Structural Change and Endogenous Resource Use Regulation∗

Natural resource decline and recovery – Structural change and endogenous resource use regulation∗

Marie-Catherine Riekhof1 and Frederik Noack2

1University of Kiel 2University of British Columbia

Preliminary Version, January 31, 2020

Abstract

Many renewable resources have been used beyond sustainable levels. While some stocks have been subsequently recovered, oth- ers are still being over-exploited, although overuse causes direct economic losses to the resource industry. We build a dynamic dual economy model of a local economy with a resource and a manufacturing sector. We focus on structural change and costly regulation as potential explanations for the observed pattern of overuse-and-recovery. We show that structural change alone

∗We would like to thank participants at the Montpellier Workshop 2019 and the Kiel Colloquium of the Agricultural Economists for helpful comments.

1 does not generate the observed patter. With the possibility of costly regulation, the pattern is generated. We also provide empirical evidence that shows that more people in agriculture—as instrument for the number of ﬁshermen under open access—are associated with resource recovery. This suggests that the value of regulation relative to open access, which is higher in case of many resource users, drives resource recovery.

1 Introduction

Human well-being depends on many different kinds of renewable resources, like fish, forests or soil. Over time, many renewable resources have gone through a period of use beyond sustainable levels and recovery—sometimes even to levels above the maximum sustainable yield (MSY) level1—, see e.g. Figure 1 for different fish species per country over time. Nevertheless, some stocks are still considered overused.2 1The maximum sustainable yield level refers to the resource stock at which the steady state harvest is maximal, which is the level at which the regeneration of the resource is maximal. In a standard logistic growth model, this is at half the carrying capacity. Resource stocks below their MSY level are considered biologically overused. 2See Figure A in the Appenddix that shows the share of overused fish stocks over time, or calculations related to the Earth Overshoot Day, https://www.overshootday. org/newsroom/past-earth-overshoot-days/, last accessed Jan 23 2020.

2 Figure 1: Standardized ﬁsh mortality across countries over time Argentina Brazil Canada Chile China

0 Iceland India Indonesia Japan Malaysia

0 Mexico Morocco Norway Peru Philippines

1 Fishing mortality [f/fmsy] 0 South Korea Spain Thailand United Kingdom United States

0 1960 1980 2000 1960 1980 2000 1960 1980 2000 1960 1980 2000 1960 1980 2000 f / fMSY is the ﬁshing mortality (harvest over stock) divided by the ﬁshing mortality that would prevail at the maximum sustainable yield level

Here, we want to examine potential drivers of these developments, especially of the (temporary) use beyond sustainable levels, and under which conditions renewable resources are more likely to be recovered and conserved in a wider context of technological progress, structural change and that regulation creates resource rents. Technological progress has oc- curred on the wider economic level, but also in renewable resource harvesting. For example, in fisheries, hydraulic equipment for gear and fish handling and electronics for fish finding have helped the fishery to ex- pand3. Fish survived as long as they were outside of human reach (Pauly

3http://www.fao.org/fishery/technology/en, last accessed Janaury 26th, 2020.

3 et al., 2002). Structural change relates to the change in sectoral employ- ment shares over time. Initially, most people worked in the natural resource sector, i.e. in agriculture, and only moved to the manufacturing sector with the on set of industrialization(Acemoglu, 2009). The number of fishermen have also declined over time (see e.g. Crilly (2011) for data on the UK). The value of regulation relates to the classical result that resource rents are zero under open access. The value of proper regulation is demonstrated e.g. in the exercise of Costello et al. (2016). who compare the profits or losses of different management strategies of global fish stocks. In our analysis, we focus on factors related to income generation and abstract from possible changes in preferences or discounting. We look at the role of technical progress for resource use, but also for its impact on labor reallocation from resource harvesting to manufacturing, i.e. structural change. We also consider the role of regulation and under which conditions it is introduced in a binding manner. To do so, we set-up a non- overlapping generations model of a dual economy in a small open economy setting with sector-specific exogenous technical change. The idea is that general technical progress spills-over to the local sectors, e.g. through investment into new equipment or the use of new methods. Our focus is on fast growing, internationally tradable renewable resources like fish. Regulation is often local, and even if it is decided upon nationally, enforcement is usually local, rendering effective regulation a local decision. We consider individuals that decide to either work in resource harvesting or in manufacturing as well as a resource manager who can decide whether and to what extent to regulate resource use. The manager faces two types of regulation costs. First, ‘enforcement’ costs may depend on the number of users that would prevail under open access. With regula-

4 tion, some of them are forced to leave the resource sector, such that regulation costs relate to dealing with opposition concerning the introduction of regulation and of enforcing regulation, i.e. of keeping some users out of the sector. Second, ‘monitoring’ costs may depend on the number of resource users that result when regulation is introduced, e.g. because their behavior needs to be monitored. In this case, the costs of regulation can be influenced by determining the number of resource users under regulation. We find that under open access with a positive rate of technical progress in resource harvesting, structural change may lead to resource conservation if income opportunities in the manufacturing sector become sufficient attractive. If this is not the case, the resource will be depleted over time. The good news is that in the set-up with declining relative regulation costs, the manager will eventually—i.e. after a period of resource use beyond long-run levels—decide to regulate the resource and the stock will recover. If regulation costs are initially high and do not decline relative to resource income, we can construct a situation in which regulation will never be im- plemented. We show that regulation levels under enforcement costs lead to a resource stock that corresponds to the maximum-sustainable yield resource stock, while regulation levels under monitoring costs lead to a resource stock that is initially—i.e. with the onset of regulation—above the maximum sustainable yield level. Over time, the stock level also converges towards the MSY level. The resource use patterns generated by the three scenarios in our model, i.e. open access, monitoring costs, and enforcement costs, can all be found in the observed fishing patterns in Figure 1. The mechanism in the model relates to technical progress that increases harvesting capacity and thereby leads to a degradation of the resource

