Not for Publication
Online Appendix For: Preferences or Private
Assessments on a Monetary Policy Committee?∗
Stephen Hansen†
Michael McMahon‡
Carlos Velasco Rivera§
May 17, 2014
∗
The paper is available at http://www2.warwick.ac.uk/fac/soc/economics/staff/academic/
mcmahon/research/hmv2012.pdf.
†
Universitat Pompeu Fabra and Barcelona GSE.
‡
University of Warwick, CEPR, CAGE (Warwick), CEP (LSE), CfM (LSE), and CAMA (ANU).
Correspondence Address: Department of Economics; University of Warwick; Coventry, CV4 7AL; United
Kingdom. Email: m.mcmahon@warwick.ac.uk. Telephone: +44(0) 24 7652 3056.
§
Princeton University.
Contents
A Threshold voting rule in a New-Keynesian model
2
B Checking for serial correlation in the signals
4
C Monte Carlo Exercise
7
D Construction of Confidence Intervals
12
E Construction of Proxy for Prior
13
E.1 Reuter’s Survey Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
E.1.1 Construction of qR . . . . . . . . . . . . . . . . . . . . . . . . . .
17
E.2 Short Sterling Options price data . . . . . . . . . . . . . . . . . . . . . .
18
F Assessing the Sincere vs. Strategic Model
F.1 Mean Absolute Deviation
20
. . . . . . . . . . . . . . . . . . . . . . . . . .
20
F.2 Correct Classification Rate . . . . . . . . . . . . . . . . . . . . . . . . . .
22
G Alternative analysis and robustness results
25
G.1 Analysis of alternative splits of the committee members . . . . . . . . . .
25
G.2 Robustness analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
1
A
Threshold voting rule in a New-Keynesian model
Here we show that a basic version of Clarida, Galí, and Gertler’s (1999) New-Keynesian
model of monetary policy leads to a threshold interest rate rule similar to that derived
in the simple model in section 3 of the main paper. Following Galí (2008), the economy
is characterized by a dynamic IS curve and a New Keynesian Phillips Curve (NKPC):
xt =Et [ xt+1 ] − φ(it − Et [ πt+1 ] − rte )
(A.1)
πt =β Et [ πt+1 ] + κxt + ut
(A.2)
where xt ≡ yt − yte is the welfare-relevant output gap, yt is the log of the stochastic
component of output, yte is (log) efficient level of output, πt as the deviation of period t
inflation from its long-run level and it is the nominal interest rate.
For simplicity we allow only for a shock to the NKPC, ut ; this shock is generally called
a cost-push shock in the literature.1 We assume this shock follows an AR(1) process:
ut =ρu ut−1 + st where st ∼ N (0, σ2s )
(A.3)
The social loss to the representative household is, to a second-order approximation,
proportional to a function that is quadratic in inflation and output. As the policymaker
has discretion to choose the interest rate at time t, based on information available at the
end of time t − 1, so as to minimize the discounted future losses, there is no way that they
can credibly commit to any pre-specified path of future policy; this reduces the problem
to a series of static problems in which the central bank takes private sector expectations
as given. The discretionary problem to determine optimal monetary policy is:
∞
2
X
πt+τ
y2
πt2
y2
+ λ t + Et
+ λ t+τ
2
2
2
τ =1 2
"
minimize
it
#
subject to πt = κxt + β Et [ πt+1 ] + ut
1
We can also include a shock to the IS curve, gt , which will enter the optimal interest rate linearly.
2
where λ is κε , and ε is the substitutability between goods in the consumption aggregator.2
The optimal interest rate is:
it =rte
1
+
φ
1
(κ + λφ) ut
κ2 + λ(1 − βρu )
!
(A.4)
Forcing the MPC member must choose between two interest rates it > it (as we do in
our main model and show is the case for most MPC meetings), the vote is given by:
vit =




it
if ijt ≥ it − 12.5bps



it
otherwise
(A.5)
To move to a situation of imperfect information of economic conditions, we use the
the certainty equivalent version of the decision rule.3 Therefore, under uncertainty about
the state of the economy, where Ωt is the information set at time t, the decision rule is
as that the policymaker will vote for the higher interest rate (it ) if and only if:
2
i
− βρu ) h
e
E[ ut | Ωt ] ≥ φ κ +(κλ(1
it − rjt
− 12.5bps
+ λφ)
!
(A.6)
This is analogous to the decision rule in our main model; the member votes high
when their belief about the economic shock exceeds their member-specific cut-off which
depends on the structural parameters of the economy.
2
We can also allow for an interest rate smoothing term.
As Clarida, Galí, and Gertler (1999) Result 9 states: “With imperfect information, stemming either
from data problems or lags in the effect of policy, the optimal policy rules are the certainty equivalent
versions of the perfect information case. Policy rules must be expressed in terms of the forecasts of target
variables as opposed to the ex post behavior.”
3
3
B
Checking for serial correlation in the signals
As discussed in section 3.2 of the paper, a potential concern with our model is that
members’ private signals are persistent in reality and we do not allow for that. This
is a problem as it would violate the assumption that individual votes are independent
conditional on the state and prior. A model to accommodate this is significantly more
complex and a different estimator would be required. This section shows empirically
that votes are not serially correlated once we control for our proxies of the prior, which
measure the information present in economic data. In particular, we fit the following
OLS regression:
vit = γi + ρvit−1 + Xt + it
(B.1)
where vit is the main vote variable taking the value of one if individual i in time period t
votes for the high rate at t and zero otherwise. vit−1 is the lagged value of this outcome,
Xt is a vector with market data available at time t, γi individual fixed effects, and it is
a normally distributed error term with mean zero and variance σ 2 .
