Political Economy of Development
Stockholm Doctoral Course Program in Economics Development Economics II
Lecture 5
Political Economy of Development
Masayuki Kudamatsu
IIES, Stockholm University Big question today How does politics
affect development?
More specific questions today
1. Why do welfare-enhancing reforms
often get stalled?
2. Is democracy good for
development?
3. What makes democracy work?
4. What makes autocracy work? reforms often get stalled?
Structural adjustment reforms in
- 1980s Streamlining procedures of setting
- up a firm (cf. Djankov et al. 2003) Formalizing property rights >Anti-corruption meas
- compensation for losers
As welfare (total surplus) increases,
- winners still better off
Once reform enacted, winners lose
- incentive for compensation
⇒ Winners’ promise not credible Reform gets stalled because...
- Losers constitute a majority
- Even if losers are a minority:
(1) Small group size solves collective
action problem to lobby govt (Olson 1965)
(2) Individuals uncertain whether to win
or lose (Fernandez & Rodrik 1991)- Uncertainty over whether losers will have political power
(Jain & Mukand 2003)
- (Majumdar
These papers look at only one
- policy reform In reality, there are many policies to
- reform, whose feasibility may depend on each other Caselli and Gennaioli (2008) tackle
- this issue
(2008)
Research questions: Deregulation of entry
- Improving contract enforcement in
- credit market (financial reform) Both increase entry and thus >welfare But politically feasi
Entry deregulation & financial
- reform:
Perhaps two of the most important
- reforms for development
Aghion et al. (2008) and Burgess &
- Pande (2005) for impact evaluations
Only analyzed separately before
- Provide a 1st example of
- endogenous (ie. market-driven) compensation of losers from a
Endowment
A continuum (of measure 1) of
- agents Each agent: endowed w/ 1 unit of
- labor & managerial talent θ Fraction λ: θ = 1 (talented)
- − λ: θ = θ(≤ 1)
Fraction 1
- (untalented)
Fraction η: also endowed w/ a firm
- (incumbent)
e.g. Family-owned firm
Fraction 1 − η: (outsiders)
- None own wealth
- ⇒ Financial reform matters
If agent w/ talent θ owns a firm and
- hires l labor (incl. his own):
1 −α
y = θl α: degree of decreasing return to
- scale
See sec. V.B. for constant return to
- scale
Outsiders can buy a firm from an
- incumbent by paying price p Each agent can run at most 1 firm
⇒ Talented incumbents cannot buy a
firm from untalented incumbents
Main results would still hold if
- otherwise (p. 1227)
- ⇒
No market for managers
Incumbent cannot hire talented agent as manager of their firm Model: Policy variable 1
ε(≥ k ): cost of setting up a firm for outsiders
- k (> 0): technologically determined fixed cost
- If k = 0, no role of market for control (pp. 1206-7)
- ε − k : degree of entry regulation
- Bureaucratic setup costs (incl. bribes) cf. Djankov et al. 2003
φ: fraction of borrower’s profit that lenders can recover in case of default Quality of financial legislation /
- contract enforcement
As no agents has assets, they need • to borrow for setting up / buying a firm ⇒ φ ↑: financial reform
Credit supply: perfectly elastic w/
Model: payoffs
Workers: w
- Incumbents who don’t sell: π + w
- (profit plus his own wage) Incumbents who sell: p + w
- Outsiders who set up a firm: >π + w − ε Outsiders who buy a firm: π + w &minu
1. Outsiders: decide whether to
become a firm owner (either by paying setup cost ε or paying p to an incumbent) by borrowing money
2. Firm owners: hire workers by
paying wage w
3. Production takes place
4. Borrowers: decide whether or not to Assumptions 1. η < λ < 1
To focus on whether talented
- outsiders can set up a firm
α−1
= αλ
2. k ⇒ At first best, no untalented agent runs a firm
Main results would still hold if α−1
αλ > k > 0 (p. 1206)
Characterize equilibrium choice of
- outsiders by:
f : total # of firms (entrepreneurship) s
: share of firms run by talented agents (meritocracy )
= η and s = λ Initially we have f
- First best: f = λ and s = 1 (Lemma
- 1)
Analysis: How to proceed (cont.)