5 stock, resulting income decline in the resource sector, and structural change. Endogenous regulation explains resource recovery. Regulation is enacted if the gain, i.e. the difference between income in the resource sector under regulation vs. under open access, is larger than weighted regulation costs. We also use regression analysis to test the model’s prediction on the relation between the number of resource users and the introduction of regulation. Results provide evidence that favors regulation over structural change to explain resource recovery. In general, the literature on endogenous regulation in resource use is scarce. Our analysis adds to the theoretical literature by combining the possibility of renewable resource depletion in the long-run (as in Riekhof et al. (2018)) with endogenous regulation (as in Copeland and Taylor (2009), Tajibaeva (2012), Costello and Grainger (2018)). Costello and Grainger (2018) model endogeneous regulation within a static economic framework, Copeland and Taylor (2009) focus on the steady state (with a positive resource stock), and Tajibaeva (2012) consider endogenous regulation in an intertemporal theoretical framework without modeling technological change and by examining the transition paths with the help of numerical simulations. Our paper is also related to the literature on governance of the commons, especially the assumption that the costs of governing the commons depends on the number of resource users (Ostrom, 1990; Baland and Plat- teau, 1996). However, our study differs in two main aspects. First, we ana- lyze the situation in an explicitly dynamic context and second, we assume that there are two groups, the resource users and the resource regulators. Especially our consideration of different types of regulation costs and their relation to observed resource use pattern adds to the literature.

6 Our study is further related to the huge literature on the Environmen- tal Kuznets Curve (EKC) (e.g. Grossman et al. (1995), Carson (2010), Brock and Taylor (2010), SSmulders et al. (2011)) and the literature on forest transition (Angelsen, 2007; Meyfroidt and Lambin, 2011). However, in contrast to this literature we do not assume perfect regulation but instead model the regulation itself as endogenous and captures different types of regulation costs. In contrast to the literature on the EKC that usually looks at pollution, the resource users of renewable resources have a direct economic costs from overuse. The next section presents the model. We then present the outcome in a given period as well as some comparative statics results, before we turn to the development over time. In our model, we made several simplifying assumptions that make the analysis easier, but do not alter the general mechanisms at work in the model. They are discussed in Section 7. In this section, we also conclude.

2 A dual economy model with costly regulation

In this section, we describe our dual-economy model with a local labor market, a manufacturing sector and sector that relates to harvesting a common pool resource, sector-speciﬁc exogenous technological change and non-overlapping periods. The set-up is that of a small open economy with exogenous prices of the resource and the manufacturing good. The set-up is motivated by village economies, as e.g. described in Noack et al. (2018) and references therein. A local resource manager can decide whether to restrict access to the resource and if, to what level. Restricting access is costly.

7 The economy is inhabited by a continuum of individuals with their mass normalized to one. Each individual is endowed with one indivisible unit of labor that can be allocated to one of the sectors to generate income. Individual effort is a combination of labor and the prevailing technology level. The normalization of the mass of individuals to one implies that that the impact of an individual on resource use is very small, i.e. zero. At the beginning of each period t, each individual decides in which sector to work by comparing incomes. It chooses the sector that generates higher income. If access to the resource sector is restricted due to regulation, the decision who is allowed to harvest the resource is made by lottery.

Individual income in the natural resource sector is denoted by YR. It is a combination of the resource price PR and the harvested amount H. Har- vest is according to a Gordon-Schaefer-type technology (Schaefer, 1957; Gordon, 1954), that combines effort—here labor enhanced by the level of technology AR—and the resource stock S according to

H(t) = AR(t)S(t). (1)

Labor costs in this setting are opportunity costs for working in the manufacturing sector. Income then is

YR(t) = PR(t)S(t)AR(t). (2)

The resource price PR(t) is determined on the world market and is exogenous for the small open economy. In some scenarios, we consider the case of the prices growing at the rare γPRProductivity increases exogenously over time according to

AR(t + 1) = AR(t)(1 + γAR) (3)

8 with the rate of technical progress γR. Natural resource dynamics in con- tinuous time τ are

dS(τ) S(τ) = ρS(τ) 1 − − S(τ)nr(τ)A (τ) dτ κ R with intrinsic growth rate ρ, carrying capacity κ and the share of individuals in resource harvesting nr. Units are such that τ = 1 equals one period, i.e. τ and t measured in the same units (see Noack et al. (2018)). We assume that resource dynamics are fast, such that a steady state with dS(τ)/dτ = 0 is reached within a period. The resulting resource stock—denoted with an asterisk—is

nr(t)A (t) S(t)∗ = κ 1 − R . (4) ρ

Income of an individual in the manufacturing sector YM(t) depends on the world price for manufacturing goods PM and on productivity AM according to

YM(t) = PM(t)AM(t). (5)

The world price is exogenous for the individuals living in the small open economy. Productivity increases over time according to

AM(t + 1) = AM(t)(1 + γM) (6) with the rate of technical progress γM. As for the resource sector, we assume that the small open economy beneﬁts from general technological progress in manufacturing. Since a change in the price or the technological level in the manufacturing sector has the same impact on income in the manufacturing sector, we only consider a change in the technological level.

