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Mahmoud Sami NABI
LEGI- Tunisia Polytechnic School
& IHEC Sousse
Credit Market Imperfection, Inequality
and Capital Accumulation
58ème Congrès de l’ AFSE
11/09/2009
Credit Market Imperfection, Inequality and Capital Accumulation
2
Outline
 Motive
 Research question
 Model
 Results
Credit Market Imperfection, Inequality and Capital Accumulation
3
Motive
 The banking system still dominates the financial system of
most developing countries.
 The importance of the legal framework:
 In case of borrower's default the bank often has the right to
seize collateral
 In practice: the implementation of this right depends on the
judicial system efficiency
 If the judicial system is weak, banks are willing to finance only
entrepreneurs providing sufficient collateral.
Credit Market Imperfection, Inequality and Capital Accumulation
4
Motive
 Considering 56 countries over the period 2002-04, regressing
the entrepreneurship density on judicial efficiency:
Credit Market Imperfection, Inequality and Capital Accumulation
5
Motive
 An economy may suffer from low entrepreneurship due to the
weakness of its judicial system.
 Possible explanation of this positive relationship between the
judicial efficiency and the entrepreneurship is credit rationing.
 This credit rationing may accentuate the income inequality in
a given economy.
 Banerjee and Duflo (2005): "one person may start a large or
more technologically advanced firm because he has money
and another may start a small and backward one because he
does not".
 Increasing income inequality
Credit Market Imperfection, Inequality and Capital Accumulation
6
Motive
 Possible explanation of this positive relationship between the
judicial efficiency and the entrepreneurship is credit rationing.
 This credit rationing may accentuate the income inequality in
a given economy.
 Banerjee and Duflo (2005): "one person may start a large or
more technologically advanced firm because he has money
and another may start a small and backward one because he
does not".
 Increasing income inequality
Credit Market Imperfection, Inequality and Capital Accumulation
7
Motive
 Regressing the GINI index on the Judicial Efficiency (JE) over
the period 1999-2001 for 42 countries.
Credit Market Imperfection, Inequality and Capital Accumulation
8
Research question
 What is the impact of the credit market imperfections
on the relationship between inequality and capital
accumulation ?
Credit Market Imperfection, Inequality and Capital Accumulation
9
Literature
 Inequality is negatively associated with growth:
Bertola (1993), Alesina and Rodrik (1994), Persson and
Tabellini (1994), Perotti (1996), …
 Growth is an inverted U-- curve of inequality:
Banerjee and Duflo (2005)
 However, the effect of credit market imperfection on the
relationship between inequality and capital accumulation
was rarely analyzed in a theoretical model.
Credit Market Imperfection, Inequality and Capital Accumulation
10
Literature
 Galor and Moav (2004) : income inequality -->
development process in the presence of credit constraints.
 Aghion and Bolton (1997) is the departure model of our
research.
 They developed a theoretical model analyzing the relation
between inequality and capital accumulation in presence of
a moral hazard problem.
Credit Market Imperfection, Inequality and Capital Accumulation
11
Literature
 Aghion and Bolton (1997) showed that the capital
accumulation process begins by widening the inequalities
but reduces them in later stages.
 Through which mechanism ?
-> "As more capital is accumulated there are more and
more funds available in the economy to finance a smaller
and smaller pool of borrowers. Thus the equilibrium lending
terms are progressively shifted in favour of borrowers.“
 Motivated by the stylized facts we expect that this result
may change if another type of financial imperfection is
considered.
Credit Market Imperfection, Inequality and Capital Accumulation
12
Model
 Add new type of credit market imperfections in addition to
the moral hazard problem: costly contract enforcement
(judicial inefficiency).
 Contrarily to Aghion and Bolton (1997), enabling wealthy
agents to undertake larger projects. The size of the project
is not normalized to one and wealthy agents could enlarge
their projects.
Credit Market Imperfection, Inequality and Capital Accumulation
13
Model
 The economy is closed and contains a sequence of one-
period-lived overlapping generations.
 Each generation is composed of a continuum of mass 1
agents indexed by i.
 The only source of heterogeneity among agents is their
inherited wealth .
 Each agent i is endowed with one unit of effort (labour)
Credit Market Imperfection, Inequality and Capital Accumulation
14
Model
 An agent undertakes a project requiring a minimum fixed
investment generating an uncertain revenue ……
or invest his wealth in a bank.
 The project could be self-financed or completed by an
external financing
Where and
Credit Market Imperfection, Inequality and Capital Accumulation
15
Model
 Agents are risk-neutral and their utility depends only on
consumption and bequest .
where is the effort cost.
 An agent divides the income he receives between
consumption and bequest.
Credit Market Imperfection, Inequality and Capital Accumulation
16
Model
 Initial distribution of wealth at date t=0 a proportion π of
the young agents has a low inherited wealth w₀<w and
constitutes the class i=l. .
 A proportion 1-π has a high inherited wealth w₀ <w₀<w
and constitutes the class .
