Ministerial Resignations in the UK 1945-1997

Torun A Dewan and Keith Dowding

London School of Economics

August 15, 2003

Abstract

The paper addresses the tension between collective cabinet responsibility

and the Prime Ministers powers of appointment. We derive the conditions

under which the Prime Minister will choose to protect ministers through

collective responsibility despite a short term incentive to replace ministers

whose resignation has been called for. We show that the level of protection

is decreasing with the number of ministers in the cabinet whose resigna-

tion has been called for and with the length of time since the start of the

administrative term. We find support for these propositions using data on

the length of ministerial tenure from the UK 1945-1997.

1. Introduction

As every student of British politics knows, the relations between ministers in the

cabinet are governed by two constitutional conventions: individual ministerial

responsibility and collective cabinet responsibility.1 According to the former min-

isters are responsible for their own conduct - both personal and departmental -

and that of the sta of their department.2 Under the terms of individual min-

isterial responsibility if the minister is involved in some private scandal of, say,

purported financial or sexual misconduct; public scandal such as a rash state-

ment concerning some aspect of his departmental responsibility or does not act

decisively following controversy over some aspect of the administration of his de-

partment, then the minister may face calls for his resignation. His Prime Minister

and cabinet colleagues may rally round and support him, or they may make clear

that he should resign.3Collective cabinet responsibility, on the other hand, says

1Prepared for delivery at the 2003 Annual Meetings of the American Political Science As-sociation, August 28-31. Copyright by the American Political Science Association. We thankSammi Berlinski for comments and Helen Cannon, Norman Cooke, Won-Taek Kang, Gita Sub-ramanyam, Dan Rubenson and Francoise Boucek for their assistance in collecting and codingsome of this data over many years. We also thank the Nueld Foundation, STICERD and theLeverhulme Foundation for providing small grants over a number of years to help collect data.

2Departments are essentially defined in terms of the responsibility of the minister concerned(with some junior ministers taking responsibility for aspects of a departmental brief overseen bytheir cabinet minister) (Dowding 1995, pp. 17-20).

3Whilst the press does talk of prime ministers firing ministers, under the British Constitutionministers hold their position at the pleasure of the Crown appointed on the recommendation ofthe Prime Minister (Jennings 1959). Ministers proer their resignation to the Prime Minister

2

that each minister takes responsibility for the policies of the government as a

whole and are expected to defend the policies of their colleagues. Ministers are

jointly responsible for government policy and are shielded from responsibility for

policy failures in their departments since responsibility for policy lies with the

cabinet as a whole. Ministers are expected to resign if they clash with colleagues

over policy, or personal, reasons.4

The Prime Ministers executive powers of appointment and patronage largely

occur through periodic cabinet reshues but also involve supporting or withdraw-

ing support for ministers involved in a resignation issue. A Prime Minister has

three possible actions when a minister is threatened. She can publicly support the

minister, not get involved (which does not always imply lack of support - for exam-

ple over comparatively minor spats) or make clear, usually through unattributed

briefings, that she does not support the minister. Dowding and Kang (1998) find

that in the post-war period (1945-97) only 11% of ministers resign if the Prime

Minister publicly supports them, whereas 56% resign where Prime Ministerial

in an amicable exchange or letters. Cases where a minister is dismissed without proferringresignation are almost unknown (Alderman and Cross 1985).

4We term all cases where a ministers position is threatened through individual or collectiveresponsibility a resignation issue. Empirically we have coded all cases where there has been acall for a minister to resign (or consider his position or some such phrase) whether or not heeventually resigns, or when there has been no such call but the minister has resigned out of theblue as a resignation issue.

3

public support is lacking. Over 90% of ministers resign where it becomes clear

the Prime Minister is not supportive. Dewan and Dowding (2002) demonstrate

that when a resignation occurs in the aftermath of a resignation issue then the

resignation more than compensates for the negative eect of the controversy on

public support. They argue that this corrective eect of ministerial resignations

provides a strong short-term incentive for the Prime Minister to enforce a resig-

nation where a minister has faced severe criticism in Parliament or where there

has been strong media criticism of the ministers performance.

Textbook analysis of cabinet relations views the increase in the number of

ministerial resignations in the post-war period as symptomatic of a decline in

collective cabinet government and the increasing power of the Prime Minister.

Commentators often cite one particular case or another as evidence that, while

collective responsibility is in decline, Prime ministerial power is in the ascendency.

The House, so the argument goes, is no longer able to hold ministers to account as

it did in the so-called golden age of Parliament. Where policies have gone wrong

the eventual outcome for the individual minister depends more upon relations

with the PM and the party than upon the gravity of the failure or upon relations

with the House (Coxal and Robins 1991, p. 154).

Whilst there is a great deal of literature on the conventions of individual and

4

collective ministerial responsibility it is mostly discursive and conceptual. The

strategic tensions created between ministers due to the interplay of individual

and collective responsibility is little addressed. In this paper we examine the

tension between the conventions of individual and collective responsibility and

between them and Prime Ministerial power of appointment. The paper has two

aims: firstly, to show how under specific assumptions, a convention of collective

responsibility can be stable despite a short-term incentive for the PrimeMinister to

replace ministers who face calls for their resignation; secondly to derive empirical

estimates of the eect of collective responsibility on ministerial risk.

