Watching our weights: Keeping GDP relevant

Watching our weights: Keeping GDP relevant Paper presented at the New Zealand Association of Economists Conference Wellington, New Zealand 1-3 July 2015 Matthew Collison Statistical Analyst, National Accounts, Statistics New Zealand P O Box 2922 Wellington, New Zealand matthew.collison@stats.govt.nz www.stats.govt.nz

Crown copyright This work is licensed under the Creative Commons Attribution 3.0 New Zealand licence. You are free to copy, distribute, and adapt the work, as long as you attribute the work to Statistics NZ and abide by the other licence terms. Please note you may not use any departmental or governmental emblem, logo, or coat of arms in any way that infringes any provision of the Flags, Emblems, and Names Protection Act 1981. Use the wording 'Statistics New Zealand' in your attribution, not the Statistics NZ logo. Liability The opinions, findings, recommendations, and conclusions expressed in this paper are those of the authors. They do not represent those of Statistics New Zealand, which takes no responsibility for any omissions or errors in the information in this paper. Citation Collison, M (2015, July). Watching our weights: Keeping GDP relevant. Paper presented at the 2015 New Zealand Association of Economists (NZAE) Conference, Wellington, New Zealand. Acknowledgements I am grateful to Bruce Omundsen for his contributions, particularly regarding constant price supplyuse balancing, and to Daniel Lensen and Hamish Grant for their input and comments. 2

Abstract Constant price series are used to show changes in quantities by excluding the effects of price changes. When constant price time series are aggregated by summing together, the relative importance, or weight, of each series to the aggregate is fixed according to its value in the base year. Rebasing is the process by which these fixed weights are updated. In the New Zealand national accounts, key production and expenditure aggregate components of gross domestic product (GDP) are reweighted annually. Some low level series, however, still contain fixed weights. Statistics New Zealand recently updated the base year and expression year for GDP volume series from 1995/96 to 2009/10 1. Using examples, we explain the distinction between base and expression years, the importance of regularly updating both, and why revisions occur. Updating the weights in the New Zealand accounts resulted in revisions to overall movements for both the production and expenditure measures of GDP. We discuss the experience of rebasing the New Zealand accounts, and possible future changes to volume series. Removing fixed weights entirely would eliminate the need for rebasing, ensure volume measures of GDP are relevant, and allow for more regular updates to the expression year. Introducing constant price supply-use balancing would expand the use of detailed annual data in volume measures and increase coherency between the production and expenditure volume measures of GDP. 1 Introduction 1.1 Purpose This paper provides insight into the importance of using up-to-date weights for constructing constant price measures, and presents the experience and results from the recent update to fixed weights and the expression year for volume GDP in New Zealand. Statistics NZ has committed to future updates to fixed weights and the expression year every five years for volume measures of GDP. We discuss the possibility of removing fixed weights entirely, which would allow annual updates to the expression year. We also discuss constant price supply-use (KPSU) balancing, in particular the benefits of introducing KPSU into the New Zealand national accounts, and the process to establish KPSU balancing. 1.2 Issues with aggregating constant price series A brief overview of current and constant prices is provided in the appendix. Alternatively, chapter two of Understanding National Accounts (Lequiller & Blades, 2014, pp. 47-77) provides a comprehensive overview of constant price and volume measures 2. When constant price time series are aggregated by summation, the relative importance (weight) of each series to the aggregate is fixed according to its current price value in the base period. If structural changes in the aggregate occur beyond the base period, such as the relative prices of commodities increasing or decreasing, then the weights become less representative of the composition of the aggregate. 1 Numerical years refer to the year ended March. For example, 1996 and 1995/96 both refer to the year ended March 1996. 2 The terms real, constant price, and volume can all refer to series which have had the effects of price change removed. We typically use the term constant price for series which have been calculated using one of the methods described in the appendix, or have been produced by summing constant price series. We use the term volume for series which have been aggregated using chain linking, as discussed in section 1.4. This convention will be followed throughout this paper. 3

