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Policy options for improving ocean health using two stage tobit and rank regression production functions

By

Kim Anh Thi Nguyen 1

Curtis M. Jolly2*

Brice Merlin Nguelifack3

_____________________________________________________________

1Kim Anh Thi Nguyen is Associate Professor of Economics and Senior Lecturer at the Faculty of

Fisheries Economics, Nha Trang University, Vietnam; 2Curtis M. Jolly is Emeritus Professor of

Agricultural Economics at Auburn University, Alabama Agricultural Experiment Station, Alabama

36849; 3Brice Merlin Nguelifack is Assistant Professor in the Department of Mathematics at the United

States Naval Academy, Maryland.

*Curtis M. Jolly is corresponding author, Tel#334-524-5092; Fax 334-844-5639; e-mail:

cjolly@auburn.edu

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Ocean health production functions using two stage regression

Abstract

The paper develops a production function for the Global Ocean Health Index (OHI) for 2013. Data from

the Ocean Health Statistics, plus from the Human Development Index (HDI) for 151 countries are used.

We employ two-stage regression model to conduct this evaluation. The tobit model, used to obtain the

estimated dependent variable, results show Coastal Protection, Livelihoods and Economies, Tourism and

Recreation, Iconic Species, Clean Water and Biodiversity, Food Provision, Artisanal Fisheries

Opportunities, Natural Products, and Carbon Storage are significant variables. The rank regression in the

second stage showed that HDI and Marine Protected Areas (MPAs) significantly influenced the predicted

value of the OHI. Policy makers should note that biodiversity increases have the greatest effect on OHI,

and its improvement is within reach of even the poorest country. Countries with varying levels of

resource endowment may choose different techniques to improve OHI, but the implementation of MPAs

should be priority.

Key words: Ocean, Health, Two, stage, production, function,

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Ocean health production functions using two stage regression

1. Introduction

Oceans cover 72 % of the surface of the blue planet and constitute more than 95% of the

biosphere (UNEP, FAO, IMO, UNDP, IUCN, GRID-Arendal (2012). Based on the UN 1982 Law an

examination of territorial areas indicate that 83 countries are more ocean than land, and 54 countries are

more than 80% ocean (Degnarain and Stone 2017). Oceans support all life forms by generating oxygen,

absorbing carbon dioxide, recycling nutrients and regulating global climate change and temperature

(Deutsch et al. 2015). It is estimated that nearly 2.6 billion people rely on oceans for their protein intake

accounting for 16 percent of total global animal protein (OECD 2017). The contribution of the ocean to

human welfare is however underestimated (Costanza et al. 1997). The OECD estimates the ocean

contribution to the world economy at US$1.5 trillion and generating 31 million fulltime equivalent jobs

(OECD 2017; The Economist Intelligence Unit Limited 2015; Ebarvia 2016).

FAO estimates that fisheries and aquaculture assure the livelihoods of 10-12 percent of the

world’s population with more than 90 percent of those employed by capture fisheries working in small-

scale operations in developing countries (FAO 2014a). Oceans are equally important for food security and

coastal communities’ livelihoods. More than 500 million people are globally engaged in ocean related

livelihoods (OECD 2017). In 2012, the fisheries sector produced roughly 160 million tons of fish and

generated over US$129 billion in exports while securing access to nutrition for billions of people (FAO

2014b). Coastal areas within 100 km of the ocean account for an estimated 61 percent of the world’s total

Gross National Product (GNP) (Ebarvia 2016). Overall, healthy oceans, coasts and freshwater ecosystems

are crucial for economic growth and food production. A healthy ocean is also fundamental to the global

effort to mitigate climate change and its impacts. “Blue carbon” sinks such as mangroves and other

vegetated ocean habitats sequester 25 percent of the extra CO2 from fossil fuels and protect coastal

communities from floods and storms (World Bank 2017a).

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Ocean resources have a vast potential to unlock growth and wealth but human activity has taken a

toll on ocean health. Overfishing, pollution, habitat loss or conversion, ocean sedimentation, climate

change and industrialization are the main causes of the diminishing ability of the oceans to provide

sustainable levels of ecosystem services (Brander 2007; Noone et al. 2014; Hoegh-Guldberg et al. 2015).

Fish stocks have deteriorated due to overfishing—the FAO estimates that approximately 57 percent of

fish stocks are fully exploited and another 30 percent are over-exploited, depleted or recovering (Watson

2013). Fish stocks are further exploited by illegal, unreported and unregulated fishing, responsible for

roughly 11 to 26 million tons of fish catches or US$10-22 billion in unlawful or undocumented revenue

(Agnew et al. 2009). Overfishing has been driven by government subsidies that encourage fishing beyond

the maximum sustainable yield (Sakai 2017). Non-point source pollution from nitrogen applied on farms

has stimulated massive algal blooms that adversely affect marine life. Fish habitats are also under

pressure from pollution, coastal development, and destructive fishing practices that undermine efforts to

rehabilitate fish populations (Shwartz 2005; OECD 2017). Climate change and acidification have resulted

in coral reef bleaching and loss of tropical coral reefs. Some of the factors including industrialization that

enhance pollution have become main problems in ocean health. Hence, it is important to evaluate the

impact of these factors on ocean health.

2. Policy Framework

Policies that advocate proper management of fisheries, investment in sustainable aquaculture and

protection of strategic habitats that encourage biodiversity can partially restore ocean health (World Bank

2017a). The Economist Intelligence Unit developed the Coastal Governance Index in 2015. This is the

first index that attempts to measure and compare the regulatory environments in fragile and often-densely

populated areas (The Economist Intelligence Unit 2015). The FAO adopted the Code of Conduct for

responsible fishing in 1995 to strengthen the international legal framework for more effective

conservation, management and sustainable exploitation and production of living aquatic resources (FAO

2010-2018). Fishing conduct helps regulate quantities of fish caught and foster biodiversity which is vital

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to ocean health. The World Bank Group also developed global policies that help countries promote strong

governance of marine and coastal resources to improve the contribution to sustainable and inclusive

growth by supporting sustainable fisheries and aquaculture, establishing coastal and marine protected

areas, reducing pollution, integrating coastal resource management and developing knowledge and

capacity around ocean health (World Bank 2017b).

The World Bank’s focus on helping to restore ocean health is mainly to support developing

countries to strengthen and reform the institutions needed to enhance benefits and services that healthy

oceans provide, and to ensure that these benefits contribute to poverty reduction and shared prosperity.

