The possibilities and limitations of national accounting

Musings from a former practitioner

Introduction

National accounts statisticians¹ are but a small percentage of total employees within a national statistical agency. Yet they are responsible for some big and vitally important statistics. Most of the other statisticians in the agency work on surveys of one kind or another.² Those others look on the national accountants with a mixture of awe and disdain. On the one hand, it appears the national accountants can produce estimates for almost any economic concept virtually at will, with no need for expensive survey design, sampling and processing. On the other hand, while they sometimes seem to fashion new and important statistics out of thin air, they make little, if any, use of classical statistical theory and unlike survey statisticians, have great difficulty quantifying the error properties of the estimates they produce. Their magic is wonderful but at what point does it become unbelievable?

So what can we say about the practise of national accounting? Does it often go too far, producing fanciful statistics that have little sound basis in the real world? Or should it be criticized more in the other direction, for being too hesitant to develop statistical estimates for important economic concepts in a timely way or to extend essential time series further back in time by linkage methods? These are the issues addressed in this paper.

Does national accounting sometimes go too far?

An example - Cannabis

On April 13, 2017 a bill to legalize cannabis in Canada was introduced in Parliament. The Senate passed the bill on June 19, 2018 and the effective legalization date was announced as October 17, 2018. Statistics Canada foresaw an emerging demand for statistics on cannabis production and consumption and set about developing these data.

A new survey of legal cannabis producers was developed and a household survey was also created to measure current household demand. But the agency had not previously produced statistics on cannabis, largely because the drug was illegal, so there were no existing cannabis-related time series to speak of. This was problematic since it implied a lack of context within which to interpret the newly created, current cannabis statistics.

At the time it was widely believed Canada had a robust, albeit unmeasured, ‘underground’ cannabis industry that had existed well back in time. Indeed the existence of this illegal industry and the considerable popularity of the drug this implied was a major reason why the Liberal Party campaigned in the 2015 election to legalize cannabis. A majority of Canadians favoured the legalization. So Statistics Canada began to think about estimating both current and past cannabis production and consumption.

A search was launched to find information about the size and character of the illegal cannabis market in the years prior to legalization day. Although a few bits of information were discovered, there were of course no time series data to be found and the facts about the cannabis market that were unearthed were scanty and quite inadequate. Nevertheless the national accountants³ did put together crude estimates of annual cannabis production and consumption all the way back to 1961. These estimates can still be found in Statistics Canada’s online table 36-10-0599-01, although the table has not been updated since 2019.

Did the national accountants go too far when they published these 57-year time series? It can be argued they did. We don’t know how wide the confidence intervals around these estimates are but they must surely be quite broad and the people who produced them would probably be quick to agree with that assertion. The estimates are derived using a number of subjective and quite debatable assumptions with very little supporting factual basis. However, the methodology was made publicly available, Statistics Canada would point out, and people are free to ignore these data if they judge them to be too unreliable.

Statistics Canada has a good reputation and most users of their data are trusting souls who surely spend little if any time delving into the associated methodologies and caveats. Once such data are published online they become “official statistics”. But should the agency be in the business of publishing such essentially fictitious numbers? If the answer is ‘yes, sometimes’, where should the line be drawn? This is a question of judgment on which reasonable people can disagree, although the cannabis example looks, in the opinion of this writer, to have crossed a significant line.

Is national accounting sometimes too conservative?

An example - changes in classification systems

The time series estimates within the Canadian System of Macroeconomic Accounts (CSMA), as well as the hundreds of survey and administrative data sources from which they are derived, depend fundamentally on several classification systems. Chief among them are the North American Industry Classification System (NAICS), used to sort on the order of two million Canadian businesses into groups of similar firms, and the North American Product Classification System (NAPCS), which assembles the many millions of different types of goods and services available to Canadian households, businesses, governments and non-residents into a manageable number of product categories.

The classification systems are key to the translation of microeconomic data into macroeconomic aggregates. Without them there would be many fewer macroeconomic statistics. They allow comparisons of industries or products and they permit these comparisons to be done internationally since nations have agreed on common standards for the classifications.

The classifications are by no means static. The natural groupings of firms and products keep changing as innovations occur, technologies change and consumer tastes evolve. This is obvious and has always been the case, but the pace of change seems to have accelerated.

