Bioeconomic diversity dynamics of a marine ecosystem

ABSTRACT

This paper models the bio-economic diversity dynamics of a marine ecosystem made up by its entire commercial fish species and, from the fitted model, obtains a quantitative measure of its resilience to disturbance in terms of recovery time after a shock. Such shocks might be produced by both, downturns in catches and/or prices related to changing regulatory and environmental conditions. To that end, monthly time series of bio-economic diversity indices will be used and the framework of a mixed cyclical ARFIMA joint with a GARCH type heteroscedaticity model will be explored to analyse the dynamic properties of such indices and, based on the estimated impulse response functions (IRF) to measure the effects and duration of a unitary random shock or disturbance. One of our findings is that bio-economic diversity is a mean-reverting process with an estimated recovery time between 7 and 10 years.

KEYWORDS:

• Bio-economic diversity
• resilience
• long memory
• short memory
• cyclical ARFIMA-GARCH model

JEL CLASSIFICATION:

• Q22
• C22
• Q57

Acknowledgements

This study has received financial support from the Spanish Ministry of Economics and Competitiveness (MINECO/Project Ref: ECO2013-44436-R) and from the Basque Govern (Consolidated Research Group “Institutions, Regulation and Economic Policy” (Ref GIC12/171)). Authors are grateful to the Managers of Santa Clara Fishermen Guilt at the fishing port of Ondarroa for having made available the dataset used in this paper, Aintzina Oienarte for her assistance in data preparation, Javier García and Josu Arteche for their generous advise related to the long memory coding framework and an anonymous referee for the valuable and constructive comments. All the errors and opinions are the author’s responsibility.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ p, q and d are, respectively, the autoregressive, moving average components and the differentiation parameter. d captures the number of the differentiations that the series requires in order to be stationary.

² The asymptotic distribution for −1/2 < d < 1/2 is.

³ When the first difference of the series is regressed on a constant, it is not significant.

⁴ Stationarity of an AR(1) requires: |ϕ₁| < 1, AR(2): ϕ₁ + ϕ₂ < 1, ϕ_{1 –} ϕ₂ < 1, |ϕ₂| < 1, AR(p): ϕ₁ + ϕ₂ … + ϕ_p ≠1. Invertibility of a MA(1) requires |θ₁| < 1, MA(2): θ ₁ + θ₂ < 1, θ_{1 –} θ₂ < 1, |θ ₂| < 1, MA(q): θ₁ + θ₂ … + θ_p ≠1.

⁵ At this stage we have taken advantage of the R package TSA (Chan and Ripley 2015).

⁶ This can also be seen through the periodogram, with no peaks standing out and all cycles contributing similarly to the variance of the series.

⁷ Volatility, interchangeably used as a synonym of risk because of its dominant connection with the field of financial economics, is concerned with the degree of variation or dispersion from an expected value, price or model (Engle 1982). Although not directly observable, it can be inferred based on specific volatility models, which are indeed concerned with the time evolution of the conditional variance.

⁸ The tail parameter (SHAPE) controls the height and tails of the density function and the asymmetry parameter (SKEW) its rate of descent. Note that as SHAPE gets smaller, the tails of the distribution become flatter and the centre becomes more peaked. Accordingly, the sged family allows for tails that are either heavier than normal (SHAPE< 2) or lighter than normal (SHAPE > 2); and density functions skewed to the right (SKEW > 0) or left (SKEW > 0).

⁹ At this stage we have taken advantage of the R package rugarch (Ghalanos 2015).

¹⁰ Asymptotic critical values for Nyblon test (10% 5% 1%) 0.35 0.47 0.75.

¹¹ Asymmetry refers to positive and negative return shocks of the same magnitude producing a differing amount of volatility.

¹² $MA(\mathrm{\infty })=x_t=\sum _{j=0}^{\mathrm{\infty }}{\pi }_j{\epsilon }_{t-j}$.

¹³ An alternative generalized way to estimate HL is based on the Augmented Dickey–Fuller regression form, where the autoregressive parameter (α) is the one associated with persistence. Then, (HL) is calculated as HL = ln(0.5)/ln(α) Despite its popularity, this estimating method of persistence has some problems as highlighted in Murray and Papell (2002). First, the usual least square estimation of a parameter exhibits downward bias in finite samples. Second, if the order of the autoregressive (AR) is superior to one, then, the calculus of HL from the ADF is not appropriated. The half-life calculated from the value of α assumes that shocks are  to real exchange rates decay at a constant rate. While this is appropriate for an AR(1) process in general shocks to a higher order of auto-regression will not decay at a constant rate. In light of this Cheung and Lai (2000) recommend calculating the half-life directly from the IRF.