Table B.1 shows displays the results from fitting equation B.1 across three different
specifications. The first column shows that when we run a regression of a individuals
vote for the high rate just on its lagged value (an including individual fixed effects),
votes appear to be serially correlated since the estimate for ρ is positive and statistically
significant. Such serially correlated votes are consistent with a model of signal persistence.
However, once we control for the proxy of the prior available at each meeting, as measured
by the data from the Reuters survey and the option prices, in columns (2)-(3), we find
that votes are no longer serially correlated as the estimate for ρ is no longer statistically
significant. In fact, columns (2) and (3) show that only the market data is predictive of
individual votes. In particular, we find that higher value of the proxy for the inflationary
state are associated with a higher probability of individual voting for the high rate.
To the extent that serial correlation in votes is driven by serial correlation in the
4
Outcome variable: vit
vit−1
(1)
(2)
(3)
0.174∗∗∗
(0.029)
0.038
(0.024)
0.021
(0.024)
0.977∗∗∗
(0.042)
0.883∗∗∗
(0.046)
Reuterst
Markett
Constant
Individual Fixed Effects
Observations
R2
Adjusted R2
Note:
0.462∗∗∗
(0.095)
0.436∗∗∗
(0.058)
0.031
(0.052)
−0.165∗∗
(0.066)
Yes
Yes
Yes
1,219
0.117
0.097
1,174
0.402
0.388
1,174
0.414
0.399
∗
p<0.1;
∗∗
p<0.05;
∗∗∗
p<0.01
Table B.1: This table presents OLS estimates of the relationship between an individual’s
vote and lagged vote for the high rate across different specifications. The first column
shows that votes exhibit serial correlation. That is, an individual’s vote at t − 1 predicts
his vote at time t. However, this relationship disappears when we control for the market
data available at a given period as shown in columns (2) and (3). In fact, the last two
columns show that only the market data is predictive of an individual vote. In particular,
higher values of the Reuters and market data are associated with a higher probability of
an individual voting for the high rate.
5
common prior, this is less of a concern for us. Persistence in the prior is not incompatible
with our model which is already written conditional on qt .
6
C
Monte Carlo Exercise
This section presents the results from a Monte Carlo simulation discussed in section 4
of the paper. These simulations evaluate the performance of the estimator used in the
empirical analyzes presented in the paper. To do so, we consider two data generating
processes: (1) when the data is generated by a sincere voting model and (2) when the
data is generated by a strategic voting model. For both specifications, in any given
iteration, we generate priors and voting data for 150 meetings. In each meeting there are
five members belonging to group A and the remaining four to group B. Members from
group A are more hawkish but have better forecast precision than those in group B. In
particular, we set the structural parameters to the following values: θA = 0.7, σA = 0.4,
θB = 0.3, σB = 0.6.
Once the data is generated for a given iteration, we follow the two-step procedure
described in the paper. As in the main body of the paper, qt denotes the true value of
the prior at time t, and κiω for ω ∈ {0, 1} the individual voting probabilities for the high
rate. We model these probabilities as follows:
exp (α0 + α1 qt∗ )
1 + exp (α0 + α1 qt∗ )
exp (β0 + β1 · qt∗ + β2 · Di + β3 · Di · qt∗ )
=
1 + exp (β0 + β1 · qt∗ + β2 · Di + β3 · Di · qt∗ )
κ0it + exp (γ0 + γ1 · qt∗ + γ2 · Di + γ3 · Di · qt∗ )
=
1 + exp (γ0 + γ1 · qt∗ + γ2 · Di + γ3 · Di · qt∗ )
qt (qt∗ ) =
κ0it
κ1it
where qt is a measure of the prior and Di corresponds to a binary variable taking the
value of 1 if individual i belongs to group A. Once we obtain the estimates for each of
these probabilities, we solve for the structural parameters as described in the paper. We
repeat this process 500 times for each of the two data generating processes.
One concern regarding the estimator employed throughout the paper is that it pro7
duces temporal variation in the point estimates of the structural parameters. Thus, the
first important check is to see how these values relate to the true value of the underlying
parameters of interest. The results for the case in which the sincere voting model is the
data generating process are presented in C.1 (the results for the strategic model specification are very similar, with the preference parameter showing slighly higher variance).
The first aspect to note from this figure is that, compared to the precision of private
forecasts, the temporal variation is slightly higher for the preference parameter. Importantly, in both cases, the center of the temporal distribution of the parameters (shaded in
dark gray and black) is consistent with underlying true values (marked with the solid vertical line). These results suggest that a measure of the center of the distribution provides
a reasonable point estimate for the parameters of interest.
C.2 presents boxplots4 with the distribution of the structural parameters pointestimates across the two groups and different data generating processes. The figure shows
that the estimator produces a distribution centered around the true value of both preference and information parameters (with the exception of the strategic voting specification,
where the estimator produces a distribution with a slight upward bias for the preference
parameter). The figure also shows that the variance for the point estimates is always
greater relative to the one resulting from the estimation under the sincere specification.
Finally, C.3 displays boxplots with the empirical distribution of point estimates for the
difference in structural parameters across the two groups and data generating processes.
Consistent with the previous figure, the figure shows that the estimator recovers the true
difference in structural parameters between the two groups for all structural parameters,
except for the small downward bias in the preference difference under the strategic voting
model. As in the previous figure, the variance of point estimates is higher under the
strategic specification.
4
Boxplots are constructed as follows. The center of the distribution is marked by the bold line inside
each box. The upper and lower edges of the box represent the 75th and 25th percentile respectively.
Finally, the whiskers correspond to 1.5 times the Inter-Quartile Range (i.e. the difference between the
first and third quartiles); any point beyond the whiskers is considered an outlier and marked with an
empty dot.