Our main argument is that the Prime Minister will consider the longer-term

eects on the performance of the cabinet overall when deciding whether to support

a minister facing problems. In our model both the Prime Minister and individual

ministers enjoy rents from holding oce. The eort of individual ministers accrue

to the government as a whole; policy success for one minister leads to a higher

poll rating for the government not simply for the minister himself. In that sense

the Prime Minister wants dynamic policy-active ministers providing high levels

of eort; but resignation issues also have a negative eect on government popu-

larity (Dewan and Dowding 2002), therefore the Prime Minister does not want

to encourage their arrival. Critically we treat the intensity (the arrival rate) of

5

such resignation issues as increasing in the eort levels of ministers. Although

not expressed as part of our formal argument we have in mind that the arrival

of resignation issues for each minister is partly determined by the level of search

activity by the opposition, media and interest groups. A minister who spends his

time in oce keeping his nose clean and merely administering policies, rather than

pressing policy initiatives to satisfy the electorate, is less likely to make enemies

than one who actively seeks policy changes dierentially aecting rival interest

groups. A minister who is policy active is more likely to aggravate opponents

and increase the likelihood that they will criticize him, cause problems or delve

more deeply into his private aairs in order smear him. Moreover the scalp of

a policy active minister is a prize for the opposition and the media to a much

greater extent than one who is less in the limelight.

There are numerous examples of ministers whom history deems to have been

policy orientated and active but whose careers have been punctuated by calls for

their resignations. Sometimes these calls are as a direct result of their policies;

at other times they are a result of scandals and smear campaigns not explicitly

related to their activism other than through the opposition and media searching

out such scandals. That the contribution of policy active ministers is valued

despite the fact that they face a higher risk of being involved in resignation issues

6

can be seen by the fact that several such ministers have been reappointed to

the cabinet following their resignation. Prominent examples of active ministers

who have resigned but returned for sparkling ministerial careers include Winston

Churchill, Anthony Eden and Harold Wilson, all of whom went on to become

Prime Minister, and well-known politicians such as Peter Thorneycroft, Enoch

Powell, Peter Carrington, Michael Heseltime, and more recently Peter Mandelson

all of whom resumed careers at the highest levels of the cabinet following earlier

resignations.

Two examples of politicians who faced grave problems due to their policy ac-

tivism include Barbara Castle and David Mellor. Castle went to the Department

of Employment and Productivity in April 1968, and the following January, with

the support of the Prime Minister and Chancellor, she brought out a sensata-

tional White Paper In Place of Strife. Popular with the electorate, the White

Paper called for a new relationship with Trade Unions in order to try to bring

order to the increasing problem of strikes in British industry. But the unions, tra-

ditional supporters of the Labour Party, organized against the proposals and with

dissension in the cabinet as well as the Labour backbenches, it became clear that

the government would lose the vote on the Bill in the House of Commons. Castle

hastily redrafted a formula to satisfy her critics and she, and the government,

7

survived (Castle 1984, Morgan 1992, pp. 298-305, Hennessy 2000, pp. 321-327).

Mellor is a more interesting example still. He resigned on 25th September

1992 after two months of media speculation about his future. Mellor had been

a keen ally during Majors bid to become leader of the Conservative Party two

years earlier. In July Mellor oered to resign following revelations about his aair

with an actress, Antonia de Sancha but the Prime Minister John Major rejected

his oer. The story was first told in The People a Sunday tabloid which, crucially,

was involved in litagation with Mona Bauwens the daughter of the Chairman of

the Palestine Liberation Fund. She was suing the paper because she claimed her

reputation had been impugned by suggesting that she was not a fit person for

decent people to associate with. The People had headlined their story Top Tory

and the PLO Paymaster and had suggested it unwise of Mellor to go on a family

holiday with Bouwens to a Spanish villa. Mellor resigned in September when

in court it emerged that Bouwens had also paid for the villa and the air tickets

for Mellor and his family. More significant still was that Mellor had taken the

1990 Broadcasting Act through parliament and ended what many Conservatives

thought was a lack of accountability of private TV companies. He had then

turned his attention to the workings of the Press Complaints Commission, a self-

regulating non-statutory body. Mellor did not believe press self-regulaton was

8

ideal and was concerned about press intrusion into privacy. He famously remarked

that the popular press is drinking in the last-chance saloon. There is little doubt

that The People saw their investigation into Mellor as a warning shot to politicians

about press freedom. Doig (1993, p. 73) says the expose by The People was seen

by both sides as an attempt to underline the consequences of tighter restrictions

on what the press could publish.5

These cases illustrate how a misalignment of incentives may occur if the Prime

Minister has a short-term incentive to maximise government support by replacing

ministers facing resignation issues. If the Prime Minister were always to act upon

this incentive she would provide ministers with incentives to minimize their risks

by being less policy active. If ministers minimise their risk by choosing lower eort

levels, overall government support will not be maximised. To address this problem

the Prime Minister can oer inducements in the form of protection for individual

ministers if there are calls for them to resign and it is in this sense that we view

collective responsibility. By supporting ministers who are involved in resignation

issues the Prime Minister induces a higher level of performance from the cabinet

as a whole. Critically, however, we show that the Prime Ministers commitment to

5The People even used the public interest defence as a motivation for their decision topublicise Mellors aair suggesting his taped comments to de Sancha that their liason made himabsolutely exhausted and seriously knackered aected his abilities as a minister (Doig 1993).