Institutional strengthening requires human capital development, income increases and awareness creation,

all of which are components of the human development index (HDI). The Bank provides some $1 billion

in financing for sustainable fisheries and aquaculture, and for efforts to conserve and enhance coastal and

ocean habitats (World Bank 2017b). The Bank also provides some $5.4 billion for coastal infrastructure

such as waste treatment, watershed management and other activities that help reduce coastal pollution.

These policies have encouraged many to rethink about the ocean as a living organism whose health is

affected by human activity (World Bank 2017a).

The Convention on Biological Diversity (CBD) Aichi Target 11, adopted in 2010 at the 10th

Conference of the Parties in Nagoya, Japan, mandates that “at least 17 per cent of wetlands and inland

water, and 10 per cent of coastal and marine areas, specifically areas of specific importance for

biodiversity and ecosystem services, should be conserved” (Heinrich 2002). The IUCN World Parks

Congress 2014 Promise of Sydney, supported by over 6,000 participants from 170 countries,

recommended the “urgent increase by 2030 in effectively and equitably managed ocean area that is in

ecologically and well-connected to systems of MPAs (World Parks Congress 2014).

The research by Brander et al. (2015) shows increasing MPA’s coverage to 30 percent globally

will generate economic benefits that significantly outweigh the costs. The net benefits of increasing

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protection to 30 per cent range from the most conservative estimate of US$490 billion and 150,000 full-

time jobs in MPA management, to the most optimistic estimate of US$920 billion and over 180,000 jobs

by 2050. MPAs provide a useful pathway to sustainable blue economies that secure healthy ecosystems

and oceans for future generations.

The ‘ecosystem approach’ is central in world wild life fund (WWF)’s vision for a healthy ocean.

This approach is described as a comprehensive, integrated management of human activities based on the

best available scientific knowledge about the ecosystem and its dynamics. Policies are formulated to take

action to secure the health of the marine ecosystems, thereby achieving sustainable use of goods and

services generated through the maintenance of the integrity of the ecosystem (World Wild Life Fund

2007). This implies human activity control of the ecosystems by contributing to the structural and

functional integrity of the ecosystem. Marine protected areas and human development are essential

elements – among other ocean health goals – for the delivery of an ecosystem approach and providing the

policy framework to implement those measures to improve ocean health. Hence, an examination of the

contribution of ocean health goals and socio-economic variables such as HDI, MPAs and use regulations

to OHI is key to policy formulation to improve ocean health. Hence it is important to examine the

magnitude of the effects of those policies on ocean health.

3. Ocean Health

Ocean health has become one of the major concerns facing humanity today. Many scientists feel

that the ocean’s health is in jeopardy and needs urgent attention (Halpern et al. 2012; Halpern et al. 2015;

Rojas-Rocha 2014). As a result, the health of the marine environment is deteriorating and marine

biodiversity loss increasingly impairs the ocean’s capacity to provide ecosystem services and its ability to

recover from trepidations (Worm et al. 2006). Coastal communities are apprehensive that the ocean

waters are becoming more polluted (Guern 2017); the fish caught are smaller now than ever before and

the amount of debris found in the oceans is increasing at an alarming rate (Thompson 2017). The world is

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awakening to these human induced changes to the ocean health even at the highest policy level. Some

believe that we cannot wait and we must act now to reverse the trend.

What, then, is a healthy ocean? An acceptable definition of a healthy ocean is one that has

abundant unpolluted waters and delivers benefits to future generations (Rapport et al. 1998; Samhouri et

al. 2011). Most of the existing definitions for ocean health are based on assumptions about the intrinsic

functional benefits that the ocean provides to a community (Samhouri et al. 2011; McLeod and Leslie

2009). Hence, there is a need to quantitatively evaluate the effects of certain factors influencing ocean

health and set sustainable management targets over time.

The health of the ocean can be treated like that of an enlarged household or community. The

broad physical, social, and economic factors that contribute to an individual’s health provide an indication

of the variables that influence ocean health. The ocean, like the household, exists within a natural

environment, and socioeconomic and anthropogenic behavior determines its health position. The

economics literature suggests that the health status of an individual or community is the result of a

production function process. In the ocean health process, physical activities, human behavior, and

socioeconomic factors influence health status in the short run (Rosenzweig and Schultz 1983). In the long

run, health status can be considered similar to capital stock that can be used and reused over time, and

there can be community investment and divestment (Grossman 1972). The ocean health production

function is comparable to those of household and community health, as it uses inputs that affect health

directly (food provision and natural products), and indirectly (regulating services, coastal protection, and

cultural services), along with central aspects of human well-being that flow from multiple services

(Lowndes et al. 2014). However, the measurement of ocean health remains a real problem. To measure

the health production one must be able to quantify what constitutes the health status of the ocean.

Halpern and others (2012) and a group of 65 scientists created the Ocean Health Index (OHI),

which is a valuation tool that scientifically measures key elements from all dimensions of the ocean’s

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health—biological, physical, economic, and social. The measures are selected to reflect human and

ecosystems sustainability, a systematic approach that evaluates the overall condition of marine

ecosystems and treats nature and people as integral parts of a healthy system (Halpern et al. 2008). The

health status index proposed by Halpern and others seems to be well thought out and transparent. Though

assessable and transparent measures are proposed, there is a need to evaluate how these measures or goals

influence ocean health (Samhouri et al. 2012). The measurement of ocean health will help in the

generation of elasticities that will enable policy makers to determine the factors to be manipulated to

maintain global ocean health that provides sustainable ecosystem services. This paper presents a health

production function using the OHI and endogenous and exogenous factors that influence ocean health.

The measurement of health status using an index, however, encounters statistical problems that result in

biased coefficient estimates (Austin et al. 2000).

4. Ocean Health Production Function and Model Specification

4.1. Conceptual Framework

The ocean provides a broad range of benefits, from food products to recreational benefits that

improve the livelihoods of coastal communities (Halpern et al. 2012). On the other hand, an unhealthy

ocean can have negative consequences for human health through consumption of contaminated seafood,

swimming in polluted water, and exposure to toxins from harmful algal blooms (Knap et al. 2002;

Dewailly et al. 2002; NRC 1999; Pew Oceans Commission 2003; Stegeman et al. 2002; Tyson et al.

2004; Fleming and Laws 2006; Fleming et al. 2006; Tyson 2012). The benefits derived from a healthy

ocean are measured using the OHI which also combines key services provided by the ocean.

