Accessible Unlicensed Requires Authentication Published by De Gruyter July 9, 2016

Voting in Central Banks: Theory versus Stylized Facts

Roman Horváth, Kateřina Šmídková and Jan Zápal

Abstract

The paper examines the ability of several alternative group decision-making models to generate proposing, voting and decision patterns matching those observed in the Bank of England’s Monetary Policy Committee and the US Federal Reserve’s Federal Open Market Committee. A decision-making procedure, common to all the models, is to vote between adoption of the chairman’s proposal and retention of the status-quo policy, with heterogeneous votes generated by private information of the models’ monetary policy committee members. The members can additionally express reservations regarding the final committee decision. The three alternative models differ in the degree of informational influence between the chairman and the remaining members. We find that a “supermajoritarian” model, in which the chairman proposes a policy she knows would be accepted by a supermajority of the committee members, combined with allowance for reservations, closely replicates real-world decision-making patterns. The model predicts no rejections of chairman’s proposals, low but non-trivial dissent, even during meetings where the chairman proposes no change in policy, and predictive power of the voting record of the whole committee regarding future monetary policy changes.

JEL Classification: C78; D78; E52; E58

Acknowledgments

We thank two anonymous referees, Marianna Blix-Grimaldi, Jakob de Haan, Michael Ehrmann, Petra Gerlach-Kristen, Etienne Farvaque, Jan Filáček, Tomáš Holub, Jarek Hurník, Jakub Matějů, Ronny Razin, Marek Rozkrut, Marek Rusnák, Andrey Sirchenko and seminar participants at the CESifo conference on central bank communication, the European Public Choice Society annual conference, the Czech Economic Society biennial conference, the Czech National Bank and the Eurasia Business and Economics Society conference for helpful discussions. We appreciate the support from the Grant Agency of the Czech Republic, no. P402/12/G097.

Appendicies

A1 Model Technical Details

Appendix A1 includes more technical details for the models from the main body of the paper so that it becomes apparent how to generate C’s proposals and Ps’ voting behaviour. We further explain finer details of our simulation exercise and the methods used.

First note that for all the models equilibrium exists by simple (within-period) backward induction argument and it is unique. The Markovian restriction (Maskin and Tirole 2001) then means all the committee members condition their actions only on the state given by the status-quo policy and their signals, not on payoff irrelevant histories.

Throughout the explanation we will often work with a vector of random variables. All those variables form a random vector r={iˉ,iP1,,iPN,iC} that has a multivariate normal distribution with, conditional on i, mean ρi and variance-covariance matrix equal to a matrix with the vector of {σu2,σu2+σP2,,σu2+σP2,σu2+σC2} on the main diagonal and all the off-diagonal elements equal to σu2. [37] Often we will need to compute the conditional expectation of r given some specific value of one or more of its elements. For this we use the well known result for the multivariate normal distribution that states that for a vector of (possibly more than two) random variables {x1,x2} distributed according to N(μ,Σ) with μ={μ1,μ2} and Σ=σ11σ12σ21σ22 where the partitioning of μ and Σ conforms to the partition of {x1,x2}, the conditional distribution of x1 given a specific value of x2 is N(μ1,σ11), where μ1=μ1+σ12σ221(x2μ2) and σ11=σ11σ12σ221σ21.

In the autarkical model, at the beginning of each period we have status-quo x, last-period optimal interest rate i and r={iˉ,iP1,,iPN,iC}. First we need to derive C’s proposal y. This will be a solution to

[5]maxyYE[(p(x,y)i¯*)2|i*,iC]

where p(x,y) is the policy adopted given proposal y and status-quo x. The optimization problem can be rewritten as

[6]maxyYpaE[(yiˉ)2|i,iC,a]+(1pa)E[(xiˉ)2|i,iC,aˆ]

where a is the event of y being accepted, aˆ is the event of y being rejected and pz is the probability of event z.

We need to calculate the probability of y being accepted against status-quo x, pa. Chairman C knows, and we show below, that the remaining players will vote for y if and only if their signal is above (or below, but this case is symmetric) a certain cut-off that we denote here by k. The other relevant information C has is iC and i. Hence we need to calculate the probability of at least N2P members voting for y given iC and i.

The probability of the first N committee members voting for y is equal to P(#|iPk|=N,#|iP<k|=NN|i,iC) and is straightforward to calculate. We know the distribution of {iP1,,iPN} and can transform the probability into P(#|iPk|=N|i,iC) by multiplying the whole problem (that is the mean and variance-covariance matrix) by {1,,1,1,,1}, where there are N negative ones and NN positive ones. Denoting the probability of the first N members accepting by PN, the probability of y being accepted becomes i=N/2NNiPi.

The key computational problem in simulating the autarkical model is computing the expected value of iˉ given iC, i and the event of y being accepted. Acceptance means that the signals iP of N2 or more P members must have been above (or below) a certain threshold k, which carries information about the unknown iˉ. We use two simple results to simplify the computation. For random variable X and two mutually exclusive and exhaustive events A and B we have

[7]E[X]=E[X|A]P(A)+E[X|B]P(B)

and the similar result for variance states that

[8]var(X)=var(X|A)P(A)+var(X|B)P(B)+(E[X|A]E[X])2P(A)+(E[X|B]E[X])2P(B).

However, the key problem remains. We need to calculate an expectation of the form E[iˉ|i,iC,#|iPk|=N,#|iP<k|=NN]. The first step is simple and amounts to calculating the distribution of {iˉ,iP1,,iPN} given i and iC. It is N(μ,Σ), with each element of μ being equal to ρiσC2+iCσu2σu2+σC2 and Σ being a matrix with the vector σ,σ+σP2,,σ+σP2 on the main diagonal and σ=σu2σC2σu2+σC2 off the main diagonal. We then convert the problem into one of finding E[iˉ|i,iC,#|iPk|=N] using the same multiplication by a vector of positive and negative ones as when calculating pa. This leaves us with a multivariate truncated normal random vector with known mean and variance. To calculate the expectation we used the results in Tallis (1961) and Lee (1979) and wrote our own MATLAB function which calculates the expectation. We checked its correctness using the “tmvtnorm” R-software package (see Wilhelm and Manjunath 2012).

With these results, we can expand the maximand in [6] and use the rules for conditional expectations and variance given above to determine the value of C’s objective function for each yY. This gives us the solution to C’s optimization problem and hence her proposal.

With C’s proposal y, we can determine the voting behaviour of the remaining P committee members. For each member j we use the voting rule [2] from the text adapted to the autarkical model

[9]E[(yi¯*)2|i*,ij]E[(xi¯*)2|i*,ij]x2y22(yx)E[i¯*|i*,ij]

with E[iˉ|i,ij]=ρiσj2+ijσu2σu2+σj2. This also proves that each P member votes for y if and only if his signal is above (or below, depending on the position of the status-quo) a certain cut-off.

In the consensual model, again given x, i and r={iˉ,iP1,,iPN,iC}, C’s proposal y will be the policy in Y closest to C’s expectation of iˉ, E[iˉ|i,iC]=ρiσC2+iCσu2σu2+σC2.

Because the P committee members extract information from C’s proposal in the consensual model, each P member j will vote based on the voting rule [2] given i, ij and the information embedded in C’s proposal y. Adapting [2] to the consensual model gives

[10]x2y22(yx)E[iˉ|i,ij,y].

It is easy to confirm that the information embedded in C’s proposal is equal to an event of iC[ilC,iuC], with the bounds given by

[11]ilC=1σu2ysˉ2(σu2+σC2)σC2ρiiuC=1σu2y+sˉ2(σu2+σC2)σC2ρi.

Using the law of iterated expectations, E[i¯*|i*,ij,iC[ilC,iuC]] rewrites as E[E[i¯*|i*,ij,iC]|i*,ij,iC[ilC,iuC]]. The inner expectations are equal to ρiσj2σC2+ijσu2σC2+iCσu2σj2σu2σj2+σu2σC2+σC2σj2 and we know that the distribution of iC given i and ij is normal with mean ρiσj2+ijσu2σu2+σj2 and variance σu2σj2σu2+σj2+σC2.

Last thing we need is to be able to calculate mean of doubly truncated normal variable. For N(μ,σ2) distributed x1 conditional expectation of x1 given x1[al,au] is Ex1|x1[al,au]=μ+σϕ(alμσ)ϕ(auμσ)Φ(auμσ)Φ(alμσ), where ϕ() and Φ() are, respectively, the probability density and cumulative distribution functions of the univariate standard normal distribution.

In the supermajoritarian model C knows the most preferred policies of all the committee members. For each player j this policy, given x, i and r={iˉ,iP1,,iPN,iC}, will be the policy in Y closest to j’s expectation of iˉ, i. e. closest to E[iˉ|i,ij]=ρiσj2+ijσu2σu2+σj2. Denote vector of the most preferred policies by {p1,,pN+1}, ordered such that pjpj+1 for j{1,,N}. Policy most preferred by the median member is denoted by pm=pN/2+1.

C’s proposal will be the policy that receives a supermajority of at least N2+2 members. Naturally this policy depends on the status-quo and it is easy to show that y as a function of x satisfies

[12]y(x)={pm1forxpm1xforx[pm1,pm+1]pm+1forxpm+1.

For voting we again use [2] along with the assumption that all the committee members extract no information from proposal y. This makes the voting stage in the supermajoritarian model equivalent to the voting stage in the autarkical model. However, by construction, C’s proposal is always accepted and receives at least N2+2 votes.