9

protection is enforced by the joint actions of the cabinet. Our main result is that

we show how collective responsibility is enforced by the self-interested behaviour

of the Prime Minister and her cabinet ministers.

This is not the whole story, however. We also show that the optimal level

of protection varies with diering political circumstances pertaining within the

cabinet. A ministers hazard increases in the cumulative number of resignation

issues over the cabinet as a whole. Protection, although enforced by the cabinet, is

a decreasing resource. This means that although the collective actions of ministers

ensure protection for some ministers involved in resignation issues such actions

also decrease the level of protection available in the future. That is, by protecting

a minister now, each minister reduces the probability that they will be protected

under similar circumstances in the future.

The results of our theoretical model also challenge the common intuition which

suggests that Prime Ministers use their power of appointment to build a cabinet

with personal loyalty to the Prime Minister. This common intuition implies that a

ministers hazard should be decreasing over time since, according to this logic, the

longer a minister survives in the cabinet the better his chances of overall survival.

Our theoretical results show to the contrary, that ministerial hazard increases over

time. This is because the overall reputation of the cabinet is aected not only by

10

the number of ministers who have experienced calls for their resignation, but also

the length of time which these resignation issues have been in the public domain

without the Prime Minister taking decisive action to deal with the situation, such

as the replacing the minister involved.

2. The Model

The game takes place in continuous time with a positive probability of termination.

The description of the play is as follows

The Prime Minister names the cabinet and states a level of protection s for

ministers

The minister then chooses a level of eort e.

Resignation issues then arise, if any, with p(e) and are above a cut-o level

s with prob=q.

The Prime Minister either protects or fires the minister.

The game terminates when an election is called and the government is defeated.

For simplicity we treat government duration as drawn from an exponential dis-

tribution with a constant termination rate l. We assume ministerial eort is the

11

ministers private information. The Prime Minister observes only the occurrence

of resignation issues which have Poisson intensity p. In line with the arguments

above we state Assumption 1 that p(e)e > 0. The minister knows his own eort

level and in addition observes a continuous history zt of all previous actions taken

by the Prime Minister; whereas the Prime Minister observes a continuous history

st of resignation issues that have occurred.

Pay os and strategies

To derive pay os we highlight the team nature of cabinet government.6 In

particular some of the eorts of each minister acrue to the government as a whole

and are realized in public support of the government. Public support for the

government is a function of the overall level of eort in the cabinet which is

represented by f(e1, ..., en). To keep things simple we assume that ministers choose

symmetrical eort levels and we can write the contribution of ministers eorts

to government support as f(e) with fe > 0. Each minister receives a pay-o

for his eorts through the fraction f(e)n. Ministerial actions may also negatively

aect government support through the electoral cost of ministerial involvement

in a resignation issue which we denote by s. Each s has a level of seriousness

6For an analysis of the application of the theory of teams to cabinet government see Spirling(2003).

12

on a continuous interval and according to s the Prime Minister chooses a level of

protection by committing to protect (not to fire) all ministers who are involved in

all resignation issues which fall in the interval (0, s) and commiting to fire all other

ministers involved in resignation issues. If a minister is involved in a resignation

issue then he must always bear the cost of that resignation issue through a one-

o cost s. If the minister stays within the government then his instantaneous

pay-o is f(e)n s, however if he is fired he receives s. To keep things simple we

make assumption 2 that f(e)n> p(e)s so that the participation constraint is always

satisfied. In this sense there are always positive rents to oce and ministers will

always accept a post when oered.

The Prime Ministers pay-o is strictly increasing through the eort level of all

the cabinet through the government support function f(e). In addition the Prime

Minister, through her decision to oer protection or to fire, decides whether to

bear the cost of a ministers reputation. If k ministers have been involved in

a resignation issue during the time interval (0, t), then the overall cost of cabi-

net reputation is ktU0

exp(rT )p(1 q(s))s dT where exp(rT ) is the constant

discount rate. The level of protection q then captures the idea of collective respon-

sibility as a commitment made by the Prime Minister on behalf of the government

to bear the cost of ministerial reputations. If the Prime Minister always fires the

13

minister (q = 1) then this is equivalent to choosing a zero level of protection, that

is, s = 0. In other words, there is no collective responsibility. Whereas if the

Prime Minister oers full protection (q = 0) then she commits the government to

bearing the cost of all resignation issues and we have full collective responsibility.

That is, everything everyone does comes under collective responsibility. In this

sense we can suppress the dependence of q on s and treat q as the Prime ministers

choice variable.

This game captures two important features of the political situation. Firstly, it

captures the symbiosis between collective responsibility and the Prime Ministers

powers of appointment. Secondly it captures directly the incentive which the

Prime Minister has to fire ministers who have been involved in resignation issues,

which previously we have referred to as the corrective eect (Dewan and Dowding

2002). To understand why the Prime Minister may ignore this incentive and would

rather protect ministers through collective responsibility we now look more closely

at the ministers problem. With this set up a strategy for the minister is a mapping

from zt to the choice of eort level. A strategy for the Prime Minister is a mapping

from st to her choice of q (0, 1).

