Appendix 5 Deflators and the national accounts

Joe Grice

A5.1 Introduction

The national accounts provide a comprehensive source of data for those who want to understand the economy. But, it is often important to separate changes in national accounts measures that occur because of changes in prices from changes that reflect movements in the underlying quantities of goods and services produced and consumed. This procedure is called deflating the national accounts, and it provides measures of economic aggregates which remove the effects of changes in prices over time.

GDP deflator
The adjustment to Gross Domestic Product (GDP) that isolates changes in prices for all the goods and services produced in an economy. It is used to capture changes in the underlying quantities of goods and services produced and consumed from year to year.

Specific GDP deflators can also be used for the components of GDP, such as household consumption and gross fixed capital formation. Using deflators is a common and useful process, but it can present some challenges and complications.

A5.2 Why use a deflator?

GDP is based on systematically accounting for the value-added at each stage of economic production. It represents the cumulative value generated by the economy. In other words, it is made up of what the economy produces, which is what is then available either for consumption now, or for investment in new capital to underpin consumption in the future.

So, in material terms, it is a measure of a country’s prosperity.

If we were interested only in a snapshot of the economy at one moment, this would be fine. The monetary value of GDP, measured with the prices at that point, would tell us what we wanted to know. But we are often interested in how this statistic is changing over time. Are we more prosperous now than we were last year, or 10 years ago, and by how much? The answer to this tells us whether the economy is growing or shrinking.

Imagine that the monetary value of GDP is higher this year than it was a year ago. It does not automatically follow that the economy is growing, because there are two possible explanations:

  • An increase in the amount of goods and services that the economy is producing. In the illustrative economy discussed in Chapter 2, we focused on pasta production. If the monetary value of the GDP for that economy is higher than it was last year, that might be because the amount of pasta produced by that economy has risen. This increase would then be available for its citizens to consume and enjoy, which would be a benefit to people.
  • An increase in prices within that economy. Even if there had been no increase in pasta or other production over that period, observed GDP in monetary terms would have increased. But, unlike in the previous case, there would be no additional pasta for people to enjoy.

These scenarios have different implications. In the first case, the economy has become more prosperous, it has grown and offers the opportunity for more consumption. In the second, there has been no growth in the opportunity to consume goods and services; the prices of these goods and services are simply higher.

GDP at current prices
This is GDP expressed in monetary terms alone. An increase may be due to higher production or consumption, higher prices, or a combination of both.
GDP at constant prices
Also known as GDP in volume terms. It captures the contribution to GDP at current prices resulting only from changes in production or consumption. Commonly known as “real GDP”, this measure is hypothetical and cannot be observed directly.

GDP expressed in monetary terms alone (GDP at current prices) cannot distinguish between the two effects of changes in prices and changes in quantities. If we can abstract from the effect of movement in prices on GDP in monetary terms, this leaves us with a hypothetical measure of “real GDP”. This is often called GDP at constant prices, and provides a measure of GDP in volume terms, which as the name suggests, aims to measure the quantity of production in the economy. From this, we can then compute the growth rate between two periods to see whether the economy has become larger or smaller, and discover how quickly it is changing.

The process of deflation is a method to calculate GDP in volume terms.

A5.3 The deflation process

If we had only a single good in the economy, the process of deflation would be straightforward. We could simply observe the physical quantity of the good produced, for example, the number of tons of pasta produced. However, our economies produce many goods and services, so although we can still observe the physical quantity of each of these, we would be left with the problem of how to weight them together. How many pounds of pasta production, for example, equal one haircut? And how many haircuts equal one washing machine?

We could impose arbitrary weights, but they would be just that, arbitrary. Instead, we prefer the market to tell us how people value goods and services relative to each other, and so we need an alternative approach.

A5.3.1 Using an index of output prices

Since we are trying to strip out the effects of what are purely price changes, the obvious strategy (see Chapter 1) would be to construct price indices so we can quantify such effects. Suppose that between two periods, A and B, we see GDP in current prices has increased 15%, but prices over the same interval have risen by 10%. As an arithmetic identity:

\[\text{Proportionate growth in GDP at current prices} \equiv \text{Proportionate growth in GDP at constant prices} \times \text{Proportionate growth in prices}\]

So, in this case, the growth in GDP at constant prices would be:

\[1.15/1.10 = 1.04545\]

or growth of just over 4.5%.

