Profit Sharing in Renewable Resource Industries: Implications for
Labor and Investment
Jacob LaRiviere∗†
May 2013
Abstract
In renewable resource industries, labor is commonly paid with a share of operating profit
rather than with a per unit-of-effort wage. This paper shows that the sharing agreements interact
with fluctuations in the natural capital stock to cause inefficient investment levels and skew
industry rents toward labor. As a consequence, optimal regulatory policy for such industries
must account for the implications of such sharing arrangements on industry level investment.
The model demonstrates why management tools like individual transferable quotas in fisheries,
may have had unexpected ecological benefits in terms of increasing and stabilizing fishery stocks.
The paper provides an illustrative example using the US Albacore fishery.
JEL Classification: Q22, J31, D24, Q58
Keywords: Rent Transfer, Efficiency, Property Rights, Fisheries
∗
Department of Economics, University of Tennessee. 525 Stokely Management Center, 916 Volunteer Blvd,
Knoxville, TN 37996-0550. email: [email protected].
†
Richard Carson, Michael Ewens, Ben Gilbert, Ted Groves, Rognvaldur Hannesson, Gunnar Knapp, Carl Lian,
Craig McIntosh, Michael Price, Dale Squires, Choon Wang, Quinn Weninger and seminar participants at Colorado’s
Environmental Workshop, Oregon, Portland State, Tennessee, Tufts, UC San Diego, Universitat Autonoma de
Barcelona and the 3rd WCERE all provided valuable comments that have greatly improved an earlier version of this
paper. Any errors are my own.
1
1
Introduction
A growing body of work examines the influence of non-traditional incentive structures on market
equilibrium and shows that market level outcomes and social welfare can be affected by small
departures from the classical economic model (Haltiwanger and Waldman (1985), Benabou and
Tirole (2006) and Ferraro and Price (2013)). While most of that literature examines consumer
preferences, there is relatively little work examining market level outcomes when firms adopt
practices at odds with classical models. One example is paying labor inputs as a percentage of
profits or revenue as opposed to with a fixed wage rate. Such “share arrangements” are common in
industries where labor’s effort is not easily observable, where output is highly variable or where the
job is inherently risky, such as renewable resource industries.
Renewable resource industries typically account for around 1.5% of US GDP. In other developed
and middle income countries such as New Zealand and Chile, renewable resource sectors can account
for up to 5% of GDP and the percentage is higher still is less developed countries. Firms in
those industries often pay labor exclusively as a percent of profit or revenue rather than with a
standard unit-of-effort wage. Share cropping agreements between land owners and farmers in the
US midwest, piece-rate logging contracts and catch share payments in fisheries are all examples of
sharing arrangements. The form and size of the split varies across resource type, but labor’s share
of costs is substantial.1 Across all industries where share remuneration is used, though, there is
generally no fixed wage component of labor factor payments, labor factor payments are significant,
and the share rate is not conditioned on the realized resource harvest.
While there has been some attention paid to the motivation for implementing share contracts,
1
In agricultural crop share arrangements in the Midwestern United States, the rule of thumb split between land
owners and farmers is 50% of the agricultural yield (Allen and Lueck (1992)). Surveys conducted jointly by US
National Marine Fisheries Service (NFMS) and the Pacific States Marine Fisheries Commission between 2003 and
2006 show that roughly 98% of of troll fleets in the US pay the crew a share of revenue less operating costs at rates
between 20 and 40% of net revenues.
2
the effects of share remuneration contracts on long run industry level investment, industry level
rents, the distribution of those rents across factors of production and optimal industry regulation
has received little attention.2 This paper uses a theoretical model of firm entry into a renewable
resource industry to evaluate how the existence of share remuneration affects investment incentives.3
The model, a generalization of Hannesson (2000), focuses on the effect of operating profit sharing,
the most common share system observed in practice, on long run industry size and the distribution
of rents within the industry under property rights management, like ITQs in fisheries. While there
are other management options such as harvest taxes, this paper focuses exclusively on property
rights management, the most widely used management practice.
In the model, risk neutral homogeneous firms make a one time entry decision into the industry
and use a homogeneous production technology for resource harvest. As is common in the literature,
we assume that the renewable resource varies stochastically period to period. While capital is
paid its fixed rental rate in every period, labor is paid as a share of operating profits: revenue less
marginal costs (e.g., fuel and other operating costs). Entry occurs until the expected marginal
benefit of investment equals marginal costs. Importantly, using a share remuneration structure
affects the rate at which profits accrue to firm owners in addition to the marginal cost of entry.
There are two main results from the theoretical model. First, in the long run, either underinvestment or over-investment in the industry is likely since the share remuneration affects both
the marginal benefit and the marginal cost of investment. In long run equilibrium, the level of
investment where the marginal expected increase in profits equals the marginal cost of entry from the
firm’s perspective is not necessarily the level at which rents are maximized from the social planner’s
2
Three common explanations for share contracts which will receive attention in the next section are moral hazard,
risk sharing and transaction costs (McConnell and Price (2006), Cheung (1969), and Gibbons (1987)). The notable
exception to the lack of attention paid to share renumeration’s affect on investment is Hannesson (2000), which this
paper extends.
3
This paper does not ask the more general question of what share level a firm will select. As a result, this is a
partial equilibrium model. However, the theoretical results of this model have general policy implications for resource
managers, regardless of the firm’s optimizing decision.
3
perspective. I show that in order for investment to be optimal in equilibrium, the firm must keep
a proportion of profits equal to capital’s share of costs. Second, if investment is optimal in the
share regime, labor must earn a share of the resource rents. From the social planner’s perspective,
additional firms are only valuable when the industry is constrained in how much they can harvest.
Relative to a fixed wage payment structure, then, a share structure must remunerate labor exactly
the equivalent of the fixed wage for the expected amount of time when the industry is harvesting at
capacity (e.g., at the investment margin). Given that labor also earns income when the industry
operates below capacity too, labor must earn rents. After showing both results in a simple model, I
show these results hold in a more general model where profits per unit of effort are allowed to vary
with the resource stock and when the share level can endogenously affect labor’s effort decision.
I then attempt to determine relative size of any inefficiencies which could result from the share
contracts. In both cases I use data from fisheries and find evidence of underinvestment under ITQ
management. First, I estimate a very simple reduced form model showing that in a particular
operating profit sharing fishery- the halibut and sablefish fishery in Alaska- that there is a significant
decrease in the percentage of total allowable catch (TAC) harvested in years where the TAC is large.
While not a test of under-capacity relative to the optimum, it is an indication that there are harvest
levels too large for the existing fleet to fully capture. Second, I perform a calibrated simulation to
identify the expected size of the investment inefficiency if one particular fishery, the North Pacific
Albacore Tuna fishery were to adopt ITQ management. I find that while there is some uncertainty
around the calibrated inefficiency, it is on the order of 2% of the calculated optimal capacity.
There are several important contributions of this paper. First, I derive a rule which can relate
share levels to optimal investment in the industry. This can help policy makers determine if ITQ
management will lead to over or underinvestment in resource industries with operating profit sharing
agreements. Second, I find theoretical evidence that labor earns a portion of rents if investment is
4
optimal in renewable resource industries. This may help to explain compensating differentials for
occupational risk of fishermen observed by Lavetti (2012). Third, the wage premium in fisheries due
to observed share contracts, has implications for fisheries managers when calculating economically
optimal TAC levels. Current practice is to use the opportunity wage that fishermen earn outside of
the fishing season which is not theoretically consistent with a model of share remuneration (nor
compensating variation for risk). Lastly, recent research shows that property rights manangement in
fisheries leads to larger fish stocks than if those same fisheries were managed with strict catch limits
(Costello et al. (2008) and Costello et al. (2009)). Underinvestment induced by share remuneration
offers an additional explanation why property rights management in fisheries have led to these
unexpected ecological benefits.
The remainder of this paper proceeds as follows: section two offers a brief literature review.