The Ministers problem. The objective of each minister is to maximise his share

of the governments support subject to his eort level. Pay os are conditional

14

upon whether or not he experiences a resignation issue and if he does whether or

not the Prime Minister protects him. The instantaneous stage game pay o for

the minister is

(1 p)f

n+ p(1 q)(f

n s) pqs

dt

where the first term captures the pay o if there is no resignation issue, the second

term the pay o where there is a resignation issue and the minister is protected,

and the final term the pay o if the minister faces calls for his resignation and

no protection is given such that he loses his job in the government. Assuming

exponential discounting and government duration we can then write the ministers

value function as

Vcm =

]

0

exp(rt) exp(l pq)(1 p)f

n+ p(1 q)

f

n s

pqs

dt

=1

r + l + pq

(1 pq)f

n ps

(1)

Proposition 1. Ministerial eort is described by the function e(q) with dedq< 0

for all values of q.

15

The Prime Ministers problem. We can now focus upon the Prime Ministers

problem. The Prime Minister maximises her short term pay-o by firing ministers

when they have been involved in a resignation issue because it is costly to bear

the ministers reputation. However by Proposition 1, ministerial eort is lower

if ministers are not protected from the risks of being policy active. Let R =tU0

exp(rT )p(1 q)s dT then the instantaneous stage game pay-o for the Prime

Minister between between t and t+ dt is

(1 p)(f kR) + pkn[q(f (k 1)R) + (1 q)(f s kR)]

+p(1 kn) [q(f kR) + (1 q)(f s kR)] dt

The first term is the pay o where there is no resignation issue; the second term is

the pay o where a resignation issue arises involving one of k ministers previously

involved in a resignation issue; the final term is the pay o in the eventuality that

a minister involved in a resignation issue has not previously been involved in one.

Simplifying gives the stage game pay-o to the Prime Minister as

kf p(1 q)s k(1 pq

n)Rldt

16

between t and t + dt. Since this term is increasing in q it implies a solution of

q = 1. However bearing in mind the implicit relationship e(q) from Proposition 1

the Prime Ministers problem in the repeated game is choose q to maximise the

Prime Ministers value function which is

Vpm =

]

0

exp(rt l)

f p(1 q)s k(1 pq

n)

t]

0

exp(rT )p(1 q)sdT

dt

=1

r + l

f p(1 q)s k

1 pq

n

t]

0

exp(rT )p(1 q)sdT

=1

r + l

(f p(1 q)s) k(1 exp(rt))

r2 + lr

1 pq

n

(1 q)ps

(2)

Proposition 2. There exists an optimal level of protection q(e) such that

0 < q < 1.

3. The Equilibrium

In the long run, due to the relationship between ministerial eort and the level of

protection which ministers receive, the Prime Ministers problem has an interior

solution. It is optimal for the Prime Minister, when taking account of the eect of

17

the longer term eects on cabinet eort, to refrain from acting upon her short term

incentive to fire ministers when a call is made for their resignation. The problem

for the Prime Minister is that she cannot commit to oering protection in the

eventuality of a resignation issue. This is due to the short term incentive which

the corrective eect provides. Hence, whether this solution to the Prime Ministers

problem is stable in equilibriumwill depend upon the strategic interaction between

ministers and the Prime Minister.

In appendix A we derive the conditions under which it is possible for the Prime

Minister to make such a commitment. The Prime Ministers condition is that the

long-run pay o which she receives through higher eort minus the long-run cost

of protecting ministers must be greater than the short run incentive to fire. If

this condition is satisfied then in the long-run the Prime Minister will always be

better o if she does not deviate from using q. Of course this can only be en-

forced if ministers are willing to punish the Prime Minister if she reneges on q.

Participation in the punishment of the Prime Minister is ensured whenever the

dierence in the probability of being involved in a scandal with a higher level of

eort, as opposed to the lower level of eort during the punishment regime, is

suciently large to oset the marginal share of the ministers higher eort if he

defects. When both conditions are satisfied the Prime Minister can commit to

18

oering ministers protection in the sense of enforcing collective responsibility. To

renege on the commitment would lead to eort levels in the cabinet being lower

with a corresponding decrease in government support. In this sense the collective

actions of ministers ensure that an optimal level of protection is provided. Minis-

ters provide higher levels of eort since it is in their interest to do so; higher eort

increases the level of support for the government, from which they, as individuals,

benefit. The Prime Minister in turn protects ministers from the higher risk which

their eort level entails. It is in the long term interest of the Prime Minister to do

so since she benefits from a higher level of eort in the cabinet, despite having to

bear the cost of some ministerial reputations. Thus mutually reinforcing strategic

behaviour by the Prime Minister and her Ministers ensures that a convention of

collective responsibility is stable.