Alternatively, if prices had risen by 18% between periods A and B, then the growth of GDP at constant prices would be given by:

\[1.15/1.18 = 0.97458\]

Which means there would have been a fall of 2.5% in GDP at constant prices over this interval.

A5.3.2 Using an index of expenditure

As we have seen, GDP can be measured either as the sum of output produced by the economy, or as the sum of expenditures for which that output is used. In principle the two approaches would give the same result, though there will usually be some discrepancy due to measurement problems.

And so also, in principle, an index of price changes in the economy could be built up either as an index of output prices or as an index of expenditure prices. In practice, the approach will be governed by which information is available and most reliable.

In the UK, as in most comparable economies, the view is that usually, though not always, better and more reliable information is available for expenditure prices than for prices of outputs. So, this is the preferred method.

GDP in current prices captures the price consumers pay for pasta, haircuts, washing machines and other goods and services they purchase, is then broken down into its constituent expenditure categories, and a price index for these individual components is calculated.

For this purpose, the standard method is a Laspeyres price index (see Appendix 1). In this case the price change between the base period 0 and the current period, t periods later, can be calculated as:

\[(P_{0,t}^{L} = \frac{\left( p_{i,t} \times q_{i,0} \right)}{\left( p_{i,0} \times q_{i,0} \right)}\]


  • Pi,t is the observed price of the ith good or service within the relevant expenditure category in the tth time period after the base period 0
  • pi,0 is the observed price of the ith good or service within the relevant expenditure category in some starting base period 0
  • qi~*~,0 is the observed quantity of the *ith good or service consumed in the base period 0.

Hence, the Laspeyres index can be thought of as a weighted average of prices in the current period t compared to a weighted average of prices in the base period 0, where in both cases the weights used are determined by the quantities of each good or service consumed in the base period.

How it’s done Choosing the type of price index

Like most national statistical offices, the Office for National Statistics (ONS) mainly uses a Laspeyres price index to deflate the national accounts. It provides a convenient and easily understood way of making the relevant calculations. But as the Eurostat manual on deflating national accounts notes, an equally good case could be made for use of a Paasche price index. This differs from a Laspeyres price index only in that the weights are based on quantities consumed in the current period, rather than in the base period. The two formulations will usually give similar results.

The Bureau of Economic Analysis in the United States uses Fisher price indices for deflating the national accounts. The Fisher price index can be thought of as giving a rough average of the Laspeyres and Paasche price indices (see Appendix 1 for more detail).

A5.3.3 Explicit and implicit deflators

explicit deflator
A deflator that uses an index calculated from observed prices in either production or expenditure.

Having calculated a price index for a particular category of GDP, it is then straightforward to use this to isolate the change in volume for that category from the observed change in current prices. Here, the price index is being used as an explicit deflator for the category of expenditure.

There are a few cases where explicit deflation is either not practical, or where we already have direct information about changes in the volume of a particular category that is more reliable than that on prices.

A good example is provided by the public services, which in the UK’s case, typically account for a fifth or more of the economy’s total size. The National Health Service is largely provided free at the point of use, as are the educational services provided by state schools. In both cases there are no directly observed prices, but on the other hand, we do have good information about the number of patients treated or the number of students taught. We can also consider other data. For example, in healthcare, some treatments are inherently more complicated and resource-intensive than others. Likewise, in education, the teaching intensity required in different age groups and types of pupils varies.

implicit deflator
An implicit deflator is obtained by dividing a current value by its real counterpart (the chain volume measure or constant price measure). Movements in an implicit deflator reflect both changes in value (price indices) and changes in the composition of the aggregate for which the deflator is calculated.

Using this information, we can calculate for each period direct measures of the change in the volume of such public services. Since we also know in monetary terms how much is spent each period on the health service or on schools, we can calculate an implicit deflator for such categories. This index may convey useful information for analysing the efficiency and effectiveness of public services, for example, how much extra patient care is generated by additional money spent on health services. In this sense, the implicit deflator can be thought of as a measure of the unit cost of providing patient care.

