Let us use for illustration a series of average UK house prices, measured annually for 2006 – 18 and given in column 2 of Table 2.3.

Some figures for the general level of prices as measured by the CPI are given in the column 3.

So first, suppose that we want to convert the figures into constant (real) prices. Given that 2009 is the ‘base’ year

(i.e., it has a value of 100 for the CPI), the easiest way to do this is simply to divide each house price at time t by the corresponding CPI figure for time t and then multiply it by 100, as per equation (2.49).

This will give the figures in column 4 of the table.

Table 2.3 How to construct a series in real terms from a nominal one Notes: All prices in British pounds; house price figures and CPI are for illustration only.

If we wish to convert house prices into a particular year’s figures, we would apply equation (2.49), but instead of 100 we would have the CPI value that year. Consider that we wished to express nominal house prices in 2018 terms (which is of particular interest as this is the last observation in the table). We would thus base the calculation on a variant of (2.49)
(2.50)
So, for example, to get the 2006 figure (i.e., t is 2006) of 105,681 for the average house price in 2018 terms, we would take the nominal figure of 83,450, multiply it by the CPI figure for the year that we wish to make the price for (the reference year, 123.6) and then divide it by the CPI figure for the year 2006 (97.6). Thus etc.