiel
Institute for the World Economy, and especially David Ardia, Luc Bauwens, Gianluca Benigno, Kai Carstensen, David-Jan
Jansen, Emmanuel Frot, Felix Hammermann, Christian Julliard, Gary Koop, William Parke, Alberto Pozzuolo, and Fabiano
Schivardi for useful comments and suggestions, and Giovanni Verga for insightful discussions on this and related topics. This
paper is based on Chapter 4 of my PhD thesis at the London School of Economics. I am extremely grateful to Gianluca
Benigno for his guidance and support during my graduate studies. All remaining errors are mine.
a
Essex Business School, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom. E-mail: [email protected]. Website:
http://carlorosa1.googlepages.com.
“As you know, the measurement of the output gap is not part of our monetary policy
concept.”
Trichet (Introductory Statement, Press Conference 2 March 2006, Q&A)
“[Ben Bernanke]
used his speech to unveil the central bank’s new strategy for
communicating with the public. In short, the Fed plans to talk more – and more often –
about its assessment of the economic outlook.”
Economist (Letting light in, November 15, 2007)
1.
Introduction
Does a Taylor-type monetary policy rule explain European Central Bank (henceforth ECB)
actions? Could we use ECB communication to learn its reaction function? What model between a
standard and dynamic ordered probit is supported by the data? These are some of the questions this
paper attempts to answer.
A monetary policy rule describes the systematic relationship between the central bank’s policy
rate and macroeconomic developments. Estimating a reaction function is interesting for two main
reasons. First, it is a useful tool to forecast future policy rates. Moreover, for central bank purposes,
the reaction function illustrates how, given economic conditions, interest rates would have been set in
the past, which may supply background information for future policy decisions. Second, by providing
explicitly one equation of the macroeconomic system, the monetary policy rule “closes” the general
equilibrium macro-econometric model of the economy and thus it allows to simulate policy
experiments. In turn, these simulations would provide a quantitative assessment of the economy’s
dynamic behavior under alternative policy experiments.
The value added of this study to the empirical monetary policy literature is twofold. On the
one hand, it highlights the key role of central bank communication to identify which macro variables
guide its monetary policy decisions. On the other hand, it performs a formal model comparison
between a dynamic probit and a standard ordered probit model, to estimate monetary reaction
functions.
The main findings of the paper can be summarized as follows. First, we consider the
information about the ECB Governing Council’s assessment of the economic outlook to understand its
interest-rate-setting behavior. By looking at ECB official documents, we find that the measurement of
the output gap is not part of its monetary policy strategy. Moreover, the ECB rarely employs the string
“output gap” in its official statements, whereas it seems to attach great weight to business and
consumer surveys. These qualitative results are confirmed empirically. Policy rates are closely tied to
1
survey data. By contrast, policy responses to output gap are weak and not significantly different from
zero once we control for survey data.
Second, formal model comparison based on Bayes factors suggests that a dynamic probit
model better takes into account both the discreteness and the serial correlation displayed by policy
rates compared to a static ordered probit technique, i.e. the workhorse model so far used in the applied
monetary policy literature. Once the model misspecification is corrected, and contrary to previous
studies based on static ordered probit models (such as Carstensen, 2006, and Gerlach, 2007), we show
that the ECB strongly reacts to inflationary pressures.
By estimating monetary policy rules, this paper is related to different strands of the literature.1
First, there are studies (among others Gerlach-Kristen, 2003, Fourçans and Vranceanu, 2004,
Carstensen, 2006, and Sauer and Sturm, 2007) that estimate the ECB’s policy reaction function by
adopting a Taylor-type specification and focusing on euro area data from 1999.2 We extend this
literature by identifying which macroeconomic variables guide the ECB’s monetary policy decisions.
For instance, we show that the real-time estimate of the output gap is not significant in its reaction
function once we control for survey data. Moreover, we find that core inflation and inflation
expectations better explains the ECB’s actions compared to headline inflation. Finally, throughout the
paper we use real-time macroeconomic data, rather than ex-post and revised data (Orphanides, 2001
and Coenen, Levin and Wieland, 2005). In other words, we employ data actually available to the ECB
Governing Council members at the time of their policy rate decision.
This work also contributes to the rapidly expanding literature on central bank communication.
Since central banking is increasingly becoming the art of managing expectations, communication has
developed into a key monetary policy instrument. A number of recent papers analyze the reaction of
asset prices to central bank qualitative announcements.3 Other studies use the ECB Governing
Council’s interpretation of economic conditions to understand its interest rate setting behavior. In
particular, Berger, de Haan and Sturm (2006) and Gerlach (2007) quantify the information of the
ECB’s President introductory statement by developing indicators that capture the Governing Council’s
assessment of inflation pressures, developments in real economic activity, and M3 growth. The focus
of this paper is on a different aspect of central bank communication by investigating whether and to
what extent central bank official documents help to learn its reaction function.
1
A very detailed list updated until July 2000 of technical and descriptive research papers on monetary policy
rules can be found at www.stanford.edu/~johntayl/PolRulLink.htm.
2
Gerlach and Schnabel (2000), Gerdesmeier and Roffia (2003) and Ullrich (2003) study the behaviour of a
“fictitious” European monetary authority prior to the start of Stage Three of the EMU (i.e. before 1999) by using
aggregated euro area data.
3
Some important studies, though this list is by no means exhaustive, include Brand, Buncic and Turunen (2006),
Ehrmann and Fratzscher (2007), Gurkaynak, Sack and Swanson (2005), Rosa (2008), and Rosa and Verga
(2008, 2007).
2
Some very limited work has been undertaken to employ a dynamic probit econometric method
to estimate empirical reaction functions for the Bank of England during the sample period 1880-1908
(Davutyan and Parke, 1995) and under the interwar gold standard 1925-1931 (Eichengreen, Watson
and Grossman, 1985). The present paper highlights the relative simplicity of estimating a dynamic
ordered probit model using a Bayesian framework based on the data augmentation approach (the
Gibbs sampler, see Casella and George, 1992) instead of a maximum likelihood procedure, and goes
one step further by performing formal model comparison based on Bayes factors between a standard
ordered and a dynamic probit model.4
The remainder of the paper is organized as follows. Section 2 starts by explaining the
theoretical framework underlying this study. Section 3 describes the choice of the data. Section 4
presents the application of Gibbs-sampling methods to estimate a standard and a dynamic ordered
probit model. Section 5 contains the estimates of simple instrument monetary policy rules for the
ECB. Section 6 computes Bayes factors to perform formal model comparison between a static and a
dynamic probit specification. Finally, Section 7 concludes.
2.
Monetary policy rules: theoretical framework
We take the canonical New-Keynesian model of the monetary transmission mechanism,
characterized by monopolistic competition and sticky prices, as a motivation for the empirical
specification used in this paper. In particular, monetary theory suggests three main prescriptions that
are relevant for this study. First, in a standard model the Taylor rule is consistent with the optimal
monetary policy rule. Second, in a more realistic and sophisticated model of the economy, an optimal
rule involves an interest rate smoothing motive. Third, if the central bank only imperfectly observes
the current inflation rate and output gap, then the monetary authority has to solve an optimal filtering
problem.
As a starting point, let monetary policy be specified by a simple Taylor rule (Taylor, 1993),
i.e. a linear static interest-rate rule of the following form:

 


1
4
Interestingly, Hamilton and Jorda (2002, page 1136) note that “the dynamic probit specification is one way [for
modeling the dynamics of limited dependent variables] but has the disadvantage of requiring difficult numerical
integrations. Monte Carlo Markov chain simulations and importance-sampling simulation estimators are
promising alternative estimation strategies.”
3
where
denotes the central bank desired policy rate implied by a static Taylor rule,  is the
is the output gap (i.e. the difference between actual and potential output),  stands the
inflation rate,
intercept, and  and
are constant “target” values for the inflation rate and the output gap.
Woodford (2003, 2001) among others shows that the Taylor rule specification is consistent
with the optimal monetary policy rule that stabilizes the price level and the output gap as long as 
and  are large enough to ensure that the rational-expectation equilibrium paths of prices and interest
rates are locally determinate (i.e. unique). In this respect, a sufficient condition is that 
1, also
known as Taylor Principle: the policy rate should adjust more than one for one with respect to
inflation in order to rule out sunspot equilibria.
The existing literature offers at least five explanations for the interest rate smoothing motive.
First, by changing policy rates gradually, central banks can reduce the likelihood that a change in
policy triggers excessive reactions in financial markets and hence may induce financial instability
(Goodfriend, 1991). Second, large interest rate changes may be difficult to achieve politically because
of the decision-making process (Goodhart, 1997) or because such changes may be interpreted by the
public as an adverse signal of inconsistency and incompetence (Goodhart, 1999). Third, uncertainty
about the structure of the economy might lead the central bank to change the interest rate gradually
(Orphanides, 2003). Fourth, the significance of lagged policy rate in the reaction function could be due
to policymakers’ reacting to one or several serially correlated variables that have been incorrectly
omitted from the estimated policy rule (Rudebusch, 2002). Finally, inertial monetary policy makes the
future path of short-term interest rates more predictable: changes in the policy rate are likely to persist
and therefore have a greater effect on long-term interest rates increasing policy effectiveness
(Woodford, 1999). For these five reasons, a slightly modified version of Equation 1 is usually
(i.e.
estimated by including on its right-hand side a gradual adjustment of the optimal policy rate
including an element of inertia represented by the lagged policy rate):
1
where
is defined in Equation 1 .
2
0,1 and captures the degree of interest rate smoothing.
In a framework of optimizing models with nominal price stickiness, where the central bank
has only partial information about the state of the economy and macroeconomic variables are
determined in a forward-looking fashion, the optimal rule can only depend on observable variables. In
particular, as proved by Aoki (2003) and Svensson and Woodford (2003), when the central bank’s
measures of current inflation and output are subject to measurement errors, the monetary authority has
to solve an optimal filtering problem, i.e. it needs to put the appropriate weights on different
information and draw the most efficient inference of potential output and inflation. Therefore, these
4
noisy indicators models imply that any variable can enter in the reaction function as long as it is
correlated with inflation and output. One of the goals of this paper consists in identifying what
observables drive ECB decisions.
3.
Data: What the ECB says
At the onset of its operational life, the ECB Governing Council promised to “offer full and
prompt explanations of its assessment of overall economic conditions, including the economic
rationale on which it is based” (Monthly Bulletin, January 1999, page 49). Given this clear statement
of purpose, this paper investigates the ECB’s official communications about its policy decisions as
well as about the underlying state of the economy to identify which macroeconomic variables guide its
reaction function. We focus our attention to statements contained in the ECB Monthly Bulletin,
because together with the ECB President’s press conference “[they] are two of the most important
communication channels adopted by the ECB” (ECB, Monthly Bulletin, November 2002, page 64).
More specifically, in order to select key macro variables we proceed in two steps. First, we apply a
mechanical counting rule. Second, we integrate the above information by reading the full editorials.
Obviously, if the ECB is transparent (Winkler, 2000), this procedure enhances our understanding of
the way its Governing Council sets the policy rate.
In order to have a broad idea of which variables can enter the ECB reaction function, we count
all economic, monetary and financial variables cited at least once in a given issue of the Editorial
section of the Monthly Bulletin from 1999 to 2002. Rather than commenting the number of
occurrences of each variable, in the interest of brevity, we summarize the most interesting findings.
First, some macroeconomic variables, i.e. Harmonized Index of Consumer Prices (henceforth HICP),
the growth of euro area real GDP, or M3 growth, are mentioned more frequently than others (indeed in
every issue of the Monthly Bulletin). Second, the string ‘output gap’ does not feature in Table 1
despite the empirical literature on monetary policy rules stresses its role to explain policy rate
decisions. Interestingly, also in the Eurosystem Staff Projection,5 there is no trace of the ‘output gap’
concept. This finding is not surprising given that the measurement of the output gap is not part of the
ECB monetary policy strategy (see separate Appendix for further details).
[Insert Table 1 about here]
To further refine the selection of which variables to include in the econometric analysis, we
also look at an additional piece of information such as the ECB explanations of the economic outlook
5
See for example http://www.ecb.int/pub/pdf/other/eurosystemstaffprojections200606en.pdf.
5
for the euro area and the analytical description of the risks to price stability. By doing so, we can better
take into account that some economic indicators may carry more information than others, and some
variables may be mentioned simply to emphasize that they are not important for the monetary policy
decisions. We discuss the details of the choice of data in the next subsections. In the interest of space,
in this paper we consider only economic activity indicators and inflation measures. The influence of
additional explanatory variables such as exchange rates and monetary aggregates is analyzed in a
companion paper (Rosa, 2009).
3.1.
Measuring real economic activity
In its statements (see excerpts available in a separate Appendix) the ECB usually refers to
business and consumer confidence to measure the position of the business cycle. Overall, survey data
present three main advantages over more standard measures of real economic activity such as GDP.
First, their data are timely released. Moreover, they seem to be leading indicators. Finally, they are
less volatile than GDP: these data are usually free from measurement errors and from seasonal and
other short-run fluctuations caused by local and sector-specific shocks.
There are many indicators to measure business and consumer confidence in the euro area,
including Economic Sentiment, EuroCOIN and EuroGrowth (for further details about these real
activity indicators see the Data sources Section). Since we have three different business cycle
indicators that co-move together (see Table 2 and Figure 1), we apply a principal component analysis
to summarize their informational contents. The first component, Factor, explains around 86% of their
variability, and is used in the econometric analysis.
[Insert Table 2 and Figure 1 about here]
The empirical literature on monetary policy rules highlights the role of the output gap to
distinguish between medium-term trends and shorter-term cyclical movements in the economy. For
this reason, despite ECB’s declarations, the output gap can be strongly significant in its reaction
function. We estimate potential output from monthly industrial production in three different ways.6 We
recursively apply (i.e., every month appending a new data point) a deterministic linear and quadratic
trending, and Hodrick-Prescott filter (see Hodrick and Prescott, 1997) with smoothing parameter
129,600 as advocated by Ravn and Uhlig (2002). In order to have a more reliable estimate, the sample
starts in 1994 (to avoid the issues related to the German reunification) instead of simply using EMU
6
Two approaches can be used to estimate the output gap: a statistical method that can be either univariate or
multivariate, and a structural approach based on the specification of a production function (cf. Baxter and King,
1999, Cerra and Saxena, 2000, and ECB Monthly Bulletin, October 2000). Interestingly, economic forecasters
(see Sauer and Sturm, 2007) considers alternative measures to assess the position of the business cycle, such as
growth-rate cycles (fluctuations in production growth).
6
data from 1999. The output gap is defined as the difference between industrial production and its fitted
linear and quadratic trend (respectively, xtL and xtQ), or Hodrick-Prescott filter (xtHP).7
3.2.
Measuring inflation
Given the ECB definition of price stability as “a year-on-year increase in the HICP for the
euro area of below, but close to, 2%” (ECB, 2003 and 1998), a natural starting point is represented by
headline inflation. As Table 1 indicates, the ECB analyses the dynamics of different price indicators.
Although the string ‘core inflation’ does not explicitly appear in its statements, the Governing Council
seems to use a core inflation measure (HICP excluding unprocessed food and energy prices, CoreInfl)
and a production price index, ProdPrices, to monitor future inflationary risks. For instance, on 21 June
2001 during the monthly press conference the ECB President Duisenberg used the core inflation idea,
instead of the Consumer Price Index, to back up the Governing Council policy rate decision by
pointing out that “Price developments continued to reflect mainly temporary upward pressure from
energy and food prices, which was taken into account in our previous decisions” (see separate
Appendix for further examples). The underlying motivation to target core inflation, instead of the
HICP, is as follows. If there is a transitory shock, then optimal monetary policy should not react to it
unless it has a permanent impact on prices.
To better take into account the forward-lookingness of the ECB monetary policy, we also
consider inflation expectations, InflExp, over the coming twelve months using data from Consensus
Economics for all euro area countries except Luxembourg.
Interestingly, the behaviour of the various inflation measures have been so far quite different
(Figure 2). Indeed, Table 3 shows that the correlation between these three measures of price stability is
fairly low, and sometimes even negative.
[Insert Table 3 and Figure 2 about here]
4.
Econometric methods
Many empirical studies on monetary policy rules use quarterly data, whereas the decision
making process of most central banks, including the ECB, takes place every month. Therefore, we use
7
We use the industrial production as a proxy for the euro area output because its data are available every month,
while GDP data are available every quarter. Even though industrial production only covers 20% of the economy,
it is generally believed that its dynamics is very positively correlated with the rest of the economy. An alternative
could be to use the quarterly GDP series and to convert it into a monthly one by applying the procedure by Chow
and Lin (1971). Following Orphanides (2001) for the United States and Gerberding, Seitz and Worms (2005) for
Germany, we acknowledge that if the ECB generated its own estimate of the output gap and this information was
publicly available, it would be desirable to use it.
7
monthly frequency data in the econometric analysis that follows. In order to measure the ECB’s
current monetary policy stance, we employ the official ECB policy rate, i.e. the minimum bid rate for
the main refinancing operations of the Eurosystem, rather than an euro area short-term money market
rate. Market rates often move endogenously with changes in economic conditions, and this may lead
to biased estimates of the reaction function coefficients. Since policy rates do not move most of the
time, and when they change they do so by a discrete amount (usually a multiple of 25 basis points, see
Table 4), ordered probit estimation (Vanderhart, 2000 and Ruud, 2000, chapter 27) takes better care of
these intrinsic characteristics of the data compared to standard time series techniques, such as GMM.
Moreover, by using real-time predetermined data we do not have any endogeneity issue.
[Insert Table 4 about here]
In order to cope with the potential non-stationarity of policy rates, we estimate an
algebraically equivalent specification of Equation 2 , rewritten as an Error Correction Model:8
∆
4.1.
1
3
Ordered probit
Equation 3 implies that changes in interest rates should be distributed continuously.
However, because the ECB sets interest rates in steps, only discrete changes are observed. Since the
estimation by ordinary least squares of the partial adjustment mechanism of Equation 2 ignores the
discrete nature of target changes, we employ a standard ordered probit model (i.e., a limited dependent
variable framework) as follows:

 

 
where 
1
, 

1
4

1
stands for the latent policy rate, and
 , 
1
,

 

, 1
,
stands for the lagged observed policy rate. The error term 8
Even though the policy rate may be stationary in large samples, Phillips Perron and augmented Dickey Fuller
tests cannot reject the presence of a unit root in our sample (results not reported but available upon request).
Moreover, Gerlach-Kristen (2004) shows that policy rules estimated in levels, rather than in ECM specification,
display both parameter instability and poor out-of-sample forecasts.
Note that if the inflation rate is I(1) and the output gap is I(0), which is what we find in the data, Equation 3
implies that in order to have a balanced regression, there should exist a long-run equilibrium relationship
between the policy rate and the inflation. While this relationship is theoretically plausible, we do not find
conclusive evidence. This is not a surprising result since it is known that cointegration tests have low power in
small samples.
8
is assumed to be normally distributed with zero mean and variance
, and subsumes both
implementation errors of the ECB and specification errors of the policy reaction function.
What is observed is the actual change in the interest rate, which depends on where the latent
variable is relative to a set of threshold values:
∆
50
if
∆
25
if
∆
0
if
∆
25
if
∆
50
if
where
5
for all j, and ∆
are threshold parameters with
.
Equations 4 and 5 illustrate a common identification problem in ordered probit models:
multiple values for the model parameters give rise to the same value for the likelihood function. Since
it is impossible to simultaneously identify the constant , the limit points
this
paper
we
impose
that
the
0.375, 0.125,0.125,0.375 for
threshold
parameters
are
, and the variance
equally
, in
spaced,
i.e.
1, … ,4. By using this identification scheme it is relatively
straightforward to generalize the baseline model by adding regime-switching parameters for the
constant and the variance. 4.2.
Dynamic probit
In this subsection we introduce the dynamic probit econometric method originally proposed
by Eichengreen, Watson and Grossman (1985). This technique postulates that the change in the
unobserved policy rate is governed by the following specification:
 