8
Figure C.1: Temporal Variation in Structural Parameter Estimates
This color gradient figure shows the temporal variation in the structural parameter estimates within each Monte Carlo simulation. True parameter values are marked by the black
solid vertical line. Darker points correspond to observations closer to the center of the
distribution, while points in light gray correspond to less frequent observations (i.e. in top
and bottom percentiles). For instance, the left panel shows that observations to the left of
0.5 occur less than 10 percent of the time. The fact that darker points - marking the center
of the distribution within a given iteration - coincide with the true parameter value is an
indication that the mean, or the median, across time provides a reasonable point estimate
of the parameter of interest.
9
1.2
Strategic
Strategic
Sincere
1.0
Sincere
True Value A
0.6
θ
0.8
●
●
True Value B
●
●
●
0.0
0.2
0.4
●
●
1.5
A
Strategic
B
Strategic
Sincere
Sincere
●
●
1.0
●
●
0.5
σ
●
●
●
●
●
●
●
●
●
●
●
0.0
●
●
A
B
Figure C.2: Empirical Distribution of Structural Parameter Estimates
The boxplots display the empirical distribution of point estimates using the two-step procedure for the structural parameters of the voting model between members of type A and B
across sincere and strategic voting data generating processes. The figure shows that under
the sincere voting data generating process point estimates are tightly distributed around
the true parameter values of individuals type A and B. Under the strategic voting data
generating process point estimates are centered around the true value in the case of the
information parameter, with a slight upward bias for the information parameter, and for
both parameters the distribution has a higher variance relative to the case where the data
is generated by a sincere voting model.
10
1.0
0.6
True Difference
0.4
●
0.5
0.0
0.2
Difference in Theta
0.8
●
●
True Difference
0.0
●
−0.5
●
●
●
●
●
●
●
●
●
−1.0
Difference in Sigma
●
●
●
●
Strategic
Sincere
Figure C.3: Empirical Distribution of Differences in Structural Parameter Estimates
The boxplots display the empirical distribution of the point estimates using the two-step
procedure for the difference in structural parameters of the voting model between members
of type A and B across strategic and sincere voting data generating processes. Except
for the difference in preference parameters under the strategic specification (where the
estimator produces a slight downward bias), the distribution of point estimates is centered
around the true value for all other parameters. Further, the variance of point estimates is
small in magnitude under sincere voting relative to the its magnitude under the strategic
voting data generating process.
11
D
Construction of Confidence Intervals
In this section we discuss the construction of confidence intervals which we briefly outline
in section 4.2 of the paper. We construct confidence intervals using a form of bootstrapping; we repeatedly sample the first-stage parameter estimates and then recalculate
the structural parameters of interest and use the resulting distribution of structural parameters to construct our measure of uncertainty. Specifically, for each of 500 iterations:
1. We take a random draw of α, β, and γ from a multivariate normal distribution centred on the first-stage coefficient point estimates and variance given by the inverse
of the negative Hessian of the MLE estimates.
2. We use these new coefficient estimates to calculate a new set of estimated structural
parameters θbtA , σbtA , θbtB , and σbtB .
3. For each relevant meeting,5 we generated an estimate of the difference between the
two groups θbtDiff = θbtA − θbtB and σbtDiff = σbtA − σbtB .
o
n
4. For each series in θbtA , θbtB , θbtDiff , σbtA , σbtB , σbtDiff we derive a time-invariant estimate by
taking the mean (and, as a robustness check, the median).
This process yields a distribution over structural parameters and their differences,
from which we extract the quantiles of interest to construct confidence intervals.
As a robustness check on the procedure outlined in this section, we also compute
differences across individuals rather than within meetings. First, we divide each of the
27 into groups A and B. Then, for each member i of group A (B), we compute the mean
A
A
B
B
value of θbi,t
and σbi,t
(θbi,t
and σbi,t
) for the meetings on which i served. This gives us a
distribution of individual θ and σ estimates for groups A and B. Finally, we take the difference in means across these two distributions. To obtain confidence intervals under this
5
We only compute the difference between A and B in the subset of meetings in which both are present,
which in most cases is identical to the full set of 137 meetings for which we can construct our proxies for
the prior. Also, when we recover θ parameter estimates in the strategic model, we only use the 117 (out
of 137) meetings with nine voters for computational simplicity.
12
specification, we sample 500 draws of first stage parameters from the multivariate normal
distribution described in step 1., and for each iteration compute the quantities of interest
as outlined in the previous sentences. The computation of confidence of intervals then is
performed by extracting from this empirical distribution the quantiles corresponding to
a given confidence level.
This approach is sometimes called a quasi-Bayesian approach. It is widely used in
other fields and within economics Hamilton (1991) and Chernozhukov and Hong (2003)
discuss applications of quasi-Bayesian estimation.
E
Construction of Proxy for Prior
Section 5 of the main paper provides a brief outline of the data construction of the proxies
for the common prior used in the estimation procedure. In the following two subsections
we provide a more complete description of these data including how we treated anomalies
in the data.
E.1
Reuter’s Survey Data
Reuters did not have the survey results stored in their database, they were unable to
provide the data to us. Instead, we have been able to collate copies of the survey results
for most periods in the sample; the two exceptions are February 2000 and March 2000.
In addition, we are unable to use the data for periods April 2000, August 2008, and
November 2008 (details of why are in the appendix). This leaves 137 out of the 142
months in our sample for which we can construct qtR .
Also, there are somewhat different formats for different sub-samples within our data
for which we follow a slightly different methodology.
The Reuters Data that we have been able to gather is divided into three segments corresponding to data availability, and each period calls for a different construction methodc
ology. Implicit in the construction is how we define D(High
Vote)it .
13
June 1997 - June 1998: Mark I Construction
We have modal data, all of which takes a value of 0, and +25, except for October 1997
in which one bank reported +50 which we treat as +25.
• qtR is computed as the total number of reports for +25 over the total number of
reports.
• Anomalies
– In the May 1998 MPC meeting there were 6 votes for no change, 1 vote for
-25 (Julius) and 1 vote for +25 (Buiter). We treat the -25 vote as a low vote
and proceed as above.
