This paper proposes an analytical framework to examine the role of public debt in financial development, which remains largely unexplored in the existing literature. We find that in countries where the banking sector extends substantial credit to government, public debt is likely to harm financial development, with unfavourable implications for economic activity. As such, our results provide an alternative explanation for the ‘contractionary fiscal expansions’. We also show that the lower the financial depth, the greater the adverse effects of public borrowing on financial development and macroeconomic outcomes.Financial sector; credit to government; public debt.

G Ozkan

M Ismihan

English

Research Papers in Economics

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Discussion Papers in Economics 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Department of Economics and Related Studies 
University of York 
Heslington 
York, YO10 5DD 
 
No. 10/14 
 
Public debt and Financial development: 
A theoretical exploration 
 
By 
 
Mustafa Ismihan, Atilim University; F. Gulcin Ozkan, University of York  Public debt and ￿nancial development
A theoretical exploration
Mustafa Ismihan
Atilim University
F. Gulcin Ozkan
University of York￿
May 17, 2010
Abstract
This paper proposes an analytical framework to examine the role
of public debt in ￿nancial development, which remains largely unex-
plored in the existing literature. We ￿nd that in countries where the
banking sector extends substantial credit to government, public debt is
likely to harm ￿nancial development, with unfavourable implications
for economic activity. As such, our results provide an alternative ex-
planation for the ￿ contractionary ￿scal expansions￿ . We also show that
the lower the ￿nancial depth, the greater the adverse e⁄ects of public
borrowing on ￿nancial development and macroeconomic outcomes.
Key words: Financial sector; credit to government; public debt.
JEL classi￿cation: E52, E63, H63
￿Corresponding author; Department of Economics, University of York, Hesling-
ton, York, YO10 5DD; Tel: 01904-434673; E-mail:fgo2@york.ac.uk.
11 Introduction
Massive ￿scal stimulus packages put into place in the wake of the recent
global ￿nancial crisis created renewed interest in ￿scal policy issues. An
important aspect of ￿scal policy especially during major ￿scal expansions
is related to the implications of budget de￿cits and public debt, on which
there is a substantial literature. One interesting ￿nding in this literature
is that ￿scal expansions may be contractionary in countries where ￿nancial
depth1 is limited (see, for example, Caballero and Krishnamurty, 2004 and
Christensen, 2005). Caballero and Krishnamurty (2004) present a model
of external crisis in an environment with limited ￿nancial depth. In their
model a rise in government expenditure crowds out private investment since
expansionary ￿scal policy worsens the quality of the country￿ s assets by
reducing their liquidity and valuation. Their results overturn standard ￿s-
cal policy prescriptions, pointing to the potential contractionary e⁄ects of
expansionary ￿scal policy.
In this paper we o⁄er an alternative explanation for ￿ contractionary ￿s-
cal expansions￿by exploring a di⁄erent channel through which ￿scal policy
in￿ uences the ￿nancial sector and economic outcomes. We show that when
the government has a dominant presence as a major borrower in the domes-
tic securities market, a rise in public debt crowds out the funds available to
the private sector ￿ a key measure of ￿nancial development￿which in turn
reduces economic activity.2 Although the determinants and the implications
of ￿nancial development have been extensively analyzed, the potential role
of ￿scal policy as a determinant of ￿nancial development has been largely
ignored in the existing literature. One exception to this is Hauner (2009)
who presents empirical evidence on the unfavourable impact of large ￿scal
de￿cits on ￿nancial development working through public sector borrowing
