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Suppose we are interested in the relationship between public or external debt and economic growth.

One can look at the debt-to-GDP ratio or debt-to-export ratio.

What may be other possible "debt-to-... ratio" indicators that might be useful to investigate the relationship between public or external debt and economic growth?

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Median household income comes to mind. This can be a useful denominator in capital-heavy economies where labour's share of income is relatively small, as it frames debt and deficit in terms of the burden faced by the most fundamental unit of concern in public policy.

In Canada, where I'm from, the OECD finds that labour share has dropped from close to 70% in 1990 to just over 60% in 2007, while nominal GDP nearly tripled in the same period. National debt, meanwhile, increased roughly 50%, and so while debt-to-GDP would have fallen over this period, the debt-to-household-income would have risen. This was a period of heavy investment in Canada's resource extraction industries, with new technologies like SAG-D coming into their own and kicking off a wave of multi-billion dollar injections of capital. I don't have time to dig up the stats for the province of Alberta for this period, but I would expect these trends to be even more extreme there, as this is where the majority of these investments occurred.

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