Section three builds and analyzes the theoretical model. Section four uses data from the Alaskan
halibut and sablefish fisheries to illustrate the influence of remuneration agreements on industry
level investment and the ecological benefits that can be associated from share remuneration in ITQ
fisheries. Section five offers some concluding remarks.
2
Previous Literature
Much of the relevant theoretical literature literature on share remuneration in renewable resource
focuses on fisheries. To manage fisheries, many OECD countries including the U.S. have recently made
formal announcements seeking to establishing use rights in fisheries and have established individual
transferable quotas (ITQS) in lieu of open access or total allowable catch (TAC) management.
While there are significant changes in rents, capacity, and other economic variables of interest upon
switching management regimes (Lian et al. (2010)), this model focuses exclusively on long run
equilibrium industry size after the adoption of ITQ management.
5
The existence of share remuneration arrangements has been attributed to both risk-sharing by
firm owners and a solution to principal-agent moral hazard problems. The risk-sharing explanation
for share labor payments is deeply entrenched in the crop sharing literature and has been studied
with respect to fisheries as well: in natural resource industries with highly variable output, share
remuneration reduces the variability of income to the principal or capital owners (Cheung (1969),
Plourde and Smith (1989), Allen and Lueck (1999)). Share remuneration in renewable resource
industries is also attributed to ameliorating the moral hazard problem of non-contractible effort in
a principle-agent setting (Bhattacharyya and Lafontaine (1995)). This explanation has received
considerable attention in the share-cropping, piece-rate forestry and fisheries literatures (Allen and
Lueck (1992), Gibbons (1987), and McConnell and Price (2006)). In both cases, this research
examines firm level outcomes such as productivity or optimal share levels. A third explanation is
that share contracts offer a vehicle for paying compensating variation for the inherent riskiness of
working in dangerous occupations like deckhand on a fishing vessel (Lavetti (2012)). The current
paper does not try to address the question of why share contracts exist but rather addresses the
implications of share contracts conditional on them existing. However, the general models show
that even if share remuneration induces effort by labor at the vessel level, the same industry level
effects persist.
While the firm level implications of share remuneration have been considered in the literature,
little work examines the industry level effects implementing a share remuneration structure in
renewable resource economics.4 The literature that does address industry level outcomes of share
contracts is limited to fisheries. There is a small literature studying how the adoption of ITQ
management affects remuneration structure and crew earnings. Casey et al. (1995) observes that
4
Weitzman (1983) and Weitzman (1985) examines the macroeconomic implications of remunerating labor by some
form of profit sharing as opposed to fixed wage payments. The main theoretical result of these papers is that there are
desirable increases in employment and production levels within firms and the macro-economy. Under some conditions,
Nordhaus (1988) finds that these results do not hold.
6
upon implementing ITQ management in the Alaskan Halibut fishery, crew remuneration shares were
kept constant in well over half of the vessels and crew shares went up or down in roughly equal
proportions in other vessels that stayed in the industry. Abbott et al. (2010) finds that share levels
stay roughly constant in Alaskan crab fisheries after the implementation of ITQs.5 In short, there is
no clear relationship between establishing property rights on the structure of labor contracts relative
to open access. Finally, in terms of share remuneration and fishery management, McConnell and
Price (2006) shows that not accounting for share remuneration at the firm level leads to important
implications for econometric estimation of fishery production functions.
This paper builds on the model of Hannesson (2000) and Hannesson (2007), the only work
to my knowledge analyzing the share remuneration issue as it relates to industry level outcomes
and resource management. Hannesson (2000) shows that revenue sharing in a fishery managed by
ITQs may lead to suboptimal investment in physical capital. Hannesson (2007) shows that only
with an appropriate landings tax will ITQs lead to optimal investment in a revenue sharing fishery.
Hannesson (2000) and Hannesson (2007) identify that revenue sharing affects the flow of revenue
to firm owners can change investment decisions and that only some policy instruments can take
this into account. This paper generalizes that model in two ways. First, this model accounts for
operating profit sharing, the most common remuneration structure observed in practice, and finds
that the extension leads to very clear implications for calculating optimal investment levels. Second,
I generalize the Hannesson (2000) model to account for variable unit of effort profits allowing for
more profitable harvests when the resource stock is larger. Lastly, I calculate the relative size of
the inefficiency a manager would expect to see in one large US fishery as a result of the observed
operating profit sharing.
5
Knapp (2006) examines the effect of quotas on employment in the Alaska Crab fishery, but not in the context of
remuneration structure. Brandt and Ding (2008) examines the implication of ITQs in the mid-Atlantic surf clam
fishery and find no statistically significant effect on pay to crew.
7
3
A Model of Share Wages and Renewable Resource Industries
This section develops a simple model taken from Hannesson (2000) designed to highlight the two
key features of share arrangements in renewable resources: the share arrangements themselves and
a stochastic resource stock. Share arrangements are taken as fixed subject to a individual incentive
compatability constraint for labor. As the goal of this paper is to consider the effects of share
remuneration on industry investment, we develop a partial equilibrium model and abstract from the
question of how the precise level of share remuneration is determined.6 Further, in order to focus on
these investment effects, the model also abtracts from resource stock dynamics: the resource stock
available for harvest in any given period is assumed to be a draw from a known, time-invariant
distribution and draws are assumed to be independent over time.7 The equilibrium results of
this model are robust to allowing for more complex resource stock dynamics but this simplifying
assumption greatly simplifies exposition and facilitates exposition. This section introduces the
model then assesses equilibrium investment with profit sharing under various economic assumptions:
constant unit of effort profit, variable unit of effort profit and an appendix with endogenously
determined effort decisions. First we assume the resource stock size doesn’t affect profit per unit
effort. We then generalize the model to allow for larger stock sizes and to increase the profitability
of harvest.
In the model, the amount of resource available for harvest in any period t is represented by Qt .
Qt is a random variable drawn from a time invariant distribution f (·) which has bounded support
[Qmin , Qmax ]. The distribution f (·) can be thought of as the distribution of potential harvests from
a resource stock which incorporates equilibrium ecological and economic variables.8
6
As discussed above, there are several potential explanations in the literature as to why firms and labor agree to
share remuneration structures: risk sharing, efficiency wages to induce effort or risk compensation (Cheung (1969),
McConnell and Price (2006), and Lavetti (2012)). Integrating those competing effects into a general equilibrium model
is an important extension and left to future work.
7
An alternative way to interpret this assumption is that the resource stock size is being optimally managed at the
stocks rent maximizing level, subject to some small perturbations (Reed (1979)).
8
For example, for a given resource observable characteristics (soil quality, forest age and size, fishery breeding
8
Following the model developed in Hannesson (2000), assume there are Nt homogeneous firms in
an industry at time t. All firms have some time invariant production capacity k. Firms are assumed
to have some capital cost K, some depreciation rate d and subject to some capital rental rate r.
More generally, K(r + d) can be thought of as the yearly fixed cost of lumpy physical capital units
which must be used in the renewable resource extraction process. In this model market participants
cannot substitute between capital and labor. These assumptions are restrictive but not entirely
unreasonable in renewable resource industries: Casey et al. (1995), Brandt and Ding (2008) and
Abbott et al. (2010) each find little significant changes in per vessel crew sizes in fisheries over time
and across management regimes. Since firms are homogeneous, the realized harvest in any period t,
Qt
Qt , is split evenly among firms. As a result, production per firm in year t is min[k, N
] where k is
t
firm level capacity.
In the model, risk neutral firms make a one-time entry decision. Given that the goal of this
paper is to determine long run effects of share contracts in renewable resource industries, firms
cannot make year on year entry decisions as a function of realized potential resource harvest. For
simplicity, assume that economic variables such as output price, p, unit costs, c, and all capital
costs are fixed across time.9 These simplifying assumptions in addition to the one time firm entry
decision assumption, greatly simplifies the model because the net present value of entry in any
period is identical.10 As a result, the net present value of entering the industry simplifies to a one
period problem.
