WPS6973
Policy Research Working Paper 6973
Learning Dynamics and Support
for Economic Reforms
Why Good News Can Be Bad
Sweder van Wijnbergen
Tim Willems
Development Economics Vice Presidency
Development Policy Department
July 2014
Policy Research Working Paper 6973
Abstract
Support for economic reforms has often shown puzzling also lead to situations in which reforms that enjoy both
dynamics: many reforms that began successfully lost public ex ante and ex post majority support will still not come
support. This paper shows that learning dynamics can to completion. The framework can be used to explain
rationalize this paradox because the process of revealing why gradual reforms worked well in China (where suc-
reform outcomes is an example of sampling without replace- cesses in Special Economic Zones facilitated further
ment. This concept challenges the conventional wisdom reform), whereas this was much less the case for Latin
that one should begin by revealing reform winners. It may American and Central and Eastern European countries.
This paper is a product of the Development Policy Department, Development Economics Vice Presidency. It is part of
a larger effort by the World Bank to provide open access to its research and make a contribution to development policy
discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org.
The authors may be contacted at s.j.g.vanwijnbergen@uva.nl and tim.willems@economics.ox.ac.uk.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Learning Dynamics and Support for Economic Reforms: Why
Good News Can Be Bad
Sweder van Wijnbergen and Tim Willems 1
JEL classification: D72, D83, P21
Key words: Learning, Political economy, Reform, Sequencing, Privatization, Special
Economic Zones
Sector board: EPOL
1
Sweder van Wijnbergen is a professor at the Department of Economics, University of Amsterdam, The
Netherlands. He is also affiliated with the Tinbergen Institute. His e-mail address is
s.j.g.vanwijnbergen@uva.nl. Tim Willems (corresponding author) is a research fellow at Nuffield College and
the Department of Economics, University of Oxford, UK. He is also a member of the Centre for
Macroeconomics. His e-mail address is tim.willems@economics.ox.ac.uk. The authors thank the editor
(Andrew Foster), two anonymous referees, Philippe Aghion, Björn Brügemann, Tom Cunningham, Allan
Drazen, Michal Horvath, Ruixue Jia, Matija Lozej, Torsten Persson, Dani Rodrik, Gérard Roland, and audiences
at the EBRD and the 2013 SITE Conference in Stockholm for useful comments and discussions.
Why have gradual economic reforms worked out well for China, whereas this is much less
the case for most Latin American and Central and Eastern European countries? How is it
possible that so many of the reforms that began successfully while enjoying majority support
subsequently lost this support, although there are also examples of reforms that did not begin
well but nevertheless managed to maintain momentum among voters?
The most dramatic example of a reformist government that lost majority support in spite of
strong economic performance is Slovakia in 2006. At that time, the Wall Street Journal
Europe wrote, 2
"Imagine you're the leader of a country where economic growth is running at 6.3%,
your government has been praised by the World Bank as the best market reformer in
the world [and] unemployment has fallen to a record low of 10.6% from around 20%
in just four years. [...]
With this record in mind, now consider that you face parliamentary elections this
Saturday at which, unless the opinion polls change dramatically, you risk annihilation
by a leftist opposition party with no experience of government and a policy agenda
filled with populist rhetoric.
Welcome to the world of Mikuláš Dzurinda, prime minister of Slovakia, who for the
past eight years has led what can reasonably claim to have been the most successful
neo-liberal government of the 21st century so far."
Despite his impressive reform successes, Dzurinda lost the 2006 elections to Robert Fico of
the SMER party (a breakaway party from the successor to the original Communist Party of
Slovakia), who reversed many of Dzurinda's reforms.
With important reforms currently being implemented in many African and Southern
European states, it is important to understand why such puzzling reversals can occur. In this
2
Robin Shepherd, "The Dzurinda Revolution", Wall Street Journal Europe, June 12, 2006.
2
paper, we focus on the interaction between learning from reform outcomes and the dynamics
of public support for gradual economic reforms. 3
We believe that learning processes play a key role in determining support for reforms. So far,
however, the literature has remained relatively silent on this issue. Although there are many
informal discussions of learning from reform outcomes, formal treatments are scarce. 4
Even if everyone gains from efficient reforms in the long run, there will almost inevitably be
losers during the transitional phase (for example, certain generations or professions). The
model we construct captures the fact that reforms typically generate reform winners and
reform losers, but (as emphasized in the seminal paper by Fernandez and Rodrik (1991))
these winners and losers cannot always be identified in advance. That is, there is individual
uncertainty, which causes the reform to have uncertain distributional consequences. As the
reform progresses over time, voters update their beliefs about whether they will end up in the
winners’ group or in the group of losers. Because the full version of our model not only
features individual uncertainty but also allows for aggregate uncertainty (which implies that
voters are unsure about the exact share of the population that will benefit from reform), this
paper can be seen as augmenting the Fernandez-Rodrik setup with aggregate uncertainty and
learning dynamics.
The fact that existing reform measures affect the distribution from which future sampling will
occur plays a key role in our analysis. Specifically, the process of revealing reform outcomes
is an example of sampling without replacement. This implies that the revelation of reform
winners deteriorates the quality of the remaining pool, thereby making unreformed agents
less eager to continue the reform process. We derive a condition under which these dynamics
are so strong that they lead to the counterintuitive situation in which reform successes make
the median voter begin opposing a reform he used to support. In these circumstances, the
reforming government suddenly loses majority support although (or because) the reform is
3
With the possible exception of price decontrol, all reforms are gradual (as opposed to "big bang"), if only
because of implementation delays. As noted, for example, by Gupta, Ham, and Svejnar (2008), even reforms
that were supposed to be "big bang" (such as the Balcerowicz reforms in Poland) were not completed
instantaneously, thereby giving voters an opportunity to update their beliefs about the effects of the reform. In
this sense, all reforms are gradual, but some reforms are "more gradual" than others.
4
Some exceptions are van Wijnbergen (1992, where voters learn about the effects of price reform), Dewatripont
and Roland (1995, where the public uses early reform outcomes to learn about the expected outcome of later
ones), Veldkamp (2009, where laid-off workers learn about their re-employment chances), Strulovici (2010,
analyzing determinants of collective experimentation), and Morrow and Carter (2013, studying the impact of
learning dynamics on the support for redistributive policies).
3
progressing in such a successful way. Consequently, even reforms that enjoy both ex ante and
ex post majority support may not come to completion.
