A question of interest: Is UK household debt unsustainable?

Lewis Kirkham and Stephen Burgess.

UK household debt is high relative to income. But is it “unsustainable”? Some commentators say “it is”; others say “there is no reason to worry”. To investigate, we build a simple model of the economic relationships between household debt, house prices and real interest rates which we believe must hold in the long run. In our model there is no single threshold beyond which debt suddenly becomes unsustainable, but we argue that household debt should be broadly sustainable under any rise in real interest rates of up to about 2 percentage points (pp) from current levels. We also show that falling real interest rates may have contributed around 20-25pp to the rise in the household debt-to-GDP ratio since the 1980s.

What constrains households’ debt levels?

Household debt has more than doubled as a share of GDP over the past 40 years (Chart 1). Elevated household debt has been identified as a key risk by the IMF and ESRB, and evidence shows that high debt levels can force prolonged downturns in spending. But there may be perfectly good reasons why households have chosen to take on more debt. So how do we know when household debt has become “too high”?

One way to judge this is to look at individual borrowers and to see how likely they are to get into difficulty as their debt levels increase. Other authors have suggested fitting trends through aggregate data. Our own approach is grounded in macro time series analysis and exploits fundamental economic relationships between the three series in Chart 1. (Throughout the blog we use data to the end of 2017).

Chart 1: Household debt and housing wealth relative to GDP, and real policy rates

Sources: ONS, Bank of England, Nationwide and Halifax.
We define the real policy rate to be Bank Rate minus the five-year moving average of the GDP deflator.

Chart 2: Household leverage and debt service ratios

Sources: ONS, Bank of England, Nationwide and Halifax.

As any prospective home-owner knows, there are usually two constraints affecting what (s)he might be allowed to borrow. The first is the size of the loan relative to the value of the property. The second is the extent to which debt service payments are a burden on household incomes. We can extend this idea to the UK as a whole and calculate two useful summary measures: households’ “leverage” – their debt relative to total housing wealth; and their debt service ratio (Chart 2).

We suspect that, when one of these two quantities is rising sharply, that may indicate the economy is on an unsustainable path. For example, in the late 1980s and mid-2000s, increases in the debt service burden were followed by large falls in household spending. But although household debt has been rising for most of the past 40 years, these two measures have moved within a relatively narrow range since the 1980s, and recently have been declining.

We capture the relationships in Chart 2 more formally in a model known as a cointegrated VAR, which we explain in more detail in a technical annex. Our model draws heavily on a previous paper for the US by Juselius and Drehmann and a second paper they co-authored with Borio and Disyatat.  Figure 1 provides a stylised illustration of the long-run relationships. Reading from the left, the first two arrows capture the leverage and debt service constraints. The third relationship, labelled “spread”, captures the way in which movements in Bank Rate pass through to the effective loan rates facing households, and hence their debt service costs.

Figure 1: Stylised illustration of the long run relationships in our model

We estimate our model back to 1975. In the earlier part of our sample, households’ leverage and debt service burdens were increasing. We suspect that growing financial liberalisation over that period allowed households to take on more debt at given levels of house prices and interest rates. We model this explicitly in our long-run equations.

In the rest of our blog we show two applications of this simple model. First, we calculate a “benchmark” level of household debt for the UK, and find that debt today is below that benchmark. Second, we try to account for why household debt increased in the past.

How does UK household debt today compare with our benchmark?

We estimate a simple “benchmark” level for household debt to judge whether or not current levels are sustainable. This will depend on the level of the real interest rate, which we define to be Bank Rate less the five-year moving average of the GDP deflator. For a given real interest rate, the three relationships in Figure 1 (shown by the blue arrows) imply a unique benchmark level for household debt in the long run.

Chart 3 shows how that benchmark measure would have evolved over time as interest rates have changed (blue line). The orange line shows the actual data for the ratio of household debt to GDP, and the red line a measure of the gap between them. The gap would have been elevated going into the 1990-2 and 2008-9 recessions, because of elevated debt service burdens, and the model would have forecast an adjustment in the economy in order to unwind the imbalance. But today, the level of household debt is well below our benchmark, suggesting that debt is not at an unsustainable level.

Chart 3: Actual household debt and our benchmark level based on contemporaneous real interest rates

Sources: ONS, Bank of England and Bank calculations.

Chart 4: Sensitivity of our view on debt and house price sustainability to the level of real interest rates

Source: Bank calculations.

Now this partly reflects low real interest rates, which may not last for ever. Evidence suggests that “equilibrium” real rates have fallen over the past 30 years, with a number of possible causes. Here we define the equilibrium real rate to be the (unobserved) value to which the real policy rate will eventually converge. So real policy rates could rise towards that equilibrium over time, or the equilibrium itself could rise. If interest rates were to rise, the blue line in Chart 3 would fall towards the orange line and the red line would pick up.