Given these assumptions, consider a firm’s decision to enter or not enter the industry and exploit
stock, etc...), exogenous environmental conditions may dictate that a particular period’s growth rate is relatively large
or small relative to the average. While this is clear in the case of farming, note that in fisheries and forestry a resource
manager normally sets industry level catch limits in accordance with underlying stock dynamics so as to maximize the
net present value of the resource or some other criteria. The above assumption has that the distribution of potential
harvests is time invariant.
9
Uncertainty over economic variables can affect the relative benefits of alternative policy instruments for resource
management, but will not affect entry decisions of risk neutral firms (Hannesson and Kennedy (2005)).
10
Put another way expected profits in any given period, conditional on a being in the indsustry are identical:
Et (πt ) = Et+j (πt+j ) ∀ j.
9
the resource. Assume initially that the firm is paying labor with a fixed wage rate w and not as a
share of profits. If there were N − 1 firms in the industry, the entrant would be the N th firm and
their expected profits would be:
E[π] =
t
Σ∞
t=0 δ (p
Z
kN
− c)
Qmin
Qt
f (Qt )dQt + k(1 − F (kN )) − (d + r)K − w.
N
(1)
Noting that δ ∈ (0, 1) is an annual discount factor, there are two important aspects of equation
(1). First, since the distribution of potential harvests is time invariant and prices are assumed to
be constant, the net present value of entry in any period is proportional to the value of profits in
any one period. As a result, the right hand side of equation (1) is proportional to the the expected
profits in a single period. The remainder of this section works exclusively with the single period
expected profits for expositional clarity. Second, the bracketed expression represents the expected
resource harvest as a function of the number of firms, N , and conditional on each firms capacity k.
The integral represents the expected resource harvest for a firm conditional on the harvest level not
exceeding the industry’s production capacity, kN . For all potential resource harvest greater than
industry capacity, Q > kN , which occur with frequency (1 − F (kN )), each firm harvests exactly
their capacity, k. Note that it will not be optimal, in general, to have large enough industry capacity
to harvest all resource harvests up to Qmax .
As is common in renewable resource industries and especially fisheries, assume that firms pay
labor a share of operating profits but that the firm fully covers the capital that they provide.11
While other remuneration structures are possible such as revenue sharing examined by Hannesson
(2000) or full profit sharing found in artisinal fisheries by McClanahan and Mangi (2001), we focus
on operating profit sharing as it is much more common in managed fisheries. This remuneration
11
This remuneration structure has the added desireable feature that costs of quota in fisheries are sometimes shared
by crew and sometimes not. This remuneration structure embeds either possibility as quota is either represented as a
unit cost to be shared or a fixed cost to be paid by the firm.
10
structure, termed “operating profit sharing”, the expected revenue accruing to the firm owner would
be:
Z
kN
EV = x(p − c)
Qmin
Q
f (Q)dQ + k(1 − F (kN )) − (d + r)K.
N
(2)
Here, x is the share of profit which accrues to the firm owner. In this case, labor’s expected share of
the profit equals:
Z
kN
E[M |x] = (1 − x)(p − c)
Qmin
Q
f (Q)dQ + k(1 − F (kN )) ≥ w.
N
(3)
It is important to recognize that in any remuneration regimes, labor’s expected remuneration
must be at least as large as their opportunity wage, w. Note that it could be the case that equation
(3) could bind and determine the industry’s production capacity, kN .12 Lastly, to simplify the
exposition here and focus on industry level effects we take the firm’s share, x, as given and not the
result of a richer dynamic optimization problem of the firm.13 Instead, we derive the share level
that induces the optimal industry size from the resource manager’s perspective.
3.1
Industry Equilibrium
This subsection introduces the model’s equilibrium conditions. We consider how private equilibrium
under property rights management, such as ITQs in fisheries, relates to optimal management. Here,
optimal management refers to maximum expected profits as a funtion of industry size. While there
are management alternatives to property rights, such as taxes on output or factor inputs, we only
consider property rights- the most common management strategy in practice- in this paper. Results
12
Indeed, labor’s participation constraint may be why this subject received little attention in the past: there is no
counterfactual where labor does not participate in a renewable resource industry, by definition.
13
There is surprising stability of crew shares over time and across management regimes: Casey et al. (1995) finds
that over half of halibut fishing vessels did not change remuneration regimes in response to the transition from open
access to ITQ management. Abbott et al. (2010) finds the same stability in Alaskan crab fisheries.
11
for taxes and fees are available from the author upon request.14
Optimal Management
By definition, optimal management maximizes expected rents in the industry. In this model,
industry size and industry capacity is of first order importance becuase there is annual variation
in the natural resource stock available for exploitation but yearly fixed costs of capital. As such,
over-investment (under-investment) implies that the industry is paying too much (too little) in
yearly capital costs relative to the natural resource stock’s instrinsic stochasticity.15
Treating the number of firms as a continuous variable as in Hannesson (2000), the maximization
problem for the social planner amounts to maximizing expected revenue, equation (1) multiplied by
N , with respect to N .16 Assuming that labor is paid with a fixed wage, social planner’s first order
condition is:
(p − c)k(1 − F (kN )) = (d + r)K + w.
(4)
Equation (4) is identical to the social planner’s first order condition in Hannesson (2000). The
equation shows that the expected marginal revenue of an additional firm must equal the marginal
social cost of adding another firm in equilibrium under optimal management. It need not be the
case that total production capacity equals the maximum amount of natural capital to be exploited.
Given that physical capital payments must be made in each period, if the chance of a very large
exploitable natural capital stock is small, it may not be efficient from the social planner’s perspective
to invest in additional capacity that may only rarely be used. Put more precisely, if the percentage
14
Hannesson (2007) considers the hybrid policies of property rights and taxes or fees in the presence of revenue
sharing.
15
An intuitive industrial organization analog is the decision of a firm’s optimal production capacity as a function of
uncertain demand.
16
While firm size is a discrete variable, an individual firm’s capacity relative to a period’s harvest is very small in
renewable resource industries, making this a reasonable solution technique.
12
of time the fleet capacity will be exceeded is small, (1 − F (kN )), then the frequency with which the
marginal firm will be needed to reach the available resource stock will be small.
Property Rights and Industry Equilibrium
Establishing enforceable property rights is perhaps the most attractive method of regulating
a renewable natural resource. In the case of the timber industry, different sections of forest are
auctioned off to be harvested by logging companies. Upon winning a contract, the company has
exclusive use rights over the resource in that area. A similar arrangement arises with share-cropping
or ITQ managed fisheries in the developed world. This section uses ITQ managed fisheries as a
concrete example of property rights management.
Equilibrium in a property rights system, such as ITQ fisheries management, is defined as the
point at which the owner of one ITQ gains the same revenue from either selling the ITQ or fishing.
Assume that a quota is evenly distributed across the fleet such that each boat receives
total allowable catch (TAC) Qt set by the regulator. If an owner of quota size
1
N
1
N
of the
wishes to cease
fishing and sell her quota to the remaining boat owners, she maximizes sale revenue when she sells
equal quota shares to all vessel owners who remain in the fishery. Therefore, the sum of each vessel
owner’s willingness to pay for additional quota is the sum of each firm’s expected increase in profits
if one vessel exits and its quota is evenly split among remaining vessels. Equilibrium occurs when
the value from quota sale is equal to the value of continue fishing.
ITQ regimes are well understood when crews are paid a parametric wage and lead to efficient
outcomes. However, ITQ management under the observed operating profit sharing is not well
understood. In the case of operating profit sharing, the sum of the industry’s willingness to pay for
additional quota is given by:
13
∂ER
−N
= x(p − c)
∂N
Z
min[kN,Qmax ]
Qmin
Q
f (Q)dQ.
