# Accountability and Motivation: A Model of Delegated Reform Decisions with
Career Concerns

Liqun Liu Ph.D. student, University of Chicago Harris School. Email:
<EMAIL_ADDRESS>
###### Abstract

Successful reform policy-making commonly involves correct policy choices
followed by quality implementation. When political decision makers carry out
these decisions, office-holding motives may prevent them from acting in the
most appropriate way. I build a formal model to examine how a decision maker
with conflicting policy and office-holding motives makes reform policies
across several salient information environments. My model highlights the
difficulty of fine-tuning the decision maker’s motives in a context where
pandering is inevitable. I show that backing away from full transparency often
helps – not by eliminating pandering, but by lending credibility to a
retention rule that is pivotal on reform outcomes – to provide a high-powered
incentive for implementation. Excessively stringent or lenient transparency
requirements direct the decision maker’s attention to acting congruently
without taking the policy consequences seriously.

Keywords: Accountability; Motivation; Pandering; Transparency

##  1 Introduction

There is a widespread perception that political decision makers are “timid”
during policy-making: they often shy away from the policies that are good for
the society but bad for their future careers (e.g. Canes-Wrone et al. (2001);
Maskin and Tirole (2004); Fox (2007)). The key to controlling this behavior is
removing their accountability, that is, they shall not be responsible
politically for unfavorable policy consequences that arise from the ex ante
appropriate policy decisions111Maskin and Tirole (2004) suggest that technical
decisions should be left to unaccountable officials; Prat (2005), Fox and Van
Weelden (2012), and Ashworth (2012) suggest that backing away from
transparency helps because the incumbent cannot be judged on unobserved
actions.. Yet in many complex reform policy-making where the quality of
implementation matters, simply joining or splitting one’s policy and office-
holding motives is not enough. The public faces excessive policy risks if
political decision makers are insufficiently motivated at the implementation
stage.

The following example illustrates this point. Dominic Cummings, a chief figure
in the Brexit campaign and a former senior advisor of Boris Johnson, used to
have enormous influence on the British civil servants. To Cummings, supporting
the Brexit is a matter of loyalty rather than policy-making for civil
servants. When Cummings just assumed his position as Johnson’s advisor,
anecdotes222“How Dominic Cummings took control in Boris Johnson’s first days
as Prime Minister”. BuzzfeedNews. 27 July 2019. suggest that he cued the
department aides to support the no-deal Brexit in return for extra money from
the Treasury; to department aides, it is “do or die”. In January 2021, after
stepping down from the Downing Street for months, Cummings continued his
propaganda. He posted on the social media “Should I name and shame the senior
officials who persistently present a disastrously incorrect picture to
ministers?” and “Many will be pleased to know this is about ideologues with EU
stars in their eyes, not the virus.”333“Dominic Cummings threatens to expose
Remainer civil servants who tried to sabotage Brexit”, Express, 6 January
2021.

Not all civil servants shared Cummings’s enthusiasm about Brexit. In fact,
many were confused, depressed, and/or annoyed at implementing the plan. After
long being trapped in the black hole of Brexit, a civil servant complained to
The Guardian: “Heaven help us if no deal (Brexit) actually happens.”444“Many
civil servants are depressed – including me. Brexit will do that to you.”, The
Guardian, 26 November 2019.  Jill Rutter, a former treaury mandarin, put
straightforwardly: “Brexit is an article of faith, rather than a pragmatic
choice.”555“The civil service must speak truth to Boris (and his Cabinet)”.
The Institute for Government. 25 July 2019. Others in the Whitehall question
the practicability of Cummings’s rush and radical changes prior to the Brexit.
Dave Penman, the head of the FDA union, pinpointed the source of
(de)motivation in reform implementation:“ There’s a huge difference between
bringing in new ideas or radical agendas and implementing untested ideologies
which, if they go wrong, will impact upon the delivery of public services to
millions of citizens.”666“Dominic Cummings role provokes alarm inside civil
service”. The Guardian, July 25 2019. Indeed, Cummings shall be happy to see
these unelected bureaucrats pander to support the Brexit. But even a Brexit-
zealot like him faces an incentive problem: how to motivate its
implementation?

This paper brings the motivation problem to a pandering context, focusing on
the right kind of accountability within the delegated reform decisions. The
delegates’ office and policy motives are imperfectly aligned; hence, to what
extent the public might fine-tune these motives determines the quality of the
reform decision-making. The only policy instrument that public can harness is
the delegates’ accountability, that is, they shall be removed from office
unless their reform decision-making admit certain “nice” features. Then the
question becomes: what are the nice features that would align the delegates’
policy and office-holding motives? Can the delegates be credibly
rewarded/punished electorally after the policy-making? And finally, what kind
of accountability would best serve the policy interest for the public?

I analyze these questions with a formal model of reform decision-making. There
is a careerist agent (he) carrying out the reform decisions and its
implementation on behalf of a principal (she). The agent must choose between
the safe status quo policy and a risky policy reform. To highlight the
motivation issue in a clear fashion, I follow Hirsch (2016) and assume that
good policy choice and good implementation are complementary to a successful
reform. As a policy expert, the agent is assumed to be better informed than
the principal about the underlying state that dictates whether the reform
might be successful. However, the agent is not a perfect delegate. On the one
hand, he does not necessarily share the principal’s policy preference. A
congruent agent prefers a successful reform to the status quo to a failed
reform just as the principal; a noncongruent (conservative) agent prefers the
status quo no matter what. On the other hand, the agent places some weight on
retention; the office benefit incentivizes him to make policy to signal
congruence to the principal. Taken together, career concerns might distort the
agent’s reform decision-making in a way that damages the principal’s policy
interest. For example, he may initiate a reform during bad times, or failing
to implement a good reform with sufficient efforts.

My main analysis concerns to which extent the principal may and should hold
the agent accountable. Since the agent cannot be judged on things that the
principal does not observe, I assume that the principal employ information
policies as devices to establish the limits of accountability. Ranging from
the least to the most transparent environments, the principal may observe 1)
the policy choice, 2) the policy choice and its outcome, and 3) the policy
choice, implementation effort, and its outcome. Roughly, they classify the
policy-making environments according to whether the agent might answer for its
decision, implementation, and outcomes. That said, the principal does not
necessarily use all data from policy-making to make the retention decision. I
study how the principal and the agent form mutually-correct guesses on the
other’s strategy, and characterize the environment that best serves the
principal’s policy interest.

Main results. I show that the right kind of accountability must involve the
principal observing the policy outcome; beyond that, the principal does not
necessarily benefit from knowing more about the reform decision-making.

Knowing the policy outcome matters because it alters the burden of proof (e.g.
Ashworth (2012)): when the public is unlikely to learn about the
appropriateness of a policy, the agent proves loyalty unless he refuses to
reform. With the policy outcome going public, the agent shows disloyalty
unless he does the reform right. Assuming in both situations the agent panders
to reform, he exerts more efforts in the latter case because he must answer
for the reform decision and outcomes. In fact, a retention rule pivotal on
reform outcomes provides a powerful incentive – the agent would internalize
the office benefit into his implementation effort. Thus, an environment with
the policy outcome observable fine-tunes the agent’s policy and office motives
in a context in which pandering is inevitable.

Can the principal improve by gleaning information about the reform
implementation before evaluating the agent? We have to caution that the
principal might not utilize all data at hand for the retention decision. The
key barrier is that, the accountability for the reform implementation and
outcomes do not always get along. More often, the reform decision together
with additional cues about its implementation enables the principal to
perfectly screen the agent. For example, if holding the office or political
promotion comes at price of an undesirable reform decision plus burdensome
midterm reviews from above, a noncongruent agent would be reluctant to go
after it at the beginning. From the principal’s perspective, as long as the
agent is willing to pay for the increased cost of congruence, he does not have
to answer for the policy consequences.

My paper is not the first to recognize the perverse effect of transparency,
but it uncovers a novel mechanism embedded in complex policy-making problems.
It is often argued that transparency could be bad for policy-making when the
correct action leads to adverse inference about the decision maker’s
competence or congruence; making the action unobservable may cure the issue by
aligning the decision maker’s policy and office motives (e.g. Prat (2005); Fox
(2007); Fox and Van Weelden (2012)). When the policy-making involves more than
a policy choice, the decision maker’s motivation at the implementation stage
is endogenous to how the public links his future to various potential policy
consequences. This often makes it impossible to completely aligning one’s
conflicting motives.

Building on these observations, I return to positive question – the principal-
optimal information policies – by comparing the agent’s incentives underlying
two good accountability. To fix ideas, let’s erase the selection issue and
suppose that the delegate is “quite” congruent; driven by career concerns,
this agent always panders to reform to avoid being mistaken as the
“noncongruent” type. When does he work harder? If his future career is tied to
the reform consequences, then the agent works to pursue its success; if
instead his future career is tied to acting congruently, then he works to
separate from the noncongruent types. Generally, these two motivations differ
in magnitude. Depending on the exact parameter values, the principal may
prefer either accountability.

These results have practical implications for how the public should motivate
the delegated reform policy-making. Crucially, more transparency does not
necessarily translate into more or less accountability; instead, it often
induces a different kind of accountability that is not necessarily better or
worse. Through comparative static analysis, I discuss the level of
transparency that induces right kind of accountability across different
environments. I find that the principal-optimal level of transparency is not
necessarily monotone with respect to the delegates’ office motive. This novel
result highlights the subtle motivation effect of career concerns as opposed
to creating a straightforward pandering incentive.

##  2 Model

Setup. Consider a model of policy-making in which an agent (he) carries out a
reform decision and its implementation on behalf of a principal (she). There
are two possible policies, a risky reform ($r$) and a safe status quo ($q$).
By risky, I mean that the reform outcome could be a success or a failure; the
status quo outcome is deterministic. The principal’s utility $v$ from these
outcomes are $1$, $d$, and $0$, with $d\in(0,1)$. In other words, she prefers
a successful reform to the status quo to a failed reform.

Following Hirsch (2016), I suppose that “choosing well” and “implementing
well” are both essential elements to a successful reform. “Choosing well”
means that a reform happens when the underlying state $\omega$ calls for it.
Specifically, the reform could be good ($\omega=G$) or bad ($\omega=B$) in
nature, with the common prior $P(\omega=G)=\phi\in(0,1)$. A bad reform always
fails; a good reform may succeed. To formalize “implementing well matters”, I
suppose that a good reform succeeds with a probability equal to the
implementation effort $e\in[0,1]$. The status quo policy induces a sure
outcome that does not vary with the implementation effort.