We emphasize that this phenomenon results from rational economic thinking and that it arises
as soon as a reform is believed to generate losers whose identity is ex ante unknown - a
feature that we see as being in accordance with many economic reforms in reality (see also
Fernandez and Rodrik 1991). In addition, sampling without replacement continues to play a
role when one adds aggregate uncertainty. In that setup, the revelation of winners may also
lead to an upward revision of the expected aggregate number of reform beneficiaries
(enhancing support for reform). However, we show that it is possible for this strategy to sow
the seeds for its own destruction.
Although this learning mechanism applies to many reform types (such as land reform, the
gradual abolition of subsidies/price controls, or the reduction in trade barriers), we often link
it to privatization. Privatization is a good example of a reform in which learning dynamics
may be important, and the choice between starting with "good" or "bad" companies arises
consistently. Because the government is the incumbent owner of the firms that are to be
privatized, it often has inside information on the profitability of these firms and on future
policies that may benefit or harm them. This situation brings up the sequencing question for
the government and the issue of learning for other agents (see, e.g., Roland 2000, chapter 2).
On a more general level, this paper develops a theory of agents who are learning from
realizations that are sampled without replacement. As a result, the sampling process itself
affects the distribution from which future sampling will take place. From the so-called
"Monty Hall problem", we know that this situation can give rise to counterintuitive dynamics
that are not easy to understand without a formal model. Building such a model may therefore
make this paper of independent interest because it may have implications for many other
economic problems (a topical example is the process of revealing the identity of good and
bad banks in a financial crisis).
Our results question the political feasibility of the so-called "sectoral gradualist" way of
privatization. This strategy has been advocated, for example, by Kornai (1990) through his
plea for the "case-by-case" approach, and it has been applied to many countries in Latin
America and Central and Eastern Europe as well as to the UK during its liberalization phase.
This strategy implies that one sector (or firm) is reformed after the other (cf. Berg and
Blanchard (1994, 53, 63)). However, as we argue below, following such a gradual, sequential
4
approach triggers the "sampling without replacement" effect presented previously. This may
explain why practitioners have experienced political difficulties with the case-by-case
strategy. Lipton and Sachs (1990, 298) note that "in almost all countries where privatizations
have been attempted, there have been major political obstacles to the case-by-case approach".
Boycko, Shleifer, and Vishny (1993, 148) state that reforms that proceed at a rather slow pace
are likely to reach a deadlock. As we argue later in this paper, "spatial gradualism"
(reforming one region after another, as China did by installing Special Economic Zones) can
avoid the "sampling without replacement" problem. Thus, the mechanisms explored in this
paper may help explain why gradual reform strategies have been more successful in China
than in Latin America and Central and Eastern Europe.
The outline of this paper is as follows. We first describe various examples of reforms for
which support dynamics have been counterintuitive. Next, we construct a learning model that
provides an explanation for these puzzling dynamics. We then consider the question of why
gradualism worked quite well for China, although this was not the case for most Latin
American and Central and Eastern European countries. Finally, we conclude.
Support Dynamics for Economic Reforms: a Short History
In addition to the case of Slovakia discussed in the introduction, there are many examples of
economic reforms that lost support despite their initial success (and vice versa). Stokes
(2001) provides a thorough analysis of support dynamics related to various reforms. In that
volume, several authors examine the public's reactions to reforms in Spain, East Germany,
Poland, Mexico, Peru, and Argentina. In her summary of the study, Stokes (2001, 25) notes
that "[their] most startling result is that in every country people sometimes reacted to
economic deterioration by supporting the government and its economic program more
strongly. Conversely, they sometimes reacted to economic improvement with pessimism and
opposition". Similar findings are reported by the econometric studies of Remmer (1991) and
Tucker (2000), who analyzed data from 12 Latin American and five post-communist
countries, respectively, and reported a negative causal effect of economic performance on
support for incumbents.
Stokes (2001) provides various specific examples of these counterintuitive dynamics. For
example, in all three Latin American countries studied (Mexico, Peru, and Argentina),
economic expansion (measured by either wage or GDP growth) was followed by pessimism
5
about the future and opposition to the reform program. Similarly, increased real wages in
Poland did not generate support for the reforms but created agnosticism instead.
With respect to the latter case, Rodrik (1995, 404) expresses surprise as well. When
discussing the return to power of the former Polish communist party in 1993, he writes, "Why
this should be so is not so easy to understand. [...] By most standards, Poland must be judged
a success case". 5
Regarding general experiences in Central and Eastern Europe, Fidrmuc (2000, 1491) notes
that "the collapse of communism occurred amidst overwhelming popular support for
fundamental economic and political reforms. However, only a few years later the pendulum
swung back and the reformers were voted out". For example, Slovenia faced great difficulties
in its reform process though it already had quite a few positive experiences with market
forces from the past (Pleskovic and Sachs 1994). Although the 1968 Hungarian reforms
began successfully, they encountered difficulties in the mid-1970s when the country
underwent periods of recentralization (Qian and Xu 1993). Similarly, after the second wave
of reforms following the demise of communism, the reformist Hungarian government lost the
1994 elections, and the former communist party returned to power (as in Poland and later in
Slovakia), a pattern that led Kornai (2000) to conclude that the gradual reform strategy may
not be feasible from a political point of view.
Latin America offers examples of countries that have had similar experiences. Puzzled by this
situation, Tommasi and Velasco (1996) ask, "Why did Venezuelans riot, twice attempt to
overthrow and eventually impeach a president (Carlos Andrés Pérez) who in 1990–2 brought
them an average growth rate of 7.8% (the highest in Latin America), while Peruvians
massively reelected Alberto Fujimori, under whose stewardship consumption dropped by
15.3% in 1990?" Similarly, Iglesias (1994, 497–8) notes, "In my country (Uruguay), which is
growing by 11.5 percent, where unemployment and inflation are down, and where reserves
are up, the popularity rating of the president is 12 percent. That's why the administration lost
its bid to privatize the telephone company". 6
5
Poland had a high unemployment rate at the time, but as Rodrik (1995, 405) notes, it is not clear whether that
was to blame for the deadlock. The unemployed group is too small to be decisive in national elections, and it is
not straightforward that their interests are best served by policies that slow reforms.
6
In 1994, Luis Alberto Lacalle (of the Partido Nacional) was president of Uruguay. After taking office in 1990,
he began significant economic reforms (in the sphere of both taxation and liberalization), but his initiatives later
lost support (despite successes; cf. Iglesias' quote). Subsequently, he lost the 1995 elections and was replaced by
Julio María Sanguinetti of the rival Partido Colorado, who reversed many of Lacalle's reforms.
