Question

18. Consider the following two price index series:
1996 = 100
2000 110
2001 112
2002 120
2003 128
2004 130




2005 = 100
2004 93
2005 100
2006 104
2007 109
2008 115

Splice the two price index series to form one continuous series with:
18.1 2004 as the base year.
18.2 2006 as the base year.

Answer 1

18.1 To splice the two price index series with 2004 as the base year, we need to adjust the second series to reflect 2004 as the base year:

1996 = 100
2000 110
2001 112
2002 120
2003 128
2004 130

2004 = 100
2004 93
2005 100
2006 104
2007 109
2008 115

Since 2005 is the base year in the second series, we need to adjust it to reflect 2004 as the base year. This involves multiplying the index values in the second series by 130/100 (the ratio of the base year index values in the two series) to adjust them to the base year of 2004:

2004 = 100
2004 93
2005 (100 * (130/100)) = 130
2006 (104 * (130/100)) = 135.2
2007 (109 * (130/100)) = 141.7
2008 (115 * (130/100)) = 149.5

Now, we have a continuous series with 2004 as the base year:
2004 93
2005 130
2006 135.2
2007 141.7
2008 149.5

18.2 To splice the two price index series with 2006 as the base year, we again need to adjust the second series:

1996 = 100
2000 110
2001 112
2002 120
2003 128
2004 130

2005 = 100
2004 93
2005 100
2006 104
2007 109
2008 115

Since 2006 is the base year in the second series, we need to adjust it to reflect 2006 as the base year. This involves multiplying the index values in the second series by 104/100 (the ratio of the base year index values in the two series) to adjust them to the base year of 2006:

2004 93
2005 (100 * (104/100)) = 104
2006 (104 * (104/100)) = 108.16
2007 (109 * (104/100)) = 113.36
2008 (115 * (104/100)) = 119

Now, we have a continuous series with 2006 as the base year:
2004 93
2005 104
2006 108.16
2007 113.36
2008 119