While nobody observes the state $\omega$ perfectly, the agent as a policy
expert knows it more than the principal. He receives a signal $s\in\\{g,b\\}$
of accuracy $p\geq\frac{1}{2}$ about $\omega$ i.e.
$P(s=g|\omega=G)=P(s=b|\omega=B)=p$.

The agent is an imperfect delegate. On the one hand, his policy interest may
differ from the principal’s. With probability $\pi$ he is “congruent”; that
is, he shares the principal’s policy preference, evaluating a successful
reform at $1$, the status quo at $d$, and the failed reform at $0$. With
probability $1-\pi$ he is “noncongruent”; he is captured by special interest
groups and averts any policy change (see also Fox (2007)). For such a
politically conservative agent, the policy utility $v_{n}$ is $d$ for the
status quo and $0$ for any reform outcome. Denote the agent’s type space
$T:=\\{c,n\\}$ where $t=c$ means congruent and $t=n$ means noncongruent.

On the other hand, unlike the principal, the agent cares about the
implementation cost and the office. A reform implementation effort $e$ costs
the agent $\frac{e^{2}}{2\lambda}$. Here $\lambda$ parameterizes the agent’s
cost sensitivity: a larger $\lambda$ means that the agent bears a lower cost
of implementation. The agent derives a utility $R>0$ from being in office
after the reform policy-making.

The principal disciplines the agent’s behavior by deciding whether to remove
him from office at the end of the day. To do so, she forms the posterior
belief $\mu$ that the agent is congruent with all policy-making information
$\mathcal{I}$ available; that is, $\mu:=P(t=c|\mathcal{I})$. I suppose that
the principal would draw another agent randomly from the same pool after she
removes this one. Hence, she retains (removes) this agent if she updates
positively (negatively) from the policy-making. Further suppose that ties are
broken in the agent’s favor. Essentially, this restriction turns the
principal’s strategy to preparing a tacit contract in the form of “a retention
set”; that is, the agent shall be retained whenever his policy-making meets a
set of implicit standards. For example, a retention set “$\\{\text{successful
reform}\\}$” means that the agent shall be retained as long as he reforms and
succeeds. This practice appears in everyday life and is quite common in the
delegation literature (e.g. Armstrong and Vickers (2010)).

The principal cares about policy-making and selecting a congruent agent, but
her selection motive comes secondary. From the eye of the principal, the agent
in-office tomorrow is congruent with probability $Q:=D\mu+(1-D)\pi$, where
$D=1$ indicates retention and $D=0$ indicates removal. I suppose that the
principal’s payoff takes the form $v(\cdot)+MQ$ with $M>0$, and focus on the
limiting case $M\downarrow 0$. This assumption enables us to see clearly how
the principal may control agent to further her policy interest; that said, my
main result does not at all rest on this knife-edge assumption. In Appendix
A.5 I argue that all conclusions go through as long as the principal’s policy
motive dominates her selection motive.

Here is the summary of payoff. The principal’s total utility is $v(\cdot)$; a
congruent agent’s total utility is $v(\cdot)-\frac{e^{2}}{2\lambda}+R\cdot D$;
a noncongruent agent’s total utility is
$u_{n}(x,y)=v_{n}(\cdot)-\frac{e^{2}}{2\lambda}+R\cdot D$.

Information environment. Let’s for the salient reality assume that the
principal always observes the agent’s policy choice. After all, it would be
absurd to see the principal retreating completely from the delegated reform
decision-making. Depending on whether the principal wishes to hold this agent
accountable for the policy implementation and its outcome, I consider three
relevant information regimes. From the least to the most transparent
environments, I allow the principal to observe 1) only the policy choice, 2)
the policy choice and its outcome, and 3) the policy choice, the effort, and
the outcome. In the Appendix A.5, I argue that the effort is a shorthand for
the agent’s moral hazard in the reform implementation. Label these
environments as “nontransparent”, “opaque”, and “transparent”.

I make two remarks about the completeness of this classification. First, my
setup assumes perfect invertibility from the outcome to actions, that is, the
principal perfectly knows whether a reform has taken place from any one of the
three potential outcomes “successful reform”, “failed reform”, and “status
quo”. As a result, my setup does not permit an environment in which the
principal knows the outcome but not the policy choice, thus eliminating the
possibility that she may be better off committing not to observe the action
(Prat, 2005). Second, there does exist an information regime in which the
principal knows the policy choice and efforts. I shall come back to this
regime only if, from an ad hoc standpoint, the agent cannot be accountable for
the policy and its implementation in those information regimes we are about to
study.

Sequence of moves. For each information regime, the game moves as follows:
first, Nature picks the random variables $(\omega,s,t)$ according to the
distribution. Second, the agent observes $s\in\\{g,b\\}$. Third, the agent
chooses $x\in\\{r,q\\}$ and effort $e\in[0,1]$. Fourth, Nature determines the
outcome of the project; Fifth, the principal decides on whether to retain the
agent conditional on observables. Finally, all players’ payoff realize.

Assumptions. Let $\mu_{+}:=P(\omega=G|s=g)=\frac{\phi p}{\phi
p+(1-\phi)(1-p)}$ and
$\mu_{-}:=P(\omega=G|s=b)=\frac{\phi(1-p)}{\phi(1-p)+(1-\phi)p}$ be the
posterior beliefs that the reform is good by nature after one receives a
good/bad signal. I make several assumptions. First, the agent’s signal $s$ is
very informative. The formal requirement is
$\mu_{+}>\sqrt{{\frac{2d}{\lambda}}}>\mu_{-}$. Second, the office rent is
moderate; that is,
$\min\\{(1+R)\mu_{-},R\mu_{+}\\}>\sqrt{\frac{2d}{\lambda}}>R\mu_{-}$. I also
impose $\lambda(1+R)\leq 1$ to ensure that $e\in[0,1]$. In the appendix Lemma
4, I show that these parameter restrictions imply $R>2d$.

Solution concept. The agent chooses an action $a\in\\{r,q\\}\times[0,1]$ based
on his type $t\in\\{c,n\\}$ and signal $s\in\\{g,b\\}$. His (mixed) strategy
$\sigma(\cdot|t,s)$ specifies a probability distribution over actions $a$ for
each type-signal tuple $(t,s)$. The principal decides whether to retain this
agent based on her information set $I\in\mathcal{I}$; her (mixed) strategy is
$\sigma_{p}:I\rightarrow[0,1]$. For each information regime, I look for the
existence of Perfect Bayesian Equilibrium (PBE) in which the principal plays a
pure retention strategy. The equilibrium condition dictates that no players
admit any profitable deviation from the equilibrium strategy; and, players
form beliefs by the Bayes’ rule whenever possible.

A preliminary observation is that the game may admit numerous equilibria
supported by ad hoc off-path beliefs. To illustrate, consider the
nontransparent regime in which the principal observes only the policy choice.
When the office motive outweighs policy considerations, there is a pooling
equilibrium in which both types of agent always choose the status quo; the
principal holds the off-path belief that whoever reforms is noncongruent. This
equilibrium is nonetheless unsatisfying – the congruent agent may make a
public speech to convince the principal that that he is willing to reform when
the signal is good. The principal might indeed buy this argument, because only
a congruent agent may benefit from this kind of action.

To restrict the off-path beliefs, I apply the universal divinity refinement
from Banks and Sobel (1987) to the PBEs of this game. Behind this refinement
is an intuitive idea: the principal believes that an unexpected action comes
from the type that is mostly likely to benefit from it. The refinement gives
rises to the notion of “strong off-path beliefs” proposed by Fox and Jordan
(2011),

######  Lemma 1 (Strong off-path beliefs).

A PBE surviving the universal divinity refinement assigns the following off-
path beliefs:

  1. 1.

if the status quo is off-path, then the principal believes that whoever
chooses it is noncongruent.

  2. 2.

if the reform is off-path, then the principal believes that whoever chooses it
is congruent.

Appendix A.1 contains its proof. Call any PBE surviving this refinement an
“equilibrium”.

##  3 Comparison of information regimes

Below I present the heuristic descriptions of equilibria across different
regimes. Formal statements and proofs are relegated to the appendix. Also, it
is useful to establish a no-accountability benchmark. This situation is
plausible, for example, if the agent is a lame duck, or if the principal
completely backs away from transparency.

######  Fact (No accountability).

An unaccountable agent chooses his favorite action. That is, only a congruent
agent reforms when the signal is good; the status quo prevails if the signal
is bad or the agent is noncongruent.

The main takeaway is that, under the model assumptions, only a congruent agent
may sometimes want to carry out a reform solely for the sake of policy-making.

###  3.1 Nontransparent regime

When the principal observes nothing but the agent’s policy choice, her
retention decision is determined by whether this policy signals congruence. In
particular, she updates positively from a certain policy if it is more likely
to be initiated by a congruent type.

I argue that initiating a reform helps one secure the office. There are two
cases: either the reform is off-path, in which case the strong off-path belief
assigns probability one to this event that the agent is congruent; or the
reform is on path. In the latter case, only a congruent agent may attach
nontrivial weights to a reform and sometimes strictly prefers implementing a
reform to the status quo policy. This means that the congruent agent must
reform at least weakly more often than a noncongruent type given any retention
strategy. As such, initiating a reform cannot be bad news for congruence.

Provided a moderate office benefit, the only plausible equilibrium in this
nontransparent regime involves both types of the agent pooling at the reform
policy. To see this, I rule out the remaining possibility that the congruent
agent reforms strictly more often on path. According to this strategy, the
status quo policy becomes bad news for retention; a career-minded agent would
rather deviate by pandering to reform despite it might go against his policy
interest.

######  Result 1 (Accountability for decision).

In the nontransparent regime, there exists a unique equilibrium in pure
strategy. In this equilibrium, both types of agent panders to reform without
sufficient implementation efforts. The principal always retains the agent on
path.

The nontransparent regime induces the accountability for decision; that is,
the agent shall be retained unless he chooses the ex ante noncongruent policy
(status quo). The reform implementation exhibits a lack of motivation because
it is either carried out at the wrong time (bad signal) or by the wrong person
(noncongruent agent). This is not surprising: by making the reform
implementation and outcome unobservable, the nontransparent regime essentially
reduces to the classic “wrong transparency” environment of Fox (2007). In both
models, the quality of policy-making is compromised by the agent’s misaligned
office and policy motives.

###  3.2 Opaque regime

Suppose in addition to the policy choice, the principal also observes its
outcome. This means that she has additional data to evaluate the agent before
making the retention decision. But for which policy outcome should this agent
be responsible? Should he be punished electorally for not reforming, for
failing to reform well, or both?