A computed production function that includes services and outcomes of ocean health benefits

may produce much needed information for policy studies. In this paper, we employ ocean health

production functions based on a-priori human and community health production functions to evaluate

how these can be used to generate information for policy decisions (Sanglimsuwan 2012). The rest of the

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paper describes a theoretical framework, implicit and explicit functions, methods, results, discussion and

policy implications.

Any such health production function can be placed within a neoclassical framework of utility

maximization:

U=U(OH,Z:Ɵ) (1)

where U is the level of utility derived from the use of the ocean, OH is the ocean health represented by an

index, Zi is a composite of fish production and ocean services, and Ɵ is the conditional parameter that is

utility based on the time preference for health status that measures the shape of the utility function. The

utility is maximized subject to the ocean health production function and its convexity and the country’s

resource endowment. OH is based on the care we provide for the ocean, by either sustainable or

unsustainable use of its products (fish, natural products, recreation, and artisanal fisheries) and services.

The ocean faces a production function that is twice differentiable, continuous, and convex. OHI is

a vector of ocean health that depends on caregiving and is conditioned by physical, environmental, and

anthropogenic factors. The partial aptitude to prevent ocean degradation and a low OHI score depends on

the society’s capacity to minimize overfishing and pollution and maximize conservation of species

through the increase of Biodiversity through the implementation of MPAs. Second, the ocean faces

resource constraints of income and human resources in terms of level of education, life expectancy, and

gross national per capita income that are measured by HDI.

Z=HDI (2)

Hence the production function is represented by:

OHI= U(OH,Z:Ɵ)+ϕ(X3(X4,X5) (X7))+g (h(X8, X9))+ø( (k) (X17,X18))+€ (L)(X6 (X10(X11,X12)) +λ(X44)+

μ(X23). (3)

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X3=food provision, X4=wild caught fish, X5=mariculture, X7=natural products, h=regulating services,

X8=carbon storage, X9=coastal protection, k=cultural services,X13=tourism and recreation,X14 sense of

place, X17= clean waters, X18=biodiversity, L =central aspects of human well-being that flow from

multiple services, X6=artisanal fishing opportunities, X10=Coastal livelihoods and economies, X11=coastal

livelihoods, X12=economies, X44=social, demographic, conservation and climate change variables,

X23=HDI.

Health status is often measured using utility indices that provide a score that reflects the health

situation of the individual (Austin et al. 2000). Measurement of health status can be subjected to a ceiling

or censoring, and these present problems resulting in inefficient and biased coefficients. Hence, a major

issue in interpreting a health status index is the meaning of extreme values in the index and categorizing

health status as healthy or unhealthy.

The Tobit model proposed by Tobin (1958) has been shown to be the most appropriate tool to

handle censored variables involved in the determination of health status. The Tobit model, also called a

censored regression model, is designed to estimate linear relationships between variables when there is

either left- or right-censoring in the dependent variable (also known as censoring from below and above,

respectively). The Tobit model is used to a limited extent to evaluate health status (Austin et al. 2000)

because of its usefulness in modeling censored variables with a ceiling in econometric studies. Censoring

from above takes place when cases with a value at or above some threshold all take on the value of that

threshold, so that the true value might be equal to the threshold, but it might also be higher. In the case of

censoring from below, those values that fall at or below some threshold are censored. In this approach, a

threshold is defined and those subjects above the threshold are considered healthy and those below

unhealthy. This is a more efficient and robust way of analyzing the data. However, one of the pitfalls of

this approach is the loss of statistical power in the analyses performed (Austin et al. 2000).

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There has been a common consensus that the use of two-stage least squares generates, to some

extent, unbiased efficient parameter estimates. The two-stage method of regression is commonly used

when the first stage represents some measure or index of a country, nation, or environment. Estimated

dependent variable (EDV) regression models are the second stage in a two-stage estimation process. Two-

stage least squares using limited dependent variables as regressors have been discussed by Heckman

(1978), Amemiya (1978 1979), Newey (1986,1987), and Angrist (2001).

The first stage uses observed data to estimate the values of the dependent variable; the EDV

model then regress these values against one or more independent variables to generate the ultimate

coefficients of interest (Lewis and Linzer 2005). The use of accurate and relevant methods such as the

Tobit model and/or rank-based regression may help improve the reliability of the statistical coefficients

by uncovering nonlinear covariate effects and improving the performance of the models for decision

making (Hastie and Tibshirani 1986). To determine the factors that influence ocean health, we use a two-

stage model with the Tobit model in the first stage and rank regression in the second stage.

4.2. Implicit Model Development

2.2.1. Standard Tobit Model

In this analysis we consider the standard Tobit model (Tobin 1958):

y i¿=α+ X i β+ϵi , i=1,2 , … ,n (4)

where y i¿ is a latent response variable, X i is an observed 1 ×k vector of explanatory variables (ocean

index goals and other socioeconomic variables), and ϵ i∼ iid N (0 ,σ 2) and is independent of X i. Instead

of observing y i¿, we observe y i:

y i={y i¿ , if y i

¿>γ0 , if y i

¿≤ γ (5)

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where γ is a nonstochastic constant. In other words, the value of y i¿ is missing when it is less than or

equal to γ .

The problem with the standard Tobit model is that γ is often not observed in economic data and is

often assumed to be zero in empirical applications. In our analysis, y i is the observed OHI when the latter

is greater than 50. The known censoring threshold, γ, is, in fact, not zero but the value that separates the

healthy and unhealthy ocean, as we have defined above. We choose γ=50 for our analysis.

4.2.2 Rank-Based Model

Second, we use rank-based estimation, which is a more robust technique to investigate the

predicted dependent variable with other variables. The rank-based estimation technique is defined as

follows. For a given linear model:

Y=XT β+e (6)

We define the rank-based objective function as

Dn(β )=∥Y−Xβ∥φ (7)

where ∥⋅∥φ is a pseudo-norm defined as

∥u∥φ=∑i=1

n

a(R(u i))ui , (8)

where R denotes the rank, a (t)=φ( tn+1

), and φ is a non-decreasing, square-integrable score function

defined on the interval (0,1). There are many other score functions, but we will consider the most

popular, known as the Wilcoxon score function, with score function satisfying ∫ φ(u)du=0 and

∫ φ2(u)du=1.

