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Computable general equilibrium modelling of economic impacts from volcanic event scenarios at regional and national scale, Mt. Taranaki, New Zealand

Abstract

The economic impacts of volcanism extend well beyond the direct costs of loss of life and asset damage. This paper presents one of the first attempts to assess the economic consequences of disruption associated with volcanic impacts at a range of temporal and spatial scales using multi-regional and dynamic computable general equilibrium (CGE) modelling. Based on the last decade of volcanic research findings at Mt. Taranaki, three volcanic event scenarios (Tahurangi, Inglewood and Opua) differentiated by critical physical thresholds were generated. In turn, the corresponding disruption economic impacts were calculated for each scenario. Under the Tahurangi scenario (annual probability of 0.01–0.02), a small-scale explosive (Volcanic Explosivity Index (VEI) 2–3) and dome forming eruption, the economic impacts were negligible with complete economic recovery experienced within a year. The larger Inglewood sub-Plinian to Plinian eruption scenario event (VEI > 4, annualised probability of ~ 0.003) produced significant impacts on the Taranaki region economy of $207 million (representing ~ 4.0% of regional gross domestic product (GDP) 1 year after the event, 2007 New Zealand dollars), that will take around 5 years to recover. The Opua scenario, the largest magnitude volcanic hazard modelled, is a major flank collapse and debris avalanche event with an annual probability of 0.00018. The associated economic impacts of this scenario were $397 million (representing ~ 7.7% of regional GDP 1 year after the event) with the Taranaki region economy suffering permanent structural changes. Our dynamic analysis illustrates that different economic impacts play out at different stages in a volcanic crisis. We also discuss the key strengths and weaknesses of our modelling along with potential extensions.

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Acknowledgements

The authors would like to thank two anonymous referees for their valuable comments.

Funding

We acknowledge funding support from the New Zealand Natural Hazards Research Platform and Resilience to Nature’s Challenges National Science Challenge.

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Corresponding author

Correspondence to G. W. McDonald.

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Editorial responsibility: L. Sandri

Appendix 1 Description of the multi-regional dynamic computable general equilibrium model

Appendix 1 Description of the multi-regional dynamic computable general equilibrium model

Overview

The CGE model in this paper is based on a standard Arrow-Debreu general equilibrium framework (Arrow and Debreu 1954), where optimisation functions are concave and have continuous first-order and second-order derivatives, thus implying a unique solution. In short, the model simultaneously solves a maximisation of utility/profit problem for multiple economic agents, i.e. industries (39 types for each region), households (one aggregate agent for each region), governments (two agents for each region—local and central government) and enterprises (one aggregate agent for each region). The model solution determines the optimal level of commodity production and consumption. Altogether, the model recognises a total of 48 different commodity types, and these can originate from within the local economy, from the rest of New Zealand or abroad. The prices of commodities and, depending on the problem, factors of production (i.e. labour and capital) are unknown variables that are adjusted by the model to maximise utility/profit of agents, while ensuring that demand and supply are balanced within all commodity and factor markets. Another important set of constraints within the model relate to agent budgets. These constraints generally ensure that net income received by each agent over a study period is equivalent to that agent’s expenditure, where net income includes net transfers from other agents and the rest of the world, less income diverted towards savings.

Utility maximising agents

Two of the agent types, households and governments, maximise utility by adjusting their consumption of commodities subject to budget constraints. These agents also own factors of production, and provide them to production sectors in exchange for income. An agent’s total income is therefore a function of its available supply of factors, and the market price for those factors. Additionally, the model assumes that a proportion of each agent’s income is simply transferred to other agents and to savings. For example, a share of households’ income from labour supply is transferred to the central government agent as tax. The household and the government utility maximisation function for each time iteration, t, takes the form

$$ {\displaystyle \begin{array}{c}\underset{x_{i,a,r}^C}{\max }\ {\mathrm{u}}_{a,r}\left({x}_{i,a,r}^C\right)\\ {} where\ {\mathrm{u}}_{a,r}\left({x}_{i,a,r}^C\right)={\left[\sum \limits_{i=1}^I{\left({A}_{i,a,r}\right)}^{\frac{1}{\upsigma_{a,r}}}{\left({x}_{i,a,r}^C\right)}^{\frac{\upsigma_{a,r}-1}{\upsigma_{a,r}}}\right]}^{\frac{\upsigma_{a,r}}{\upsigma_{a,r}-1}}\\ {}s.t\ \sum \limits_{i=1}^I{p}_{i,r}^D{x}_{i,a,r}^C={y}_{a,r}\end{array}} $$

The utility of an agent a in region r, u a, r , is therefore a function of the quantity of each commodity i consumed by that agent, \( {x}_{i,a,r}^C \). A i, a, r is a share parameter of commodity i for agent a in the region r, and σ a, r is an elasticity of substitution between commodities for that agent. The constraint also ensures that the subject agent’s total income, y a, r , is equivalent to the total value spent on purchases of commodities which, in turn, is determined by quantity of each commodity consumed and the domestic commodity price for each commodity, \( {p}_{i,r}^D \).

Redistributive agents

The enterprise agent within each region is simply an accounting entity which collects income from ownership of capital and redistributes this income to the household and government agents.