9 At the beginning of each period, the regulator decides whether to regulated the resource or not, and, in case of regulation, which share of the population is allowed to harvest the resource. Let this share be denoted by n∗. The regulator may face two types of regulation costs: First, mon- ∗ itoring costs Cm(n ) that depend on the allowed share of resource users; r Second, enforcement costs Ce(n ) that depend on the resource users that would result under open access. We assume that regulation costs are lin- ear in the respective share of resource users. The regulator enacts n∗ if the ∗ ∗ r net income in the resource sector under regulation n YR − Cmn − Cen is larger than income under open access. The case of resource-use independent set-up costs Cs is discussed in the appendix. A brief remark on the timing in our model is in order. We focus on set- ups in which resources grow fast relative to technical progress, as resource dynamics reach a steady state within a period and technological progress happens between periods. We think of this as technological change em- bodied in harvesting equipment: Once in a while—here, every period—, resource harvesters need to buy new equipment. This new equipment will be more productive than the previous one due to technological progress. Assuming that investment costs in each sector are similar, we do not include them into the model. The impact of investment costs as a potential barrier to structural change is discussed in Noack et al. (2018). For a further discussion see Section 7.

10 3 Outcome within a period

Under open access, income in the resource sector is nr(t)A (t) Y (t) = P (t)A (t)κ 1 − R , (7) R R R ρ with 0 ≤ nr(t) ≤ 1. The allocation of individuals across sectors is determined by nr(t)A (t) max P (t)A (t)κ 1 − R , P (t)A (t) , (8) R R ρ M M such that three outcomes related to labor allocation under open access depicted by nr(t) can be differentiated, namely

 ( ) 1 for P (t)A (t)κ 1 − AR t > P (t)A (t)  R R ρ M M  R n (t) = 0 for PR(t)AR(t)κ < PM(t)AM(t)   ρ P (t)A (t)  1 − M M else. AR(t) PR(t)AR(t)κ Incomes in the resource sector may be higher—or lower—than in the manufacturing sector, even if everyone—or no one—harvests the resource. In- comes may also be the same in both sectors. The dependence on time shows that the number of resource harvesters may change from period to period. We now consider the problem of the resource manager. The manager has to decide whether to regulate, and in case of regulation, what population share n∗(t) should be allowed to harvest the resource. With fast resource dynamics, the manager can decide at the beginning of each period whether to regulate. We start by considered the share of population that should be allowed to harvest the resource n∗, assuming the situation is such that the manager decides to regulate. Subsequently, we will derive conditions under which the manager will introduce regulation.

11 We omit the dependence on time whenever this does not lead to confu- sion, e.g. when we present outcomes for a speciﬁc period. We will do this in the following. To ﬁnd n∗, the manager considers nAR ρ PM AM max nPR ARκ 1 − − Cmn − Ce 1 − . (9) n ρ AR PR ARκ Based on the FOC of (9), nA A P A κ 1 − R − nP A κ R − C = 0, R R ρ R R ρ m one obtains ρ C n∗ = 1 − m . (10) 2AR PR ARκ Results show that the manager sets the level of regulation, i.e. n∗ such that the stock reaches its MSY level (for Cm = 0) or even at levels above MSY ρ the MSY level (for Cm>0), with n = stating the population share in 2AR the resource sector that corresponds to a stock at its maximum sustainable yield (MSY) level.4 The latter is the case for positive monitoring costs.The intuition for this result is that costs are per resource user n∗, such that a lower number—resulting in a higher resource stock for a given technology level—reduces regulation costs. We now turn to the conditions under which a manager will enact the regulation just described. First, from the proposition, we have

Cm < PR ARκ, (11) i.e. marginal (or monitoring) costs per resource user need to be smaller than income from the resource sector when the resource stock is at its maximal level, i.e. at the carrying capacity. Second, regulation only needs to

4The maximum sustainable yield level refers maximum steady state harvest, which occurs of the stock level SMSY = κ/2. Setting SMSY equal to S∗ gives nMSY = ρ . 2AR

12 be enacted when the resource is used under open access, i.e. when nr > 0, which results for

PR ARκ > PM AM. (12)

Third, regulation is only necessary if the optimal effort is smaller than the effort that will prevail under open access, i.e. if n∗ < nR. Plugging in and re-arranging leads to

C + P (t)A (t)κ m R R > P (t)A (t). (13) 2 M M

Fourth, a manager only introduces regulation if

∗ ∗ ∗ r r r n YR(n ) − Cmn − Cen > n YR(n ), (14) i.e. if beneﬁts minus costs generate a higher income than under open access. The next two propositions summarize the conditions for regulation related to the number of resource users under open access and for the different regulation cost types, respectively.