A critical observation is that, conditional on the initiation of a reform, the
principal might not credibly hold an agent accountable to its potential
outcomes. In a situation where the principal’s retention rule does not vary
with the reform outcome, the opaque regime has no bite because only the policy
choice matters. Is this uninteresting case plausible? Indeed. As a better-
motivated reformer, a congruent agent in general reforms more often and
implements better than a noncongruent type. From the principal’s perspective,
she is sure that more reform successes come from the congruent type. But she
cannot determine which type fails more often. When the congruent agent’s extra
reform attempts more than compensate for his lower failure probability, more
failures are attributable to the congruent type, thus rendering a failed
reform also good news about congruence.

To eliminate this possibility, I impose an informativeness condition that
guarantees a reform failure to be bad news about congruence. Notate
$\gamma=\frac{1-p}{p}$ and $z=\frac{1-\phi}{\phi}$:

######  Definition 1 (Informativeness condition).

$z-\lambda\frac{1}{1+\gamma
z}\leq\gamma[\lambda(1+R)\frac{\gamma}{\gamma+z}-1]$.

The informativeness condition derives from the most plausible case that a
reform failure could but does not have to be good news for congruence; that
is, a congruent agent always reforms, whereas a noncongruent agent reforms
when the signal is good. The condition depends on the signal accuracy $p$, the
prior probability of a good state $\phi$, the cost sensitivity $\lambda$ and
the office benefit $R$. $p$ and $\phi$ pin down how more often a congruent
type reforms relative to a noncongruent type (i.e. receiving a bad signal).
$\lambda$ and $R$ describe how more motivated a congruent type is relative to
a noncongruent type at the reform implementation. These parameters summarize
different agents’ reform “quantity” and “quality” in relative terms; they are
essential for the principal’s inference.

Suppose the informativeness condition holds throughout.

######  Result 2 (Accountability for outcomes).

In the opaque regime, there exists a unique equilibrium in pure strategy. In
this equilibrium, the congruent agent always reforms and implements with
efforts internalizing the office benefit. The noncongruent agent chooses the
status quo unless the signal is good, in which case he reforms with an effort
completely motivated by the office benefits. The principal removes this agent
unless she observes a successful reform.

The opaque regime induces the accountability for policy outcomes. In this
case, choosing the congruent policy (reform) no longer secures office; doing
it right would. To the principal’s delight, this accountability provides a
high-powered incentive for reform implementation by linking the agent’s policy
and office motives. That is, under a retention rule pivotal on reform
outcomes, a reform success brings the joint benefits of policy and office vis-
a-vis a reform failure. As a result, the agent would internalize the office
benefit into the reform implementation efforts. Now that the agent’s policy
choice has again been distorted by his career concerns, the opaque regime
makes a case in which motivating in spite of pandering is possible.

The equilibrium has several interesting features. The noncongruent agent’s
policy choice always varys with signals; the congruent agent reforms even if
the signal is bad. Their equilibrium behaviors seem to suggest that the
noncongruent agent is more responsive, whereas the congruent agent is too
“timid” to hold on to his policy judgement. That said, the noncongruent
agent’s policy responsiveness derives purely from his office-holding motive to
gamble for resurrection. Such a motive misalignment exposes the principal to
an excessively high risk of reform failure.

The accountability for outcomes echoes prior works in the pandering
literature. For example, Fox and Shotts (2009) show that an agent may signal
congruence/competence from his policy choice/outcomes in what they call a
“delegate equilibrium” and “a trustee equilibrium” respectively. But my
accountability mechanism is novel; here, both the policy choice and outcomes
matter for retention because each of them enables the principal to learn
something about the agent’s congruence. That is, the principal screens a
noncongruent agent upon observing the status quo; conditional on a reform
taking place, she is more convinced about facing a congruent agent upon a
successful outcome.

###  3.3 Transparent regime

I continue to study the most transparent policy-making environment, in which
the principal knows the agent’s effort in addition to his policy choice and
outcome.

At face value, the principal may further her policy interest by conditioning
her retention decision on all observables. For example, she may want to
safeguard the reform quality by promising the agent: “you shall be removed
unless you reform with a good effort and the reform succeeds.” Per Hölmstrom
(1979), the principal would do better if this promise is credible.

But not all information is equally relevant for retention. In fact, the
principal would have cast her vote upon observing whether an agent acts
congruently, regardless of whether the reform ends up successfully or not. Put
differently, the accountability for implementation and outcomes do not get
along. Behind this incompatibility lies a simple idea: excessive transparency
constrains the principal’s capacity to “guess” the agent’s congruence from
unobserved actions. In the transparent regime we shall expect either perfect
or no screening, but nothing in between.

My analysis below focuses on the separating equilibria. This is done purely
for technical convenience – the welfare comparison with respect to the
separating equilibria is cleaner and entails no loss of generality. I shall
return to the welfare issue shortly; for now, let’s rest assured that agent
must face the same kind of accountability in both separating and pooling
equilibria. Because the reform success is a chance event, the principal does
not penalize the agent electorally if both types act in the same way (pooling
equilibria). If instead two types behave differently, the principal identifies
the congruent agent and rewards accordingly (separating equilibria). These two
classes of equilibria share a common element: the action matters for
retention; the consequence does not. I describe such a retention rule as
exerting the “accountability for processes”.

Other considerations for selecting on the separating equilibria include: 1)
more information about policy-making raises the cost of pooling; thus we tend
to believe that more transparency improves sorting. 2) Separating equilibria
are more robust to parameter changes. A separating equilibrium always exists
because the congruent agent is a better-motivated reformer. A pooling
equilibrium surviving the universal divinity refinement exists only if the
cost of implementation is not too low (Lemma 7).

Among the class of separating equilibria, the divinity refinement uniquely
selects the least costly one also known as the “Riley outcome” (Riley (1979)):

######  Result 3 (Accountability for processes).

In the transparent regime, there exists a unique separating equilibrium
surviving the universal divinity refinement. In this equilibrium, the
congruent agent always reforms and implements with efforts just enough to
separate; the noncongruent agent always chooses the status quo. The principal
retains whenever observing a reform with an implementation effort beyond the
minimal requirement.

Contrary to our expectation, more transparency does not necessarily affect
accountability in a monotone manner; rather, it induces a different kind of
accountability. An agent shall be retained whenever he is willing to bear the
increased cost of acting congruently; that is, initiate and implement the
reform with an effort exceeding the minimal requirement. He shall not be
responsible for any negative reform consequences.

The transparency regime begets two interesting effects. First, the reform
decision becomes completely partisan – the congruent agent always reforms, and
the noncongruent one always stays with the status quo. This improves sorting
but hurts discipline. Second, the accountability for processes also encourages
the congruent agent to implement well, but his motivation comes from
separating with a noncongruent type rather than pursuing a successful reform.

###  3.4 Comparison

Compare Results 1-3 with the no-accountability benchmark. We note a pattern
that echoes previous literature: when the principal sees more, the agent is in
general accountable for more aspects of the policy-making (e.g. Crémer (1995);
Dewatripont et al. (1999)); this also engenders pandering incentives (Maskin
and Tirole (2004); Fox (2007)). More important are the following novelties:

  1. 1.

More transparency tends to improve sorting because it discourages the
noncongruent agent from signaling congruence via costly means. But more
transparency does not translate into a higher or lower level of
accountability; rather, it holds the agent accountable for different aspects
of policy-making that are not necessarily rankable.

  2. 2.

The principal’s best hope is to motivate implementation in spite of the
agent’s pandering incentive; she cannot employ any information regime to
completely eradicate this behavior. The underlying reason is that a congruent
agent faces irreconcilable conflicts between office-holding and policy motives
across all information regimes: the policy motive always recommends a policy
decision responsive to signals, whereas the office motive always recommends
shying away from the status quo.

  3. 3.

Motivating implementation by partially aligning the agent’s policy and motive
office is possible. Specifically, a retention rule that is pivotal on reform
outcomes provides a high-powered incentive for implementation. Such a rule is
possible only within the opaque regime in which the equilibrium political
selection is informative but noisy. A retention rule asking for reforming with
a minimal effort requirement also motives the agent. Such a rule is made
possible by the transparent regime, where a congruent agent works hard to
avoid being perceived as noncongruent.

##  4 Mechanism Design

Building on the equilibrium analysis in previous sections, I am ready to
answer the positive question for the principal: what is the right kind of
accountability?

###  4.1 Optimal accountability

Suppose the agent behaves as what I have described in Results 1-3.

######  Result 4.

1) In a nontransparent regime, where the agent is accountable for his policy
decision, the principal’s welfare is lowest. 2) Depending on model parameters,
either the opaque or the transparent regime could prevail; that is, the right
kind of accountability is either the accountability for processes or outcomes.

The core of this result concerns which kind of accountability elicits the most
implementation efforts from an agent who panders to reform. The principal’s
policy interest is always damaged by the nontransparent regime because a
career-minded agent never inputs serious effort. In other words, the
accountability for decision induces unproductive pandering.

Either one of the other two information regimes may induce the right
accountability. Relative to the transparent regime, the opaque regime is not
necessarily better at motivating a congruent agent; the exact comparison
hinges on whether the congruent finds it harder to succeed in the reform, or
to separate from a noncongruent type. At the same time, the opaque regime is
not necessarily worse in terms of distorting a noncongruent agent’s policy-
making – from the principal’s standpoint, she may prefer this demotivated
reformer to occasionally gamble for resurrection by reforming rather than
always stay with an unattractive status quo.

###  4.2 Comparative Statics

Suppose that, for some baseline parameters, the principal-optimal information
regime inducing the right accountability is the opaque regime. I assess
whether and how certain parameter changes might affect its optimality,
assuming players behave according to Results 1-3. Subject to the changes, the
principal is unwilling to switch information policies if the opaque regime
becomes even better at motivating an agent than the transparent regime.

#### Better reform outlook

A better reform outlook (a higher prior $\phi$ of a good reform) makes the
opaque regime more appealing to the principal.

Intuitively, if an agent is ex ante more certain that the reform is good by
nature, then he would exerts more efforts at the implementation stage. This
change allows the opaque regime to elicit more efforts than the transparent
regime. The rationale lies in the composition of the agent’s motivation:
unique to the opaque regime is the part of efforts coming from the agent
internalizing the office rent, which is also increasing in the stronger prior.

#### Lower effort cost/better signal

When the cost of efforts decreases, and/or the signal accuracy increases, the
principal often stays with the opaque regime.

