Disinflation and its costs in the Dadsas model

What do we mean by disinflation costs? Consider a country that decides to cut money growth, and thus eventually inflation, in half. From what we learned in Chapter 8 about inflation and income dynamics in the DAD-SAS model, the income losses accompanying this disinflation depend on two factors: the speed at which inflation expectations are reduced, as indicated by the downward shift of the SAS curve; and the flexibility of nominal wages, as indicated by the slope of the SAS curve. Figure 13.14 looks at the first factor.

Starting from point A, suppose that the central bank announces in period 0 that it plans to halve money growth in period 1. What happens to income (and inflation) in period 1 depends on the responsiveness of inflation expectations to (or the credibility of) this announcement. Consider three stylized cases:

■ If the labour market does not believe the disinflation announcement, SAS stays in SASAE and the economy moves to point B. Some inflation reduction is achieved, but there is also a large fall in income. The income loss per achieved reduction in inflation is high.

■ The labour market believes the disinflation announcement. It adjusts inflation expectations rationally, shifting SAS down to SASre. The inflation rate falls to the new target rate at no cost in terms of income losses. Inflation has been reduced without any cost.

■ An intermediate case is that the labour market assigns some, but not full, credibility to the disinflation announcement. Attributing a probability of 50% for the policy change to happen puts SAS in the intermediate dashed position. Inflation is lower than in the first case and higher than in the second. The income loss is higher than in the second and lower than in the first case.

13.3

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Belgium

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Finland

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Germany

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Italy

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Portugal-Spain

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Spain

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United Kingdom

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Norway-Switzerland

United States-Japan

Norway

Switzerland

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United States-Japan

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Denmark

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reland

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Netherlands

Sweden

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Figure 13.13 Inflation rates in Europe and the world, 1960-2002.

Source: IMF, OECD.

Figure 13.14 Being at A, the CB announces in period 0 that money growth will be reduced from mHI to 0.5 mHI next period. If this pledge is not credible, SAS stays in the dark blue position as under adaptive expectations. The economy ends up at B. If it is credible and its effects on inflation are foreseen, SASRE obtains and we move directly to D. If the announcement is half-heartedly believed, SAS moves to the dashed position and C obtains.

Figure 13.14 Being at A, the CB announces in period 0 that money growth will be reduced from mHI to 0.5 mHI next period. If this pledge is not credible, SAS stays in the dark blue position as under adaptive expectations. The economy ends up at B. If it is credible and its effects on inflation are foreseen, SASRE obtains and we move directly to D. If the announcement is half-heartedly believed, SAS moves to the dashed position and C obtains.

Figure 13.15 deals with the second influence on disinflation costs. To isolate this argument from the effect on expectations discussed above, consider the case in which the disinflation begins unexpectedly. Again the goal is to halve inflation by halving money growth. If nominal wage growth responds slowly to labour market disequilibria and, hence, the SAS curve is rather flat, only a small part of the hoped-for reduction of inflation is achieved in period 1, at the cost of large income losses (point B). A more flexible labour market implies a steeper SAS curve and leads to point C. Finally, if wage growth is perfectly flexible, and hence the SAS curve is vertical, the inflation target is achieved immediately at no income-related cost.

The transition from a high inflation equilibrium to a low inflation equilibrium is costless in only two ideal scenarios: when the disinflation is announced prior to its implementation and this announcement is fully credible, or when the labour market is perfectly flexible, meaning that nominal wages move to balance supply and demand at all times. Whenever reality

Figure 13.15 Beginning at A, money growth is cut in half unexpectedly in order to reduce inflation by 50%. If wages are very sticky, which makes SAS flat, inflation falls a little and income falls a lot. More flexible wages provide for a steeper SAS curve, giving more inflation reduction and lower income losses. Perfect wage flexibility makes SAS vertical. Inflation immediately falls to half its initial value at no sacrifice in income.

Figure 13.15 Beginning at A, money growth is cut in half unexpectedly in order to reduce inflation by 50%. If wages are very sticky, which makes SAS flat, inflation falls a little and income falls a lot. More flexible wages provide for a steeper SAS curve, giving more inflation reduction and lower income losses. Perfect wage flexibility makes SAS vertical. Inflation immediately falls to half its initial value at no sacrifice in income.

Figure 13.16 To reduce inflation from 9% to 3% in one step, as the big-leap approach recommends, DAD must shift to DAD1. To this effect, money growth must be 0. The accompanying income loss, if SAS has slope 1, is 6. To keep inflation at 3% in period 2, money must grow again in period 2 to shift DAD up to DAD2.

