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

Have we now seen the end for the Riksbank’s leaning against the wind, after the numbers reported by Executive Board member Martin Flodén’s Ekonomistas post (English translation) and the Riksbank’s latest Monetary Policy Report? According to these numbers, the “cost,” in terms of an increase in the unemployment rate, would be at least 10 times, and even at least 50 times the “benefit,” in the form of a better outcome in a possible future crisis.

According to the published numerical data for the figures in chapter 2 of the Monetary Policy Report, a 1 percentage point higher policy rate during 4 quarters will lead to about a 0.5 percentage points higher unemployment rate. The “cost” of the higher policy rate in terms of a higher unemployment rate is thus about 0.5 percentage points.

According to the same numerical data, a 1 percentage point higher policy rate during 4 quarters will lead to a 1.8 percentage points lower debt ratio. According to the estimate in Martin’s Ekonomistas post (English translation) and a more extensive background note, a 1 percentage point lower debt ratio leads to a 0.02 percentage points lower increase in the unemployment rate in a crisis. Then the 1.8 percentage points lower debt ratio leads to a lower increase in the unemployment rate of 1.8 * 0.02 = 0.036 percentage points. If a crisis occurs with certainty, the “benefit” of the higher policy rate in terms of a lower increase in the unemployment rate is thus about 0.04 percentage points. If a crisis occurs with a probability less than one, the expected benefit is lower.

The cost, in terms of the unemployment rate, of the “leaning against the wind” is thus about 0.5 percentage points, whereas the benefit is about 0.04 percentage points if a crisis occurs. Thus, the cost is about 0.5/0.04 = 13 times the benefit, if a crisis occurs with certainty. If a crisis does not occur with certainty but with with the high probability of 25 percent, the expected benefit is then only about 0.01 percentage points. Then the cost is 0.5/0.01 = 50 times the expected benefit. Need I say more? Can we now end the debate about the Riksbank’s “leaning against the wind”?

There are two things behind this. First, as I have pointed out in this post, the effect of the policy rate on the debt ratio that the Riksbank reports is so small, that it is not *economically* significant. Neither is it *statistically* significant. That is, one cannot exclude the hypothesis that it is zero or that a higher policy rate actually increases the debt ratio rather than lowers it (something that I have argued follows from realistic assumptions and probably would be the result of the Riksbank’s estimate, if it were done in a correct way, as discussed in the post).

Second, the effect of the debt ratio on the increase in the unemployment rate in a crisis that Martin reports appears to be *statistically* significant. But it is not *economically* significant for monetary policy. With a coefficient of only 0.02, it is simply too small to matter for monetary policy, which at most may be able to affect the debt ratio a few percentage points.

Figure 1 shows this in greater detail. It shows the effect of a 1 percentage point higher policy rate during 4 quarters (black line) on the unemployment rate (red line) and the debt ratio (blue line), following from the numerical data for figures 2.13, 2.15, and 2.19 in chapter 2 in the Monetary Policy Report. (The figures and the numerical data show the deviations of the unemployment rate and the debt ratio for a 0.25 percentage point higher policy rate during 4 quarters; I have multiplied these by 4 to get the effect of a 1 percentage point increase in the policy rate.) A 1 percentage point higher policy rate during 4 quarters thus leads to about a 0.5 percentage points higher unemployment rate within 1-2 years and a 1.8 percentage points lower debt ratio in quarter in about a year.[1]

By multiplying the effect on the debt ratio by 0,02, I then get the effect on the increase in the unemployment rate in a crisis. It is at most 0,02 * 1,8 = 0,036 percentage points lower for quarter 4, the yellow curve, which deviation from zero is barely visible in the figure.

It is thus a matter of comparing the “cost,” the increase in the unemployment rate during the next few years, with the “benefit,” the lower increase in the unemployment rate in a crisis. Figure 2 shows this in a larger scale. The increase in the unemployment rate is at most about 0.5 percentage points. It should be compared with the lower increase of the unemployment rate in a crises, which is at most about 0.04 percentage points. The cost is about 13 times the benefit, if a crisis will occur with certainty. If a crisis will occur with as high a probability of 25 percent, the cost is a full 50 times the expected gain.

[1] The effects on the debt ratio is a bit larger than in those reported in the box in the Report, probably because the policy rate returns to the baseline somewhat more slower.

The crisis must occur within a few years, before the effect of the policy rate on the debt ratio has evaporated. The effect on the debt ratio is somewhat persistent, but it disappears after 5-6 years, as shown in the Riksbank’s box. ”Leaning against the wind” thus has no long-run effects on the debt ratio according to the box.

If one takes into account that inflation and the price level in Sweden have become unexpectedly low under a long period, “leaning” may lead to a persistent *increase* in real debt, loan-to-value ratios and the debt ratio, see this post. Then the expected benefit is even smaller, and probably even a cost.