6
A similar story holds with respect to India: notwithstanding the successes of the Indian
liberalization policies adopted in the 1990s, India is currently struggling to implement new
reforms and has turned into "a place that has fallen out of love with reform" (as stated in The
Economist, 24 March 2012, 14). More generally, Sachs and Warner (1995) have documented
how many countries slowed down (or even reversed) their liberalization policies in the 1960s
and 1970s, though the economic performance under the more liberal regime was impressive.
These examples suggest that a successful beginning of a reform is by no means a sufficient
condition for the reform to maintain majority support along the way. This observation is at
odds with the conventional wisdom that a favorable start facilitates continuation.
At the other end of the spectrum are the gradual economic reforms in China. There, the
government established Special Economic Zones in 1980, after which the economies of those
regions began booming. In contrast to the experiences of Central and Eastern Europe and
Latin America, the initial successes of these Chinese reforms led to increased support for
further reforms in China (Litwack and Qian 1998; Qian, Roland, and Xu 1999, 2006).
In the next section, we develop a model that is able to rationalize the confusing support
dynamics in Latin America and Central and Eastern Europe while simultaneously shedding
light on the question of why the initial Chinese reform successes did not invoke such a
paradoxical public response.
Support Dynamics for Economic Reforms: a Model
In this section, we describe our model. Although we frame the model in the context of
economic reforms, it can also be seen as a more general model of agents who are learning
from realizations that are sampled without replacement.
Our model is dynamic and contains uncertainty at both the aggregate level and the individual
level. The former makes agents in the model uncertain about the total number of reform
winners, whereas the presence of the latter implies that the reform will have uncertain
distributional consequences. Implementing reform takes time. Consequently, reforms are
completed gradually (as in reality; recall footnote 3), and agents have the opportunity to
update beliefs about their chances of benefiting from the reform as it progresses over time.
This belief updating process lies at the heart of our paper. The model presented by Fernandez
and Rodrik (1991) emerges as a special case of our framework without learning dynamics
and without aggregate uncertainty.
7
To build intuition for the mechanisms at play and to set the stage for our full model, we first
consider a setup in which there is only individual uncertainty but no uncertainty in the
aggregate. That is, in the first subsection, individuals know what fraction of the population
will gain from the reform, but ex ante they do not yet know who these winners will be.
Subsequently, we add aggregate uncertainty. Then, individuals are also not sure about what
fraction of the population will benefit from reform. The existence of such uncertainty has
often been named as a reason to reform gradually by starting with the revelation of reform
winners (cf. Roland 1994, 1164). However, as we show, it is still possible that a successful
beginning to a reform will sow the seeds for its own destruction in that setup.
Without Aggregate Uncertainty
To build intuition, we first illustrate our point in a setup without aggregate uncertainty. Time
is discrete, the horizon is infinite, and there is a large number of risk-neutral voters aligned
uniformly between 0 and 1, indexed by i. Each voter i can be thought of as representing
individuals associated with a particular firm or sector. We assume that voters are rational and
forward looking. 7
Voters are faced with a reform proposal Rγ, which is to replace the status quo. This proposal
is assumed to leave everyone with a net present value payoff of 0. Reform Rγ, in contrast, is
known to benefit a fraction γ > 1/2 of the population with certainty (yielding them a net
present value payoff of S > 0). The losing fraction (1 – γ) is assumed to receive a symmetric
negative payoff of –S (where the symmetry simplifies the algebra, without loss of
generality). 8
This implies that there is no aggregate uncertainty and because γ > 1/2, the reform is
efficiency enhancing (according to the Kaldor-Hicks criterion) and would always be
welcomed by a majority ex post.
7
Whether voters are forward looking or backward looking is somewhat debated. Although the early papers on
this issue report that voters are myopic and backward looking (see, e.g., Kramer 1971), more recent studies tend
to find that rational forward-looking behavior dominates (cf. MacKuen, Erikson, and Stimson 1992; Fidrmuc
2000). Introducing retrospective voting would produce goodwill for the reforming government after early
reform successes, somewhat similar to what arises when there is aggregate uncertainty (see Section II). As in
that setup, the pace at which the various forces operate will then determine which effect eventually dominates.
8
With asymmetric payoffs, such as when winners obtain G and losers receive -L with G > L, reforms with γ <
1/2 could also be welfare enhancing in the Kaldor-Hicks sense (and vice versa when L > G). This generalization
would lead to a different set of reforms that can be implemented through majority voting but do not affect the
mechanics of the "sampling without replacement" effect central to this paper because the "sampling without
replacement" effect refers to the availability of winning places relative to the losing ones, not to the exact
magnitude of the associated gain or loss. To see this, note that replacing S with G (respectively L) in equations
(3) and (4) below does not change any of our results.
8
However, the electorate faces individual uncertainty. In response to this uncertainty, voters
form (potentially heterogeneous) beliefs about the effects of the reform on their personal
well-being. We allow for belief heterogeneity in a discrete way: there is a fraction αt that
believes (or already knows) ex ante that it will belong to the group of reform winners,
whereas a fraction βt believes/knows that it will be among the losers (with 0 < αt, βt < 1/2).
The remaining fraction (1 – αt – βt) (which we assume to share a common prior) does not
know at time t whether it will gain or lose from reform. The members of that fraction will
base its decision upon the expected value of the reform for them. If we sort all individuals
(indexed by i) such that the γ ex post winners of the reform are located on the left of the
interval and the (1 – γ) losers are on the right, we obtain the configuration shown in Figure
1. 9
Figure 1: Graphical illustration of the setup
Voters with i < α know that they are among the reform winners, whereas voters with i > 1 – β
(where the "one minus" follows from the fact that β is measured from the right) know that
they are among the losers. At the beginning of the reform, α and β can be equal to 0, but this
does not necessarily have to be the case; it is perfectly possible that some agents already
operate under the new regime before the reform has started (for example, as a remnant of
uncompleted past reform attempts) or that their identity is obvious up front. Agents between
α and 1 – β are uncertain about their identity and do not know whether they will be a reform
winner or a reform loser. Because the identity of more and more individuals is revealed as the
reform progresses over time, α and β become time varying and thus obtain a time index. In
contrast, γ is a time-invariant structural parameter characterizing the reform (with aggregate
uncertainty, the public's estimate of γ can become time varying, though γ itself is fixed, which
is what we allow for in the next section).
9
We rule out partial reform (e.g., reform the winners and keep the losers under the state wing) as a desirable
outcome. Clearly, a formal analysis of such an outcome would require the introduction of interactions between
reformed and unreformed parts of the economy and of costs associated with the use of public funds (keeping
loss-making, government-owned firms in operation is costly to society). Incorporation of this point would
detract from the clarity of our core message; thus, we do not introduce these obfuscating factors here. See
Murphy, Shleifer, and Vishny (1992) for a model that addresses the problems related to partial reforms. In
addition, Dewatripont and Roland (1992) show that partial reforms are typically time inconsistent and therefore
unsustainable.
