On the interplay between intergenerational transfers and natural resources

On the interplay between intergenerational transfers and
natural resources
South-Eastern Europe Journal of Economics, 12(2):
167-199.
Roberto Iacono
Norwegian Uni. of Science and Tech. (NTNU) & Sør-Trøndelag University College (HiST)
Trondheim, 20.03.2015
Roberto Iacono (Institute) Iacono (2014), SEEJE, 12(2): 167-199. Trondheim, 20.03.2015 1 / 21

Aim of the paper
To study the e¤ects of resource regeneration rate γ on
intergenerational transfers (volume, growth performance, …nancing)
in an OLG model in which:
Education transfers matter for human capital accumulation.

Aim of the paper
Natural resources are a necessary factor of production.

Aim of the paper
Natural resources are a necessary factor of production.
Q: would more abundant resources slow down human capital
accumulation and decrease transfers?

Motivation and policy relevance
Large policy debates in resource-rich countries (e.g. Norway,
Venezuela) on long-term sustainability of social security policies
(Harding & van der Ploeg, 2013).
Does higher resource renewability undermine or guarantee long-term
sustainability?
Lack of existing studies on the interplay between resource
regeneration and intergenerational transfers.

Preview of results
For γ = γlow : transfers create a substantial gap in growth rates
between CMA (g ) and IMA (g]) allocations: g g] > 0
For γ = γhigh: (i) volume of transfers increases; (ii) higher growth
rates (g ; g]); (iii) higher gap (g g]) in growth rates.
Lump-sum tax τ case: transfers can be …nanced through a constant
share of output τt
yt
.

Background theoretical literature
Intergenerational transfers: Rangel (2003), Boldrin and Montes
(2005).
Natural capital as production input: Mourmouras (1991).

General set-up
Three period OLG model with sel…sh agents, natural resources and
human capital externalities.
First period t: young agents invest in education et to acquire ht+1
units of knowledge.

General set-up
units of knowledge.
Second period t + 1: adult agents supply inelastically their human
capital ht+1 to the production sector.

General set-up
units of knowledge.
Second period t + 1: adult agents supply inelastically their human
capital ht+1 to the production sector.
Third period t + 2: agents retire and consume their income.

General set-up: log-linear model
Production. A physical good Yt is produced according to the
following technology:
Yt = F (Ht , Xt ) = Hα
t X1 α
t , (1)
where: Ht ht `t = aggregate human capital; Xt = resource use.
Preferences. The utility function of an agent born at t 1 is:
ut 1 (ct , dt+1) = v (ct ) + β v (dt+1) , (2)
where: v ( ) = ln ( ); (ct , dt+1) = consumption for adult and old
agents; β 2 (0, 1) = private discount factor.

General set-up: human capital accumulation
Human capital ht+1 linearly depends on the economy’s propensity to
spend in education εt
et
yt
:
ht+1 = η ht ,
et
yt
= ht 1 + µ
et
yt
, (3)
where µ > 0 is the constant exogenous marginal impact of education
investment.
When εt = 0, human capital is constant: ht+1 = ht .

General set-up: resource dynamics
Resource stock Rt obeys the dynamic law:
Rt+1 = (Rt Xt ) (1 + γ) , (4)
where γ > 0 is the constant rate of biological renewal. For γ = 0,
resources are exhaustible (e.g. oil, minerals).
In each period, the fraction of Rt not destroyed in production
constitutes resource assets At :
Rt = Xt + At . (5)

General set-up: household behaviour
Adult and old agents exchange shares of At on a perfectly
competitive …nancial market. Net Present Value of resource incomes
over the life-cycle is:
1
Na
t
qt+1At+1 + pt+1Xt+1
1 + it+1
qt At , (6)
where it+1 is the implicit rate of return on resource wealth.
Given (4) and (5), the maximization of (6) implies two basic
conditions of no arbitrage:
1 Price equalization between resource assets and resource use pt = qt , in
each period.

General set-up: household behaviour
Adult and old agents exchange shares of At on a perfectly
competitive …nancial market. Net Present Value of resource incomes
over the life-cycle is:
1
Na
t
qt+1At+1 + pt+1Xt+1
1 + it+1
qt At , (6)
where it+1 is the implicit rate of return on resource wealth.
Given (4) and (5), the maximization of (6) implies two basic
conditions of no arbitrage:
1 Price equalization between resource assets and resource use pt = qt , in
each period.
2 The dynamics of resource rents must satisfy the generalized Hotelling
rule
pt+1
pt
=
qt+1
qt
=
1 + it+1
1 + γ
. (7)

Complete markets allocation (CMA)
The typical consumer maximizes utility (2) subject to:
ct = wt ht st bt 1 (1 + it ) bt (1 + n) , (8)
dt+1 = st (1 + it+1) + bt (1 + n) (1 + it+1) , (9)
ht = η ht 1,
et 1
yt 1
, with et 1 = bt 1. (10)
The solution to this problem yields the focs:
v0 (c?
t )
βv0 d?
t+1
= 1 + i?
t+1, (11)
w?
t
∂η ht 1, e?
t 1/yt 1
∂e?
t 1
= 1 + i?
t . (12)

Complete markets allocation (CMA)
Log utility with Cobb-Douglas production technology gives the
following balanced growth path:
(1 + i?
) = (αµ)α
(1 + γ)1 α
, (13)
H?
t+1
H?
t
= (1 + n) (1 + µε?
) , (14)
X?
t+1
X?
t
=
1 + γ
αµ
(1 + n) (1 + µε?
) , (15)
Yt+1
Yt
=
1 + γ
αµ
1 α
(1 + n) (1 + µε?
) , (16)
where the equilibrium interest rate factor (1 + i?) is a constant
weighted average of γ and µ.

