On the interplay between intergenerational transfers and natural resources

On the interplay between intergenerational transfers andnatural 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 effects of resource regeneration rate γ onintergenerational transfers (volume, growth performance, financing)in an OLG model in which:

Education transfers matter for human capital accumulation.

Natural resources are a necessary factor of production.Q: would more abundant resources slow down human capitalaccumulation and decrease transfers?


Aim of the paper


Education transfers matter for human capital accumulation.Natural resources are a necessary factor of production.

Q: would more abundant resources slow down human capitalaccumulation and decrease transfers?


Aim of the paper


Education transfers matter for human capital accumulation.Natural resources are a necessary factor of production.Q: would more abundant resources slow down human capitalaccumulation 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-termsustainability?

Lack of existing studies on the interplay between resourceregeneration and intergenerational transfers.


Preview of results

For γ = γlow : transfers create a substantial gap in growth ratesbetween CMA (g ∗) and IMA (g ]) allocations:

(g ∗ − g ]

)> 0

For γ = γhigh: (i) volume of transfers increases; (ii) higher growthrates (g ∗; g ]); (iii) higher gap (g ∗ − g ]) in growth rates.Lump-sum tax τ case: transfers can be financed through a constantshare of output τt

y ∗t.


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 selfish agents, natural resources andhuman capital externalities.

First period t: young agents invest in education et to acquire ht+1units of knowledge.

Second period t + 1: adult agents supply inelastically their humancapital ht+1 to the production sector.Third period t + 2: agents retire and consume their income.


General set-up


First period t: young agents invest in education et to acquire ht+1units of knowledge.Second period t + 1: adult agents supply inelastically their humancapital ht+1 to the production sector.

Third period t + 2: agents retire and consume their income.


General set-up


First period t: young agents invest in education et to acquire ht+1units of knowledge.Second period t + 1: adult agents supply inelastically their humancapital 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 thefollowing technology:

Yt = F (Ht ,Xt ) = Hαt X

1−αt , (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 oldagents; β ∈ (0, 1) = private discount factor.


General set-up: human capital accumulation

Human capital ht+1 linearly depends on the economy’s propensity tospend in education εt ≡ et

yt:

ht+1 = η

(ht ,etyt

)= ht ·

(1+ µ

etyt

), (3)

where µ > 0 is the constant exogenous marginal impact of educationinvestment.

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 productionconstitutes resource assets At :

Rt = Xt + At . (5)


General set-up: household behaviour

Adult and old agents exchange shares of At on a perfectlycompetitive financial market. Net Present Value of resource incomesover the life-cycle is:

1Nat·(qt+1At+1 + pt+1Xt+1

1+ it+1− qtAt

), (6)

where it+1 is the implicit rate of return on resource wealth.

Given (4) and (5), the maximization of (6) implies two basicconditions of no arbitrage:

1 Price equalization between resource assets and resource use pt = qt , ineach period.

2 The dynamics of resource rents must satisfy the generalized Hotellingrule

pt+1pt

=qt+1qt

=1+ it+11+ γ

. (7)


Complete markets allocation (CMA)

The typical consumer maximizes utility (2) subject to:

ct = wtht − 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−1yt−1

), with et−1 = bt−1. (10)

The solution to this problem yields the focs:

v ′ (c?t )βv ′(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 thefollowing balanced growth path:

(1+ i?) = (αµ)α (1+ γ)1−α , (13)

H?t+1H?t

= (1+ n) (1+ µε?) , (14)

X ?t+1X ?t

=1+ γ

αµ(1+ n) (1+ µε?) , (15)

Y ∗t+1Y ∗t

=

(1+ γ

αµ

)1−α

(1+ n) (1+ µε?) , (16)

where the equilibrium interest rate factor (1+ i?) is a constantweighted average of γ and µ.


Incomplete markets allocation (IMA)

Incomplete markets: young agents are not able to borrow to financetheir education. The consumer maximizes utility (2) subject to:

ct = wtht − st , (17)

dt+1 = st (1+ it+1) , (18)

ht = ht−1. (19)

The solution to this problem yields:

v ′ (ct ) = β (1+ it+1) v ′ (dt+1) . (20)

The growth rate of human capital will no longer be endogenouslydetermined by the model:

H ]t+1H ]t

=ht+1`t+1ht`t

= (1+ n)ht+1ht

= (1+ n). (21)


Incomplete markets allocation (IMA)

Log utility with Cobb-Douglas production technology gives thebalanced growth path:(

1+ i ])=

[(1+ β− α) (1+ n)

αβ

]α

(1+ γ)1−α , (22)

H ]t+1H ]t

= (1+ n), (23)

X ]t+1X ]t

=αβ

1+ β− α(1+ γ) , (24)

Y ]t+1Y ]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 2012

13

14

15

16

17

18

19Gamma (low)=0.5

Time

Out

put C

MA

& IM

A (le

vels

)

5 10 15 200

1

2

3

4

5

6

7

8Gamma (low)=0.5

Time

Out

put g

ap C

MA

IMA

(leve

ls)


Simulation: results

5 10 15 2010

12

14

16

18

20

22

24

26

28

30Gamma (high)=0.8

Time

Out

put C

MA

& IM

A (le

vels

)

0 5 10 15 200

1

2

3

4

5

6

7

8

9

10Gamma (high)=0.8

Time

Out

put g

ap C

MA

IMA

(leve

ls)


Simulation: results

5 10 15 201

2

3

4

5

6

7

8Gamma (low) & (high)

Time

Out

put

gap

CM

AI

MA

(le

vels

)

5 10 15 200

0.5

1

1.5

2

2.5

3Transfers effect (levels)

Time

Diff

eren

ce in

out

put

gaps

5 10 15 200

1

2

3

4

5Gamma (low) & (high)

TimeOut

put

CM

A &

IM

A (

grow

th r

ates

, %

)

5 10 15 201.6

1.62

1.64

1.66

1.68

1.7Transfers effect (growth rates)

Time

Gap

in g

row

th r

ates

(%

)


The revenue side: financing transfers

Assume that a planner wants to implement transfers. For any t, alump-sum tax τt is levied on adults to finance transfers zPt and z

Et :

ct = wtht − st −[zEt + z

Pt

], (28)

dt+1 = (1+ it+1)(st + zPt

); (29)

zPt = bt (1+ n) , zEt = e?t−1 (1+ i

?) , (30)

Nat · τt = Nyt · zEt +Not · zPt . (31)

then the competitive equilibrium achieves again the effi ciency of theCMA allocation.

Does the share of output devoted to transfers financing vary with γ ?

τty ?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 zPt and zEt and stronger

H ?t+1H ?t,

which combined with more abundant resources boosts g ∗.

IMA: only more abundant resources boosts g ].

γhigh expands the gap in growth performance between CMA and IMAallocations induced by transfers.

Lump-sum tax case: share of output devoted to transfers τty ?tis not a

function of γ.


Concluding remarks

Intuition: results indicate potential large positive effects on socialsecurity policies from more renewable resources.

Future research:Evaluation of different taxation instruments.

The other side of the story.

Thanks for attention!


Concluding remarks


Future research:

Evaluation of different taxation instruments.




Concluding remarks


Future research:Evaluation of different taxation instruments.




On the interplay between intergenerational transfers and natural resources

Economy & Finance

Transcript of On the interplay between intergenerational transfers and natural resources