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The rank-based estimator of β is therefore defined as:

βφ=Argmin∥Y−Xβ ∥φ (9)

This estimator is highly efficient and is robust in the Y -space: that is, it is not influenced by strange

outliers.

For the rank-based estimation, we do not need any specific assumption about the error terms

other than the requirement that they are drawn from an absolutely continuous density function.

5. Method

5.1. Explicit Model Development

The OHI is expressed as a function of a set of 10 generally accepted public goals (food provision,

artisanal fisheries, natural products, carbon storage, coastal protection, coastal livelihoods and economies,

tourism and recreation, sense of place, clean water, and biodiversity) for the contributions they make to

society, plus gross national income (GNI), life expectancy, and the level of education of a country.

Methods for calculating the OHI, and the conceptual framework and rationale for how it is constructed,

are detailed extensively by Halpern et al. (2012). The index considers the relations between coastal

human societies and ocean ecosystems and their services. The OHI model is therefore represented as:

Y=f 3 ( X3 )+ f 6 ( X6 )+ f 7 ( X7 )+ f 8 ( X8 )+ f 9 ( X9 )+ f 10 ( X10 )+ f 13 ( X13 )+ f 14 ( X14 )+f 17 ( X17 )+ f 18 ( X18 )+f 22( X22)+f 23 ( X23 )+ f 24 ( X24 )+ f 25 ( X25 )+f 27( X27)

(10)

As with least squares, the goal of rank-based regression is to estimate the vector of coefficients,

B, of a general linear model of the form:

Ŷ=β0 1n+βX+e (11)

where Ŷ= [ y1 , y2 ,⋯ , yn ]T is the n ×1vector of responses, X=[ x1 , x2,⋯ , xn ]T is the n × pdesign

matrix, β=[ β1 , β2 ,⋯ , βn ]T is the p ×1 vector of parameter, and e=[ e1 , e2 ,⋯ , en ]T is the n ×1vector of

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error terms. Here 1n represents an n ×1 vector with all 1s. The only assumption on the distribution of the

errors is that it is continuous; hence the model is general. We also assume without loss of generality that

the design matrix of predictors (covariates) X is centered and has full column rank, so that the dimension

of the range of X , say , is p. Since we also want to achieve robustness in data analysis, we employ the

predicted value of the response from the Tobit model to analyze a second stage of the data, but this time

using the rank-based modeling approach. In the second stage the EDV (Ŷ i ¿ is regressed on some added

variables such as HDI value, CO2 emissions, marine protected areas, nitrous oxide (NO2) emissions, and

PM2.5 air pollution.

Ŷ i= f 23 ( X 23 )+ f 27 ( X27 )+ f 29 ( X29 )+f 31 ( X31 )+f 32 ( X32 )+ f 34 ( X34 ) (12)

The Ocean Health Index (Y) is a global measure that generates information on ocean health status

based on the ocean’s capacity to deliver certain goods and services sustainably to humans. OHI scores

range from 0 to 100, and are derived from 10 internal human goals that represent crucial ecological and

socioeconomic benefits that a healthy ocean can generate (Halpern et al. 2012) and external HDI goals

that influence the OHI. The index, therefore, recognizes linkages between human societies and ocean

ecosystems, and that people are part of coastal and ocean systems. A healthy ocean is characterized by an

OHI score greater than 50 and is scored 1, whereas an unhealthy ocean scores less than 50 and is given a

value of 0. The variables for the Tobit and rank models are defined below.

Food provision (X3 ¿=¿ (X 4 , X5) is the greatest contribution of a healthy ocean to human society

(FAO 2012). The food provision goal measures the amount of seafood sustainably harvested in a given

Exclusive Economic Zone (EEZ) or region through any means for use in human consumption, and thus

includes wild-caught commercial fisheries, mariculture, artisanal-scale fisheries, and recreational

fisheries. Food provision received the second lowest global score: 33 over 100. The only goal receiving a

lower score was natural products harvest, which received a score of 31 (Cohen 2013). It is estimated that

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the world will need 70 percent more fish to meet its target by the year 2050. The food provision index is

influenced by national and global policies. Hence a positive relationship is expected between OHI and the

goal of food provision, (B3). Wild caught fish (X 4) represents fish caught sustainably from the wild, and

is designed to assess how much seafood is being provided in a renewable way for local consumption or

export, given the ecosystem’s productive potential (Sinclair et al. 2002). The measure of minimum of the

maximum sustainable yield reference point (mMSYR) provides a suitable point of departure for

sustainable extraction that is based on established concepts in fisheries biology with known caveats and

shortcomings (Pet-Soede et al. 1999; Kleisner et al. 2013).

Mariculture (X5) is defined as the strict production of marine species from both the marine and

brackish water FAO categories, excluding aquatic plants such as kelps and seaweeds, which were

assumed to contribute predominantly to medicinal and cosmetic uses rather than as a source of food.

Artisanal fisheries (X6) refers to fisheries involving households, cooperatives, or small firms (as

opposed to large, commercial companies) that use relatively limited capital and energy, employ small

fishing vessels (if any), make relatively short fishing trips, and use fish mainly for local consumption or

trade. Over 400 million people in the poorest countries in Asia and South Asia obtain at least half of their

essential protein and mineral intake from catch in small-scale fisheries (Dulvy and Allison 2009; Bell et

al. 2009; Allison 2011). Artisanal fisheries employ 90 percent of the 35 million fishers worldwide and

provide 90 million additional jobs in associated sectors (Halpern et al. 2012; Teh and Sumaila 2013). A

healthy ocean is necessary for artisanal fisheries to reach their target of supplying much needed food to

the developing world. Hence a positive relationship is expected between OHI and artisanal fisheries

,(B6>0).

Natural products (X7) is the sustainable harvest of non-food natural products, important to local

economies and for international trade. Through this goal the community maximizes the sustainable

harvest of living marine resources, such as corals, shells, seaweeds, and fish for the aquarium trade. It

does not include nonliving resources such as oil, gas, and mining products that are not sustainable when

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harvested on a large scale. It also does not include bioprospecting that focuses on potential (largely

unknowable and potentially infinite) value rather than current realized value (Lam and Roy 2014).

Globally, natural products generate 2.5 billion US dollars in revenue. This provides jobs and economic

support to communities around the world. A positive relationship is expected between ocean health and

natural products, (B7>0¿.