– In the June 1998 MPC meeting there were 8 votes for +25 and 1 vote for -25
(Julius). Again, we treat -25 as a low vote.
July 1998 - December 2001: Mark II Construction
We have partial probability distribution data over rise, no change, and cut. In some
periods only two of these three options are available.
• We compute the average probability placed on rise, cut, and no change.
• For all periods in which we observe votes that lie in the set -25,0,25 we treat the
data as if the probability of rise is the probability of +25 and the probability of cut
is the probability of -25.
• For periods in which the votes are +25 and 0 we construct qtR as the total average
probability put on +25 over the total average probability placed on +25 and 0.
• For periods in which the votes are 0 and -25 we construct qtR as the total average
probability put on 0 over the total average probability placed on 0 and -25.
• For periods in which all votes are for +25 we construct qtR over the total average
probability put on +25 over the total average probability placed on +25 and 0.
14
• For periods in which all votes are for -25 we construct qtR over the total average
probability put on 0 over the total average probability placed on 0 and -25.
• For periods in which all votes are for nochange we construct qtR as the total average
probability put on +25 over the total average probability placed on +25 and 0 if the
total average probability placed on +25 is larger than the total average probability
placed on -25, and construct qtR as the total average probability put on 0 over the
total average probability placed on 0 and -25 if the total average probability placed
on -25 is larger than the total average probability placed on +25.
• Anomalies
– In August 1998 there were 7 votes for no change, 1 vote for -25 (Julius) and 1
vote for 25 (Buiter). The total average probability placed on +25 is 0.39 and
the total average probability placed on -25 is 0.001. So we treat +25 as high
vote and compute as the total average probability place on +25.
– In January 1999 there was one vote for no change (Plenderleith), 7 votes for
-25, and one vote for -50 (Julius). We treat the vote for -25 and -50 as low
votes and compute qtR as the total average probability placed on nochange over
the total average probability placed on nochange and cut.
– In March 1999 8 people voted for no change and 1 person (Buiter) voted for
-40. We treat the -40 vote as a vote for -25 and proceed as above.
– In April 2000 3 people voted for +25 and six for 0, but Reuters survey does
not ask for probability of rise. We treat these data as missing in this period.
– In January 2000 the votes were over +25 and +50 and we set qtR = 0.5.
– In April 2001, May 2001, October 2001, and November 2001, the votes were
over -25 and -50 and we set qtR = 0.5.
January 2002 - November 2008: Mark III Construction
We have full distribution data over +50, +25, 0, -25, -50.
15
• We compute the average probability placed on +50, +25, no change, -25 and -50.
• For periods in which there are two unique votes we take qtR as the total average
probability placed on the higher of the two votes over the total average probability
placed on both votes.
• For periods in which all votes are for +50 we construct qtR over the total average
probability put on +50 over the total average probability placed on +50 and +25.
• For periods in which all votes are for -50 we construct qtR over the total average
probability put on -25 over the total average probability placed on -25 and -50.
• For periods in which all votes are for no change we construct qtR as the total average
probability put on +25 over the total average probability placed on +25 and 0 if the
total average probability placed on +25 is larger than the total average probability
placed on -25, and construct qtR as the total average probability put on 0 over the
total average probability placed on 0 and -25 if the total average probability placed
on -25 is larger than the total average probability placed on +25.
• We follow a similar procedure as the above for periods in which all votes are for
+25 or -25.
• Anomalies
– In May 2006 there were six votes for no change, one vote for +25 (Walton)
and one vote for -25 (Nickell). The market put probability 0.08 on -25 and
probability 0.03 on +25. So we take 0 to be high vote and compute qtR as
(meannochange + meanrise25)/(meancut25 + meannochange + meanrise25).
– In April 2008 there were votes for 0, -25, and -50. We take 0 as a high
vote and -25 and -50 as low votes, and compute the high vote as (meannochange)/(meancut25 + meannochange + meancut50).
16
– In August 2008 there were votes over -25, 0, +25 but the market placed roughly
equal probability on -25 and +25 so we set qtR as missing.
– In November 2008 there was unanimity on -150, which was not considered by
respondents, and we set qtR as missing.
December 2008 - March 2009: Mark IV Construction
We again have modal data.
• In December 2008 everyone vote to cut -100 and -100 was the lower bound on the
modes. We set -100 as low vote and compute qtR as all modes not equal to -100 over
all modes.
• In January 2009 everyone votes to cut by -50 or -100 and these make up most
modes. We set qtR as the number of -50 modes over all modes equal to -50 or -100.
• In February 2009 everyone votes to cut -50 or -100. We take qtR as the total number
of modes not equal to -100 over the total number of modes.
• In March 2009 everyone votes to cut -50. We set -50 as the high vote and set qtR as
all modes -50 or greater over all modes.
E.1.1
Construction of qR
Table E.1 illustrates a hypothetical example of the survey and how we use it. The two
outcomes with the highest average probability are a rise of 50 basis points and a rise of 25
basis points. So, if we observed a unanimous vote of +25, our proxy measure for the prior
would be qtR =
23.75
23.75+71.25
= 0.25 and we would set vit = 0 for all members. Following this
procedure we are in a position to construct the voting data for all periods regardless of
whether the vote was unanimous.