from the banking sector. Our paper is the ￿rst that provides a theoretical
framework on the role of public debt on ￿nancial development that may
underlie such empirical evidence.
1Financial depth is de￿ned as supply of funds available to the government and the
private sector.
2Costs of ￿nancing large ￿scal de￿cits in domestic securities markets, especially in
countries where the ￿nancial depth is low and the banking sector is the dominant player
in shaping the debt structure have been recently highlighted by Hauner (2008, 2009) and
Emran and Farazi (2009).
22 The Basic Model
We utilize a simple, two-period policy-making model with monetary and
￿scal authorities and the banking sector.3
2.1 Policy makers￿preferences
Consider a ￿scal policy-maker whose preferences can be summarized by the
following loss function:
LG
t =
1
2
T=2 X
t=1
￿t￿1
G [￿1￿t
2 + (xt ￿ xt)2 + ￿2(gt ￿ gt)2] (1)
where LG
t denotes the welfare losses incurred by the government, ￿1 and
￿2 represent, respectively, the government￿ s relative dislikes for the devia-
tions of in￿ ation (￿t) and public spending as a share of output (gt) from
their target levels (0 and gt respectively) relative to the deviations of output
(xt) from its target level (xt) and ￿G is the government￿ s discount factor.
Monetary policy is made by an independent central bank (CB) whose
preferences can be described as:
LCB
t =
1
2
T=2 X
t=1
￿t￿1
CB[￿1￿t
2 + (xt ￿ xt)2] (2)
where LCB
t denotes the welfare losses incurred by the CB, ￿1 is the CB￿ s
in￿ ation stability weight, ￿CB is the CB￿ s discount factor. In addition, the
CB is more conservative than the elected government; ￿1 > ￿1 and it does
not discount the future at as high rate as the elected government; ￿CB > ￿G.
Since the CB does not have any target for public spending, no terms relating
to gt enter the CB￿ s loss function.
3A similar model is used by Beetsma and Bovenberg (1999) and Ismihan and Ozkan
(2004) among others, though, the framework used in these studies excludes the ￿nancial
sector. Our set up is closer to that of Ozkan et al. (2010) which examines the implications
of public sector borrowing from the banking sector. However, in their model the govern-
ment is the only borrower and thus crowding out and ￿nancial development issues do not
arise.
32.2 Output supply
Consider the following form of the production function: Yt = b AtN
￿
t , where
Yt; Nt; and b At represent output, labor, and productivity, respectively, in
period t and 0 < ￿ < 1: The representative competitive ￿rm￿ s problem is to
maximize pro￿ts Pt(1 ￿ ￿t) b AtN
￿
t ￿ WtNt, where Pt is the price level, Wt is
the wage rate and ￿t is the tax rate on the total revenue of the ￿rm in period
t. The representative ￿rm chooses labor to maximize pro￿ts by taking Pt,
Wt and ￿t as given. The resulting output supply function, utilizing wt = pe
t,
where superscripts e denote expectation, is yt = ￿(￿t+1
￿at￿￿e
t￿￿t)+z;where
￿e
t is expected in￿ ation and lower case letters represent logs.
We now turn to establishing the link between credit availability and real
economic activity, as has long been recognized (see, for example, Levine,
1997). One channel through which the availability of credit a⁄ects the func-
tioning of an economy is through its impact on productivity (see, for ex-
ample, King and Levine, 1993). It therefore follows that the productivity
parameter, de￿ned above, can be modi￿ed as follows: b at = b a0 + ￿lT
t ; where
lT
t is the level of total bank credits to the private sector as speci￿ed below,
b a0 is a constant and positive parameter and ￿ > 0. Substituting b at into
the output supply function derived above, normalizing output by subtract-
ing the constant term z0 = z + ￿b a0=￿ for simplicity yields the following
normalized output supply function:
xt = ￿(￿t ￿ ￿e
t ￿ ￿t + ￿lT
t ) (3)
where xt denotes normalized output and ￿ = ￿
￿:
2.3 Demand for borrowing
Demand for borrowing is determined as an outcome of ￿scal and monetary
policy decisions taken by the government and the independent CB, respec-