To keep up with these never-ending changes, Statistics Canada, like other national statistical agencies, updates its classifications periodically, typically every five years or so. This is important if the information is to remain currently relevant, but it also means established time series are broken.

Lengthy and consistent time series are important for many reasons, so Statistics Canada does make an effort to ‘concord’ or ‘reconcile’ a new classification system with the previous one. A classification concordance shows where the industries in the previous classification are now located in the new one. Using this concordance, Statistics Canada will often recast the various time series developed under the previous classification so they are as consistent as possible with those from the new classification and then link them to the new time series. Many users want the longest time series possible so today’s economic developments can be analyzed in an historical context.

But there are limits to how far back this recasting process can reasonably be done. The further back one goes, the more incongruent the older classifications are with the latest one. Just how far back one can go is a matter of judgment, but if one goes back too far the time series start to become misleading.⁴⁵

This problem is greatest the more detailed are the classification categories. More aggregate categories in the classification can sometimes be linked further back, without becoming misleading. For example, when dealing with different versions of NAICS it might be possible, for some statistical time series, to carry “Manufacturing” (NAICS 31-33) further back than “Computer and peripheral equipment manufacturing” (NAICS 3341). But the word “might” is important here, in part because sometimes more detailed categories in a classification are relocated between higher-level categories in a new version (out of manufacturing and into wholesale trade, for example).

The issues discussed here have a further twist at the break points when today’s NAICS and NAPCS classifications were first created, in 1997 and 2007.⁶ These classifications were harmonized among Canada, the United States and Mexico and as such, incorporated compromises to facilitate comparability across the three nations. They are different in some fundamental ways from their Canadian predecessors and this adds to the difficulty of linking time series if the objective is to go further back in time than 1997 for NAICS and 2007 for NAPCS.

So it is not as straightforward as might be expected to link time series based on a new classification backward over long periods of time. The further back one goes with the linking, the more incongruent the linked data are likely to be. How far back should one go? It involves a judgment about where the linkage becomes sufficiently specious that users would be led astray.⁷

Another example - changes to the international System of National accounts

The national accounts are developed under the framework of the United-Nations-approved international System of National Accounts (SNA). In this they are analogous to business accounting which is done under the framework overseen by the International Accounting Standards Board. The first version of the SNA was released in 1953 and updated versions were issued in 1968, 1993 and 2008. The latest edition, SNA 2025, was approved by the United Nations in March 2025.

In other words, these updates to the international SNA standard are infrequent compared to those for the classification systems. They sometimes involve changes in concept as well as in presentation. For example, SNA 2008 recognized research and development expenditures as a form of capital formation, rather than as intermediate expenses as was the case in SNA 1993, and it also classified military weapons systems as fixed capital assets. These changes meant that the new concept of gross domestic product was bigger than the old one. To link the previous SNA-1993-based estimates of GDP to the new post-SNA-2008 estimates required that the former time series be revised upward to include estimates of these two types of investment. Revisions of this nature may or may not be practical depending on the availability of the required data from previous years.

It was a big task to implement the various recommendations of SNA 2008. Statistics Canada ultimately switched over to the new system in stages between 2012 and 2015, bringing the new framework into the income and expenditure accounts time series all the way back to 1981. But many users were unsatisfied and urged Statistics Canada to carry the revisions even further back. The agency responded by starting a special project to revise the estimates from the 1961-to-1980 period to be as consistent as possible with SNA 2008. In doing so, there were situations where the required source data were unavailable, as Canada’s statistical system was very different in the 1960s and 1970s from what it is today. But reasonable assumptions were made where necessary and the task was eventually completed. The task was carried out by a highly capable and experienced senior employee as a post-retirement part-time project.⁸

But of course the full body of Canada’s national accounts estimates do not begin in 1961. Rather, the quarterly estimates begin in 1947 and the annual estimates in 1926. Should efforts be made to revise the estimates for these even-earlier time periods, to be consistent with the SNA 2008 recommendations? This again is a judgment call where reasonable minds can differ, but Statistics Canada has no plans to try to do that as far as I know, and for good reasons.⁹ It remains to be seen what the agency will do when it implements SNA 2025.