4. Comparative Statics

Having shown that not only is it optimal for the Prime Minister to oer protec-

tion to ministers, but that in equilibrium such protection will be provided, we

now turn to an analysis of which factors aect the level of protection which is pro-

vided. A useful feature of our theoretical framework is that it allows us to derive

comparative statics on the eects of time on a ministers likelihood of survival as

19

a member of the government. Analysis of the optimal level of protection yields

the following propositions:7

Proposition 3. The likelihood that a minister survives decreases as a function

of the length of time spent in ministerial oce.

The theoretical interest of this finding is that for most forms of hazard analysis

where time plays a role the opposite relationship is expected. For example suppose

that survival capacities of ministers are related to some skill they display doing

their job. A subset of such skills might be, for example, the propensity to work

hard, provide a loyal service and display a similar ideological outlook to that of the

Prime Minister. Here we should expect that those displaying these skills would

last longer than those without them. Over time only those with such skills would

survive so average ministerial survival rates should increase (hazard rates would

drop) as a function of length of time spent in ministerial oce. We do not find

this in our model because of the worsening overall reputation of the government

over time. The governments reputation is aected by the number of ministers

involved in resignation issues and the length of time which these issues have been

in the public domain without the Prime Minister being seen to take corrective

7The details for these propositions are provided in appendix B.

20

actions. As such a minister may be removed from oce in light of a relatively

trivial resignation issue which ocurs late in the administrative term, where more

serious oenders have survived previously. In addition to the direct eect of time

we also find the following relationship:

Proposition 4. The likelihood that a minister survives decreases as a function

of the number of ministers who have been involved in a resignation issue who are

in the cabinet at time t.

We find that each ministers likelihood of survival is related to the number of

ministers involved in a scandal but who have previously been protected by the

Prime Minister. This is an interesting result when seen alongside the equilibrium

behaviour decribed in the model. In equilibrium the willingness of ministers to

collectively punish the Prime Minister if she reneges on the promised degree of

protection ensures an optimal level of protection for each minister. However pro-

tection is a decreasing resource. The greater the number of ministers who receive

protection the less likely any minister will survive subsequent calls for resigna-

tion. This proposition captures some of the interesting nuances of the resignation

process. Where a large number of ministers have been protected ministers are

more likely to be fired even for relatively trivial oences. In other words collective

21

cabinet responsibility has an eect upon the survival capacity of each minister.

Ministers who have faced resignation calls in the past bear not only the weight

of their own reputation but also that of the government as a whole. Collective

responsibility aects the working of individual ministerial responsibility when res-

ignation issues arise. As collective responsibility grows in the past so individual

responsibility grows in the future. Sometimes a minister has to resign over an issue

not so much because of the problems he faces now, but because of the problems

his colleagues faced in the past.

Figure 1. Proposed proportional hazard function

h(t, k=1)h(t, k=0)

Hazard forministers(mi,mn)

Timejs ResignationIssue at t

js ResignationIssue at t

22

To test these hypotheses we use duration analysis where our dependent variable

is the length of time that a minister serves in the government. We focus upon the

failure rate of ministers where a failure refers to the removal of a minister from

the cabinet either trough an individual ministerial resignation or through the exit

of a minister in a cabinet reshue.We refer to this failure rate as the ministers

hazard. Since in our case we have a specific proposition about the eect of time

on the dependent variable which we wish to test we use a parametric duration

model. In particular our hypothesis states that the ministers hazard is increasing

with respect to time passed and that the hazard varies with k; as such we express

ministerial hazard as a function of both t and k so we have h(t) = f(t, k). Figure 1

depicts a hypothetical hazard function which fits our propositions in a proportional

hazard format. The hazard is seen to be growing at a constant rate but within the

time interval (t, t) the constant hazard is higher due to a resignation issue aecting

minister j at t. Following js removal from the cabinet at t the hazard falls back

onto the same time dependent path as before the resignation issue occured. We

can estimate this hazard process with the following Weibull model

hi(t|, , k) = t1 exp() exp(k), (3)

23

where the first term t1 describes the shape of a monotone hazard function with

estimating its gradient. We refer to this as the baseline hazard of the minister

and as depicted in Figure 1 the baseline hazard may shift upwards or downwards

with an increase or decrease in k (the number of resignations issues which aect

the cabinet at t). The coecient estimates the magnitude of the shift in the

hazard due to an increase or decrease in k.

As with all forms of regression analysis, to derive unbiased estimates of

and we need to take account of heterogeneity in our sample. Heterogeneity

can be particularly problematic in duration models since the observed gradient of

the hazard function may be due to unobserved variables which, if included, would

yield a flat hazard function (Heckmann and Singer 1985). Heterogeneity may take

two forms: firstly ministers within the same cabinet may share a similar hazard

due to features other than k. For example dierent Prime Ministers may dier

in their leniency towards cabinet ministers who have been involved in resignation

issues and may have dierent propensities to reshue their cabinets. Secondly

the hazard rate of individual ministers may vary due to unobservables such as the

quality of the minister. We deal with group level heterogeneity by including a fixed

eect for each post war government which begins at the start of an electoral term

and runs through to the end of the term. To deal with unobserved individual level

24

eects we assume an unknown source of heterogeneity with gamma distribution

for each minister. We rewrite the term in equation 3 as ij = 00+0g+i where

0g captures the heterogeneity which is due to the shared experience of members

of the same government, and where the remaining individual level heterogeneity

is captured by i which has a gamma distribution with mean 1 and variance 2.