1. Derive payoffs as functions of (f , s)
2. Analyze how (f , s) change with ε
φ and
3. Identify winners and losers from
reforms ( ε ↓ and φ ↑)
⇒ Assess political feasibility of
reforms (by assuming the more winners, the more feasible) Analysis 1: equilibrium payoffs
given w
clearing c. Obtain π as a function of exog. variables & (f , s) Analysis 1a: labor market
- 1 −α
Firm owner solves:
max θl − wl
l
By FOC, the optimal labor demand
- by firm owner of talent θ is: � (1 − α)θ � 1
- ∗ ∗
- ∂π H
- ∂π H
- α
- As a function of w , minimized at
- w = 1 − α α {f ,s} max w (f , s) = (1 − α)λ < 1 − α
- ⇒
- α
- Max w (f , s) = (1 − α)λ could be
- larger than this λ is large Which happens if
- We’ll see in such a case no one will
- set up a firm and thus wage does not reach its maximum
- a. Set up a firm by paying ε
- borrow How much can they bor
- Default: π − φπ
- ⇒ ≤ φπ
− L = 0 if L ≤ φπ
L- φπ − L < 0 if L > φπ •
- want to set up a firm if π(f , s) ≥ ε
- can set up a firm if φπ(f , s) ≥ ε
- encourage entry
- All the results would still hold
- otherwise
- ⇒ If some untalented enter, all
- enter after all talented entered (w/ no firm sale)
- Entry iff φπ
- At least some talented outsiders set up new firms
- No Entry iff
No outsider sets up a firm
- If larger than the set-up cost ε, talented agents enter the market ( ⇒ f ↑, s ↑) until π
- Untalented outsiders won’t set up a
- firm (lemma 2)
- L
- L
But π > 0, ∀f , s (by α > 0)
- ≥ π (f , s) want to sell if p
- H
- want to buy if π (f , s) ≥ p H • can buy if p ≤ φπ (f , s)
- Financial reform encourages the sale of a firm from untalented to talented
- Consistent w/ evidence by Rossi & Volpin (2004)
- p: determined by bargaining power btw. seller & buyer
- For much of analysis, the exact p does not matter (fn. 17)
- No Sales if φ < g
- NO untalented incumbents sell
- No Entry if φπ H
- Entry otherwise (by Proposition 1)
- All Sell if
- ALL untalented incumbents sell
- No Entry if
φπ
H - Entry otherwise
- sells
- condition for sale as long as φ ≥ g:
- Transition from φ < g to φ ≥ g: s jumps up to 1
- This change would be smooth if
- continuous θ (p.1233)
- φ ↑ or ε ↓ ⇒ s ↑
- Djankov & Murrell 2002
- ε ↑⇒ f ↓
- Klapper, Laeven, & Rajan 2004
- Fisman & Sarria-Allende 2004 >φ ↑ may redu
- ?
- from the two reforms? Assumption 3:
- In the status quo ( ε , φ ), the
- equilibrium is No Entry No Sale
- Outsiders: always win (Prop 4
• Their payoff: at least w (f , s)
- Talented incumbents: always lose (Prop 4(ii))
- Both φ ↑ & ε ↓ erode π H
- Maximum wage (w
- For φ < g, wage cannot be large
- enough to compensate profit loss
For φ ≥ g, price of firm ↓
- H >
- constant at w (η, 1) while the firm price increases Entry equilibrium: wage goes up
- with φ via f ↑ while the firm price is
- induces entry before All Sell equilibrium achieved In this case, untalented incumbents’
- payoff goes down with φ ↑ due to profit erosion
- endogenously compensated by market for control
- run by more talented By selling firms to talented,
- untalented incumbents share the benefit of financial reform
- to support financial reform w/ higher ε ⇐ Because higher entry barrier kills the profit-reducing effect of financial reform
- deregulation
- reform
- Now untalented incumbents have
- become workers supporting the reform
- incorporates political-economy But perhaps naive to assume that
- political feasibility goes up with # of supports What’s the role of political
- institutions?
