by F Gaspart ECRUUCL and B Verheyden CEPSINSTEAD Motivations 1 How do young institutions start No State gt local provision of public goods No enforcement gt noncooperative framework ID: 238470
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Slide1
Choosing the Subscribers
by
F. Gaspart (ECRU/UCL)
and B. Verheyden (CEPS-INSTEAD)Slide2
Motivations (1)
How do young institutions start ?
No State => local provision of public goods
No enforcement => non-cooperative framework
Voluntary subscription
minimal authority :
a Principal choosing the group of subscribersSlide3
Motivations (2)
Lack of social security => investment motive for children if they exhibit ascending altruism
Endogenous fertility = choosing the number of subscribers
Education expenses = choosing the endowments of the subscribersSlide4
Literature on fertility and education
Becker & Lewis (1973) : consumption motive
Caldwell, Boldrin & Jones (2002) : investment motive with ascending altruism
Baland & Robinson (2000) :
short-term incomeSlide5
Our contribution
A theory of young institutions
A unified framework for all three motives of endogenous fertility and education
Individualized returns to education, revealed after birth => unequal education expenses
The role of savings in demographic transitionsSlide6
Timing
(1) The Principal P chooses n, the size of the group N of subscribers.
(2) Nature reveals the vector
k
of individual returns to education.
(3) P chooses the vector
e
of education expenses and the level of savings s.
(4) Each agent i in N chooses t
i
, his contribution to the public good.Slide7
Utilities
P's utility is V(a;b;B(n,
f
))
Short-term consumption : a = I(n) - s -
e
i
Old-age consumption (public good) : b = rs + T
Transfers : T =
t
i
*
Consumption motive : B(n,
f
)
Agent i's program is t
i
* = argmax U
i
( c
i
; b )
Private consumption : c
i
= f
i
-t
i
(C =
c
i
)
Returns to education : f
i
= f(e
i
,k
i
) (F =
f
i
*)Slide8
Relevant assumptions ? (1)
Strict binormality of agent's goods
say U( c,b ) = c + u(b)
=>
T = u'
-1
(1) – r s
=> s* = e* = 0 and n* = argmax I(n)
The vehicle of causality : income effects on transfers to parents
Eviction of savings
Collective action between childrenSlide9
Relevant assumptions ? (2)
I(n) is concave and has an interior maximum.
P is risk neutral.
The component B(n,
f
) :
For the sake of clarity, say B is a constant for now.
The discussion will state whenever other assumptions mitigates our results.Slide10
Voluntary subscription : a reminder
For a clear explanation of the proofs, see Cornes & Hartley (2007).
Existence and unicity
Comparative statics :
A transfer among positive subscribers
leaves equilibrium consumptions unaffected.
leaves total contribution unaffected
Agents with the same utility function contribute the same amount.Slide11
The Principal's problem (1)
Partly a profit maximization problem :
for a given total expenditure E on education,
e
* = argmax T = argmax F is necessary.
Convex returns to education :
Empirically relevant
Theoretically trivial : invest in one agent only, s*=0, « stopping rule » on n* (as Ejrnaes & Pörtner, 2004).
Concave returns to education in the sequel.Slide12
The Principal's problem (2)
Basic idea : the marginal rate of substitution between components a and b is equal
to the marginal return on savings, eviction included.
to the marginal impact of education on transfers, dilution included.
Take the sum of all agents' budgets in equilibrium :
c
i
*(b) = f
i
-t
i
* => T = -C(T+rs) + F(E,
k
)Slide13
The Principal's problem (2b)
Call m = 1 / ( 1+C'(b) ) ; from the implicit function theorem, we have :
Eviction : dT/ds = -r(1-m) < 0
Dilution : dT/dE = dT/de
i
= f' m < f'
Proposition 1:
for all agent with a positive education, r = f'(e
i
,k
i
)
Proof :
dV/ds = -V
a
+ V
b
(r+dT/ds) = 0
dV/dE = -V
a
+ V
b
dT/dE = 0Slide14
Choosing the number of subscribers
Risk-neutrality : simply
E
Σ
f(e
i
,k
i
) = F*(E,n) .
Proposition 2 :
if s* is interior, n*
≥
argmax I(n)
Proof :
Having a value T for a given E, V is maximized w.r.t. E and s. Take expectations : T* = F*-C(T*+rs*) .
n* = argmax V ( I(n)-E*-s*, T*+rs*, B)
By the envelope theorem, we have :
dV/dn = V
a
I'(n*) + V
b
dT*/dn
For E* fixed, dT*/dn
≥
0 ; therefore if I'(n)>0, dV/dn >0 .
The only case where dT*/dn=0 is when the marginal agent doesn't transfer anything.Slide15
Predictions
Proposition 3 :
if s* is interior, dn*/dr < 0
Proof :
T* = F*(E*,n)-C*(T*+rs*) => d(dT*/dn*)/dr <0 .
Empirically relevant case : convexity between school types, strong local concavity at completion years.
Becker's consumption motive mitigates inequalities among children, directly affects n* and diminishes | dE*/dr | .Slide16
Borrowing or saving constraints
Proposition 4 :
if s* is at a corner in 0, n*>argmax I(n), but n* is smaller than if r were as high as F'(E).
Proof of the first part :
Again, dT/dn*
≥
0 and I'(n)
>
0 => dV/dn >0
If s*>0 but a constraint is limiting savings, the Principal chooses more subscribers because of the constraint.Slide17
Conclusions
No concavity of returns to education means no investment motive for fertility.
The eviction of savings and dilution of altruistic incentives cancel each other. Education is driven by return rates.
A demographic transition can occur early in the modernization process if good savings opportunities arise.
Borrowing constraints reduce fertility, saving constraints stimulate fertility.