9
The expected value of the reform for uncertain individuals (i.e., those with i ∈ (αt,1 - βt))
equals
Et R | i t ,1 t t .St 1 t . St . (1)
Individuals in that group follow the decision rule
1 if Et R | i t ,1 t 0
t , (2)
0 if Et R | i t ,1 t 0
where δt is a support indicator that takes the value 1 if the uncertain group votes in favor of
the reform and zero otherwise. Because αt and βt are both smaller than 1/2, the decisive
median voter is located in this uncertain group. 10
The expected value of this uncertain group (expressed by (1)) can be negative for a wide
range of parameter combinations, thereby making all (1 – αt – βt) uncertain individuals
oppose the reform package ex ante. Because αt < 1/2, this implies that the reform does not
enjoy majority support up front, though it would be welcomed by a majority ex post (because
γ > 1/2). 11
As in Fernandez and Rodrik (1991), the presence of individual uncertainty can thus prevent
efficiency-enhancing reforms from being implemented. In particular, there are currently ex
post winners blocking the reform ex ante because they do not know that they will be among
the ex post winners.
Because individual uncertainty lies at the core of the problem, one may think that reducing
individual uncertainty by revealing winners (i.e., increasing αt to αt+1 = αt + Δαt+1, bringing it
closer to γ) would make a yes vote more likely. This turns out not to be true, opening an
interesting perspective on voter dynamics. To see this, consider how the expected value for
uncertain individuals changes with α:
10
We follow Fernandez and Rodrik (1991) and many others in assuming that a reform is more likely to be
adopted if there is a larger number of individuals in favor of it, but we use the language of majority voting for
concreteness. The model can, however, also be interpreted as describing support dynamics for reforms in non-
democratic countries. Decision rule (2) could then be interpreted in terms of joining an anti-reform protest or not
(in that case, it might be realistic to include a "protest cost").
11
Here, one should note that the Fernandez-Rodrik model assumes that it is not possible to compensate the
losers ex post. As noted by Messner and Polborn (2004, 118), this assumption is "standard (and often even
implicit) in the literature". Given the well-known difficulties that governments face in committing to future
policies, this assumption may not be unrealistic.
10
Et R | i t ,1 t S
0 . (3)
t
Therefore, a decrease in individual uncertainty brought about by the revelation of additional
winners makes individuals who remain uncertain more negative about their chances of
gaining from the reform. The reason is that in the absence of aggregate uncertainty (which is
added in the next section), increasing αt to αt+1 implies that there are Δαt+1 fewer gaining
places left for those who remain uncertain (because the revelation of reform outcomes is an
example of sampling without replacement). This makes these uncertain individuals more
pessimistic about their chances of ending up as reform winners (because the revelation of
winners deteriorates the quality of the remaining pool). When the median voter is located
within this uncertain group, he also becomes more pessimistic.
Revealing losers, in contrast, increases the expected value of the reform for those who remain
uncertain:
Et R | i t ,1 t S 0. (4)
t
At this stage, one should note that there is a wide range of values for α and β where changes
in uncertainty will not change the outcome of the vote. If the vote is initially "no", then
increases in α will only make ������������ ������������� |������ ∈ (������������ , 1 − ������������ )� more negative, and the median voter
will continue to oppose the package.
There is an intriguing possibility if the median voter initially supports the reform package. To
see this, hold βt constant at ������̅ for a moment 12 and let us investigate what happens if the
government tries to complete the reform gradually by increasing αt (i.e., revealing winners).
If the increase in α is small enough, δ will remain 1, and the median voter continues to vote
"yes", pushing the overall vote in favor. However, because of the effect captured by (3), one
can define a critical value for α (call it α*) such that if α rises above α*, the median voter
swings around, causing a rejection of the package. 13
12
The same argument applies, mutatis mutandis, to changes in βt if the median voter initially opposes reform.
However, in that case, the reform cannot be started along democratic lines.
13
The last part of this statement, of course, assumes that α* < 1/2, a condition to which we will return to in the
next section.
11
The critical value α* is thus the point at which the median voter begins to oppose a reform
that he used to support. Crossing it from below implies that the reform process stalls.
Mathematically, α* is defined by ������������ ������������� |������ ∈ ������� ∗ , 1 − ������̅ ��; thus, from (1), we can derive
* 2 1 . (5)
More formally, we can now see that if the median voter initially favors the reform (i.e., δt =
1), the total supporting fraction (given by ������������ = ������������ + �1 − ������������ − ������̅ ������������� ) will remain constant at
1 − ������̅ if α increases to an αt+1 < α*.
In this case, the revelation of Δαt+1 additional winners does not make α cross the critical value
α*. When α is increased, there are more individuals supporting the reform (because they have
now learned that they are reform winners), but the uncertain block (which also supports the
reform in this case) shrinks one-for-one with the increase in α. On balance, total support for
reform remains unaffected.
However, as more winners are revealed, α will eventually exceed α*. If this happens when α*
< 1/2 (a condition to which we return to in the next subsection), the median voter switches
sides and begins opposing the reform package that he used to support. A sudden loss of
majority support for the reforming government results.
This opens the possibility of a reform that starts well (individuals involved with reformed
firms/sectors turn out to be better off), but as individual uncertainty continues to decrease, the
"sampling without replacement" effect captured by (3) eventually causes the median voter to
swing against the package. Thus, the model produces support dynamics that are very much
like the practical experiences of many reformist governments (as noted above).
Hence, once one accounts for individual uncertainty and the "sampling without replacement"
effect, the conventional sequencing wisdom that one should begin by reforming firms or
sectors that are most likely to benefit from reform (to boost public support) is challenged.
This conventional wisdom, to which we adhered before analyzing a formal model, is
expressed, for example, in Roland (1994, 1164), who writes that "if the best firms get
privatized first [...] the likelihood of a successful economic performance will be higher. Initial
economic successes for privatized firms will enhance support for privatization and build
constituencies for further reforms". Similarly, The Economist of March 24, 2012, writes
about the opposition the Cuban reform process is currently experiencing and states that to
12
increase public support for the reform process, "Raúl Castro urgently needs to create some
winners" (p. 20). However, this line of reasoning only seems to consider aggregate
uncertainty and overlooks individual uncertainty and the accompanying "sampling without
replacement" effect. By allowing for these elements, the present paper points out that Raúl
Castro may very well decrease support for his reforms even further by revealing winners.