A5.3.4 Calculating the aggregate GDP deflator

Using explicit and implicit deflators, we can obtain deflated or volume estimates for national accounts categories, in principle, at any level of disaggregation in which we are interested. We can also add together the volume estimates for all the components of GDP, and so arrive at an aggregate measure of GDP in volume terms. It tells us what GDP would have been in any period, had there been no change in the price level. This is exactly what we need to determine whether the economy has been growing or shrinking, and by how much.

We can at this stage also compute the aggregate GDP deflator. Expressed as an index at 100 in the base year, it is given by the identity:

\[\text{GDP deflator in period } t \equiv 100 \times \frac{\text{Monetary value of GDP in period }t}{\text{GDP in volume terms in period } t})\]

Note that in the terminology used earlier, this is an implicit deflator. No price index is being directly compiled, but it is calculated indirectly from this identity. Nevertheless, the GDP deflator conveys useful information as the most general measure available of what has been happening to prices in the whole economy.

A5.4 Chain-linking for deflators

Until the early 2000s, most national statistical offices, including the ONS, carried out deflation of the national accounts as described above. But this created a problem in the timeliness of the information that was being used to calculate the movement in prices. The process would be “rebased” (when the base year for the Laspeyres index would be reset) every five to seven years in the UK and, in many other countries, even less frequently.

For example, in 1999, the base year might be reset to 1997. This would then become the new base year, but it might not be changed again until 2006. By this time, the price level used to deflate the national accounts was being calculated using a pattern of expenditure which, in our example, was almost a decade out of date. Given that expenditure patterns can change far more quickly, for example consider information and communications spending, this would mean the weights used to compile the national accounts no longer applied to the real world.

One option might be to replace the Laspeyres index by a Paasche index, where the weightings would be determined by the current year’s expenditure patterns. But that would not solve the problem because spending patterns would be appropriate when calculating the current period price index, but not for calculating the price index for previous years.

A solution is to chain-link the index (see Appendix 1 for more detail):

  • The ONS uses a Laspeyres index to calculate the growth of prices for any year compared with the previous year. Spending patterns would have changed over that year, but not by much.
  • In the next year, the process would be moved on by one year, with the Laspeyres index for that year calculated using the weights given by the spending patterns only one year earlier. In this way we obtain a series of growth rates in prices calculated for one year at a time.
  • For periods of more than one year, the growth in prices can be calculated as the growth in each individual year multiplied (chained) together.

Chain-linking has the great advantage of being based on weights that are up to date, but it has two drawbacks. It is harder to calculate because weights have to be recalculated each year, although improved technology means this is now less of an issue. More importantly, the algebra of chain-linking means that additivity is not preserved. So, estimates of the volumes of particular subcategories of consumer spending obtained in this way do not quite add up to estimates derived from applying the procedure to total consumer spending.

However, the overall advantages of chain-linking greatly outweigh the relatively minor drawbacks and it is now the approach recommended by all international guidance (see the System of National Accounts 2008 (SNA 2008)).

A5.5 Quality change

So far, we have explained the deflation of the national accounts as being essentially about splitting price changes from quantity changes. In a broad sense, this is true. But we must be careful what we mean by “quantity”. Using the illustrative pasta example again, there might have been no change in the physical tonnage produced, but there might have been an improvement in the quality of the pasta. It might now taste better, or it might cook more easily. In that case, there would have been an increase in the benefit that consumers receive from the pasta production and we should allow for this quality improvement in our volume estimates.

The international guidance (see again SNA 2008) is clear that volume estimates in the national accounts should make allowance for quality change, although this is easier said than done.

One traditional approach has been to disaggregate between expenditure categories with known different qualities. Taking restaurant meals as an example, we might differentiate between fast food and fine dining. Fine dining will cost more, and so have a higher weight. If there is no change in restaurant meals provided in total, but a shift towards more expensive, higher quality meals, this will be reflected in a higher volume estimate overall.