For example, take an economy which produces only two commodities, A and B. The quantity produced and price for commodity A remains constant, while both quantity and price increase for commodity B: Table 1a: Commodity A Year Price Quantity Current price Constant price, base year 1 Constant price, base year 2 Constant price, base year 3 1 10 10 100 100 100 100 2 10 10 100 100 100 100 3 10 10 100 100 100 100 Table 1b: Commodity B Year Price Quantity Current price Constant price, base year 1 Constant price, base year 2 Constant price, base year 3 1 5 10 50 50 100 200 2 10 15 150 75 150 300 3 20 20 400 100 200 400 Table 1c: Weights Year Current price A Current price B Current price total Weight commodity A Weight commodity B 1 100 50 150 67% 33% 2 100 150 250 40% 60% 3 100 400 500 20% 80% Table 1d: Constant price commodity A + commodity B, sum and growth rate Year Sum, base year 1 Growth, base year 1 Sum, base year 2 Growth, base year 2 Sum, base year 3 Growth, base year 3 1 150 200 300 2 175 17% 250 25% 400 33% 3 200 14% 300 20% 500 25% Table 1d demonstrates that the constant price growth rate varies depending on the base year chosen. The weight for commodity B increases for base years 2 and 3. A greater weight for the commodity for which quantities are increasing results in a higher growth rate for the constant price sum. In general, the further from the base year the less representative the price weights. This means growth rates for published constant price statistics can be significantly affected by the choice of base year, and if the base year is particularly out of date then growth rates will not reflect actual real-world events at all. Where the composition of an aggregate changes rapidly, for example with increased uptake of smartphones by consumers, even a relatively recent base year may not be representative. Having up-to-date weights is important as statistics which do not properly reflect real-world events are less valuable to users. A constant price measure of GDP with out-of-date weights could lead to poor investment or policy decisions, for example. To ensure the composition of an aggregate is being captured as accurately as possible, weights should be updated annually. This is achieved using chain-linking. 4

1.3 Overcoming the limitations of fixed weights This section gives a brief technical overview of chain-linking. For more information on chainlinking, see the System of National Accounts (System of National Accounts 2008, pp. 295-324). To construct a chain-linked volume series, a volume movement between each year Y t and the next year Y t+1 is calculated using constant prices from year Y t. This effectively means that every volume movement uses weights from the previous year. Linking these movements together as shown in the equation below gives an annually reweighted Laspeyres volume index, or chain-volume series. If an index has a value L 0 = 1000 in year Y 0, then the value in year Y t is calculated as: L t = 1000 P 0 Q 1 P 0 Q 0 P 1 Q 2 P 1 Q 1 P 2 Q 3 P 2 Q 2 P t 1 Q t P t 1 Q t 1 where P x and Q x are the respective prices and quantities in year Y x. Using the example introduced in section 1.2, a chain-volume series can be constructed. Movement from year 1 to year 2: Movement from year 2 to year 3: 10 10 + 5 15 10 10 + 5 10 = 175 150 = 1.167 10 10 + 10 20 10 10 + 10 15 = 300 250 = 1.200 If year 1 is given an index value of 1000, then year 2 will have an index value of 1167, and year 3 will have an index value of 1400. Chain-volume series are constructed as a linked series of movements, and commonly expressed as an index. It is also possible to express chain-volume series in the prices of a chosen year, known as the expression year. To achieve this, the index is scaled to the current price aggregate in the expression year. Table 1e: The chain-volume series calculated above, expressed in the prices of years 1, 2, and 3 (from table 1c) Year Current price total Chain-volume movements Chain-volume expressed in year 1 prices Chain-volume expressed in year 2 prices 1 150 150 214 357 2 250 1.167 175 250 417 3 500 1.200 210 300 500 Chain-volume expressed in year 3 prices By constructing a chain-volume series, weights are updated every year rather than being fixed 3. The advantage of such an approach is that structural changes in the composition of the aggregate are accounted for through annually reweighting note that the movement in 3 Annual updates of fixed weights are preferred to quarterly updates of fixed weights. Quarterly updates tend to reflect one-off events and other short term volatility, resulting in greater fluctuations in weights which do not represent structural changes in the economy. 5