17
Table E.1: Example of Survey Data
UBS
Goldman Sachs
JP Morgan
AIB
Average
+50bps
15%
20%
45%
15%
23.75%
+25bps
0
-25bps
80%
5%
75%
5%
45%
10%
85%
71.25% 5%
-50bps
Notes: This table shows an example of the survey we use and how we calculate the proxy
measure of qt using these data. First, we average the probability attached to each possible
decision across the surveyed banks (average down the columns in this table to get the final
row labelled "Average"). We then choose the two most likely decisions based on this average;
+50bps and +25bps in this case. Finally, we calculate qtR equal to the average probability
placed on the higher rate over the total average probability placed on both rates; in the
23.75
= 0.25.
example, qtR = 23.75+71.25
E.2
Short Sterling Options price data
Here we outline the assumptions underlying the options price data that we use; full
details about these data, as well as the data itself, are provided by the Bank of England
(see Bank of England (2011a), Bank of England (2011b) and Lynch and Panigirtzoglou
(2008)). Short sterling futures contracts are standardized futures contracts which settle
on the 3 month London Interbank Offered Rate (LIBOR) on the contract delivery date.
Short sterling futures options are a European option (it only settles on the delivery date
and not before) on the short sterling futures contract but since the futures contract
settles on 3 month LIBOR, the option is effectively an option on 3 month LIBOR. The
Bank of England computes the expected value of 3 month LIBOR consistent with a
risk neutral trader being willing to hold the option at each observed price; this yields a
distribution over risk-neutral traders’ beliefs on 3 month LIBOR. The Bank then publishes
the 0.05, 0.15, . . . , 0.95 percentiles of this CDF. Figure E.1 displays the spot 3 month
LIBOR rate as well as various percentiles of this CDF. We subtract the actual value
of LIBOR on the Wednesday of the MPC meeting (before the decision is made on the
Thursday) to express the CDF in terms of traders’ beliefs on changes in 3 month LIBOR.
We denote this transformed CDF as F , and an individual belief about a change x.
18
8
Interest Rate (level, pp)
2
4
6
0
1997m1
2000m1
2003m1
Date
Current Libor
45% to 55%
2006m1
2009m1
25% to 75%
5% to 95%
Figure E.1: Short-Sterling Implied PDF and 3 Month LIBOR
Notes: This figure shows the spot 3 month LIBOR rate (black line) and the shaded areas
represent various percentiles of the risk neutral CDF derived from short sterling (3 month
LIBOR) futures contracts.
Since base rate changes are made in discrete 25 point movements while traders’ beliefs
are continuous, we consider beliefs that lie within 12.5 basis points on either side of the
corresponding change to be beliefs associated with that change being more likely. So, for
example, our ideal proxy measure for qt in a period in which no change and a 25 point
rise are on the agenda would be
Pr [ 12.5 ≤ x ≤ 37.5 ]
F (37.5) − F (12.5)
=
.
Pr [ −12.5 ≤ x ≤ 37.5 ]
F (37.5) − F (−12.5)
Unfortunately we only observe certain percentiles of F . To correct for this, we linearly
interpolate between the two percentiles in which a rate change falls. So, for example,
suppose that we observe that F (10) = 0.1 and F (20) = 0.3; then we would construct
F (12.5) = 0.15. Using this method we are able to build qtM for all but four time periods,
meaning that we observe the markets data for 138 meetings out of 142 possible meetings
in our sample.6
6
The missing periods are February and March 2000, August 2008, and November 2008. These data
are missing due to thin or illiquid short-sterling options markets which mean that no options pdf data
19
F
Assessing the Sincere vs. Strategic Model
This section presents more details on the results of the test to assess the performance of
the sincere and strategic models in predicting the votes of the Bank of England’s MPC
members. We discuss the results in section 6.2 of the main paper.
In our sample there are a total of 142 meetings, although 5 are missing because there
are no prior data associated with them. In the following section, we will refer to meetings
by a meeting number where 1 corresponds to the meeting in June 1997, and meetings are
numbered chronologically from that date.
Our test is based on out-of-sample prediction. That is, we use the votes associated
with a subsample of meetings in the data to estimate the preference and information
parameters for internal and external members across the sincere models and strategic
models, to then produce predictions (and assess their accuracy) for the votes in the subsample not used in the estimation stage. We rely on two different metrics to assess model
performance: (1) the mean absolute deviation between observed votes and predicted
probabilities (MAD) and (2) the predicted probabilities correct vote classification rate.
The out-of-sample predictive tests are conducted across the following four samples: (1)
Data with meetings 101-142 (Sample C); (2) Data with meetings 51-100 (Sample B); (3)
Data with meetings 1-50 (Sample A); and (4) Data with a random set of meetings (Random Sample).7 Our results show that the sincere model produces a marginal advantage
over the strategic model across both metrics and samples. In the rest of the section we
discuss the details of the model performance test.
F.1
Mean Absolute Deviation
The first test to assess model performance relies on MAD. This metric involves first taking
the estimates of the preference and information parameters under a given subsample of the
is available on the days in the run up to MPC meeting.
7
The meetings in the random sample are the following: 1, 4, 5, 13, 21, 32, 36, 49, 50, 52, 54, 62, 65,
68, 72, 76, 78, 79, 82, 84, 86, 87, 90, 91, 93, 94, 100, 105, 107, 110, 112, 119, 121, 122, 124, 125, 127, 128,
130, 131, 136, and 140.
20
data to generate predictions about the individual votes in the subsample of meetings not
used in the estimation stage. The construction of predictions involves three steps. First,
we use the Reuters and Market data, the first stage estimates for the mixture probability,
and the estimates of the structural parameters to obtain a cutoff signal according to
equations (3) and (5) in the paper. Second, using the cutoff signals we then generate
probabilistic predictions for a high vote based on the following equation:
ŝ∗ (·) − 1
p̂i ≡ q̂ × 1 − Φ i
σ̂i
!!
ŝ∗ (·)
+ (1 − q̂) × Φ i
σ̂i
!!
(F.1)
where q̂ is the predicted value of the prior given the Reuters and Market data, and 1−Φ(·)
is the voting probability of voting for the high rate given the inflationary state, the cutoff
estimate ŝ∗i , and information parameter σ̂i for the ith vote in the data not used in the
estimation stage. Finally, we compute MAD as follows:
1 X
|vi − p̂i |.
