Econometric, Probability and Non-Mathematical Model Methods:

This section evaluates other quantitative approaches including probability and econometric regression methods. This assesses climate change risks and impacts for MSCs. Unlike qualitative data, these approaches’ research designs, methods, variables and hypotheses are pre- determined. Risk management method characteristics identified in existing studies aim to estimate risks on various activities, stakeholders, assets or infrastructure. Current examples seldom apply this for entire supply chain systems, (Rehdanz 2004; Simpson et al. 2010; Australian Department of Climate Change and Energy Efficiency 2012). Very few satisfying these characteristics, with actual values and equations provided; have been located, (even for individual supply chain stages). Existing related research favours standard assessment methods, results and solutions from qualitative data (Das 2006, Coleman 2006). It frequently omits equations, actual probabilities, risk model characteristics and assumptions. These sources propose risk identification but do not prove methods from theory or through probability distributions (Conrow 2003, Ong 2006). However, effective risk management applied to climate change and supply chains requires understanding of probability distribution characteristics. This validates this quantitative approach rather than only employing phenomenology methods of risk perceptions using surveys/interviews. This is proposed by few risk management sources (Sutton 1992; Koller 2005; Garlick 2007). To justify the proposed section 3.3 framework for risk identification; it proposes any equations and theory are confirmed through Poisson distribution characteristics. These are vindicated in standard econometric textbooks (Manfield 1991; Gujarati and Porter 2011). It satisfies the following assumptions. First, it must be possible to divide the time interval used into large areas with correspondingly small probabilities of an event occurrence. The probability of a risk occurrence in each sub-interval must remain constant through the period. The occurrences must be independent across any sub-interval i.e. the two variables do not affect each other. Expected frequency values are computed separately for each level of one categorical variable at each level of other variables. Poisson probability distribution can be tested and applied to estimate the probability of a climate

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change event using historical information: This derives Equation 3.1 to calculate the historic probability of a risk event occurring.

𝑃(𝑥) = 𝑒−λλ𝑥

𝑥! 𝑓𝑜𝑟 x = 0, 1, 2 and λ > 0 . (3.1)

where: x = number of climate change, risk events

p(x) = the probability of x risk events occurring in the given time period

𝛌 = the expected (or mean) rate of occurrence of the climate change, risk event in the designated time period

e = Euler’s constant,  2.71828

The Poisson mean equals its variance µ =λ =σ2_{. The Poisson distribution is useful in modelling} risk events such as climate change based on the following theoretical assumptions. It calculates the probability of x occurrences per unit time, allowing for fewer observation values than the normal distribution with a normality assumption for a continuous distribution of all possible values. Its advantage occurs in being able to determine how many risk events were observed/did occur but not to determine the number of events that did not occur. The distribution only requires the mean number of occurrences and range. The validity of the Poisson distribution over others can be reaffirmed through the Chi square test. This uses the null hypothesis H0: The distribution follows the Poisson distribution. As provided in standard textbooks on statistical probability theory (Levin and Rubin 1991; Gujarati and Porter 2011); this test is used when two variables exist from a single population/data sample. This tests for variable independence or if a significant association exists between the two variables, based on the above hypotheses (Lind, Marchal and Wathon 2012). This indicates whether an observed frequency distribution approximates the Poisson distribution with several degrees of freedom. The longer the data interval, the larger the probability with discrete rather than continuous, random variable values.

The Poisson distribution can also link to determining the conditional probability of a MSC asset failure from a specific climate change, risk event for KRQA unlike other distributions. A Poisson distribution’s advantage includes approximating the binomial distribution if the number of trials is very large and the probability of occurrence is very small. The binomial distribution does not apply to time series data where n independent Bernoulli trials exist. Binomial distribution assumptions are the number of trials, is fixed and only two outcomes, "success" and "failure” exist. Climate change isn’t risk static with a fixed number of independent trials. Its risks are more frequent in recent years across all locations and risk types. Risk events are not mutually exclusive for climate change. The thesis equations consider events to be based on accumulated risk, future risk or the joint probability of two risk events occurring simultaneously.