tively. There are three sources of ￿nance for public spending; tax revenues,
money creation and public borrowing. More formally, the budget constraint
facing the government at time t is given by:
(1 + rt￿1)dt￿1 + gt ￿ ￿t ￿ k￿t = dt (4)
where dt￿1 denotes the amount of single-period debt issued (as a ratio
of output) in period t ￿ 1 and to be re-paid in period t, rt￿1 represents the
4rate at which it is borrowed, dt is the new debt issue in period t and k is
the real money holdings as share of output.
It is straightforward to derive the equilibrium outcome by utilizing back-
wards induction. Government and the independent CB play a Nash game
in both periods to minimize their respective losses. Equilibrium values of
in￿ ation, output and public borrowing, for given levels of r and lT; are listed
in Table 1.
Table 1- Equilibrium Outcome in t = 1 and t = 2
￿2 = ￿2
￿1
e ￿￿[( 1
￿x2 + g2) + (1 + r1)(g1 + 1
￿x1 + (1 + r0)d0 ￿ ￿lT
1 )]
x2 = ￿￿2
￿
e ￿￿[g2 + (1 + r1)(g1 + 1
￿x1 + (1 + r0)d0 ￿ ￿lT
1 )] + (1 ￿ ￿2
￿2e ￿￿)x2
d1 = ￿[g1 + 1
￿x1 + (1 + r0)d0 ￿ ￿lT
1 ￿ z(g2 + 1
￿x2)]
￿1 = ￿2
￿1
e D￿￿[g2 + 1
￿x2 + (1 + r1)(g1 + 1
￿x1 + (1 + r0)d0 ￿ ￿lT
1 )]
x1 = ￿￿2
￿ [ e D￿￿[g2 + 1
￿x2 + (1 + r1)(g1 + (1 + r0)d0 ￿ ￿lT
1 )]] + (1 ￿ ￿2
￿2￿)x1
Note: e ￿ = 1
(1+e ’); e ’ = ￿2
￿2+ k￿2
￿1 ; e D = ( ￿2
￿2+ ￿2￿1
￿2
1
+1)e ￿
2
; e D￿ = (1+r1)￿FA e D;
z = (1 + e ’) e D￿;￿ = 1
1+(1+r1)z;￿ = e D￿￿(1 + r1). Also, (1 ￿ ￿) > 0;
(1 ￿ ￿2
￿2￿) > 0 and (1 ￿ ￿2
￿2e ￿￿) > 0:
2.4 Supply of loanable funds
We now consider the determination of the supply of loanable funds avail-
able to the government and the private sector in this economy. Consider
a ￿nancial sector that is composed of n banks. Banks compete with each
other both in collecting deposits and in lending the collected funds. In the
deposit market, the relationship between the deposit rate o⁄ered by bank i
and the supply of deposits facing the bank is summarized by the following:
zi
t =
1
n
(A + ￿rzi
t ) + !
n X
j=1;j6=i
(rzi
t ￿ r
zj
t ) (5)
where zi
t is the deposit supply facing bank i, rzi
t is the deposit rate o⁄ered
by bank i, r
zj
t is the vector of deposit rates paid by all other banks and A;
￿ and ! are positive parameters characterizing the structure of the deposit
market. The parameter ￿ measures the sensitivity of deposit supply with
respect to the deposit rate. The parameter ! measures the competitiveness
5of the banking sector; the higher is !, the more competitive is the banking
sector in the deposit market.
The banking industry also competes for private sector borrowers. The
demand function for loans facing bank i among the private sector borrowers
is given by
li
t =
1
n
(Al ￿ "rli
t ) ￿  
n X
j=1;j6=i
(rli
t ￿ r
lj
t ) (6)
where li
t denote the private sector demand for borrowing from bank i; rli
t
is the loan rate charged by bank i, r
lj
t is the vector of loan rates charged by
all other banks and Al, " and   are positive parameters that relate to the
structure of the credit market.
Bank i￿ s pro￿t function can be written as
V Bi
t = rli
t li
t + rtbi
t ￿ r
zi
t zi
t ￿
c
2
￿
li
t + bi
t ￿ ￿zi
t
￿2
(7)
where V Bi
t is bank i￿ s pro￿t function at time t, bi
t is the bank i￿ s bond
holdings of government securities, rt is the rate of interest on these securities
and c is the cost associated with illiquidity (see, Cukierman, 1991). These
costs are assumed to increase at an increasing rate as illiquidity increases.
The maximum that a bank can lend is then the di⁄erence between the
amount of deposits that it collects and the amount that it needs to hold as
required reserves, as captured by ￿ in equation (7).
Bank i chooses the deposit rate, r
zi
t ; the loan rate, rli
t ; and the demand
for public sector bonds, bi
t; to maximize its pro￿ts in (7).
Di⁄erentiating (7) w.r.to r
zi
t ;rli
t and bi
t, re-arranging the relevant ￿rst
order conditions and imposing rzi
t = r
zj
t and rli
t = r
lj
t yield the following
equilibrium values for bi
t, rli
t and rzi
t :
bi
t =
(￿ + n1)￿
n(n1 + 2￿)
A ￿
(" + n2)
n(n2 + 2")
Al + (8)
[
[(c￿2 + c￿n1)￿2 + nn1 + 2n￿]
cn(n1 + 2￿)
+
(" + n2)"
n(n2 + 2")