The result comes from a subtle observation about the bar of separation in the
transparent regime; that is, a congruent agent does not have to implement with
an unnaturally high effort to distinguish himself from a noncongruent type. By
“unnaturally high”, I mean this agent exerts an effort exceeding what he would
have done in the absence of career concerns. In fact, it is entirely plausible
that a congruent agent’s natural implementation effort would suffice to
separate. Were this true, then the transparent regime cannot even beat the no-
accountability case (because it induces pandering when the state calls for the
status quo), let alone the opaque regime.

The parameter changes reinforce this possibility: given a congruent agent who
can act “naturally” to separate within a transparent regime, lower effort
costs and/or better signals make this sort of separation even easier.

#### Larger office rent

Matters are entirely different if the office rent $R$ increases. A more
attractive office better motivates an agent to pursue a successful reform in
the opaque regime; it also incentivizes a congruent agent to work harder for
separation in the transparent regime. A priori, it is hard to tell which
effect dominates.

In the appendix, I show that from the office rent the principal benefits
quadratically via the motivation effect and linearly via the separation
effect; furthermore, these two benefits intersect for different values of the
office rent. As a result, the principal may wish to switch her information
regime more than once as the office rent increases.

##  5 Conclusion

This paper studies the motivation issue in the context of reform policy-making
with career concerns. My analysis highlights two novelties. First, the
principal in my setup wishes her delegate to not only choose well, but also
work hard. While this feature of policy-making has appeared in previous models
(e.g. Hirsch (2016)), it has not yet been integrated into the pandering
literature in a theoretically serious way. I argue that the motivation issue
is real in policy-making. That is, it does not go away if the principal simply
keeps or removes the delegates’ accountability; rather, it forces the
principal to choose the right kind of accountability that links the delegates’
policy and office motives. I formalize this problem in a setting where the
delegate faces conflicting office and policy motives, and compare several
possible solutions. In general, I show that the principal must hold the
delegates accountable for more than the policy decisions. The right kind of
accountability – one that elicits the maximal reform implementation efforts –
hinges on whether the delegate finds it harder to act congruently or to
succeed in a reform.

Second, I highlight the difficult commitment problem in complex reform policy-
making with career concerns. This is rarely an issue if the the careerist
delegates are evaluated on the basis of a binary potential outcome; there, the
good news for retention often takes a simple form, be it a
“congruent/noncongruent” action or a “good/bad” outcome. In complex reform
decision environment with more than two potential outcomes, such a clear-cut
standard is often lacking. An evaluator must bear in mind that the credibility
of her retention rule is endogenous to what she can observe about the policy-
making. A retention rule pivotal on reform outcomes provides high-powered
incentives for implementation, but it requires the evaluator to refrain from
knowing the reason why a reform succeeds/fails and thus back away from full
transparency. The electoral mechanism through which secrecy helps is closely
tied to Ashworth and Bueno de Mesquita (2014).

How should we relate the theoretical results to the real world? When the
public cannot commit to rewarding career-minded officials electorally, one
remedy is to establish an “outcome-based” accountability. That is, the
officials are granted autonomy in the decision-making processes, and evaluated
on the basis of whether the decision succeeds. The expression of granting
process-autonomy dated back to no later than Sun Tzu’s Art of War (Sun, 1988,
original traditionally dated circa 500 BC). He wrote in the chapter of
Adaptations (italics are mine):

> There are routes not to be followed, armies not to be attacked, citadels not
> to be besieged, territory no to be fought over, orders of civilian
> governments not to be obeyed.

Cao Cao, a Chinese warlord, statesman and poet during the end of the Han
dynasty, interpreted it as “when it is a matter of expediting your work, don’t
be limited to the commands of the civilian leadership”777Ibid.. Such a
principle guided Chinese generals for millennia. My results explain why it
worked: a process-autonomy decision-making environment encourages the generals
to pursue a successful battle because this is the only way to signal either
competence or loyalty.

Finally, we observe that the outcome-based accountability is a second-best
solution to the motivation problem. Ideally, the public could write a
constitutional provision specifying a set of retention probabilities
corresponding to each hypothetical policy outcomes. But not all actions,
particularly the political ones, are contractible. For example, it perhaps
goes beyond Cummings’s capacity to enforce a list of promotions and
punishments on his Whitehall fellows for every consequence of the Brexit. When
motivation is necessary to guarantee the quality of policy-making, it is often
a good idea for the public to maintain an arm’s length relationship with the
officials.

##  Appendix A Appendix

###  A.1 Preliminary

######  Definition 2.

An arbitrary event $I\in\mathcal{I}$ is neutral news about congruence if
$P(t=c|I)=\pi$; it is good (bad) news if $P(t=c|I)>(<)\pi$.

I first justify the strong off-path belief.

###### Proof of Lemma 1.

Following the notations in Fudenberg and Tirole (1991) I let
$D((t,s),\mathcal{M},x^{\prime})$ ($D^{0}((t,s),\mathcal{M},x^{\prime})$) be
the set of the principal’s mixed-strategy best response – the set of
principal’s retention probability – to the agent’s action $x^{\prime}$ and
belief concentrated on $\mathcal{M}\subset\\{c,n\\}\times\\{g,b\\}$ that makes
a type $(t,s)$ agent strictly benefits (indifferent) by taking $x^{\prime}$
relative to his equilibrium action. Here $t\in T=\\{c,n\\}$ is the agent’s
payoff type; $s\in\\{g,b\\}$ is the agent’s signal. The divinity condition
says that fixing some off path action $x^{\prime}$, if for some
$s\in\\{g,b\\}$ and $t\in\\{c,n\\}$ we have
$D((t,s),\mathcal{M},x^{\prime})\cup
D^{0}((t,s),\mathcal{M},x^{\prime})\subset\bigcup_{(t^{\prime},s^{\prime})\neq(t,x)}D((t^{\prime},s^{\prime}),\mathcal{M},x^{\prime})$
then we can assign probability $0$ that the deviation comes from type $(t,s)$.
We iterate this process if necessary until the divine equilibrium is found.

It is useful to note that $(n,b)$ and $(n,g)$ share the same preferences.
Hence from now on I use $(n,\cdot)$ to denote these two types if they shall be
preserved or ruled out together. Note also that we may arrange types
$(c,g),(c,b),(n,\cdot)$ in the descending order of their motivation in reform.
To establish the claim, we would like to 1) strike type $(n,\cdot)$ if the
principal observes $(r,e)$ for some $e\in[0,1]$, and 2) assigns probability
$1$ to the type $(n,\cdot)$ if the principal observes $q$. To save notations,
I simply notate $x^{\prime}=r$ if reform is off path and the agent in this
deviation reforms with some effort $e\geq 0$.

Let $\underline{p}^{(c,s)}(\mathcal{M},x^{\prime})$ be the retention
probability that a congruent agent with signal $s$ finds indifferent to his
equilibrium payoff after he deviates to action $x^{\prime}$; similarly we
define $\underline{p}^{n}(\mathcal{M},x^{\prime})$. Then
$D((t,s),\mathcal{M},x^{\prime})=\\{p:p>\underline{p}^{(c,s)}(\mathcal{M},x^{\prime})\\}$
and
$D((n,\cdot),\mathcal{M},x^{\prime})=\\{\underline{p}^{n}((t,s),\mathcal{M},x^{\prime})\\}$
where $p$ is the retention probability. To prove the claim, it suffices to
verify whether
$\underline{p}^{(c,s)}(\mathcal{M},q)>\underline{p}^{n}(\mathcal{M},q)$ for
all $s$ and
$\underline{p}^{(c,s)}(\mathcal{M},r)<\underline{p}^{n}(\mathcal{M},r)$ for
all $s$.

Consider the case in which $q$ is off-path. This suggests that in equilibrium,
every type of the agent reforms and the principal retains on path. Let
$e^{*}_{(n,\cdot)}$ and $e^{*}_{(c,s)}$ be the equilibrium effort level of a
noncongruent and a congruent agent with a signal $s$.

1) If efforts are observable then
$e^{*}:=e^{*}_{(n,\cdot)}=e^{*}_{(c,g)}=e^{*}_{(c,b)}$. To see this, if on
path there are two different actions $(r,e),(r,e^{\prime})$ with
$e^{\prime}>e$ such that the principal retains on both actions, then the
noncongruent agent would always play one with the lower action $(r,e)$. Then
the action $(r,e)$ becomes bad news about congruence and the principal should
replace on path. Hence, any pooling equilibrium must take the form that both
types pool with at unique action of the form $(r,e)$.

2) If efforts are not observable then $e^{*}_{n}=0$ and
$e^{*}_{(c,s)}\in\arg\max\mu(s)e-\frac{e^{2}}{2\lambda}$ with $\mu(s)=\mu_{+}$
if $s=g$ and $\mu_{-}$ if $s=b$. This follows from the requirement of
sequential rationality in any PBE.

Now, the definition of $\underline{p}$ requires that if efforts are
observable, $\underline{p}^{(c,s)}(\mathcal{M},q)\cdot R+d=R+\mu
e^{*}-\frac{{e^{*}}^{2}}{2\lambda}$ for all $s$ and
$\underline{p}^{n}(\mathcal{M},q)\cdot R+d=R-\frac{{e^{*}}^{2}}{2\lambda}$. If
efforts are unobservable then $\underline{p}^{(c,s)}(\mathcal{M},q)\cdot
R+d=R+\max_{e}\\{\mu(s)e-\frac{{e}^{2}}{2\lambda}\\}$ and
$\underline{p}^{n}(\mathcal{M},q)\cdot R+d=R$. One concludes that in both
cases $\underline{p}^{(c,s)}(\mathcal{M},q)>\underline{p}^{n}(\mathcal{M},q)$.
In other words, the noncongruent has more to gain by deviating to the status
quo policy than the congruent one during both good and bad times. This implies
that we can strike $(c,b)$ and $(c,g)$ in sequence with the universal divinity
refinement. The off-path belief about the payoff type $t$ following
$\\{x=q\\}$ surviving the divinity condition is noncongruent for sure.

The same logic applies to the case in which $r$ is off-path – the congruent
agent has more to gain from a deviation. Let’s fix a pooling equilibrium at
$x=q$ and consider the deviation to $x=r$ with any nonnegative effort
$e^{\prime}$. Since for any $e^{\prime}$ the type $(n,\cdot)$ always obtains
strictly less reform payoff than both congruent types $(c,g)$ $(c,b)$,
whenever the deviation benefits some888For a deviation with prohibitively high
efforts, the divinity condition has no bite. When this is the case, we may
nonetheless assign the “strong off-path belief”. congruent types the divinity
condition strikes type $(n,\cdot)$. ∎

Now I describe the agent’s behavior subject to different retention incentives.