Carbon storage (B8) measures the ocean’s ability to store CO2 and prevent it from escaping to

increase the chances of global warming. Coastal ecosystems are recognized for the part they play in

combating climate change through carbon sequestration – and, conversely, their potential to become

sources of carbon emissions when degraded (Crooks et al., 2011). Coastal vegetation – such as seagrass

beds, mangroves and salt marshes –stores and sequesters carbon very effectively (Murray et al., 2018).

The ocean represents the largest potential sink for anthropogenic CO2. It already contains an estimated

40,000 GtC (billion metric tons of carbon) compared with 750 GtC in the atmosphere and 2200 GtC in

the terrestrial biosphere (Herzog and Golomb 2004). The three main coastal habitats known to provide

significant carbon storage are mangroves, seagrass, and salt marshes. The physical-chemical mechanisms

driving the ocean sink are well understood but are not directly amenable to human management and

policy regulations (Moore 2008). Hence a positive relationship is expected between OHI and carbon

storage,(B¿¿8>0). ¿

Coastal protection (X 9) measures the degree of protection offered by ocean habitats to coastal

areas that people value. The protection and restoration of coastal vegetation like mangrove could provide

coastal and island communities with important economic opportunities on the carbon offset market

(Hastings et al. 2014). Here, we hypothesize that all coastal areas have value (and equal value) and

consider the total area and condition of key habitats within each EEZ (without regard for their precise

location relative to coastal areas). The habitats that provide protection to coastal areas for which we have

global data include mangroves, coral reefs, seagrasses, salt marshes, and sea ice (Katona 2013).

Approximately 20% of the world’s coral reefs have been lost and another 20% degraded. Mangroves have

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been reduced to 30-50% of their historical cover and it is estimated that 29% of seagrass habitats have

disappeared since the late eighteen hundreds (Nellemann et al. 2009). Protection can be influenced by

national and global policies. The protection and restoration of mangrove forest provide coastal

communities with important economic opportunities on the carbon offset market (Hastings et al. 2014). A

positive relationship is expected between OHI and coastal protection, (B9>0¿ .

Coastal livelihoods and economies (X10 ¿=¿ (X11 , X12) measure the coastal livelihoods and

economies provided by the ocean. About 500 million people are engaged in ocean-related livelihoods.

The oceans represent an enormous economic opportunity. This includes traditional industries such as

fisheries, shipbuilding, maritime transport and tourism as well as emerging industries such as offshore

aquaculture, sea-bed mining, renewable energy and the new bio-economy sectors based on marine

biotechnology. All of these industries have important economic and environmental implications that need

to be considered (OECD 2017). The jobs and revenue produced by marine-related industries are of

immense value to many people, even those who do not directly participate in the industries but value

community identity, tax revenue, and indirect economic and social impacts of a stable coastal economy,

(B¿¿10>0) .¿

Tourism and recreation (X13) capture the value that people have for experiencing and enjoying

coastal areas (Halpern et al. 2015). Tourism and recreation are major components of thriving coastal

communities and measure how much people value ocean systems: i.e., by traveling to coastal and ocean

areas, people express their preference for visiting these places. In 2012 tourism supported 9% of global

jobs and generated US$ 1.3 trillion or 6% of the world’s export earnings. International tourism has grown

from 25 million in 1950 to 1,035 million in 2012 and the UNWTO forecasts further growth of 3-4% in

2013 to 2024; the forecast for 2030 being 1.8 billion (UNWTO 2013). A large portion of global tourism is

focused on the marine and coastal environment and it is set to rise (OECD 2012). Trends in aging

populations, rising incomes and relatively low transport costs will make coastal and ocean locations ever

more attractive. Tourism and recreation might have an indeterminate effect on OHI. In the first case,

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preparation for tourism and recreation might force coastal communities to improve OHI, but in the second

case, an overabundance of tourism and recreation may damage the fauna and flora of the ocean bed and

have a negative effect on OHI, (B¿¿13>0∨¿0).¿

Sense of place (X14) captures the aspects of coastal and marine systems that people value as part

of their cultural identity. This definition includes people living in all proximity to the oceans. Cultural

value: Last, but by no means least, the ocean provides important cultural services – aesthetic, artistic,

educational, recreational, scientific and spiritual values. The goal is divided into two sub-goals—iconic

species and lasting special places—and an assigned equal weight is attributed when combining them to

create a single goal score, (B¿¿14>0) .¿ The iconic species¿¿) sub-goal focuses on those species seen

as iconic whose existence has cultural, spiritual, or aesthetic value. Lasting special places¿¿), the other

sub-goal, refers to places that provide intangible but significant resources that sustain economic

opportunities.

Clean water (X17) measures the degree of clean water that people enjoy from the ocean. People

value marine waters that are free of pollution and debris for aesthetic and health reasons. Contamination

of waters comes from oil spills, chemicals, eutrophication, algal blooms, disease pathogens (e.g., fecal

coliform bacteria, viruses, and parasites from sewage outflow), floating trash, and mass kills of organisms

due to pollution. People are sensitive to these phenomena occurring in areas that they access for

recreation or other purposes, as well as to simply knowing that clean waters exist. This goal scores

highest when the contamination level is zero. It is expected that(B¿¿17>0)¿.

Biodiversity (X18) estimates the diverse number of species existent around the world and how

well they are being maintained. The risk of species extinction generates great emotional and moral

concern for many people. As such, this goal assesses the conservation status of species based on the best

available global data through two sub-goals: species¿) and habitats ¿¿). There is a positive relationship

between the productivity and resilience of ecosystems and the health of biodiversity (Worm et al. 2006;

19

Stachowicz et al. 2007; Cardinale et al. 2012).We also assess habitats as part of the ecosystems and

biodiversity goal in that they support a broad array of species,(B¿¿18>0) .¿

The Human Development Index (HDI) (X23) is a composite measure of average achievement in

three basic dimensions of human development: life expectancy, education, and per capita income. The

index is used to rank countries into tiers of human development. Lowndes et al. (2014) found that HDI is

the greatest predictor of OHI. The HDI is expected to have a positive effect on OHI,(B¿¿23>0) .¿