where

6
stands for the Governing Council’s optimal policy rate change between time
and
1, and the rest of the notation is the same as before.
Equation 6 cannot be directly estimated, because
is not observed by market
participants. Instead, both the public and the econometrician observe the realized change, ∆
hence is a limited dependent variable. We assume that the observed rate,
, and
, changes according to
Equation 5 .
9
The dynamic probit specification not only explicitly accounts for the discrete nature of the
dependent variable, as the static probit, but also for the serial correlation displayed by the data. The
impetus for a policy rate change, given by
, as opposed to the change in the desired level,
∆ , can be decomposed as:
∆
7
The first term in the right-hand side of Equation 7 , ∆ , represents the dependent variable
used in the dynamic probit specification, while the second term,
, allows a certain degree
of memory. In other words, the impetus for a change in the policy rate builds over time rather than
suddenly appearing and disappearing.
The dynamic probit generalizes the static model and describes the central bank actual interest
rate setting behavior much more realistically. To make this point as clear as possible, we use a
numerical example. Suppose that in the last few months the central bank left the policy rate
unchanged, while this month the policy rate was raised by 25 basis points to a level of 2.75. According
to the dynamic specification, this situation is consistent with many different scenarios: the latent
policy rate of the previous month could have been any value between 2.375 and 2.625, while the latent
value of this month could be any number between 2.625 and 2.875. Thus, the change in the
macroeconomic environment could have triggered a change in the desired level as low as 1 basis point
(for example, from 2.62 to 2.63), or as high as 50 basis points (from 2.375 to 2.875). In other words,
the dynamic probit uses a continuous measure of the impetus for a policy rate change. Instead, the
static ordered model does not keep track of the previous month latent rate, and always posits that it is
equal to the observed level. In the above example, this means that the change in the economic
conditions has triggered a change in the latent rate between 12.5 and 37.5 basis point. Hence, in the
latter case, a change in the realized policy rate takes place only when the impetus reaches a critical
threshold level.
While Equation 6 describes the changes in
, the inequalities reported in 5 are concerned
with its level. This feature introduces stochastic dynamics into
through the accumulation of
disturbances t over time. In fact, by recursively solving 6 backwards:
1
1