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The normal distribution is not favoured for various reasons. These are based on certain issues identified by Taleb (2001) in the Black Swan and this section for low probability, high impact cost events. The probability of the sample population mean is not always close to the normal distribution. Given low lambda ranges for time series data and expected number of observations, the Poisson distribution is more mathematically valid since the normal distribution is recommended for large sample values – i.e. when 𝛌>1000. The normal distribution focuses on mediocrity, average or expected values, considering sudden risk events within the Gaussian bell curve unlike the Poisson. The Poisson can incorporate average/expected value, joint probability, and accumulated risk value increases. Although the Mandelbrotian is preferable for fractal randomness of events (where the ratio is preserved across scales) (Taleb 2001). Unlike the Gaussian; it ignores time series data with average/expected values). Deviations may potentially exist across any time series, data period, risk type and location. This cannot be sufficiently accounted by the Gaussian curve. Yet the Poisson provides a greater approximation of risk than the normality distribution. The Gaussian bell curve is un-scalable, underestimating tail end, risk events, especially for impact/probability of occurrence. Its theory limitations assume risk decreases exponentially, not increasing with observations/over time and values away from expected values. The normal distribution ignores significant increases in trends as potential results.

Climate change risks assume outliers in time will become more frequent. The time series data and derived equations do not reflect normal distributed, data assumptions but reality, which in addition incorporates scalable randomness. Based on certainty and these data assumptions, random selections do not apply to climate change events with multiple variable parameters of uncertainty, about the frequency of specific risk event types in a given year. Standard deviation does not apply, as a number merely scalable to Gaussian bell curves. Significant deviations can occur in any particular time period, location and risk event type. Finally, even Monte Carlo methods based on theoretical risk simulations rely on Poisson distribution assumptions.

Quantitative, regression method approaches involve mathematical formulae, theories and assumptions to estimate climate change, impact costs and benefits. These are further analysed in section 3.5. Econometric/regression methods are also used in related risk management and impact cost studies e.g. Policy Research Corporation (2009). This evaluated an impact cost analysis for the EU coastal economy sector, including ports. Its dataset uses 15 nations. Simple regression and market valuation methods estimate costs for European assets within 500 metres of a coastline at $500,000,000-$1,000,000,000. Net adaptation benefits were estimated at 3.8-4.2

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billion euros, depending on SLR. Its performance is undermined in providing only aggregate estimates and ignoring key impacts e.g. intangible costs.

Godwin (2011) suggests this method for Cartagena port, Columbia. The proposed thesis regression model adds a scenario, where estimated total costs and benefits are considered. Stenek et al. (2011) and Rycerz (2015) also apply a climate change, cost-benefit analysis to Cartagena port. These establish projections to examine specific consequences of event risk variables including temperature, precipitation, SLR and wind velocity increases for ports. Dependent variables indicate 13 major risk variable categories related to port performance. Variables include demand, trade level, trade patterns, navigation, berthing, goods handling and storage. Variables include social/environmental performance, inland transport, insurance, infrastructure, building and equipment damage. The sources’ form a similar, financial based modelling approach. This calculates a port’s economic impact costs with and without climate change. It then evaluates climate change impacts in terms of net present value (NPV) defined:

𝑁𝑃𝑉 = (𝐵0− 𝐶0)+ 𝐵₁−𝐶₁ (1+𝑟)+ 𝐵₂−𝐶₂ (1+𝑟)𝑛)+ ⋯ + 𝐵_𝑛−𝐶_𝑛 (1+𝑟)𝑛). (3.2)

This method’s performance is ascertained by comparing costs and benefits for individual adaptation solutions i.e. for raising a causeway, with flooding costs of $2,4,00,000 by 2030, (yet $380,000 to elevate and adapt). It offers discounted and undiscounted estimates, to adjust for different time horizons and projected uncertainty. These add costs, discounted over future periods. It estimated business disruption costs compared to the extent of adaptation and insurance. As with existing quantitative approaches, these provide final values rather than exact equations. Possible risk costs and benefits are frequently summarised for ports and supply chains separately. Kong et al. (2013) concentrates on refining an economic, impact analysis model for climate change for Australian port infrastructure. Its method is a life cycle costing model. This compares asset deterioration, inspection, maintenance, rehabilitation, salvage and other costs of not enhancing resilience for new and existing infrastructure. Independent climate variables include sea level, precipitation, temperature and waves. Dependent variables involve port, land, sea and transport assets including berthing structures, port protection barriers, superstructure, channels, basins, road and rail infrastructure. This is modelled in separate scenarios, using graphical user software and climate model variations. A seaport structure’s lifecycle cost is summarised as

𝐿𝐶𝐶 = 𝐼0+ 𝐶𝐼+ 𝐶𝑚+ 𝐶𝑅+ 𝐶_𝑠. (3.3)

