Financial markets in development, and the
development of financial markets
Jeremy Greenwood, Bruce D. Smith
Ekta, Kritika
Indian Statistical Institute, Delhi
March 21st, 2016
Relationship between markets and development?
I
Growth successes of Belgium and Scotland in the early 19th
century attributed primarily to the efficiency of their financial
markets.
Role of Financial Markets in Industrial Revolution
I
Hicks (1969) and North (1981): Distinguishing feature of the
industrial revolution was not particularly the development of
new technology
Role of Financial Markets in Industrial Revolution
I
Hicks (1969) and North (1981): Distinguishing feature of the
industrial revolution was not particularly the development of
new technology
I
It was a revolution because, for the first time, the
implementation of technical advances became a highly
capital-intensive process.
I
Provision of liquidity and the sharing of risk associated with
financial market development substantially reduced the
perceived costs of investing in innovation.
Themes explored
I
Markets enhance growth via
I
Resource allocation to highest social return activities
I
Eliminating idiosyncratic risk
I
Market formation is an endogenous process
I
Competition in provision of market services - efficient outcome
for market participants
The Environment
I
Infinite Sequence of two-period OLG
I
Continuum of identical agents with unit mass
I
Single consumption good
I
Produced using intermediate inputs via CRS
The Environment
I
Intermediate inputs produced using capital and labor
I
Each agent i produces a unique intermediate good using
I
Own labour, lt (i) (inelastic supply)
I
Capital input, kt (i)
I
Technology xt (i) = Akt (i)lt (i)1
I
Only young endowed with labour
I
Capital supplied by the old
I
Depreciation = 1
The Environment
I
Final goods - Consumption and Capital
I
1 unit Consumption ! R units of capital tomorrow
ct + kt+1 /R =
"Z
1
0
#1
✓
xt (i)✓ di
✓<1
The Environment
I
Identical preferences of young
u(c1t , c2t : ) =
[(1
)c1t + c2t ]
I
: Individual specific, iid (across agents) shock
I
= 0 with probability 1
⇡
u(c1t , c2t : ) =
I
[c1t ]
= 1 with probability ⇡
u(c1t , c2t : ) =
[c2t ]
>
1
Final Goods Sector Optimization
I
Competitive setting
I
pt (i): Price charged for intermediate input i
I
Current consumption - numeraire
I
Optimization Problem
"Z
1
max
xt (i)
I
#1
✓
✓
xt (i) di
0
Z
1
pt (i)xt (i)di
0
Inverse Demand Schedule
where yt =
"
R1
0
pt (i) = yt1
#1
✓
xt (i)✓ di
✓
xt (i)✓
1
Intermediate Inputs Sector Optimization
I
Individuals are price setters
I
Obtain Capital inputs in competitive rental market
I
Rental rate of capital = ⇢t
I
Optimization Problem
max
s.t. lt (i) = 1
[pt (i)xt (i)
⇢t kt (i)]
Intermediate Inputs Sector Optimization
I
Substituting pt (i), xt (i)
max
kt (i)
I
FOC {kt (i)}:
{yt1
✓yt1
✓
✓
[Akt (i)]✓
A✓ kt (i)✓
1
⇢t kt (i)}
= ⇢t
Equilibrium
I
Symmetric agents
xt (i) = xt
kt (i) = kt
8 i 2 [0, 1]
I
yt = xt = Akt
I
⇢t = ✓A
I
Maximized income for agent i (young) = wt (i)
wt (i) = max{pt (i)xt (i)
I
⇢t kt (i)}
Imposing equilibrium conditions
wt (i) = wt = (1
✓)Akt
Savings Behaviour
I
Depends on the kind of financial system they have access to
I
3 types: Financial Autarky, Banking and Equity markets
I
For now, type of system - exogenous
Timing Structure
Portfolio Decision
Financial Autarky
I
Young agents store goods and accumulate capital on their
own behalf
I
If an agent holding capital is hit with a liquidity shock (i.e.