8
This complicates the maximum likelihood estimation procedure, since it requires to
numerically evaluate a normal distribution of the same dimension as the sample size. More formally,
10
denote the interval containing
let
,…,∆
∆
∆
. The likelihood function for the observed data
can be written as:
,…,∆
, ; ,
…
,…,
| , ; ,
…
9 …
where
data:
. and
,…,
…
. stands for probability density functions,
, ,
,
stands for the entire history of the
, ,
for the dynamic probit model or
standard probit, and let for notational convenience
,  ,  ,
Maximizing 9 analytically is in principle feasible because
,
for the
.
,…,
is directly observable,
but in practice a numerical integration strategy is required. Since it is computationally onerous and not
readily available in standard econometric packages, in the existing literature the dynamic probit
estimation technique has been somehow neglected. Fortunately, the above maximum likelihood
estimation is relatively easy to implement by Markov Chain Monte Carlo methods such as Gibbs
sampling. The basic insight is that Equation 6 has an underlying normal regression structure on
latent continuous data, and the idea consists of treating the unobserved values of the latent policy rate,
, as additional parameters to be estimated. For instance, values of the latent data can be
simulated from suitable truncated normal distributions. Once the latent data become known, then the
posterior distribution of the parameters can be computed using standard results for normal linear
models (see Albert and Chib, 1993, Chib, 1996, and Dueker, 1999). We provide the details of the
Gibbs sampling method in the next subsection.
4.3.
Gibbs sampling
By employing a data augmentation strategy and a specified set of conditional distributions, we
generate random draws of the parameters and the latent levels of the policy rate. Specifically, for both
the static and dynamic probit model we need to simulate three types of parameters:
P1:
variance of the error term.
P2:
regression coefficients.
P3:
sequence of the latent “desired” policy rate.
10
11
Gibbs sampling consists of iterating through cycles of draws from conditional distributions for
1, … ,
(number of draws) as follows:
1  2
, 3
,
2  1 , 3
,
11
3  1 , 2 ,
where superscript
indicates the number of the iteration through the Gibbs sampler, and
. stands
for any conditional density function. Note that at each step, a value for the variable P is drawn from its
conditional distribution. The key insight of the Gibbs sampling is that after a sufficient number of
iterations, the draws from the respective conditional distributions jointly represent a draw from the
joint posterior distribution, which is impossible or computationally cumbersome to evaluate directly.
The Appendix specifies prior and posterior conditional distributions for
, , . Note that when the
prior is not informative, the Gibbs sampling method is equivalent to maximize the Likelihood
function. Indeed, as a cross-check, we also estimate Equation 4 by maximizing its Maximum
Likelihood function, and we obtain basically the same results with accuracy up to the second decimal.
In this paper, we use MCMC methods to estimate the standard probit specification for maximum
comparability of the results between the static and the dynamic probit models.
The Gibbs sampler technique can be used to estimate both the standard probit and the dynamic
probit model. However, the details of the implementation crucially differ for generating latent
variables. In the dynamic probit model the entire vector of latent variables should be sampled jointly
from
, … , I , … , IT . But this would require to evaluate a density equivalent to the cumbersome
likelihood function of Equation 9 . By exploiting the Markov structure of the dynamic probit model,
it can be shown after some algebra that it is sufficient to draw the latent policy rate from the following
univariate truncated normal distribution:
~
where
1
1
1
1
, ,
,
1
  ,
,
1
12
1
1
1
, and the rest of the notation is the same as before.
The Gibbs sampler was run for a total of 30,000 iterations in each estimation. The first 15,000
iterations were discarded to allow the sampler to converge to the posterior distribution. Standard
Markov Chain Monte Carlo diagnostics cannot reject the null hypothesis of convergence. For brevity,
in a separate Appendix, we provide detailed results of different MCMC convergence diagnostics, such
12
as Raftery and Lewis (1995) percentile-based measure of convergence, and Geweke (1992) relative
numerical efficiency and Chi-squared test on the means from the first 20% of the sample versus the
last 50%. Moreover, we can be confident the sampler had converged after 15,000 iterations because
the posterior means remained virtually identical if we discarded the first 495,000 iterations before
saving 5,000. As a further robustness check we also tried different starting values of the Gibbs
sampler, and the estimation results were not affected.
5.
Estimation results
5.1.
Ordered probit
As a baseline model, we start by studying the ECB reaction function using standard Taylor-
type macroeconomic variables, such as inflation and output gap. Table 5 reports the coefficient
estimates of Equation 4 for the sample period February 1999 – December 2006 by using a static
ordered probit econometric method, and using different measures of inflation and output gap.9 In the
interest of brevity, we only present the estimates for , ,  ,  (cf. Equation 4 ), and report in a
separate Appendix the estimates and confidence bands for , ,  ,  (cf. Equations 1 and 2 ).
[Insert Table 5 about here]
In the interest of space, we summarize the most interesting findings instead of commenting all
the regressions individually. First, the inflation coefficient is not statistically different from zero,
except in one case. Second, the smoothing parameter, i.e. the coefficient of the lagged policy rate, is
not statistically different form one, which is very large compared to the existing literature on reaction
functions, and suggests that the policy rate follows a random walk process. Finally, the coefficient of
the output gap is strongly significant. These results seem problematic, especially because they are
robust both with respect to the use of different output gap measures, and different inflation measures.
However, it is premature to conclude that the ECB has violated the Taylor principle, and followed a
destabilizing monetary policy rule. In fact one can question whether the econometric models that led
to these results are correctly specified.
9
We use the sample period February 1999 – December 2006 for two main reasons. First, we avoid the recent
period of financial turmoil, where the ECB policy rate decisions have been triggered not only by changes in
macroeconomic fundamentals but also by changes in financial conditions and liquidity issues. Second, we make
our estimation results directly comparable to Gerlach (2007) that employs a static ordered probit model to
estimate the ECB reaction function.
13
Table 6 reports the estimates of the ECB expectation-augmented reaction function by using
Factor as indicator of economic activity rather than the output gap and InflExp as indicator of
inflationary pressures.
[Insert Table 6 about here]
The coefficient on the lagged policy rate is smaller than one, indicating that the policy rate
follows a stationary process. Second, the coefficient of HICP is positive and marginally statistically
significant at the 10% level. In this respect, the Taylor principle is sometimes satisfied (which, given
the first-difference specification, corresponds to a situation where the absolute magnitude of the
coefficient on the inflation rate is larger than the right-hand side coefficient on the lagged policy rate).
The coefficient on CoreInfl is positive, although not statistically significant at the 5% level. Moreover,
the coefficient of InflExp is positive and marginally statistically significant at the 5% level. Third, the
importance of the output gap as explanatory variable completely disappears once Factor is included in
the specification. This last finding is in line with the seminal work of Orphanides and van Norden
(2002): given the end-of-sample estimation problem, real time estimates of the output gap are fairly
unreliable irrespective of the de-trending methodology that has been applied.
The interpretation of the above result is as follows. In order to stabilize the economy, central
bankers need some measures of the business cycle. Moreover, because of the lags of the monetary
transmission mechanism, these measures are needed well in advance. Hence, the members of the ECB
Governing Council have to infer the output gap or even actual output from a range of other observable
variables, such as survey data. This implies that the policy rate will be correlated with all the
indicators the ECB has used in its filtering problem.
To sum up, the information contained in the ECB’s statements is helpful to better understand
its reaction function. The ECB is transparent, not only by announcing the likely future path of its
policy rate (see Rosa and Verga, 2008, 2007), but also by communicating to the public what
observables are most important to solve its optimal filtration problem. Nevertheless, the results
discussed above raise one important question. Does the ECB really react to inflationary risks? More
specifically, why the coefficients of inflation pressures are only marginally statistically significant?
We address this question in the next subsection where we employ the dynamic probit specification.
5.2.
Dynamic probit
Table 7 and Table 8 report the coefficients of the ECB reaction function by estimating a
dynamic probit model. In the interest of brevity, we summarize the most interesting findings instead of
commenting all the regressions individually. First, the estimation results presented in Table 7, i.e.
14
standard Taylor-type macroeconomic variables, are broadly in line with the findings of Table 8, except
that the magnitude of the estimated standard deviation of the error term of the dynamic probit model is
around 0.07 compared to 0.14 in the static ordered probit model. Hence, the memory property of the
dynamic probit implies a gradual adjustment in the policy rate, and consequently on average a smaller
policy shock.
[Insert Table 7 about here]
Table 8 reports the estimates of the ECB expectation augmented reaction function using
Factor as indicator of economic activity and InflExp as indicator of inflationary pressures. Contrary to
our previous findings and the recent literature on the ECB reaction function (such as Carstensen, 2006
and Gerlach, 2007), the parameter on inflation (either HICP or CoreInfl) is always positive and
strongly significant. In other words, inflationary pressures are always associated with monetary
tightening. Hence, it seems that past inflation is a leading indicator of future inflation, confirming
previous studies that have found that inflation is a highly persistent economic series. Moreover, we
find that the coefficient on inflation expectations is statistically larger than one only in the dynamic
probit specification, thus suggesting that the ECB followed a stabilizing monetary policy rule.
Second, the coefficient of the lagged policy rate is between 0.93 and 0.97, a number that is
comparable to other empirical studies on reaction functions such as Clarida et al. (1998). Note that the
significance of the output gap as explanatory variable completely disappears once Factor is included
in the specification.
[Insert Table 8 about here]
Figure 3 displays the observed and the latent policy rate for both the static (top diagram) and
dynamic probit model (bottom diagram) using as explanatory variables a constant, CoreInfl, Factor,
and the lagged observed policy rate (static probit) or the lagged latent policy rate (dynamic probit). As
expected, the latent rate moves much more continuously in the dynamic model compared to the static
specification. More specifically, the difference between the latent policy rate estimated by the dynamic
probit and the standard probit models is particularly evident at turning points of the policy cycles.
Interestingly, there are periods where the latent rate is systematically different from the policy rate.
For instance, in the beginning of 2002 a policy rate cut was very likely but did not materialize, while
in the beginning of 2005 the level of the latent policy rate has almost triggered a policy rate hike. The
dynamic probit model also suggests that changes in macro fundamentals do not completely explain a
policy rate change of 50 basis points. Indeed when the policy rate changes by 50 basis points, the
latent policy rate systematically equals the value of the threshold coefficient.
15
[Insert Figure 3 about here]
Overall, the dynamic probit estimation seems to produce more precise results than standard
ordered probit regression. Given the relative simplicity of implementing a Gibbs sampling algorithm,
this paper shows the usefulness of Markov Chain Monte Carlo methods to estimate qualitative
response models that take into account both the discrete nature of the dependent variable and its serial
correlation. The use of a different econometric model could produce, as we show above, very
different, and potentially misleading, conclusions about the importance of current inflation in the ECB
reaction function. Hence, there is an important, and yet unanswered, question that this paper brings to
the fore: what model between a static and a dynamic probit do the data support? Formal model
comparison based on Bayes factors is discussed in the next section.
6.
6.1.
Formal model comparison
Theory: Chib (1995)
In a seminal paper, Chib (1995) develops a simple approach to compute the marginal
likelihood that relies on the output of the Gibbs sampling algorithm. The approach is fully automatic
and stable. In particular, importance sampling, or any other tuning function, is not required (cf.
Gelfand and Dey, 1994). The approach proposed by Chib is based on two related ideas. First, the
marginal density of the data,
, can be written as:
|
13
|
where the numerator is the product of the sampling density and the prior, with all the integrating
constants included, and the denominator is the posterior density of the estimated parameters
specific case,
and
Second, for a given
(in the
). Equation 13 is also known as the basic marginal likelihood identity (BMI).
(say
), the posterior ordinate
|
can be estimated by exploiting the
information contained in the conditional densities employed in the Gibbs sampling algorithm. Note
that if the posterior density estimate at
is denoted by
| , then the estimate of the marginal
density on the logarithm scale is:
|
|
14
16
In the application below, we apply the “three vector blocks” case (see Chib, 1995, page 1315),
where the parameters
are defined in Equation 10 . The BMI expression has been evaluated at a
high density point (as recommended by Chib to improve the accuracy of the estimate), either the
posterior mean or the posterior median, and the estimation results of Equation 14 are basically
identical. In the dynamic probit model, the likelihood of the data depends not only on the parameters
and
, but also on the latent variables
. Hence, it requires the evaluation of a density equivalent to
Equation 9 . To avoid this computational burden, we estimate the likelihood by applying the RaoBlackwellization technique proposed by Gelfand and Smith (1990) as follows:
,
1
,
where
,
1
,
denote the sequence of latent policy rates, and are drawn from the truncated normal
| ,
distribution
,
by sampling for an additional G iterations (for further details see again
Chib, 1995). The Bayes factor for any two models k and l can be directly calculated as
|
|
. An estimate of the posterior odds of any two models is
given by multiplying the estimated Bayes factor by the prior odds.
Chib (1995, page 1316) also derives the accuracy achieved by the marginal density estimate
obtained from the Gibbs output by applying the delta method. Recall that the numerical standard error
gives the variation that can be expected in the estimate if the simulation were to be done afresh, but the
point at which the ordinate is evaluated is kept fixed
6.2.
Empirical results
Table 9 reports the logarithm of the marginal likelihood along with its numerical standard
error for both the static and dynamic probit model. From this Table it can be seen that the marginal
likelihood is very precisely estimated in all the fitted models, especially for the static probit
specifications. Of course, these results are obtained with 15,000 draws, and further improvements in
accuracy can be achieved by increasing the number of draws.
For the static probit model the data strongly support the expectation augmented reaction
function versus the baseline specification, with a Bayes factor of around
10 . In particular, the
model that features InflExp and Factor appears superior to all the other specifications. For the dynamic
probit model, the data again strongly support the expectation augmented reaction function versus the
baseline specification. However, the most interesting and original finding is that given the same
specification the dynamic probit is always superior to the corresponding static probit model, with a
17
12 and
Bayes factor that ranges between
22 . Hence, we find decisive evidence in favor of
the dynamic probit model.
[Insert Table 9 about here]
7.
Conclusions
Although a Taylor rule is a standard and popular tool for evaluating monetary policy
decisions, its mechanical application could lead to serious pitfalls and to an inadequate explanation of
the central bank’s interest rate setting behavior. This paper contributes to our understanding of the
ECB monetary policy management by estimating an interest rate rule from monthly data for the
sample period 1999-2006.
The monetary authority operates under considerable uncertainty about the state of the
economy. Moreover, as noted among others by Duisenberg (1999), “monetary policy measures only
have an impact on prices with long, variable and not entirely predictable time-lags of between 1.5 and
2 years”. Therefore, to identify the existence of potential risks to price stability, the central banker has
to solve a signal-extraction problem using information from many different variables. In other words,
the monetary authority has to infer the future inflation from a set of observable variables. Obviously,
the indicators the ECB uses in its filtering problem will be correlated with its policy rate.
The value added of this study to the empirical monetary policy literature consists of
highlighting the importance of central bank communication to identify which macro variables guide its
monetary policy decisions. We consider the information about the ECB Governing Council’s
assessment of the economic outlook to understand its interest-rate-setting behavior. We show that the
real-time estimate of the output gap is not significant in its reaction function once we control for
survey data. Moreover, by using Bayes factors we find that core inflation better explain the ECB’s
actions compared to headline inflation.
Second, although the workhorse model to estimate a reaction function has recently been a
static ordered probit framework where the explanatory variables include the observed lagged value of
the policy rate, this paper shows that the interest rate smoothing is with regard to the latent policy rate
. More specifically, there are two apparent motivations for doing so. One, an intuitively appealing
idea that discrete changes in the rate emerge as the result of building “pressure” from the latent
variable slowly moving towards the threshold. Two, a better fit of the model (cf. Table 9). Put it
differently, we provide decisive evidence that the dynamic probit model is more strongly supported by
the data under consideration than the standard ordered probit model. We also highlight the relative
simplicity of estimating a dynamic ordered probit using Markov Chain Monte Carlo methods.
18
Of course, various important issues are not considered here and deserve further study. Our
econometric analysis contains only in-sample regression analysis. An out of sample forecast of policy
decisions would be required to show that our proposed empirical reaction function is a useful tool in
forecasting future ECB monetary policy moves (Rosa, 2009, tackles this issue in a static probit
framework). Furthermore, since we use a single equation reduced-form model, our reaction function is
useful for forecasting as long as the underlying equilibrium or filtering problem does not change. Put it
differently, the usefulness of any reduced form relationship is vulnerable to the Lucas critique.
Table 1 lists around 40 economic and monetary variables, while in our regression
specifications we just use seven of them. A mix of consensus, parsimony, and above all ECB
explanations of its monetary policy decisions guided our choice. Another possibility would be to apply
Sala-i-Martin (1997) empirical strategy: first, to estimate all possible models, then to analyze the entire
distribution of the regression coefficients of the variables of interest. Yet another alternative method
would be to use a factor analysis to extract a price, an activity and a monetary aggregate indicator. It
would even be possible to introduce time-varying weights to allow for variables that are mentioned in
one statement to receive an extra weight for that month.
19
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23
Table 1 – Economic and monetary variables featuring in the ECB Monthly Bulletin
Prices
HICP
Wages
Energy prices
Oil price
Raw material prices
Services prices
Consumer prices
Producer prices
Food prices
Economic Activity
Growth of euro area real GDP
Capacity utilization
Industrial / Consumer confidence
Industrial production
Fiscal policy
Employment
International factors
World / USA economy
Exchange rate
Market interest rates
Government bond yields
Bond yields
Yield curve
Nominal interest rate
Real interest rate
Short-term interest rate
Long-term interest rate
Monetary Variables
M3
M1
Credit growth
c/c deposit growth
Loans to private sector
Deposit with agreed maturity < 2 years
Credit to general government
Uncertainty in stock market
1999
2000
Monthly Bulletin
2001
2002
Total
12
8
11
9
3
6
4
2
8
12
12
9
12
0
1
6
6
3
12
12
10
9
0
3
1
3
9
12
12
9
7
0
4
0
2
10
48
44
39
37
3
14
11
13
30
12
2
9
5
5
9
12
4
9
4
9
12
12
2
10
1
11
10
12
0
7
0
7
9
48
8
35
10
32
40
11
11
9
12
8
6
11
5
39
34
1
10
5
3
2
7
6
3
9
6
3
0
1
5
2
6
1
1
1
6
7
0
3
0
3
0
4
0
6
28
12
10
3
18
18
12
1
5
3
9
3
2
0
12
3
4
0
12
0
1
0
12
2
2
0
10
0
1
4
12
6
0
0
11
0
0
7
48
12
11
3
42
3
4
11
NOTE: January 1999 – December 2002. The table reports economic and monetary variables cited at least once in
a given issue of the ECB Monthly Bulletin (Editorial section). From January 1999 to December 2002 there were
48 issues of the Monthly Bulletin. Exceptional (one-time) events (e.g. 11 September 2001 terrorist attack,
Kosovo conflict, UMTS auction, etc.) are not reported.
24
Table 2 – Survey data correlation matrix
Sentiment
Eurocoin
Eurogrowth
Eurocoin
0.684
Eurogrowth
0.919
0.768
Factor
0.939
0.874
0.968
NOTE: The sample is January 1999 – December 2006.
25
Table 3 – Prices correlation matrix
HICP
CoreInfl
ProdPrices
CoreInfl
0.163
ProdPrices
0.589
-0.462
InflExp
0.794
0.049
0.707
NOTE: The sample is January 1999 – December 2006.
26
Table 4 – Changes in the ECB policy rate
i t
-0.50
-0.25
No change
+0.25
+0.50
Total
Count
5
3
74
11
2
95
NOTE: The sample is February 1999 – December 2006.
27
Table 5 – Ordered probit: baseline specification
Constant
HICPt
-0.030
[-0.069, 0.011]
0.100
[-0.068, 0.268]
0.002
[-0.073, 0.077]
-0.111
[-0.164, -0.058]
0.209
[ 0.040, 0.378]
0.082
[ 0.003, 0.160]
-0.010
[-0.049, 0.029]
0.034
[-0.129, 0.196]
0.013
[-0.060, 0.087]
-0.043
[-0.089, 0.004]
0.096
[-0.021, 0.214]
0.063
[-0.056, 0.182]
CoreInflt
0.051
[ 0.023, 0.079]
0.003
[-0.016, 0.023]
0.037
[ 0.008, 0.065]
0.147
[ 0.124, 0.175]
95
0.148
[ 0.125, 0.175]
95
ProdPricest
xtHP
0.040
[ 0.020, 0.060]
0.057
[ 0.034, 0.079]
x tL
x tQ