- important political institutions Development assistance >practitioners: often advocate democracy as a means to good governance # of democracies: ↑ recently (Fi
- policy-makers are chosen in a competitive popular election
- treats different aspects of democracy as
- (recently updated by Cheibub et al. 2010)
- which political regime can achieve higher growth cf. Przeworski & Limongi (1993) for an early literature survey Acemoglu et al. (2008) provide
- three stylized facts
- 1. Democracy ⇒ Development
- 1900-2000 (Fig.4)
- 1. Very long-run effect of democracy on
- Positive cross-sectionally
- Zero for changes after WWII (Besley
- & Kudamatsu 2006, Ross 2006)
- Positive cross-sectionally • Zero for changes after WWII, if years • of schooling used (Acemoglu et al. 2005) Positive for changes after WWII or
1865, if enrollment ratio used
- education, emergence of middle
class, etc. (Lipset 1959)
transitory negative income shock(Brucker & Ciccone 2011)
- cross-counry micro panel data on survival of a woman’s babies to
- Conflict of interest
- among citizens
- Conflict of interest
- between govt & citizens
- Firm managers and Workers • Firm managers prefer
- Low tax rate
- Entry barrier to keep wages low
- Workers prefer >High tax rate for redistribution
- Tax ↑ ⇒ Investment ↓ ⇒ Short-run growth ↓ ↑ ⇒ Innovation ↓ • Entry barrier ⇒ Long-run growth ↓
- Tax ↑ ⇒ Investment ↓ ⇒ Short-run growth ↓ ↑ ⇒ Innovation ↓ • Entry barrier ⇒ Long-run growth ↓
- Innovation
- Democracy: good for growth in >sectors where innovation is more important than capital accumulation ⇒ Aghion et al. (2008) provide evidence consistent with this Theory uncovers heteroge
- contest Citizens can replace incompetent >leaders w/ (potentially) better ones ⇒ Incentives for leaders to behave well So democracy is always g
- autocracy (Fig.7)
- autocracy (Fig.7) Jones & Olken (2005): Natural
- death of a leader ⇒ Changes in growth in autocracy, but not in democracy
- may intensify de facto political power to nullify de jure political power of poor ⇒ Regime change may not be followed by policy change
- What makes democracy work?
- What makes autocracy work?
- Competitive election per se may not bring benefits to citizens
- What institutions are complementary to elections?
- Literature has so far identified:
- Free media (or information provision)
Reservation of political office
- Enfranchisement
- punish incumbents who chose wrong policies Unless citizens observe what policy
- is chosen, however, they won’t be able to punish Role of media crucial to make
- politicians accountable in
- empirically show this complementary role of media (or information provision in general)
newspaper circulation in India
Ferraz & Finan (2008) for corruption- audit in Brazil Enikolopov, Petrova, & Zhuravskaya
- (2011) for independent media in Russia
- policy-makers cannot commit to electoral platforms Disadvantaged groups (women,
- minority ethnic groups, etc.) tend to be underrepresented in democratic politics
- by reserving political office to disadvantaged groups
- randomly chosen in a state: only women can become municipality prime minister (Pradhan) By Constitution, some seats in state • legislature reserved for scheduled castes (SC) and scheduled tribes (ST), and seat share should equal to
- empirically show that reservation for women increases adoption of policies cared by women Pande (2003) empirically shows
- reservation for SC and ST increase redistribution to them
- extension leads to policy change Before WWII, suffrage often first
- given to men, then to women Women more concerned on child
- health than men Miller (2008) shows enfranchising
- women reduced child mortality in
- have universal suffrage In reality, poor people are effectively
- barred from voting
candidate’s name on the ballot
Poll taxes, literacy test in US South- until 1960s (cf. Besley, Persson, & Sturm 2010)
- be “de facto” enfranchisement Fujiwara (2010) estimates its
- impact in Brazil
- Using RD design, Fujiwara (2010) finds that due to electronic vot># of invalid votes ↓
- public health care spending ↑
- LBW for uneducated mothers ↓
- limit
- the past (e.g. Latin America)
- Brazilian mayors who cannot run for re-election due to term limit are more corrupt
- the votes of their workers in exchange for money, favors, or policies from politicians
- century Chile until 1958
- No secret ballot in these cases
- Ballots have to be obtained from >candidates Voter’s decision can be induced from
- choice unobservable to landlords Landlords then cannot fire tenants
- who voted against their will Baland & Robinson (2008) provide
- such evidence in Chile: landlord party’s vote share ↓ after secret ballot introduced in 1958
- autocracy
- states, etc.