Gross national income (GNI) (X27) represents the standard of living per capita, expressed in

constant 2011 international dollars converted using purchasing power parity (PPP) rates. GNI expresses

the income accrued to residents of a country, including international flows such as remittances and aid,

and excluding income generated in the country but repatriated abroad. Thus, GNI is a more accurate

measure of a country’s economic welfare than GDP. The GNI coefficient is expected to have a positive

effect on the OHI(B¿¿27>0) .¿

CO2 emission(B¿¿29<0)¿ in metric tons per capita 2011 to 2015 (World Bank 2015) represents

the largest potential sink for anthropogenic CO2 measured in the air. Experts have stated that oceans are

heating, losing oxygen, and becoming more acidic because of CO2, and are at risk of irreversible damage

if these conditions continue (Gray et al., 2014), (B¿¿29<0) .¿

Marine Protected Areas (MPAs) (B¿¿31>0)¿ as a percentage of territorial waters 2011 to 2015

(World Bank 2015) are protected areas for the preservation of species that are likely to be lost to habitat

fragmentation (Ovaskainen 2012), which is a sound strategy to expand biodiversity. MPAs help reduce

overexploitation of vulnerable species, and therefore, are supported by many nations and international

bodies as a means of improving biodiversity. Bio-economic modeling of commercial fishing, recreational

fishing, and tourism shows that the economic and biological benefits of well-managed MPAs far

outweigh the cost of implementing MPAs (Reimer et al. 2015; Sala et al. 2013). The establishment and

management of MPAs can be executed by local coastal communities at a low cost(B¿¿31>0)¿.

20

Nitrous oxide (N2O) in thousand metric tons CO2 equivalent (B¿¿32<0)¿ is emitted during

agricultural and industrial activities as well as during the burning of fossil fuels and solid wastes. N2O,

like other greenhouse gases, is supposed to have a positive effect on global warming and may increase

fish mortality (B¿¿32<0) .¿

PM2.5 air pollution (B¿¿34<0)¿ is the mean annual exposure (micrograms per cubic meter,

2013) of direct emissions of particulate matter and secondary particle formation caused by oxidation of

sulfur dioxide, nitrogen dioxide, and aerosol organic carbon. Levels of airborne particles affect natural

ecosystems through reduced productivity, disruption of nutrient cycles, and massive summer fish kills, as

observed in the Chesapeake Bay and Long Island Sound this decade (Pascale et al. 2016).

5.2. Data Sources and Analytical Procedure

The Ocean Health Index and 10 measured goals for 151 selected countries for 2013 were

extracted from the Excel spreadsheet for 2014. The index recognizes linkages between human societies

and ocean ecosystems, and that people are part of coastal and ocean systems within a country’s EEZ. HDI

data were taken from the United Nations Development Program (2013) and from the World Bank (2015)

Environment Bank database.

The researchers estimated scores for each area from data around the world. Globally, the ocean’s

health was scored at 60 out of 100. Scores for individual countries ranged from 33.3 to 86, with most

scoring below 70. Scores for developed countries were generally higher than those for developing

countries. In Europe, Germany scored highly at 73 and Poland scored poorly at 42. Similar total scores

could be achieved through different routes. For instance, while the UK scored 62 with high scores for

natural products and food provision, the US scored 63 with high scores for coastal protection and coastal

livelihoods and economies. Haiti, on the other hand, had an overall score of 44.24 with a food provision

index of 1.01, while Nicaragua had an overall score of 45.05 with a food provision index of 37.31.

21

5.3. Scatterplot Matrix

We examine how well our model fits the data. We start with plots of the residuals to assess their

absolute as well as relative (Pearson) values and assumptions such as normality and homogeneity of

variance. We present the estimation techniques, check the required assumptions together with a table of

correlation coefficients and descriptive statistics, and then present the results and a detailed interpretation.

First of all, the log-likelihood of -147.7078 on 290 degrees of freedom suggests a small p-value.

Thus our model will compete when compared to any nested models. We recall that for the Tobit model,

degrees of freedom are computed as follow: df =2 n−γ−2, where γ represent the number of predictors

considered in the model.

The three plots on the first row in Figure 1 in the appendix from absolute as well as relative

(Pearson) residuals are used to check the homogeneity of variance. Since neither of those plots shows a

particular pattern, we suspect a non-violation of the homogeneity of variance.

{PLACE FIGURE I IN APPENDIX HERE}

The first two plots on the second row of Figure 2 in appendix, known as the quantile-quantile plot

of the residuals, are used to check the normality. Since the two plots suggest a moderate linear

association, we can say that the residuals come from an approximate or fairly normal distribution. To

confirm this we performed the Shapiro–Wilk test which utilizes the null-hypothesis principle to check

whether a sample X1 , X2 ,⋯ , Xn ,came from a normally distributed population. The test provided a p-

value= 0.1534554 which is greater than the significance level α = 0.05. Thus we do have enough evidence

to say that the sample residuals come indeed from a normally distributed population.

The graphs at the bottom right in appendix figure 2 show the predicted, or fitted values plotted

against the actual. This can be particularly useful to investigate how accurately our model fits the data.

We also calculated the correlation between these two, as well as the squared correlation, to get a sense of

22

how accurately our model predicts the data and how much of the variance in the outcome is accounted for

by the model.

The correlation between the predicted and observed values of Ocean Health Index (OHI) is

0.9967. If we square this value, we get the multiple squared correlation; this indicates that predicted

values share 99.34 percent of their variance with OHI, which is of course variance accounted for.

To this end, we adopt a combination of the Tobit regression model and a rank-based modeling

approach. In fact, there are long lists of analytical methods we may have encountered or performed. Some

of the methods listed are reasonable, while others have fallen out of favor or have limitations.

5.4. Importance of Model Influence of Predictors

Table 1 in the appendix presents the relative influence of the predictor variables. The relative

variable influence on ocean health shows that biodiversity received the highest rank, with a score of 17.15

percent; in second place is coastal protection with a score of 11.55 percent, and in third place is clean

water with 10.99 percent. The variable, wild caught fisheries, was in fourth place, with a score of 10.12

percent. The choice of variables in our final model is partly based on the relative influence score

considering OHI as the dependent variable.

{PLACE TABLE I IN APPENDIX HERE}

6. Results

The descriptive statistics in Table 1 for a sample of 151 countries for which data were available

indicate that the mean OHI is 62.70, with a standard deviation (SD) of 9.38, a minimum value of 43.72,

and a maximum of 82.55. The food provision index was 54.57, with the lowest value being 1.01 and with

a maximum of 98.00. Biodiversity had the highest mean value, 83.85, with a minimum of 64.67 and a

maximum of 98.26. HDI had an average of 0.70 with a median of 0.72, while MPA had a mean of 12.1

23

with a median of 5.8. Figure 1 shows that there is a positive relationship between HDI and OHI, with

those countries with an HDI greater than 50 or a score of 1 having a higher OHI throughout. A similar

relationship exists between MPAs and OHI, where those countries with an OHI greater than 50 have

higher MPAs (Figure 2).