Chart 4 shows what our model indicates about current levels of UK household debt and house prices as real interest rates vary. We do not presume to know a precise value of the equilibrium rate, but this chart illustrates why it is important. At a current real interest rate of less than -1% (blue dashed line), debt is below its benchmark level. If you thought that real rates would eventually settle at a long-run equilibrium of close to 1%, then current debt levels look broadly sustainable (orange dashed line), though house prices would then be higher than our benchmark. By way of comparison, in the late 1980s and mid-2000s, both household debt and house prices would have been well into the “red zone” at the real interest rates prevailing at the time. When debt is in the red zone it does not necessarily imply that a large adjustment will happen soon, but it does indicate an above-average level of vulnerability.

How can we account for rises in household debt over the past?

These calculations can tell us a lot, even though they just use the long-run reduced form relationships in our model. We can do much more if we estimate a full dynamic model, and introduce structural shocks. As we show in the technical annex, our VAR has several nice features, though the fit of the model is less good in the early part of the sample where the data are most volatile. We therefore focus more on the broad conclusions, which we feel are robust, rather than the precise numerical results.

By “identifying” the VAR under certain assumptions, we can decompose the factors which may have driven up household debt over the past 40 years. We explain the details in our technical annex. We note that our identification scheme is theoretically contentious in some respects, so what follows is more speculative than the rest of our blog.

Chart 5 shows how our identified VAR explains the rise in household debt over the past 40 years. We find that most of the rise in household debt in the 1980s was due to financial liberalisation (dark blue bars), which allowed households to take on more debt for given interest rates and house prices.

But since 1990, the biggest contribution has come from shocks to “equilibrium real interest rates” (in the red bars). We find that a shock which ultimately lowers real policy rates by 1pp eventually raises the ratio of household debt to GDP by about 8pp. This could mean that falling interest rates since the 1980s have pushed up household debt by about 20-25pp relative to GDP.

Chart 5: Factors driving the rise in household debt relative to GDP

Sources: ONS, Bank of England, Nationwide, Halifax, IMF and Bank calculations.


We have shown in this post that a full analysis of debt sustainability needs to go beyond just headline debt numbers: it’s also important to think about the economic forces which constrain debt accumulation. Over the past 30 years, falling real interest rates have allowed UK households to take on more debt, and that larger stock of debt looks as though it should be sustainable, provided real rates do not rise by too much.

But since interest rates are unlikely to remain as low as they are now indefinitely, we can only assess debt sustainability properly by making a judgement about their future path, which is challenging. Plenty of researchers are now studying the causes of low real interest rates, and whether they might persist for a long time. We think our analysis reinforces why this is such an important question, and we hope it inspires future work.

Lewis Kirkham works in the Bank’s Monetary Projections and Outlook Division and Stephen Burgess works in the Bank’s Macrofinanical Risks Division.

If you want to get in touch, please email us at bankunderground@bankofengland.co.uk or leave a comment below.

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Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.

3 thoughts on “A question of interest: Is UK household debt unsustainable?

  1. “Household leverage (Debt/Gross housing wealth)”

    Increased debt helps to push up house prices and thereby gross housing wealth. Is this considered in any way? What if for instance rate increases lessens the overall debt financing houses and thereby causes house prices to weaken or even fall?

  2. Your analysis backs up the consensus that believes (and has to believe) that high house price don’t matter as long as low interest rates keep the monthly payments in line with normal levels. The thing you miss is that interest rates and wage growth are correlated and first time buyers are very financially stressed at the start of a mortgage. As rates come down it takes longer and longer for them to normalise their financial stress level (in a 5% rate environment payments drop from 30% to 20% of income after 10 years compared with 25% in a 3% rate environment because implied wage growth is lower). this means they struggle to create the financial slack that enables them to move their lives forwards and accommodate the needs of a growing family. This is a very big diminution in the lives of median wage earners and, with its bedfellow low wage growth, is sufficient to explain the extreme political unrest we face. it also means that if wages surprise expectations and do actually grow (salvation one might think) they will be put into negative equity by rising interest rates; causing a negative feedback loop that caps wages.

  3. The issue which this analysis seems not to have taken account of is the relationship between GDP and wages, and particular the wages of the lower three quartiles. If the distribution of wealth associated with GDP is changing, the conclusions may not be applicable to lower to middle income groups, who often hold substantial debt, and who may therefore be more vulnerable to interest rate changes than this model would forecast. From a broader economic perspective, the risks associated with shocks within that group have real and significant impacts for the economy as a whole. I would therefore recommend that you include in your modeling an income distribution function.

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