- Thailand, Fiji, Guinea, Honduras, • Mali, Guinea-Bissau, Egypt
- section 2) for a literature review Best paper in this literature so
- Extracting enormous rents from power
Personal wealth equivalent of
country’s foreign debt- Extensive & very inefficient redistribution
- Buy crops from farmers for way below world price
- Bloated bureaucracy
- Active support from sizable share of
- economy explain these three stylized facts?
- citizens of mass 1 Proportion π
- A : group A; the rest
- impossible to change (e.g. skin color)
- t
- ω = 0) a A A t if engage in activity a (z
- ω − θ if activity b (z = 1) • t b B
- ω if engage in activity b (z = 0) • b B B t t
ω − θ if activity a (z = 1)
- i θ (i ∈ {A, B}): comparative adv.
- e.g. tree crops (cocoa etc.), ethnic
- Tax on each activity: τ
- Patronage to each group: η
- S a A a t
- z (ω − θ − τ )
- R(η ) � �� � t
- Group B citizens
- z
- R(η
- t S a t
- τ [π z + (1 − π )(1 − z )]
- δ: discount factor for both group
- S t
- t = S t w/ prob. γ
- 1 t S t
- t t
- 1 t S S t t
- Uncertainty of leadership succession
- in autocracy
- 1 S t
- 1 S t
- otherwise steal more (3): Why not leader seeks sup
- payoff-relevant state variable S &
- such as trigger strategy (see sec 3.1)
B
- Group A citizens:
- A S A A
- Case of S = B can all be analyzed
- symmetrically
- citizens in state S
- in state S A B
- continuation value
- A a Aa a A Ab
- Aa B Ab B Aa
- Ab B Aa
- τ τ
- group A
- If s
- R(η
- δγ
- If s = 0 (oust)
- δγ
- (1 − π
- δγ
- τ
- τ
- τ
- τ
- supported
∗ α
l (θ) = w
Analysis 1b: labor market (cont.)
Labor market clearing:
= fsl (1) + f (1 − s)l (θ)
1 � 1 − α � 1 α α 1 = f (s + (1 − s)θ ) w
⇒ Equilibrium wage: 1 α α α
w (f , s) = (1 − α)f [s + (1 − s)θ ] Analysis 1c: profit function
To obtain profit function
1 ∗ −α ∗
π(θ) = θl (θ) − w(f , s)l (θ)
∗
we also need expression for l (θ) optimal labor input
l
∗
(θ) = � [(1 − α)θ] w (f , s) � 1 α
= [(1 − α)θ] 1 α
[(1 − α)f
α
[s + (1 − s)θ 1 α ]
α
] 1 α =
θ 1 α f [s + (1 − s)θ 1 α ] Analysis 1c: profit function (cont.)
π(θ) = θl
∗
(θ)
1 −α
− w(f , s)l
∗
(θ) =
θ ∗ θ 1 −α α [f [s + (1 − s)θ 1 α ]]
1 −α
− (1 − α)f
α
[s + (1 − s)θ 1 α ]
α
θ 1 α f [s + (1 − s)θ 1 α ] =
αθ 1 α
Analysis 1c: profit function (cont.)
For talented firm owners
H α−1 α−1
π (f , s) ≡ αf [s + (1 − s) g ] For untalented firm owners
L H
π (f , s) ≡ π (f , s)
g
where α 1
g ≡ θ (≤ 1)
< 0:
H
∂π L (f ,s) ∂s
< 0,
(f ,s) ∂s
< 0: ⇐ More firms push up wage
∂π L (f ,s) ∂f
< 0,
(f ,s) ∂f
(f , s)
(f , s) ≡ gπ
Analysis 1c: profit function (cont.)
L
π
α−1
[s + (1 − s)g]
α−1
(f , s) ≡ αf
H
π
As f or s goes up:
H H α (1−α) 1−α
π (f , s) + w(f , s) decreases
π (f , s) = [ ]
w (f ,s)
Talented incumbents prefer lower f , s if they don’t sell Untalented incumbent’s payoff (See Proof of Proposition 3)
As f or s goes up:
L α π (f , s) + w(f , s) is...