the chain-volume series is the same for all expression years. The main drawback is the loss of additivity series usually do not sum to the aggregate, except in the expression year. Updating the expression year known as a re-expression is a simple mathematical procedure in which chain-volume indexes are scaled to the price level of a different expression year. Re-expression and rebase are distinct procedures and may be carried out independently. A re-expression does not cause revisions to movements in chain-volume series. Instead, the values used to present these movements change resulting in a level shift in the series. The size of the level shift is equal to the ratio of the price level in the new expression year to the price level in the previous expression year. Figure 1: Re-expressed chain-volume series from example Note that it is necessary to have both quantity and price information to construct chainvolume series. For a Laspeyres index, quantity information is needed for all years. If price information is not available for the most recent years, prices (weights) are held constant from when they were last available. A Laspeyres volume index is used instead of alternatives, such as Paasche and Fisher indexes, due to data availability. 1.4 Volume series in the New Zealand national accounts and overseas Statistics NZ first adopted chain-volume measures in 2000, with an expression year of 1996. Key production and expenditure components of GDP are compiled as chain-volume measures. At lower levels series are compiled as constant price series, either as series in their own right, or as fixed weight series comprising many subcomponents. A rebase refers to the update of the base year for the fixed weight series. While it is possible to rebase and re-express independently, Statistics NZ elects to keep the base year for fixed weights and expression year consistent to avoid confusion. In 2014, Statistics NZ updated the base year and expression year from 1996 to 2010. 6

Internationally, the expression year used and the frequency of updating the expression year can vary widely. For example, the Australian Bureau of Statistics re-expresses volume GDP every year. This is possible partly due to the absence of fixed weights in the compilation of Australian GDP. An alternative approach is to publish chain-volume GDP as a set of indexes, forgoing the use of an expression year entirely. The advantages of this approach are index results being less likely to be misinterpreted than volume series expressed in dollars, and re-expression is no longer necessary. The down side is that series expressed as indexes have less meaning for customers than series expressed in dollars. 2 Updating fixed weights 2.1 Fixed weights in New Zealand GDP As stated in section 1.4, some lower level series are compiled as fixed weight series. Prior to the 2014 updates to the base year and expression year, the weights for these series were set using prices from 1996. The fixed weight series were not evenly spread among the components of the production and expenditure measures of GDP, being most prevalent in areas such as mining, parts of manufacturing, and parts of investment. The presence of fixed weights is mostly due to a combination of the information available for 1996, and the retention of some methods used for low-level constant price series in GDP prior to the introduction of chain-linking. In particular, the inter-industry study 1996 (Statistics New Zealand, 1996) 4 provided more detailed price information than is typically available in other years, and obtaining such detailed information is not possible without a similar study. 2.2 Methods Updating fixed weights can be approached in different ways updating the base year for the fixed weights to 2010, removing fixed weights by using an alternative constant price series, or removing fixed weights by introducing chain-linking from the lowest level. The approach taken for each series was dependant on the information available, in particular which price information was available for 2010, and whether that price information was readily available for other periods and on an ongoing basis. 2.2.1 Updating base year This approach needed suitable data sources to update the fixed price weights. Investigating data availability is a resource intensive exercise. Some price data was obtained through additional processing of existing data, and some obtained through one-off requests from private and public enterprises. Where data was easily obtainable, and would continue to be for other years, we were able to consider chain-linking as discussed in section 2.2.2. In general, 2010 weights were used to recalculate a series from a certain point in time onwards, then linked onto a back series calculated using 1996 weights. This is because 1996 weights better represent the structure of the economy for older periods. The year for linking 1996-weighted and 2010-weighted series is not uniform across all industries, as shown in section 3.1. Industries in which this method was used include agriculture, mining, and manufacturing. 2.2.2 Removing fixed weights Where price data for 2010 was not available, or where price data was easily obtainable for 2010 and other years, we sought to remove fixed weights. 4 A very detailed survey and study of transactions between industries and final users of products. 7

