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Empirical Testing of Genuine Savings as an Indicator of Weak Sustainability: A Three-Country Analysis of Long-Run Trends

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Genuine Savings has emerged as a widely-used indicator of sustainable development. This approach to conceptualising what sustainability is about has strong links to work published by Anil Markandya and colleagues over 20 years ago. In this paper, we use long-term data stretching back to 1870 to undertake empirical tests of the relationship between Genuine Savings (GS) and future well-being for three countries: Britain, the USA and Germany. Our tests are based on an underlying theoretical relationship between GS and changes in the present value of future consumption. Based on both single country and panel results, we find evidence supporting the existence of a cointegrating (long run equilibrium) relationship between GS and future well-being, and fail to reject the basic theoretical result on the relationship between these two macroeconomic variables. This provides some support for the GS measure of weak sustainability.

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  1. Also referred to as Adjusted Net Savings or Comprehensive Investment.

  2. Note that Pearce et al. (1989) use these terms rather differently: they define weak sustainability as a situation where, across a portfolio of projects and over time, the net environmental cost of implementing the portfolio is zero or negative. For strong sustainability, they require this non-positive condition to hold for every time period: see Chapter 5. It is interesting that by the time the “new blueprint” was published Barbier and Markandya (2013), the difference between weak and strong sustainability revolves around the substitutability of different forms of capital for each other. Thus, weak sustainability takes rule (1) as being the relevant rule; strong sustainability takes rule (2).

  3. Pearce and Atkinson state: “To do this we adopt a neoclassical stance and assume the possibility of substitution between ‘natural’ and ‘man-made’ capital” (page 104).

  4. Note that our British data goes back to 1760, but for the present paper we restrict our attention to the period from 1870 onwards, since that allows a comparison on a like-for-like basis between the three countries.

  5. We do not include a wealth dilution term in the calculations of per capita GS in this paper.

  6. We are not convinced that the theory makes clear what one does about new discoveries in GS accounting. Clearly, finding an oil deposit increases the known stock of reserves, although it only increases the known economic reserve if the price/cost ratio is bigger than one. However, it does not increase the finite stock in the ground. Depletion, however, clearly reduces both the known stock and the un-known stock. For all of the non-renewable resources included in the database for Germany, the USA and Britain, we use production (ie extraction) in year t as the measure of depletion in that year. Finding new resources in year t might affect production, and thus measured depletion in years \(t\,+\,1, t\,+\,2 {\ldots }\), but we do not include this in the depletion term for year t.

  7. Pezzey et al. (2006) also include the value of natural resource capital gains in their measure of the value of time. However, this element is excluded in our measure in the absence of convincing evidence that relative prices favour natural capital in the long-run (Greasley et al. 2014).

  8. The output measure in the TFP is conventional GDP and not alternative “Green” adjusted variants nor does our TFP calculation incorporate “green” capital (e.g. see Mota et al. 2010 for discussion).

  9. Note that we have adopted a slightly different convention to calculating the consumption variable here compared to Greasley et al. (2014). In the present paper, we add up the discounted values of differences between pairs of years (t) and (\(t\,+\,1\)) over the requisite time interval, as per Ferreira et al. (2008). Greasley et al. took the present value of the difference between the first year and the last year of each interval. This actually makes little difference to the results.

    Fig. 3
    figure 3

    Consumption per capita, US, Britain and Germany 1870–2008

  10. Given that estimation is effectively bi-variate the potential issue of potential multiple cointegrating vectors is ruled-out.

  11. The second approach considered estimates the model using FMOLS and applies the Hansen (1992) test for cointegration. The results, not presented here due to space considerations, confirm all the qualitative conclusions on cointegration (and hence robustness) of Table 4 above and re-establish the weak sustainability conclusion, over the 50 year horizon, for the GSTFP variant with the non-rejection of \({\upbeta }_{0}=0\) and \({\upbeta }_{1}=1\) jointly; and \({\upbeta }_{1}=1\). Although other methods provide similar results, those reported are based upon the optimal method for the particular circumstance, i.e., when potential endogeneity exists we report IV method results etc. Reporting potentially sub-optimal method results in addition to those regarded as econometrically optimal appears redundant.

  12. Please note that these German results do not coincide exactly with those in Blum et al. (2013) due to some differences in estimation and a longer time-span used by Blum et al. (2013) starting in 1850.

  13. In this case, utilizing FMOLS and Hansen (1992) does not resolve the issue, as it did with the US. This is likely due to the size of the discontinuity experienced by Germany vis a vis the US: contrasting the effects of World War Two on Germany with those of the Great Depression on the USA.

  14. The results for the three countries embed country specific discount rates, reflecting their real long term interest rates. Our findings are somewhat sensitive to the choice of discount rate. If a common 2.5 %/year discount rate (this is a consumption discount rate adopted present day by the UK Treasury, and also the long term real UK interest rate), then the estimated \({\upbeta }_{1}\) in the case of the US gives results, for GS, as B1 \(= 1.04*, 1.17*\), \(-0.03^{+}\) and, for GSTFP, B1 \(=0.5*^{+}\), 0.7*\(^{+}\), 1.25*\(^{+}\) for 20, 30 and 50 year horizons respectively. For Germany, also using a 2.5 discount rate for consumption and TFP, gives B1 for GS as \(1.16*, 1.38*^{+}\), and 0.32 and for GSTFP B1 \(= 0.621*^{+}, 0.880*, 1.23*\) over 20, 30 and 50 year horizons. Where * denotes significantly different from 0 and \(^{+}\) denotes significantly different from 1. US results using a 2.5 % discount rate are higher than those presented in Table 3 whereas the German results using a 2.5 % discount rate are lower than those in Table 5; in both cases reflecting the lower (2.5 vs. 3.5 %)/ higher (2.5 vs. 1.95 %) discount rate. Our preference, like that of Ferreira et al. (2008) is to use country specific discount rates.


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Nick Hanley thanks the University of Waikato for hosting him during the writing of this paper. We thank The Leverhulme Trust for funding this work under the project “History and the Future: the Predictive Power of Sustainable Development Indicators” (Grant Number F00241). We also thank three referees and the editor of this special issue for helpful comments on earlier versions of the paper. Thanks also to Giles Atkinson, Kirk Hamilton and Jack Pezzey for many suggestions.

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Correspondence to Nick Hanley.

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Submitted to special issue of Environmental and Resource Economics in honour of Anil Markandya.

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Hanley, N., Oxley, L., Greasley, D. et al. Empirical Testing of Genuine Savings as an Indicator of Weak Sustainability: A Three-Country Analysis of Long-Run Trends. Environ Resource Econ 63, 313–338 (2016).

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