N
(5)
Intuitively, the willingness to pay for additional quota of the vessel owners who stay in the fishery is
equal to the increase in expected profit they gain by purchasing the quota. Boat owners gain from
purchasing additional ITQ only when their catch share is less than vessel capacity, Qt /N < k.
For a given share level, x, in ITQ management equilibrium the the expected revenue from
selling quota to existing vessels must be equal to the expected revenue from continued fishing.
This condition is represented by setting equation (5) equal to the expected benefits of fishing with
operating profit remuneration, equation (2). The resultant property rights equilibrium condition
simplifies to:
x(p − c)k(1 − F (kN )) = (d + r)K.
(6)
Equation (6) implicitly defines industry size, N , as a function of the firm’s share, x, and other
parameters. Therefore, given the motonicity of F (·), N is increasing x in equilibrium as long as
labor’s participation constraint is satisfied. Intuitively, as the share accruing to the firm rises, the
economic value of continued harvesting rises faster than the revenue from selling the property right
because purchasing additional quota is only worthwhile when a firm harvest is below firm capacity,
Qt /N < k. As a result, additional firms enter by buying the right to harvest up to the point where
the operating profit earned by capital owners equals the price which they could earn by selling the
property right and exiting the industry.
14
3.2
Analysis
This subsection presents analytical results showing how operating profit sharing in renewable resource
industries affects equilibrium investment under property rights management. Most generally, we find
regulatory policy constructed under the assumption of fixed wage payments in renewable resource
industries using share remuneration will often lead to inefficient levels of investment in the industry
and inefficient harvesting rules. We argue that insufficient investment from share remuneration is
one possible explanation for the success of ITQ management in rebuilding fish stocks.
Consider equilibrium under property rights management in an industry using operating profit
share remuneration, such as as with many ITQ managed fisheries. Equilibrium industry capacity
given fixed wage remuneration is implicitly defined by equation (4) and by equation (6). The
same conditions determine equilibrium capacity if labor is remunerated by operating profit sharing.
Rearranging terms, the following set of equations show equilibrium industry capacity in each case,
with N ∗ representing optimal industry size under fixed wage remuneration and N OP representing
equilibrium industry size under operating profit sharing:
(p − c)k(1 − F (kN ∗ ) = (d + r)K + w
x(p − c)k(1 − F (kN OP )) = (d + r)K
(7)
(8)
These two equations immediately lead to the following proposition:
Proposition 1:
If labor earns at least their opportunity wage, operating profit sharing remuneration in conjunction
with property rights management leads to an efficient industry size if and only if the share that
15
accrues to firms equals the capital cost’s share of total costs.
Proof. Since the harvest cdf, F (·) is strictly monotonic, there is a unique industry capacity
which satisfies equation (7). Impose N OP = N ∗ and divide equation (8) by equation (7). The
condition under which sharing operating profit property rights management will give the optimal
fleet capacity:
(r + d)K
=x
(r + d)K + w
(9)
This expression gives the desired result.
Proposition 1 states that for any set of parameters, there exists a unique share level, x, which
leads to optimal industry size. However, there is no reason why the share that accrues to capital
owners must equal the unique share level which guarantees optimality in general. If the share
accruing to a firm is less than the capital cost share, it means that the value of fishing for the capital
owner is too little relative to their capital contribution to the production process and investment is
too low relative to the optimum. On the other hand, as the marginal value of harvesting increases
via quota owners’ share increasing, firms stay in the industry until there is over-investment.
This phenomenon is shown explicitly in Figure 1. Investment represented as the number of firms
is shown on the x-axis. The marginal benefit and marginal cost of investment in the fixed wage
system are the upper curves. The lower curves are marginal benefit and marginal cost curves in the
share remuneration structure. The share marginal benefit curve is everywhere rotated down by x%
of the fixed wage marginal benefit curve. Additionally, the marginal cost curve is shifted down by
the labor’s wage. The Figure shows the case where equilibrium investment in the operating profit
case is less than optimal investment in the fixed wage case: N op < N ∗ . In general, though, it could
be that N op ≥ N ∗ . Note that as the share level that accrues to firm owners increases, the benefit
16
Dollars
Investment
MB
M Bshare
MC
M Cshare
x
N op
N∗
Investment
Figure 1: Share versus fixed wage remuneration. Investment in units of N .
of investment increases (e.g., the marginal benefit of investment in the share system rotates up
increasing N op in Figure 1). At the same time, the remuneration that accrues to labor falls as the
share accruing to firm owners increases.17
Now consider the implication of labor’s remuneration constraint on industry size reached in the
private equilibrium. In a profit sharing regime, optimal industry size might not be attainable without
violating labor’s participation constraint. In order to determine the effect of the remuneration
constraint on investment, compare the equilibrium condition in operating profit sharing with property
rights management, equation (8), and the equilibrium condition under optimal management, equation
(7). Comparing these two conditions immediately leads to the following proposition:
Proposition 2:
In an operating profit sharing regime under property rights management, labor’s expected remuneration is always above their opportunity wage at optimal fleet capacity.
17
An appendix considers the case of allowing the share level to endogenously affect effort decisions of labor and
therefore profits. The appendix shows that suboptimal investment is still possible in a model accounting for effort
feedbacks.
17
Proof : Equilibrium under property rights management in operating profit sharing remuneration
is given by
op
x[(p − c)k(1 − F (kNIT
Q ))] = (d + r)K.
Algebraic manipulation gives:
op
op
(p − c)k(1 − F (kNIT
Q )) − (p − c)(1 − x)k(1 − F (kNIT Q )) = (d + r)K.
Equilibrium under property rights management in the fixed wage payment case is given by
(p − c)k(1 − F (kN ∗ )) = (d + r)K + w.
op
∗
Assume that NIT
Q = N . Substitution implies that:
op
(p − c)(1 − x)k(1 − F (kNIT
Q )) = w.
However, expected remuneration in operating profit sharing is
Z
kN
E[M |x] = (1 − x)(p − c)
Qmin
As long as
R kN
Q
Qmin N f (Q)d(Q)
Q
f (Q)d(Q) + k(1 − F (kN )) .
N
> 0, it must be the case that E[M |x] > w at N ∗ giving the desired
result.
The intuition for this result is as follows: labor is paid a share of operating profits at both the
maximum harvest capacity (e.g., the investment margin) in addition to every level below harvest
capacity. However, in order for industry size to be optimal with share remuneration, the wage rate
18
must be equal to expected remuneration for the amount of time the industry harvests at capacity.
At the optimal industry size, then, labor earns more than the amount they would have been with a
fixed wage because firms share profits even when the realized harvest is lower than capacity. This
creates a rent transfer to labor. As a result, the only way that there can be an efficient level of
investment is if labor earns resource rents above the opportunity cost of labor.
While this condition might seem to imply that the labor market in such industries is in
disequilibrium, there is reason to believe that it is not. Resource extraction industries are notoriously
dangerous occupations. Lavetti (2012) finds that labor in fisheries does earn market premiums over
similar occupations not bearing the same risk levels. Therefore, it seems plausible that the embedded
riskiness of working in resource extraction could be compensated in the form of implicit rent sharing
in the form the observed share remuneration structure. While this phenomenon has been noted
in the past at the firm level, the implications for this arrangement have not been extended to
industrywide equilibrium (McConnell and Price (2006)).
3.3
Variable Unit Profits
Profit per unit of output in renewable resource harvests is sometimes thought to vary with the
size of the renewable resource stock. Intuitively, if the resource stock is very large, then unit cost
of resource harvest may be lower as firms harvest lower marginal cost units first. If the target
harvest size chosen by the resource regulator is indicative of the stock size, as almost always the
case in well managed renewable resource industries, then it is important to understand how relaxing
the constant unit profit assumption affects investment dynamics addressed in this paper. This
section extends the model to allow for variable profit per unit effort. The results from the previous
subsection directly extend to the more general model.