Where no new price data was available for the existing constant price series, we sought to switch to an alternative measurement. Either a single constant price series was used, or multiple constant price series from which a chain-volume series could be constructed. Finding a suitable alternative data source is not always possible, an outcome discussed in section 4.2. Where price data is readily available, a chain-volume series can be constructed using the existing constant price series. In some cases the data necessary for chain-linking had been available for some time, but not used. Implementing chain-linking for low level series generally requires significant system changes. Removing fixed weights causes revisions to more years. The upside is the introduction of annual reweighting, meaning revisions to these series will not result from future updates to the base year. Areas where chain-linking was introduced at the lowest level include nonprofit institutions, infrastructure investment (introduced in 2013), and exports and imports for the period between 1990 and 2000 (previously from 2000 onwards only). 3 Results 3.1 Industry level outcomes This section looks at the results from rebasing for selected published GDP series. Note that revisions in movements occur after a certain point in some series. As discussed in section 2.2.1, 1996 weights better represent the structure of the economy for older periods. Therefore series use 2010 weights from a point in time, and movements from the existing constant price series prior to this point. Figure 2: Annual growth, mining 8

Figure 2 demonstrates the impact of the rebase for the mining industry. Fixed weights are used for the different types of materials extracted. For example, gold had a higher weight in 1996 than 2010, while the weight of coal was higher in 2010 then 1996. Revisions to volume movements prior to 2006 are the result of methodology improvements. Figure 3: Annual growth, petroleum, chemical, polymer, and rubber manufacturing Figure 3 shows petroleum, chemical, polymer, and rubber manufacturing. Updating fixed weights caused volume movements to revise downwards from 2008 onwards. This downward revision indicates that faster growing components had higher weights in 1996 than in 2010. 3.2 Aggregate results The following figures show the impact of updating fixed weights on the production measure of GDP. Please note that we also introduced some other changes into the accounts alongside the rebase and re-expression of volume measures, such as updating to the latest international standards for compiling the national accounts 5. The majority of revisions to volume movements prior to 2011 were due to updating fixed weights. From 2011 onwards there are also significant revisions from updated annual benchmarks and updated chaining weights. 5 In November and December 2014 national accounts publications included updates to reflect the latest standards from the System of National Accounts 2008. An explanation of these updates can be found in the revisions section of Gross Domestic Product: September 2014. 9

Figure 4: Annual growth, chain-volume gross domestic product (production measure) Figure 4 shows revisions to growth rates for total GDP. The revisions for most years are small (less than 0.2 percentage points). This is due to the small impact of fixed weights in most industries, and the use of chain-linking for key aggregates. See section 3.3 for an indication of the size of revisions if aggregates were not chain-linked. Figures 5 and 6 below show the separate effects of updating fixed weights and updating the expression year for total GDP. Figure 4 shows the volume GDP time series with 1996 weights and 2010 weights, but with both series expressed in 1996 prices. This shows the effect of the rebase and other changes, but excludes re-expression. 10

Figure 5: Annual gross domestic product (production measure) expressed in 1996 prices Figure 6 shows the effect of re-expressing GDP. The series are identical except for the expression year. Re-expression causes a level in volume series, but movements are not affected. Figure 6: Annual gross domestic product (production measure), 2010 base year 11

3.3 What if total GDP was calculated as a summed constant price series? As shown in figures 4 and 5 above, the effect of updating fixed weights had a small impact on total GDP 6. To demonstrate the importance of chain linking, the following shows the effect of rebasing if total GDP was calculated as the sum of industries rather than a chainvolume series. This comparison is done by summing New Zealand Standard Industry Output Categories (NZSIOC) level 4 industries. The majority of industries at this level are constant price series, although some are chain-volume. Figure 7 shows growth rates for GDP if it was aggregated by summing NZSIOC level 4 industries. Figure 7: Annual growth, constant price gross domestic product (production measure) Revisions are noticeably larger than those for chain-volume GDP, shown in figure 4. This is also demonstrated in figure 8 below, which shows the size of revisions for each method of aggregating GDP. When GDP is calculated as a sum of level 4 industries, updating the base year from 1996 to 2010 results in far larger revisions than GDP constructed as a chain-volume series. Additionally, with the summed GDP series, the revisions are all downwards. This means that, on average, 2010 weights are relatively lower for high growth industries than 1996 weights. Conversely, 2010 weights are relatively higher for low growth industries than 1996 weights. When weights are updated annually, as with the chain-volume series, this does not occur. 6 As stated in section 3.2, the limited use of fixed weight series and chain-linking reduce the potential revision from updating fixed weights. 12