######  Lemma 2.

Absent retention incentives, a noncongruent agent always take the status quo
policy; a congruent agent initiates the reform with effort $\lambda\mu_{+}$
after $s=g$ and keeps the status quo after $s=b$.

###### Proof.

The noncongruent agent’s optimal behavior is obvious. Let $\mu$ be the
congruent type’s posterior belief that the reform is good. Conditional on
initiating a reform, his objective is

$\displaystyle\max_{e}\mu e-\frac{e^{2}}{2\lambda}$

The optimal effort is $\lambda\mu_{+}$ after $s=g$, and $\lambda\mu_{-}$ after
$s=g$; The agent’s reform payoffs are respectively
$\frac{\lambda}{2}\mu_{+}^{2}$ and $\frac{\lambda}{2}\mu_{-}^{2}$. By the
moderate office rent assumption, he initiates reform if $s=g$ and keep the
status quo if $s=b$. ∎

######  Lemma 3.

Suppose the principal retains if and only if observing a successful reform.
Let $\mu$ be the agent’s posterior belief about the state being $\omega=G$.
Then conditional on a reform, the congruent agent exerts effort
$\lambda(1+R)\mu$ while the noncongruent agent exerts effort $\lambda R\mu$.

###### Proof.

Rewrite the agent’s objective function as

$\displaystyle\text{Congruent}\qquad\max_{e}\mu e(1+R)-\frac{e^{2}}{2\lambda}$
$\displaystyle\text{Nonongruent}\qquad\max_{e}\mu eR-\frac{e^{2}}{2\lambda}$

The result follows immediately. ∎

######  Lemma 4.

$\min\\{(1+R)\mu_{-},R\mu_{+}\\}>\sqrt{\frac{2d}{\lambda}}>R\mu_{-}$ and
$\lambda(1+R)\leq 1$ imply $R>2d$.

###### Proof.

Suppose the noncongruent agent secures retention conditional on a successful
reform. His objective is $\max_{e\in\\{0,1\\}}\mu eR-\frac{e^{2}}{2\lambda}$
with $\mu$ being the belief that the reform is good. This means that the
noncongruent agent’s maximum payoff is $\frac{\lambda R^{2}\mu^{2}}{2}$. By
our assumption on $R$, this value is larger than $d$ if $\mu=\mu_{+}$. On the
other hand, $\frac{\lambda R^{2}\mu^{2}}{2}\leq\frac{\lambda
R^{2}}{2}<\frac{R}{2}$ since $\lambda R<\lambda(1+R)\leq 1$. This means that
$R>2d$. ∎

###  A.2 Equilibrium characterization

The proof of Fact follows directly from Lemma 2. Let us formalize and prove
Results 1-3.

#### Nontransparent regime

######  Proposition 1 (Restating Result 1).

Under the nontransparent regime, there exists a unique equilibrium in pure
strategy. In this equilibrium, the congruent agent always chooses $r$; he
implements with effort $\lambda\mu_{+}$ after $s=g$, and $\lambda\mu_{-}$
after $s=b$. The noncongruent agent always chooses $r$ with effort $0$
regardless of signals. The principal always retains the agent.

###### Proof.

First check the equilibrium conditions. With the strong off-path belief, the
principal replaces whenever observing $x=q$. Since $R>d$, no agent would
deviate from $x=r$. The agent chooses effort $\lambda\mu$ for each posterior
belief $\mu\in\\{\mu_{-},\mu_{+}\\}$ and the noncongruent agent chooses zero
effort.

Second, I rule out other pure-strategy equilibrium possibilities under the
strong off-path beliefs. 1) It cannot be the case that in equilibrium, one
type of agent keeps the status quo more often than the others. Suppose in
equilibrium the congruent type does $q$ more often than the noncongruent type.
Then $\\{x=q\\}$ is good news for retention and the noncongruent type would
deviate to keeping the status quo. Suppose instead the noncongruent agent does
$q$ more often. Then $\\{x=q\\}$ is bad news and $\\{x=r\\}$ is good news for
retention. Since $R>2d$, the noncongruent agent would deviate to choosing $r$
for all signals. 2) It cannot be the case that both types of agent takes $x=q$
regardless of signals: the congruent agent would initiate the reform with
effort $\lambda\mu_{+}$ after a good signal and convince the principal that he
is congruent and thus get reelected. 3) It cannot be the case that both types
of agent chooses $r$ after $s=g$ and chooses $q$ after $s=b$. When this is the
case, the noncongruent type would deviate to choosing $q$ after a good signal.
Since $x=q$ is neutral news, the noncongruent type will be retained while
enjoying his preferred policy. ∎

#### Opaque regime

######  Proposition 2 (Restating Result 2).

Suppose the informativeness condition holds. Then there exists a unique
equilibrium in pure strategy. In this equilibrium, 1) the congruent agent
always chooses $r$. He implements with effort $\lambda(1+R)\mu_{+}$ after
$s=g$ and $\lambda(1+R)\mu_{-}$ after $s=b$. 2) the noncongruent agent chooses
$r$ with effort $\lambda R\mu_{+}$ after $s=g$, and $x=q$ after $s=b$. The
principal retains the agent after a successful reform and replaces otherwise.

There are a few steps:

First, I rule out cases in which the agent’s policy choices are signal-
invariant. Per earlier discussions, it cannot be part of an equilibrium that
both types choose $x=q$ regardless of signals. It cannot be part of an
equilibrium that the congruent agent always chooses $x=r$ with some
nonnegative effort and the noncongruent agent always chooses $x=q$; otherwise,
the noncongruent type would deviate to $x=r$ to secure reelection. Note also
that it cannot be the case that both types choose $x=r$ and exert some signal-
dependent efforts. When this is the case, the principal infers that a
successful is good news and a failed reform is bad news about congruence. But
a noncongruent agent wants to deviate from this strategy: after a bad signal,
by choosing $x=r$ with effort $\lambda R\mu_{-}$ he obtains
$\frac{\lambda}{2}R\mu^{2}_{-}$. By the moderate office rent assumption, this
payoff is lower than the status quo payoff $d$.

Next, I consider cases in which the agent’s policy choice responds to signals.

######  Claim 1.

The following strategies cannot be part of an equilibrium: both types choose
$x=q$ after $s=b$; they choose $x=r$ and exert nonnegative efforts after
$s=g$.

###### Proof.

Following this strategy $\\{x=q\\}$ is neutral news about congruence. Hence a
noncongruent type would deviate to $x=q$ after observing $s=g$. ∎

######  Claim 2.

The following strategy cannot be part of an equilibrium: the noncongruent
agent always chooses $x=q$ and the congruent agent chooses $x=q$ after $s=b$
and chooses $r$ with some nonnegative effort $e\geq 0$ after $s=g$.

###### Proof.

According to this strategy, $\\{x=q\\}$ is bad news about congruence. There
are two cases to consider. First, the principal retains on policy. Then both
types of agents would deviate to choosing $x=r$ and get retained. Second, the
principal retains whenever a reform succeeds. When this is the case, the
congruent agent wants to deviate to $x=r$ after $s=b$: in doing so, she
obtains a payoff of $\frac{\lambda}{2}(1+R)\mu_{-}^{2}$. By the moderate
office rent assumption, this payoff is better than $d$. ∎

It is also straightforward to rule out pathological strategies in which the
agent reforms when the signal is bad and takes the status quo when the signal
is good. The only sensible strategy profile that may constitute an equilibrium
is what is described in Proposition 2.

######  Claim 3.

Under the strategy specified in Proposition 2, a successful reform is good
news and a failed reform is bad news for congruence whenever the
informativeness condition holds.

###### Proof.

A successful reform being good news follows from the fact that the congruent
type always exerts more effort than the noncongruent type after a good signal.
It remains to check when a failed reform is bad news. Let $S,F$ denote the
event that a reform succeeds/fails.

By the Bayes’ rule,

$\displaystyle P(t=c|F)=\frac{P(t=c,F)}{P(F)}$

and $P(t=c,F)=P(t=c,s=g,F)+P(t=c,s=b,F)$

$\displaystyle P(t=c,s=g,F)$
$\displaystyle=P(s=g,\omega=g)[1-\lambda(1+R)]\mu_{+})+P(s=g,\omega=b)$
$\displaystyle=\phi p[1-\lambda(1+R)\mu_{+}]+(1-\phi)(1-p)$ $\displaystyle
P(t=c,s=b,F)$ $\displaystyle=P(s=b,\omega=g)[1-\lambda
R\mu_{+}]+P(s=b,\omega=b)$ $\displaystyle=\phi(1-p)[1-\lambda
R\mu_{+}]+(1-\phi)p$ $\displaystyle P(t=c,F)$
$\displaystyle=1-\phi\lambda(1+R)[p\mu_{+}+(1-p)\mu_{-}]$

Likewise,

$\displaystyle P(t=n,F)$ $\displaystyle=P(t=n,s=g,F)$
$\displaystyle=P(s=g,\omega=g)(1-\lambda R\mu_{+})+P(s=g,\omega=b)$
$\displaystyle=\phi p(1-\lambda R\mu_{+})+(1-\phi)(1-p)$

Since $P(t=c|F)\leq\pi\Leftrightarrow P(t=c,F)\leq P(t=n,F)$, we can rewrite
the necessary and sufficient condition to

$\displaystyle 1-\phi\lambda(1+R)[p\mu_{+}+(1-p)\mu_{-}]$
$\displaystyle\leq\phi p(1-\lambda R\mu_{+})+(1-\phi)(1-p)$
$\displaystyle\Leftrightarrow\qquad\phi(1-p)+p(1-\phi)$
$\displaystyle\leq\phi\lambda p\mu_{+}+\phi(1-p)\lambda\mu_{-}(1+R)$
$\displaystyle\Leftrightarrow\qquad p[1-\phi-\lambda\phi\mu_{+}]$
$\displaystyle\leq\phi(1-p)[\lambda\mu_{-}(1+R)-1]$

Substitute in $\gamma=\frac{1-p}{p}.z=\frac{1-\phi}{\phi}$, the last
inequality is $z-\lambda\frac{1}{1+\gamma
z}\leq\gamma[\lambda(1+R)\frac{\gamma}{\gamma+z}-1]$ as desired. ∎

######  Remark 1 (Technical).

The informativeness condition is statistical. Note that the RHS is negative
because $\lambda(1+R)\leq 1$. This means that for any $\lambda$,
$\exists\bar{z}$ such that for all $z\leq\bar{z}$, we can find sufficient
small $\gamma$ such that the inequality holds. Put differently, we have one
degree of freedom to choose an element in $(\lambda,R)$ satisfying
$\lambda(1+R)\leq 1$ such that the set of parameters supporting the
informativeness condition is nonempty.

