Not for Publication Online Appendix For: Preferences or Private Assessments on a Monetary Policy Committee?∗ Stephen Hansen† Michael McMahon‡ Carlos Velasco Rivera§ May 17, 2014 ∗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: [email protected] 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 Bank of England (2011a): “Notes On The Bank Of England Option-Implied Probability Density Functions,” http://www.bankofengland.co.uk/statistics/ impliedpdfs/BofEOptionImpliedProbabilityDensityFunctions.pdf, last accessed 12 March 2011. (2011b): “Option-Implied Probability Density Functions for Short Sterling Interest Rates and the FTSE 100,” http://www.bankofengland.co.uk/statistics/ impliedpdfs/index.htm, last accessed 12 March 2011. Botev, Z., J. Grotowski, and D. P. Kroese (2010): “Kernel density estimation via diffusion,” Annals of Statistics, 38(5), 2916–2957. Chernozhukov, V., and H. Hong (2003): “An MCMC approach to classical estimation,” Journal of Econometrics, 115(2), 293–346. Clarida, R., J. Galí, and M. Gertler (1999): “The Science of Monetary Policy: A New Keynesian Perspective,” Journal of Economic Literature, 37(4), 1661–1707. Galí, J. (2008): Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework. Princeton University Press, Princeton, USA and Oxford, UK. Hamilton, J. D. (1991): “A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions,” Journal of Business & Economic Statistics, 9(1), 27–39. Lynch, D., and N. Panigirtzoglou (2008): “Summary statistics of option-implied probability density functions and their properties,” Bank of England Working Paper 345, Bank of England. 31

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