Fisher Dynamics Revisited

Back in the 2010s, Arjun Jayadev and I wrote a pair of papers (one, two) on the evolution of debt-income ratios for US households. This post updates a couple key findings from those papers. (The new stuff begins at the table below.)

Rather than econometric exercises, the papers were based on a historical accounting decomposition —  an approach that I think could be used much more widely. We separated changes in the debt-income ratio into six components — the primary deficit (borrowing net of debt service payments); interest payments; real income growth; inflation; and write downs of debt through default — and calculated the contribution of each to the change in debt ratios over various periods. This is something that is sometimes done for sovereign debt but, as far as I know, we were the first to do it for private debt-income ratios.

We referred to the contributions of the non-borrowing components as “Fisher dynamics,” in honor of Irving Fisher’s seminal paper on depressions as “debt deflations.” A key aspect of the debt-deflation story was that when nominal incomes fell, the burden of debt could rise even as debtors sharply reduced new borrowing and devoted a greater share of their income to paying down existing debt. In Fisher’s view, this was one of the central dynamics of the Great Depression. Our argument was that something like a slow-motion version of this took place in the US (and perhaps elsewhere) in recent decades.

The logic here is that the change in debt-income ratios is a function not only of new borrowing but also of the effects of interest, inflation and (real) income growth on the existing debt ratio, as well as of charge offs due to defaults.

Imagine you have a mortgage equal to double your annual income. That ratio can go down if your current spending is less than your income, so that you can devote part of your income to paying off the principal. Or it can go down if your income rises, i.e. by raising the denominator rather than lowering the numerator. It can also go down if you refinance at a lower interest rate; then the same fraction of your income devoted to debt service will pay down the principal faster. Our of course it can go down if some or all of it is written off in bankruptcy.

It is possible to decompose actual historical changes in debt-income ratios for any economic unit or sector into these various factors. The details are in either of the papers linked above. One critical point to note: The contributions of debt and income growth are proportional to the existing debt ratio, so the higher it already is, the more important these factors are relative to the current surplus or deficit.

Breaking out changes in debt ratios into these components was what we did in the two papers. (The second paper also explored alternative decompositions to look at the relationship been debt ratio changes and new demand from the household sector.) The thing we wanted to explain was why some periods saw rising debt-income ratios while others saw stable or falling ones.

While debt–income ratios were roughly stable for the household sector in the 1960s and 1970s, they rose sharply starting in the early 1980s. The rise in household leverage after 1980 is normally explained in terms of higher household borrowing. But increased household borrowing cannot explain the rise in household debt after 1980, as the net flow of funds to households through credit markets was substantially lower in this period than in earlier postwar decades. During the housing boom period of 2000–2007, there was indeed a large increase in household borrowing. But this is not the case for the earlier rise in household leverage in 1983–1990, when the debt– income ratios rose by 20 points despite a sharp fall in new borrowing by households.

As we explained:

For both the 1980s episode of rising leverage and for the post-1980 period as a whole, the entire rise in debt–income ratios is explained by the rise in nominal interest rates relative to nominal income growth. Unlike the debt deflation of the 1930s, this ‘debt disinflation’ has received little attention from economists or in policy discussions.

Over the full 1984–2011 period, the household sector debt–income ratio almost exactly doubled… Over the preceding 20 years, debt–income ratios were essentially constant. Yet households ran cumulative primary deficits equal to just 3 percent of income over 1984–2012 (compared to 20 percent in the preceding period). The entire growth of household debt after 1983 is explained by the combination of higher interest payments, which contributed an additional 3.3 points per year to leverage after 1983 compared with the prior period, and lower inflation, which reduced leverage by 1.3 points per year less.

We concluded:

From a policy standpoint, the most important implication of this analysis is that in an environment where leverage is already high and interest rates significantly exceed growth rates, a sustained reduction in household debt–income ratios probably cannot be brought about solely or mainly via reduced expenditure relative to income. …There is an additional challenge, not discussed in this paper, but central to both Fisher’s original account and more recent discussions of ‘balance sheet recessions’: reduced expenditure by one sector must be balanced by increased expenditure by another, or it will simply result in lower incomes and/or prices, potentially increasing leverage rather than decreasing it. To the extent that households have been able to run primary surpluses since 2008, it has been due mainly to large federal deficits and improvement in US net exports.

We conclude that if reducing private leverage is a policy objective, it will require some combination of higher growth, higher inflation, lower interest rates, and higher rates of debt chargeoffs. In the absence of income growth well above historical averages, lower nominal interest rates and/or higher inflation will be essential. … Deleveraging via low interest rates …  implies a fundamental shift in monetary policy. If interest-rate policy is guided by the desired trajectory of debt ratios, it no longer can be the primary instrument assigned to managing aggregate demand. This probably also implies a broader array of interventions to hold down market rates beyond traditional open market operations, policies sometimes referred to as ‘financial repression.’ Historically, policies of financial repression have been central to almost all episodes where private (or public) leverage was reduced without either high inflation or large-scale repudiation.

These papers only went through 2011. I’ve thought for a while it would be interesting to revisit this analysis for the more recent period of falling household debt ratios. 

With the help of Arjun’s student Advait Moharir, we’ve now brought the same analysis forward to the end of 2019. Stopping there was partly a matter of data availability — the BEA series on interest payments we use is published with a considerable lag. But it’s also a logical period to look at, since it brings us up to the start of the pandemic, which one would want to split off anyway.

