Trade, Tragedy and the Commons

Brian R. Copeland and M. Scott Taylor (2009)

American Economic Review

99(3) 725-749

1

THE RESEARCH QUESTION

• What is the effect of trade liberalization on the welfare of a resource-abundant small economy when the resource management regime is endogenous?

• Previous Literature: when the management regime is exogenous and fixed and the economy exports the resource:

i) under efficient management, trade liberalization (p) increases real income (gains from trade)

ii) under open access, trade liberalization (p) exacerbates production externalities, inducing resource depletion and (likely) lowers real income.

2

Model Overview

•A Ricardian small economy with two sectors, manufacturing and a renewable resource (i.e. fishery, forest), where labor is the factor of production.

•Dynamic production externality: overcapacity in the resource sector may lead to resource depletion and even extinction

•The government regulates the use of a renewable resource by a set of agents who have a right to harvest. More specifically, it sets rules limiting the maximum fraction of labor-time allocated to the resource sector.

•However, enforcement is not perfect and agents may cheat on their allocations by the government and face the risk of punishment.

•Thus, property rights are endogenous in this setting because the government must take into account agents’ incentives to cheat.

3

Agents

•Continuum of agents with mass N

•Consume two goods: harvest from the renewable resource (H), and a numeraire manufactured good (M).

•define p as (relative price) of harvested goods

•Are risk neutral

•Share common discount rate δ

•Preferences are homothetic and identical

•Face an instantaneous probability of death given by θ• spontaneously replaced upon death

•Each agent is endowed with 1 unit of labor per unit of time4

Agents continued

The expected present discounted value of lifetime utility for a representative consumer member of vintage v can be written:

v

vt dtetvRUvW ))(()),(()(

Where’d that come from?

5

Resource (S)

•Logistic growth (G) function for the resource:

•Characteristics: •zero growth if resource is depleted or at carrying capacity•“critical depensation level” is zero: all you need is a fraction of a fish to regenerate the stock

)/1()( KSrSSG

6

Technologies and Endowments

•Schaeffer harvesting technology:

•Technology in the manufacturing sector:

•Full employment condition:

SLH h

mLM

hm LLN

7

Assumptions

• the resource is capable of generating rents:

– i.e. the price of the resource, p, is sufficiently high that pαS-w >0 for some S≤ K. (7)

• But, there is (potential) overcapacity in the resource sector: N>r/α

8

The Social Planner’s Problem

The resource manager solves the following problem:

0

)())(( dtetRUNWMax t

tL

Subject to:

LSK

SrS

dt

dS

1

mLM

LLN m

(1)

(2)

(3)

(4)

Incentive Constraint (IC)

Note: since manufactures are numeraire and have linear production technology, w=1 provided some manufactured goods are produced

9

Things to notice:

• we assume regulator has same rate of time preference as individual citizens

• but regulator doesn’t worry about death since her constituency is all citizens, including future generations, who instantly replace the deceased

• regulator acts as if maximizing the welfare of N infinitely lived agents with discount rate δ

0

)())(( dtetRUNWMax t

tL

10

The Incentive Constraint (IC)

•In order the manage the resource, the government has to impose restrictions on how much people can harvest

•policy instruments:

•government chooses l (lowercase L) = fraction of a person’s time they are allowed to spend harvesting the resource

•government imposes a fine, F, on anyone caught cheating

•ρ = exogenous probability a cheater is caught

•Problem: if the rewards are large enough, people will cheat

•Government needs to derive a set of rules that people will want to abide by

11

Some useful notation

• Let VC(t) be the expected present discount value of the income streams for an agent currently working in the resource sector and cheating for a short time interval dt.

• Let VNC(t) be the expected present discount value of the income streams for an agent who is working in the resource but not cheating.

• Let VM(t) be the discounted income stream for an agent that works only in the manufacturing sector.

wSpC wlSpl and

instantaneous rents from cheating

instantaneous rents from not cheating

12

where

)}()1()]()([){1)(1()( dttVdtdttFdttVdtdtdtdtphtV RRCC

)]()[1)(1(])1([)( dttVdtdtwdtlphdttV RNC

)](),(max[)( sVsVsV CNCR with

13

Write the incentive constraint in terms of VC etc

IV. The Incentive Constraint:

At every point in time agents choose VR(t). Thus, the condition to deter cheating is VR(t)=VNC(t), or equivalently, VNC(t) ≥ VC(t):

][ CF0]]1][1[)[()()( dtFdtdttVtV CCNC

14

Further assume the fine takes following form: those caught cheating are never allowed to harvest again (and on this you can’t cheat)

)]()([ tVtVF MR ordt

dVF

R

)(

Interest rate x asset value=dividends + capital gains

Useful aspects of this punishment:•the more valuable the resource sector is, the more costly the fine

