New Ekonomistas blog (in Swedish). Here is an English translation:

In the last few years, the Riksbank has conducted a monetary policy that has led to substantially lower inflation than the inflation target and unnecessarily high unemployment. The Riksbank has more recently justified this policy by maintaining that a lower policy rate would increase the household debt ratio (the ratio of debt to disposable income) and thereby any risks associated with the debt. But the Riksbank has not presented any analysis of how monetary policy and the policy rate affect household indebtedness. It has simply taken as given that a higher policy rate leads to a lower debt ratio than a lower policy rate.

But does a higher policy rate really lead to a lower debt ratio? I have examined this issue in a new paper entitled “‘Leaning against the wind’ increases (not reduces) the household debt-to-GDP ratio.” The paper shows that a higher policy rate leads to a higher debt ratio, not a lower one. This result may be surprising to some, at least at the Riksbank, which has apparently made a sign error in its assumptions. The result is actually quite easy to understand once one carefully considers how debt, GDP and inflation are affected by a higher policy rate.

A higher policy rate during a year leads to temporarily lower inflation, real GDP, and real housing prices for a few years. After 3-5 years, inflation, real GDP, and real housing prices have returned to the level they would have been at without the temporary policy-rate increase. For each year from year 0, figure 1 shows how a higher policy rate during year 1 than a baseline leads to deviations from the baseline of inflation, real GDP, and real housing prices. The deviations of the policy rate and inflation are expressed in percentage points; the deviations of real GDP and real housing prices are expressed in percent of the baseline level.¹

Figure 1.

The temporarily lower inflation leads to a permanently lower price level and permanently lower nominal GDP and nominal housing prices relative to the baseline. Lower nominal housing prices mean that new mortgages will be lower. But a year’s new mortgages are only a limited share of the mortgage stock, say 14 percent, corresponding to an average loan length of 7 years. Since the turnover of the mortgage stock is small, the total nominal debt will fall slowly. The price level and nominal GPD will fall faster to their new lower permanent level. This is shown in figure 2, which shows the deviation from the baseline of the price level, nominal GDP, nominal housing prices, and total nominal debt.

Figure 2.

Since the nominal debt falls so slowly and the price level and nominal GDP fall much faster, the real debt will rise almost as much and as fast as the price level falls, and the debt-to-GDP ratio will rise almost as much and as fast the nominal GDP falls. After a few years when the price level and nominal GDP have reached their permanent lower level, real debt and the debt-to-GDP ratio start to fall back towards the baseline. After some 7-8 years, they have returned to the baseline and the level they would have had in the absence of the temporary policy-rate increase. This is shown in figure 3.

Figure 3.

Disposable income moves in the same direction as GDP but not as much. This means that the ratio of debt to disposable income, the debt-to-income ratio, also first rises during a few years, more than real debt but less than the debt-to-GDP ratio. Then it falls back to reach the baseline in some 7-8 years.

The conclusion is that a higher policy rate increases the household real debt and the debt-to-income ratio. The higher policy rate indeed reduces nominal housing prices and new mortgages, but since the new mortgages are a limited share of total mortgages, the total nominal debt falls slowly. At the same time, nominal GDP and nominal disposable income fall faster. The debt-to-GDP and the debt-to-income ratios rise. This is contrary to what the Riksbank has stated in a number of monetary policy reports and updates. The Riksbank justification of its policy is simply not valid!

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1. This post has been revised in line with a revision of the background paper. New mortgages are now assumed to be 14 percent of the total mortgage stock, corresponding to an assumption of an average loan period of 7 years instead a previous assumption of 6-7 percent and 15 years, respectively. See the paper for details.