Minimized at w (f , s) = (1 − α)g
An outsider’s decision to
paying p
Either way, an outsider needs to
Let L be amount of loan, π profit Repay: π − L
Repay iff L Lenders’ profit
⇒ Maximum loan: φπ See fn 7 for what if wage can be • Analysis 2a: entry
Outsiders:
If ⇒ φ < 1, credit constraint (want to own a firm, but cannot borrow for it)
Deregulation & financial reform both
Lemma 2: No untalented outsiders set up a firm under assumption 2 (ie.
α−1
k = αλ ) This simplifies analysis below
π > π
talented should have already entered
L
π : largest when 1st untalented
L ⇒ If such π is smaller than ε/φ, Proof of Lemma 2 (cont.)
λ
L
φπ (η + λ(1 − η), ) η + λ(1 − η)
λ
H
≤ π (η + λ(1 − η), ) η + λ(1 − η) � � α−1
λ + η(1 − λ)g
α−1
= α(η + λ(1 − η)) η + λ(1 − η)
α−1
= α[λ + η(1 − λ)g]
α−1
< αλ = k (by Assumption 2) Proposition 1
Assume no market for control. The unique equilibrium is:
H
(η, λ) ≥ ε
φπ
H
(η, λ) < ε
φπ
H
(η, λ): Amount of money talented agents can borrow if no one sets up a firm in the equilibrium
H
(f , s) goes down to ε. Corollary 1
Without market for control, ε ↓ or φ ↑ ⇒ Both f & s: ↑
⇒ # of talented outsiders setting up a firm ↑ ⇒ f ↑ & s ↑
1st best cannot be achieved
1st best: no untalented owns a firm
π : lowest at ε = k , φ = 1
Untalented incumbents:
Talented outsiders:
⇒ Transaction takes place if L H
π (f , s) ≤ p ≤ φπ (f , s) ⇐⇒ φ ≥ g Talented incumbents won’t sell
If market for control exists, the unique equilibrium is
(η, λ) < ε
φ ≥ g
(η, 1) < ε
φ ε g
1 k φ
= ε/π
H
(η, 1) φ
= ε/π
H
(η, λ)
Entry No sales Entry All sell
No entry All sell
No entry
No sales Proposition 2 (cont.)
Why all sell, not some sell? One more untalented incumbent
⇒ Labor demand ↑ (talented demand
more)
H ⇒ ↑, π ↓
Wage But this does not affect the
If φ does not cross the φ = g line, ε ↓ or φ ↑ ⇒ Both f & s: ↑
H ⇒ π (f , s) goes down
⇒ Fewer talented agents set up a firm
Consistent w/ empirical findings
(& new empirical implications)Who are the winners and losers
more than they increase wage
(λ, 1)) at 1st-best is not large enough to compensate profit loss
Can untalented incumbents be winners
Proposition 4 (iii)
Untalented incumbents’ payoff: Always ↓ by deregulation
where ε ∈ [k , π ˜ (η, 1))
↑ by financial reform if ε > ˜ ε Why untalented incumbents’ payoff goes up with φ ↑?
Once All Sell equilibrium achieved, their
H
payoff: w (f , 1) + φπ (f , 1) No Entry equilibrium: wage
Untalented incumbents:
Welfare gain by financial reform: firms
Untalented incumbents: more likely
⇒ To enact financial reform, raising ε
is a good idea! Optimal sequence of reform can then be
(section IV.C)
First, financial reform without entry
so untalented incumbents support the
Then entry deregulation
Democracy: perhaps most
Figure 1 (Besley 2006, p. 5)
What is democracy, BTW?
Definition in this lecture: A political system in which
Digression: Democracy datasets
Polity IV or Freedom House
substitutes
Przeworski et al. (2000)
treats different aspects of democracy as complements cf. Munck and Verkuilen (2002) for
2-1. Evidence
Large social science literature on
2-1 Evidence (cont.)
democratic (Fig.2)
Figure 2 (Acemoglu et al. 2008, p. 809)
2-1 Evidence (cont.)
democratic (Fig.2) This could be either due to
2. Development ⇒ Democracy 3. 3rd Factor ⇒ Development & Democracy
2-1 Evidence (cont.)
income and changes in democracy in 20th century
1975-1990 (Fig.3)
Figure 4, 1900-2000 (Acemoglu et al. 2008, p. 812)
2-1 Evidence (cont.)
changes in income and changes in democracy in the very long run: 1500-2000 (Fig.5) Figure 5, 1500-2000 (Acemoglu et al. 2008, p. 832)
2-1 Evidence (cont.)
run: 1500-2000 (Fig.5) This could be either due to
development
on democracy
3. 3rd factor driving both changes
2-1 Evidence (cont.)