]r1
rli
t =
Al
(n2 + 2")
+
(" + n2)
(n2 + 2")
r1 (9)
6rzi
t = ￿
A
(n1 + 2￿)
+
(n1 + ￿)￿
(n1 + 2￿)
r1 (10)
where n1 = !(n ￿ 1)n and n2 =  (n ￿ 1)n:
2.5 Equilibrium in the bonds market
It is now straightforward to determine the bond rate, rt; by combining the
banks￿total demand for bonds, bt = nbi
t; with the government￿ s demand
for borrowing (supply of bonds), dt. The bond rate adjusts till the demand
for bonds is exactly matched by its supply thereby eliminating any excess
demand for borrowing and thus any excess supply of bonds. More formally,
in equilibrium
Ed
t (rt) = dt(rt) ￿ bt(rt) = 0 (11)
where Ed
t (rt) denotes excess demand for borrowing expressed in terms
of the bond rate; and dt(rt) and bt(rt); are, respectively, the demand for
borrowing (supply of bonds) and the demand for bonds. It follows from
above that @rt=@dt > 0 and @rt=@bt < 0:
3 Discussion
Let us now turn to the impact of public borrowing on the availability of
credit to the private sector and the macroeconomic implications of this re-
lationship. The framework developed above highlights the possibility of a
￿nancial crowding-out where government borrowing replaces private bor-
rowing in the banking sector￿ s loan portfolios. Given that bank credit to
private sector is widely viewed as an important indicator of ￿nancial devel-
opment, we can now establish the link between public debt and ￿nancial
development.
Result 1. A rise in public sector borrowing from the banking sector re-
duces the scope of bank lending to the private sector and is therefore harm-
ful for ￿nancial development. Moreover, the lower the ￿nancial depth, the
greater the degree of public borrowing￿ s crowding out of credit to the private
sector.
7Proof 1 By imposing rli
t = r
lj
t = rl
t in (6) and utilizing lT
t = n li
t we
can establish that the total bank credits to the private sector amounts to
lT
t = Al ￿ "rl
t. It therefore follows that a rise in dt reduces the total bank
credits to the private sector, lT
t since both @rl
t=@rt = "+n2
n2+2" and @rt=@dt
are unambiguously positive and @lT
t =@rl
t = ￿" is unambiguously negative;
thus @lT
t =@dt < 0. Also, in economies with lower ￿nancial depth, a given
rise in public borrowing is expected to bring about a greater rise in interest
rates, that is both @r1=@d1 and @rl
1=@d1 are greater in size. Hence, the fall
in private sector lending will be greater in such economies.
An interesting question relates to the macroeconomic implications of the
deterioration in ￿nancial development following a rise in public borrowing,
as established under Result 1. The relationship between credit availability
to the private sector and the macroeconomic performance is formalized by
Result 2.
Result 2. A fall in credit availability to the private sector is associated
with a worse economic outcome in terms of higher in￿ation and lower output
both in current and future periods.
Proof 2. It is straightforward to show @￿1=@lT
1 = ￿￿(1+r1) ￿2
￿1
e D￿￿ and
@￿2=@lT
1 = ￿￿(1+r1) ￿2
￿1
e ￿￿ are both unambiguously negative and @x1=@lT
1 =
￿(1 + r1)￿2
￿ e D￿￿ and @x2=@lT
1 = ￿(1 + r1)￿2
￿
e ￿￿ are both unambiguously
positive.
4 Concluding remarks
This paper has explored the role of public debt on ￿nancial development
that has so far remained unexplored in the existing literature. We have
shown that in countries where credit to government makes up a major share
of total bank lending, public debt is likely to harm ￿nancial development,
with unfavourable implications for economic activity. As such, our results
establish a potential contractionary e⁄ect of ￿scal expansions especially in
countries with limited ￿nancial depth and ￿nancial development, likely to
be the case in emerging markets and other developing countries.
8References
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9

Public debt and Financial development: A theoretical exploration

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Public debt and Financial development: A theoretical exploration

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