 An agent of class i=l,h with an initial wealth {t}^{i}≥w
could self-finance his project. He may have an incentive to
ask for a bank loan in order to enlarge it.
Credit Market Imperfection, Inequality and Capital Accumulation
17
Model
 Even the project succeeds, an agent may have an
incentive to default on the loan.
 the bank seizes a fraction of the output.
The unseized fraction corresponds to an enforcing
repayment cost (the efficiency's level of the judicial
system).
Credit Market Imperfection, Inequality and Capital Accumulation
18
Model
 An optimal investment contract between the agent and the
bank specifies the repayment schedule for the class i
agent asking for an external financing
 In order to prevent the borrower's default, the repayment
….. should be at most equal to the default's cost ……..
 The maximum amount of loan the bank grants to the agent
of class i is
Credit Market Imperfection, Inequality and Capital Accumulation
19
Model
 Given the unit repayment rate the borrower chooses the
effort to supply and the amount of loan in order to
maximize his expected revenue net of both repayment and
effort costs
Credit Market Imperfection, Inequality and Capital Accumulation
20
Model
 Given that:
 The economy comprises at each date t a continuum of
agents belonging to the two classes,
 The random returns of the project are iid
 The proportion of successful projects is for the class i.
 The return of the banks from loans granted to the agents of
class i is deterministic and is given by .
 Assuming a competitive banking system 
Credit Market Imperfection, Inequality and Capital Accumulation
21
Model
 Only agents with an initial endowment prefer strictly
becoming depositors.
 Those with prefer becoming entrepreneurs.
 The threshold is determined by the indifference
condition
Credit Market Imperfection, Inequality and Capital Accumulation
22
Results
 The wealth inequality widens between the two classes of
agents in a first stage of development. Outside, it remains
constant or widens depending on the deposit interest rate
ceiling.
Why ?
Without a ceiling on the deposit interest rate there exists
always a value of such that making the
low inheriting agents always preferring depositing and the
high inheriting agent preferring undertaking a project
Credit Market Imperfection, Inequality and Capital Accumulation
23
Results
Numerical simulations of the judicial efficiency effect on the
wealth inequality (measured by the GINI index) in the case of
an interest rate ceiling
 An increase of the judicial efficiency:
 reduces the speed of convergence of the GINI index to its
long run level.
 decreases the long run level of wealth inequality.
Credit Market Imperfection, Inequality and Capital Accumulation
24
Results
Credit Market Imperfection, Inequality and Capital Accumulation
25
Results

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Credit Market Imperfection, Inequality and Capital Accumulation

  • 1. 1 Mahmoud Sami NABI LEGI- Tunisia Polytechnic School & IHEC Sousse Credit Market Imperfection, Inequality and Capital Accumulation 58ème Congrès de l’ AFSE 11/09/2009
  • 2. Credit Market Imperfection, Inequality and Capital Accumulation 2 Outline  Motive  Research question  Model  Results
  • 3. Credit Market Imperfection, Inequality and Capital Accumulation 3 Motive  The banking system still dominates the financial system of most developing countries.  The importance of the legal framework:  In case of borrower's default the bank often has the right to seize collateral  In practice: the implementation of this right depends on the judicial system efficiency  If the judicial system is weak, banks are willing to finance only entrepreneurs providing sufficient collateral.
  • 4. Credit Market Imperfection, Inequality and Capital Accumulation 4 Motive  Considering 56 countries over the period 2002-04, regressing the entrepreneurship density on judicial efficiency:
  • 5. Credit Market Imperfection, Inequality and Capital Accumulation 5 Motive  An economy may suffer from low entrepreneurship due to the weakness of its judicial system.  Possible explanation of this positive relationship between the judicial efficiency and the entrepreneurship is credit rationing.  This credit rationing may accentuate the income inequality in a given economy.  Banerjee and Duflo (2005): "one person may start a large or more technologically advanced firm because he has money and another may start a small and backward one because he does not".  Increasing income inequality
  • 6. Credit Market Imperfection, Inequality and Capital Accumulation 6 Motive  Possible explanation of this positive relationship between the judicial efficiency and the entrepreneurship is credit rationing.  This credit rationing may accentuate the income inequality in a given economy.  Banerjee and Duflo (2005): "one person may start a large or more technologically advanced firm because he has money and another may start a small and backward one because he does not".  Increasing income inequality
  • 7. Credit Market Imperfection, Inequality and Capital Accumulation 7 Motive  Regressing the GINI index on the Judicial Efficiency (JE) over the period 1999-2001 for 42 countries.
  • 8. Credit Market Imperfection, Inequality and Capital Accumulation 8 Research question  What is the impact of the credit market imperfections on the relationship between inequality and capital accumulation ?
  • 9. Credit Market Imperfection, Inequality and Capital Accumulation 9 Literature  Inequality is negatively associated with growth: Bertola (1993), Alesina and Rodrik (1994), Persson and Tabellini (1994), Perotti (1996), …  Growth is an inverted U-- curve of inequality: Banerjee and Duflo (2005)  However, the effect of credit market imperfection on the relationship between inequality and capital accumulation was rarely analyzed in a theoretical model.