Correlation with health
Correlation with education
2-1 Evidence (cont.)
Very difficult to identify causal effect of democracy Democracy: endogenous
Kudamatsu (2012): use
2-2 Beyond simple comparison
4 reasons for why simple comparison is fruitless
a. Representation theory of politics⇒ Heterogenous treatment effect
b. Accountability theory of politics
⇒ Complementary institutions to make
democracy work c. One more stylized fact⇒ Autocracy: highly heterogenous Digression: 2 views on politics
Representation
cf. Persson & Tabellini (2000, ch. 3 & 5)
Accountability
cf. Persson & Tabellini (2000, ch. 4),
Besley (2006, ch. 3)
2-2a Representation perspective
Acemoglu (2008)’s model nicely summarizes this perspective for the impact on growthAutocracy: Firm managers decide policies •
1. Tax: low ⇒ Short-run growth: high
2. Entry barrier: high ⇒ Long-run growth: low
Democracy: Workers decide policies •
1. Tax: high
⇒ Short-run growth: low
2. Entry barrier: low
⇒ Long-run growth: high Impact of democracy on growth has
two channels
Investment
2-2b Accountability perspective
Democracy: regularized leadership
This argument makes (at least) 3
implicit assumptions
1. Voters know what leaders did ⇒ w/o free media, this is unlikely
2. Voters behave as one agent
⇒ w/ conflict of interest among
voters, this is unlikely3. Challenger is better than bad-behaving incumbent
⇒ w/o complementary institutions, democracy won’t work
2-2c One more stylized fact
More volatile economic growth in autocracy than in democracy Performance varies a lot more for
2-2c One more stylized fact
More volatile economic growth in autocracy than in democracy Performance varies a lot more for
⇒ Autocracy appears to be VERY heterogeneous ⇒ Not an ideal control group to estimate the impact of democracy
2-2d de facto political power
Acemoglu & Robinson (2008): Rich
More fruitful questions to ask:
3-1 Free Media
Political agency model: citizens
3-1 Free Media (cont.)
Quite a few papers by now
Besley & Burgess (2002) for
3-2 Political Reservation
Citizen-candidate model:
⇒ Their preferred policies won’t be
3-2 Political Reservation (cont.)
India has attempted to correct this
In 1992, 1/3 of rural municipalities
3-2 Political Reservation (cont.)
Chattopadhyay & Duflo (2004)
3-3 Franchise extension
Median voter theorem: suffrage
3-3 Franchise extension (cont.)
Today, all democratic countries
Illiterate people cannot write a
The following pictures are taken from Figures 1 and 2 of
Fujiwara (2010)Before
After
If you enter correct candidate # ...
If you enter wrong candidate # ...
3-4 Term limit
Some democracies impose term
Often due to the nasty dictatorship in
Ferraz & Finan (2011) show those
3-5 Secret Ballot
In agrarian society, landlords supply
Britain, Germany, France in 19th
Some developing countries: still
China, Cuba, North Korea, many Gulf
Military coups: still relevant
See Besley & Kudamatsu (2007,
Research question
What characteristics of autocracy &
A continuum of infinitely-lived
group B
Group identity: observable &
∈ {A, B} in Leader of group S
power (government) Model: technology & citizens’ actions a A
Group A:
Group B:
network (Banerjee & Munshi 2004, Model: leader S
t
’s actions (policies)
S t a t
, τ
S t b t
⇐ No state capacity to tax income
S t A t
, η
S t B t ⇐ Group identity observable
Group A citizens
(1 − z )(ω − τ )
t t
S b A a A tt t S A t
R > 0, R < 0, R(0) = 0, R (0) > 1 • S A t
⇒ Social optimal η > 0, satisfying
t(ω
S t B t
)
S t a t
− τ
B
− θ
b
B
t
)
S t b t
− τ
b
)(ω
B t
(1 − z
Model: preference (cont.)
) Model: preference (cont.)