Transforming equation 3 we have

hi(t|, , k) = t1 exp(ij) exp(k). (4)

In this specification each minister may have a dierent hazard but the systematic

eects in which we are interested, (those of t and k) are assumed to be the same

same for all ministers.

Within this model are nested a number of dierent hazard processes. For

example, if = 1 and = 0 then the minister faces a constant hazard. This hazard

function describes the situation where, contrary to our hypothesis, a ministers

chance of surviving from one day to the next are unaected by the passage of time

and where the hazard is unaected by changes in k. If = 1 and > 0 then the

the hazard is a constant function but this constant eect is aected positively by

an increase in k,indicating support for Proposition 4 but not for proposition 3. If

25

however > 1 and > 0 there is evidence to support both propositions since we

would observe positive time dependence of the hazard function which is in turn

aected positively by k.

5. Data and Estimates

To test these propositions we use data from the UK on the length of ministerial

tenure for all ministers entering government within the period spanning from the

start of the Atlee government in 1945 to the end of the Major government in

1997. We provide details of this data in a data appendix. The results shown

in the the first column of Table 1 refer to the model specified in Equation 3.

This model gives an estimated slope to the hazard rate of = 1.277 with a

standard error of 0.033 and an estimate of the shift in the hazard rate due to an

increase in the number of ministers in the cabinet who have faced calls for their

resignation of = 0.037 with a standard error of 0.013. The coecent of time

indicates a positively sloped hazard function as expected, whereas the estimated

value for corresponds to a 3.7 % increase in the ministerial hazard rate for

each additional member of the government who has been involved in a resignation

issue. The results in the second column refer to the model specified in Equation

26

4 which controls for dierent sources of heterogeneity. In this model the hazard

function has a somewhat steeper gradient of 1.348 and the estimated shift due

to an increase in the number of ministers in the cabinet who have faced calls for

their resignation is comparable to that estimated in the first model. However,

with these specifications we cannot be sure that the estimate of is not driven by

the increase in the individual hazard rate of the kth minister who has experienced

a call for his resignation. To distinguish between these eects we include an

additional term in Model 2 which is a time varying covariate for the number of

resignation issues in which a minister has been involved during his term of oce.

We allow this eect to vary with the position of the minister. In this model the

estimated indicates a steeper gradient of 1.49 with a slightly lower estimate of

=0.033 which corresponds to a 3.3 % increase in the ministerial hazard rate for

each additional member of the government who has been involved in a resignation

issue.

What inferences can be drawn from our results? Our results lead us to reject

the hypothesis of a hazard which is either constant or decreasing as a function of

time. To see this we can take the natural log of the estimated from Model 3.

This gives ln(1.490) = 0.399 with a standard error of 0.035. Since ln(1) = 0 we

can reject the hypothesis of a constant hazard rate and the result lends support to

27

the proposition that the hazard rate is increasing with time. The implication of

this result is that, as hypothesised in Proposition 4 and contrary to conventional

wisdom, the odds of ministerial survival are decreasing with each day that the

minister serves as a member of the government. Moreover we also reject the

hypothesis that = 0,that is, that there is no shift eect upon the baseline

hazard of an increase in the number of ministers in the cabinet who have been

involved in resignation issues. Our results indicate support for the proposition that

the hazard rate of individual ministers increases in the total number of ministers

involved in resignation issues.

28

Table 1. The eect of time and number of ministers involved in

resignation issues on the hazard rate of British ministers (1945-1997)

(1) (2) (3)

Cabinet reputation 0.037 0.038 0.033(0.013)*** (0.013)*** (0.012)***

Ministers reputation 0.557(0.206)***

Position 0.434(0.055)***

Ministers reputation*position

1.277 1.348

-0.492(0.187)

1.490(0.033)*** (0.082)*** (0.053)***

-10.480 -10.949 -13.128(0.381)*** (0.603)*** (0.522)***

Log Likelihood

Total observationsNumber of ministersNumber of resignations

-971.807

22877996567

0.114(0.115)

-971.207

22877996567

0.000(0.000)

-936.983

22877996567

Note: Standard errors in parentheses * significant at 10%;** significant at 5%; *** significant at 1%Note: Each model includes fixed effects for each post war government.

29

Whilst these results show support for Propositions 3 and 4 they are derived

form a model which allows only for a monotonically increasing or decreasing haz-

ard function through the eect of . Other hazard functions which also show

positive time dependence may provide a better fit with the data although at a

cost of including additional parameters. For example the Gompertz model which

has one additional parameter would allow for a hazard rate which increases at an

increasing rate. The Gamma hazard model by contrast allows for non monotonic-

ity and this model would fit the data better if the underlying process were such

that ministerial hazard is increasing in the period following an appointment but

falling o towards the endpoint of the administration. A wrongly specified base-

line hazard aects not only the consistency of our estimated but may induce

sensitivity of the estimated coecients of the hazard function to the specification

of the distribution of the random component for unobserved heterogeneity in ij

(see Heckmann and Springer 1984).