The table below is a reworked version of tables in the two papers, updated through 2019. (I’ve also adjusted the periodization slightly.) 

		Due to …
Period	Annual PP Change in Debt Ratio	Primary Deficit	Interest	Growth	Inflation	Defaults
1929 – 1931	3.7	-5.5	2.9	2.8	2.9	*
1932 – 1939	-1.2	-1.5	2.4	-1.6	-0.7	*
1940 – 1944	-3.8	-1.6	1.3	-2.5	-1.9	*
1945 – 1963	2.6	2.5	2.6	-1.5	-0.8	*
1964 – 1983	0.0	0.8	5.1	-2.4	-3.5	*
1984 – 1999	1.7	-0.3	7.5	-2.9	-2.1	-0.4
2000 – 2008	4.5	2.4	7.2	-1.7	-2.5	-0.8
2009 – 2013	-5.4	-3.7	5.8	-3.1	-2.3	-2.4
2014 – 2019	-2.0	-1.4	4.6	-3.4	-1.3	-0.6

Again, our central finding in the earlier papers was that if we compare the 1984-2008 period of rising debt ratios to the previous two decades of stable debt ratios, there was no rise in the primary deficit. For 1984-2008 as a whole, annual new borrowing exceeded debt service payments by 0.7 percent of income on average, almost exactly the same as during the 1964-1983 period. (That’s the weighted average of the two sub-periods shown in the table.) Even during the housing boom period, when new borrowing did significantly exceed debt service, this explained barely a third of the difference in annual debt-ratio growth (1.6 out of 4.5 points).

The question now is, what has happened since 2008? What has driven the fall in debt ratios from 130 percent of household income in 2008 to 92 percent on the eve of the pandemic?

In the immediate aftermath of the crisis, sharply reduced borrowing was indeed the main story. Of the 10-point swing in annual debt-ratio growth (from positive 4.5 points per year to negative 5.4), 6 points is accounted for by the fall in net borrowing (plus another 1.5 points from higher defaults). But for the 2014-2019 period, the picture is more mixed. Comparing those six years to the whole 1984-2008 period of rising debt, we have a 4.7 point shift in debt ratio growth, from positive 2.7 to negative 2. Of that, 2.1 points is explained by lower net borrowing, while almost 3 points is explained by lower interest. (The contribution of nominal income growth was similar in the two periods.) So if we ask why household debt ratios continued to fall over the past decade, rather than resuming their rise after the immediate crisis period, sustained low interest rates are at least as important as household spending decisions. 

Another way to see this is in the following graph, which compares three trajectories: The actual one in black, and two counterfactuals in red and blue. The red counterfactual is constructed by combining the average 1984-2008 level of net borrowing as a fraction of income to the actual historical rates of interest, nominal income growth and defaults. The blue counterfactual is similarly constructed by combining the average 1984-2008 effective interest rate with historical levels of net borrowing, nominal income growth and defaults. In other words, the red line shows what would have happened in a world where households had continued to borrow as much after 2008 as in the earlier period, while the blue line shows what would have happened if households had faced the same interest rates after 2008 as before. 

As the figure shows, over the 2008-2019 period as a whole, the influence of the two factors is similar — both lines end up in the same place. But the timing of their impact is different. In the immediate wake of the crisis, the fall in new borrowing was decisive — that’s why the red and black lines diverge so sharply. But in the later part of the decade, as household borrowing moved back toward positive territory and interest rates continued to fall, the more favorable interest environment became more important. That’s why the blue line starts rising after 2012 — if interest rates had been at their earlier level, the borrowing we actually saw in the late 2010s would have implied rising debt ratios. 

As with the similar figures in the papers, this figure was constructed by using the law of motion for debt ratios:

where b is the debt-income ratio, d is the primary deficit, i is the effective interest rate (i.e. total interest payments divided by the stock of debt), g is income growth adjusted for inflation, π is the inflation rate, and sfa is a stock-flow adjustment term, in this case the reduction of debt due to defaults. The exact sources and definitions for the various variables can be found in the papers. (One note: We do not have a direct measurement of the fraction of household debt written off by default for the more recent period, only the fraction of such debt written down by commercial banks. So we assumed that the ratio of commercial bank writeoffs of household debt to total writeoffs was the same for the most recent period as for the period in which we have data for both.)

Starting from the actual debt-ratio in the baseline year (in this case, 2007), each year’s ending debt-income ratio is calculated using the primary deficit (i.e. borrowing net of debt service payments), the share of debt written off in default, nominal income growth and the interest rate. All but one of these variables are the actual historical values; for one, I instead use the average value for 1984-2007. This shows what the path of the debt ratio would have been if that variable had been fixed at its earlier level while the others evolved as they did historically.  In effect, the difference between these counterfactual lines and the historical one shows the contribution of that variable to the difference between the two periods.

Note that the interest rate here is not the current market rate, but the effective or average rate, that is, total interest payments divided by the stock of debt. For US households, this fell from around 6 percent in 2007 to 4.4 percent by 2019 — less than the policy rate did, but still enough to create a very different trajectory, especially given the compounding effect of interest on debt over time. So while expansionary monetary policy is not the whole story of falling debt ratios since 2008, it was an important part of it. As I recently argued in Barrons, the deleveraging of US households is unimportant and under appreciated benefit of the decade of low interest rates after the crisis.