samlet årgang - Økonomisk Institut - Københavns Universitet

INTEREST-RATE DEVELOPMENT IN DENMARK 1875-2003 – A SURVEY 159
time-periods one may try to measure inflation expectations more directly from the yield
on inflation-index-linked bonds. 9 However, in the case of Denmark such an approach is
complicated by a rather illiquid market for index-linked bonds. Furthermore, special tax
provisions may distort the results, cf. e.g. Topp (1996) and Hansen (2004).
Another approach could be to try to utilise information about price expectations from
consumer surveys, cf. e.g. Christensen (1996) and Knudsen (2002). However, in Denmark
such surveys only cover the period since the middle of the 1970s.
A third approach could be to use »independent« (i.e. non-governmental) inflation
forecasts from macroeconomic projections as a measure of expected inflation. In Denmark
such forecasts are available from the Danish Economic Council since the beginning
of the 1960s, cf. Det Økonomiske Råd. Formandskabet (1987).
In order to derive ex ante real interest rates for the entire period since 1875 from the
nominal interest rates, one needs to make some more crude assumptions regarding inflation
expectations. Figure 3 shows three different indicators of the real-interest-rate
development in Denmark in the period since 1875:
– The »real short-term interest rate« is measured as the difference between the contemporaneous
short-term nominal interest rate and the contemporaneous rate of
consumer price inflation.
– The »real long-term interest rate (SE)« is measured as the difference between the
contemporaneous nominal long-term interest rate and the contemporaneous rate of
consumer price inflation. This corresponds to an ex ante long-term real interest rate
under the assumption of »static expectations« about future long-term inflation
development.
– The »real long-term interest rate (PF)« is measured as the difference between the
contemporaneous long-term interest rate and annual average consumer price inflation
7 years ahead. 10 This corresponds to an ex ante long-term real interest rate under
the assumption of »perfect foresight« (PF) (or »rational expectations«) about
future long-term inflation development.
All the three measures for the real interest rate in Denmark show an average around
3 per cent per annum 11 for the period since 1875. Taken at face value the »real long-
9. A commonly used measure for inflation expectations derived from inflation-index-linked bonds is the
so-called »break-even inflation«, i.e. the rate of expected inflation at which the return on an inflation-indexlinked
bond is equal to the return on an equivalent nominal bond.
10. The horizon of 7 years has been chosen because it roughly corresponds to the Macaulay Duration of a
10-year par bullet bond at an interest rate level (6.36 per cent per annum) equal to the average annual yield
on Danish government bonds for the period 1875-2003, cf. table 1.
11. The real short-term interest rate is 2.9 per cent per annum, the real long-term interest rate (SE) is 3.1 per
cent per annum, and the real long-term interest rate (PF) is 3.1 per cent per annum.