To simulate each of the models, we start in the first period of a given path, with the previous optimal interest rate and monetary policy rate being zero. In all the simulations we restrict the policy space to be in the [10,10] interval so that with our choice of sˉ the policy space is equal to Y={10,9.75,,9.75,10}. We do not need to look at a larger policy space, as the optimal interest rate and players’ signals stay well away from its border. As explained in the text, it is inconsequential that we allow the optimal interest rate and the monetary policy rate to attain negative values, as all the results and estimates are invariant to adding a constant to the optimal interest rate.

The values of the random variables used in the simulations are kept constant across the different models. That is, when we simulate, say, the first path for the baseline scenario of the autarkical model, the random variables used are the same as when simulating the first path of any other scenario for the same model or of any other model for the same scenario. This holds even across the N=4 and N=6 simulations, where we naturally have to add two more random variables for the two extra players, but the remaining random variables are kept the same.

A2 Further Simulation Results

Table A1:

Predictive power of voting record and decision-making statistics: Autarkical model without reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)4.16 [1.64]*4.10 [1.63]*4.30 [1.65]*18.2 [4.53]***
Δpt(a2)0.65 [0.54]0.75 [0.53]0.78 [0.53]3.56 [0.64]**
Meeting types0.00/0.20/0.800.00/0.20/0.800.00/0.20/0.800.27/0.51/0.22
Stats0.42/0.430.42/0.430.41/0.420.15/0.46
0.00/0.570.00/0.570.00/0.580.27/0.82
mse0.0270.0270.0270.008
High volatility scenario (σudoubled)
skewt(a1)2.20 [1.06]2.19 [1.04]2.16 [1.05]6.98 [2.74]*
Δpt(a2)0.17 [0.24]0.24 [0.24]0.29 [0.24]3.11 [0.37]***
Meeting types0.00/0.34/0.660.00/0.33/0.670.00/0.33/0.670.00/0.66/0.34
Stats0.30/0.280.31/0.280.31/0.280.22/0.26
0.00/0.720.00/0.720.00/0.720.00/0.74
mse0.0410.0430.0410.013
Bad information scenario (σC, σPdoubled)
skewt(a1)3.43 [1.52]*3.43 [1.50]3.58 [1.53]19.3 [6.40]**
Δpt(a2)0.19 [0.49]0.29 [0.48]0.38 [0.47]3.26 [0.61]**
Meeting types0.00/0.24/0.760.00/0.25/0.750.00/0.27/0.730.37/0.53/0.11
Stats0.41/0.430.40/0.430.39/0.410.07/0.45
0.00/0.570.00/0.570.00/0.590.37/0.91
mse0.0480.0480.0490.008
Pbad information scenario (σPdoubled)
skewt(a1)4.93 [1.78]**4.97 [1.79]*4.83 [1.76]*19.7 [6.85]**
Δpt(a2)0.76 [0.56]0.82 [0.54]0.87 [0.53]3.28 [0.61]**
Meeting types0.00/0.20/0.800.00/0.21/0.790.00/0.22/0.780.38/0.53/0.10
Stats0.46/0.510.45/0.500.44/0.490.07/0.46
0.00/0.490.00/0.500.00/0.510.38/0.92
mse0.0410.0410.0410.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A2:

Predictive power of voting record and decision-making statistics: Autarkical model without reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)5.07 [1.65]**5.15 [1.66]**4.94 [1.66]**19.6 [5.32]***
Δpt(a2)1.00 [0.56]1.08 [0.56]1.12 [0.55]3.53 [0.63]**
Meeting types0.00/0.14/0.860.00/0.13/0.870.00/0.14/0.860.31/0.50/0.19
Stats0.45/0.470.44/0.450.44/0.450.13/0.46
0.00/0.530.00/0.550.00/0.550.31/0.85
mse0.0260.0260.0260.008
High volatility scenario (σudoubled)
skewt(a1)2.38 [1.03]*2.37 [1.02]*2.35 [1.02]8.62 [3.13]**
Δpt(a2)0.21 [0.24]0.28 [0.24]0.33 [0.25]3.16 [0.38]***
Meeting types0.00/0.26/0.740.00/0.26/0.740.00/0.25/0.750.00/0.65/0.35
Stats0.33/0.300.33/0.310.34/0.310.24/0.26
0.00/0.700.00/0.690.00/0.690.00/0.74
mse0.0390.0400.0400.013
Bad information scenario (σC, σPdoubled)
skewt(a1)3.62 [1.49]*3.57 [1.47]*3.59 [1.48]*21.0 [7.62]**
Δpt(a2)0.33 [0.51]0.40 [0.49]0.46 [0.48]3.24 [0.61]#x002A;*
Meeting types0.00/0.18/0.820.00/0.19/0.810.00/0.20/0.800.38/0.52/0.09
Stats0.44/0.460.42/0.440.42/0.440.06/0.46
0.00/0.540.00/0.560.00/0.560.38/0.93
mse0.0470.0470.0470.008
Pbad information scenario (σPdoubled)
skewt(a1)5.56 [1.72]**5.31 [1.71]**5.23 [1.70]**21.5 [8.47]**
Δpt(a2)0.94 [0.57]1.00 [0.55]1.04 [0.54]3.25 [0.61]**
Meeting types0.00/0.15/0.850.00/0.16/0.840.00/0.17/0.830.39/0.52/0.09
Stats0.49/0.520.48/0.510.47/0.500.06/0.46
0.00/0.480.00/0.490.00/0.500.39/0.93
mse0.0410.0410.0410.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A3:

Predictive power of voting record and decision-making statistics: Autarkical model with reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)5.27 [1.63]**5.22 [1.63]**5.39 [1.64]*18.2 [4.53]***
Δpt(a2)0.78 [0.53]0.89 [0.53]0.92 [0.52]3.56 [0.64]**
Meeting types0.00/0.00/0.000.00/0.00/0.000.00/0.00/0.000.27/0.00/0.00
0.16/0.76/0.080.17/0.75/0.080.17/0.75/0.080.51/0.22/0.00
Stats0.43/0.430.43/0.430.42/0.420.15/0.46
0.00/0.570.00/0.570.00/0.580.27/0.82
mse0.0270.0270.0270.008
High volatility scenario (σudoubled)
skewt(a1)2.77 [0.97]2.74 [0.96]2.75 [0.97]6.99 [2.74]
Δpt(a2)0.15 [0.22]0.22 [0.22]0.27 [0.23]3.11 [0.37]
Meeting types0.00/0.00/0.000.00/0.00/0.000.00/0.00/0.000.00/0.00/0.00
0.18/0.63/0.180.18/0.63/0.180.18/0.63/0.190.66/0.34/0.00
Stats0.37/0.280.37/0.280.37/0.280.22/0.26
0.00/0.720.00/0.720.00/0.720.00/0.74
mse0.0410.0430.0410.013
Bad information scenario (σC, σPdoubled)
skewt(a1)3.77 [1.51]*3.75 [1.48]*3.96 [1.51]*19.3 [6.40]**
Δpt(a2)0.21 [0.49]0.30 [0.48]0.40 [0.46]3.26 [0.61]**
Meeting types0.00/0.00/0.000.00/0.00/0.000.00/0.00/0.000.37/0.00/0.00
0.22/0.75/0.030.23/0.74/0.030.24/0.72/0.030.53/0.11/0.00
Stats0.41/0.430.41/0.430.40/0.410.07/0.45
0.00/0.570.00/0.570.00/0.590.37/0.91
mse0.0480.0480.0490.008
Pbad information scenario (σPdoubled)
skewt(a1)5.72 [1.78]**5.65 [1.78]**5.54 [1.74]**19.7 [6.85]**
Δpt(a2)0.85 [0.55]0.88 [0.54]0.94 [0.52]3.28 [0.61]**
Meeting types0.00/0.00/0.000.00/0.00/0.000.00/0.00/0.000.38/0.00/0.00
0.19/0.73/0.080.19/0.72/0.090.20/0.71/0.090.53/0.10/0.00
Stats0.46/0.510.46/0.500.45/0.490.07/0.46
0.00/0.490.00/0.500.00/0.510.38/0.92
mse0.0410.0410.0410.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A4:

Predictive power of voting record and decision-making statistics: Autarkical model with reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)6.08 [1.65]***6.26 [1.66]**6.09 [1.66]***19.6 [5.32]***
Δpt(a2)1.12 [0.55]1.22 [0.55]*1.27 [0.55]*3.53 [0.63]**
Meeting types0.00/0.00/0.000.00/0.00/0.000.00/0.00/0.000.31/0.00/0.00
0.10/0.79/0.110.10/0.79/0.110.11/0.78/0.110.50/0.19/0.00
Stats0.46/0.470.45/0.450.45/0.450.13/0.46
0.00/0.530.00/0.550.00/0.550.31/0.85
mse0.0260.0260.0260.008
High volatility scenario (σudoubled)
skewt(a1)2.91 [0.95]**2.89 [0.94]**2.92 [0.95]**8.64 [3.13]**
Δpt(a2)0.18 [0.23]0.26 [0.23]0.32 [0.23]3.16 [0.38]***
Meeting types0.00/0.00/0.000.00/0.00/0.000.00/0.00/0.000.00/0.00/0.00
0.11/0.62/0.260.11/0.63/0.260.11/0.62/0.260.65/0.35/0.00
Stats0.39/0.300.40/0.310.40/0.310.24/0.26
0.00/0.700.00/0.690.00/0.690.00/0.74
mse0.0390.0400.0400.013
Bad information scenario (σC, σPdoubled)
skewt(a1)3.82 [1.47]*3.81 [1.45]*3.81 [1.45]**21.0 [7.62]**
Δpt(a2)0.33 [0.50]0.41 [0.49]0.46 [0.47]3.24 [0.61]**
Meeting types0.00/0.00/0.000.00/0.00/0.000.00/0.00/0.000.38/0.00/0.00
0.15/0.83/0.020.17/0.82/0.020.17/0.81/0.020.52/0.09/0.00
Stats0.44/0.460.43/0.440.43/0.440.06/0.46
0.00/0.540.00/0.560.00/0.560.38/0.93
mse0.0470.0470.0470.008
Pbad information scenario (σPdoubled)
skewt(a1)5.72 [1.68]***5.48 [1.68]**5.39 [1.65]**21.5 [8.47]**
Δpt(a2)0.94 [0.56]1.00 [0.55]1.04 [0.53]3.25 [0.61]**
Meeting types0.00/0.00/0.000.00/0.00/0.000.00/0.00/0.000.39/0.00/0.00
0.13/0.79/0.080.14/0.78/0.080.14/0.77/0.080.52/0.09/0.00
Stats0.49/0.520.48/0.510.48/0.500.06/0.46
0.00/0.480.00/0.490.00/0.500.39/0.93
mse0.0410.0410.0410.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A5:

Predictive power of voting record and decision-making statistics: Consensual model without reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)5.90 [3.24]5.93 [3.29]6.33 [3.25]15.0 [15.6]
Δpt(a2)–0.02 [0.46]0.07 [0.45]0.15 [0.45]2.64 [0.53]**
Meeting types0.38/0.39/0.230.38/0.39/0.230.37/0.40/0.230.45/0.52/0.02
Stats0.07/0.410.07/0.410.07/0.410.01/0.45
0.38/0.970.38/0.970.37/0.970.45/1.00
mse0.0330.0320.0330.008
High volatility scenario (σudoubled)
skewt(a1)3.05 [2.50]2.59 [2.43]2.68 [2.48]12.5 [7.47]
Δpt(a2)–0.04 [0.21]0.01 [0.21]0.04 [0.21]2.96 [0.37]***
Meeting types0.20/0.58/0.220.19/0.58/0.220.19/0.58/0.220.26/0.69/0.05
Stats0.08/0.240.08/0.240.08/0.240.01/0.26
0.20/0.960.19/0.960.19/0.950.26/1.00
mse0.0500.0490.0490.014
Bad information scenario (σC, σPdoubled)
skewt(a1)6.79 [3.58]6.84 [3.59]7.01 [3.67]11.2 [10.9]
Δpt(a2)–0.03 [0.47]0.08 [0.46]0.11 [0.45]2.12 [0.42]**
Meeting types0.40/0.39/0.220.39/0.40/0.210.38/0.41/0.210.45/0.53/0.01
Stats0.06/0.420.06/0.410.06/0.390.00/0.46
0.40/0.980.39/0.980.38/0.980.45/1.00
mse0.0520.0520.0520.008
Pbad information scenario (σPdoubled)
skewt(a1)8.86 [6.25]9.98 [6.24]8.77 [6.08]7.17 [74.3]
Δpt(a2)–0.28 [0.42]–0.19 [0.41]–0.14 [0.41]1.08 [0.24]**
Meeting types0.37/0.53/0.100.37/0.53/0.100.36/0.53/0.100.45/0.54/0.00
Stats0.02/0.370.02/0.380.02/0.370.00/0.45
0.37/1.000.37/1.000.36/1.000.45/1.00
mse0.0360.0360.0360.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A6:

Predictive power of voting record and decision-making statistics: Consensual model without reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)6.57 [3.25]6.57 [3.30]6.70 [3.24]19.5 [17.4]
Δpt(a2)0.06 [0.46]0.14 [0.46]0.22 [0.45]2.99 [0.58]**
Meeting types0.38/0.35/0.280.38/0.34/0.280.37/0.35/0.280.45/0.52/0.03
Stats0.08/0.410.08/0.420.08/0.410.01/0.45
0.38/0.970.38/0.970.37/0.970.45/1.00
mse0.0330.0320.0330.008
High volatility scenario (σudoubled)
skewt(a1)3.25 [2.45]3.01 [2.43]2.91 [2.48]14.2 [7.79]
Δpt(a2)–0.03 [0.21]0.02 [0.21]0.05 [0.21]2.99 [0.37]***
Meeting types0.20/0.54/0.260.19/0.54/0.270.19/0.54/0.270.26/0.68/0.07
Stats0.08/0.240.08/0.240.08/0.240.02/0.26
0.20/0.950.19/0.950.19/0.950.26/1.00
mse0.0490.0490.0490.014
Bad information scenario (σC, σPdoubled)
skewt(a1)7.53 [3.63]7.60 [3.67]8.24 [3.66]15.7 [14.4]
Δpt(a2)0.05 [0.48]0.15 [0.47]0.21 [0.45]2.41 [0.48]**
Meeting types0.40/0.33/0.270.39/0.34/0.270.38/0.36/0.260.45/0.53/0.02
Stats0.07/0.420.07/0.410.06/0.390.00/0.46
0.40/0.980.39/0.980.38/0.980.45/1.00
mse0.0520.0520.0520.008
Pbad information scenario (σPdoubled)
skewt(a1)11.2 [6.57]12.4 [6.61]11.6 [6.45]13.6 [108.]
Δpt(a2)–0.22 [0.43]–0.13 [0.42]–0.07 [0.42]1.66 [0.33]**
Meeting types0.37/0.49/0.140.37/0.49/0.140.36/0.50/0.140.45/0.54/0.01
Stats0.03/0.370.03/0.370.03/0.360.00/0.45
0.37/1.000.37/1.000.36/1.000.45/1.00
mse0.0360.0360.0360.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A7:

Predictive power of voting record and decision-making statistics: Consensual model with reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)7.92 [2.98]**7.92 [3.01]*8.41 [3.00]*15.0 [15.6]
Δpt(a2)0.05 [0.45]0.13 [0.44]0.21 [0.44]2.64 [0.53]**
Meeting types0.34/0.04/0.000.34/0.04/0.000.33/0.04/0.000.45/0.00/0.00
0.37/0.25/0.000.37/0.24/0.000.38/0.25/0.000.52/0.02/0.00
Stats0.09/0.410.09/0.410.09/0.410.01/0.45
0.38/0.970.38/0.970.37/0.970.45/1.00
mse0.0330.0320.0330.008
High volatility scenario (σudoubled)
skewt(a1)4.67 [1.95]*4.64 [1.93]4.68 [1.94]*12.5 [7.47]
Δpt(a2)–0.08 [0.20]–0.02 [0.20]0.01 [0.21]2.96 [0.37]***
Meeting types0.13/0.07/0.000.13/0.06/0.000.12/0.07/0.000.26/0.00/0.00
0.46/0.33/0.010.47/0.33/0.010.47/0.33/0.010.69/0.05/0.00
Stats0.13/0.240.13/0.240.13/0.240.01/0.26
0.20/0.960.19/0.960.19/0.950.26/1.00
mse0.0500.0490.0490.014
Bad information scenario (σC, σPdoubled)
skewt(a1)8.05 [3.44]**8.20 [3.44]**8.05 [3.51]*11.2 [10.9]
Δpt(a2)0.02 [0.47]0.13 [0.45]0.14 [0.44]2.12 [0.42]**
Meeting types0.38/0.02/0.000.37/0.02/0.000.36/0.02/0.000.45/0.00/0.00
0.38/0.22/0.000.39/0.22/0.000.40/0.22/0.000.53/0.01/0.00
Stats0.07/0.420.07/0.410.07/0.390.00/0.46
0.40/0.980.39/0.980.38/0.980.45/1.00
mse0.0520.0520.0520.008
Pbad information scenario (σPdoubled)
skewt(a1)8.98 [6.21]10.2 [6.21]8.87 [6.06]7.17 [74.3]
Δpt(a2)–0.28 [0.42]–0.19 [0.41]–0.14 [0.41]1.08 [0.24]**
Meeting types0.37/0.00/0.000.37/0.00/0.000.36/0.00/0.000.45/0.00/0.00
0.53/0.10/0.000.53/0.10/0.000.53/0.10/0.000.54/0.00/0.00
Stats0.02/0.370.02/0.380.02/0.370.00/0.45
0.37/1.000.37/1.000.36/1.000.45/1.00
mse0.0360.0360.0360.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A8:

Predictive power of voting record and decision-making statistics: Consensual model with reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)8.92 [3.03]**8.97 [3.07]*9.10 [3.02]**19.5 [17.4]
Δpt(a2)0.14 [0.45]0.22 [0.45]0.31 [0.44]2.99 [0.58]**
Meeting types0.32/0.06/0.000.32/0.06/0.000.32/0.06/0.000.45/0.00/0.00
0.32/0.30/0.000.32/0.30/0.000.32/0.30/0.000.52/0.03/0.00
Stats0.09/0.410.09/0.420.09/0.410.01/0.45
0.38/0.970.38/0.970.37/0.970.45/1.00
mse0.0330.0320.0330.008
High volatility scenario (σudoubled)
skewt(a1)4.94 [1.93]*5.07 [1.93]*5.08 [1.96]*14.2 [7.79]
Δpt(a2)–0.08 [0.20]–0.02 [0.20]0.01 [0.21]2.99 [0.37]***
Meeting types0.11/0.08/0.000.11/0.08/0.000.11/0.08/0.000.26/0.00/0.00
0.39/0.40/0.020.39/0.40/0.020.39/0.40/0.020.68/0.07/0.00
Stats0.14/0.240.14/0.240.14/0.240.02/0.26
0.20/0.950.19/0.950.19/0.950.26/1.00
mse0.0490.0490.0490.014
Bad information scenario (σC, σPdoubled)
skewt(a1)9.17 [3.51]*9.26 [3.54]*9.63 [3.54]*15.7 [14.4]
Δpt(a2)0.13 [0.47]0.21 [0.46]0.26 [0.45]2.41 [0.48]**
Meeting types0.36/0.03/0.000.36/0.03/0.000.34/0.03/0.000.45/0.00/0.00
0.32/0.28/0.000.33/0.28/0.000.35/0.27/0.000.53/0.02/0.00
Stats0.07/0.420.07/0.410.07/0.390.00/0.46
0.40/0.980.39/0.980.38/0.980.45/1.00
mse0.0520.0520.0520.008
Pbad information scenario (σPdoubled)
skewt(a1)11.3 [6.55]12.6 [6.59]11.7 [6.43]13.6 [108.]
Δpt(a2)–0.21 [0.43]–0.13 [0.42]–0.07 [0.42]1.66 [0.33]**
Meeting types0.37/0.00/0.000.37/0.00/0.000.36/0.00/0.000.45/0.00/0.00
0.49/0.14/0.000.49/0.14/0.000.50/0.14/0.000.54/0.01/0.00
Stats0.03/0.370.03/0.370.03/0.360.00/0.45
0.37/1.000.37/1.000.36/1.000.45/1.00
mse0.0360.0360.0360.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A9:

Predictive power of voting record and decision-making statistics: Supermajoritarian model without reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)6.22 [6.56]5.25 [6.40]7.06 [6.31]17.3 [45.6]
Δpt(a2)1.62 [0.77]1.63 [0.74]1.86 [0.73]*2.72 [0.52]**
Meeting types0.59/0.23/0.170.59/0.23/0.170.58/0.25/0.170.46/0.52/0.02
Stats0.04/0.590.03/0.590.03/0.580.00/0.46
0.59/1.000.59/1.000.58/1.000.46/1.00
mse0.0340.0330.0330.008
High volatility scenario (σudoubled)
skewt(a1)0.91 [3.65]0.69 [3.65]0.77 [3.60]15.0 [11.7]
Δpt(a2)0.54 [0.29]0.60 [0.29]0.66 [0.29]*3.13 [0.37]***
Meeting types0.37/0.41/0.220.37/0.41/0.220.37/0.41/0.220.28/0.68/0.04
Stats0.04/0.370.04/0.370.04/0.370.01/0.28
0.37/1.000.37/1.000.37/1.000.28/1.00
mse0.0450.0440.0450.013
Bad information scenario (σC, σPdoubled)
skewt(a1)6.50 [6.53]6.05 [6.47]5.67 [6.19]11.4 [14.1]
Δpt(a2)1.00 [0.67]1.04 [0.64]1.06 [0.61]1.64 [0.32]**
Meeting types0.57/0.28/0.150.56/0.30/0.150.53/0.31/0.160.46/0.53/0.01
Stats0.03/0.570.03/0.560.03/0.530.00/0.46
0.57/1.000.56/1.000.53/1.000.46/1.00
mse0.0520.0520.0520.008
Pbad information scenario (σPdoubled)
skewt(a1)7.36 [6.57]6.53 [6.43]6.46 [6.16]13.4 [74.6]
Δpt(a2)1.22 [0.70]1.25 [0.67]1.33 [0.64]2.06 [0.42]**
Meeting types0.58/0.26/0.160.57/0.27/0.160.55/0.28/0.170.46/0.53/0.01
Stats0.03/0.580.03/0.570.03/0.550.00/0.46
0.58/1.000.57/1.000.55/1.000.46/1.00
mse0.0490.0490.0490.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A10:

Predictive power of voting record and decision-making statistics: Supermajoritarian model without reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)7.65 [5.40]7.41 [5.30]8.16 [5.21]16.6 [14.4]
Δpt(a2)1.98 [0.85]2.05 [0.81]*2.19 [0.80]**2.93 [0.57]**
Meeting types0.57/0.17/0.260.57/0.17/0.260.56/0.18/0.260.46/0.51/0.03
Stats0.05/0.570.05/0.570.06/0.560.01/0.46
0.57/1.000.57/1.000.56/1.000.46/1.00
mse0.0300.0300.0290.008
High volatility scenario (σudoubled)
skewt(a1)1.86 [3.04]1.69 [2.99]1.39 [2.92]13.3 [9.25]
Δpt(a2)0.54 [0.30]0.63 [0.30]0.65 [0.31]3.19 [0.38]***
Meeting types0.34/0.33/0.340.33/0.33/0.340.33/0.32/0.350.27/0.66/0.06
Stats0.07/0.340.07/0.330.07/0.330.01/0.27
0.34/1.000.33/1.000.33/1.000.27/1.00
mse0.0360.0360.0360.013
Bad information scenario (σC, σPdoubled)
skewt(a1)6.70 [5.23]7.44 [5.09]6.22 [5.05]14.0 [109.]
Δpt(a2)1.11 [0.69]1.16 [0.65]1.15 [0.63]2.13 [0.42]**
Meeting types0.54/0.23/0.230.52/0.25/0.230.51/0.26/0.230.46/0.53/0.01
Stats0.05/0.540.05/0.520.05/0.510.00/0.46
0.54/1.000.52/1.000.51/1.000.46/1.00
mse0.0500.0510.0500.008
Pbad information scenario (σPdoubled)
skewt(a1)7.73 [5.26]7.86 [5.08]6.69 [5.04]14.8 [73.0]
Δpt(a2)1.28 [0.72]1.36 [0.68]1.38 [0.66]2.43 [0.49]**
Meeting types0.55/0.22/0.230.54/0.23/0.230.52/0.24/0.240.46/0.52/0.02
Stats0.05/0.550.05/0.540.05/0.520.00/0.46
0.55/1.000.54/1.000.52/1.000.46/1.00
mse0.0480.0480.0470.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A11:

Predictive power of voting record and decision-making statistics: Supermajoritarian model with reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)10.8 [3.12]***10.7 [3.09]**11.0 [3.06]**17.3 [45.6]
Δpt(a2)1.71 [0.65]**1.80 [0.63]**1.92 [0.62]**2.72 [0.52]**
Meeting types0.37/0.22/0.000.38/0.21/0.000.36/0.21/0.000.46/0.00/0.00
0.18/0.22/0.010.18/0.21/0.010.19/0.22/0.010.52/0.02/0.00
Stats0.10/0.590.10/0.590.10/0.580.00/0.46
0.59/1.000.59/1.000.58/1.000.46/1.00
mse0.0340.0330.0330.008
High volatility scenario (σudoubled)
skewt(a1)3.96 [1.80]3.88 [1.82]4.15 [1.81]*15.3 [11.9]
Δpt(a2)0.41 [0.27]0.49 [0.27]0.54 [0.27]3.16 [0.38]***
Meeting types0.10/0.24/0.030.10/0.24/0.030.10/0.24/0.030.28/0.00/0.00
0.17/0.36/0.090.17/0.36/0.090.18/0.36/0.100.68/0.04/0.00
Stats0.21/0.370.21/0.370.22/0.370.01/0.28
0.37/1.000.37/1.000.37/1.000.28/1.00
mse0.0450.0440.0450.013
Bad information scenario (σC, σPdoubled)
skewt(a1)9.78 [3.75]*9.58 [3.72]*9.05 [3.60]*11.4 [14.1]
Δpt(a2)1.07 [0.59]1.10 [0.57]1.12 [0.55]1.64 [0.32]**
Meeting types0.44/0.13/0.000.43/0.13/0.000.41/0.13/0.000.46/0.00/0.00
0.25/0.18/0.000.26/0.18/0.000.27/0.19/0.000.53/0.01/0.00
Stats0.07/0.570.07/0.560.07/0.530.00/0.46
0.57/1.000.56/1.000.53/1.000.46/1.00
mse0.0520.0520.0520.008
Pbad information scenario (σPdoubled)
skewt(a1)8.86 [3.74]*8.46 [3.70]*8.04 [3.56]*13.4 [74.6]
Δpt(a2)1.21 [0.62]1.26 [0.59]1.33 [0.57]*2.06 [0.42]**
Meeting types0.45/0.13/0.000.44/0.13/0.000.42/0.13/0.000.46/0.00/0.00
0.23/0.19/0.000.25/0.18/0.000.25/0.20/0.000.53/0.01/0.00
Stats0.07/0.580.07/0.570.07/0.550.00/0.46
0.58/1.000.57/1.000.55/1.000.46/1.00
mse0.0490.0490.0490.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A12:

Predictive power of voting record and decision-making statistics: Supermajoritarian model with reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)11.4 [3.19]***11.7 [3.20]***11.5 [3.16]**16.6 [14.4]
Δpt(a2)2.14 [0.68]**2.31 [0.67]***2.32 [0.65]***2.93 [0.57]**
Meeting types0.31/0.26/0.000.31/0.26/0.000.30/0.25/0.010.46/0.00/0.00
0.12/0.28/0.030.12/0.29/0.020.12/0.29/0.030.51/0.03/0.00
Stats0.12/0.570.12/0.570.12/0.560.01/0.46
0.57/1.000.57/1.000.56/1.000.46/1.00
mse0.0300.0300.0290.008
High volatility scenario (σudoubled)
skewt(a1)3.91 [1.87]3.79 [1.86]3.74 [1.85]13.5 [9.21]
Δpt(a2)0.42 [0.26]0.52 [0.26]0.56 [0.26]3.19 [0.38]***
Meeting types0.06/0.23/0.050.05/0.23/0.050.05/0.22/0.050.27/0.00/0.00
0.10/0.38/0.180.10/0.38/0.180.10/0.38/0.180.66/0.06/0.00
Stats0.23/0.340.23/0.330.23/0.330.01/0.27
0.34/1.000.33/1.000.33/1.000.27/1.00
mse0.0360.0360.0360.013
Bad information scenario (σC, σPdoubled)
skewt(a1)9.66 [3.70]**10.3 [3.64]*9.10 [3.60]*14.0 [109.]
Δpt(a2)1.23 [0.61]1.26 [0.58]1.25 [0.56]2.13 [0.42]**
Meeting types0.39/0.15/0.000.37/0.15/0.000.37/0.14/0.000.46/0.00/0.00
0.19/0.26/0.010.20/0.27/0.010.21/0.27/0.010.53/0.01/0.00
Stats0.08/0.540.08/0.520.08/0.510.00/0.46
0.54/1.000.52/1.000.51/1.000.46/1.00
mse0.0500.0510.0500.008
Pbad information scenario (σPdoubled)
skewt(a1)9.53 [3.72]*9.57 [3.64]*8.40 [3.60]*14.8 [73.0]
Δpt(a2)1.33 [0.63]1.40 [0.60]*1.42 [0.59]*2.43 [0.49]**
Meeting types0.40/0.15/0.000.38/0.15/0.000.37/0.15/0.000.46/0.00/0.00
0.18/0.26/0.010.19/0.27/0.010.19/0.28/0.010.52/0.02/0.00
Stats0.08/0.550.08/0.540.08/0.520.00/0.46
0.55/1.000.54/1.000.52/1.000.46/1.00
mse0.0480.0480.0470.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A13:

Predictive power of voting record and decision-making statistics: Full information independence without reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)5.46 [2.14]*5.19 [2.13]*5.51 [2.10]*14.9 [92.2]
Δpt(a2)0.94 [0.59]0.98 [0.58]1.07 [0.56]3.02 [0.58]**
Meeting types0.39/0.19/0.420.39/0.20/0.420.38/0.20/0.420.45/0.51/0.04
Stats0.18/0.540.18/0.550.18/0.530.01/0.46
0.39/0.840.39/0.840.38/0.840.45/0.99
mse0.0320.0320.0320.008
High volatility scenario (σudoubled)
skewt(a1)2.33 [1.23]2.24 [1.23]2.38 [1.22]9.24 [5.46]
Δpt(a2)0.23 [0.25]0.29 [0.25]0.34 [0.25]3.02 [0.37]***
Meeting types0.20/0.34/0.460.19/0.34/0.470.19/0.34/0.470.25/0.67/0.08
Stats0.19/0.350.19/0.350.19/0.350.03/0.28
0.20/0.850.19/0.850.19/0.850.25/0.98
mse0.0480.0470.0470.013
Bad information scenario (σC, σPdoubled)
skewt(a1)5.53 [2.35]*5.31 [2.38]4.99 [2.31]13.7 [74.0]
Δpt(a2)0.49 [0.54]0.58 [0.52]0.57 [0.51]2.56 [0.50]**
Meeting types0.40/0.25/0.350.39/0.27/0.340.38/0.28/0.340.45/0.53/0.02
Stats0.15/0.520.14/0.510.14/0.490.01/0.46
0.40/0.880.39/0.880.38/0.890.45/0.99
mse0.0520.0520.0520.008
Pbad information scenario (σPdoubled)
skewt(a1)7.01 [1.96]**6.82 [1.99]**6.62 [1.91]**16.4 [1.77]
Δpt(a2)0.93 [0.57]0.93 [0.55]0.94 [0.53]2.86 [0.55]**
Meeting types0.36/0.19/0.450.36/0.20/0.440.36/0.20/0.440.45/0.53/0.02
Stats0.22/0.580.22/0.570.21/0.560.01/0.46
0.36/0.790.36/0.790.36/0.790.45/0.99
mse0.0450.0440.0450.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A14:

Predictive power of voting record and decision-making statistics: Full information independence without reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)6.11 [2.14]**5.90 [2.12]**5.88 [2.10]**14.9 [9.68]
Δpt(a2)1.19 [0.61]1.25 [0.60]1.25 [0.59]3.12 [0.59]**
Meeting types0.38/0.15/0.470.39/0.14/0.470.38/0.15/0.470.45/0.51/0.04
Stats0.20/0.560.20/0.560.20/0.550.01/0.46
0.38/0.830.39/0.830.38/0.830.45/0.99
mse0.0320.0320.0320.008
High volatility scenario (σudoubled)
skewt(a1)2.47 [1.22]2.53 [1.22]2.48 [1.22]9.94 [5.48]
Δpt(a2)0.26 [0.25]0.34 [0.26]0.38 [0.26]3.03 [0.37]***
Meeting types0.20/0.28/0.520.19/0.28/0.530.19/0.27/0.530.25/0.65/0.09
Stats0.20/0.360.20/0.350.21/0.350.03/0.28
0.20/0.840.19/0.840.19/0.840.25/0.98
mse0.0460.0460.0460.013
Bad information scenario (σC, σPdoubled)
skewt(a1)5.46 [2.35]*5.33 [2.36]5.11 [2.31]*16.6 [24.1]
Δpt(a2)0.56 [0.56]0.67 [0.54]0.66 [0.52]2.66 [0.52]**
Meeting types0.40/0.21/0.390.39/0.22/0.390.38/0.23/0.390.45/0.53/0.02
Stats0.16/0.530.15/0.520.15/0.500.01/0.46
0.40/0.870.39/0.870.38/0.880.45/0.99
mse0.0520.0520.0520.008
Pbad information scenario (σPdoubled)
skewt(a1)7.46 [1.98]***7.25 [2.00]**7.17 [1.94]***19.9 [25.5]
Δpt(a2)1.03 [0.58]1.10 [0.56]1.11 [0.54]2.95 [0.56]**
Meeting types0.36/0.15/0.490.36/0.16/0.480.36/0.17/0.480.45/0.53/0.03
Stats0.23/0.590.23/0.580.23/0.570.01/0.46
0.36/0.770.36/0.780.36/0.780.45/0.99
mse0.0470.0450.0460.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A15:

Predictive power of voting record and decision-making statistics: Full information independence with reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)7.41 [1.82]***7.07 [1.83]***7.35 [1.79]***14.9 [92.2]
Δpt(a2)1.12 [0.55]1.16 [0.55]1.25 [0.53]*3.02 [0.58]**
Meeting types0.23/0.16/0.000.23/0.15/0.000.22/0.16/0.000.45/0.00/0.00
0.16/0.44/0.020.16/0.44/0.020.16/0.44/0.020.51/0.04/0.00
Stats0.24/0.540.24/0.550.24/0.530.01/0.46
0.39/0.840.39/0.840.38/0.840.45/0.99
mse0.0320.0320.0320.008
High volatility scenario (σudoubled)
skewt(a1)3.10 [1.00]**3.03 [1.00]**3.21 [1.01]**9.33 [5.45]
Δpt(a2)0.19 [0.23]0.26 [0.23]0.32 [0.23]3.02 [0.37]***
Meeting types0.04/0.14/0.010.04/0.14/0.010.04/0.14/0.010.25/0.00/0.00
0.17/0.51/0.120.17/0.51/0.120.17/0.52/0.120.67/0.08/0.00
Stats0.32/0.350.32/0.350.32/0.350.03/0.28
0.20/0.850.19/0.850.19/0.850.25/0.98
mse0.0480.0470.0470.013
Bad information scenario (σC, σPdoubled)
skewt(a1)6.79 [2.06]**6.60 [2.06]**6.11 [2.00]**13.7 [74.0]
Δpt(a2)0.58 [0.52]0.65 [0.50]0.62 [0.49]2.56 [0.50]**
Meeting types0.30/0.10/0.000.29/0.10/0.000.28/0.10/0.000.45/0.00/0.00
0.23/0.37/0.000.24/0.37/0.000.25/0.37/0.000.53/0.02/0.00
Stats0.18/0.520.18/0.510.18/0.490.01/0.46
0.40/0.880.39/0.880.38/0.890.45/0.99
mse0.0520.0520.0520.008
Pbad information scenario (σPdoubled)
skewt(a1)6.91 [1.77]***6.65 [1.78]***6.48 [1.72]***16.4 [1.77]
Δpt(a2)0.87 [0.55]0.86 [0.53]0.89 [0.51]2.86 [0.55]**
Meeting types0.26/0.10/0.000.25/0.10/0.000.25/0.11/0.000.45/0.00/0.00
0.17/0.46/0.010.18/0.45/0.010.18/0.45/0.010.53/0.02/0.00
Stats0.26/0.580.25/0.570.25/0.560.01/0.46
0.36/0.790.36/0.790.36/0.790.45/0.99
mse0.0450.0440.0450.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A16:

Predictive power of voting record and decision-making statistics: Full information independence with reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)8.19 [1.85]***8.09 [1.86]***8.04 [1.82]***14.9 [9.68]
Δpt(a2)1.40 [0.58]1.49 [0.57]1.48 [0.55]3.12 [0.59]**
Meeting types0.19/0.19/0.000.19/0.19/0.000.18/0.19/0.000.45/0.00/0.00
0.10/0.48/0.030.10/0.48/0.030.11/0.48/0.030.51/0.04/0.00
Stats0.26/0.560.26/0.560.26/0.550.01/0.46
0.38/0.830.39/0.830.38/0.830.45/0.99
mse0.0320.0320.0320.008
High volatility scenario (σudoubled)
skewt(a1)3.23 [1.00]**3.29 [0.99]**3.34 [1.00]**10.0 [5.48]
Δpt(a2)0.22 [0.23]0.31 [0.23]0.35 [0.23]3.03 [0.37]***
Meeting types0.02/0.15/0.020.02/0.15/0.020.02/0.15/0.020.25/0.00/0.00
0.10/0.51/0.180.10/0.52/0.180.11/0.51/0.180.65/0.09/0.00
Stats0.34/0.360.34/0.350.34/0.350.03/0.28
0.20/0.840.19/0.840.19/0.840.25/0.98
mse0.0460.0460.0460.013
Bad information scenario (σC, σPdoubled)
skewt(a1)6.93 [2.07]**6.97 [2.06]**6.51 [2.01]**16.6 [24.1]
Δpt(a2)0.66 [0.54]0.79 [0.52]0.75 [0.50]2.66 [0.52]**
Meeting types0.27/0.13/0.000.26/0.13/0.000.25/0.13/0.000.45/0.00/0.00
0.17/0.42/0.010.18/0.42/0.010.19/0.43/0.010.53/0.02/0.00
Stats0.20/0.530.19/0.520.19/0.500.01/0.46
0.40/0.870.39/0.870.38/0.880.45/0.99
mse0.0520.0520.0520.008
Pbad information scenario (σPdoubled)
skewt(a1)7.31 [1.78]***7.09 [1.79]***7.00 [1.74]***19.9 [25.5]**
Δpt(a2)0.96 [0.56]1.02 [0.54]1.04 [0.52]2.95 [0.56]
Meeting types0.23/0.13/0.000.23/0.13/0.000.22/0.13/0.000.45/0.00/0.00
0.13/0.50/0.010.14/0.49/0.010.14/0.49/0.010.53/0.03/0.00
Stats0.27/0.590.27/0.580.27/0.570.01/0.46
0.36/0.770.36/0.780.36/0.780.45/0.99
mse0.0470.0450.0460.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A17:

Predictive power of voting record and decision-making statistics: Majoritarian model without reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)6.53 [3.22]6.58 [3.19]6.58 [3.14]12.0 [9.72]
Δpt(a2)1.45 [0.75]1.51 [0.72]1.65 [0.72]*3.04 [0.59]**
Meeting types0.46/0.19/0.360.45/0.19/0.360.44/0.19/0.360.46/0.51/0.03
Stats0.11/0.460.11/0.450.11/0.440.01/0.46
0.46/1.000.45/1.000.44/1.000.46/1.00
mse0.0250.0240.0250.007
High volatility scenario (σudoubled)
skewt(a1)1.77 [1.78]1.82 [1.78]1.76 [1.79]9.58 [5.40]
Δpt(a2)0.28 [0.27]0.37 [0.27]0.40 [0.28]3.10 [0.37]***
Meeting types0.23/0.34/0.440.22/0.34/0.440.22/0.33/0.440.26/0.66/0.08
Stats0.12/0.230.12/0.220.13/0.220.02/0.26
0.23/1.000.22/1.000.22/1.000.26/1.00
mse0.0260.0260.0260.013
Bad information scenario (σC, σPdoubled)
skewt(a1)5.71 [3.22]5.11 [3.11]5.23 [3.09]10.1 [9.86]
Δpt(a2)0.72 [0.62]0.70 [0.59]0.76 [0.57]2.37 [0.48]**
Meeting types0.45/0.25/0.300.43/0.27/0.300.42/0.28/0.300.46/0.53/0.02
Stats0.09/0.450.09/0.430.09/0.420.01/0.46
0.45/1.000.43/1.000.42/1.000.46/1.00
mse0.0470.0480.0470.008
Pbad information scenario (σPdoubled)
skewt(a1)5.89 [3.24]5.90 [3.13]5.65 [3.07]11.1 [11.2]
Δpt(a2)0.95 [0.66]0.95 [0.63]1.00 [0.60]2.74 [0.54]**
Meeting types0.46/0.23/0.320.44/0.24/0.320.43/0.25/0.320.46/0.52/0.02
Stats0.09/0.460.09/0.440.09/0.430.01/0.46
0.46/1.000.44/1.000.43/1.000.46/1.00
mse0.0430.0440.0430.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A18:

Predictive power of voting record and decision-making statistics: Majoritarian model without reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)7.35 [3.37]**7.66 [3.36]7.73 [3.34]13.1 [9.52]
Δpt(a2)1.88 [0.81]*1.99 [0.79]*2.13 [0.79]**3.15 [0.61]**
Meeting types0.47/0.14/0.400.46/0.13/0.400.46/0.14/0.400.46/0.50/0.04
Stats0.11/0.470.11/0.460.11/0.460.01/0.46
0.47/1.000.46/1.000.46/1.000.46/1.00
mse0.0240.0230.0240.008
High volatility scenario (σudoubled)
skewt(a1)2.03 [1.88]2.11 [1.86]2.10 [1.88]10.4 [5.71]
Δpt(a2)0.38 [0.29]0.44 [0.29]0.50 [0.29]3.19 [0.38]***
Meeting types0.23/0.27/0.500.22/0.27/0.510.22/0.26/0.510.26/0.65/0.09
Stats0.13/0.230.13/0.220.13/0.220.02/0.26
0.23/1.000.22/1.000.22/1.000.26/1.00
mse0.0230.0230.0230.013
Bad information scenario (σC, σPdoubled)
skewt(a1)6.08 [3.28]5.65 [3.16]5.58 [3.13]13.1 [14.0]
Δpt(a2)0.86 [0.65]0.85 [0.62]0.92 [0.59]2.48 [0.50]**
Meeting types0.45/0.21/0.340.43/0.22/0.340.42/0.23/0.340.46/0.52/0.02
Stats0.09/0.450.09/0.430.09/0.420.01/0.46
0.45/1.000.43/1.000.42/1.000.46/1.00
mse0.0470.0470.0470.008
Pbad information scenario (σPdoubled)
skewt(a1)6.51 [3.30]6.14 [3.18]6.01 [3.14]13.4 [12.3]
Δpt(a2)1.10 [0.69]1.04 [0.64]1.14 [0.63]2.66 [0.54]**
Meeting types0.46/0.19/0.350.44/0.20/0.360.43/0.21/0.360.46/0.52/0.02
Stats0.10/0.460.10/0.440.10/0.430.01/0.46
0.46/1.000.44/1.000.43/1.000.46/1.00
mse0.0440.0440.0440.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A19:

Predictive power of voting record and decision-making statistics: Majoritarian model with reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)7.86 [2.70]**7.95 [2.72]**7.74 [2.67]**12.0 [9.72]
Δpt(a2)1.60 [0.67]*1.67 [0.66]*1.77 [0.65]**3.04 [0.59]**
Meeting types0.34/0.12/0.000.34/0.11/0.000.33/0.11/0.000.46/0.00/0.00
0.16/0.37/0.010.16/0.37/0.010.17/0.38/0.010.51/0.03/0.00
Stats0.14/0.460.14/0.450.14/0.440.01/0.46
0.46/1.000.45/1.000.44/1.000.46/1.00
mse0.0250.0240.0250.007
High volatility scenario (σudoubled)
skewt(a1)2.43 [1.52]2.39 [1.52]2.55 [1.54]9.62 [5.40]
Δpt(a2)0.27 [0.24]0.35 [0.25]0.40 [0.25]3.10 [0.37]***
Meeting types0.09/0.12/0.020.08/0.12/0.020.08/0.12/0.020.26/0.00/0.00
0.21/0.44/0.120.21/0.44/0.120.21/0.44/0.120.66/0.08/0.00
Stats0.21/0.230.21/0.220.21/0.220.02/0.26
0.23/1.000.22/1.000.22/1.000.26/1.00
mse0.0260.0260.0260.013
Bad information scenario (σC, σPdoubled)
skewt(a1)6.62 [2.92]6.04 [2.85]5.86 [2.80]10.1 [9.86]
Δpt(a2)0.80 [0.59]0.78 [0.56]0.80 [0.54]2.37 [0.48]**
Meeting types0.38/0.06/0.000.37/0.06/0.000.36/0.06/0.000.46/0.00/0.00
0.24/0.31/0.000.25/0.31/0.000.26/0.32/0.000.53/0.02/0.00
Stats0.10/0.450.11/0.430.10/0.420.01/0.46
0.45/1.000.43/1.000.42/1.000.46/1.00
mse0.0470.0480.0470.008
Pbad information scenario (σPdoubled)
skewt(a1)6.31 [2.94]6.28 [2.87]5.78 [2.80]11.1 [11.2]
Δpt(a2)0.98 [0.63]0.98 [0.60]1.00 [0.57]2.74 [0.54]**
Meeting types0.39/0.06/0.000.38/0.06/0.000.37/0.06/0.000.46/0.00/0.00
0.21/0.33/0.000.23/0.33/0.000.24/0.33/0.000.52/0.02/0.00
Stats0.11/0.460.11/0.440.11/0.430.01/0.46
0.46/1.000.44/1.000.43/1.000.46/1.00
mse0.0430.0440.0430.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A20:

Predictive power of voting record and decision-making statistics: Majoritarian model with reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)9.01 [2.83]**9.26 [2.83]**9.02 [2.81]**13.1 [9.52]
Δpt(a2)2.08 [0.71]**2.19 [0.71]**2.26 [0.70]**3.15 [0.61]**
Meeting types0.29/0.17/0.000.29/0.17/0.000.29/0.16/0.000.46/0.00/0.00
0.11/0.40/0.030.10/0.41/0.020.11/0.41/0.030.50/0.04/0.00
Stats0.15/0.470.15/0.460.15/0.460.01/0.46
0.47/1.000.46/1.000.46/1.000.46/1.00
mse0.0240.0230.0240.008
High volatility scenario (σudoubled)
skewt(a1)2.59 [1.60]2.74 [1.59]2.81 [1.61]10.5 [5.70]
Δpt(a2)0.34 [0.25]0.42 [0.25]0.47 [0.26]3.20 [0.38]***
Meeting types0.05/0.14/0.040.05/0.14/0.040.05/0.13/0.040.26/0.00/0.00
0.13/0.44/0.200.12/0.45/0.200.13/0.44/0.200.65/0.09/0.00
Stats0.23/0.230.24/0.220.23/0.220.02/0.26
0.23/1.000.22/1.000.22/1.000.26/1.00
mse0.0230.0230.0230.013
Bad information scenario (σC, σPdoubled)
skewt(a1)7.12 [2.97]*6.79 [2.88]*6.44 [2.86]13.1 [14.0]
Δpt(a2)0.95 [0.61]0.96 [0.58]0.98 [0.57]2.48 [0.50]**
Meeting types0.36/0.09/0.000.34/0.09/0.000.34/0.09/0.000.46/0.00/0.00
0.19/0.36/0.000.20/0.36/0.000.21/0.36/0.000.52/0.02/0.00
Stats0.11/0.450.11/0.430.11/0.420.01/0.46
0.45/1.000.43/1.000.42/1.000.46/1.00
mse0.0470.0470.0470.008
Pbad information scenario (σPdoubled)
skewt(a1)7.07 [2.99]*6.82 [2.90]*6.49 [2.88]*13.4 [12.3]
Δpt(a2)1.13 [0.65]1.10 [0.61]1.17 [0.60]2.66 [0.54]**
Meeting types0.37/0.09/0.000.35/0.09/0.000.34/0.09/0.000.46/0.00/0.00
0.17/0.37/0.010.18/0.37/0.000.19/0.38/0.010.52/0.02/0.00
Stats0.12/0.460.12/0.440.12/0.430.01/0.46
0.46/1.000.44/1.000.43/1.000.46/1.00
mse0.0440.0440.0440.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A21:

Predictive power of voting record and decision-making statistics: Autarkical model with information sharing without reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)2.51 [2.79]2.43 [2.79]2.32 [2.81]11.8 [11.2]
Δpt(a2)0.15 [0.69]0.21 [0.69]0.27 [0.71]2.92 [0.56]**
Meeting types0.46/0.14/0.400.45/0.14/0.410.45/0.13/0.420.47/0.51/0.02
Stats0.12/0.460.12/0.450.12/0.450.01/0.47
0.46/1.000.45/1.000.45/1.000.47/1.00
mse0.0180.0180.0180.007
High volatility scenario (σudoubled)
skewt(a1)0.80 [1.64]0.86 [1.66]0.55 [1.68]7.61 [7.07]
Δpt(a2)–0.04 [0.24]0.01 [0.24]0.00 [0.25]3.26 [0.39]***
Meeting types0.22/0.33/0.460.22/0.32/0.450.23/0.32/0.460.29/0.66/0.06
Stats0.12/0.220.12/0.220.12/0.230.02/0.29
0.22/1.000.22/1.000.23/1.000.29/1.00
mse0.0180.0180.0180.011
Bad information scenario (σC, σPdoubled)
skewt(a1)1.82 [2.87]1.95 [2.81]1.25 [2.80]9.25 [10.2]
Δpt(a2)0.02 [0.65]0.16 [0.62]0.17 [0.61]2.23 [0.45]**
Meeting types0.51/0.19/0.300.50/0.19/0.310.49/0.20/0.300.46/0.53/0.01
Stats0.09/0.510.09/0.500.09/0.490.00/0.46
0.51/1.000.50/1.000.49/1.000.46/1.00
mse0.0380.0380.0380.008
Pbad information scenario (σPdoubled)
skewt(a1)1.28 [2.94]1.48 [2.85]0.64 [2.82]8.19 [9.70]
Δpt(a2)0.09 [0.71]0.20 [0.67]0.15 [0.67]2.23 [0.44]**
Meeting types0.54/0.16/0.300.52/0.17/0.310.53/0.17/0.300.46/0.53/0.01
Stats0.09/0.540.09/0.520.09/0.530.00/0.46
0.54/1.000.52/1.000.53/1.000.46/1.00
mse0.0350.0350.0340.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A22:

Predictive power of voting record and decision-making statistics: Autarkical model with information sharing without reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)3.25 [2.96]3.09 [3.00]2.63 [3.01]11.6 [12.0]
Δpt(a2)0.45 [0.80]0.48 [0.81]0.49 [0.81]2.91 [0.57]**
Meeting types0.48/0.07/0.450.48/0.07/0.460.48/0.07/0.450.47/0.50/0.03
Stats0.13/0.480.13/0.480.13/0.480.01/0.47
0.48/1.000.48/1.000.48/1.000.47/1.00
mse0.0170.0170.0160.007
High volatility scenario (σudoubled)
skewt(a1)1.14 [1.67]1.04 [1.69]0.66 [1.70]7.60 [7.63]
Δpt(a2)–0.00 [0.26]0.03 [0.26]0.03 [0.26]3.33 [0.39]***
Meeting types0.22/0.22/0.550.22/0.21/0.560.23/0.21/0.560.29/0.64/0.07
Stats0.14/0.220.14/0.220.14/0.230.02/0.29
0.22/1.000.22/1.000.23/1.000.29/1.00
mse0.0150.0140.0140.010
Bad information scenario (σC, σPdoubled)
skewt(a1)1.88 [3.05]1.50 [2.97]0.75 [2.95]11.0 [18.9]
Δpt(a2)0.14 [0.73]0.20 [0.70]0.19 [0.69]2.38 [0.47]**
Meeting types0.54/0.13/0.330.53/0.13/0.340.53/0.14/0.330.46/0.52/0.01
Stats0.09/0.540.09/0.530.09/0.530.00/0.46
0.54/1.000.53/1.000.53/1.000.46/1.00
mse0.0370.0360.0360.008
Pbad information scenario (σPdoubled)
skewt(a1)1.46 [3.12]0.97 [3.07]0.52 [3.03]9.24 [17.7]
Δpt(a2)0.19 [0.77]0.24 [0.75]0.26 [0.73]2.15 [0.44]
Meeting types0.56/0.11/0.330.56/0.12/0.320.55/0.12/0.330.47/0.52/0.01
Stats0.09/0.560.09/0.560.09/0.550.00/0.47
0.56/1.000.56/1.000.55/1.000.47/1.00
mse0.0350.0350.0340.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types (1.0/2.0/2.1), coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A23:

Predictive power of voting record and decision-making statistics: Autarkical model with information sharing with reservations, N=4.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)3.58 [2.53]3.38 [2.55]3.13 [2.55]11.8 [11.2]
Δpt(a2)0.35 [0.65]0.39 [0.65]0.43 [0.66]2.92 [0.56]**
Meeting types0.36/0.10/0.000.35/0.10/0.000.35/0.10/0.000.47/0.00/0.00
0.13/0.40/0.010.13/0.41/0.010.13/0.42/0.010.51/0.02/0.00
Stats0.14/0.460.14/0.450.14/0.450.01/0.47
0.46/1.000.45/1.000.45/1.000.47/1.00
mse0.0180.0180.0180.007
High volatility scenario (σudoubled)
skewt(a1)1.40 [1.57]1.36 [1.58]1.06 [1.60]7.80 [6.87]
Δpt(a2)–0.01 [0.23]0.04 [0.23]0.04 [0.23]3.26 [0.39]***
Meeting types0.09/0.11/0.020.09/0.10/0.020.09/0.11/0.020.29/0.00/0.00
0.28/0.40/0.100.28/0.40/0.100.28/0.40/0.100.65/0.06/0.00
Stats0.18/0.220.18/0.220.18/0.230.02/0.29
0.22/1.000.22/1.000.23/1.000.29/1.00
mse0.0180.0180.0180.011
Bad information scenario (σC, σPdoubled)
skewt(a1)2.76 [2.53]2.63 [2.49]1.92 [2.45]9.25 [10.2]
Δpt(a2)0.16 [0.61]0.26 [0.59]0.26 [0.57]2.23 [0.45]**
Meeting types0.43/0.09/0.000.41/0.09/0.000.41/0.09/0.000.46/0.00/0.00
0.18/0.30/0.000.19/0.31/0.000.20/0.31/0.000.53/0.01/0.00
Stats0.11/0.510.11/0.500.11/0.490.00/0.46
0.51/1.000.50/1.000.49/1.000.46/1.00
mse0.0380.0380.0380.008
Pbad information scenario (σPdoubled)
skewt(a1)2.22 [2.51]2.05 [2.46]1.37 [2.39]8.19 [9.70]
Δpt(a2)0.26 [0.65]0.29 [0.62]0.28 [0.61]2.23 [0.44]**
Meeting types0.44/0.10/0.000.43/0.10/0.000.42/0.10/0.000.46/0.00/0.00
0.16/0.30/0.000.16/0.31/0.000.17/0.31/0.000.53/0.01/0.00
Stats0.11/0.540.12/0.520.12/0.530.00/0.46
0.54/1.000.52/1.000.53/1.000.46/1.00
mse0.0350.0350.0340.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

Table A24:

Predictive power of voting record and decision-making statistics: Autarkical model with information sharing with reservations, N=6.