Resource constraints

It should be no surprise that national accountants have limited resources, just as we all do. It is difficult, in their resource-constrained environment, to give priority to re-estimating old numbers, often with very little "cloth" from which to “stitch” the product, in an attempt to make them more consistent with today's numbers. Users care very much about what has been happening recently, so that gets top priority. The further back one goes in time, the less most users of the data care. They do need context for today's numbers, so time series going back several years are also important,¹⁰ but the context provided by numbers, say, three, four, five or more decades ago are less important. In other words, national accountants are trying to keep their data-using clients as happy as they can, but they do not have the resources — not just the number of statisticians in general, but also the number of highly capable, experienced and knowledgeable statisticians — to keep everyone fully satisfied. They cannot do everything everybody wants and they must choose priorities. Sometimes, therefore, when new estimates for previous periods are requested by users but are not developed, the reason may be as much, or more, because of resource limitations as because of concerns by national accountants about the expected poor quality of any such estimates.

Supply and use tables

The supply and use tables (SUT) are the heart of Canada’s national accounts. They are estimated annually, with a lag of almost three years from the end of the reference period. These accounts are incredibly detailed. They contain estimates in five basic dimensions: products, industries, provinces and territories, final demand categories and years. And they are statistically reliable.¹¹ The first estimates of GDP and its components that one sees about two months after a particular month or quarter are much higher-level projections off the supply and use estimates from about three years earlier. These preliminary estimates are based on more limited monthly and quarterly source data since most administrative data and all annual survey data are not yet available. When the SUT are finally available, the elements of the national accounts for which more timely estimates were released previously are revised to be consistent with those tables.

The SUT estimates are not normally revised because they are prepared when no more relevant source data are likely to become available. But when a new version of the international SNA standard is released, such as SNA 2025, revisions become necessary to adapt to new concepts. Statistics Canada does its best to make these revisions back to the year 1997, but the revisions have to be more selective, mostly just incorporating important new or changed concepts, since data availability and the costs involved in revising such a big and complex set of estimates in a comprehensive way are prohibitive. The same is true when the NAICS and NAPSC are updated.

Why 1997? Because in that year Statistics Canada received a large and permanent budget increase for the specific purpose of building and updating detailed by-province supply and use tables. These statistics are used for calculating fair shares of revenue from the Harmonized Sales Tax (HST) among the federal government and the harmonized provinces. Provincial and territorial SUT were not produced prior to 1997, nor were many of the new surveys that were initiated around 1997 and form the basis of the SUT estimates. The monthly estimates of real GDP by industry are also available in time series stretching back to 1997 because these estimates are, in effect, distributions of the SUT annual value-added estimates across the twelve months of each year.¹²

Historical linkages by analysts

Nothing in what has been written above is intended to discourage people from performing their own linkages in order to create longer time series. Indeed Statistics Canada provides many historical data sets that are archived in their online database to make this possible. When an analyst constructs longer time series by doing the linking themselves, they are of course expected to do so with an awareness of the limitations associated with their efforts and to document the appropriate caveats.

Conclusions

Statistics Canada’s national accounts estimates are an enormously valuable resource for Canadians. They are tightly integrated, accurate, very detailed, reasonably timely and conform to international standards to facilitate country-to-country comparisons. Importantly they also adapt to changing circumstances in the economy as the industrial structure evolves, different kinds of goods and services appear/disappear, and the economic concepts upon which the accounts are based are updated to satisfy current requirements.

But this unending and essential process of adaptation to meet changing circumstances creates a dilemma: Time series are broken, as an inevitable part of the process. There is no perfect way to cope with this dilemma. However second-best solutions are available and they work fairly well if they are not over-used. The difficulty comes in judging where to draw the line. This paper has outlined various aspects of this line-drawing and has tried to explain how Statistics Canada does its best to navigate between, on the one hand, meeting the demands of its users for the longest time series possible and, on the other, conserving its scarce resources and avoiding the pitfall of endorsing fanciful estimates.

References

Firestone, O.J., [1960] “Development of Canada’s Economy, 1850-1900,” Trends in the American Economy in the Nineteenth Century, Conference on Research in Income and Wealth, U.S. National Bureau of Economic Research, Princeton University Press.

Leacy, F.H., M.C. Urquhart and K.A.H. Buckley (eds) [1983], Historical Statistics of Canada, second edition, published by Statistics Canada.