= 0)
I
Old age consumption gives no utility
I
Capital can not be rented (factor markets have closed)
I
Capital can not be sold (no equity market for transferring
claims to ownership of capital)
I
Autarkic agents with
= 0 lose their capital investment
Financial Autarky
I
Portfolio decision made by a young agent:
I
sta : goods stored, return n independent of when consumption
occurs
I
a
Kt+1
: value in current consumption of capital accumulated
I
I
Return = 0
if
=0
Return = R⇢t+1
if
=1
R⇢t+1 = RA✓
Financial Autarky
Optimization problem of a young agent:
max
a
a
ct1 ,ct2 ,st ,Kt+1
Subject to:
I
a
sta + Kt+1
 wt
I
c1t  nsta
I
a
c2t  nsta + (RA✓)Kt+1
[(1
⇡)c1t + ⇡c2t ]
Financial Autarky
Define qta =
a
Kt+1
wt
I
ct1 = n(1
qta )wt
I
ct2 = n(1
qta )wt + (RA✓)qta wt
Rewriting the optimization problem:
max
a
0qt 1
wt {(1
⇡)[n(1
qta )]
+ ⇡[n(1
qta )wt + (RA✓)qt ]
}
Financial Autarky
I
FOC{qta }: qta = Q a (RA✓) ⌘
(RA✓) ⌘
I
"
[ (RA✓) 1]
[ (RA✓) 1]+(RA✓/n)
⇡(RA✓ n)
(1 ⇡)n
#
1
1+
There is an interior optimum (0 < qta < 1) i↵
(RA✓) > 1
,
⇡(RA✓ n)
(1 ⇡)n
>1
, ⇡RA✓ > n
(assumed to hold)
where
Banking
I
I
I
Banks - Take deposits
I
Invest in capital
I
Hold goods in storage
To each depositor it promises to pay
I
r1t per unit if withdrawal at t
I
r2t per unit if withdrawal at t+1
In equilibrium, only agents with
= 0 withdraw ’early’
Bank’s Portfolio Decision
I
Assumption: All savings deposited in the bank
I
Bank receives a per person deposit of wt out of which
I
I
stb - goods storage (per depositor)
I
b
Kt+1
- capital investment (per depositor)
Constraints:
b
 wt
sbt + Kt+1
(1
⇡)r1t wt  nsbt
b
b
⇡r2t wt  R⇢t+1 Kt+1
= (RA✓)Kt+1
Bank’s Optimization
I
Banking industry - competitive
I
Bank maximizes expected utility of representative depositor
I
Define qtb ⌘
I
Optimization
b
Kt+1
wt
max
(fraction invested in capital)
wt [(1
⇡)r1t + ⇡r2t ]
qtb )
⇡)
r1t 
n(1
(1
r2t 
(RA✓)qtb
⇡
s.t.
Bank’s Optimization
I
Solution to the maximization problem:
qbt = Q b (R⇢t+1 ) = Q b (RA✓)
Q b (RA✓) ⌘
⌘(RA✓) =
⌘(RA✓)
1 + ⌘(RA✓)
⇡(RA✓/n) /(1+
(1 ⇡)
)
Risk Neutrality
I
!
1 (Risk neutral): Q b (.) ! 1
wt [(1
(1
⇡)r1t + ⇡r2t ]
⇡)r1t wt
⇡r2t wt
+
= wt
n
RA✓
Utility f n
Budget Const.
Risk Aversion
I
I
= 0 (Logarithmic): Q b (.) = ⇡
Q b (.) - decreasing in
i.e
Higher the risk aversion ) Less savings in illiquid capital by
the bank
Depositors willing to accept relatively less in good times to
ensure more in bad times (ex-ante)
Proposition I
1. Q b (RA✓) > Q a (RA✓) i↵
⇡
(1
⇡)
>
"
⇡
(1
⇡)
#1/1+ "
(RA✓ n)
(RA✓)
#1/1+
"
n
RA✓
#1/1+
A sufficient condition for above
(⇡
0.5)
0
2. Q b (RA✓) > ⇡Q a (RA✓) always holds.
In Autarky (1
- Lost!
⇡) fraction of long-term investment projects
Equity Markets
I
After each agent’s value of
is known at t, an equity market
opens
I
zt : number of units of storage exchanged for 1 unit of capital
Equity Markets
Optimization problem faced by the young agent:
max
e
[(1
⇡)c1t + ⇡c2t ]
e
ct1 ,ct2 ,st ,Kt+1
Subject to:
I
e
ste + Kt+1
 wt
I
e
c1t  nste + nzt Kt+1
I
e
e
c2t  (R⇢t+1 )[Kt+1
+ ste /zt ] = (RA✓)[Kt+1
+ ste /zt ]
Equity Markets
Let qte ⌘
I
e
Kt+1
wt
If zt > 1
e
e
) nzt Kt+1
> nKt+1
) No storage
) qte = 1
I
If zt < 1
) No capital
) qte = 0
Equity Market
I
Optimal choice of qte satisfies
I
qte = 1 if zt > 1
I
qte = 0 if zt < 1
I
qte 2 [0, 1] if zt = 1
I
Supply of capital at t = (1
I
Demand for capital at t :
I
⇡(1
I
0
qte )wt /zt
⇡)qte wt
if RA✓ > nzt
if RA✓ < nzt
Equity Market
I
Equilibrium in equity market requires zt = 1
I
(1
⇡)qte = ⇡(1
)qte = ⇡
qte )/zt = ⇡(1
qte )
General Equilibrium
I
Financial Autarky
I
kt+1 = R{⇡Q a (RA✓)wt }
I
kt+1 = R{⇡Q a (RA✓)}(1
I
Growth rate of capital stock and output:
a
I
= (1
✓)Akt
✓)RA⇡Q a (RA✓)
Banking
I
kt+1 = R{Q b (RA✓)wt }
I
kt+1 = R{Q b (RA✓)}(1
I
Growth rate of capital stock and output:
b
= (1
✓)RAQ b (RA✓)
✓)Akt
Proposition II
The growth rate of an economy with banks exceeds that of a
financially autarkic economy.
