This work investigates the relationship between countries’ participation in virtual water trade and their vulnerability to external shocks from a network perspective. In particular, we investigate whether (i) possible sources of local national crises may interact with the system, propagating through the network and affecting the other countries involved; (ii) the topological characteristics of the international agricultural trade network, translated into virtual water-equivalent flows, may favor countries’
vulnerability to external crises.
Our work contributes to the debate on the potential merits and risks associated with openness to trade in agricultural and food products. On the one hand, trade helps to ensure that even countries with limited water (and other relevant) resources have access to sufficient food and contribute to the global saving of water. On the other hand, there are fears that openness may increase the vulnerability to external shocks and thus make countries worse off. Here we abstract from political considerations about food sovereignty and independence from imports and focus instead on investigating whether the increased participation in global trade that the world has witnessed in the last 30 years has made the system more susceptible to large shocks.
Our analysis reveals that: (i) the probability of larger supply shocks has not increased over time; (ii) the topological characteristics of the VW network are not such as to favor the systemic risk associated with
shock propagation; and (iii) higher-order interconnections may reveal further important information about the structure of a network. Regarding the first result, fluctuations in output volumes, among the sources of shock analyzed here, are more likely to generate some instability. The first implication is that, on one side, past national or regional economic crises were not necessarily brought about or strengthened by global trade. The second, more remarkable, implication is that, on the other side, supporting a national policy of self-sufficiency in food production while progressively reducing the participation in international agricultural trade does not necessarily protect a country from economic instability. Moreover, it is well established in the literature that, over time, international food trade has favored more efficient use of water resources, at the global level (e.g. Aldaya, Allan, & Hoekstra, 2010;
Chapagain, Hoekstra, & Savenije, 2006; De Fraiture, Cai, Amarasinghe, Rosegrant, & Molden, 2004;
Oki & Kanae, 2004). This fact, together with our conclusions, highlights the important role of international trade in driving the efficient allocation of water resources.
To sum up, our evidence reveals that the increased globalization witnessed in the last 30 years is not associated with an increased frequency of adverse shocks (in either precipitation or food production).
Furthermore, building on recent advances in network analysis that connect the stability of a complex system to the interaction between the distribution of shocks and the network topology, we find that the world is more interconnected, but not necessarily less stable.
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1 See Section 2 for an explanation.
2 Producing one kilogram of grain in an arid country can require two or three times more water than producing the same amount in a humid country (Hoekstra, 2003).
3 Throughout the paper, we use the country-specific measures of VW content provided by Mekonnen & Hoekstra (2011). Dalin et al.
(2012) and Konar et al. (2011) use instead the H08 global hydrological model developed by Hanasaki et al. (2008a, 2008b) to determine the virtual water content of different goods.
4 We owe a debt of gratitude to these authors, who shared the data on virtual water trade flows.
5 For a definition of water resource components, see Falkenmark & Rockström (2006). Freshwater pollution (grey water) is excluded from the calculations, due to the strong uncertainties inherent in its determination (see Hoekstra, Chapagain, Aldaya, & Mekonnen, 2011).
6 For an overview of the literature on financial networks, see Allen & Babus (2009) or Bougheas & Kirman (2014).
7 Acemoglu et al. (2012) study the likelihood of large economic downturns, showing that it is determined by the interplay between the inter-sectoral input–output linkages and the nature of the idiosyncratic sectoral shocks. Even though some economies exhibit the same deviation properties as balanced structures in the presence of normally distributed shocks, they may experience significantly more frequent downturns in the presence of exponential-tailed shocks.
8 In the presence of a thin-tailed probability distribution, the upper tail declines to zero exponentially or faster. Such a distribution has a moment generating function, and all moments exist. A normal or a gamma distribution is an example of the thin-tailed probability distribution function, as is any distribution with finite supports, like a uniform distribution or a discrete-point finite distribution. On the contrary, a fat-tailed distribution falls to zero much more slowly. The standard example of a fat-tailed probability distribution function is the power law or Pareto distribution, although a Student-t or inverted-gamma distribution is also fat-tailed.
9 See http://www.fao.org.
10 Data are available for the years 1987, 1992, 1997, and 2002.
11 The p-value of the sample for the year 1987 is slightly above the 5% significance level (0.056).
12 The same result is valid for all the other simulations in the present paper, when performing a Clauset test on the sample distribution.
13 This test fits the power law form only for the part of the distribution above xmin. If xmin is large, then only a small fraction of the data set falls above it and thus the larger the value of xmin, the larger the total value of n needed to reject the power law. That is, the higher the percentage of values above xmin, the lower the probability of a fat-tailed sample of data.
14 We also compute the Hill estimator of the tail index – HI (Hill, 1975), but it does not provide any useful results.
15 1986: China, -13%; 1990: China, -11%; 1995: China, -6%; 2000: Russia, -11%; 2005: India, -4%; 2010: Russia, -24%. As a percentage of global agricultural production, these lower output volumes are respectively: -2.7%, -2.5%, -1.5%, -0.3%, -0.4%, and -0.6%.
16 In the applied literature, one often finds that many social networks display positive assortativity, while the opposite holds true for technological and biological networks (Costa, Rodrigues, Travieso, & Boas, 2007; Newman, 2003).
17 In fact, the same analysis is also carried out on the distributions of the outdegree and total degree (the sum of the in- and outdegree net of bilateral links). The qualitative picture is unchanged. The interested reader will find a sample of results derived from the analysis of the outdegree in the Appendix.
18 Embrecht, Klueppelberg, & Mikosch (1997) suggest that a necessary condition for saying that a distribution follows a power law is that its MEF tends to infinity.
Appendix
We present a sample of results derived from the analysis of the outdegree probability distribution functions, for the same selected years. A comparison with the indegree analysis carried out previously shows that the qualitative picture does not change.
Figure A1. Normalized outdegree distributions (first order).
Table A1. Indexes of tail heaviness: Outdegree distributions (first order).
Year % Out of
Figure A2. MEF of the original sample and aggregated data set (first-order outdegree).
Years 1990 (left panel) and 2000 (right panel).
Figure A3. Normalized outdegree distributions (second order).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Table A2. Indexes of tail heaviness: Outdegree distributions (second order).
Figure A4. MEF of the original sample and aggregated data set (second-order outdegree).
Years 1995 (left panel) and 2005 (right panel).
Table A3. Descriptive statistics. First- and second-order outdegree distributions.
Indegree Second-Order Indegree
Figure A5. Left panel: Weighted first-order outdegree distributions for selected years.
Right panel: Weighted second-order outdegree distributions for some selected years. X-axis: log scale.
Table A4. Indexes of tail heaviness. Weighted first- and second-order outdegree.
Year
Weighted First-Order Degree Weighted Second-Order degree
% of Values
Figure A6. MEF of the original sample (weighted first-order outdegree) and aggregated data set.
Year 1990 (left panel) and year 2000 (right panel).
100 101 102
Figure A7. MEF of the original sample (weighted second-order outdegree) and aggregated data set.
Year 1990 (left panel) and year 2000 (right panel).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
MEF
threshold
original sample 1990 aggregation by 2 aggregation by 6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
threshold
MEF
original sample 2000 aggregation by 2 aggregation by 6