Leader of group S
A A A B
τ [π (1 − z ) + (1 − π )z ]
t t t S b t A A A B
t t t S A S B
A A
t t− π η − (1 − π )η
t t If ousted, leader’s payoff is 0 from t on
Group S t : decide whether to
support leader S t (s = 1) or to
t S t
oust him (s = 0)
t S t S t
If s = 1, S
S t
If s = 0, S = S w/ prob. γ
γ > γ
1 Leader of S chooses policy vector
tS a S b S A S B
t t t t
P ≡ {τ , τ , η , η }
t t t t t
2 Group S decides whether to t S t
support leader, s ∈ {0, 1}
t
3 Both groups decide whether to A B
switch activity, z , z ∈ {0, 1}
t t
Model: Timing of events (cont.)
S t= 1, P
4(a) If s t implemented, payoffs
t S t= S realize, S t t w/ prob. γ
4(b) If s = 0, leader ousted, t
P ≡ {0, 0, 0, 0} implemented,
r payoffs realize, S = S w/ prob. t t
γ Model: discussion on assumptions
(1) No collective action problem (2) No repression
(3) Group j �= S never supports leader
tof S t (1) & (2): fine as leader would
Focus on Markov Perfect Equilibrium (MPE)
Strategies: contingent only on the
t
prior actions within the same period
Exclude history-dependent strategies
⇒ Below time subscript t dropped
State transitions: as described in
Digression: Equilibrium concepts
for repeated gamesA repeated game has many SPEs ⇒ Economists focus on a subset of them that are most plausible
1. Stationary SPEs
2. SPEs on the Pareto frontier (& take
a stance on relative bargaining power of players)
⇐ Baland & Robinson (2008) Definition of equilibrium (cont.)
Pure-strategy MPE: set of the following 4 strategies that are best responses to each other
A
= P Leader of A: P
Leader of B: P = P
σ (S, P ) = {s , z } Group B citizens:
j
V (S): value function for group j
j
(S): value function for leader of j W
(B) = 0, W (A) = 0 W
Choice of z : no impact on
B b Ab b B Aa
< ω
⇒ z = 1 iff ω − τ − θ − τ t A
Likewise, choice of z :
< ω z = 1 iff ω − τ − θ − τ
t Analysis: switching (cont.)
Tax revenue from a citizen of group B
Ab B Ab B Aa
τ if z = 0 ⇐⇒ τ ≤ θ + τ
τ if z = 1 ⇐⇒ τ > θ + τ
⇒ Maximized at τ = θ + τ
Tax Revenue from a citizen of group B τ Aa 45 o B Aa Ab
θ
Same is true for tax revenue from
Aa Ab ⇒ Leader sets (τ , τ ) so that
A B
z = z = 0
⇒ Upper limit on tax rates: Aa A Ab
τ ≤ θ + τ
Ab B Aa
τ ≤ θ + τ
)V
A
)V
A
V A (A) + δ(1 − γ
A
a
ω
(B)
A
A
V A (A) + δ(1 − γ
A
)
AA
Aa
− τ
a
= 1 (support) ω
Analysis: support for incumbent
(B)
Analysis: support for incumbent
(cont.)⇒
s = 1 iff
Aa AA
τ − R(η )
A A A A
≤ δ(γ − γ )(V (A) − V (B))
A
≡ Φ
LHS: Net tax payment
Ab
(A) subject to
Aa
≤ θ
A
Ab
, τ
≤ θ
W
B
Aa
Aa
− R(η
AA
) ≤ Φ
A
A
A
Aa
Analysis: leader’s problem
max
τ Aa ,τ Ab ,η AA ,η AB
π
A
(τ
− η
)
AA
)
A
)(τ
Ab
− η
AB
η
1. = 0: no transfer to excluded
group
⇐ Excluded group cannot affect leader’s survival
Ab B Aa 2. τ = θ + τ : tax revenue from
excluded group maximized
Excluded group cannot affect leader’s • survival ⇒ Leader can tax them until they are
indifferent btw. activities a & b Aa A Ab Lemma 1 (cont.) Aa A AA
3. τ = Φ + R(η ): tax on leader’s
group constrained
⇐ Leader’s group would kick leader out Aa if higher τ than this In equilibrium, leader is always
⇒ Leader’s objective function:
A A AA AA
π max (Φ + R(η ) − η ) AA
η A B A AA