My last post reflected on the Borio/ Vlieghe idea that the Equilibrium Real Rates (ERR) should perhaps be defined not just by inflation, but also by changing debt levels. Since then I have been thinking about that list of tricksy questions I listed at the end of the post. I want to have a stab at one – specifically, whether it is possible to define the ‘optimal nonfinancial debt’ for an economy. Short answer: maybe, but I don’t have the skills to know*; in the meantime I’ve got a way to think about it from 30k feet. 

Thinking about optimal debt loads from 30k feet by cleverer people than me has had a frankly shocking record.** That said, my MPhil thesis on the geopolitics of emerging market finance, has given me familiarity with debt sustainability models that I think could maybe be helpful. The bottom line of debt sustainability frameworks tends to be that there is rarely an impossible level of debt, but debt does get meaningfully tougher to service as debt rises, rates rise, and growth slows. Big surprise.

Let’s look at the UK household sector as a whole through the lens of a super-simplified sovereign debt dynamics framework.*** We know what disposable household income growth and effective interest rates have recently been. And we know where the household debt stock has got to. As the chart below shows, it has risen to 138% of disposable income.


So what is the ‘primary surplus’ (or in the households’ case the net acquisition of financial liabilities minus interest payments as a percentage of household disposable income) required to stabilise household debt-to-disposable-income at 138%? The answer is around about 2% right now. And what is the actual ‘primary surplus’? Around -2%. So debt is growing, and is growing quickly. And the Bank of England appears to be worried about this worrying rise in household debt. (Again, read the last blog on this here.)

We can compare the primary surplus required to stabilise debt levels over time (blue line in the chart below) to the actual primary surplus recorded by households (grey line). You may notice that when the grey line is below the blue line, debt rises. When the grey line is above the blue line, debt falls. It’s a super-simplified little framework. The chart on the right compares the gap between the two lines to the change in debt-to-income: we can see that it doesn’t capture everything, but it sort of works(ish).


While extremely simple, this framework highlights the degree to which the issue of changes in debt sustainability (a somewhat different and easier question to the optimal debt load question) is a function of income growth, interest rates and debt loads. And in seeking to answer the question as to why households have re-levered recently, we can quickly hypothesise an answer that doesn’t involve a spending splurge. (The incredibly smart Neville Hill at Credit Suisse, who kindly shared his data with me that I used to calculate the blue line, argues exactly that here.)

What pushes the blue line up and down so erratically? Well, the most volatile input to the little debt dynamics ‘model’ is household income growth. The spike up in the blue line in recent quarters appears to have been driven by a collapse in nominal household income growth through 2016. In other words, it sort of looks like households are expecting the sharp recent slowdown in income growth to be temporary.

If the slowdown in household income growth isn’t temporary and the Bank of England raise rates to try to control household debt growth, the blue line gets a double-whammy. The following projection shows the path of the breakeven primary surplus in an environment where household disposable income growth continues at the sluggish pace of the last year and three rate rises over the next three quarters:


Actual household consumption would have to drop consumption pretty darn quickly to stabilise debt levels. And I can see households interpreting this as monetary policymakers arguing that the beatings will continue until morale improves.

Where does this leave the idea that an understanding of the ERR should take into account debt growth? I’m still scratching my head on this, but it seems to introduce some qualifications at the least.
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* Given the importance of this question for all sorts of things, it is frankly weird that there hasn’t been more research on it. I feel pretty confident that it might be advanced by some awesome econometricians who have experience in mining large panels of ONS household data, but is there anything to say on the matter before then?

** In the wake of the GFC, Ken Rogoff and Carmen Reinhart’s empirical work on debt at a sovereign level attracted sufficient policymaker attention to get them cited as the intellectual handmaidens of austerity. Indeed, ex-UK Chancellor George Osborne cited their work directly ahead of the fact as the rationale supporting austerity. But since the aspects of the R&R work looking for debt optimality has been shown to be uncharacteristically error-strewn.

*** Simply d[(r-g)/(1+g)]=pb, where d = debt/ disposable income; r = effective household interest rate; g = annual growth in household disposable income, and; pb = household net acquisition of financial liabilities minus interest payments as a percentage of household disposable income.