Figure 13.16 To reduce inflation from 9% to 3% in one step, as the big-leap approach recommends, DAD must shift to DAD1. To this effect, money growth must be 0. The accompanying income loss, if SAS has slope 1, is 6. To keep inflation at 3% in period 2, money must grow again in period 2 to shift DAD up to DAD2.

The sacrifice ratio is the loss of income (usually measured in percentage of potential income) caused by reducing inflation by one percentage point.

The big-leap approach attempts to produce a desired reduction of inflation in one giant step.

falls short of these ideal requirements, disinflations can only be engineered at the cost of income losses - and they take time.

To see how the incurred costs relate to the obtained benefits, economists use a standardized measure of disinflation costs: the sacrifice ratio. This is computed by first adding up all income losses (or gains, if they occur) incurred during the disinflation (as a percentage of potential income) and then dividing this sum by the achieved reduction of inflation (in percentage points):

Sacrifice ratio =

Total income looses Inflation reduction

So the sacrifice ratio is the price of one percentage point less inflation in terms of potential income forgone. For an illustration of how the sacrifice ratio is computed, suppose that a central bank decides to reduce inflation from 9% to 3%. Assume that an announcement is not credible. Instead, inflation expectations are formed adaptively according to pe = p—1. Figure 13.16 shows the big-leap approach to achieving the inflation target in period 1 immediately.

In Figure 13.16, money growth must come to a halt ( mi = 0) in order to shift DAD1 far enough down to bring inflation down to its target level immediately ( p = 3). This is at the expense of an income drop by 6%, however [(Y* — Y{)/Y* = 6%]. The current inflation rate of 3 is the rate expected for period 2. This shifts SAS into the light blue position. Appropriate demand management holds inflation constant at P2 = 3 and brings income back up to potential income Y*.

Note two things. First, disinflation affects income only in period 1. Income is still in equilibrium in period 0, before the disinflation starts, and back in equilibrium in period 2, after the disinflation is over. So the sacrifice ratio is

Second, to achieve the inflation target quickly, money growth must follow a rather volatile pattern. (Recap: to identify this period's money growth in the

Figure 13.17 To bring inflation down from 9% to 3% in three steps, in line with the gradualist approach, DAD must first shift to DAD1. Facing 5A52, the next reduction to 5% in period 2 calls for another shift of DAD to DAD2. When the inflation target of 3% is reached in period 3, income is still below Y*. Only in period 4 is the new low inflation equilibrium reached.

Figure 13.17 To bring inflation down from 9% to 3% in three steps, in line with the gradualist approach, DAD must first shift to DAD1. Facing 5A52, the next reduction to 5% in period 2 calls for another shift of DAD to DAD2. When the inflation target of 3% is reached in period 3, income is still below Y*. Only in period 4 is the new low inflation equilibrium reached.

The gradualist approach attempts to achieve a desired reduction of inflation slowly, in a series of small steps.

graph, look for the point of intersection between this period's DAD curve and the vertical line over last period's income.) From a pre-disinflation rate of 9, money growth must fall to 0 in period 1, rise to 6 in period 2, and then fall back to 3 where it can stay. In particular, the acceleration in money growth from 0 to 6% in period 2, after the inflation target has already been reached, may create credibility problems for the central bank's new low inflation policy.

To avoid such wild swings in money growth, but particularly as a hedge against a severe recession, a gradualist approach to disinflation is often recommended. Figure 13.17 looks at such an example.

Here the central bank reduces inflation from 9% to 3% in equal steps over a period of three years. In period 1 inflation is reduced to 7%. This surprise disinflation drives income down by two units to Y1 = 98. Further disinflation steps, to 5% in period 2 and to 3% in period 3, keep income at 98, but do not drive it down any further. Once inflation is being kept stable at 3% in period 4, income rises back up into equilibrium and the disinflation is over.

Consider the sacrifice ratio for this gradual disinflation. Adding up the income losses for the disequilibrium periods 1, 2 and 3 we obtain

100[(Y* - Yi) + (Y* - Y2) + (Y* - Ys)]/Y* 2 + 2 + 2

Rather unexpectedly, the sacrifice ratio is exactly the same as with the big-leap approach. What is different, and what might be of concern, is the distribution of income losses over time. A deep recession (with an income drop of 6) in one year may not be the same as a minor recession (with an income deficit of 2) lasting three years.

The independence of the sacrifice ratio from the speed of the disinflation is a robust result as long as inflation expectations are being formed in a mechanical adaptive fashion. For markets that monitor monetary policy closely, it may be of interest in this context that the gradualist approach permits a more steady path of money growth. From periods 0 to 5, money growth rates are 9, 6, 5, 3, 4 and 3.

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