{PLACE TABLE I HERE}

We first recall that for the Tobit model the linear effect is on the uncensored latent variable, not

the observed outcome. See McDonald and Moffitt (1980) for more details. The correlation between the

predicted and the observed values of OHI is 0.997. If we square this value, the Tobit model has an R2 of

0.993, which means that 99.3 percent of the variation in the dependent variable is accounted for by the

variation in the independent variables. The likelihood ratio is -148 with 290 degrees of freedom with an

AIC of 319. Hence, we can say the Tobit model is acceptable for measuring the factors that influence

OHI. For example, for a 1-unit increase in biodiversity there is a 0.14 increase in OHI and for food

provision, there is a 0.103 increase in the predicted OHI value. Also, for a 1-unit increase in natural

products, there is a 0.105 increase in the predicted OHI value (Table 2). The same interpretation can be

carried out for the rest of the predictors or variables that contribute to the OHI via the Tobit model. The

ancillary statistic of -0.331808 can be compared with the SD of the response OHI, which was 9.378793, a

substantial reduction. This implies that all predictors positively contribute to the predicted value of the

OHI.

{PLACE TABLE II HERE}

The overall Wald test of the rank regression is 90 at a p-value of 0, which indicates a significant

association between the response and the predictor variables. The rank regression showed that HDI and

MPAs significantly influenced the predicted value of the OHI. A 1 percent increase in HDI will result in a

0.32 percent increase in OHI, while a 1 percent increase in MPAs results in a 0.03 percent increase in

OHI.

24

{PLACE FIGURE I HERE}

7. Discussion and Conclusion

The scatterplot and the diagnostic statistics suggest that the two-stage model is appropriate. The

influence factors show that biodiversity received the highest rank, and in second and third places are

coastal protection and clean water. In fourth place are natural products. For the Tobit model, the variable

biodiversity has a major effect on ocean health and contributes succinctly to the variation in OHI. This is

understandable, since the other variables interact to foster a biodiverse environment that may influence

OHI.

There may also be trade-offs (Selig et al. 2015) among goals as countries attempt to improve one

goal, biodiversity, at the expense of another, coastal habitat for species. Healthy marine biodiversity

determines the proper functioning of the ecosystems and its ability to provide goods and services. Coastal

and high seas ecosystem goods and services include production of oxygen, fish and shellfish, key

components for the development of (new) medicine, nutrient recycling, decomposition of waste, coastal

protection, carbon sequestration to mitigate climate change, recreational opportunities and spiritual

appreciation of the ocean (Beaumont et al. 2007; Böhnke-Henrichs et al. 2013). Expansion of

biodiversity is an important policy decison to improve ocean health. Development of the habitat and

species sub-goals is essential for the enhancement of OHI through the reduction of habitat devastation,

which poses the greatest threat to biodiversity (Ovaskainen 2012).

Other goals that affect OHI are livelihoods and economies, sense of place, clean water, and

artisanal fisheries. The evaluation of each factor separately helps one to develop an understanding of goal

substitution. However, increasing livelihoods and economies may have a negative effect on OHI if the

level of exploitation is too intensive, and may negatively affect the coastal habitat and species

biodiversity. The livelihoods and economies relate to clean water and artisanal fisheries. The transfer of

25

power to local communities so that they can exert control over their lives and create local institutional

structures that link sustainable livelihood approaches to habitat and species preservation is essential to the

successful improvement of livelihoods and economies. Hence, coastal communities can adopt a

participatory approach to decision making through a process of co-management to improve ocean health

(Divakarannair 2007).

{PLACE FIGURE II HERE}

Sense of place is important in terms of cultural symbolism. People and communities place

intangible value on places and iconic species and are likely to make an effort to preserve those (Selig et

al. 2015). However, some countries only place value on a limited number of places, and therefore, receive

a low total score for this variable. The identification of a sense of place and the reassurance of cultural

preservation is a sound strategy to encourage the expansion of biodiversity, and hence the improvement

of OHI.

Clean water influences OHI and can be controlled by communities at a reasonable cost. Reducing

non-point source pollution, protecting water from pollution by defending the Clean Water Act, and

establishing new pollution limits can be done through legislation, enforcement, and increasing water

efficiency strategies to decrease the amount of waste water entering the ocean. Polluted beaches that

make swimmers sick may result in economic losses to coastal communities in terms of loss of jobs and

revenue. Clean water can be achieved by raising community awareness and reducing the amounts of

debris and trash dumped in the ocean. Erikson et al. (2014) reported an estimate of the total number of

plastic particles and their weight floating in the world's oceans 5.25 trillion particles weighing 268,940

tons. The abundance of microscopic fragments was greater in the 1980s and 1990s than in previous

decades (Barnes et al., 2009). Education is an important element in the advancement of clean ocean

waters and hence a healthy ocean.

26

The artisanal fisheries goal indicates how individuals in a community access fishing opportunities

to support their livelihoods. Fish harvesting is usually done by a large number of limited-resource

fishermen and a few larger fishing businesses. There is a belief that the involvement of large numbers of

limited-resource poor fishers may have serious consequences for food provision and human well-being,

but on the other hand, the extraction of abusive quantities of fish might undermine progress in

biodiversity improvement and have a deleterious effect on OHI.

In the second model, HDI and MPAs significantly influenced OHI. Human development can

engender positive change to reverse the trend of deteriorating ocean health and rebuild the oceans’ natural

capital. Most of these actions occur in the context of the institutions that govern the way ocean ecosystem

services are valued and used. For this reason, the World Bank’s focus in helping to restore ocean health is

to support developing countries to strengthen and reform the institutions needed to both enhance the

benefits and services that healthy oceans can provide, and to ensure that these benefits contribute to

poverty reduction and shared prosperity (World Bank 2017). This support generally includes the training

of manpower and increase in per capita income to ensure the availability of human and investment capital

to manage a healthy ocean. HDI is positively related to OHI: countries with high HDI, like many

European countries and the US, also have high OHI. Lowndes et al. (2014) found that HDI is the greatest

predictor of OHI.