N i∈N
(F.2)
where vi = 1 if the ith vote was for the high rate and zero otherwise and N is the total
number of votes in the sub-sample not used in the estimation stage. This metric is
highest when p̂i = 0.5 and becomes decreases as the value of predicted probability for
a high vote is closest to the observed vote vi . We opt for this metric as opposed to the
Root Mean Square Error (RMSE) for a simple reason. The outcome of interest is binary
and thus its absolute deviation from the probability of a high vote will always be less
than 1. Therefore, if we were to rely on the RMSE we would impose smaller penalties to
deviation with poorer “fit”. Instead, the metric we propose imposes a linear penalty to
all deviations.
Table F.1 presents the results of our model performance test when relying on the
absolute mean deviation metric across four samples. The first row in the table shows
that the sincere model produces a mean absolute deviation 2-percentage points smaller
than the strategic model when using the estimates for θ and σ based on a sample with
21
C Sample
B Sample
A Sample
Random Sample
Sincere
0.368
0.345
0.429
0.394
Strategic Difference
0.388
-0.020
0.378
-0.033
0.443
-0.014
0.419
-0.025
Table F.1: Mean Absolute Deviation: Sincere vs. Strategic Models
Notes: This table shows the mean absolute deviation between the observed individual votes
and predicted probabilities for a high vote across different samples and model specifications.
The first row under column 1 shows that under the sincere model the mean absolute deviation when using the estimates derived from sample with meetings 1-100 to predict votes in
sample C (with meetings 101-142) is 36.8 percentage points. The figure under the strategic specification is 38.8, producing 2-percentage point difference (shown under the third
column) in favor of the sincere model. As shown in rows (2)-(4), this result is robust to
different sample specifications.
meetings 1-100 to predict votes in sample C with meetings 101-142. As rows 2 − 4 show,
the marginal advantage of the sincere model is robust across all four samples.
F.2
Correct Classification Rate
As an alternative, we conduct a test relying on the correct vote classification rate as the
metric to assess model performance. This test involves taking the predicted probabilities
for a high rate, constructed as described in the previous subsection, and creating deterministic predictions about individual votes in the out-of-sample data. In particular, we
predict a vote for a high rate hi = 1 given a cutoff c if p̂i > c and for a low rate (hi = 0)
otherwise, and then take these predictions to compute the correct classification of votes
according to the following equation:
r≡
1 X
{vi × hi + (1 − vi ) × (1 − hi )}.
N i∈N
(F.3)
Figure F.1 presents the value of this metric across four different samples under both
the sincere and strategic model. Across all four samples, the sincere model exhibits a
marginal advantage over the strategic model. For instance, panel F.1a shows that for
cutoffs in the interval [0.52, 0.68] both models produce an r close to 65 percent when
22
assessing out-sample prediction on the sample with meetings 101-142 (i.e. sample C).
However, for the vast majority of values outside this interval we see that that sincere
voting model produces a higher r. On average, outside this interval the sincere model
produces a 3.1-percentage point gain in r. As shown in panels F.1b-F.1d, this result is
robust to different samples in the data.
23
Share Correctly Classified Votes
(a) Classification of votes in Sample C
(b) Classification of votes in Sample B
0.8
0.8
0.7
0.7
Sincere
Strategic
0.6
0.6
0.5
0.5
0.4
0.4
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
Cutoff
(c) Classification of votes in Sample A
Share Correctly Classified Votes
0.6
0.8
1.0
Cutoff
(d) Classification votes in Random Samples
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.0
0.2
0.4
0.6
0.8
1.0
0.0
Cutoff
0.2
0.4
0.6
0.8
Cutoff
Figure F.1: Correct Vote Classification Rate: Sincere vs. Strategic Models
Notes: This figure shows the correct classification rate of votes under the sincere and
strategic models across different classification cutoffs and different samples. Panel F.1a
shows the correct classification rate of votes in sample C based on the predictions computed
with the estimates of the structural parameters (θ and σ) under a samples with meetings 1100. The panel shows that for values between 0.52 and 0.68, both the sincere and strategic
models produce the same classification rates. However, outside this interval the sincere
model produces an average gain of 3.1 percentage points. Panels F.1b-F.1d shows a similar
pattern, with the sincere model producing a marginal gain over the strategic one in terms
of the correct classification of votes.
24
1.0
G
Alternative analysis and robustness results
This section provides figures for alternative analysis and robustness discussed in section
6.3 and 6.4 respectively.
G.1
Analysis of alternative splits of the committee members
In section 6.3 of the main paper, we discuss the results of examining a number of alternative splits of the committee by different group characteristics. In this section we present
figures that summarise these results. The alternative splits that we consider are based
on: type of appointment, career at the Bank, age, professional background in the private
sector, academic career, and academic background. The member allocation according to
each of these grouping variables is provided in table G.1.
The remainder of the figures in this section show the estimated difference between the
groups for each of the characteristics. The figures that we use each present the estimated
distribution of the structural parameter of interest for each split. The distribution is the a
kernel density estimated on the 500 boot-strapping draws of the first stage parameter estimates. The kernel density is estimated using the diffusion method of Botev, Grotowski,
and Kroese (2010). In each figure, the vertical lines mark zero, the point estimate of the
difference between the groups, and the 95% confidence bounds. The difference between
internal and external members, the main result in the paper, is plotted in each figure for
comparison.
G.2
Robustness analysis
In section 6.4 of the main paper, we discuss the robustness of the baseline results to a
number of alternative choices regarding how we report the results and alternative first
stage estimation equations. The figures in this section show the estimated difference
between structural parameters for internal and external members under each alternative
approach. As in the last subsection, the figures each present the estimated distribution of
25
Figure G.1: Members’ Background Characteristics
Notes: This figure shows the tenure of members serving on the MPC for the period 06/9703/09 and how they are split into groups across six covariates of interest: type of appointment, career at the Bank, age, professional background in the private sector, academic
career, and academic background. The top left handside panel shows, for example, that
Edward George was appointed to serve on the MPC as an internal member and his tenure
spans the period 06/97-06/03. In contrast, Tim Besley was appointed as an external members and served in our sample during the period 06/06-03/09.