Observations
-0.031
[-0.069, 0.008]
0.098
[-0.024, 0.220]
0.148
[ 0.125, 0.175]
95
0.140
[ 0.118, 0.167]
95
0.043
[ 0.023, 0.062]
0.145
[ 0.122, 0.172]
95
NOTE: Monthly observations on days of ECB Governing Council meetings, February 1999 – December 2006. The econometric method is static ordered probit estimated
via Gibbs sampling. The Gibbs sampler was run for a total of 30,000 iterations in each estimation. The first 15,000 iterations were discarded to allow the sampler to
converge to the posterior distribution. We report both the posterior means for the regression coefficients and their 95% empirical confidence intervals.
28
Table 6 – Ordered probit: empirical reaction function
-0.054
[-0.092, -0.016]
0.040
[-0.110, 0.190]
0.058
[-0.012, 0.127]
Constant
HICPt
-0.057
[-0.094, -0.019]
0.020
[-0.133, 0.172]
0.068
[-0.004, 0.141]
-0.046
[-0.107, 0.015]
0.021
[-0.169, 0.211]
0.053
[-0.022, 0.129]
-0.059
[-0.102, -0.017]
0.042
[-0.107, 0.193]
0.062
[-0.010, 0.134]
-0.056
[-0.097, -0.015]
0.116
[ 0.007, 0.225]
-0.046
[-0.082, -0.011]
0.118
[ 0.012, 0.224]
0.060
[-0.033, 0.152]
CoreInflt
0.009
[-0.005, 0.023]
ProdPricest
-0.079
[-0.123, -0.035]
0.087
[-0.081, 0.255]
-0.000
[-0.103, 0.103]
0.125
[ 0.007, 0.245]
0.019
[-0.005, 0.042]
0.069
[ 0.037, 0.101]
0.068
[ 0.045, 0.091]
0.055
[ 0.035, 0.075]
0.068
[ 0.044, 0.091]
0.136
[ 0.004, 0.268]
0.061
[ 0.042, 0.080]
-0.006
[-0.034, 0.023]
0.130
[ 0.109, 0.155]
95
0.130
[ 0.110, 0.156]
95
0.130
[ 0.109, 0.155]
95
0.127
[ 0.106, 0.152]
95
0.128
[ 0.107, 0.153]
95
InflExpt
0.064
[ 0.045, 0.083]
Factort
xtHP
0.075
[ 0.044, 0.105]
-0.013
[-0.042, 0.015]
0.069
[ 0.031, 0.107]
-0.056
[-0.092, -0.019]
-0.082
[-0.310, 0.148]
-0.078
[-0.122, -0.033]
0.003
[-0.333, 0.341]
-0.013
[-0.126, 0.099]
0.113
[-0.012, 0.237]
0.014
[-0.015, 0.043]
0.072
[-0.173, 0.314]
0.068
[ 0.044, 0.093]
-0.078
[-0.123, -0.033]
-0.001
[-0.332, 0.331]
0.127
[ 0.106, 0.152]
95
0.127
[ 0.106, 0.152]
95
0.109
[-0.013, 0.231]
0.013
[-0.014, 0.039]
0.062
[-0.164, 0.288]
0.069
[ 0.046, 0.092]
-0.007
[-0.048, 0.034]
x tL
x tQ

