EC9012 - Economic Analysis: Macro
Irfan Qureshi
University of Warwick
November 1, 2015
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
1 / 17
Today
Summary of the paper
Question - 1
Question - 2
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
2 / 17
The Model
Two approaches to understanding poverty traps:
Mechanical obstacles low income agents face (indivisible investment,
credit constraints...)
More recently, behaviour of agents (conspicuous consumption...)
Galor-Zeira is old fashioned, since it assumes that the poor face
mechanical obstacles.
Indivisibility plays a huge role for the results.
Examples from the real world?
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
3 / 17
The Model
Empirical Data: Strong correlation between income distribution and
income-per-capita
Equity positively related to with both level and growth of income
This paper:
I
I
I
Explores the theoretical linkages between income distribution and
macro through investment in human capital in the presence of
imperfect capital markets.
Distribution of wealth can significantly affect aggregate economic
activity both in the short run and long run.
Countries with different inequality levels may also converge to different
steady states.
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
4 / 17
The Model
Equilibrium model of open economies with two period OLG and
inter-generational altruism.
Good produced by skill-intensive or unskilled-intensive process.
First period: Invest in human capital and acquire education or work
unskilled.
Second period: Second period: Work according to skill, consume and
leave bequests.
Only difference between individuals: inherited wealth.
Enforcement costs (supervision) on individual borrowers, so borrowing
rate higher than lending rate.
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
5 / 17
The Model
Inheritance determines decision to invest in human capital.
Distribution of wealth determines the aggregate investment of both
types of agents + output.
Rich dynasties: All generations invest in human capital, work as
skilled, leave bequests.
Poor dynasties: People inherit less, work as unskilled and leave lower
bequests.
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
6 / 17
The Model
Credit markets are imperfect (interest rate higher for individual
borrowers). In the model this effects economic activity in the
short-run.
Investment in human capital is indivisible (non-convex technology
-non ergodicity of long run dynamics).
If borrowing is difficult and costly, those who inherit a large initial
wealth, and do not need to borrow, have better access to investment
in human capital.
Therefore the distribution of wealth affects the aggregate amount of
investment in human capital and of output.
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
7 / 17
Question - 1 (a)
No effect on long run output implies no poverty trap.
Initial distribution determines fraction of rich and poor.
Lets think of two conditions sufficient rather than necessary
If you start increasing Aw u what happens?
If we calculate the exact A that brings you to the intersection, that
would be a sufficient and necessary condition.
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
8 / 17
Question - 1 (a)
With returns Aw s and Aw u to skilled workers and unskilled workers,
respectively, the resulting dynamic system for intra-dynasty bequests
is:

for
bti < b̂
 β[Aw u + bti R]
i
s
i
i
bt+1 =
β[Aw + (h − bt )θR] for bt ∈ [b̂, h)

β[Aw s + (h − bti )R] for
bti > h
where b̂ =
A(w s −w u )+θRh
R(θ−1)
b̂ is cut-off point. Anyone who inherits less than it returns to low
steady state (b L ).
Critical point, b T : inheritance less than this point imples some
positive investment in human capital but in the long run converge to
low steady state (b L ).
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
9 / 17
Question - 1 (a)
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
10 / 17
Question - 1 (a)
Note what is the effect of an increase in A; it will shift the intercept of all
pieces, shifting up the phase curve ϕ(bti ). To make sure that exists a high
steady state (b H ) we need two assumptions:
βAw s > h. This guarantees that the kink between steady states B
and C in figure is above the 45 degree line
Rβ < 1. Which as in the original model, guarantees that the first and
third pieces of the phase curve intersect the 45 degree line.
To find the cutoff  such that for A >  income distribution will have no
effect on long-run output, we need the case in which b̂ = b L as shown in
figure (b). In the intermediate piece of ϕ(bti ):
b̂ = β(Aw s + (h − b̂θR) → Â = (hθR − b̂θR +
b̂ 1
)
β ws
(1)
Then using the general expression for b̂, we can pin down Â
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
11 / 17
Question - 1 (b)
This will follow the assumptions stated in the lecture notes. Note that now
b̂ is:
u
(w − w s ) + θRh
b̂ = A
= Ab̂original
(2)
R(θ − 1)
where b̂original is the cut-off in the original version of the model. Go
through the assumptions of the model, and see which one is changed.
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
12 / 17
Question - 1 (b)
The return to investing in physical capital R is sufficiently small to
make investing in human capital attractive:
Aw s − Aw u > AhR ⇔ w s − w u > hR, which is the original
assumption. So this is unchanged.
The cost of borrowing θ is high enough such that for someone with no
bequests it is unprofitable to invest in human capital (to borrow h): θ
is sufficiently large such that Aw s − Aw u < AhθR ⇔ w s − w u < hR.
Again, the assumption is unchanged.
R is sufficiently small and w s is sufficiently large such that Rβ < 1
and βAw s > Ah ⇔ βw s > h. The first part does not depend on A.
The second part is equivalent.
w u is sufficiently small such that b̂ > β[Aw u + b̂R]. Because now b̂
depends on A, it turns out that b̂original > β[Aw u + b̂original R]
Therefore regardless of A, initial conditions have an impact on the
economy in the long-run.
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
13 / 17
Question - 2 (a)
Assume:
γw > R. This implies that return to investing in human capital is
greater than return to investing in physical capital
γw < θR. This implies that individuals do not borrow for investment
in human captial.
Income will be:
i
It+1
=
w (a + γbti )
for
w (a + γ ē) + R(bti − ē) for
bti < ē
bti ≥ ē
This means that individuals will invest all of their bequest in human
capital if it less than ē and will invest up to the cut-off ē and the rest,
bti − ē will go in investment in physical capital.
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
14 / 17
Question - 2 (a)
i
i . Hence:
From the UMP we that bt+1
= βIt+1
i
bt+1
=
i
βIt+1
=
βw (a + γbti )
for
βw (a + γ ē) + Rβ(bti − ē) for
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
bti < ē
= ψ(bti )
bti ≥ ē
November 1, 2015
15 / 17
Question - 2 (b)
Note that ψ(bti ) is concave and piecewise linear with slope:
βw γ for bti < ē
0 i
ψ (bt ) =
βR
for bti ≥ ē
By assumption βw γ > βR. Because the intercept of the first piece is > 0,
then there will always exists a unique, globally stable, non-zero steady
state for any set of parameters (i.e. income distribution will not play a
role). Note that the position of the kink in the ψ(bti ) function, and
therefore the steady state, will depend on the cut-off value ē
Irfan Qureshi (University of Warwick)
EC9012 - Economic Analysis: Macro
November 1, 2015
16 / 17
Question - 2 (b)
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EC9012 - Economic Analysis: Macro
November 1, 2015
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