The following lemma makes this point precise.

######  Lemma 5.

Suppose $z<\lambda$. Then $\exists\bar{p}\in(\frac{1}{2},1]$ that is
independent from other parameters such that for all $p\geq\bar{p}$, the
informativeness condition holds.

###### Proof.

Rearrange this inequality to $z\leq\lambda\frac{1}{1+\gamma
z}+\gamma[\lambda(1+R)\frac{\gamma}{\gamma+z}-1]$. Define
$F(\gamma)=\lambda\frac{1}{1+\gamma
z}+\gamma[\lambda(1+R)\frac{\gamma}{\gamma+z}-1]$. Under the assumption
$\lambda(1+R)\leq 1$, we claim that $F$ is decreasing in $\gamma$. To see it

$\displaystyle F^{\prime}(\gamma)$ $\displaystyle=\lambda[-\frac{z}{(1+\gamma
z)^{2}}+(1+R)(1-\frac{z^{2}}{(\gamma+z)^{2}})]-1$
$\displaystyle\leq\lambda(1+R)(1-\frac{z^{2}}{(\gamma+z)^{2}})]-1$
$\displaystyle\leq(1-\frac{z^{2}}{(\gamma+z)^{2}})]-1<0$

This means that as long as $F(0)>z$, there must be some $\bar{\gamma}\in(0,1]$
such that $F(\gamma)\geq z$ for all $\gamma\leq\bar{\gamma}$. The lemma
follows by substituting in $\gamma=\frac{1-p}{p}$. ∎

######  Lemma 6.

Let $v=(\lambda,R,\phi,p)$ and
$v^{\prime}=(\lambda^{\prime},R^{\prime},\phi^{\prime},p^{\prime})$ be two
vectors of parameters where $v^{\prime}\geq v$ component-wise with at least
one inequality strict. If the informative condition holds for $v$, then it
also holds for all $v^{\prime}$.

###### Proof.

The results for $\lambda,R$ and $\phi$ are immediate from inspecting the
informativeness condition; the result for $p$ follows from Lemma 5. ∎

Finally, let’s verify that the strategies and beliefs specified in Proposition
2 indeed constitute an equilibrium.

###### Proof of Proposition 2.

According to the strategies in Proposition 2, the status quo is bad news. Now
that a successful reform is good news and a failed reform is bad news for
congruence, the principal retains only after observing a successful reform.
The agent’s efforts follow from Lemma 3. ∎

#### Transparent regime

######  Proposition 3 (Restating Result 3: Existence).

Under the transparent regime, there exists a separating equilibrium that
survives the universal divinity refinement. In this equilibrium the congruent
type always chooses $r$; he implements with effort
$e_{H}=\max\\{\sqrt{2\lambda(R-d)},\lambda\mu_{+}\\}$ after $s=g$ and
$e_{L}=\max\\{\sqrt{2\lambda(R-d)},\lambda\mu_{-}\\}$ after $s=b$; the
noncongruent type always chooses $q$. Given her observation $(r,e)$, the
principal’s belief about the type $(t,s)\in\\{c,n\\}\times\\{g,b\\}$ is that
$P((c,g)|(r,e_{H}))=1$, $P((c,b)|(r,e_{L}))=1$ and $P((c,s)|(q,0))=0$ for all
$s\in\\{g,b\\}$; the off-path belief is $P((c,s)|(r,e):e<e_{H},e\neq e_{L})=0$
for all $s\in\\{g,b\\}$ and $P((c,g)|(r,e):e>e_{H})=1$. She retains whenever
observing $(r,e)$ with $e\geq e_{H}$ or $(r,e_{L})$.

###### Proof.

Let us verify that the strategies and beliefs in Proposition 3 indeed
constitute a PBE. First, the noncongruent agent does not want to mimic a
congruent one even when the signal is good. To see it, the noncongruent agent
values retention at $R$ and the status quo payoff at $d$; he is unwilling to
initiate a reform if it entails a cost higher than $R-d$, which amounts to an
effort $\sqrt{2\lambda(R-d)}$. This means that as long as the congruent agent
is willing to exert an effort above this level, separation happens. Notate
$\mu$ as a congruent agent’s posterior belief that the state is good. His
policy payoff is single-peaked at the $\lambda\mu$. This means that the
congruent agent exerts effort $\max\\{\sqrt{2\lambda(R-d)},\lambda\mu\\}$ in
equilibrium.

Now we verify that this equilibrium survives the universal divinity
refinement. Let’s consider whether a deviation $(r,e^{\prime})$ with
$e^{\prime}\notin\\{e_{H},e_{L}\\}$ may benefit anyone. Recall that there are
three payoff types $(c,g),(c,b),(n,\cdot)$ arranged in the descending order
with respect to the incentive to reform. Clearly, no profitable deviation may
occur with $e^{\prime}\geq e_{H}$. So we consider cases
$e^{\prime}\in(e_{L},e_{H})$ and $e^{\prime}<e_{L}$.

  * •

$e^{\prime}\in(e_{H},e_{L})$. Then among the reformers, only the type $(c,g)$
may benefit from this deviation when
$e_{H}=\sqrt{2\lambda(R-d)}>\lambda\mu_{+}$ because it allows him to save
effort for separation; the type $(c,b)$ cannot benefit from this deviation.
But the principal then regards this as bad news for retention. To see it, we
again use the notation $\underline{p}^{(c,g)}$ and $\underline{p}^{n}$ to
represent the retention probability that respectively make a type $(c,g)$
agent and a type $(n,\cdot)$ agent indifferent between deviation and obtaining
the equilibrium payoff; it suffices to show that
$\underline{p}^{n}<\underline{p}^{(c,g)}$ i.e. the noncongruent agent benefits
more from this deviation and thus can tolerate more retention loss. By
definition, $\underline{p}^{n}\cdot R-\frac{{e^{\prime}}^{2}}{2\lambda}=d$ and
$\underline{p}^{(c,g)}\cdot
R+\mu_{+}e^{\prime}-\frac{{e^{\prime}}^{2}}{2\lambda}=R+\mu_{+}e_{H}-\frac{{e_{H}}^{2}}{2\lambda}=d+\mu_{+}e_{H}$.
Since $e_{H}>e^{\prime}$, straightforward comparison suggests that
$\underline{p}^{n}<\underline{p}^{(c,g)}$. It happens because the noncongruent
agent has less stake in reform and so he does not suffer as much as the
congruent type in reducing efforts. As such, the principal must replace this
agent $(c,g)$ and the agent cannot benefit from this deviation.

  * •

$e^{\prime}\in(0,e_{L})$. Then this deviation may benefit the $(c,b)$ if
$\lambda\mu_{+}>e_{L}=\sqrt{2\lambda(R-d)}>\lambda\mu_{-}$ and the principal
retains; it may benefit both types of $(c,g)$ and $(c,b)$ if
$e_{L}=\sqrt{2\lambda(R-d)}>\lambda\mu_{+}$ the principal retains. We consider
the first case; the second one follows analogously. The main observation goes
just as above: whenever the congruent agent benefits from this deviation, the
noncongruent type benefits more because he does not suffer from the loss of
reform benefit. More precisely, $\underline{p}^{n}\cdot
R-\frac{{e^{\prime}}^{2}}{2\lambda}=d$ and $\underline{p}^{(c,b)}\cdot
R+\mu(b)e^{\prime}-\frac{{e^{\prime}}^{2}}{2\lambda}=R+\mu(b)e_{L}-\frac{{e_{L}}^{2}}{2\lambda}=d+\mu(b)e_{L}$.
Straightforward comparison shows that
$\underline{p}^{n}<\underline{p}^{(c,b)}$. This suggests that the principal
strikes $(c,b)$ if she observes any deviation to $(r,e^{\prime})$ with
$e^{\prime}\in(0,e_{L})$ and believes that this deviation comes from type
$(n,\cdot)$.

Hence, we have established the proposition. ∎

######  Lemma 7 (Restating Result 3: Uniqueness).

  1. 1.

Among all separating equilibria, the universal divinity refinement selects
uniquely on the least costly separating equilibrium described in Proposition
3.

  2. 2.

If $\lambda\mu_{+}^{2}<2(R-d)$, the universal divinity refinement cannot rule
out a class of pooling equilibrium with the following properties: both types
of agent choose $x=r$ with effort $e^{*}$, where
$e^{*}\in[\lambda\mu_{+},\sqrt{2\lambda(R-d)}]$. Otherwise, no pooling
equilibrium may survive the universal divinity criterion.

###### Proof.

Part 1. Proposition 3 describes the least costly separating equilibrium or the
Riley outcome that survives the universal divinity refinement.

Consider other possibility of separation. First consider perfect separation in
which an agent reforms if and only if he is congruent. We claim that the only
plausible equilibrium in this category is the one characterized in Proposition
3. To see it, $\sqrt{2\lambda(R-d)}$ is the minimal effort to deter a
noncongruent agent from mimicking. Any other equilibrium must involve the
congruent exerting an effort weakly larger than this. However, any other
separating equilibrium in which a type $(c,g)$ chooses $(r,e^{\prime}_{H})$
and a type $(c,b)$ chooses $(r,e^{\prime}_{L})$ with either
$e^{\prime}_{H}\neq e_{H}$ and/or $e^{\prime}_{L}\neq e_{L}$ does not survive
a deviation to the strategy specified in Proposition 3. For a concrete
example, suppose towards contradiction that indeed a type $(c,g)$ agent
chooses $(r,e^{\prime}_{H})$. Then he benefits most by deviating to
$(r,e_{H})$; upon observing this observation, the principal believes according
to the divinity condition that the agent has type $(c,g)$. Consequently, the
only equilibrium possibility is one described in Result 3.

Next we rule out “semi-separating” possibilities in which either 1) not all
congruent types reform and all noncongruent types stay with the status quo or
2) not all noncongruent type stays with the status quo and all congruent types
reform. In the first case, not reforming is bad news about congruence. If on
path the type $(c,b)$ agent does not reform, the he may profitably deviate by
reforming with effort $\lambda\mu_{-}$; upon this deviation the principal
applies the divinity criterion and assigns probability $1$ to type $(c,b)$ and
retains. Same story applies to type $(c,g)$. In the second case, since the
types of $(n,g),(n,b)$ share the same policy preference, they should behave
the same in equilibrium. So we can rule out this possibility as well.

All other semi-separating equilibrium possibilities involving one of
$(c,g)\&(c,b)$ reforms and one of $(n,g)\&(n,b)$ keeps the status quo can be
easily ruled out.