Observations
0.129
[ 0.108, 0.154]
95
0.129
[ 0.108, 0.155]
95
0.130
[ 0.109, 0.156]
95
NOTE: Monthly observations on days of ECB Governing Council meetings, February 1999 – December 2006. The econometric method is static ordered probit estimated
via Gibbs sampling. The Gibbs sampler was run for a total of 30,000 iterations in each estimation. The first 15,000 iterations were discarded to allow the sampler to
converge to the posterior distribution. We report both the posterior means for the regression coefficients and their 95% empirical confidence intervals.
29
Table 7 – Dynamic Probit: baseline specification
Constant
HICPt
-0.023
[-0.041, -0.005]
0.097
[ 0.022, 0.173]
-0.006
[-0.041, 0.029]
-0.113
[-0.140, -0.085]
0.197
[ 0.113, 0.282]
0.091
[ 0.050, 0.132]
-0.001
[-0.018, 0.016]
0.025
[-0.045, 0.095]
0.007
[-0.026, 0.041]
-0.045
[-0.067, -0.022]
0.081
[ 0.029, 0.135]
0.091
[ 0.029, 0.153]
CoreInflt
0.060
[ 0.045, 0.074]
-0.002
[-0.011, 0.007]
0.045
[ 0.032, 0.058]
0.073
[ 0.061, 0.087]
0.072
[ 0.060, 0.087]
ProdPricest
xtHP
0.043
[ 0.033, 0.052]
0.060
[ 0.049, 0.072]
x tL
x tQ