With Aggregate Uncertainty
To capture the reasoning underlying the aforementioned conventional wisdom, which relies
upon the existence of aggregate uncertainty, we next investigate what happens when we add
such uncertainty to the model. In that case, voters also do not know the true value of γ (the
fraction of individuals who will benefit from the reform ex post) with certainty. Instead, the
public has beliefs about γ. Let us use γt to indicate the beginning of period t estimate of γ.
Any valuable information that becomes available during period t will lead to an updated
estimate, γt+1 (where updating occurs via the application of Bayes' rule).
Voters hold a prior belief about γ that is given by a Beta(α,β) distribution. This distribution is
a natural choice because it is the conjugate prior of the binomial distribution underlying the
present model. Assuming a symmetric loss function (for example, the traditional quadratic
loss function underlying OLS, which also has the convenient property that the point estimate
for gamma summarizes all relevant information and therefore becomes the sole object of
interest) then implies that for α = αt and β = βt, the time t estimate of γ equals
t
ˆt
. (6)
t t
Expression (6) is intuitive: (αt + βt) represents the total sample of outcomes we have gathered
so far, whereas αt is the fraction of winners in this sample relative to the unit interval. The
ratio of these two is the time t estimate of γ.
After revealing Δαt+1 additional winners and Δβt+1 additional losers during period t, Bayes'
rule implies that the posterior estimate of γ, which is the prior at the beginning of period t+1,
equals (see, e.g., Kvam and Vidakovic (2007, chapter 4))
t t 1
t
ˆ
. (7)
t t 1 t t 1
13
From equations (6) and (7), one can confirm the intuitive notion that the application of Bayes'
rule leads to an upward revision of the expected fraction of reform beneficiaries (γ) when
Δαt+1 additional winners are revealed (and vice versa after the revelation of losers). Because
this implies that beliefs about γ can change over time, the critical value for α (α*) also
becomes time varying. In particular, after plugging (6) into (5), we obtain
*
t
t t 1 .
2ˆ (8)
∗
Now, the key question is whether we can obtain αt ≥ 1/2 before αt ≥ ������������ . If this is the case, the
government is able to reveal that the median voter is a reform winner (which happens when αt
crosses 1/2) before this pivotal voter begins opposing the reform package (which happens if
∗
and only if αt exceeds ������������ while αt < 1/2). Subsequently, the government can complete the
reform with no risk of losing majority support.
Because empirical studies such as those of Carlin and Mayer (1992), Frydman, Rapaczynski,
and Earle (1993), Marcincin and Van Wijnbergen (1997), and Gupta, Ham, and Svejnar
(2008) all present evidence that reforms start by revealing ex post winners, it is interesting to
see what our model predicts would happen if the reform follows such a selective path. 14 To
investigate this, we make the following assumption on the sequencing within the reform:
Assumption 1. Sequencing is such that the reform starts by revealing ex post winners.
The reason for the presence of this selection bias can be twofold. First, it can result from a
situation of asymmetric information in which the government knows ex ante who will benefit
and who will lose from reform (but, as in Perotti (1995), the government is unable to transmit
this information credibly to the public). 15
Especially in our privatization example, this assumption seems realistic because the
government (as the incumbent owner of the firms that are to be privatized) has inside
information on firm profitability and future policies that may benefit or harm each firm. If
this government then follows the conventional wisdom and begins by reforming the ex post
14
Roland (2008, 4) nicely summarizes this literature by noting, "The few studies on the determinants of
privatizations suggest that the more profitable firms were privatized first, which is consistent with political
economic theories of privatization where the sequencing of privatization is used to gather support for further
privatization".
15
In this sense, the government in our model is a bit like Monty Hall in the "Monty Hall problem": he knows ex
ante behind which doors the gains and losses are located. Note that the counterintuitive solution to the Monty
Hall problem follows from the fact that sampling takes place without replacement.
14
winners (which is often recommended to reformers in practice; cf. Roland 2000, 49),
Assumption 1 materializes.
Second, in light of our application to privatization, Assumption 1 can also result from the fact
that better firms tend to find buyers more rapidly (Roland, 2000, 248). This point has also
been recognized by policy makers. According to Egyptian government officials in the New
York Times of June 27, 2010, Egypt suspended its privatization program in 2009 because
"most of the likely candidates had already been either privatized or dissolved, leaving hard-
to-sell industries that were technologically outdated and overstaffed with ill-trained workers".
In the Appendix, we explore the alternative case in which the government is not able to
identify winners and losers in advance. That case is probably more relevant to trade reform
because this type of reform does not come with a natural selection process, and it is not clear
that the government knows the identity of the winners and losers up front in that setting.
Then, reform outcomes are sampled randomly from the true underlying distribution.
Crucially, the Appendix shows that the "sampling without replacement" effect continues to
be present under random sampling. This leads to two regions in the (α,β) space where the
dynamics are anomalous (i.e., favorable reform outcomes decreasing support for reform and
vice versa). More generally, the importance of the "sampling without replacement" effect is
increasing in the tightness of the prior belief on γ: the tighter the prior on γ is, the less
responsive voters' beliefs on γ are to news and the more dominant the "sampling without
replacement" effect becomes (because the latter works independently of the tightness of γ's
prior). In the limit, because the prior on γ converges on a point, the model collapses to the one
discussed in the previous subsection (without aggregate uncertainty).
Turning to the setting in which Assumption 1 holds, it is instructive to first think through
what would happen if voters do not account for the selection bias and hold a diffuse prior
belief on γ at the start of the reform (call this "time 0"). In particular, let us assume that both
α₀ and β₀ (the fractions of winners and losers whose identities are clear ex ante) are close to
zero (which minimizes the tightness of the prior). Then, Bayes' rule implies that voters’
������� /������������������ = ������������ /(������������ + ������������ )2 >
beliefs about γ are revised upward when winners are revealed (������������
0). In particular, voters’ beliefs about γ will quickly converge to 1 because voters only
observe favorable reform outcomes and erroneously think that this is the result of random
∗
sampling from the underlying true distribution of winners and losers. This implies that ������������ →
1 (cf. equation (8)), which allows the reforming government to reveal that the median voter is
15
∗
a reform winner before ������������ ≥ ������������ (provided that γ > 1/2, of course). Subsequently, the reform
can be completed with no risk of losing majority support.
Therefore, when voters have a diffuse prior belief on γ at the start of the reform and when
they do not take the selection bias into account, the government is able to complete efficient
reforms gradually by revealing winners while running no risk of losing majority support.
This case, however, imposes an unrealistically high degree of naivety on voters; they think
that the reform is sequenced in a truly random way and do not take into account that the
government (or nature; recall our discussion following Assumption 1) starts by revealing
reform winners.