Table 2 shows the log likelihood for each of these models, the number of pa-

rameters used to describe the hazard in each, and its score on the AIC criterion

which takes into account the additional parameters used to estimate the shape of

the hazard. The AIC score is -2 log likelihood + 2 (no. of degrees of freedom

+1) and the creterion is to minimise this value. The results indicate that both

30

the Weibull and the Gamma model fit the data reasonably well when compared to

the other models tested. Although we would select the Gamma model as having

a marginally better fit there is no evidence in evaluating these models that our

results are due to a misspecification of the hazard.

Table 2: AIC criterion for selected models.

Distribution Parameters Log likelihood AIC score

Exponential 1 -987.482 2016.965

Weibull 2 -936.983 1915.966

Gompertz 2 -963.703 1969.406

Gamma 3 -936.588 1915.177

Lognormal 2 -998.983 2037.967

6. Conclusions

This paper has addressed a central issue in the study of Prime Ministerial and

cabinet relations. Empirical evidence suggests that the Prime Minister has a

short-term incentive to sack ministers who face calls for their resignation (Dewan

and Dowding 2002); why then does the convention of collective responsibility

arise and what makes it stable? In this paper we suggest that the short-term

31

incentive to fire conflicts with providing ministers with incentives to be dynamic

and policy active. Such dynamism and activism brings long-term benefits for

government popularity as perceived social or economic problems are addressed,

even though active ministers will be more of a focus of criticism and investigation

by the opposition parties and the media. There are many examples of policy

active ministers who have faced calls for their resignation when their policy eorts

have created enemies among pressure groups and the media. Theoretically we

have shown that the collective actions of cabinet ministers ensure that the Prime

Minister can foster a reputation for protecting ministers when they face resignation

calls; this is due to the Prime Ministers concern for the long-term eect of her use

of appointment power upon the overall level of performance within the cabinet.

A convention of collective responsibilty is therefore stable due to the mutually

enforcing self-interested behaviour of ministers.

The theoretical model has a number of simplifying features and relaxing these

may lead to its extension. The restriction of symmetric eort levels and sub-game

perfection rules out some types of behaviour which are theoretically plausible and

may be prevalent. For example, it is possible that ministers with dierential repu-

tations might adopt dierent strategies. Moreover, we treat government duration,

as opposed to ministerial duration, as exogenous and a richer model should allow

32

this term to vary with the number of resignation issues and the level of minis-

terial eort. Nevertheless we believe that the simple model which is developed

here does help to illustrate the strategic tensions between individual and collec-

tive responsibility. Moreover our analysis of collective responsibility has produced

testable propositions concerning the hazard rate of cabinet Ministers and how it

is aected by the collective reputation of the cabinet. We show that the reputa-

tion of the cabinet is due to two factors: the number of ministers who have faced

resignation calls and the length of time that these issues have been in the public

domain without their having lead to a resignation. The ministerial hazard rate

is thus increasing with respect to both time and the number of ministers in the

cabinet at each point in time who have been involved in resignation issues. In this

sense protection, though enforced by the cabinet, is a decreasing resource. Min-

isterial hazard rates increase over time, even though we should expect that those

individual characteristics favoured by the Prime Minister - loyalty, dynamism and

ideological committment - should grow in the cabinet.

The estimates we derive of the ministerial hazard rate support the propositions

which follow from the model. Hence we not only show the existence of collective

responsibility as a convention which is sustainable through self-interested behav-

iour, we demonstrate its magnitude through the hazard rate of individual minis-

33

ters. We believe that if collective responsibility has any real meaning, other than

as a legalistic doctrine which governs the behaviour of cabinet ministers and the

Prime Minister, then it must be in the sense of a shared risk by cabinet members.

The estimates which we derive are the first empirical estimates concerning how

much of the overall reputation of the cabinet is shared by individual ministers in

terms of the additional risk which they face.

7. Appendix A

We show that if the conditions f(e)p(1q)s

l> s and f(e)

n (1p(e

)) f(e)

n2

p(e) > s are

satisfied then the following strategy profile is sub-game perfect: the Prime Minister

chooses qand each minister produces an eort level which satisfies Vpme = 0|

q = q for all histories of the game where only q is observed. If ever the Prime

Minister chooses q > q then each minister produces an eort level which satisfies

Vpme = 0| q = 1 and the Prime Minister chooses q = 1.

This follows from the satisfaction of the Prime Ministers no deviation con-

straint. From 2 we have the value function for the Prime Minister for the history

where she has always played along the equilibrium path which is

34

V pm =1

r + l

f(e) p(1 q)s k1 exp(rt)

r2 + lr(1 pq

n)(1 q)s

.

The value function for the Prime Minister if she deviates when one of k is involved

in a resignation issue is and she plays o the equilibrium path is

Vpm = s+1

r + l

f(e) (k 1)1 exp(rt)

r2 + lr(1 pq

n)(1 q)s

where the first term on the RHS is the pay-o due to the corrective eect and

the remaining term is the pay-o with (k 1) ministers with reputations in the

cabinet instead of k such reputations and q = 1. Since the Prime Minister knows

that,following her defection, ministers will provide low eort there is no incentive

for the Prime Minister to choose anything other than q = 1 having once defected.