•“the punishment reflects the severity of the crime”

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(12)

Substitute expression for F into (11) to get

• IC requires

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Evaluate in the steady state(i.e. where dS/dt=dVR/dt=…=0)

•In steady state dVR/dt=0, and the incentive constraint simplifies to:

,

17

• Define

• Φ ≥ 1• Φ measures a government’s enforcement power

– increasing in the detection probability– decreasing in rate of time preference– decreasing in probability of death

• Also define L as the number of hours the population spends harvesting; assuming the IC constraint holds,

)(

)(

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•So in the steady state (with π>0), the incentive constraint simplifies to

which in turn gives the steady state resource stock size

/NLT

)/(1

rL

KST

T

,

(13)

(14)

19

But wait…

What if ST is inconsistent with positive rents?

Then government “chooses” a smaller value of L, defined as L0, which satisfies

0 wSp OC

)/(1

rL

KSO

Owhere

]/1)[/( KpwrLO

•Thus, we can finally write the incentive constraint facing the regulator as follows:

],min[ TO LLL

(15)

LO>LT → rents sustainableLO<LT → rents unsustainable

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III. Restate the Social Planner’s Problem:

The resource manager solves the following problem:

0

)())(( dtetRUNWMax t

tL

Subject to:

K

SrSLS

dt

dS1

mLM

LLN m

(1)

(2)

(3)

(4)

],min[ TO LLL

21

22

Proposition 1

The steady state is unique. It exhibits either de facto open access, limited harvesting restrictions, or an outcome equivalent to that of the unconstrained first best.

Proof:

1. When the IC binds, Lh is either LT or L0

2. ii) When the IC does not bind, the first best L* is found maximizing the current value Hamiltonian:

])([)(

]1[SLSG

p

NLSpUH h

h

No rents

Proof of prop. 1 continued

• We can rule out corner solutions as follows:– Lh=N would drive the resource to extinction

because of maintained assumption N>r/α

– Lh=0 is not a solution when p>0 since have assumed πC>0 for some S≤K

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Proof of Prop. 1 continued

Differentiate H to get necessary conditions for an unconstrained optimum:

(i) or

(ii)

(i) into (ii) and

0)(

)1()('

Sp

SpRU

L

H

h

Sp

SpRU

)(

)1()('

dt

dLSG

p

LpRU

S

Hh

h ])([)(

)( ''

1)('

Sp

LSG h

0dt

d(A1)

24

25

Thus the unconstrained optimum solves

(iii) (A2)

Equations (A1) and (A2) determine Lh and S.

At home, walk yourself through their explanation as to why the solution is interior and unique.

0)(

SLSGH

h

)/1( KSr

Lh

Some things worth noting

• The unconstrained solution Lh is increasing in p, while the unconstrained stock size S is decreasing in p.– this makes sense: as p rises, opportunity costs of

leaving fish in the sea rises, so you leave fewer fish behind.

• Why is this important? – Because it tells us that it’ll be easier for the resource

manager to satisfy the IC constraint---by depleting the resource---when the resource price is higher.

26

27

3 types of Economies

Goal of this section

• Identify primitives (i.e. parameters) that determine whether a country will ever be able to escape the open access problem.

28

29

Proposition 2

[By definition], Hardin economies will always exhibit the facto open access in steady state. For any finite relative price p of the harvest good, we have L=LO(p) and no rents are earned in the resource sector. [Hardin economies are characterized by Ω/Φ≥1]

Intuition: •There’s excess capacity (Ω>1) by assumption. •Manager’s enforcement power (Φ) shrinks excess capacity. •But if Ω>Φ then the capacity that the manager cannot deter from harvesting still wipes out all the resource rents.

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Proposition 3

Whenever and there is overcapacity ( Ω=N/(r/α) > 1 ) in the resource sector, all economies will exhibit open access and zero rents at low resource prices.

Intuition: If the price is low enough, then resource rents are positive only if the stock is very large. Maintaining such a large stock requires L (total allowed harvest effort) be very small, which the manager cannot ensure.

0 wSpC for some KS

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Definition: OSTROM ECONOMIES(strong enforcement power, not much overcapacity, weak

incentive to extinguish)

At low resource prices (specifically, at p<p+), it’s not possible to deter cheating and maintain resource rents (de facto open access) •But at p>p+ don’t require such a large stock in order to maintain rents

• constrained optimum•However, since , i.e. the incentive to extinguish is small, maximum

rents aren’t sustainable since the (unconstrained) optimal resource stock is too large—not incentive compatible.

r

r

2

)(

21

2

32

Definition: CLARK ECONOMIES(strong enforcement power, not much overcapacity, and

strong incentive to extinguish)

At low resource prices, i.e. p<p+, not possible to deter cheating without letting rents go to zero (de facto open access)

•If p+<p<p++: constrained optimization (positive but less than maximum rents obtained)

•If p>p++: optimal restriction is incentive-compatible = first best

•Intuition: in economies with high incentives to extinguish, optimal stock size isn’t that big.