Incomplete markets allocation (IMA)
Incomplete markets: young agents are not able to borrow to …nance
their education. The consumer maximizes utility (2) subject to:
ct = wt ht st , (17)
dt+1 = st (1 + it+1) , (18)
ht = ht 1. (19)
The solution to this problem yields:
v0
(ct ) = β (1 + it+1) v0
(dt+1) . (20)
The growth rate of human capital will no longer be endogenously
determined by the model:
H]
t+1
H]
t
=
ht+1`t+1
ht `t
= (1 + n)
ht+1
ht
= (1 + n). (21)

Incomplete markets allocation (IMA)
Log utility with Cobb-Douglas production technology gives the
balanced growth path:
1 + i]
=
(1 + β α) (1 + n)
αβ
α
(1 + γ)1 α
, (22)
H]
t+1
H]
t
= (1 + n), (23)
X]
t+1
X]
t
=
αβ
1 + β α
(1 + γ) , (24)
Y ]
t+1
Y ]
t
= (1 + n)α αβ (1 + γ)
1 + β α
1 α
. (25)

Simulation: calibration
1 period = 25 years.
Growth rate of population n = 0.
α = 0.85; (1 α) = 0.15.
β = 0.61 (annual β = 0.98).
H0 = 10; R0 = 100.
As regards γ 0, I compare two cases:
γlow = 0.5, (26)
γhigh = 0.8. (27)

Simulation: results
5 10 15 20
12
13
14
15
16
17
18
19
Gamma (low)=0.5
Time
OutputCMA&IMA(levels)
5 10 15 20
0
1
2
3
4
5
6
7
8
Gamma (low)=0.5
Time
OutputgapCMA-IMA(levels)

Simulation: results
5 10 15 20
10
12
14
16
18
20
22
24
26
28
30
Gamma (high)=0.8
Time
OutputCMA&IMA(levels)
0 5 10 15 20
0
1
2
3
4
5
6
7
8
9
10
Gamma (high)=0.8
Time

Simulation: results
5 10 15 20
1
2
3
4
5
6
7
8
Gamma (low) & (high)
Time
5 10 15 20
0
0.5
1
1.5
2
2.5
3
Transfers effect (levels)
Time
Differenceinoutputgaps
5 10 15 20
0
1
2
3
4
5
Gamma (low) & (high)
Time
OutputCMA&IMA(growthrates,%)
5 10 15 20
1.6
1.62
1.64
1.66
1.68
1.7
Transfers effect (growth rates)
Time
Gapingrowthrates(%)

The revenue side: …nancing transfers
Assume that a planner wants to implement transfers. For any t, a
lump-sum tax τt is levied on adults to …nance transfers zP
t and zE
t :
ct = wt ht st
h
zE
t + zP
t
i
, (28)
dt+1 = (1 + it+1) st + zP
t ; (29)
zP
t = bt (1 + n) , zE
t = e?
t 1 (1 + i?
) , (30)
Na
t τt = Ny
t zE
t + No
t zP
t . (31)
then the competitive equilibrium achieves again the e¢ ciency of the
CMA allocation.
Does the share of output devoted to transfers …nancing vary with γ ?
τt
y?
t
= ε?
1 +
αµ
1 + µε?
. (32)

Are you lost? The paper in a nutshell
More abundant resources due to γhigh ! higher i and i].

CMA: higher i ! larger transfers zP
t and zE
t and stronger
H?
t+1
H?
t
,
which combined with more abundant resources boosts g .

t and zE
t and stronger
H?
t+1
H?
t
,
IMA: only more abundant resources boosts g].

t and zE
t and stronger
H?
t+1
H?
t
,
γhigh expands the gap in growth performance between CMA and IMA
allocations induced by transfers.

t and zE
t and stronger
H?
t+1
H?
t
,
γhigh expands the gap in growth performance between CMA and IMA
allocations induced by transfers.
Lump-sum tax case: share of output devoted to transfers τt
y?
t
is not a
function of γ.

Concluding remarks
Intuition: results indicate potential large positive e¤ects on social
security policies from more renewable resources.

Concluding remarks
Future research:

Concluding remarks
Future research:
Evaluation of di¤erent taxation instruments.

Concluding remarks
Future research:
The other side of the story.

Concluding remarks
Future research:
The other side of the story.
Thanks for attention!

On the interplay between intergenerational transfers and natural resources

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