Part 2. There are a few steps:
Step 1. Claim: In any pooling equilibrium that survives the divinity
refinement, it must be that the agent reforms with an effort
$e\geq\lambda\mu_{+}$.

###### Proof.

Suppose not. This boils down to two possibilities: all types of agents
$(c,g),(c,b),(n,\cdot)$ 1) pool on the status quo, or 2) pool on the reform
with effort $e<\lambda\mu_{+}$. In either case, however, a $(c,g)$ type can
profitably deviate by choosing $(r,\lambda\mu_{+})$. Upon this deviation, the
divine condition assigns the probability 1 that this deviation comes from a
type-$(c,g)$ agent since he benefits more than other types. The agent will be
retained, thus contradicting the equilibrium condition. ∎

Step 2: Fix a pooling equilibrium in which everyone reforms with effort
$e^{*}\geq\lambda\mu_{+}$. Let’s use the divinity condition to pin down the
off-path beliefs. On path, every type shall be retained. For any deviation to
be profitable it must be that either (1) the deviation involves the agent
reforms with an effort $e^{\prime}<e^{*}$, or (2) the agent chooses the status
quo.

Case (1). As before define $\underline{p}^{(\cdot)}$ as the break-even
retention probability after deviation. By definition,

$\displaystyle
R\underline{p}^{(c,g)}+\mu_{+}e^{\prime}-\frac{(e^{\prime})^{2}}{2\lambda}$
$\displaystyle=R+\mu_{+}e^{*}-\frac{(e^{*})^{2}}{2\lambda}$ $\displaystyle
R\underline{p}^{(c,b)}+\mu_{-}e^{\prime}-\frac{(e^{\prime})^{2}}{2\lambda}$
$\displaystyle=R+\mu_{-}e^{*}-\frac{(e^{*})^{2}}{2\lambda}$ $\displaystyle
R\underline{p}^{n}-\frac{(e^{\prime})^{2}}{2\lambda}$
$\displaystyle=R-\frac{(e^{*})^{2}}{2\lambda}$

By the assumption that $e^{*}>e^{\prime}$, we deduce
$\underline{p}^{(c,g)}>\underline{p}^{(c,b)}>\underline{p}^{n}$; in other
words, the noncongruent type benefits from the deviation the most. The the
principal assigns probability 1 that the agent is of type-$n$ following any
deviation $(r,e^{\prime})$ with $e^{\prime}<e^{*}$.

Case (2). Repeat steps in Case (1) and modify the deviation to $q$. By
definition,

$\displaystyle R\underline{p}^{(c,g)}+d$
$\displaystyle=R+\mu_{+}e^{*}-\frac{(e^{*})^{2}}{2\lambda}$ $\displaystyle
R\underline{p}^{(c,b)}+d$
$\displaystyle=R+\mu_{-}e^{*}-\frac{(e^{*})^{2}}{2\lambda}$ $\displaystyle
R\underline{p}^{n}+d$ $\displaystyle=R-\frac{(e^{*})^{2}}{2\lambda}$

As before, $\underline{p}^{(c,g)}>\underline{p}^{(c,b)}>\underline{p}^{n}$.
The the principal assigns probability 1 that the agent is of type-$n$
following any deviation $(r,e^{\prime})$ with $e^{\prime}<e^{*}$.

Taken together, I have shown that any deviation that might benefit the agent
would make the principal more suspicious that he is a noncongruent type.

Reversing the argument, it is straightforward to verify that the divinity
condition assigns any unprofitable deviation to $(r,e^{\prime})$ with
$e^{\prime}\in(e^{*},\sqrt{2\lambda(R-d)}]$ a belief that the agent is of type
$(c,g)$ with probability 1. Hence if $\lambda\mu_{+}>2(R-d)$, the following
pooling equilibrium survives the divinity refinement: All types of agent pool
on the action $(r,e^{*})$ with
$e^{*}\in[\lambda\mu_{+},\sqrt{2\lambda(R-d)}]$; the principal assigns
probability $1$ that the agent is noncongruent upon observing $x=q$ or
$(r,e^{\prime})$ with $e^{\prime}<e^{*}$; and she assigns probability $1$ that
the agent is congruent & has received the signal $s=g$ upon observing
$(r,e^{\prime})$ with $e^{\prime}>e^{*}$. ∎

###  A.3 Mechanism Design

Formalize Result 4 as follows:

######  Proposition 4.

The nontransparent regime induces the lowest welfare. Either the opaque or the
transparent regime may induce the highest welfare for certain parameter values
$(p,\phi,d,\lambda,R,\pi)\in\Omega$.

###### Proof.

Across three regimes, the congruent agent always initiates reforms. He exerts
the least effort under the nontransparent regime. To see why the congruent
agent shirks most there, after taking the “correct” position he no longer
worries about office. In other two regimes, the congruent agent has to either
gamble for success or separate from the noncongruent type. Together with the
fact that the noncongruent agent always fails a reform after exerting zero
effort, the principal’s policy payoff is the lowest under the nontransparent
regime.

To see why the opaque regime may prevail, it suffices to check whether the
congruent agent works hardest under this regime. Were this true, then the
principal would prefer this regime when there is a sizable proportion of
congruent agents in the pool ($\pi$ high). A sufficient condition is
$\lambda(1+R)\mu_{-}\geq\sqrt{2\lambda(R-d)}$ or equivalently
$\lambda(1+R)^{2}\mu_{-}^{2}\geq 2(R-d)$. RHS is bounded above by
$2(R-\frac{\lambda}{2}R^{2}\mu_{-}^{2})$ using the condition
$d\geq\frac{\lambda R^{2}\mu^{2}_{-}}{2}$ so it is sufficient to show that
$R\leq\frac{\lambda}{2}\mu_{-}^{2}[R^{2}+(1+R)^{2}]$. This condition can be
further simplified to $2\leq\lambda\mu^{2}_{-}[2R+2+\frac{1}{R}]$. For
sufficiently small $R$, we can always find $\lambda\in[0,1]$ satisfying this
inequality and the parameter restriction $\lambda(1+R)\leq 1$. Further, per
Remark 1 we can identify a set of parameters satisfying the informativeness
condition. Finally, there exists a set of sufficiently small $d$ satisfying
the assumptions on signal accuracy.

There also exist parameters such that the transparent regime prevails.
Examples are available in the proof of Proposition 5. ∎

###  A.4 Comparative Statics

We collect comparative static results into a proposition:

######  Proposition 5.

Given a vector $w=(p,\phi,d,\lambda,R,\pi)$ under which the opaque regime is
optimal. Then

  1. 1.

The principal would continue to use this regime if $\phi$ increases; moreover,
the principal strictly benefits from this.

  2. 2.

Suppose further that $2(R-d)<\lambda$. Then 1) there exists
$p^{\prime}\in(\frac{1}{2},1)$ such that for all $p\in(p^{\prime},1]$, the
principal would continue to use this regime if $\lambda$ increases; 2)
$\exists p^{\prime\prime}\in(\frac{1}{2},1)$ such that for all
$p\in(p^{\prime\prime},1]$, the principal would continue to use this regime if
$p$ increases. In both cases, the principal strictly benefits from this
parameter changes.

  3. 3.

An increase in $R$ may cause the principal to switch to the transparent
regime. Specifically, fixing sufficiently high $p$, $\phi$, and $\pi$, and
assuming $\lambda(1+d)\leq\frac{1}{2}$, there exists a pair
$\underline{R}=\underline{R}(\lambda,d)$ and $\bar{R}=\bar{R}(\lambda,d)$ such
that 1) for all $R\in(\underline{R},\bar{R})$ the transparent regime
dominates; for $R>\bar{R}$ and $R<\underline{R}$ the opaque regime dominates.
2) $\underline{R}$ is increasing in $\lambda$ and $d$; $\bar{R}$ is decreasing
in $\lambda$ and $d$.

###### Proof.

(Sanity check) I claim that the set of parameter values satisfying (a)
$2(R-d)<\lambda$, (b) several model assumptions, and (c) the informativeness
condition, is nonempty.

To see it, suppose that the signal accuracy is very high or $p\approx 1$; it
overwhelms a weaker prior $\phi$ (e.g. $\phi=\frac{3}{4}$), resulting in
$\mu_{+}\approx 1$ and $\mu_{-}\approx 0$. Now I check these restrictions one
by one.

  1. 1.

With $p\approx 1$ Lemma 5 guarantees the informativeness condition if
$z<\lambda$.

  2. 2.

With $\mu_{-}\approx 0$, two model assumptions reduce to
$\max\\{(1+R)\mu_{-},R\mu_{+}\\}>\sqrt{\frac{2d}{\lambda}}$ and
$\mu_{+}>\sqrt{\frac{2d}{\lambda}}$. If we pick
$\lambda>\max\\{\frac{2d}{R^{2}\mu_{+}^{2}},\frac{2d}{\mu_{+}^{2}}\\}\approx\max\\{\frac{2d}{R^{2}},2d\\}$
then these two assumptions hold.

  3. 3.

We also need $\lambda(1+R)\leq 1$.

  4. 4.

Need to verify that $\lambda\mu_{+}^{2}>2(R-d)$

Taken together, we may choose parameters like this: pick
$p=\frac{99}{100},\phi=\frac{3}{4}(z=\frac{1}{3}),\lambda=\frac{1}{2},R=\frac{1}{4},d=\frac{1}{80}$.
This gives $\mu_{+}\approx 0.996$ and $\mu_{-}\approx 0.03$ and
$\sqrt{\frac{2d}{\lambda}}\approx 0.22$. $\lambda\mu_{+}^{2}\approx 0.496$ and
$2(R-d)=0.475$. All restrictions are met.

Part 1. A larger $\phi$ makes the opaque regime more appealing to the
principal because the agent works harder when he is more certain that the
reform is good by nature. This “strong prior” effect benefits the transparent
regime only if 1) the agent is congruent and 2)
$\sqrt{2\lambda(R-d)}<\lambda\mu$ for some $\mu\in\\{\mu_{+},\mu_{-}\\}$;
otherwise, the agent’s policy choice and implementation effort remain
invariant to the prior. But under these two conditions, the opaque regime
strictly dominates by encouraging the agent to exert more effort
($\lambda(1+R)\mu>\lambda\mu$).