The most common model in renewable resource economics where profits are responsive to
19
resource stock size is in fisheries. For example, the classical Gordon-Schaefer model specifies that
total fishing profits are π(X) = P qEX α − cE where P is price, q is the catchability coefficient (a
measure of firm productivity), E is a metric for fishing effort, X is the stock size of the target
species and α is the stock elasticity. The stock elasticity indicates how sensitive costs are to the
size of the target species: for a given level of fishing effort and stock size, a larger α induces higher
unit profits where α ∈ [0, 1]. Formally, in the Gordon-Schaefer model profit per unit effort is:
π(X)
E
= P qX α − c. As a result, the Gordon-Schaefer model embeds the constant unit profit model
when α = 0.
The first and second derivative of unit profits are
∂ π(X)
E
= αP qX α−1
∂X
∂ 2 π(X)
E
= (α − 1)αP qX α−2 .
∂X 2
By inspection, the first derivative of unit profits is positive and the second derivative is negative.
Due to the expression α(1 − α) the second derivative of unit profits is zero if α = 1 or α = 0 and is
largest in magnitude when α = .5.
Now consider a generalization of the earlier model in which unit profits are a function of stock
size and there is a monotonic function mapping stock size X to realized TAC Q. Without loss of
generality, unit profits can be written as π(Q) where π 0 (Q) > 0 and π 00 (Q) < 0, as implied by the
Gordon-Schaefer model. The following two equations show the augmented total expected value
from resource harvest in the model with variable unit profit under exogenous wage payments and
operating profit sharing:
20
Z
EV
kN
Z
π(Q)f (Q)dQ − (d + r)KN − wN(10)
kN
Qmin
Z kN
EV
Qmax
π(Q)Qf (Q)d(Q) + kN (1 − F (kN ))
=
= x
Z
Qmax
π(Q)f (Q)dQ − (d + r)KN (11)
π(Q)Qf (Q)d(Q) + kN (1 − F (kN ))
Qmin
kN
As before, the equations differ only by the exclusion of the exogenous wage in equation and
inclusion of owner share level x in equation (11). The key difference between the variable unit
of effort profits case is that for the proportion of time that realized harvest is greater than fleet
capacity, the social planner accounts for the expected unit of effort profits of the entire range of
very large stock sizes. Unlike when realized harvest is below capacity, the industry only harvests
a total amount equal to capacity KN . As a result, when the social planner maximizes expected
rents over industry size N by maximizing the expected value equations the subsequent first order
conditions are more complicated. For ease of exposition, we show the first order condition with
respect to the exogenous wage compensation only:
∗
∗
∗
∗
∗
2
∗
∗
2
∗
Z
Qmax
π(kN )kN f (kN )k − π(kN )f (kN )k N (1 − F (kN )) − k N f (kN )
kN ∗
Z Qmax
+ k(1 − F (kN ∗ ))
π(Q)f (Q)dQ = (d + r)K + w
π(Q)f (Q)dQ
(12)
kN ∗
The second row in equation (12) corresponds exactly to equation (4): the direct effect of adding
another firm is the additional expected profits from harvesting previously unattainable levels of
harvest on the extensive margin. The first row also shows that adding stock dependent unit of effort
profits creates an indirect effect on the instensive margin as well. There are three different intensive
margin effects of a new firm on existing firms. The first term on the top row represents the increase
21
in expected profit when harvest is exactly at capacity due to the extra vessel. The second term in
the top row represents the fall in the expected profit margin conditional on harvest being larger
than capacity. The third term in the top row represents the decrese in expected profit for firms
already in the industry due to harvest being above capacity with lower probability.
There are two important technical differences between the constant unit of effort profit and the
variable profit first order conditions. First, with constant unit of effort profits the analogs of the
first and third terms in the top row of equation (12) cancel but in the variable profits case they do
not because unit of effort profits are larger when the resource stock is larger. Second, the middle
term in the top row is a novel addition due to allowing profits to vary as a function of stock size. It
represents a decrease in profits of adding a new firm on the intensive margin: the new firm decreases
the profit of firms already in the indsutry because the industry must split capacity profits with one
more vessel at capacity, kN ∗ .
Now consider the equilibrium level of operating profit sharing needed to induce the optimal level
of capital in the following Proposition:
Proposition 3:
Operating profit sharing remuneration with variable unit of effort profits in conjunction with
property rights management leads to an efficient industry size if and only if the share that accrues
to firms equals the capital cost’s share of total costs.
Proof : Equilibrium under property rights management in operating profit sharing remuneration
is given by:
22
Z Qmax
π(Q)f (Q)dQ
π(kN ∗ )kN ∗ f (kN ∗ )k − π(kN ∗ )f (kN ∗ )k 2 N ∗ (1 − F (kN ∗ )) − k 2 N f (kN ∗ )
kN ∗
Z Qmax
∗
+ k(1 − F (kN ))
π(Q)f (Q)dQ = (d + r)K + w
kN ∗
Equilibrium under property rights management in the fixed wage payment case is given by:
x[π(kN op )kN op f (kN op )k − π(kN op )f (kN op )k 2 N op (1 − F (kN op ))
Z Qmax
Z Qmax
2
op
op
−k N f (kN )
π(Q)f (Q)dQ + k(1 − F (kN ))
π(Q)f (Q)dQ] = (d + r)K
kN op
kN op
Assume that N op = N ∗ . Dividing the left hand side and right had side of each equilibirum condition
gives:
(r + d)K
= x.
(r + d)K + w
This gives the desired result.
There are two implications of Propostion 3. First, Propostion 3 shows that profits the key
result of the paper extends to this more general model and that in general that share remuneration
structure will not lead in general to optimal levels of investment. Second, it is unclear how allowing
for variable profits affects the steepness of the marginal benefit of investment curve. This is most
clear in Figure 2. Since unit of effort profits are assumed to increase in stock and therefore harvest,
the additional terms in the variable profits model enter into the first order condition negatively.18
More precisely, π(kN ∗ ) <
(12) jointly enter negatively.
18
R Qmax
kN ∗
π(Q)f (Q)dQ. Therefore the first and third terms in the first row of equation
23
Dollars
Investment
M Cshare
M Bshare
N op
Investment
Figure 2: Share system with variable versus fixed unit of effort profits. Investment in units of N .
However, the slope of the marginal benefit curve (e.g., the derivative of marginal benefits) could
be greater or less than the fixed unit of effort profit case as the relative magnitudes of the various
indirect effects cannot be signed without more structure on the model.19 The slope of the marginal
benefit function has important policy implications: a flat marginal benefit of investment curves
implies that small perturbations from the optimal share level will have large effects on equilibrium
investment.
Lastly, the rent sharing implications of the fixed unit of effort profit for labor can be extended
to this more general model:
Proposition 4:
In an operating profit sharing regime under property rights management with variable unit of
effort profits, labor’s expected remuneration is may not always be above their opportunity wage at
optimal fleet capacity.
Proof : Assuming that x∗ is the share level which leads to optimal investment, substitution as
in the proof of Proposition 2 leads to:
19
A proof of this result is available from the author upon request.
24
(1 − x∗ )[π(kN ∗ )k 2 N ∗ f (kN ∗ ) − π(kN ∗ )f (kN ∗ )k 2 N ∗ (1 − F (kN ∗ ))
Z Qmax
Z Qmax
∗
2
∗
π(Q)f (Q)dQ + k(1 − F (kN ))
π(Q)f (Q)dQ] = w
− k N f (kN )
kN ∗
kN ∗
But expected remuneration is:
E[M ] = (1 − x∗ )
"Z
kN ∗
Qmin
Q
π(Q)f (Q)d(Q) + k(1 − F (kN ∗ ))
N
Z
#
Qmax
π(Q)f (Q)dQ
kN ∗
Subtract the first equation from expected remuneration. If the sign of the resulting expression is
positive then labor earns rents in the variable profits case. By inspection:
kN ∗
Q
f (Q)d(Q) − π(kN ∗ )k 2 f (kN ∗ )
N∗
Qmin
Z Qmax
∗
∗ 2
∗
2
∗
+ π(kN )f (kN )k (1 − F (kN )) + k f (kN )
π(Q)f (Q)dQ] > 0
Z
(1 − x)[
π(Q)
kN ∗
since the expected unit of effort profit is greater when harvest is above capacity than when it is
equal to capacity by assumption. This gives the desired result.