  • 10. Credit Market Imperfection, Inequality and Capital Accumulation 10 Literature  Galor and Moav (2004) : income inequality --> development process in the presence of credit constraints.  Aghion and Bolton (1997) is the departure model of our research.  They developed a theoretical model analyzing the relation between inequality and capital accumulation in presence of a moral hazard problem.
  • 11. Credit Market Imperfection, Inequality and Capital Accumulation 11 Literature  Aghion and Bolton (1997) showed that the capital accumulation process begins by widening the inequalities but reduces them in later stages.  Through which mechanism ? -> "As more capital is accumulated there are more and more funds available in the economy to finance a smaller and smaller pool of borrowers. Thus the equilibrium lending terms are progressively shifted in favour of borrowers.“  Motivated by the stylized facts we expect that this result may change if another type of financial imperfection is considered.
  • 12. Credit Market Imperfection, Inequality and Capital Accumulation 12 Model  Add new type of credit market imperfections in addition to the moral hazard problem: costly contract enforcement (judicial inefficiency).  Contrarily to Aghion and Bolton (1997), enabling wealthy agents to undertake larger projects. The size of the project is not normalized to one and wealthy agents could enlarge their projects.
  • 13. Credit Market Imperfection, Inequality and Capital Accumulation 13 Model  The economy is closed and contains a sequence of one- period-lived overlapping generations.  Each generation is composed of a continuum of mass 1 agents indexed by i.  The only source of heterogeneity among agents is their inherited wealth .  Each agent i is endowed with one unit of effort (labour)
  • 14. Credit Market Imperfection, Inequality and Capital Accumulation 14 Model  An agent undertakes a project requiring a minimum fixed investment generating an uncertain revenue …… or invest his wealth in a bank.  The project could be self-financed or completed by an external financing Where and
  • 15. Credit Market Imperfection, Inequality and Capital Accumulation 15 Model  Agents are risk-neutral and their utility depends only on consumption and bequest . where is the effort cost.  An agent divides the income he receives between consumption and bequest.
  • 16. Credit Market Imperfection, Inequality and Capital Accumulation 16 Model  Initial distribution of wealth at date t=0 a proportion π of the young agents has a low inherited wealth w₀<w and constitutes the class i=l. .  A proportion 1-π has a high inherited wealth w₀ <w₀<w and constitutes the class .  An agent of class i=l,h with an initial wealth {t}^{i}≥w could self-finance his project. He may have an incentive to ask for a bank loan in order to enlarge it.
  • 17. Credit Market Imperfection, Inequality and Capital Accumulation 17 Model  Even the project succeeds, an agent may have an incentive to default on the loan.  the bank seizes a fraction of the output. The unseized fraction corresponds to an enforcing repayment cost (the efficiency's level of the judicial system).
  • 18. Credit Market Imperfection, Inequality and Capital Accumulation 18 Model  An optimal investment contract between the agent and the bank specifies the repayment schedule for the class i agent asking for an external financing  In order to prevent the borrower's default, the repayment ….. should be at most equal to the default's cost ……..  The maximum amount of loan the bank grants to the agent of class i is
  • 19. Credit Market Imperfection, Inequality and Capital Accumulation 19 Model  Given the unit repayment rate the borrower chooses the effort to supply and the amount of loan in order to maximize his expected revenue net of both repayment and effort costs
  • 20. Credit Market Imperfection, Inequality and Capital Accumulation 20 Model  Given that:  The economy comprises at each date t a continuum of agents belonging to the two classes,  The random returns of the project are iid  The proportion of successful projects is for the class i.  The return of the banks from loans granted to the agents of class i is deterministic and is given by .  Assuming a competitive banking system 
  • 21. Credit Market Imperfection, Inequality and Capital Accumulation 21 Model  Only agents with an initial endowment prefer strictly becoming depositors.  Those with prefer becoming entrepreneurs.  The threshold is determined by the indifference condition
  • 22. Credit Market Imperfection, Inequality and Capital Accumulation 22 Results  The wealth inequality widens between the two classes of agents in a first stage of development. Outside, it remains constant or widens depending on the deposit interest rate ceiling. Why ? Without a ceiling on the deposit interest rate there exists always a value of such that making the low inheriting agents always preferring depositing and the high inheriting agent preferring undertaking a project
  • 23. Credit Market Imperfection, Inequality and Capital Accumulation 23 Results Numerical simulations of the judicial efficiency effect on the wealth inequality (measured by the GINI index) in the case of an interest rate ceiling  An increase of the judicial efficiency:  reduces the speed of convergence of the GINI index to its long run level.  decreases the long run level of wealth inequality.
  • 24. Credit Market Imperfection, Inequality and Capital Accumulation 24 Results
  • 25. Credit Market Imperfection, Inequality and Capital Accumulation 25 Results