Expansion of marine protected areas (MPAs) for the preservation of species that are likely to be

lost to habitat fragmentation (Ovaskainen 2012) is also a sound strategy to expand biodiversity. New

research (Brander et al. 2015) shows there is also a strong economic case for protecting ocean assets

through expanding MPAs globally. Scientists have shown that MPAs can contribute to reducing poverty,

building food security, creating employment and protecting coastal communities (Van Beukering et al.

2013; Ferrario et al. 2014; FAO 2014; Brander et al. 2015). MPAs assist in the reduction of

overexploitation of vulnerable species, and therefore, have the support of many nations and international

bodies as a means of improving biodiversity. Policy formulation to encourage development of MPA

27

networks, that are ecologically coherent and that protect 30 per cent of each habitat in our oceans is

essential(WPC 2014). MPAs are expected to contribute significantly to the recovery of marine

biodiversity and a productive ocean (Roberts & Hawkins 2000; Gell & Roberts 2003; Halpern 2003).

8. Policy Implications

Ocean health is dependent on ecosystem resilience that is based on adequate protection and

rebuilding of biodiversity in the face of pressures such as ocean overexploitation. The ability of an

ecosystem to withstand and rebound from stress is essential for dealing with the impacts of overfishing,

pollution, habitat loss or conversion, ocean sedimentation, industrialization and climate change. The Blue

Economy food security relates to the sustainable use of biodiversity principally where it concerns to the

exploitation of wild fisheries (GPO 2013). Policy makers should note elasticity of biodiversity and its

likely impact on OHI and encourage its enhancement since such changes may be within the reach of even

the poorest country.

The importance of artisanal fisheries in food security and livelihood should be priority in

development policy. That means addressing policies that consider decline in artisanal fisheries and its

effects on livelihoods and ocean health. Conservation methods should be introduced to manage the

resource with reference to a holistic approach at coastal ecosystem conservation. Natural stocks

preservation policies should be implemented for the improvement and restoration of juveniles. Countries

should be mandated to link their policies to the FAO Code of Conduct of responsible fishing and

aquaculture, the IUCN World Parks Congress 2014 Promise of Sydney, the CBD and the World Bank

initiatives to enhance ocean health through the improvement and regulation of ocean health goals such as

natural products, carbon storage, coastal protection, coastal livelihoods and economies, tourism and

recreation, sense of place, and clean water.

Countries with varying levels of resource endowment and in the upper level of HDI may choose

different techniques to improve OHI, but the implementation of MPAs should be a priority for all, since

28

they have a major effect on OHI. A policy of international assistance from countries with high OHI to

those with low HDI is opportune at this moment. The assistance may be in the form of awareness creation

or education about the need to put in place systems to improve the global OHI. International bodies like

the World Bank, the United Nations, should work in close collaboration with groups such as Mangroves

for the Future, Blue Action Fund, the International Blue Carbon Partnership, Biodiversity and Friends of

Ecosystem based Adaptation (EbA), to encourage sustainable practices that influence ocean health. The

global policy makers should develop networks with international and regional organizations, national and

local governments, and communities and civil society organizations – to safeguard and foster

conservation, sustainable management and use of marine and coastal ecosystems and biodiversity.

Acknowledgement

The authors would like to thank the NORHED project "Incorporating Climate Change into Ecosystem

Approaches to Fisheries and Aquaculture Management in Srilanka and Vietnam" team members for their

assistance in preparing this paper.

29

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Table 1: Descriptive statistics of the variables

Variables N Mean Sd Median Min Max Se

Wild Caught Fisheries (X 4 ) 151 56.01 24.40 61.56 1.01 98.00 1.99

Mariculture (X5) 151 35.98 31.25 26.97 0.01 100.00 2.54AF Opportunities (X6) 151 61/51 12.24 61.45 41.42 100.00 1.00Natural Products (X7) 151 63.31 26.12 62.66 0.06 100.00 2.13Carbon Storage (X 8) 151 68.09 21.33 62.66 5.53 100.00 1.74

Coastal Protection (X 9) 151 56.98 25.85 62.66 5.46 100.00 2.10Livelihoods (X11) 151 77.54 23.04 83.63 0.17 100.00 1.87Tourism, Recreation (X13) 151 36.54 26.56 28.91 2.54 100.00 2.16Iconic Species (X15) 151 56.72 7.03 56.03 37.13 78.29 0.57Lasting Special Places (X16) 151 66.57 34.10 74.42 0.12 100.00 2.78Clean Water (X17) 151 65.50 11.09 64.47 34.74 93.92 0.90Species (X19) 151 81.97 4.70 81.07 73.32 96.52 0.38Habitat (X20) 151 85.73 13.36 90.13 50.48 100.00 1.09Mean Years of Schooling (X25)

151 9.89 10.21 8.50 1.60 62.66 0.83

GNI/capita (X27) 151 19042.54 27492.45 11477.00 62.66 267711.00 2237.3

Ocean Health Index (X2)Food Provision (X3)Livelihood & Economies (X10)Sense of Place (X14)Biodiversity (X18)Human Dev. Index (X23)Marine Protected Areas(X31)

151151151

151151151151

62.7054.5783.2

57.9983.850.7012.10

9.3824.1616.5

21.917.360.1516.9

62.7060.1184.5

64.4685.360.725.80

43.721.013.5

18.7964.670.340.0

82.5598.00100

10098.260.949.5

0.761.971.3

1.780.600.011.4

40

Table 2: Results of the two stage equation with Tobit at stage one and the rank regression as stage two

41

Figure 1: OHI plotted against HDI for countries with an OHI greater than 50. The regression equation for the line through the points is: OHI=39.30+33.21 HDI

42

Figure 2: OHI plotted against MPA for countries with an OHI greater than 50. The regression equation for the line through the points is:OHI=60.0332+0.2175 MPAs

43

Appendix Table1: Importance of variables in the model using relative influence ranks

Variables Relative influence

Biodiversity (X18) 17.154614Coastal Protection(X 9) 11.547042Clean Water(X17) 10.991649Wild Caught Fisheries(X 4) 10.117793Natural Products(X7) 8.845601Iconic Species(X14) 7.863998Tourism, Recreation(X13 ) 7.086078Livelihoods and Economies(X10) 6.851335HDI value (X 23) 6.024677AF Opportunities(X 6) 5.668185Carbon Storage(X 8) 4.142504GNI/capita 2011(X 27) 2.176117Mariculture(X5) 1.530407GNI/capita 2011 Squared 0.000000

44

Appendix Figure 1: Checking Assumptions model and diagnostics for the Tobit Model