RDP 2019-05: Cost-benefit Analysis of Leaning against the Wind 2. A Simple Illustration

Trent Saunders and Peter Tulip

July 2019

Table 1 provides a simple illustration of the issues, based on the IMF's survey of the international research (Habermeier et al 2015). As discussed below, this is a ‘back-of-the-envelope’ exercise. It integrates most of the relevant research in a simple, transparent way. However, as we discuss in subsequent sections, it ignores some important complications.

The IMF assumes a 100 basis point increase in interest rates is maintained for one year. A range of empirical estimates they survey suggests this would reduce the level of real debt by up to 0.3 to 2 per cent over a two to four year period, depending on the model. They estimate this would reduce the probability of a crisis, with a peak effect between 0.04 and 0.3 percentage points.[2] To present results favourable to leaning against the wind, row 1 of Table 1 shows the maximum of this range.

In the IMF's central scenario, the unemployment rate is assumed to be higher by 5 percentage points for six years in the event of a crisis (rows 2 and 3). We discuss this assumption in Section 3.5.

The estimated benefit of leaning against the wind, shown in row 4, is the product of the lower probability of a crisis, the unemployment gap in a crisis squared (assuming a quadratic loss function), and the duration of the crisis.

Table 1: Illustrative Example – Effect of a 100 Basis Point Increase in Interest Rates
  Benefits
1 Lower crisis probability (percentage points) 0.3
2 Unemployment gap in crisis (percentage points) 5
3 Duration of crisis (years) 6
4 Benefits (0.3 × 52 × 6) / 100 0.45
  Costs
5 Unemployment gap (percentage points) 0.5
6 Duration of higher unemployment rate (years) 4
7 Costs (0.52 × 4) 1.00
8 Benefit-cost ratio 0.45

Source: Habermeier et al (2015)

Rows 5 and 6 show costs. The non-crisis unemployment rate increases by ½ percentage point, for a period of four years, in response to the higher policy rate, as estimated by the IMF's GIMF model. In row 7, the cost of leaning against the wind is calculated as the increase in the non-crisis unemployment gap squared, multiplied by the duration of this higher non-crisis unemployment rate.

Row 8 is the ratio of the estimated benefits to costs, 0.45. That is, the costs of leaning against the wind are likely to be about double the benefits. As noted above, this estimate assumes a large effect of interest rates on the crisis probability. The IMF emphasise alternative estimates, based on the average reduction in the probability of a crisis over time, which imply a benefit-cost ratio of 0.03.

Footnote

The IMF emphasise estimates of the average reduction in the probability of a crisis over time, which tend to be tiny. However, if one is summarising changing effects with a single number, peak effects may be more relevant given the nonlinearity of the loss function. [2]