Consider, therefore, the more realistic case in which the public does consider the selection
bias. Then, the revelation of additional outcomes provides no valuable information; the public
realizes that these draws do not come from the true underlying distribution, as a result of
which, Bayes' rule no longer leads to a revision of the prior belief. 16
������� remains constant at γ₀ ∀t
Consequently, agents cannot update their estimate of γ, and ������
(where γ₀ is the exogenously given belief on γ at the start of the reform). This leads to the
following results.
Proposition 1. If the public believes that the reform starts by revealing the ex post winners
3 1
and if it believes that the reform is "sufficiently efficient" (in the sense that ������
�0 ≥ 4 − 2 ������0), the
reform can still be completed gradually by revealing only winners from time 0 onwards.
∗3 1 1
Proof. From equation (8), it follows that ������
�0 ≥ 4 − 2 ������0 ⇔ �
������0 ≥ 2. Revealing only winners
∗ ∗ 1
(keeping ������������ constant at ������0) implies that �
������������ remains constant at �
������0 ≥ 2 over time. This
∗ 1
implies that the threshold �
������������ ≥ 2 ∀t, as a result of which the reforming government can
reveal that the median voter is a reform winner before this voter begins opposing the reform
1 ∗
������� ≥ 2 before ������������ > ������
(i.e., the government can push ������ ������� ).
16
The only thing that is revealed if αt is increased to αt+1, is that γ ≥ αt+1 (which was already known given that
αt+1 < 1/2, whereas voters know that the reform is efficient, i.e., γ > 1/2). However, under Assumption 1, this is
by no means informative about how many winners are located beyond 1/2. More formally, Bayes’ rule states
that ������ (������|������) = ������(������)������ (������ |������)/������(������ ), where “A” is a particular hypothesis of interest (e.g., γ > 0.6) and “B”
represents the new incoming data (∆������������+1 or, equivalently, ∆������������+1 ). When sampling is such that the winners are
revealed first, ∆������������+1 will always be equal to 0 as long as we move to an ������������+1 < ������, both conditional on
hypothesis A as well as unconditionally (remember that the latter case still conditions on voters knowing that γ >
1/2). Consequently, ������ (∆������������+1 = 0|������) = ������(∆������������+1 = 0) = 1, and Bayes’ rule implies that the posterior belief
equals the prior belief (i.e., ������ (������|������ ) = ������ (������)). In this case, beliefs are no longer revised.
16
Proposition 2. If the public believes that the reform starts by revealing the ex post winners
3 1
but if ������
�0 < 4 − 2 ������0), even reforms that are believed to be efficient (i.e., reforms for which
1
�0 > 2) can never be completed gradually by revealing only winners from time 0 onwards.
������
∗ 3 1 1
Proof. From (8), it now follows that ������
�0 < 4 − 2 ������0 ⇔ �
������0 < 2. This implies that the reform is
not believed to be "sufficiently efficient" (as defined in Proposition 1). Revealing only
winners (i.e., keeping ������������ constant at ������0) then decreases the expected value of the median
∗ ∗ 1
voter via (3). Because the constancy of ������������ again implies constancy of �
������������ (at �
������0 < 2),
∗ 1
������������ > �
������0 before ������������ > 2, and majority support is lost before the reform is completed.
Hence, those reforms on which initial prior beliefs are not sufficiently optimistic (such that
3 1
�0 < 4 − 2 ������0) can no longer be completed gradually by revealing only winners. This result
������
arises even if the reform enjoys majority support at its beginning and even if the reform is
believed to be efficient (in the sense that it is believed to generate more winners than losers,
1
i.e., ������
�0 > 2).
The intuition for what is going on is exactly as in the previous subsection: every additional
winner revealed reduces the perceived probability of ending up as a winner for those who
remain uncertain. As a result, the median voter will, at some point, begin opposing the reform
that he used to support.
Similar dynamics arise when we drop Assumption 1 and instead assume that reform
outcomes are sampled randomly from the underlying distribution (see the Appendix for a
discussion of this case). Then, the revelation of winners also implies that voters become more
enthusiastic about the reform as they revise their estimate of the aggregate fraction of winners
�) in the upward direction. However, when the prior belief on the aggregate state is
(������
sufficiently tight, the updating process in the aggregate dimension will proceed at a rather
slow pace, and the "sampling without replacement" effect will dominate. 17
17
To see how the speed of updating is inversely related to the tightness of the prior, consider two priors with an
′ ′ ′ ′ ′
identical mean estimate, ������ ������� = ������������ /(������������ + ������������ ) = ������������ /(������������ + ������������ ), where ������������ > ������������ and ������������ > ������������ . Consequently, by the
′ ′
standard formula for the variance of the Beta-distribution, ������������������������ ������ , ������������ (������ ) > ������������������
������ ( ������ ������ , ������������ ), so the prior driven by
′ ′
(������������ , ������������ ) is tighter than that driven by (������������ , ������������ ). Now consider a given ∆������������+1 (of equal size in both cases). Because
′ ′)
(������������ + ������������ > (������������ + ������������ ), equation (7) implies that this will lead to a smaller upward revision for the tighter prior
′ ′)
driven by (������������ , ������������ . This holds for other distributions as well. Intuitively, an agent with a tighter prior is more
certain that the true ������ = ������ ������� , as a result of which he revises his beliefs by less after receiving new information.
Consequently, learning will occur at a slower pace for such an agent.
17
Returning to the setup in which Assumption 1 does hold, revealing losers immediately ends
majority support.
Proposition 3. If the public believes that the reform starts by revealing the ex post winners,
1
any reform will lose majority support as soon as a loser is revealed before ������������ > 2.
The proof is intuitive and simply follows from the fact that the public expects the government
to start by revealing reform winners. If a loser appears, the public thinks that all winners have
already been revealed and that those individuals who are still uncertain about their identity
1
will all be losers. If this happens while ������������ < 2, majority support is immediately lost.
Summarizing
Fernandez and Rodrik (1991) pointed out that welfare-enhancing reforms that would enjoy
majority support ex post may not enjoy majority support ex ante because the reform winners
cannot always be identified up front.
In a way, the message of this paper is more discouraging: even welfare-enhancing reforms
that enjoy both ex ante and ex post majority support may still not come to completion
because of the learning dynamics that are triggered through the initiation of the reform
process. Revealing winners launches the "sampling without replacement" effect (as a result of
which majority support will be lost at some point if initial beliefs about the aggregate
dimension of the reform are not sufficiently optimistic), whereas revealing losers
immediately ends support. The reforming government thus finds itself seemingly trapped and
destined to lose majority support irrespective of what action it takes.
