Analytical retrospective superlative index based on New Zealand’s CPI: 2017

Analytical retrospective superlative index based on New Zealand's CPI: 2017 presents the results of an analytical retrospective superlative index time series calculated between the June 2002 and September 2017 quarters.

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Summary of key points

This paper draws on and extends work previously published by Stats NZ (2007, 2008, 2011, and 2015) and presents the results of an analytical retrospective superlative index time series calculated between the June 2002 and September 2017 quarters. It also highlights the benefits of reweighting the CPI frequently:

• The published consumers price index (CPI), which is calculated using a fixed-weight Laspeyres-type formula, increased 35.9 percent between the June 2002 and September 2017 quarters, an average of 2.0 percent per year.
• The analytical superlative time series, which is calculated using a Fisher formula, increased 32.3 percent between the June 2002 and September 2017 quarters, an average of 1.9 percent per year.
• If no CPI reweights had happened after 2002, the CPI would have increased 42.8 percent between the June 2002 and September 2017 quarters, an average of 2.4 percent per year.
• If no CPI reweight had happened in 2014, the CPI would have increased 4.0 percent between the June 2014 and September 2017 quarters (an average of 1.2 percent per year), compared with an increase of 3.1 percent for the published CPI over the same period (an average of 0.9 percent per year).

Introduction to CPI reweighting

On average, the New Zealand CPI is reweighted once every three years. Once each new set of CPI expenditure weights is calculated, the previous and new weights can be used to calculate a superlative index on a retrospective basis. This shows the impact of commodity substitution on the fixed-weighted CPI. Commodity substitution occurs when households react to changes in relative prices by reducing purchases of goods and services that have increased in price and instead buying more goods and services that haven’t increased as much.

Stats NZ implemented a review of the CPI in the December 2017 quarter covering the periods up to and including the September 2017 quarter. The new weightings have been used from December 2017. The review involved reselecting and reweighting the basket of representative goods and services to ensure it continued to reflect household spending patterns.

This paper also shows how the CPI might have tracked had no reweight, or only some reweights, occurred since 2002.

Retrospective superlative index

In this section we introduce the analytical retrospective superlative index, outline how it was constructed, and present the results in comparison with the published Laspeyres time series, and the tradables/non-tradables series.

Introduction to the superlative index

Under normal economic conditions, households tend to react to changes in relative prices by reducing purchases of goods and services that have increased in price and instead buying more goods and services that haven’t increased as much. For example, if apple prices increased a lot, but pear prices only a little, consumers might buy more pears and fewer apples than before. Continuing to price the same quantities of apples and pears would overstate the actual price change faced by consumers. Under such circumstances, a base-weighted Laspeyres index will be greater than a current-weighted Paasche index. In other words, a Laspeyres index will overstate price change, whereas a Paasche index will understate price change.

In New Zealand, as in most countries, the CPI is calculated using a Laspeyres formula, where weights reflect expenditure shares in some historical period. The CPI is therefore subject to upper-level (or item) substitution bias, unlike indexes calculated using a superlative index formula such as the Fisher index formula (which is the geometric mean of the overstating Laspeyres index and understating Paasche index). For this reason, many national statistical organisations calculate superlative indexes to help show the level of upward bias that can result when CPIs are not regularly reviewed or reweighted.

International studies (eg Shoemaker, 2013, and Van Kints & Bishop, 2013) have found the long-term difference between superlative and Laspeyres CPI indexes to be about 0.2 of a percentage point a year. In other words, annual price changes would be around 0.2 of a percentage point lower if the CPIs accounted for commodity substitution. In another study (Clews, Sanderson, & Ralph, 2014) found that in the short term, the difference can be as high as half a percentage point a year.

How the superlative index was constructed

A superlative index is the geometric mean of a Laspeyres and a Paasche index. The formula used to calculate these three index types can be found in the appendix.

Stats NZ based the analytical retrospective superlative index from the June 2002 quarter to the September 2017 quarter. (This would normally be the June quarter, however, the most recent review was delayed one quarter following the 2016 Kaikoura earthquake.) There were six reweights in this period. (These indexes are expressed on a base where 2002=1000.)

We based the most recent CPI reweight, implemented in the December 2017 quarter, on expenditure information from the 2015/16 Household Economic Survey (HES) and other sources, price-updated to the September 2017 quarter.

At each reweight, we price-update the expenditure weights to the price reference period. The effect of price-updating, recommended for CPIs by the International Labour Organization (ILO) and common international practice, is to express the underlying quantities of the weight reference period (ie the HES period) in the prices of the price reference period. We also made volume adjustments in 2017 to reflect trend changes in quantities since the 2015/16 weight reference period.

The retrospective superlative index between the June 2014 and September 2017 quarters is based on the underlying quantities for 2012/13 and 2015/16 (although in some cases adjustments were made to reflect quantity changes after both weight reference periods). We then linked the resulting three-year series to the June 2002 to June 2014 quarter series at the June 2014 quarter.

As part of a CPI review/reweight, we add and remove some goods and services from the basket. To calculate the Paasche index, we reallocate the expenditure weights of goods and services added to the basket across similar goods and services at each reweight year. The expenditures of goods and services removed from the basket are reallocated across similar, remaining goods and services. Table 1 gives a summary of the HES data time periods and number of items in the basket for each reweight.