Part 2. Assuming the bar for separation is low
($\sqrt{2\lambda(R-d)}<\lambda\mu$), the congruent agent must exert less
effort under the transparent regime than in the opaque regime. Sufficiently
accurate signals guarantee this low bar for separation. To see it, a higher
$p$ does two things: it reinforces the separation condition
($\sqrt{2\lambda(R-d)}<\lambda\mu_{+}$) by inducing a sufficiently high
posterior; it also tilts the principal’s welfare calculus towards the
realization of a good signal999With a bad signal, the reform is doomed to fail
and confers almost zero payoff; the status quo policy confers $d>0$. Since the
agent’s equilibrium strategies remain invariant to the parameter changes, the
welfare impact conditional on a bad signal is minimal from the principal’s
perspective. A higher $\lambda$ also guarantees this bar for separation.

Part 3. We want to construct a pair of vectors
$w^{\prime}=(p,\phi,d,\lambda,R,\pi),w^{\prime\prime}=(p,\phi,d,\lambda,R^{\prime},\pi)$
with $R^{\prime}>R$ that satisfying the model assumptions, the informativeness
condition, and $\lambda(1+R)<1$, such that the principal prefers the opaque
regime under $w^{\prime}$; she prefers the transparent regime under
$w^{\prime\prime}$.

To simplify matters, I assume that the agent is likely to be congruent
($\pi\approx 1$); I let $p=\phi=1-\epsilon$ for $\epsilon$ sufficiently small.
Consequently, $\mu_{+}\approx 1$ and $\mu_{-}=\frac{1}{2}$. With these two
assumptions, the agent is unlikely to receive a bad signal (which occurs with
probability $p(1-\phi)+\phi(1-p)\approx 2\epsilon$); the welfare comparison
reduces to which information policy would elicit more efforts from a congruent
agent when the signal is good.

Under the opaque regime, the congruent agent exerts effort
$\lambda(1+R)\mu_{+}$. Under the transparent regime, he exerts
$\max\\{\sqrt{2\lambda(R-d)},\lambda\mu_{+}\\}$ (which is true in both
separating and pooling equilibria). The transparent regime may elicit more
effort whenever $\sqrt{2\lambda(R-d)}\geq\lambda(1+R)\mu_{+}$ or
$\lambda\mu_{+}^{2}(1+R)\leq 2(R-d)$. Define
$\hat{\lambda}=\lambda\mu_{+}^{2}$ and $H(R)=\hat{\lambda}(1+R)^{2}-2(R-d)$.
$H$ has real solutions if $1\geq 2\hat{\lambda}(d+1)$; in this case, two
solutions are
$\underline{R}=\frac{1-\hat{\lambda}-\sqrt{1-2(1+d)\hat{\lambda}}}{\hat{\lambda}}>0$
and
$\bar{R}=\frac{1-\hat{\lambda}+\sqrt{1-2(1+d)\hat{\lambda}}}{\hat{\lambda}}$.
Given the quadratic shape of $H$, for all $R<\underline{R}$ the opaque regime
dominates; for $R\in(\underline{R},\bar{R})$ the transparent regime dominates.
This suggests that if $R$ is close enough to $\underline{R}$ or $\bar{R}$,
then the principal is willing to switch information regimes when there is
small perturbation to $R$; if $R<\underline{R}$ or $R>\bar{R}$ then a local
increase in $R$ would not induce a regime switch.

We claim from the expression $\underline{R},\bar{R}$ that:

######  Claim 4.

$\underline{R}$ is increasing in $\lambda$ and $d$; $\bar{R}$ is decreasing in
$\lambda$ and $d$.

###### Proof.

($\underline{R}$): Since $\hat{\lambda}=\lambda\mu_{+}$ it suffices to verify
$\frac{\partial\underline{R}}{\partial\lambda}\geq 0$ and
$\frac{\partial\underline{R}}{\partial d}\geq 0$. The latter is obvious. Note
also that

$\displaystyle\frac{\partial\underline{R}}{\partial\lambda}=\frac{\frac{\lambda(1+d)}{\sqrt{1-2(1+d)\lambda}}-(1-\sqrt{1-2\lambda(1+d)})}{\lambda^{2}}$

Denote
$k=\sqrt{1-2(1+d)\lambda}\Leftrightarrow(1+d)\lambda=\frac{1-k^{2}}{2}$. The
numerator of the above expression is
$\frac{1-k^{2}}{2k}-(1-k)=\frac{1}{2}(k+\frac{1}{k})-1\geq 0$.

($\bar{R}$): Similarly, $\frac{\partial\bar{R}}{\partial\lambda}\geq
0\Leftrightarrow-\frac{\lambda(1+d)}{\sqrt{1-2(1+d)\lambda}}\geq\sqrt{1-2(1+d)\lambda}$
which is always false; the case for $d$ is again straightforward. ∎

It remains to verify that the vector thus constructed
$(p,\phi,d,\lambda,R)=(1-\epsilon,1-\epsilon,d,\lambda,\bar{R})$ may satisfy
all necessary assumptions. We have the freedom to choose $d$ and $\lambda$. I
let $\epsilon\downarrow 0$ for simplicity.

  1. 1.

$\lambda(1+\underline{R})\xrightarrow{\epsilon\downarrow
0}\lambda+1-\lambda-\sqrt{1-2(1+d)\lambda}<1$.

  2. 2.

The informativeness condition is guaranteed for $p=\phi=1-\epsilon$ and
$\lambda>0$. To see it, $z=\gamma=\frac{\epsilon}{1-\epsilon}\approx 0$ so the
condition $z-\lambda\frac{1}{1+\gamma
z}\leq\gamma[\lambda(1+R)\frac{\gamma}{\gamma+z}-1]$ reduces to $\lambda>0$.

  3. 3.

The assumption on signal accuracy requires
$1>\sqrt{\frac{2d}{\lambda}}>\frac{1}{2}$ for $\epsilon$ arbitrarily small.
This means that fixing $\lambda$ it must be that
$d\in(\frac{\lambda}{8},\frac{\lambda}{2})$.

  4. 4.

The assumption on moderate office rent simplifies to
$\max\\{\frac{1+\underline{R}}{2},\bar{R}\\}>\sqrt{\frac{2d}{\lambda}}>\frac{\underline{R}}{2}$.
Unpacking the expression
$\underline{R}=\frac{1-\hat{\lambda}-\sqrt{1-2(1+d)\hat{\lambda}}}{\hat{\lambda}}$,
letting $\hat{\lambda}\rightarrow\lambda$ (since $\epsilon\downarrow 0$), a
sufficient condition is

$\displaystyle
1-\lambda-\sqrt{1-2(1+d)\lambda}<2\sqrt{2d\lambda}<1-\sqrt{1-2(1+d)\lambda}$

There is a large set of pairs $(d,\lambda)$ satisfying the above three
conditions. For example, we can let $d=0.05$ and $\lambda=0.3$. Condition 1, 2
and 3 are immediate. Condition 4 simplifies to $0.0917<0.346<0.39$.

Finally, from $w=(1-\epsilon,1-\epsilon,0.05,0.3,\bar{R})$ we may construct
$w^{\prime}=(1-\epsilon,1-\epsilon,0.05,0.3,\bar{R}-\delta)$ and
$w^{\prime\prime}=(1-\epsilon,1-\epsilon,0.05,0.3,\bar{R}+\delta)$ with
$\delta>0$ sufficiently small such that the principal chooses the opaque
regime under $w^{\prime}$ and the transparent regime under $w^{\prime\prime}$.
∎

###  A.5 Robustness

####  Nontrivial selection

The baseline model makes a simplifying assumption that the principal is almost
entirely policy-motivated. One may wonder to what extent this assumption
drives my results; after all, it is quite reasonable to assume that the
principal may attach nontrivial weight on selecting a congruent agent.

I argue that all results continue to hold as long as the principal’s weight on
selection is not too high. Crucially, note that the principal’s retention
happens at the last stage. Since the principal retains on good news about
congruence, her retention strategy remains invariant to the weight of
selection. Also note that a policy-motivated principal’s optimal information
policy is generically101010The set of parameters that give rise to more than
one optimal policy is meager in the parameter space. unique. This means that
even if this principal starts to care about selection, she would not change
her information regime if selection is not as important as policy-making.

####  More data on implementation

In the baseline model I use a single parameter $e$ to capture the moral hazard
in the reform implementation. I claim that this approach entails no loss of
generality.

Consider a more general environment in which the reform implementation
involves a vector of necessary inputs $(e_{1},e_{2},...e_{n})$, each
determining the success probability $h$ of a good reform according to the
function $h=h(e_{1},e_{2},...e_{n})$. Let the cost function be
$C(e_{1},e_{2},...e_{n})$. Now, suppose an agent wants to target a level of
success probability $\bar{h}$. He shall solve a textbook minimization problem
(up to regularity conditions)
$\min_{e_{1},...e_{n}}C(e_{1},e_{2},...e_{n})\quad
s.t.\;h(e_{1},e_{2},...e_{n})\geq\bar{h}$, and derive an induced cost function
for $h$. That is, achieving the level of success probability $h$ for a good
reform costs one $C(h)$. This gives us a single-variable representation of
moral hazard.

From this standpoint, we may interpret the effort parameter $e$ as a “score”
summarizing all useful information for reform policy-making that is under the
agent’s control.

####  Modeling congruence

I model (non)congruence along the line of Fox (2007). One may wonder whether
alternative notions of congruence (e.g. Maskin and Tirole (2004)) might induce
similar or different results.

I argue that the current setup presents the motivation issue in a clean
fashion. By contrast, an alternative setup closer to Maskin and Tirole (2004)
often involves the noncongruent type discounting future differently than the
congruent type.

To see this, suppose the noncongruent type is a reform saboteur – he prefers a
failed reform to the status quo to a successful reform. Per Maskin and Tirole
(2004), we would like this type of agent to reform whenever the timing is bad,
and stays with the status quo whenever the state calls for a reform. This
equilibrium behavior could be induced, for example, when efforts and the
policy choices are substitutes for reform success: a good reform always
succeeds, and a bad reform succeeds with a probability equal to effort. The
main issue is that, the agent cannot control the (risky) reform outcome in a
deterministic way; this renders asymmetry in the continuation payoffs to two
types of agent. In the modified setup above, the congruent type at least
secures $R+\phi$ by holding office in the period 2 (reform without effort);
the noncongruent type obtains at most $R+(1-\phi)$. The congruent agent
benefits more from holding office at least when the prior is biased towards
reform ($\phi\geq\frac{1}{2}$). In this case, career concerns discipline the
congruent agent more strictly than the noncongruent one; accordingly, it makes
type-separation easier relative to the main model. While this observation
lends extra credibility that an opaque information regime may prevail (since
the congruent agent exerts less effort on path under the transparent regime),
it is not obvious whether its optimality comes mainly from the motivation
effect of a pivotal decision rule or just the asymmetric discipline effects.

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