Proposition 4 shows that even in this more general model in which profits are allowed to vary
with the resource stock and harvest level, labor will earn rents. The intuition is the same as in the
simpler model: in order to just addition investment at the margin, the expected benefit to vessel
owners must equal the capital cost. However, this implies that labor will earn their opportunity
wage only for the time that the industry is operating at capacity. Since labor earns wages even
when the industry is not at capacity, it causes them to earn rents.
25
This section has shown that in general operating profit sharing will not lead to optimal levels of
industry investment in property rights management. Further, in the case that industry investment
is optimal, labor must earn some proportion of resource rents. These results are robust to allowing
profit per unit of effort to vary over the resource stock size and harvest levels.20 Note that if
investment is too low, it could be that the industry will harvest less TAC than the permitted amount
in any given period. As a result, underinvestment due to share remuneration structure could lead
to a resource manager announcing harvest targets that lead to consistently lower than expected
actual harvests. This economic inefficiency on the resource manager’s part, though, could lead to an
ecological benefit in the form of a larger than expected resource stocks if not accounted for explicitly.
4
Empirical Example and Calibration Exercise
Ideally, in order to empirically test whether the presence of share remuneration can cause underinvestment or overinvestment the econometrician would like to have cross sectional vessel level data
on various fisheries with variation in share levels and management regimes. Unfortunately, data
with those characteristics does not exist. Further, it would be difficult to appropriately control for
the important intrinsic characteristics of each species (e.g., the distribution of harvests). As a result,
we use a simple reduced form model for a single fishery, the Alaskan halibut and sablefish fishery,
to motivate the potential existence of underinvestment in an ITQ managed fisheries using share
remuneration. The theoretical model is then calibrated to data from the North Pacific albacore
tuna fishery in order to predict the relative size of an inefficiency should that fishery adopt ITQ
management.
Before 1995, both the sablefish and halibut fisheries in Alaska were managed by industry level
20
An online appendix also considers the effect of letting the share level affect the effect decision of labor and therefore
endogenously affect profit per unit of effort. Through simulation, the appendix shows how that all the results shown
analytically in this section extend to that model as well but that the steepness of the marginal benefit of investment
curve are significantly affected by the nature of the relationship between effort and unit costs.
26
total allowable catch limits (TACs). Any licensed vessel could enter and fish until the sum of all
vessels’ catch reached the fishery’s catch limit.21 From 1979-1994 the fleet exceeded catch limits by
an average of roughly 5% (CGER 1999).
In 1995, the regulatory body overseeing the two fisheries implemented tradeable use rights over
both the Alaskan halibut and sablefish longline fisheries. Due to congruent season times, fishing gear
and fishing techniques, all owners of halibut quota also own sablefish quota. Operating profit sharing
was the remuneration scheme before and after the ITQ management implementation (Casey et al.
(1995)). In this fishery, quota shares are transferable but the total amount of landings associated
with a quota share fluctuates in direct proportion to the quota share as in this paper’s theoretical
model. This is widely considered a well-managed fishery.
The model presented here implies that operating profit sharing in a property rights management
regime such as ITQs in fisheries can lead to either over- or under-capacity of the fishing fleet
relative to the social planner’s optimum. If this particular fishery suffered from over-investment
then regardless of TAC, we might expect the entire TAC to be caught in every period. Alternatively,
if the fishery were under-capitalized, we would expect to observe less than 100% of the TAC taken
in on average and that in high TAC years we observe relatively lower takes in percentage terms.
Data was collected for TAC levels and landings levels for both sablefish and halibut from
1991-2009 by NFMS. The data from 1991-1994 is included to show the dramatic over-harvesting that
occured during that time period. Data from the 1980s was not included, as there was significant
fishing pressure from other nations such as Taiwan and Russia during that time period. Summary
statistics are presented in Table 1, organized by years.
The data show that after the implementation of ITQ management lower harvest rates have been
the norm.22 This is especially surprising for halibut given the price premium on halibut relative to
21
At the end of the season, it was common during this time for the regulator to place effort controls on the fishery
to avoid passing the TAC.
22
Redstone (2007) found that ITQ managed fisheries generally don’t catch the entire TAC in a given year but are
27
Table 1: Summary Statistics for Alaskan Halibut and Sablefish Fisheries by Season: 1991-2009
Species
Sablefish
Halibut
1995-2009
Average
32,600
29,700
.912
52,000
50,100
.96
Data Type
TAC Weight (tons)
Catch Weight (tons)
Catch/TAC
TAC Weight (tons)
Catch Weight (tons)
Catch/TAC
St. Dev.
4948
4264
.02
7500
7,920
.03
pre-1995
average
47,200
47,400
1
47,100
48,400
1.03
NOTE: Data from National Marine Fisheries Service Alaska Regional Office
sablefish since ITQ implementation.
23
As such, it is reasonable to see that the percent take of
the TAC is significantly lower for sablefish than for halibut, as fishermen substitute effort toward
sablefish only when marginally profitable to do so.
If under-capacity is an issue in this fishery, the econometrician would observe that in years where
the TAC for halibut is high, the percent of TAC for sablefish taken would be low, given the price
premium earned by fishermen on halibut. Table 2 presents the results of two regression specifications
that test whether this is observed in the data. In each specification, the dummy variables are used
to control for data before the adoption of property rights management in 1995 and the first year
after implementing ITQ management was controlled for to account for the transition to a new
management regime. In every specification, these controls are highly significant and not reported.
The coefficient estimates that are reported are only those on post-ITQ management explanatory
variables.
In both specifications the data are disaggregated by species. Each specification has the following
reduced form, with specification two including the additional bracketed explanatory variable.
agnostic as to why.
23
Matulich and Clark (2003) found a 35% price premium on halibut in 1999-2000. Over this time period, the whole
sale price of sablefish was $ 3.01/pound versus $ 4.15/pound for halibut.
28
catchit
T ACit
T AChalibut,t
= α + D0 δ +
β1
max(T AChalibut )
T AChalibut,t
+ 1 (i = sablef ish) ·
β2 + it .
max(T AChalibut )
(13)
Both specifications have the percentage of TAC caught for a given species in a given year. In
both specifications, the vector D represents various controls for the adoption of a new management
regime. The independent variable of interest is a given year’s TAC for halibut as a percent of the
maximum observed TAC for halibut of the entire time perdiod. In specification one, the coefficient
on this variable is the coefficient of interest: if a fleet is capacity constrained then we would expect
that as the TAC of the more valuable species is large relative to other years, then the realized catch
as a percentage of that TAC would be small. Specification three includes the interaction term for
sablefish and the ratio of the current period TAC for halibut to the maximum TAC for halibut.
Specification three is the preferred specification for this reason: since sablesifh is less valuable,
one would expect in when there is a large halibut harvest that a capacity constrained industry
would substitute effort away from sablefish and toward halibut. As a result, if the industry were
constrained we expect a negative coefficient on this variable.
The variable of interest in specification 1 isn’t significant, but the the coefficient on the added
explanatory variable in specification 2 is both significant and has the expected sign. The interpretation of the coefficient’s value, -.137, is that if the halibut fishery is allocated its maximum TAC,
then the model predicts that the sablefish fishery will catch 1.37% less of their TAC allocated in
that season than they would have if the halibut fishery was allocated 90% of their maximum TAC.