Figure 8: Revisions to annual growth, gross domestic product (production measure) 4 Lessons learned and future initiatives 4.1 Lessons from the rebase Updating the fixed weights in GDP was a challenging task. The 14 year gap between base periods meant it was difficult to obtain usable price data for many fixed weight series, and we were unable to recalculate previous periods using new weights consistently across series. Additionally, this length of time meant that revisions from both the rebase and re-expression were likely larger than if these tasks were undertaken more frequently. We also simultaneously updated the international standards used to compile national accounts. Resource constraints meant that systems were not structured to easily separate out revisions from updating fixed price weights, revisions from updating international standards, and routine revisions from updated annual benchmarks and system improvements. 4.2 Future updates to the base and expression year Statistics NZ has committed to updating base and expression periods for GDP every five years in order to meet customer demand for more relevant statistics. This means that the next updates to New Zealand GDP will likely happen by the end of 2019. Ideally there would be no fixed weights in GDP. Updates to fixed weights would no longer be required, and more frequent updates to the expression year would be possible so volume data would be more meaningful to customers. In particular, chain-volume series could be additive from the expression year. This occurs when the expression year is updated annually to the latest year for which current price annual benchmarks are available. This is an outcome we are progressing towards. The work described in this paper did allow us to remove some fixed weights by either introducing chain-linking, or replacing a fixed weight series with an alternative. We have also started to investigate removing further fixed weights. 13

For some industries, suitable alternative series will be difficult to find, and methodology changes may be required. Revisions will result for periods which are recalculated using a different series or methodology. However, by progressively removing fixed weights we will be reducing the magnitude of revisions from future updates to the base year, and reducing the resources required to perform the task. Completely removing fixed weights would ensure the relative importance of each component of GDP is up to date. However, it will not aid in reconciling the production (GDPP) and expenditure (GDPE) measures of volume GDP. Conceptually both GDPP and GDPE measure economic growth, so should produce the same growth rates. However, as each series uses independent data and estimation techniques, some differences between the alternative measures arise. Figure 9: Difference in annual GDP volume growth rates Figure 9 above shows that GDPP and GDPE can give very different pictures of economic growth in some years, such as 2010. This is important as these differences mean the results are telling an inconsistent story about economic growth, making the data less useful to users. 5 Reconciling the volume measures of GDP: Constant price supplyuse balancing 5.1 The benefits of constant price supply-use balancing Supply-use balancing is the process by which all products supplied are matched with all products used in an economy. In New Zealand, supply-use balancing is currently used to confront and reconcile the annual current price production and expenditure estimates of GDP. 14

Incorporating constant price supply-use (KPSU) balancing will improve the informational value of volume measures of GDP. Balanced KPSU components reveal a more complete picture of goods and service flows across the economy. Statistics NZ is now in the early stages of developing a system to deliver improvements associated with KPSU balancing. This is part of a broader improvement programme for macro-economic statistics, based on international best practice. We will be testing the new system in 2017. The overall suite of macro-economic statistics produced by Statistics NZ will be enhanced by KPSU balancing through better integration with current price GDP data. Some enhancement could be achieved through additional steps to the current process for balancing supply and use components. Supply and use components are currently balanced in nominal terms only up to 2012. However, international best practice is to run a process to balance volume and nominal components simultaneously. Simultaneous balancing will lead to more coherence in nominal, volume and price measures. One example of practical benefits from this integration is that more reliable conclusions could be made about economic responses to price change. The main informational benefit of KPSU balancing will be a coherent picture of supply and demand in volume terms across the economy. The collective term supply and use is comparable to supply and demand in that it represents economic transactions which, in concept, are balanced across the economy. This picture of economy-wide supply and use components is built up from constant measurements at the level of individual products. The product level of detail reveals further coherent information about the flow of goods and services between sectors and industries. As discussed in section 4.2, GDPP and GDPE are equal in concept. Balanced KPSU components are consistent with this concept, so introducing KPSU balancing will mean that annual growth rates for GDPP and GDPE will be equal. The first year for which the supply and use components can be balanced will be decided at a later stage of the work programme. However, there is limited scope to retrospectively balance supply and use volumes. It should also be noted that KPSU balancing will be coordinated with the current time-frame from nominal balancing. This means that there will continue to be discrepancies in volume growth rates for the last 2 or 3 years. The time required for data collection and analysis needed for the balancing is the cause of this lag. Consequently the most recent GDPP and GDPE annual volume growth rates will not necessarily be equal, but will be enhanced from using much improved and balanced recent year benchmarks. 5.2 The process to establish KPSU balancing The KPSU balancing process relies on a set of price measures which are consistent with the GDP components of supply and use. This consistency is achieved through a common conceptual framework as defined by the System of National Accounts. Figure 10 shows the supply and use components defined within the framework and the conceptual link with published measures of price change. 15