2

1 and

33

Proposition 4

Assume a group of Hardin, Ostrom and Clark economies exist, and let them share the same minimum price pmin =w/αK at which rents in the resource sector are zero. Then there exists a plow > pmin such that for any p<plow, all countries exhibit de facto open access. There also exists a finite phigh>plow such that for p>phigh, there is heterogeneity in the world’s resource management with some countries at open access, others with limited management, and some with perfect property rights protection and full rent maximization.

Proof:

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APPLICATIONS

35

TRADE LIBERALIZATION

Suppose the country is a small economy exporting the resource and resource prices rise (from γp to p, where γ<1)

Aside: are assuming “iceberg” transport costs, where γ measures the fraction of goods that survive shipment; 1- γ melts away during transit.Accordingly, if you are a resource exporter, you will receive only γp for each unit of resources that you ship. Thus the domestic price of the good will be pd= γp.

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Proposition 5:

Suppose the planner’s discount rate approaches zero and the country exports the resource good; then the marginal fall in trade frictions will:

(i) reduce steady state real income in a Hardin economy.

(ii) increase steady state real income for a Clark or Ostrom economy, if γp≥p+

(iii) decrease steady state real income for a Clark or Ostrom economy if γp<p+, but there exists a p such that if p > p, then an elimination of trade frictions leads to the emergence of a management regime and increases the steady state real income.

(iv) for a Clark economy, if γp<p+, and p > p++ then the elimination of trade frictions results in a transition from de facto open access to fully efficient management. Steady state real income rises.

Intuition

• Part (i) a marginal fall in trade frictions will reduce steady state real income in a Hardin economy.

• Intuition: Hardin economies exhibit open access (i.e. no resource rents are earned) both before and after price change, so price change leaves nominal incomes unchanged; since price of resource good rose, real incomes must fall.

37

Intuition

(ii) a marginal fall in trade frictions will increase steady state real income for a Clark or Ostrom economy, if γp≥p+

Intuition: p↑ raises value of cheating and value of penalty by identical

amountsrecall from (13) and (14) that LT and ST are independent of

pconsequence: provided new price < p++, allowable effort

and harvest (LT and ST) unchanged→ harvest exactly the same as before earns rents; Since p↑ is a terms of trade improvement, real income rises

38

Intuition

• (iii) decrease steady state real income for a Clark or Ostrom economy if γp<p+, but there exists a p such that if p > p, then an elimination of trade frictions leads to the emergence of a management regime and increases the steady state real income.

• intuition: p↑ raises profitability of resource• resource can now sustain incentive compatibility without

requiring rents be fully dissipated• provided p rises high enough, increased rents outweigh

rise in price of good

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• (iv) for a Clark economy, if γp<p+, and p > p++ then the elimination of trade frictions results in a transition from de facto open access to fully efficient management. Steady state real income rises.

• Implications of (iii) and (iv)– The success of an economy’s resource management after trade

liberalization isn’t necessarily predicted by it’s pre-liberalization success

• a price increase may drive a Clark economy from de facto open access to optimal management

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EXTENSIONS AND ROBUSTNESS CHECKS

41

42

Endogenous Monitoring

Now probability of being caught is related to labor allocated to enforcement (Le) such that the total cost of achieving a rate ρ of catching cheaters is C(ρ)=w ρ/ρo and Ф=Ф(ρ). The planner maximizes steady state surplus less monitoring costs, and

Implication: all economies are now Ostrom economies•when p sufficient low, set ρ=0 (no enforcement)•when p sufficiently high

• choose ρ high enough that some rents obtained (no Hardin economies)• never obtain full rents because marginal benefits from monitoring are

vanishingly small, so marginal cost of monitoring remains finite (dissipating some rents)

)}()(max{arg* C

If in addition to taking away the right to harvest, the government confiscates a fraction β of the agent’s future earnings in manufacturing (1- β)VM(t), the IC becomes:

No more Hardin economies•instead, when p sufficiently low, there exist low-rent equilibria with some limits on harvests

• “arbitrarily close to open access”

CNL /]1[]/1[/

Stringent Fines

43

44

CONCLUSIONS

•Existing analysis that focus on the polar cases of either i) no property rights protection or ii) perfect property rights protection, fail to explain why some resources are well managed and some poorly or why some countries succeed and other fail in the sustainable management of their resources.

•When the efficiency of the resource management, and hence the de facto property rights regime, is determined endogenously, a new set of conclusions arise. For example, trade liberalization appears more favorable for resource exporting countries than previously thought, because it might bring about the transition from an open access regime to the efficient harvesting of the resource.