Put another way, each 10% that the halibut TAC increases, the sablefish fishery catches 1.37% less
of their allotment. This result implies that fishermen target halibut over sablefish and that this
29
Table 2: Regression Results for TAC and Catch in Alaskan Halibut and Sablefish Fishery
Explanatory Variable
year one
% max total TAC
% max Halibut TAC
Sablefish x % max Halibut TAC
intercept
r2
n
Specification
(1)
(2)
-.06** -.059***
(.029)
(.019)
-
-
-
-
-.008
.06*
(.033)
(.031)
-
-.137***
-
(.054)
.969***
.911***
(.03)
(.028)
.60
38
.65
38
This data was taken from the Alaska Regional Fisheries office of the NOAA.
*** = significant at 1%, ** = significant at 5%, 1 = significant at 10%.
Robust standard errors are used.
fishery is indeed capacity constrained. While this is suggestive evidence that capacity constraints
lead to forgone economic rents, it also might lead to an ecological benefit of a larger resource stock.
We now calibrate the model presented above using data from the albacore troll fishery off the
west coast of the United States. This fishery remunerates labor as a share of operating profit.
Currently, the troll fishery is open access but they are considering adopting ITQ management in
order to increase rents. If the albacore fishery were to adopt ITQs as a management regime, then we
would expect the number of vessels participating in the fishery to fall dramatically. The goal of the
calibration is to show the magnitude of the difference between the optimal fleet size which would
result in the fixed wage case versus the expected fleet size under the observed operating profit share
remuneration. Pacific albacore was chosen because the species has a relatively stable biomass, which
gives a lower bound to the magnitude of the investment effect of the share economy in renewable
natural resources.
The catch and biomass data are those used for the international resource stock assessments of
30
North Pacific albacore and range from 1981 to 2006 (McDaniel et al. (2006)). Over this time period
there was no formal limited entry agreement and this fishery can be thought of as open access.
Data on costs is taken from surveys collected by the South Pacific albacore industry from 1996-1999
(Squires et al. (2003)). We extrapolate the South Pacific Albacore cost structure because costs data
for the north Pacific Fleet is not available. However, the vesseel technology is very similar across
these two fisheries. Costs are divided into 2 groups: fixed costs and variable costs. Variable costs
include both labor costs and other variable costs such as fuel and bait costs. According to the survey
cost data, the crew’s remuneration regime in this fishery is operating profit sharing. Fixed costs to
vessels are paid by boat owners and variable costs like fuel and bait are shared with the crew.
A Leontief production function is assumed such that the crew’s share of the variable cost is
constant over time. This assumption could be called into question if relative prices lead to change
in investment rates but for this simple calibration that concern is ignored. Further, there was some
variation at the vessel level for the precise crew share, but that information is not available as the
publically available data set is aggregated.
Table 3 shows summary statistics for costs in the US North Pacific Albacore fishery from
1996-1999. Note that operating profit in Table 3 is calculated before the crew’s share is removed.
The crew’s remuneration accounted for an average of 43.6% of the variable costs in this fishery
between 1996 and 1999. Using Baa bond ratings for capital costs from Moody’s as in ?, variable
costs account for, on average, 45.6% of total costs. A simplification made here is that vessel capacity
is assumed to be uniform: for the calibration we take 180 short tons to be the capacity of an
individual vessel.24
Table 5 shows that the average vessel earned just positive accounting profits between 1996 and
24
This level is assumed in order to match the days at sea data taken from Squires et. al. (2003). Anecdotal evidence
from the American Albacore Fishing Association suggest that a large modern albacore vessel could have a capacity of
nearly 300 short tons. One explanation for the low catch per vessel is not only competition due to open access but
fisherman not exclusively targeting Albacore throughout the fishing season. Note that using a percentage difference
from optimal fleet capacity can abstract from this parameter.
31
Table 3: Cost Data from US South Pacific Albacore Troll Fishery, 1996-1999
Data Level
Fleet Level
Vessel Level
2001 USD/vessel
(per ton)
Ecological
Metric Tons
Category
Number Vessels
Days per Vessel
Catch per Vessel (tons)
Price Albacore
(2001 USD/ton)
Crew Remuneration
Other Variable Costs
Fixed Costs
Total Costs
Total Revenue
Operating Profit
Biomass
Yield
Ave. Yield/Biomass
Average
866
39
59.5
1,717.56
19,035 (194.40)
24,608.97 (413.60)
52,008 (874.08)
95,651.97 (1,607.60)
102,194.82 (1717.56)
77,585.85 (1303.96)
211,130
13,915
.066
St. Dev.
214.8
10.0
27.6
410.8
11,567
14,460
4,613
22,093
56,123
22,935
16,378
2,829
Data taken from Squires et al. (2003), McDaniel et al. (2006), and Squires and Vestergaard (2013)
1999 although the average vessel. This result is not unexpected given that this fishery was open
access over this period. 27.8% of operating profit accrued to the crew.25
Stock assessments from McDaniel et al. (2006) were fit to a normal distribution.26 Parameters
for potential US TAC allocations were taken from the highly migratory species fisheries management
plan as ratified by the National Marine Fisheries Service in 2007 in order to give accurate values for
ITQ management. The model is calibrated such that the Pacific albacore fishery continues to be
sustainably harvested with the TAC taken to be the function of biomass estimates taken from the
distribution described by the data.
Unit costs are primarily a function of fuel, damage to product, and bait. The component in
variable unit costs associated with diesel fuel is conservatively parameterized at 60%. This price of
diesel fuel was updated to reflect the average price from June 2010 to June 2011 taken from the EIA,
25
It is important to note that fleet capacity for this fishery is not fixed over the time period in which the data were
collected since tuna trollers can also be used in other fisheries in seasons that overlap with the albacore tuna fishery.
Therefore we calibrate the model using cost and harvest data only for trollers that exclusively fished albacore over this
period. This accounts for over 73% of the observed albacore catch. A different specification using all available data
was also performed and yield even more pronounced results.
26
A Shapiro-Wilk test for normality failing to reject the normality assumption.
32
Figure 3: The Share Economy and US West Coast Albacore Calibration
normalized to 2001 US dollars. As such, we use unit costs of $810 per ton tuna rather than the $414
per ton in the original survey data, although both specifications yield similar results. The model
was then used to find the expected fleet size relative to the optimal fleet size. Optimal fleet size is
derived by assuming that the wage rate observed in the data is the risk adjusted opportunity wage.
Figure 3 shows how fleet capacity in an operating profit regime varies relative to parametric
wages over different levels of both owner’s share and variation of the fish stock. Variation in stock
is shown as the coefficient of variation ( σµ ) of the distribution of the resource stock. The point
highlighted on the graph shows the amount of under-capacity, almost 1.3%, that we would expect
to see in this fishery given the observed coefficient of variation ( σµ =.21) and operating profit owner’s
share (x=.72) observed in the data. Proposition 1 implies that a share level of .732 would give first
best fleet size. Intuitively, the calibration shows that the size of the inefficiency is increasing with
the amount of variation due to the share remuneration structure. As such, in renewable resource
33
industries with more variable resource stocks, the size of the inefficiency would clearly be larger
given these price levels as the shadow value of capacity constraints increase. In order to address this
under-capacity, the regulator could subsidize fishing activity. An alternative management strategy
would be for the regulator to account for the the industry not catching the entire TAC allocation in
any given year. The new distribution of announced harvests accounting to incomplete harvesting
would first order stochastically dominate the old distribution, thereby inducing more entry.
Lastly, the calibration predicts that the crew earns more than their previous wage after ITQs
are in place so long as the level of share structure does not change. The implications for the
political economy of stake-holders in renewable resource industries is clear. In the case of fisheries,
although the total quantity of labor employed in the fishery will fall if an ITQ management system
is implemented, those who stay in the fishery are predicted to earn more than their opportunity
wage as rents would be shared in the property rights regime.