How Can the Loss-of-Support Problems Be Avoided?
Is there anything reformers can do to overcome these loss-of-support problems? The Chinese
reform experience in particular suggests that a route exists toward successful gradual reform.
After all, China also followed a more gradual path, and with quite some success. In sharp
contrast to the experiences of many Latin American and Central and Eastern European
countries, the initial Chinese reform successes seem to have only increased support for
further reforms. Obviously, the voting mechanism is absent in China (also recall footnote 10),
but reforms there could still generate dissatisfaction and opposition, which does not seem to
be the norm in China (cf. Litwack and Qian 1998; Qian, Roland and Xu, 1999, 2006). This
18
raises the question of why the experiences with gradualism have been so different across
countries.
In this respect, it is crucial to note that the Chinese gradual reform strategy differs from the
Latin American and Central and Eastern European approaches. Whereas most countries in the
latter regions tried to reform gradually along the sectoral dimension (which implies that one
firm or sector is reformed after the other; cf. our discussion of the "case-by-case" approach to
privatization in the introduction), China reformed gradually along the spatial dimension. In
particular, China first introduced market forces in 1978 in the inland province of Sichuan
(which was the first province to abolish collective agriculture and begin state-owned
enterprise reform) and in the coastal province of Guangdong in 1980.
By reforming gradually along the spatial dimension, Chinese policy makers enabled the
Chinese public to learn about the effects of new policies by looking at outcomes in reformed
regions. Of course, the citizenry will only find the information generated via the spatial
dimension useful if those regions are believed to be informative to the rest of the country.
Here, China had an advantage over many other countries. As noted by Qian, Roland, and Xu
(2006, 394), the Chinese economy is organized along territorial lines. This implies that its
regions (such as Sichuan) are rather self-contained and relatively representative of the
Chinese economy as a whole. As Démurger et al. (2002) argue, this is the result of a
conscious decision made by Mao Zedong. In addition to the two key principles of Soviet
development (common ownership and central planning), Mao added a third principle:
regional economic self-sufficiency. This principle required each region to be self-sufficient,
not only in food production but also in industrial goods. The Soviet Union did not adhere to
this principle at all; their ideology called for an organization of the country along industrial
lines with high degrees of industrial concentration (Qian and Xu 1993). Consequently, each
Soviet region was much more specialized, dependent on other regions, and less representative
of the Union as a whole.
Because of this, China had (in contrast to, for example, Russia) the possibility to start reforms
by taking informative samples of small mass (in the form of certain regions) and using them
to show the public where the gains and losses of the proposed reform were likely to occur. In
particular, the coastal Special Economic Zones were instructive to inhabitants of other coastal
regions (with approximately one-third of the total Chinese population living near the coast),
whereas Sichuan fulfilled a similar role for inland areas. This strategy reduces individual
19
uncertainty about the distribution of gains and losses (the root of all problems), but - crucially
- insulates the main part of the country from the "sampling without replacement" effect. 18
For the main part of the country, this sampling strategy does not affect the distribution from
which future sampling will take place because it is a form of sampling from a different,
smaller urn (where the distribution of balls in this smaller urn is taken randomly from the
large urn, the latter representing the main part of the country, which remains untouched in
this sampling strategy).
An alternative way to think about this is by conceiving a model that has two dimensions: 19 a
sectoral one (as in our model presented above) and a spatial one. For a country that is
perfectly diversified, these two dimensions are orthogonal to each other, as a result of which
reforming gradually along the spatial dimension does not trigger the "sampling without
replacement" effect (which exists along the sectoral dimension 20). When there is some
correlation between the two dimensions (as is the case when certain sectors are concentrated
in particular areas), orthogonality no longer holds, and sampling without replacement begins
to play a role again. In the extreme situation where there is a perfect correlation between
"sectors" and "space", the two dimensions merge and we are back in our original one-
dimensional setup where any gradual reform strategy launches the counterintuitive support
dynamics.
For this reason, a spatial reform strategy would not have been a viable option for Russia: over
there, reform outcomes in one region were not only less relevant to those in other regions
(due to the higher degree of spatial heterogeneity) but the higher degree of industrial
concentration would have also given a "sectoral flavor" to any spatial reform strategy. After
all, if certain sectors are concentrated in certain areas, reforming one area is equivalent to
reforming one sector. Then, "sampling without replacement" would re-enter the story. 21
18
Obviously, this effect will be present within the reform region itself, but if that is only a region of relatively
small mass, then the reform runs no risk of losing country-wide majority support.
19
Thanks to our referees for putting us on track for this interpretation. Formally developing such a two-
dimensional model goes beyond the scope of this paper but could be an interesting avenue for future research.
20
The "sampling without replacement" effect exists due to heterogeneity (the existence of winners and losers),
but in a country that is perfectly diversified, all regions are alike in terms of economic structure (each district is
a miniature version of the country as a whole), so there is no heterogeneity along the spatial dimension.
21
As Dani Rodrik pointed out to us, the spatial strategy could be applied to reforms that entail only one
particular sector ("sector X"). The "sampling without replacement" effect would then operate within sector X
(because cross-sectoral heterogeneity no longer plays a role). In the case of one-sector reforms, governments
could get around this effect by first transforming a region of small mass that contains a representative sample of
sector X firms into a Special Economic Zone. Subsequently, the sector X firms inside the Zone could be used to
reduce individual uncertainty by giving other firms in the sector outside the Zone an idea of what the reform
20
For the spatial strategy to work, it is crucial that agents who know that they will be among the
winners (i.e., those with ������ < ������������ ) cannot self-select into the reformed regions because doing so
would imply that the zone becomes less instructive to the relevant other parts of the country.
To continue the urn analogy, the smaller urn needs to be isolated from the larger one.
Interestingly, this is precisely what the Chinese "hukou" system (which restricts the mobility
of citizens within China) achieves. Therefore, although one could debate the fairness of this
system (just like one could debate the fairness of mobility restrictions between different
countries), it does seem to play an economic role in the Chinese reform process.
Finally, this view of Special Economic Zones shines a new light on their raison d'être. In a
static setup, Hamilton and Svensson (1982) show that Special Economic Zones are actually
welfare decreasing in a second-best world where the suboptimal regime continues to apply
outside the zone. This raises the question of why governments bother installing them in the
first place. In this respect, the present paper argues that Special Economic Zones could
produce large dynamic gains because they can facilitate the implementation of reforms that
bring the entire country closer to the first-best.