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The method’s performance considered multiple factors for risk probability and impact costs. For example, the probability of corrosion for a Gladstone port, concrete structure is estimated around 29% under a 2070 scenario. A risk and impact analysis concentrating on MSCs could incorporate a fixed constant. This considers an asset’s actual value over its projected lifespan against its asset replacement cost, as an event consequence. This further helps to evaluate port infrastructure, structural resilience against projected disruption risks, answering whether adaptation costs are necessary and cost effective. This thesis methodology similarly considers ascertaining projected costs for long-term risks e.g. SLR and temperature, as a fixed constant. This can include factors occurring over an asset’s lifespan e.g. repair, maintenance and replacement costs. It can also be adapted to different risk scenarios and time horizons along with measuring other assets not just port but other supply chain stages.

Sawyer (2014) also proposes an initial risk-vulnerability assessment to ascertain the extent to which specific disruption risks will affect projected impact costs for Canadian transport assets. A risk-vulnerability analysis also aids in determining specific risk locations and which assets to prioritise for stakeholders with scarce time, fiscal, skilled labour, technology and other resources. It links these to an economic impact cost analysis. Variables include direct, indirect and accelerated maintenance, asset costs. The model’s performance is evaluated in output indicators for existing impacts. For example, a road from Tibbet to Contwoyto was open for 42 days. This contrasts with a historic average of 70 days. 13,000 tons of cargo and 11,000 of fuel was airlifted. An investment of $1,000,000 in Mississauga public infrastructure increased the GDP by $1,340,000.

Smith (2015) concentrates on applying the above economic, impact cost analysis for the ports of Bremerton, San Diego and Rotterdam. This can be adapted to Pacific MSCs stages. Including several case studies can further improve empirical model validity, impact analysis and underlying assumptions. This thesis proposes panel data for future research with several Pacific supply chains. Smith also affirms the necessity of stabilising a model sufficiently robust to consider climate change’s dynamic nature and uncertainty through scenarios. It also proposes including cost- effectiveness analysis to measure the extent to which solutions justify adaptation costs. For example, for Bremerton-Kitsap it considers assets depreciate for only 32 years, yet projected lifespan is 67 years. Quantifying direct impacts as costs and benefits through the NPV standard equation above, can aid stakeholders to allocate scarce resources and prioritise adaptation strategies. Yet the method’s performance is limited, as it does not calculate examples with specific

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probabilities of risk occurrence. Smith (2015) ignores risks or stakeholder concerns. The method possesses empirical concerns of cost estimation and optimization, without an integrated risk assessment mechanism incorporating direct and indirect, economic impacts with accurate risk projections. None of these studies considers results might vary between different ports, transport infrastructures or supply chains. However, this thesis methodology will include both. It specifically concentrates on how projected risk types, resources, constraints, adaptation policies, scenarios and impact costs may differ for Pacific MSCs.

Quantitative models have more flexible research advantages for climate change, impact methodologies (Bryman 2001, Gujarati 2011; Web Centre for Social Methods Research 2015). Utilising probability distributions identifies and provides risk estimates. It is cheaper, less time- consuming and safer than real risk events, especially with low actual probabilities of occurrence. Stakeholders can consider multiple outcomes, scenarios, possibilities, causes and responses based on hypotheses, parameters or existing information. This helps when limited data exists. This thesis’s method improves upon existing qualitative method studies by including as many supply chain stakeholders as possible, for a single commodity. It incorporates customs, the financial and insurance sector, beneficiation, consumers, subsistence fisherfolk, ecosystems and small entrepreneurs. These stakeholders are all ignored by past cited sources.

The specific disadvantages of normal, Gaussian, binomial, Poisson and Mandelbrotian, probability distributions are previously summarised. Section 3.4 analyses advantages and disadvantages of climate change, risk probability theory applied to maritime and other supply chains. Sources failing to provide distributions for risk management are criticised for weak theoretical or quantitative methods. These often deny qualitative information aspects and practical solutions that might directly assist affected stakeholders. Current risk management studies ignore how probability distributions can include climate change. Examples include Australian Department of Climate Change (2010), Baker and Week (2013) and Cox (2013) for Pacific, climate change, consequences on coastal infrastructure. Mach (2012) notes advantages to including monetary valuation, co-benefits, risks, behaviour dimensions and uncertainties. He mentions profit-retention, commercial opportunities and self-interest. Business for Social Responsibility (BSR 2015) focus on economic and social co-benefits of endorsing increasingly sustainable, supply chain infrastructure and development. It points out ultimate survival. These provide more psychologically compelling arguments to reluctant stakeholders. This can convince them to prioritise and concentrate resources/efforts in climate change preparation, mitigation and adaptation. They offer