Proof: This follows from the fact that Q b (RA✓) > ⇡Q a (RA✓)
(Proposition I)
I
Banks raise the rate of growth for one or both of these
reasons:
I
banks shift savings into capital [ if Q b (RA✓) > Q a (RA✓)]
I
banks prevent premature liquidation of capital
[Q b (RA✓) > ⇡Q a (RA✓)]
General Equilibrium
I
Equity markets
I
kt+1 = R⇡wt
I
kt+1 = R⇡(1
I
Growth rate of capital stock and output:
e
= ⇡(1
✓)Akt
✓)RA
Proposition III
1.
e
>
a
2.
e
>
b
I
holds i↵
>0
More risk-averse the agents are, lesser the proportion of
deposits invested by banks in capital, lower the growth rate
Endogenous Formation of Financial Institutions
I
In earlier discussion, structure of financial markets - Exogenous
I
Hurdles to the formation of financial markets
I
I
Formation and operational costs
I
Legal or regulatory inhibitions
Practically, second point is quite important but in further
analysis, we look at only operating costs
Endogenous Formation Framework
I
I
I
Utility loss from
I
contacting Banks - e
I
Being active in equity markets - e’
v a (RA✓)wt
- Autarkic agent’s indirect utility
v a (RA✓) ⌘
[(1 ⇡){n[1 Q a ]}
+⇡{n[1 Q a ]+RA✓Q a }
Similarly, maximized expected utility of an agent
v b (RA✓)wt
- using Banks
v e (RA✓)wt
- using Equity markets
]
Endogenous Formation Framework
I
Note
v b (RA✓) ⌘
v e (RA✓) ⌘
I
h
(1 ⇡)
n
[(1 ⇡)n
n(1 Q b )
(1 ⇡)
o
+⇡(RA✓)
+⇡
]
n
RA✓Q b
⇡
o i
Banks can always achieve the utility level provided by equity
markets
Endogenous Formation Framework
I
Note
v b (RA✓) ⌘
v e (RA✓) ⌘
I
h
(1 ⇡)
n
[(1 ⇡)n
n(1 Q b )
(1 ⇡)
o
+⇡
+⇡(RA✓)
]
n
RA✓Q b
⇡
o i
Banks can always achieve the utility level provided by equity
markets
) v b (RA✓)
v e (RA✓)
Strict Inequality unless
I
8 (RA✓)
=0
Also, v b (RA✓) > v a (RA✓)
8 (RA✓)
n
Endogenous Bank Formation
I
Agents will choose banks if
v b (RA✓)wt
v b (RA✓)wt
I
Assumption : e 0
e
e
e
v a (RA✓)wt
v e (RA✓)wt
e0
8 wt
(consistent with observation)
) Only banking can operate, not equity markets!
Endogenous Bank Formation
I
Let t ⇤ be the first date at which banks operate
I
If t ⇤ > 0
wt ⇤
I
(
e
[v b (RA✓)
v a (RA✓)]
)
1
wt ⇤
1
Substituting wt
(1 ✓)A(
a t⇤
)
(
e
[v b (RA✓)
v a (RA✓)]
)
1
1
k0
(1 ✓)A(
a t⇤ 1
)
Endogenous Bank Formation I
I
Four Possibilities
(1
✓)Ak0 <
1. k0 satisfies (I) and
(
a
e
[v b (RA✓)
v a (RA✓)]
)
1
>1
) 9 unique, finite date t ⇤ > 0 when banks open
At t ⇤ , growth rate of the economy increases by
b
a
>1
(I )
b
a
, where
Endogenous Bank Formation II
2. k0 violates (I) and
b
1
) Financial intermediaries operate at all dates
Growth rate of the economy is always
3. k0 violates (I) and
b
b
<1
) t ⇤ = 0 and Banks close at a finite date, t̄ where
(
) 1
(1 ✓)A(
b )t̄ 1 k
0
e
[v b (RA✓) v a (RA✓)]
(1 ✓)A(
b )t̄ k
0
Endogenous Bank Formation III
4. k0 satisfies (I) and
) t⇤ = 1
a
1
Banks never open
Growth rate of the economy is always
a
Why is subsidization of equity markets observed in
developing countries?
I
If
>0
I
I
e
>
b
Equity markets never form
Government which attaches sufficient ’weight’ to the utility of
future generations might choose to subsidize the formation of
equity markets.
Conclusion
I
Financial markets promote economic growth by directing
resources to their highest return uses
I
Provision of liquidity by financial markets limits the exposure
of savers to idiosyncratic risks, and prevents the costly
premature liquidation of long-term capital investment
Conclusion
I
It is the latter e↵ect on saving, rather than liquidity provision
per se, that is growth-promoting
I
Single asset
I
Liquidation at t : n, t+1 : R with 0 < n < R
I
Presence of intermediaries in this environment increases
growth i↵
I
⇣ n ⌘ 1+
>1
RA✓
This condition holds only when
< 0 (agents desire a return
on early withdrawals of less than n)
I
Intermediaries are not insuring against the shock, and not
providing liquidity