The no deviation constraint for the Prime Minister is then

1

r + l(f(7e) p(1 q)s) > s+

(1 exp(rt)(1 pqn)(1 q)

r2 + lrps.

where 7e is the dierence between in the eort level of the cabinet for q = qand

35

q = 1. Allow r 0 to give the condition for the Prime Ministers cooperation.

To be sure the equilibrium is reached when the Prime Ministers condition

is satisfied we also need to show that ministers will not defect from the stipu-

lated punishment regime. We need only focus upon the dierence in the stage

game pay-o if the minister cooperates with the punishment regime and that if

he defects. To cooperate the ministers additional risk through the dierence be-

tween p(e) and p(e) must oset the addition to his marginal share of the output

which is f(e)

n2(since all other ministers will choose e). Hence if the minister co-

operates he receivesk(1 p(e))f(e)

n p(e)s

ldt whereas if he defects he receives

k(1 p(e))

f(e)n+ f(e

)n2

p(e)s

ldt. We write the ministers no deviation con-

straint as

[p(e) p(e)] f(e)n (1 p(e))f(e

)

n2> [p(e) p(e)] s.

Let p(7e) = p(e) p(e) which is strictly positive. Dividing through by this term

gives the condition f(e)n(1 p(e))f(e

)n2

p(7e) > s.

36

8. Appendix B

Proof of proposition 1. We make use of Assumption 1 and Assumption 2 and

the implicit function theorem. From the implicit function theorem we have that

eq =2Vcm/2e2Vcm/eq . The sign of the numerator follows from Assumption 1; since

the positive eect of eort on the ministers pay-o is oset by the increase in

the probability of incurring a cost due to involvement in a resignation issue there

exists an optimum level of eort and hence 2Vcm2e is negative. To derive the sign

of the denominator we use the first-order condition of Vcm with regard to e which

is

1

r + l + pq

1

n

fe qpn

fe qfn

pe p

es

=

1

(r + l + pq)2qpe

(1 pq)f

n ps

where the bracketed term on the RHS is the stage game pay-o and the bracketed

term on the LHS the first-order condition of the stage game pay-o with regard

to e. The result follows from Assumption 2 which states that stage game pay-os

are positive, hence that RHSq < 0.

37

Proof of proposition 2

Follows from the first and second-order conditions on Vpm. The first-order

condition is

(1 pqn)

pe

eq(q s) + ps

Y + p(1 q)s

pe

eqq

n p

2

n

Y

=1

r + l

fe

eq (1 + q)p

eeqs+ ps

where Y = k(1exp(rt)r2+lr

pe

eq . From proposition (1) we have that

2e2q = 0 from which

it follows that 2Vpm2q =

p3qsn p2qs

n

Y .

Proof of Propositions 3 and 4.

These follow from Propositions (1) and (2) and the implicit function theorem.

From the latter we have that qt =2Vpm/2q2Vcm/qt . From Proposition (2) we have that

the numerator of this term is negative and from Proposition (1) that 2Vpm2q = 0.

To derive the sign of the denominator we need only focus on the leading terms

involving t and k. Thus we need only focus on Z = k(1exp(rt))r2+lr

(ps (1 + p)p2qsn)

and the results follow from the fact that both Zt andZk are positive.

38

9. Data Appendix

The entry and exit dates of all ministers 1945-1997 (start of Atlees government to

end of Majors) were coded from Butler and Butler (2000). Ministers were coded:

1=Ministers in Cabinet, 2=Ministers outside the Cabinet and Ministers of State,

3=Junior Ministers, 4=Whips. (Some Chief Whips are given Cabinet posts and

are coded 1.) Where a minister leaves government following the loss of power of

his party in a General Election his data is censored, allowing us to distinguish

ministers who exit following a resignation from those exiting due to loss of power.

The procedure for data collection on resignation issues is as follows

(i) The Times index is consulted year-by-year noting all references to depart-

ments, ministers by job and ministers by name. These are cross-referred to events

to build up a comprehensive picture of the major political events of each year.

(ii) All potential resignation issues are consulted in The Times on microfilm,

latterly through online sources with some cross-reference to other newspapers,

Hansard and through biographies, autobiographies and other historical sources in

order to verify reasons for resignation. (During the period of non-publication of

The Times, The Daily Telegraph was used.)

(iv) The data thus collected is then categorized as one of eleven proximate

39

reasons for resigning, and also coded for contributory factors and the role of the

Prime Minister, ministers own party, the opposition parties, and media was coded

as For, Against, Not Involved.

A resignation is easy to observe, but non-resignations not so and were

identified by noting when someone in Parliament or the press, or from some pro-

fessional organization or pressure suggests that the minister should resign, or the

press suggests that the issue is seriously damaging or some similar phrase then

it is defined as a resignation issue.

The date of the resignation issue is coded as the day it is reported in the

media. The resignation date is as announced in the media or from Butler and

Butler (2000). Where ministers hold similtaneous jobs, the lesser job is coded and

ignored in analysis. Similarly when jobs overlap (ministers may be reshued to

a new post and ocially hold their old post until a new minister is announced,

several days, or in a few cases weeks later) the minister is coded as having left one

job the day he enters a new one. The new minister is counted as having entered

the day his position is announced.

40

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42