Observations
-0.023
[-0.040, -0.006]
0.091
[ 0.037, 0.145]
0.072
[ 0.060, 0.086]
95
0.076
[ 0.063, 0.092]
95
0.046
[ 0.037, 0.055]
0.069
[ 0.058, 0.083]
95
95
95
NOTE: Monthly observations on days of ECB Governing Council meetings, February 1999 – December 2006. The econometric method is dynamic ordered probit
estimated via Gibbs sampling. The Gibbs sampler was run for a total of 30,000 iterations in each estimation. The first 15,000 iterations were discarded to allow the sampler
to converge to the posterior distribution. We report both the posterior means for the regression coefficients and their 95% empirical confidence intervals.
30
Table 8 – Dynamic Probit estimation: empirical reaction function
-0.049
[-0.066, -0.031]
0.019
[-0.052, 0.090]
0.061
[ 0.026, 0.095]
Constant
HICPt
-0.052
[-0.070, -0.034]
-0.007
[-0.081, 0.068]
0.074
[ 0.037, 0.112]
-0.023
[-0.059, 0.012]
-0.041
[-0.141, 0.061]
0.045
[ 0.006, 0.084]
-0.052
[-0.073, -0.031]
0.019
[-0.052, 0.090]
0.064
[ 0.028, 0.100]
-0.048
[-0.067, -0.029]
0.100
[ 0.051, 0.149]
-0.039
[-0.056, -0.023]
0.100
[ 0.051, 0.150]
0.053
[ 0.009, 0.098]
CoreInflt
0.008
[ 0.001, 0.014]
ProdPricest
-0.073
[-0.095, -0.051]
0.070
[-0.020, 0.160]
-0.000
[-0.060, 0.060]
0.127
[ 0.061, 0.191]
0.018
[ 0.005, 0.032]
0.067
[ 0.050, 0.084]
0.066
[ 0.055, 0.077]
0.055
[ 0.045, 0.064]
0.067
[ 0.055, 0.079]
0.122
[ 0.058, 0.186]
0.060
[ 0.051, 0.069]
-0.005
[-0.020, 0.011]
0.069
[ 0.057, 0.083]
95
0.067
[ 0.056, 0.081]
95
0.068
[ 0.057, 0.082]
95
0.068
[ 0.056, 0.082]
95
0.068
[ 0.057, 0.082]
95
InflExpt
0.063
[ 0.053, 0.072]
Factort
xtHP
0.076
[ 0.060, 0.092]
-0.015
[-0.030, 0.000]
0.080
[ 0.057, 0.103]
-0.047
[-0.064, -0.030]
-0.079
[-0.187, 0.030]
-0.072
[-0.095, -0.050]
0.033
[-0.139, 0.205]
-0.006
[-0.072, 0.058]
0.120
[ 0.050, 0.190]
0.016
[-0.000, 0.032]
0.033
[-0.093, 0.160]
0.067
[ 0.055, 0.080]
-0.072
[-0.094, -0.050]
0.028
[-0.147, 0.200]
0.067
[ 0.056, 0.081]
95
0.068
[ 0.056, 0.082]
95
0.118
[ 0.051, 0.184]
0.015
[ 0.001, 0.030]
0.031
[-0.087, 0.150]
0.068
[ 0.057, 0.079]
-0.021
[-0.047, 0.005]
x tL
x tQ

Observations
0.069
[ 0.057, 0.083]
95
0.068
[ 0.057, 0.083]
95
0.068
[ 0.056, 0.082]
95
NOTE: Monthly observations on days of ECB Governing Council meetings, February 1999 – December 2006. The econometric method is dynamic ordered probit
estimated via Gibbs sampling. The Gibbs sampler was run for a total of 30,000 iterations in each estimation. The first 15,000 iterations were discarded to allow the sampler
to converge to the posterior distribution. We report both the posterior means for the regression coefficients and their 95% empirical confidence intervals.
31
Table 9 – Log Marginal likelihoods
Static Probit
Log(Marginal)
Num SE
Dynamic Probit
Log(Marginal)
Num SE
Baseline specification
HICP, xHP
HICP, xL
HICP, xQ
CoreInfl, xHP
ProdPrices, xHP
-110.112
-105.992
-108.594
-109.104
-111.389
0.005
0.005
0.005
0.005
0.005
-87.153
-87.850
-87.058
-87.527
-88.689
0.014
0.015
0.016
0.013
0.014
Empirical reaction function
HICP, Factor
HICP, xHP, Factor
HICP, xL, Factor
HICP, xQ Factor
CoreInfl, Factor
ProdPrices, Factor
HICP, CoreInfl, ProdPrices, Factor
InflExp, Factor
HICP, CoreInfl, ProdPrices, InflExp, Factor
CoreInfl, ProdPrices, InflExp, Factor
-100.143
-104.224
-104.228
-104.556
-100.410
-102.317
-105.897
-98.780
-108.063
-104.985
0.005
0.007
0.007
0.007
0.006
0.006
0.008
0.006
0.009
0.008
-85.369
-90.026
-89.106
-90.412
-84.637
-84.878
-92.960
-83.169
-93.962
-89.982
0.016
0.018
0.018
0.016
0.023
0.039
0.024
0.026
0.034
0.042
NOTE: The static probit specification includes as explanatory variable the lagged observed policy rate. The
dynamic probit specification includes the lagged latent policy rate. All models also contain an intercept.
Log(Marginal) stands for the marginal density of the sample data (marginal likelihood) given parameter draws
from the posterior distribution. Num SE stands for the numerical standard error of the estimate.
32
Figure 1 – Real economic activity indicators
3
2
1
0
-1
-2
Sentiment
Eurocoin
Eurogrowth
-3
1999 2000 2001 2002 2003 2004 2005 2006
NOTE: The chart displays the standardized Sentiment (solid line), Eurocoin (dotted line) and Eurogrowth (dashed line)
survey indicators. The sample is from January 1999 to December 2006.
33
Figure 2 – Different measures of inflation
NOTE: The chart displays the HICP (solid line), the HICP excluding food and energy prices (CoreInfl, dotted line),
industrial producer prices (ProdPrices, dashed line) and inflation expectations (InflExp, square symbol). The sample is
from January 1999 to December 2006.
34
Figure 3 – Observed and latent policy rate
NOTE: This chart displays the observed (empty circle) and latent (filled circle) policy rate from January 1999 to
December 2006. The latent policy rate is estimated by the ordered probit model using as explanatory variables the
lagged observed policy rate, a constant, core inflation, and Factor.
NOTE: This chart displays the observed (empty circle) and latent (filled circle) policy rate from January 1999 to
December 2006. The latent policy rate is estimated by the dynamic probit model using as explanatory variables the
lagged latent policy rate, a constant, core inflation, and Factor.
35