Profit-maximising agents

The production sector consists of 39 industries producing 48 different types of commodities that are either sold to domestic consumers or exported to another region or overseas. As is common practice in CGE modelling, the production functions for industries are ‘nested’, with each level of the nest specifying the degree of substitution that may occur between groups of production inputs. At the top level, total industry output depends on a constant ratio of inputs (i.e. no substitution possible) of total (composite) factors and intermediate goods. The model also assumes no substitution between individual intermediate goods. At the next level, down within the production nest, factors are decomposed into capital and labour as per the constant elasticity of substitution (CES) functional form. The approach means that the relative quantities of capital and labour demanded by each industry depend on the relative prices of those commodities, and the degree to which each industry can substitute factors in the production process. In summary, a production sector (industry) j within region r faces the profit maximisation function:

$$ {\displaystyle \begin{array}{c}\underset{x_{i,j,r}^P,{x}_{i,,r}^U}{\max }\ \sum \limits_{i=1}^I{P}_{i,r}^P{x}_{i,j,r}^P-\sum \limits_{i=1}^I{P}_{i,r}^D{x}_{i,j,r}^U-\sum \limits_{k=1}^K{P}_{k,r}{f}_{j,k,r}\\ {}s.t.{x}_{i,j,r}^P=\min \left(\frac{1}{a_{j,r}^F}{\left[{\upvarphi}_{j,r}{\left(\frac{K_{j,r}}{\overline{K_{j,r}}}\right)}^{\frac{\updelta_{j,r}-1}{\updelta_{j,r}}}+\left(1-{\upvarphi}_{j,r}\right){\left(\frac{L_{j,r}}{\overline{L_{j,r}}}\right)}^{\frac{\updelta_{j,r}-1}{\updelta_{j,r}}}\right]}^{\frac{\updelta_{j,r}}{\updelta_{j,r}-1}},\frac{x_{1,j,r}^U}{a_{1,j,r}^U},\dots, \frac{x_{I,j,r}^U}{a_{I,j,r}^U}\right)\times {z}_{i,j,r}\end{array}} $$

The first part of the maximisation function defines the total income received by the industry from the sale of its produced commodities, where \( {P}_{i,r}^P \) is the producer’s price of commodity i in region r and \( {x}_{i,j,r}^P \) is the quantity of commodity i produced by that industry. The second two parts of the equation define, respectively, the total costs of production in terms of intermediate goods and factor inputs. As per above, \( {P}_{i,r}^D \) is the domestic price of commodity i within region r, while P k, r is price of factor k within that region. Also, \( {x}_{i,j,r}^U \) and f j, k, r are the quantities of commodity i and factor k used in production by the relevant sector and region.

The constraint contained in the second line of the optimisation problem ensures that the quantity of a particular commodity produced by industry i within region r, \( {x}_{i,j,r}^P \), is determined by the coefficient z i, j, r , which specifies the ratio of good i produced relative to total industry j production, and a production function specifying the level of total industry output as a function of the quantities of capital, labour and intermediate goods available. As already stated, total (composite) factors and intermediate inputs are ordinarily used in fixed ratios, and hence, the production function is a minimum function referencing industry-specific technological coefficients for factors (\( {a}_{j,r}^F \)) and intermediate inputs (\( {a}_{1,j,r}^U,{a}_{2,j,r}^U,{a}_{3,j,r}^U,\dots, {a}_{I,j,r}^U \)). A CES function is also nested within the industry production function, determining the quantity of composite factors available based on the individual quantities of capital, K j, r , and labour, L j, r , for each industry. Note that \( {\overline{K}}_{jr} \) and \( {\overline{L}}_{jr} \) are the baseline capital and labour used in production, and δ is the elasticity of substitution.

International and interregional trade

The New Zealand economy is assumed to be sufficiently small such that changes in the domestic market have a negligible effect on world commodity prices. The implication is that prices for international export and import goods are exogenous in foreign currency terms.

Commodities produced within local markets are distinguished from commodities produced in other New Zealand regions or abroad even when the commodities are classified in statistical accounts as the same good. This enables us to reconcile the existence of two-way trade (frequently termed cross-hauling) in one type of commodity. The degree of similarity/difference between local and imported goods is reflected in the elasticity of substitution in a CES function. This is a common approach within CGE modelling to distinguish commodity demands between local and imported goods, and is known as the Armington assumption (Armington 1969). The derived demands for imported and local goods will thus reflect the magnitude of total demand, and the relative prices of goods sourced from different origins.

Turning now to the supply side, it is similarly assumed that industries may supply the commodities they produce to domestic or international/interregional markets. The process of distributing goods by location is represented by the constant elasticity of transformation (CET) function.

Market clearing conditions

For the model to produce a balanced solution, where the total supply of each commodity and factor is equal to demand, we need to also specify market-clearing conditions. In short, these market-clearing conditions ensure at any time iteration

  • Total supply of a commodity i to a region r equals total use of commodity i within region r. Note that sources of supply include local industry production, imports from other New Zealand regions and imports from other nations. Similarly, uses of a commodity include both local demands for production and consumption, as well as exports to other New Zealand regions and nations.

  • The domestic price of a commodity is equal to the production price, plus any relevant taxes and/or transportation costs imposed.

  • Total capital and total labour used by all industries are equal to the respective quantities of these factors supplied by households, governments and enterprises.

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McDonald, G.W., Cronin, S.J., Kim, JH. et al. Computable general equilibrium modelling of economic impacts from volcanic event scenarios at regional and national scale, Mt. Taranaki, New Zealand. Bull Volcanol 79, 87 (2017). https://doi.org/10.1007/s00445-017-1171-3

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  • DOI: https://doi.org/10.1007/s00445-017-1171-3

Keywords

  • Taranaki volcanism
  • Scenario analysis
  • Computable general equilibrium modelling
  • Economic impacts
  • Eruption impacts