Genuine (i.e., quality-adjusted) saving takes into account the depreciation of physical, human and natural capital. Countries that run down their stocks of physical and natural capital will have low, perhaps even negative, genuine saving rates which, therefore, may be taken as a rough indication of the physical and economic durability of their capital and the sustainability of their natural resource management, at least in a physical sense. Genuine saving is intended to indicate the difference between sustainable net national product and consumption, where sustainable net national product means the maximum amount that could be consumed without reducing the present value of national welfare along the optimum path. Genuine saving rates are higher than net saving rates in those countries where improvements in human capital outweigh the deterioration of natural capital, and conversely. 

For more on the relationship between genuine saving and growth, see my recent paper "Natural resources and economic growth: The role of investment" with Gylfi Zoega and the associated slide show

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