This disaggregation technique is useful, but in some important cases it is not sufficient. Sometimes improved quality is integral to the design of the product:

  • Technology goods and services. A mobile phone purchased today embodies a different and expanded set of services and capabilities from one purchased a few years ago, and a very different set from a mobile phone purchased in the 1990s. So, simply looking at the prices of mobile phones over the years without recognition of the changing nature and quality could give a misleading impression. The same would be true for a range of communications and IT products. A laptop today is vastly more powerful than those manufactured only a few years ago. So, again, simple comparison of prices over time may not be meaningful.
  • Public services. We could measure the output of the health service by counting the number of patients treated and derive our implicit price deflator for the service on this basis. But presumably what matters to patients is not just that they are treated, but that they derive benefit from the treatment in that they are cured or become healthier. Those results might not have been possible until recently, reflecting advances in medical know-how. The output of schools similarly depends not just on the number of pupils taught, but on whether they derive educational benefit from that teaching. Better quality teaching will give more benefit than poorer. The quality of public services, such as in these examples, is clearly important alongside the quantity of the service delivered. If the quality of healthcare or teaching is changing over time, that ought to be considered.

Florence Nightingale became famous for improving the nursing care of army casualties during the Crimean War in the 19th century. She took medical statistics seriously and recorded the number of patients she and her colleagues nursed. But she also divided them into categories of outcome, to help her evaluate her overall impact:

  • cured
  • improved
  • not improved
  • died.

One might think of this as rather a broad-brush set of quality categories. But patients would have appreciated the importance of moving up one quality category in her table of outcomes.

Private services, as well as public ones, change their quality. Business services, such as accountancy, consultancy, architecture and design, real estate, and commercial lawyers represent more than 10% of the UK economy. The way the services are provided, and what they cover, have changed markedly over the years. In each case, there are obvious questions as to whether the quality of such services has been changing for the better or the worse and by how much. These are some of the most interesting and challenging issues in the ongoing improvement of economic statistics.

A5.6 The importance of deflation

Some idea of how important deflation is can be taken from looking at how GDP in volume terms has differed from GDP measured at current prices. Figure A5.1 summarises how the two series have changed since 1970, along with the GDP deflator.

  Current price GDP GDP in chained volume GDP deflator
1970 to 1975 105.2 10.4 86.4
1975 to 1980 125.7 11.7 102.1
1980 to 1985 59.6 12.3 42.1
1985 to 1990 61.4 18.9 35.7
1990 to 1995 27.2 8.4 17.3
1995 to 2000 28.9 19.3 8.0
2000 to 2005 27.1 14.2 11.3
2005 to 2010 15.3 2.6 12.4
2010 to 2015 19.5 10.5 8.1
2016 3.9 1.7 2.2
2017 3.7 1.7 2.0
2018 3.5 1.3 2.2
2019 3.6 1.4 2.2
2020 −4.8 −9.8 5.6

Figure A5.1 Percentage changes in two measures of GDP and the size of the GDP deflator, UK, 1970 to 2020

Percentage changes in two measures of GDP and the size of the GDP deflator, UK, 1970 to 2020

ONS Resource

For the UK, the Office for National Statistics has published a strategy for taking forward the agenda on national accounts deflators in National Accounts, Deflator Strategy: September 2020. It is an excellent starting point for further reading about the issues and problems involved.

As we can see, the growth has been very different, both over the five-year periods to 2015 and for the single years shown since:

  • GDP at current prices has consistently grown more quickly than GDP in volume terms. This was particularly true up to the 1990s when UK prices were rising very quickly.
  • Since the 1990s, inflation has been lower, but prices have still risen, albeit at slower rates.

This shows us that trying to infer what had been happening to UK growth, without using deflators to abstract from price changes, would have resulted in misleading conclusions.

A5.7 Summary

This appendix has covered the subject of deflating the national accounts, discussing the procedures for separating out movements in aggregates that arise from changes in price levels from those that arise for other reasons. It is a crucial step when making inferences about the “real” changes in the economy, such as whether the economy is growing or shrinking, and by how much.

We have also looked at some of the issues that arise in carrying out deflation. The solutions to some of these issues, such as accounting for quality change across the economy, are at the leading edge of innovations in compiling national statistics. Improving deflation methods, in the UK and in other countries, is important and will require sustained effort.

A5.8 Further reading