ρ=0.90ρ=0.95ρ=0.99ρ1=1.95, ρ.2=0.98
Baseline scenario (σu=σC=σP=14for AR(1) andσu=120for AR(2))
skewt(a1)4.68 [2.67]4.73 [2.69]4.10 [2.67]11.6 [12.0]
Δpt(a2)0.76 [0.74]0.84 [0.75]0.81 [0.74]2.91 [0.57]**
Meeting types0.31/0.16/0.000.31/0.16/0.000.31/0.16/0.010.47/0.00/0.00
0.07/0.44/0.010.06/0.45/0.010.07/0.44/0.010.50/0.03/0.00
Stats0.16/0.480.16/0.480.16/0.480.01/0.47
0.48/1.000.48/1.000.48/1.000.47/1.00
mse0.0170.0170.0160.007
High volatility scenario (σudoubled)
skewt(a1)1.69 [1.60]1.62 [1.62]1.19 [1.64]8.11 [7.01]
Δpt(a2)0.03 [0.24]0.07 [0.25]0.07 [0.25]3.34 [0.39]***
Meeting types0.05/0.13/0.050.05/0.13/0.050.05/0.13/0.050.29/0.00/0.00
0.18/0.44/0.160.17/0.44/0.160.18/0.43/0.160.64/0.07/0.00
Stats0.21/0.220.21/0.220.21/0.230.02/0.29
0.22/1.000.22/1.000.23/1.000.29/1.00
mse0.0150.0140.0140.010
Bad information scenario (σC, σPdoubled)
skewt(a1)2.86 [2.63]2.55 [2.52]1.89 [2.49]11.0 [18.9]
Δpt(a2)0.32 [0.67]0.39 [0.64]0.38 [0.62]2.38 [0.47]**
Meeting types0.41/0.13/0.000.40/0.14/0.000.39/0.14/0.000.46/0.00/0.00
0.12/0.34/0.000.12/0.34/0.000.13/0.34/0.000.52/0.01/0.00
Stats0.12/0.540.12/0.530.12/0.530.00/0.46
0.54/1.000.53/1.000.53/1.000.46/1.00
mse0.0370.0360.0360.008
Pbad information scenario (σPdoubled)
skewt(a1)2.45 [2.60]2.00 [2.52]1.59 [2.49]9.24 [17.7]
Δpt(a2)0.38 [0.69]0.43 [0.67]0.45 [0.65]2.15 [0.44]**
Meeting types0.42/0.14/0.000.41/0.15/0.000.40/0.15/0.000.47/0.00/0.00
0.10/0.33/0.000.11/0.33/0.000.11/0.34/0.000.52/0.01/0.00
Stats0.12/0.560.12/0.560.12/0.550.00/0.47
0.56/1.000.56/1.000.55/1.000.47/1.00
mse0.0350.0350.0340.008

  1. Note: All entries averaged over 101 random paths. The first two rows of each panel are ordered probit estimates of Δpt+1=a0+a1skewt+a2Δpt+ut+1, with [standard errors]. ***/**/* indicates significance at the 1 %/5 %/10 % level. Meeting types show the fraction of meetings of given types, 1.0/1.1/1.2 (first row), 2.0/2.1/2.2 (second row), with the residual 2.3 not shown, coded as x.y, where x is the number of alternatives put to vote and y is the number of alternatives with a positive number of votes (excluding the proposal). Stats show average dissent, the fraction of meetings with no policy change (first row), the fraction of meetings with the proposal equal to the status-quo and the fraction of meetings with the chairman’s proposal accepted (second row). mse is the mean squared difference between the adopted and the optimal policy.

References

Apel, M., C. A. Claussen, P. Gerlach-Kristen, P. Lennartsdotter, and O. Roisland. 2013. “Monetary Policy Decisions: Comparing Theory and ‘Inside’ Information from MPC Members.” Norges Bank Working Paper Series No. 2013/13. Search in Google Scholar

Baron, D. P., and E. Kalai. 1993. “The Simplest Equilibrium of a Majority-Rule Division Game.” Journal of Economic Theory 61 (2):290–301. Search in Google Scholar

Blinder, A. S. 2004. The Quiet Revolution: Central Banking Goes Modern. New Haven: Yale University Press. Search in Google Scholar

Blinder, A. S. 2007. “Monetary Policy by Committee: Why and How?.” European Journal of Political Economy 23 (1):106–23. Search in Google Scholar

Blinder, A. S. 2009. “Making Monetary Policy by Committee.” International Finance 12 (2):171–94. Search in Google Scholar

Budd, A. 1998. “Economic Policy, With and Without Forecasts.” Bank of England Quarterly Bulletin 38 (4):379–84. Search in Google Scholar

Chappell, H. W.Jr, R. R. McGregor, and T. A. Vermilyea. 2005. Committee Decisions on Monetary Policy, Evidence From Historical Records of the Federal Open Market Committee. London: MIT Press. Search in Google Scholar

Claussen, C. A., E. Matsen, O. Roisland, and R. Torvik. 2012. “Overconfidence, Monetary Policy Committees and Chairman Dominance.” Journal of Economic Behavior & Organization 81 (2):699–711. Search in Google Scholar

Gerlach-Kristen, P. 2004. “Is the MPC’s Voting Record Informative About Future UK Monetary Policy?.” Scandinavian Journal of Economics 106 (2):299–313. Search in Google Scholar

Gerlach-Kristen, P. 2008. “The Role of the Chairman in Setting Monetary Policy: Individualistic Vs. Autocratically Collegial MPCs.” International Journal of Central Banking 4 (3):119–43. Search in Google Scholar

Gerlach-Kristen, P. 2009. “Outsiders at the Bank of England’s MPC.” Journal of Money, Credit and Banking 41 (6):1099–115. Search in Google Scholar

Gerling, K., H. P. Gruner, A. Kiel, and E. Schulte. 2005. “Information Acquisition and Decision Making in Committees: A Survey.” European Journal of Political Economy 21 (3):563–97. Search in Google Scholar

Hansen, S., M. McMahon, and C. Velasco Rivera. 2014. “Preferences or Private Assessments on a Monetary Policy Committee?.” Journal of Monetary Economics 67:16–32. Search in Google Scholar

Horvath, R., K. Smidkova, and J. Zapal. 2012. “Central Banks’ Voting Records and Future Policy.” International Journal of Central Banking 8 (4):1–19. Search in Google Scholar

Lahner, T. 2015. “Inconsistent Voting Behavior in the FOMC.” Leibniz Universitaet Hannover Working Paper Series No. 546. Search in Google Scholar

Lee, L.-F. 1979. “On the First and Second Moments of the Truncated Multi-Normal Distribution and Simple Estimator.” Economics Letters 3 (2):165–9. Search in Google Scholar

Mahadeva, L., and G. Sterne, eds. 2000. Monetary Policy Frameworks in a Global Context. London: Routledge. Search in Google Scholar

Maier, P. 2010. “How Central Banks Take Decisions: An Analysis of Monetary Policy Meetings.” In Challenges in Central Banking, edited by P. L. Siklos, M. T. Bohl, and M. E. Wohar, 320–56. New York: Cambridge University Press. Search in Google Scholar

Maskin, E., and J. Tirole. 2001. “Markov Perfect Equilibriumml: I Observable Actions.” Journal of Economic Theory 100 (2):191–219. Search in Google Scholar

Meade, E. E. 2005. “The FOMC: Preferences, Voting, and Consensus.” Federal Reserve Bank of St. Louis Review 87 (2):93–101. Search in Google Scholar

Raskin, S. B. 2011. Monetary Policy and Job Creation. Washington DC: Speech delivered at the University of Maryland Smith School of Business Distinguished Speaker Series. Search in Google Scholar

Riboni, A. 2010. “Committees as Substitutes for Commitment.” International Economic Review 51 (1):213–36. Search in Google Scholar

Riboni, A., and F. J. Ruge-Murcia. 2008a. “The Dynamic (in)Efficiency of Monetary Policy by Committee.” Journal of Money, Credit and Banking 40 (5):1001–32. Search in Google Scholar

Riboni, A., and F. J. Ruge-Murcia. 2008b. “Preference Heterogeneity in Monetary Policy Committees.” International Journal of Central Banking 4 (1):213–33. Search in Google Scholar

Riboni, A., and F. J. Ruge-Murcia. 2010. “Monetary Policy by Committee: Consensus, Chairman Dominance, or Simple Majority?.” Quarterly Journal of Economics 125 (1):363–416. Search in Google Scholar

Riboni, A., and F. J. Ruge-Murcia. 2014. “Dissent in Monetary Policy Decisions.” Journal of Monetary Economics 66:137–54. Search in Google Scholar

Tallis, G. M. 1961. “The Moment Generating Function of the Truncated Multi-Normal Distribution.” Journal of the Royal Statistical Society. Series B (Methodological 23 (1):223–9. Search in Google Scholar

Weber, A. 2010. “Communication, Decision Making and the Optimal Degree of Transparency of Monetary Policy Committees.” International Journal of Central Banking 6 (3):1–49. Search in Google Scholar

Wilhelm, S., and B. G. Manjunath. 2012. “Tmvtnormml: Truncated Multivariate Normal and Student T Distribution.” R Package Version 1:4–6. Search in Google Scholar

Note

This paper is based on the 3rd chapter of the doctoral dissertation of Jan Zápal at the London School of Economics.

Published Online: 2016-7-9
Published in Print: 2016-10-1

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