Proposition 1 (Regulation and Resource Users under Open Access). A decrease in the number of resource users under open access nr leads to regula- r tion if 1 > 2n (t)AR(t)/ρ. An increase in the number of resource users under open access nr leads to r regulation if 1 < 2n (t)AR(t)/ρ and Ce small.

r r n (t)AR(t) Proof of Proposition 1. Use YR(n ) = PR(t)AR(t)κ 1 − ρ and re- arrange (14) to

∗ ∗ ∗ r r r n YR(n ) − Cmn > n YR(n ) + Cen , | {z } RHS ∂RHS nr(t)A (t) = P (t)A (t)κ 1 − 2 R + C . ∂nr R R ρ e

13 r r For 1 > 2n (t)AR(t)/ρ, ∂RHS/∂n > 0 results and fewer resource users r lead to regulation. If 1 < 2n (t)AR(t)/ρ and Ce small, the opposite will result.

The impact of the number of resource users under open access on the introduction of regulation is ambiguous, as there are two opposing effects. First, fewer resource users decrease regulation costs. Second, fewer resource users also decrease the gains from regulation.

Proposition 2 (Conditions for Regulation). If Conditions (11) and (13) are fulﬁlled, regulation is enacted when

• only monitoring costs prevail (Cm > 0,Ce = 0) and

P A κ 2 R R − P A > P A κC − C2 , 2 M M R R m m

• only enforcement costs prevail (Cm = 0,Ce > 0) and

P A κ 2 R R − P A > C (P A κ − P A ) . 2 M M e R R M M

Proof of Proposition 2. If Conditions (11) and (13) are fulﬁlled, Condition

Cm+PR(t)AR(t)κ (12) is also fulﬁlled, as PR ARκ > 2 . r Using that YR(n ) = PM AM and  ρ Cm  1 − AR(t) ∗ 2AR PR ARκ YR(n ) = PR(t)AR(t)κ 1 −  ρ 0.5Cm = PR(t)AR(t)κ 0.5 + PR ARκ P A κ + C = R R m 2

14 one obtains

∗ ∗ ∗ r r r n YR(n ) − Cm(n ) − Ce(n ) > n YR(n ), P (t)A (t)κ − C n∗( R R m ) > nr(P A + C ), 2 M M e ρ Cm PR ARκ − Cm ρ PM AM 1 − ( ) > 1 − (PM AM + Ce). 2AR PR ARκ 2 AR PR ARκ

Now set one of the costs to zero and re-arrange to obtain results, taking into account that

P A κ 2 P A κ 2 R R − P A P A κ + (P A )2 = R R − P A . 2 M M R R M M 2 M M

The Proposition shows that regulation is enacted when the resource in-

PR ARκ come under regulation (at the MSY level, 2 ) is sufﬁciently larger than income in the resource sector under open access, which equals income in the manufacturing sector, as compared to weighted regulation costs. In other words, regulation is enacted when the beneﬁts in terms of a higher income compared to open access outweigh the regulation costs.

4 Comparative statics

In the following, we derive some comparative static results, i.e. we ask: how does a variable impact the introduction of regulation and its strictness, keeping everything else equal? We ﬁrst consider impacts on the strictness of regulation, assuming that

15 Cm < PR ARκ holds. We ﬁnd

∂n∗ 1 C = 1 − m > 0; ∂ρ 2AR PR ARκ ∂n∗ ρ ρC ρ C = − + m = m − < 2 3 2 1 0, ∂AR 2AR 2PR ARκ 2AR PR ARκ | {z } <0 ∂n∗ ρ C = m > 2 0, ∂PR 2AR PR ARκ ∂n∗ ρ C = m > 2 0, ∂κ 2AR PR ARκ i.e. the strictness of regulation reacts to the properties of the resource, i.e. the intrinsic growth rate and the carrying capacity. A less productive resource (a lower regeneration rate and a lower carrying capacity) leads to stricter regulation. Regulation also reacts to harvesting technology, with a more efﬁcient technology per resource harvester reducing the share of harvesters allowed. Furthermore, in the case of positive monitoring costs

Cm, regulation is stricter if the resource price is smaller. The resulting smaller n∗ reduces total regulation costs, and increases individual resource income. A lower intrinsic growth rate calls for stricter regulation, but does not impact the introduction of regulation (compare Proposition 2), such that especially slower growing resource stocks are in danger of overuse, even if a resource manager is assigned. Proposition 3 summarizes some further results on the introduction of regulation.

Proposition 3 (Impacts on the introduction of regulation). If the resource price PR or the carrying capacity κ are higher, regulation will be introduced at a lower development level AR.

16 Proof of Proposition 3. An increase in PR, κ or AR makes regulation more likely if PR ARκ/2 − PM AM > Ci, i = e, m holds. Re-write conditions from Proposition 2 and deﬁne

• for the case that only monitoring costs prevail (Cm > 0, Cs = Ce = 0):

P A κ 2 L := R R − P A − P A κC + C2 > 0, m 2 M M R R m m

• for the case that only enforcement costs prevail (Cm = Cs = 0, Ce > 0):

P A κ 2 L := R R − P A − C (P A κ − P A ) > 0. e 2 M M e R R M M

Now check whether a change in a certain variable increases the LHS and thus makes it more likely that a condition holds:

∂L i = P A κ/2 − P A − C , for i = m, e; z = P , κ, A ∂z R R M M i R R

For higher PR, κ, or AR, Conditions (11) and (13) are more likely to be fulﬁlled.