Table 1

Analytical retrospective superlative index results

CPI all groups

The analytical retrospective superlative index, calculated using a Fisher formula, increased 32.3 percent between the June 2002 and September 2017 quarters, while the published CPI all groups index, calculated using a fixed-weight Laspeyres-type formula, increased by 35.9 percent over the same period.

Between the June 2014 quarter and the September 2017 quarter, the analytical retrospective superlative index increased 2.6 percent, compared with a 3.1 percent increase for the Laspeyres-type index over the same period.

Table 2 below shows the superlative index time series from the June 2002 quarter to the September 2017 quarter. At the September 2017 quarter, the analytical Fisher all groups series was 1323, which was 36 index points lower than the Laspeyres-type index, at 1359.

Table 2

From the June 2002 quarter to the September 2017 quarter, the Laspeyres-type index rose an average of 2.0 percent a year, compared with 1.9 percent for the Fisher index. (Note that alternative housing weights were used from the June 2002 to June 2006 quarters. More information about this can be found in the appendix.) Over the three years from the June 2014 quarter to the September 2017 quarter, the Laspeyres-type index rose an average of 0.9 percent a year, compared with 0.8 percent for the Fisher index.

Tradables and non-tradables

The tradables and non-tradables components of the CPI divide CPI goods and services into two categories – one contains goods and services that are imported or in competition with foreign goods, either in domestic or foreign markets (tradables); and the other contains goods and services that do not face foreign competition (non-tradables). Movements in the tradables category (tradable inflation) demonstrate how international price movements and exchange rates affect movements in consumer prices. The non-tradables category shows how domestic demand and supply conditions affect consumer prices.

Table 3 below shows the Laspeyres and analytical Fisher index time series for tradables and non-tradables. At the September 2017 quarter, the difference for the tradables component was 39 index points, while the difference for the non-tradables component was only 15 index points.

Table 3

From the June 2002 quarter to the September 2017 quarter, the published tradables Laspeyres-type index rose an average of 0.6 percent a year, compared with 0.3 percent for the analytical Fisher index. Over the same period, the published non-tradables Laspeyres-type index rose an average of 3.2 percent a year, compared with 3.1 percent for the analytical Fisher Index.

The reason for the difference between the tradables and non-tradables is partly because the former experiences large price decreases and associated large quantity and quality increases (eg the audio-visual equipment class, and the telecommunication equipment subgroup), while the latter does not.

Impact of reweighting the CPI basket

This section examines how the CPI would have tracked under the following four scenarios:

• Scenario 1 – CPI reweights in 2006, 2008, 2011, and 2014. This time series is identical to the published CPI.
• Scenario 2 – no CPI reweights between 2002 and 2017. Shows the situation where the CPI is not reweighted at all.
• Scenario 3 – CPI reweights in 2006, 2008, and 2011, but not 2014. Shows the short-term effect of not reweighting for one review period.
• Scenario 4 – CPI reweights in 2008, 2011, and 2014, but not 2006. Shows the long-term effect of not reweighting for one review period.

Table 4 below shows the Laspeyres-type index time series from the June 2002 quarter to the September 2017 quarter for each scenario. At the September 2017 quarter, the difference between the scenario 1 and scenario 2 indexes is 69 index points.

Table 4

Note: The 2006 reweight was implemented four years after the previous reweight in 2002, a year later than usual. However, the 2008 reweight was implemented two years after the 2006 reweight, bringing the CPI back to a three-yearly review cycle.

Between the June 2002 and September 2017 quarters, the published CPI (scenario 1) increased 35.9 percent (2.0 percent per year).

Had reweights not taken place in 2006, 2008, 2011, or 2014 (scenario 2) the index would have increased 42.8 percent (2.4 percent per year).

This compares with 37.1 percent had the index been reweighted in 2006, 2008, and 2011, but not in 2014 (2.1 percent per year – scenario 3). Or 36.9 percent had the index been reweighted in 2008, 2011, and 2014, but not in 2006 (also 2.1 percent per year – scenario 4).

Figure 2

Appendix

The time series presented in this paper use housing weights for 2002 that are different from the housing weights used in the official CPI. We calculated the alternative housing weights to be consistent with the method used to calculate the 2006, 2008, 2011, 2014, and 2017 housing weights. These differences affect the time series from the June 2002 quarter to the June 2006 quarter. From the June 2006 quarter onwards, weights used match those in the official CPI. For more details on these alternative housing weights, see Consumers price index: Retrospective superlative index and impact of alternative housing weights (Statistics NZ, 2007).

Prices for fresh fruit and vegetables are not seasonally adjusted for the analytical retrospective time series, between the June 2002 and September 2017 quarters. In the official CPI, prices for fresh fruit and vegetables were seasonally adjusted between the June 2002 and June 2006 quarters but not after that.

Price index formulae

The Laspeyres price index formula, expressed in terms of expenditure weights and price relatives is:

The Paasche price index formula, expressed in terms of expenditure weights and price relatives is:

The Fisher price index is the geometric mean of the Laspeyres and Paasche price indexes:

Where:

P_L = Laspeyres price index

P_P = Paasche price index

P_F = Fisher price index

w_i0 = expenditure weight of the ith good or service for the base period 0

w_i1 = expenditure weight of the ith good or service for the current period 1

p_i0 = price or index number of the ith good or service for the base period 0

p_i1  = price or index number of the ith good or service for the current period 1

ISBN 978-1-98-852892-2