Figure 10: Conceptual connections between supply and use components and published price indices Supply Components Use Components Sales price of products sold by producers, used to compile the Output Producer Price Indices (PPIs) Prices of products paid at NZs border by importers, used in the Import Overseas Trade Output of products by NZ producers Imports of products by NZ residents Components of supply that reconcile the price received by producers and paid by consumers. This includes trade margins and taxes on products net of subsidies. Consumption of products by NZ Producers Consumption of products by NZ households Investment in products by NZ residents Export of products by NZ residents Price of products purchased by producers, used to compile the input PPIs Price of products purchased by households, used to compile the Consumer Price Indices (CPIs) Price of products purchased for investment, used to compile the Capital Goods Price Indices (CGPIs) Price of products received by exporters at NZs border, used to compile Export OTIs Price measurements at the product level are also consistent with the framework represented in figure 10. This enables alignment of data to deflate values, which is an initial requirement for KPSU balancing. Another major requirement is that price elements for all products are aligned across the product flows. Independent and efficient collection of price change for each supply and demand component will never result in perfect alignment. Issues such as under-coverage and sample errors are expected in all macro-economic statistical systems. Alignment through the removal of discrepancies results in a coherent set of current price, volume, and price measurements. System development also involves an extensive review of volume measurement methods to achieve the best possible alignment of price component. This is a key design aspect for the system to balance KPSU components. After the first annual measurements of balanced KPSU components have been produced, the system will enable the balancing reconciliation to occur on an ongoing basis. References European Communities, International Monetary Fund, Organisation for Economic Co-operation and Development, United Nations and World Bank. (2009). System of National Accounts 2008. New York. Retrieved from http://unstats.un.org/unsd/nationalaccount/sna2008.asp Lequiller, F., & Blades, D. (2014). Understanding National Accounts: Second Edition. OECD Publishing. doi:http://dx.doi.org/10.1787/9789264214637-en Statistics New Zealand. (1996). Inter-industry study 1996. Retrieved from http://www.stats.govt.nz/browse_for_stats/businesses/business_growth_and_innovation/i nter-industry-study.aspx Statistics New Zealand. (2006). New Zealand Standard Industry Output Categories classification tables. Retrieved from http://www.stats.govt.nz/browse_for_stats/industry_sectors/anzsic06-industryclassification/tables.aspx 16

Appendix Current and constant price measures Nominal or current price measures can be thought of as the sum of transactions in dollar amounts at the time the transactions took place. An increase or decrease in a current price measure, therefore, means that the aggregate dollar amount from transactions has increased or decreased. It does not tell us whether the volume (quantity) of transactions has changed, or the price (value) of the transactions has changed, or a combination of the two. Changes in current price measures can result from either changes in the volume of transactions, or changes in the prices for goods and services. An economy is typically deemed to be performing better if it is producing a greater volume of goods and services. Comparisons over time using current price series give less information on what is causing growth as price and volume changes are not shown separately. Real or constant price series have had the effects of price changes removed, and are expressed in the prices of a chosen base period. Constant price series expressed in dollar terms show only changes in volumes because the prices have been held constant. There are three methods of deriving the constant price series: Quantity revaluation In this method, the price in the current period is replaced with the price in the base period, so that the quantity is valued in the base period price. This method is usually adopted where there is an extensive range of quantity and price data available. Quantity revaluation is currently used in measuring the gross output of agricultural industries. Price deflation This method uses a price index, which measures the change in prices over time, to separate out the price movement from the current price series. The current price series is divided by the price index, with the resulting series only reflecting the change in quantity, or volumes. Volume extrapolation In this method, a volume index is used to reflect the change in quantity over time. This volume index is used to multiply the base period value. This results in a constant price series, where movements reflect the movements in the volume index over time. 17