5 Patterns of resource use

Now we are interested in development over time, i.e. over several periods. We focus on settings that are in line with the three stylized facts of technological progress, structural change and valuable regulation. To determine whether we see the pattern of resource use beyond-the-sustainable-level- and-recovery, we need to determine the long-run level under regulation. Proposition 4 summarizes outcomes in case of regulation.

17 Proposition 4 (Resource use under regulation over time). With enforcement costs, the level of resource use enacted under regulation—and thus the resource stock—is constant over periods and corresponds to the MSY level, while the share of resource users approaches zero. With monitoring costs, the level of resource use enacted under regulation is lower than MSY but approaches the level of resource use enacted if monitoring costs were zero.

Proof of Proposition 4. We have ρ ρ ∗( ) = MSY( ) = = n t n t t , 2AR(t) 2AR(0)(1 + γAR) such that n∗(t) → 0 as t → ∞. Plugging this into (4) yields n∗(t)A (t) S(t)∗ = κ 1 − R ρ ρ κ = κ 1 − = , 2ρ 2 ∗ ∗ κρ and total harvesting effort S (t)n (t) ∗ AR(t) = 4 constant. With monitoring costs, ρ C ∗( ) = − m n t t 1 t , 2AR(0)(1 + γAR) PR AR(0)(1 + γAR) κ

Cm and the case of no monitoring costs is approached as t → 0 PR AR(0)(1+γAR) κ as t → ∞.

If regulation is enacted, resource use approaches the same level, independent of the type of regulation costs. In the present model, this will be the maximum sustainable yield level. So this is the level that we consider to be the long-run sustainable level. Accordingly, we would see the pattern of resource use beyond-the-sustainable-level-and-recovery if temporarily, resource use beyond MSY occurs, e.g. regulation is only introduced after harvest under open access leads to a resource stock below MSY.

18 We next ‘calibrate’ our model to match technological progress in resource harvesting and structural change. The former implies γAR > 0, to match the latter, we assume (a) a high initial resource stock above the max- MSY imum sustainable yield level, S(0) > S —fulfilled for ρ > 2AR(0)—, (b) that all individuals work initially in the resource sector nr(0) = 1— fulfilled for YR(0) > YM(0), and (c) γAR > 0, which is sufficient to generate structural change, given γM ≥ 0 as increasing harvesting productivity will eventually drive down the resource stock to so low levels that the manufacturing sector becomes attractive. To also have that regulation matters, the system needs to be eventually in a state in which n∗(t) < r n (t). This will occur for γAR > 0. The outcome under open access is illustrated by the blue (dark) lines in Figure 2.

Figure 2: Development in the dual economy over time

κ = 15; ρ = 0.6, pr = pm = 1, AR(0) = 0.24, AM(0) = 1.92, γm = 0.025; γAR = 0.03;

Ce = 1.2; Cm = 1.6

19 It shows that initially all individuals work in the resource sector. While the resource stock declines right from the beginning, resource harvest and individual income can be kept constant or even slightly increased for some time due to increasing harvest productivity. This means that initially the technology is so low that people are unable to overharvest, not unusual in many developing countries. Eventually, the decline in the resource stock dominates and harvest and resource income decline. They decline until individual income in the resource sector equals income in the manufacturing sector and individuals start to leave the resource sector. The outcome with regulation in the case of monitoring costs in addition to the outcome under open access is illustrated in the same ﬁgure, Figure 2, with red (light) lines. It shows that regulation leads to structural change and to resource rents, which can be seen in the high income in the resource sector. With the introduction of regulation, the resource stock recovers immediately. This is driven by the assumption of a fast growing resource. In line with the results stated in Proposition 4, regulation is such that the resource stock recovers beyond its MSY level and then, subsequently, it approaches the steady state level from above. The next proposition discusses resource use under open access when no resource manager is in place over time and related to structural change.

Proposition 5 (Resource use under open access over time). Starting from a situation with all individuals in the resource sector and a resource stock above MSY levels, under open access,

1. no structural change and no resource use below MSY will occur for γPR ≥

γPM + γM ≥ 0 and γAR = 0,

20 2. structural change and no resource use below MSY will occur if γPR =

γAR = 0 and γPM > 0 or γM > 0,

3. structural change and resource exhaustion in the long-run will occur if

γAR + γPR > γM,

4. structural change and S = PM(0)AM(0)/(PR(0)AR(0)) in the long-run

will result for γM = γAR, γPR = 0,

5. structural change and S = κ in the long-run will result for γM > γAR +

γPR.

Proof of Proposition 5. Starting conditions imply YR(0) > YM(0) and AR(0) < ρ/2. MSY (1) Initially, YR(0) > YM(0) and S(0) > S . With only PR growing, the resource will never be overharvested. With γPR ≥ γPM + γM, resource harvesting will remain the more attractive income opportunity. r (2) Pm Am grows over time until Yr = Ym. Then n shrinks until Pm(t)Am(t) ≥

PR(t)AR(t)κ. (3) nr(t)A (0)(1 + γ )t S(t)∗ = κ 1 − R AR , ρ nr(t)A (0)(1 + γ )t S(t)∗ ⇒ 0 as t ⇒ ∞ if R AR ⇒ 1, ρ i.e. the resource stock approaches zero over time if users leave according to

r t −1 n (t) = ρ(1 + γAR) ) /AR(0).