26
Andrew Sentance (10/06−03/09)
Charles Goodhart (06/97−05/00)
Christopher Allsopp (06/00−05/03)
David Blanchflower (06/06−03/09)
David Walton (07/05−06/06)
DeAnne Julius (11/97−03/01)
Kate Barker (06/01−03/09)
Marian Bell (06/02−06/05)
Richard Lambert (06/03−03/06)
Stephen Nickell (06/00−05/06)
Sushil Wadhwani (06/99−05/02)
Tim Besley (06/06−03/09)
Willem Buiter (06/97−05/00)
Charles Bean (10/00−03/09)
David Clementi (11/97−08/02)
Edward George (06/97−06/03)
Howard Davies (06/97−07/97)
Ian Plenderleith (06/97−05/02)
John Gieve (01/06−03/09)
John Vickers (06/98−11/00)
Mervyn King (06/97−03/09)
Paul Fisher (03/09−03/09)
Paul Tucker (06/02−03/09)
Rachel Lomax (07/03−06/08)
Spencer Dale (07/08−03/09)
Non−Academic
Andrew Large
Andrew Sentance
David Clementi
David Walton
DeAnne Julius
Edward George
Howard Davies
Ian Plenderleith
John Gieve
Kate Barker
Marian Bell
Mervyn King
Paul Fisher
Paul Tucker
Rachel Lomax
Richard Lambert
Spencer Dale
Sushil Wadhwani
Academic
Charles Goodhart
Christopher Allsopp
David Blanchflower
John Vickers
Stephen Nickell
Tim Besley
Willem Buiter
Academic Career
External
Appointment
Internal
David Clementi
David Walton
DeAnne Julius
Kate Barker
Marian Bell
Richard Lambert
Sushil Wadhwani
Private Sector
Andrew Large
Charles Bean
Charles Goodhart
Christopher Allsopp
David Blanchflower
Edward George
Howard Davies
Ian Plenderleith
John Gieve
John Vickers
Mervyn King
Paul Fisher
Paul Tucker
Rachel Lomax
Spencer Dale
Stephen Nickell
Tim Besley
Willem Buiter
Non−Private Sector
Professional Background
Andrew Large
Andrew Sentance
Charles Bean
Charles Goodhart
Christopher Allsopp
David Blanchflower
David Clementi
David Walton
DeAnne Julius
Howard Davies
John Gieve
John Vickers
Kate Barker
Marian Bell
Rachel Lomax
Richard Lambert
Stephen Nickell
Sushil Wadhwani
Tim Besley
Willem Buiter
Outsider
Bank Career
Ian Plenderleith
Mervyn King
Paul Fisher
Paul Tucker
Spencer Dale
Insider
Christopher Allsopp
David Clementi
David Walton
Edward George
Howard Davies
Ian Plenderleith
John Gieve
Kate Barker
Marian Bell
Paul Tucker
Rachel Lomax
Richard Lambert
Spencer Dale
No PhD
Academic Background
Andrew Sentance
Charles Bean
Charles Goodhart
David Blanchflower
DeAnne Julius
John Vickers
Mervyn King
Paul Fisher
Stephen Nickell
Sushil Wadhwani
Tim Besley
Willem Buiter
PhD
Charles Bean
David Walton
DeAnne Julius
Howard Davies
John Vickers
Kate Barker
Marian Bell
Mervyn King
Paul Fisher
Paul Tucker
Spencer Dale
Sushil Wadhwani
Willem Buiter
Younger
Age
Andrew Large
Charles Goodhart
Christopher Allsopp
David Blanchflower
David Clementi
Edward George
Ian Plenderleith
John Gieve
Rachel Lomax
Richard Lambert
Stephen Nickell
Tim Besley
Older
(a) Private Sector vs Other - Sin-(b) Private Sector vs Other (c) Private Sector vs Other - σ
cere θ
Strategic θ
7
50
7
45
6
6
40
35
4
Private Sector vs Other
Internal vs External
3
5
Private Sector vs Other
Internal vs External
30
Density
Density
Density
5
25
20
15
2
Private Sector vs Other
Internal vs External
4
3
2
10
1
1
5
0
−0.3
−0.2
−0.1
0
0.1
0.2
θ Difference
0.3
0.4
0
−0.2
0.5
−0.15
−0.1
−0.05
0
θ Difference
0.05
0.1
0
−0.6
0.15
−0.4
−0.2
0
0.2
0.4
0.6
σ Difference
0.8
1
1.2
1.4
(d) Academic vs Non-academic -(e) Academic vs Non-academic (f) Academic vs Non-academic - σ
Sincere θ
Strategic θ
8
50
7
45
7
6
40
6
Academic vs Non−Academic
Internal vs External
3
5
Academic vs Non−Academic
Internal vs External
30
Density
4
Density
Density
35
5
25
20
15
Academic vs Non−Academic
Internal vs External
4
3
2
2
10
1
1
0
−0.3
5
−0.2
−0.1
0
0.1
0.2
θ Difference
0.3
0.4
0.5
0
−0.35
−0.3
−0.25
−0.2
−0.15
−0.1
−0.05
θ Difference
0
0.05
0.1
0
−0.8
−0.6
−0.4
−0.2
0
σ Difference
0.2
0.4
0.6
Figure G.2: Experience prior to joining MPC Splits
Notes: These figures show the kernel density of the difference for members who joined
from the private sector compared with those from other backgrounds (top panel) and those
coming from academic jobs compared to the others (bottom panel). The distribution of the
internal versus external difference is reported for comparison. Neither of the alternative
splits yields significant differences.
the structural parameter of interest for each alternative. The distribution is the a kernel
density estimated on the 500 boot-strapping draws of the first stage parameter estimates.