Our results thus indicate that countries can ease their reform process if they have the
possibility to begin the reform by first implementing it in a region of small mass that is
instructive to the rest of the country (because such an action decreases individual
uncertainty). In this sense, there is an important difference between sectoral and spatial
gradualism. This difference may be key as to why the gradual reform strategy has worked for
China but has worked much less for many other countries.
Conclusion
In this paper, we have modeled the learning process surrounding economic reforms when
there is both aggregate and individual uncertainty. The process of revealing reform outcomes
entails sampling without replacement. We have shown that this implies that the revelation of
winners early in the reform process makes those who remain uncertain about whether they
will gain or lose from reform more pessimistic about their chances of ending up as reform
winners. This channel can be so strong that it can even induce the median voter to start
opposing a reform that he used to support - in which case the reforming government loses
majority support. As a result, even reforms that enjoy both ex ante and ex post majority
would do to them. The Special Economic Zones in Malaysia and Mauritius seem to have fulfilled such a role
successfully for the electronics and apparel sectors, respectively (Auty 2011).
21
support may still not come to completion. The conditions under which such a destructive
interaction between rational learning and political support will occur are relatively mild. As
soon as one combines the presence of individual uncertainty with rational belief updating, the
"sampling without replacement" effect kicks in.
This situation challenges the conventional wisdom that sequencing should be such that
favorable reform outcomes are revealed first. Instead, our model illustrates that a reform
strategy based on revealing winners first may backfire. The reason is that such an approach
leads to a deterioration in the quality of the remaining pool, triggering reform fatigue in spite
of the successes of those firms that have already been reformed. Strikingly, this is consistent
with the puzzling experiences that many reformers have had in practice. There are numerous
examples of reforms that began while enjoying majority support but subsequently lost this
support even though they were progressing in a successful way.
We have also outlined a strategy that is able to overcome the problems related to the learning
process. In particular, if a country happens to contain individual regions that are instructive to
the rest of the country, the "sampling without replacement" effect can be avoided by
reforming gradually along the spatial (rather than along the sectoral) dimension. This could
explain the success of the “Special Economic Zone” approach to reforms taken by China.
On a more general level, this paper has developed a theory of agents who are learning from
realizations that are sampled without replacement, which may have other applications as well.
In many environments, the distribution from which future sampling will take place is not
static and time invariant; it changes over time, often as a result of past sampling actions (the
process of authorities revealing the identity of good and bad banks in a financial crisis is a
clear example). From the so-called "Monty Hall problem", we know that this can give rise to
counterintuitive dynamics that are not easy to understand without formalism (whereas a
formal model clarifies things significantly). Applying the concepts developed in this paper to
problems that entail sampling without replacement might therefore be a fruitful avenue for
further research. 22
22
In this respect, it was pointed out to us that the mechanisms underlying this paper also relate to those in
Konrad (2004, although he does not establish the link to sampling without replacement, nor does he allow for
aggregate uncertainty). However, that paper addresses strategic rather than dynamic issues and shows that a
party that is campaigning to implement a particular reform may obtain an incentive to point out ex ante who will
be a reform loser (a phenomenon that Konrad refers to as "inverse campaigning").
22
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26
Appendix
Although there are certain reform types (such as privatization) for which the government is
likely to have an ex ante idea about where the gains and losses of the reform will be located,
there are also cases in which the reforming government does not have such information. This
Appendix therefore explores the properties of our model when we drop the assumption that
the reform is sequenced in a non-random, selective way.
Suppose that the government cannot identify the reform winners and losers up front. In
addition, we assume that there is no natural selection process that could lead to a non-random
sequencing of events. Consequently, reform outcomes are sampled randomly from the true
distribution. Moreover, we assume that the public believes that these outcomes are sampled
randomly, as a result of which they perceive new observations to be informative and apply
Bayes' rule to update their estimate of γ (the aggregate fraction of winners) in response to
new information.
Because we feel that this case may deserve a closer study in its own right, we leave a full
analysis for future work, but we present some main results in this Appendix. In particular, we
show that the "sampling without replacement" effect discussed in the main text continues to
in this alternative setting.
The core of the model is unaffected, and the critical value for α (α*) is still given by
t
*
t
2 t 1 . (A.9)
t t
Using expression (A.1), one can analyze how the distance between ������������ (the fraction of sure-
∗
winners) and ������������ (the cut-off level for ������������ above which the median voter starts opposing the
reform) varies with the revelation of additional winners and losers. In particular, it holds that
*
t
t
2t
1 . (A.10)
t t t
2
∗
Here, the first term shows that the revelation of winners pushes up ������������ (because it leads to an
������� through application of Bayes'
upward revision of the expected fraction of reform winners ������
rule), whereas the second term ("−1") indicates that the revelation of winners simultaneously
makes those who remain uncertain more pessimistic about their individual chances of ending
27
up winners. In particular, this term reflects the fact that revealing a reform outcome is an
example of sampling without replacement. From (A.2), one can derive that as long as
t 2t t , (A.11)
the "sampling without replacement" effect dominates. Under condition (A.3), the public's
estimate of γ increases less than one-for-one with ������������ (mathematically,
*
t ˆt / t 1 ), and the median voter becomes more pessimistic as
t / t 0
favorable reform outcomes are increasingly revealed. Hence, under this condition, the
������� that is insufficient to compensate
revelation of additional winners produces an increase in ������
for the fact that sampling occurs without replacement.
Similarly,
*
t
t
2 t
1 (A.12)
t t t
2
captures the same two effects for the revelation of losers. In this case, the median voter
∗
becomes more optimistic when additional losers are revealed (i.e., ������(������������ − ������������ )/������������������ > 0) as
long as
t 2 t t . (A.13)
Conditions (A.3) and (A.5) yield two regions of (α,β) combinations, displayed as the shaded
areas in Figure 2, where one can characterize the learning dynamics as "anomalous". That is,
in region A3, good reform outcomes decrease support for the reform, whereas the revelation
of bad reform outcomes increases support for reform in region A5.
Now, one can ask whether the government is able to complete the reform without a loss of
majority support along the way. Because the sequencing of the reform is random in this case
(because the government (or nature) is no longer able to select the winners up front), it is no
longer possible to analyze this question analytically. Instead, one would have to simulate the
reform process, and the answer to the question would depend upon the amount of time a
typical simulation spends in the shaded areas of the state space. Because we feel that this
issue deserves a full discussion in its own right, we leave this for future work.
28
The main point to take away from this Appendix is that the "sampling without replacement"
effect continues to be present when reform outcomes are revealed in a truly random fashion.
This leads to two regions in the (α,β) space where the support dynamics can be characterized
as "anomalous".
Figure 2. Regions where favorable reform outcomes decrease support for the reform (A3) and
vice versa (A5)
29