This happens if γAR + γPR > γAM, see ρ P (0)A (0)(1 + γ )t) r( ) = − M M AM n t 1 t t . AR(t) PR(0)(1 + γPR) AR(0)(1 + γAR) κ

21 Note that n∗(t) = ρ . 2AR(t) (4) If γM = γAR, γPR = 0, ρ P (0)A (0) nr(t) = 1 − M M , AR(t) PR(0)AR(0)κ and resource users will leave the sector as technology develops. The resulting resource stock P (0)A (0)) S∗(t) = κ 1 − 1 + M M . PR(0)AR(0)κ

(5) With γM > γAR + γPR, YM(t) > YR(t) for some t onward.

From the possible outcomes discussed in the proposition, only (3) and (4) match the data in the sense that they generate structural change and resource overuse. Resource users leave the resource sector to keep incomes equal across sectors. As the wage of resource harvesters is represented by opportunity costs in this model, it means that proﬁts reduce over time and are then kept at zero. Both scenarios do not generate recovery. Scenario (5), in turn, may generate overuse and in that case will also generate recovery. Recovery in this scenario occurs up to the point that the resource is not harvested anymore, i.e. that the stock reaches its carrying capacity level. Since this is not the typical case, and since for all resource stocks in the data that have recovered over time the level is below MSY, we summarize that no pattern of resource overuse and recovery occurs under open access. One additional remark is in order. In this model, it is shown that declining natural resource productivity is a channel for structural change, in addition to potentially better job opportunities in manufacturing. Second, The next proposition relates to the introduction of regulation.

Proposition 6 (Resource use under a sole owner or a resource manager ). • Under a sole owner, resource use will increase up to the MSY level and then stay at that level.

22 • For constant prices and constant regulation costs, the resource will either eventually be regulated or structural change will render regulation obsolete.

∗ • If monitoring costs, say c,˜ were related to the harvested amount, i.e. cn˜ ARS,

PR(0) < c,˜ and γPR = 0 and γAR > γm, regulation will never be introduced.

Proof of Proposition 6. We represent a sole owner by zero regulation costs. Related to (14),

∗ ∗ r r n YR(n ) > n YR(n ), and the MSY level will be chosen as soon as the technology allows to do so. LHS grows faster than RHS in Equations in Proposition 2) or all indi-

Cm+PR(t)AR(t)κ viduals will leave the resource sector (Cond. 13, 2 > PM(t)AM(t). Modify (14) to obtain

∗ ∗ r r n PR ARS − cn˜ ARS > n YR(n ), and with PR(t) < c˜ for all t, regulation will never be introduced.

The results stated in Proposition 6 show two results that matter for un- derstanding regulation and long-run regulation use. First, if non-resource sectors are sufﬁciently attractive, structural change can lead to resource conservation without regulation. Second, the cost structure of regulation matters for whether it will eventually be introduced. Our next exercise relates to comparing the prediction of our model ‘cal- ibrated’ to structural change for four scenarios, namely ‘Open access’, ‘En- forcement costs’, ‘Monitoring costs’, as well as ‘Low (enforcement) costs’ to the data on ﬁsheries as depicted in Figure 1. Our model gives the predictions presented in Figure 5.

23 κ = 15; ρ = 0.6, pr = pm = 1, AR(0) = 0.24, AM(0) = 1.92, γm = 0.025; γAR = 0.03;

Ce = 1.2; Cm = 1.6; Ce,low = 0.1

In all cases, resource use starts below and eventually crosses the MSY level (in the figures, the MSY level corresponds to one). In the case of open access, harvest relative to the resource stock keeps increasing. In the other cases, regulation is introduced eventually. The main difference between the different regulation costs is the timing and the level of regulation. For low enforcement costs, nearly no harvest above the MSY level occurs. With higher enforcement costs, some overuse occurs. Only when the gain of regulation in terms of fishery income under MSY compared to open access is sufficiently large, regulation at the MSY level is introduced. In the case of monitoring costs, some resource use above the long-run level occurs before regulation is enacted. In this case, the level of regulation

24 leads to a ﬁshing mortality below the MSY level. The different resource use patterns, i.e. starting below MSY and reach- ing MSY, and then either (a) keep increasing (under open access), (b) remain at MSY (with low enforcement costs) , (c) cross MSY and eventually return to MSY (with higher enforcement costs), or (d) cross MSY and return to a level below MSY (with monitoring costs) can be found in the data, i.e. in Figure 1. Overall, the discussion of the different scenarios has shown that only the case of (costly) regulation generates the observed pattern of resource- use-beyond-sustainable-levels and recovery. In the next section, we relate our results to the data.