5
Conclusion
The findings here suggest that share remuneration has important industry level implications in
renewable resource industries. Share remuneration distorts the rate at which benefits accrue to
firms thereby affecting the entry and exit decisions of firms so long as the exploitable resource
stock is subject to some intertemporal variation. Further, share remuneration can shift industry
rents toward labor. This can explain the payment of risk premia paid to fishermen estimated by
Lavetti (2012). The relationship between compensating wage differentials, rent transfers and share
remuneration is a fruitful are for future research. Further, the theoretical model implies that a
regulator can improve efficiency by accounting for the level remuneration structure that exists in
the industry. For example, if a regulator knew an ITQ managed fishery were undercapitalized, it
could adjust industry catch limits to account for expected catches below the yearly limit, thereby
34
increasing expected harvests and costlessly increasing investment.
This model also finds that there could be ecological gains for the renewable resource stock
attributable to share remuneration if it leads to under-investment. The ecological stability observed
in ITQ managed fisheries as observed by Costello et al. (2008) may be partially explained by the
share remuneration structure observed in fisheries, as this leads to the inability of fleets under
ITQ management to catch as much resource biomass as they otherwise would have under TAC
management. While enforcement of catch limits in ITQ fisheries is another likely cause of increased
fish stocks, that ITQ managed fisheries consistently harvest below catch limits cannot be ignored as
an additional potential explanation Redstone (2007). Insofar as share remuneration can lead to
underinvestment relative to optimum levels, this paper offers another unexpected explanation.
35
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6
Appendix: Profit Sharing with Feedbacks
It is possible that as the share of profit to be received by labor increases, labor will work harder
to increase the profit margin in order to increase their own pay. This feedback effect, discussed
by McConnell and Price (2006), may affect the yield per unit effort if effort is endogenously. For
example, for a fishery time at sea, fuel use and time to the processor might all be reduced if
remuneration rates are increased in a model with effort feedbacks. This appendix developes and
simulates a theoretical model in which share remuneration has this endogenous effect on effort and
firm level profits. As with the main model, endogenizing the firm’s selection of an optimal share
level to future work. This appendix shows that suboptimal investment is still possible in a model
accounting for effort feedbacks.
Consider a profit sharing remuneration regime where the percent of operating profit which
accrues to labor, (1 − x), endogenously affects labor’s effort and in turn the firm’s unit costs. For
the exposition that follows we consider a fishery although the same model can clearly be applied to
forestry or agriculture.
In the fishery, the expected revenue accruing to the vessel owner under profit sharing with
feedback effects is
Z
EV = x (p − c(e))
kN
Qmin
Q
f (Q)d(Q) + k(1 − F (kN )) − (d + r)K.
N
Here, c(e) is a strictly convex function representing the marginal per unit cost of fishing, with e
representing crew effort. The accompanying expected crew remuneration in this model is
Z
E[M |x] = (1 − x) (p − c(e))
kN
Qmin
Q
f (Q)d(Q) + k(1 − F (kN )) .
N
Assume labor is represented by a single risk averse agent. The agent will maximize expected
39
utility which is an increasing function of expected remuneration and is a decreasing function of
effort. Assume, then, the following function form of crew utility:
Z
kN
= (1 − x)(p − c(e))
E[U ] = E[M |x, e] − g(e)
Qf (Q)d(Q) + k(1 − F (kN )) − g(e).
Qmin
Labor’s problem is therefore to maximize expected utility with respect to their level of effort, e.
The crew’s first order condition takes the form
Z
0
kN
(1 − x)(−c (e))
Qmin
Q
f (Q)d(Q) + k(1 − F (kN )) = g 0 (e).
N
This familiar expression simply says that the marginal benefit of effort is equal to the marginal
cost of effort. For added intuition, note that
Z
kN
(1 − x)
Qmin
g 0 (e)
Q
f (Q)d(Q) + k(1 − F (kN )) =
.
N
(−c0 (e))
(14)
Assuming that c0 (e) < 0, if the crew share (1 − x) increases, then the denominator on the right hand
side of equation (11) must decrease. Since c(e) was assumed to be decreasing and strictly convex,
that implies that c0 (e) will be becoming less negative as effort increases; e.g., c0 (e) approaches zero
as e → ∞. As a result, −c0 (e) will be decreasing in e. This is an intuitive result: as the crew is paid
a larger share of the boats profit, they work harder to reduce operating costs. This in turn increases
overall profits which affects the incentive of the quota owner to overinvest.
As a result, effort feedbacks imply that increasing the labor’s share of profit will decrease profits
from the boats owner directly, but the feedback effect could mitigate that effect. We now show
40
simulation results for an operating profit sharing remuneration structure when there are effort
feedbacks effects. We simulate two different functional relationships between cost and effort in the
model presented above:
• 1) c(e) = 1 −
e1−γ
1−γ
• 2) c(e) = exp−γe
• g(e) = e
• f (Q) =
1
Qmax −Qmin
• F (Q) =
Q−Qmin
Qmax −Qmin
• Qmin = 0 and Qmax = 100
These functional forms for cost and effort were chosen to show the sensitivity of the simulation
results to the relative curvature of the cost function. Cost specification 1 has decreasing absolute
curvature as defined by Arrow-Pratt, γ/e, and specification 2 has constant absolute curvature, γ.
The implication is that in specification 1, costs are less sensitive to effort at high levels than low
levels. All other functional forms are taken directly from Hannesson (2000). As in Hannesson (2000)
the model is parameterized such that optimal fleet size is 50.
The simulations show how different levels of the operating profit share, x, and different measures
of cost function and effort feedback curvature affect equilibrium industry investment. Figure 4
shows how fleet size varies with both x and γ in the model of scale wages with feedback effects with
cost specification 1. Figure 5 shows the same graph using cost specification 2. In both cases, the
plane is set at 50, the parameterized optimal fleet size.
Figure 4 shows that for a given responsiveness of cost with respect to effort, γ, the number of
boats in the fleet is essentially constant across different crew shares. However, equilibrium fleet size
41
Figure 4: Investment under operating profit remuneration and ITQ management with feedback
effects under cost function 1. Plane is set at 50, the fleet size under optimal management.
varies significantly over different levels of γ. Whereas excluding effort feedbacks implies fleet capacity
is increasing in the owners’ revenue share when the remuneration constraint doesn’t bind, including
effort feedbacks that may imply that fleet capacity is not always increasing in owners’ revenue share.
The reason is the decision by the crew to trade off between income and effort. The implication is
that if the crew’s expected remuneration is low, they will shirk and reduce the potential profit to be
received by the quota owner because the unit costs of fishing are now relatively higher. Further,
additional entry will decrease the average share of profits for each pre-existing crew. This externality
imposed on the remuneration of all crews by newly introduced vessels reduces the incentive to invest
since additional vessels will decrease effort and increase unit costs via lower expected remuneration
for all levels of effort.
Figure 5 shows that while feedbacks can potentially temper the distortion caused by profit sharing
in renewable resource production processes, it can also exacerbate them. If the cost function exhibits
constant relative curvature, then the resulting inefficiency from the share economy in renewable
42
Figure 5: Investment under operating profit remuneration and ITQ management with feedback
effects under cost function 2. Plane is set at 50, the fleet size under optimal management.
resources could be made worse. It is important to note that it makes drawing industry-specific
conclusions about profit sharing an empirical question.
It is apparent in these figures that fleet size is increasing in the elasticity of cost with respect to
effort. This makes intuitive sense since the marginal benefit of effort to workers is greater when effort
is increased. As such, lower unit costs lead to increased value of resource extraction. In sum, overor under-capacity is tempered by effort feedbacks if the cost function exhibits decreasing relative
curvature and is potentially exacerbated if the cost function exhibits constant relative curvature.
In a property rights management with fixed wage payments, as the wage rate falls, investment
will rise. We find the opposite result may be possible here: if labor is to be paid a low profit share,
then there could be less of an incentive to invest since little effort is expended and unit costs are
high. When the labor is paid a higher share, there is more effort, increased industry profits, and as
a result, more investment.
43