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further reasons to select adaptation including lower pollution, improved health, environment, economic activity, time saving, food and energy security. It further indicates potential cost consequences that not prioritising climate change immediately; or adapting globally will entail. Quantitative models, information, effects and variables are often conditional on certain theoretical assumptions. Further research disadvantages include factors are often situation specific and lack specific relevance to this thesis’s KRQA. This thesis agrees with Marra (2014) that many quantitative model-based approaches often ignore location/site, specific characteristics e.g. port, shipping, supply chain, commodity, event, environment and Pacific climate. Generalised methods frequently cause issues with related individual, stakeholder consequences, requirements, concerns and solutions. However, economic impact cost analyses for climate change provide certain advantages over qualitative research. These include more consistent, replicable, valid, objective and transparent data. This can assist to evaluate key research questions and consider relationships between variables. Impact cost analyses are however, rejected by Netherlands Environmental Assessment Agency (2014) for certain research disadvantages. Method applications seldom incorporate sudden, large scale, risk shocks and complexities in accurately calculating these costs. Often aggregate costs insufficiently allow for variance across individual stakeholder examples. Certain impacts are difficult to ascribe a pure economic value. These impacts include any environment, species extinction and life replacement costs or the opportunity costs of a commodity delayed through a supply chain (IPCC 2010).

3.2.4: Addressing Current Literature Method Gaps: Establishing an Integrated, Climate Change, Impact Methodology for Pacific MSC Stakeholders

Since Pernetta and Hughes (1989), no coordinated methodology has been identified and globally accepted for MSCs and climate change risks in other studies. Whilst qualitative, simulation and econometric/numerical methods possess certain characteristics, advantages and disadvantages summarised above, global and Pacific stakeholders lack a consistently defined method. Assessing these methods ensures the most appropriate, cost and risk-effective methodology is applied to this thesis. To address current literature method gaps, it proposes a synthesised, multistage methodology in subsequent sections. This chapter connects ground theory, simulation projection, probability and econometric methods to apply to MSCs. This is necessary given countless stakeholder constraints and the uncertainty of forecasting exact climate change impacts.

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This thesis favours an integrated, conceptual framework providing accuracy, flexibility and other research advantages of a consistent and coordinated response. This seeks to combine research strengths with minimal, past adaptation method limits summarised in section 3.2. It retains the further advantage of adjusting for global, regional Pacific and individual, island specific variations in projected risks. It provides the benefit of field research visits for specific, Pacific case studies. It proposes all research stages chosen should satisfy several criteria to be included as an integrated methodology and conceptual framework, proposed to replace existing literature, theory gaps. Stages should be justified by significant peer-reviewed literature. Methods should be relevant and specifically apply to the thesis research questions. The researcher should identify each’s unique, conceptual contribution over existing methods for Pacific MSCs. Methods should be logically consistent to support the thesis structure. To answer current literature and method gaps; this thesis establishes a combined climate change risk-vulnerability assessment, impact cost analysis and adaptation strategy, evaluation method. This includes stakeholder consultation to address KRQA- KRQC. Certain advantages exist in combining qualitative, simulation and quantitative methods in one conceptual framework. This addresses stakeholder concerns over uncertain, climate change projections, diverse methodologies and a lack of previous literature examples. This aids stakeholders, given geographical distances, time, financial and other constraints limit sample size, data and information availability of stakeholder consultation for Pacific and other developing states. 3.3: CLIMATE CHANGE RISK-VULNERABILITY, CONCEPTUAL FRAMEWORK FOR MSCs (STAGE II)

To address KRQA in Chapter 5, this method is proposed from risks identified through field research, stakeholder consultation and peer-reviewed sources. The IMO (2007), formal safety assessment model in Figure 3.1 advanced a framework for systematic risk identification, management and evaluation. This model incorporates a cost-benefit analysis for policy stakeholders (as seen below). This is conventionally utilised in formal, maritime safety conditions. Its advantages consist of incorporating both qualitative and quantitative risks with impact cost types from a stakeholder perspective. Kontovas and Psaraftis (2009) identify several model concerns; including determining which risks should be incorporated or which method to select. Methods to