6 Data / Empirical Evidence

In this section we compare our theoretical predictions with observed pattern of overuse and recovery in resource use. The main purpose of this section is to show that individual resource extraction paths follows the pattern suggested by our theory with respect to technological progress and to examine how the number of resource users relates to the introduction of regulation. To measure resource extraction, we use the data of Costello et al. (2016). The data comprise catches of all commercially-used species world wide. The catches are matched with stock assessments where available and esti- mated stocks sizes based on observed catch histories. We follow Costello et al. (2016) in normalizing the resource extraction rate (i.e. extraction of the remaining resource stock in percent) by the ﬁsh stock speciﬁc resource extraction rate that would maximize sustainable yields. After this normal-

25 ization, extraction rates above 100 % imply harvesting beyond biologically sustainable levels independent of the biological growth of the resource. However, we are not only interested in the extraction path but also in the introduction of regulation. Regulation is almost impossible to measure for all 6000 distinct fish stocks in our data base over the 50 years that it cov- ers. Even if we had information about the introduction of regulation we could not observe enforcement or the strictness of enforcement. However, in our theory section we show that recovery or a reduction of the extraction rate only occurs if regulation is introduced. In open access, extraction stays constant after it reached the zero profit level and only the number of resource users declines as technology progresses (see discussion after Proposition 5). We use this result to define regulation. We say that regulation is introduced after extraction reached its fish stock specific peak and declines afterwards. Formally we define a fish stock as regulated if t > tmax and f < 0.9 fmax and fmax > 100. Here, tmax is the year in which the maximum resource extraction rate fmax is reached. We say that regulation starts after extraction rates have declined to 90 % to account for random fluctuations.

Finally, the condition fmax > 100 ensures that overuse existed. We match these resource data to economic data to measure technological progress and the number of ﬁshermen. Technological progress in our theory section measures the productivity per labor unit. It therefore also includes capital and is more related to GDP per capita. We therefore use real GDP per capita from the World Bank Word Development Indicators. Fishermen number are available from the OECD statistics and the FAO Fisheries and Aquaculture Statistics, but their number is endogeneous and responds to ﬁsheries regulation as suggested by the theoretical section of

26 Table 1: GDP and resource extraction

Dependent variable: log(resource extraction) (1) (2) log(GDP) 3.94∗∗∗ 3.67∗∗∗ (0.70)(0.64) log(GDP)2 −0.23∗∗∗ −0.22∗∗∗ (0.04)(0.03) Observations 167848 167848 R2 (full model) 0.17 0.41 R2 (proj model) 0.03 0.03

∗∗∗ p < 0.01, ∗∗ p < 0.05, ∗ p < 0.1

this paper. We therefore use the labor share in agriculture and the rural population also from the World Bank Word Development Indicators as exogeneous proxies, especially for the number of fishermen that would result under open access. Table 1 presents the results for the relation of GDP per capita and resource extraction (or fishing mortality). All specification include country and year fixed effects. Standard errors are clustered at the country and species level. The results show that resource extraction as an inverted U- shape relation with GDP. Resource extraction increases with GDP until it reaches it’s maximum at a GDP level of about 5000 USD and then start declining with increasing GDP levels again. Including species fixed effects in specification (2) has little impact on these estimates. Table 2 shows our results with respect to resource regulation and the number of fishermen. We measure resource regulation with a dummy that indicates if resource extraction dropped below 90 % of its maximum level.

27 Table 2: GDP and resource regulation

Dependent variable: regulation Model 1 Model 5 log(GDP) 0.03 0.07∗∗ (0.04)(0.03) Rural.Pop 0.01∗∗∗ (0.00) Observations 167848 167848 R2 (full model) 0.42 0.42 R2 (proj model) 0.00 0.01

∗∗∗ p < 0.01, ∗∗ p < 0.05, ∗ p < 0.1

Our theory states that the impact of the number of resource users under open access on the introduction of resource use regulation is ambiguous (see Proposition 1). Fewer resource users decrease regulation costs, but fewer resource users also reduce the gains from regulation. As regulation costs relative to incomes matter, we can use GDP per capita to control for the ﬁrst channel. Table 2 shows results. Results from GDP on the introduction of regulation are as expected. Furthermore, the positive impact of the number of resource users under open access on the introduction of regulation is in line with the model’s predictions on the higher gain of regulation when many individuals use the resource. Implicitly, it also supports the role of regulation for resource recovery, as resource recovery due to structural change would predict a negaitve coefﬁcient.

28 7 Discussion and conclusion

We present a dynamic model of a dual economy in which relative regulation costs decline with development, such that after a phase of natural resource use above long-run levels, the introduction of regulation leads to resource recovery. We show that structural change is not sufﬁcient to explain the pattern of resource-use-beyond-sustainable-levels-and-recovery, while the existence of an appointed resource manager who is in charge of regulation, but faces different costs, can generate the pattern. With open access or regulation and different types of regulation costs, our model matches several observed patterns of resource use in ﬁsheries. Further empirical evidence on resource regulation supports our results. We could extent the model in several directions or relax several simplifying assumptions without changing major results. For example, we could consider utility instead of income and take into account, that some resource harvesters may want to stay in the sector because they gain additional utility fro that. Furthermore, we could introduce a parameter λ that scales down resource use under open access because some (informal) rules are in place. We could consider decreasing regulation costs, as e.g. satellite data can be used for monitoring. We could also introduce hetero- geneous resource users or endogenous technical change. All this aspects will affect the exact timing of structural change and resource regulation, but they will not alter the general results of the analysis, as technological change without regulation will lead to declining resource income and structural change. Some remarks on the type of regulation and on resource dynamics are in order. In our set-up, regulation only occurs at the extensive margin, i.e. the number of resource harvesters can be restricted by regulation, but

29 not individual effort. This is just an approximation. Especially when the number of resource users becomes low, cultural preferences or resource harvester’ utilities may favor a relatively larger number of resource users with restricted effort. In this paper, the focus is on the timing on regulation and less on the type of regulation. Also, we focuses on fast resource dynamics, leading to a resource stock at its steady state level within a period, and thereby abstracting from spill-overs of resource use between different periods. Even in this setting, we ﬁnd that relatively slower growing resources are more prone to overuse, as a lower intrinsic growth rate leads to stricter regulation, but the introduction of regulation is independent from the growth rate, so that no mechanisms that ensures regulation in case of slower growing resources exists. With even slower growing resources that do not match the set-up of our model, two aspects need to be considered. First, as the stock remains low initially when resource regulation is enacted, the value of regulation in terms of income in a given period is smaller compared to fast growing resources. Second, the impact of regulation would now impact several periods, such that gains from regulation in subsequent periods as well as discounting need to be taken into account.