The kernel density is estimated using the diffusion method of Botev, Grotowski, and
Kroese (2010). In each figure, the vertical lines mark zero, the point estimate of the
difference between the groups, and the 95% confidence bounds. The baseline difference
between internal and external members, the main result in the paper, is plotted in each
figure for comparison.
27
(a) PhD vs No PhD - Sincere θ (b) PhD vs No PhD - Strategic θ
9
(c) PhD vs No PhD - σ
50
PhD vs No PhD
Internal vs External
8
7
45
6
40
7
5
35
PhD vs No PhD
Internal vs External
5
4
Density
30
Density
Density
6
PhD vs No PhD
Internal vs External
25
20
4
3
3
15
2
2
10
1
1
5
0
−0.2
0
−0.08
−0.1
0
0.1
0.2
θ Difference
0.3
0.4
0.5
−0.06
−0.04
−0.02
0
0.02
θ Difference
0.04
0.06
0.08
0
−0.6
(d) Older vs Younger - Sincere θ (e) Older vs Younger - Strategic θ
10
Old vs Younger
Internal vs External
0
0.2
σ Difference
0.4
0.6
0.8
7
45
6
40
7
35
6
30
5
4
5
Old vs Younger
Internal vs External
Density
8
Density
Density
−0.2
(f) Older vs Younger - σ
50
9
−0.4
25
20
3
15
2
10
1
5
0
−0.2
0
−0.06
Old vs Younger
Internal vs External
4
3
2
1
−0.1
0
0.1
0.2
θ Difference
0.3
0.4
0.5
−0.04
−0.02
0
0.02
θ Difference
0.04
0.06
0.08
0
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
σ Difference
0.1
0.2
Figure G.3: Education and Age Splits
Notes: These figures show the kernel density of the difference for members who hold a PhD
compared with those who do not (top panel) and those joining the MPC younger than 50
compared to older joiners (bottom panel). The distribution of the internal versus external
difference is reported for comparison. Neither of the alternative splits yields significant
differences.
28
0.3
0.4
(a) Alternative 1 - θ
(b) Alternative 1 - Strategic θ
(c) Alternative 1 - σ
7
7
Alternative Specification 1
Baseline
50
6
40
4
3
Alternative Specification 1
Baseline
5
Density
Alternative Specification 1
Baseline
Density
Density
5
6
30
4
3
20
2
2
10
1
0
0
1
0.05
0.1
0.15
0.2
0.25
0.3
θ Difference
0.35
0.4
0.45
0
0
0.5
(d) Alternative 2 - θ
0.01
0.02
0.03
0.04
0.05
θ Difference
0.06
0.07
0.08
0
−0.6
(e) Alternative 2 - Strategic θ
−0.5
−0.4
−0.3
−0.2
−0.1
0
σ Difference
0.1
0.2
0
0.2
0
0.1
(f) Alternative 2 - σ
8
7
7
Alternative Specification 2
Baseline
50
6
6
5
Alternative Specification 2
Baseline
4
Density
Density
Density
40
5
30
Alternative Specification 2
Baseline
4
3
3
20
2
2
10
1
1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
θ Difference
0.35
0.4
0.45
0
0
0.5
0.01
0.02
0.03
0.04
0.05
θ Difference
0.06
0.07
0.08
0
−1.2
−1
−0.8
−0.6
−0.4
σ Difference
−0.2
Figure G.4: Alternative Specifications for Internal vs External Split
Notes: These figures show the estimated distribution of the difference in the parameters
between internal and external members for alternative specification 1 (top panel) and alternative specification 2 (bottom panel) as described in the robustness section of the paper.
For reference, the estimated distribution between internal and external members using the
mean is also reported (the dashed line).
(a) Using Median - Sincere θ
(b) Using Median - Strategic θ
(c) Using Median - σ
7
8
120
Median
Mean
6
7
100
6
5
Median
Mean
4
3
Density
Density
Density
80
60
5
Median
Mean
4
3
40
2
2
20
1
0
0
1
0.05
0.1
0.15
0.2
0.25
0.3
θ Difference
0.35
0.4
0.45
0.5
0
−0.01
0
0.01
0.02
0.03
0.04
θ Difference
0.05
0.06
0.07
0.08
0
−0.6
−0.5
−0.4
−0.3
−0.2
σ Difference
−0.1
Figure G.5: Robust to using Median
Notes: These figures show, for each structural parameter, the estimated distribution of the
difference in the parameters between internal and external members when we use the median
rather than the mean of the temporal estimates (solid distribution line); for reference,
the estimated distribution between internal and external members using the mean is also
reported (the dashed line).
29
(a) Across Member - Sincere θ
(b) Across Member - Strategic θ
8
(c) Across Member - σ
50
Across Banker
Across Time
7
7
45
6
40
6
5
4
3
30
Density
Density
Density
35
5
Across Banker
Across Time
25
20
15
Across Banker
Across Time
4
3
2
2
10
1
1
0
0
5
0.1
0.2
0.3
0.4
θ Difference
0.5
0.6
0.7
0
0
0.02
0.04
0.06
θ Difference
0.08
0.1
0.12
0
−0.6
−0.5
−0.4
−0.3
−0.2
σ Difference
−0.1
Figure G.6: Robust to using Mean Across Member (rather than time)
Notes: These figures show, for each structural parameter, the estimated distribution of
the difference in the parameters between internal and external members when we take the
mean across individual MPC members rather than across time (solid distribution line);
for reference, the estimated distribution between internal and external members using the
mean across time is also reported (the dashed line).
30
0
0.1
References
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31