30 References

ACEMOGLU, D. (2009): Introduction to Modern Economic Growth, Prince- ton University Press, 1 ed.

ANGELSEN, A. (2007): Forest cover change in space and time: combining the von Thunen and forest transition theories, The World Bank.

BALAND,J.-M. AND J.-P. PLATTEAU (1996): Halting degradation of natural resources: is there a role for rural communities?, Food & Agri- culture Org.

BROCK, W. AND M.TAYLOR (2010): “The Green Solow Model,” Journal of Economic Growth, 15, 127–153.

CARSON, R. T. (2010): “The environmental Kuznets curve: seeking empirical regularity and theoretical structure,” Review of Environmental Economics and Policy, 4, 3–23.

COPELAND,B.R. AND M.S.TAYLOR (2009): “Trade, Tragedy, and the Commons,” American Economic Review, 99, 725–49.

COSTELLO,C. AND C.A.GRAINGER (2018): “Property rights, regu- latory capture, and exploitation of natural resources,” Journal of the Association of Environmental and Resource Economists, 5, 441–479.

COSTELLO,C.,D.OVANDO, T. CLAVELLE,C.K.STRAUSS,R.HILBORN,

M.C.MELNYCHUK, T. A. BRANCH,S.D.GAINES,C.S.SZUWALSKI,

R.B.CABRAL, ETAL. (2016): “Global ﬁshery prospects under contrast- ing management regimes,” Proceedings of the National Academy of Sciences, 201520420.

31 CRILLY,RUPERT;ESTEBAN, A. (2011): “Value slipping through the net: managing ﬁsh stocks for public beneﬁt,” Tech. rep., New Economics Foundation.

GORDON, H. S. (1954): “The Economic Theory of a Common-Property Resource: The Fishery,” Journal of Political Economy, 62, 124–142.

GROSSMAN,G.M.,A.B.KRUEGER, ETAL. (1995): “Economic Growth and the Environment,” The Quarterly Journal of Economics, 110, 353– 377.

MEYFROIDT, P. AND E. F. LAMBIN (2011): “Global forest transition: prospects for an end to deforestation,” .

NOACK, F., M.-C. RIEKHOF, AND M.QUAAS (2018): “Development in a Dual Economy: The Importance of Resource-Use Regulation,” Journal of the Association of Environmental and Resource Economists, 5, 233– 263.

OSTROM, E. (1990): Governing the Commons: The Evolution of Institutions for Collective Action, Cambridge University Press, 1 ed.

PAULY, D., V. CHRISTENSEN,S.GUÉNETTE, T. J. PITCHER,U.RASHID

SUMAILA,C.J.WALTERS,R.WATSON, AND D.ZELLER (2002): “To- wards sustainability in world ﬁsheries,” Nature, 418, 689–695.

RIEKHOF,M.-C.,E.REGNIER, AND M. F. QUAAS (2018): “Economic growth, international trade, and the depletion or conservation of renewable natural resources,” Journal of Environmental Economics and Management, S0095069616303254.

32 SCHAEFER, M. B. (1957): “Some considerations of population dynamics and economics in relation to the management of the commercial marine ﬁsheries,” Journal of the Fisheries Board of Canada, 14, 669–681.

SSMULDERS,S.,L.BRETSCHGER, AND H.EGLI (2011): “Economic Growth and the Diffusion of Clean Technologies: Explaining Environ- mental Kuznets Curves,” Environmental and Resource Economics, 49, 79––99.

TAJIBAEVA, L. S. (2012): “Property rights, renewable resources and economic development,” Environmental and Resource Economics, 51, 23– 41.

A Appendix

100

0 Global fish stocks below MSY level [%] MSY level Global fish stocks below 1960 1970 1980 1990 2000 2010

Source: Based on calculations from F. Noack related to Costello et al. 2016 in PNAS MSY: Maximum Sustainable Yield

33 B Set-up costs

∗ MSY Consider the case of set-up costs Cs. In this case, n = n , as the costs are independent of n∗. Regulation is enacted when Conditions (11) and (13) are fulﬁlled, and only set-up costs prevail (Cm = Ce = 0, Cs > 0) and

P A κ 2 R R − P A > C P A κ. 2 M M s R R

For the Proof, use

∗ ∗ ∗ r r r n YR(n ) − Cs − Cm(n ) − Ce(n ) > n YR(n ), P (t)A (t)κ − C n∗( R R m ) > nr(P A + C ) + C , 2 M M e s ρ Cm PR ARκ − Cm ρ PM AM 1 − ( ) > 1 − (PM AM + Ce) + Cs. 2AR PR ARκ 2 AR PR ARκ and compare to the proof of Proposition 2.