Urquhart, M.C., [1993] Gross National Product, Canada, 1870-1926, McGill-Queen’s University Press.

1. Most fundamentally, the national accounts statistician is an aggregator and integrator. The underlying framework for this purpose is financial accounting. National accounts are essentially aggregations of the financial accounts of households, businesses and governments. They provide aggregate statistics on such accounting concepts as revenue, expenditure and surplus or deficit, and their basic unit of measure is the national currency. But of course the accounts of households, businesses and governments are not always readily available and the accounting concepts and rules used by these actors are not uniform. Such accounts as are available often fail to provide all the necessary detail. So national accountants must often go beyond aggregating, into imputing or modelling to fill gaps in the source data.

2. The public needs information about topic X, so the agency plans and conducts a survey to collect the needed information. The topic might be something like the monthly sales of retailers, a key indicator of the state of the economy. Or it might be about the labour market status of the population - the percentage of working-age people looking for jobs or already having one. The former example requires a survey of businesses and the latter a survey of households. Most of the resources of a typical national statistical agency are devoted to surveys. This includes the biggest and most expensive survey of them all, the Census of Population, which aims to canvas all persons resident in the country on a specific day in order to collect information about their household composition, age, residence location, income and many other characteristics. The census is a vital piece of a nation’s infrastructure providing a basis for drawing electoral boundaries, allocating scarce resources fairly across the country, detecting and diagnosing socio-economic problems, framing statistical surveys and many other purposes.

3. I must confess that I was one of them, working part-time on a post-retirement assignment at Statistics Canada.

4. Note that the quality of a linkage is unlikely to be transitive. The linkage of a time series available from 2010 to 2019 to one from 2020 forward might be judged of reasonable quality and a similar judgment might be made about a linkage of a time series available from 2000 to 2009 with the one from 2010 to 2019. But if these two linked time series are themselves linked, the comparability of the data from 2000 to 2009 to the data from 2020 forward might be of poor quality.

5. There is an important difference here between national accounts per se, which are measured at current prices, and national accounts volume and price indexes, which measure relative change only and have no inherent units of measure. Modern index numbers are calculated with a chaining approach that links current estimates to previous ones period-by-period. This approach can yield very long time series, although the well-known “drift” problem tends to hurt comparisons widely separated in time. National accounts estimates at current prices, in contrast, are measured in dollars and are required to add up correctly. When these estimates are linked, due to classification or concept changes, an “apples and oranges” problem is created at the linkage points, thereby damaging the quality of measured rates of change.

6. After the initial version in 1997, NAICS was revised in 2002, 2007, 2012, 2017 and 2022. NAPCS was first released in 2007 and updated in 2012, 2017 and 2022.

7. Note here that users of the statistics are generally relying on Statistics Canada to make these judgments since they usually lack the time and/or knowledge to make them themselves.

8. Depth of knowledge and experience is necessary for this kind of task. Without it the updated and linked time series might inadvertently draw a new picture of the past bearing characteristics very unlike those portrayed in the unrevised time series. Recessions might change their timing or even disappear, for example, or “shocks” resulting from such causes as natural disasters or big labour disputes might inadvertently be smoothed away. The national accountants who derived the original estimates lived through these events and made sure they were properly reflected in numbers. It would be wrong to revise them away, perhaps as a result of some smoothing or proportionality assumptions.

9. Indeed some users of the national accounts might urge Statistics Canada to go even further back, into the 1800s, drawing from and expanding upon Firestone, O.J., [1960] and Urquhart, M.C., [1993].

10. Several years of data are needed for purposes of seasonal adjustment if the estimates are monthly or quarterly, for example.

11. The reliability of the supply and use tables is confirmed by the innumerable supply-and-use identities embedded within them. When the total ex post supply of a commodity is measured independently of the ex post demand for it, the two should be equal and any divergence points to the need for corrective action. Similarly from the industry perspective, industry A’s purchases of a commodity from industry B must be equal to industry B’s sales of the commodity to industry A. When revenue and expense data from the two industries are collected separately, a balancing check becomes available.

12. Statistics Canada did release estimates of real value-added by industry for many years prior to 1997. See for example archived Statistics Canada tables 36-10-0387-01 (1919-1971, annual - K$), 36-10-0383-01 (1946-1971, quarterly - K$) and 36-10-0399-01 (1961-1997, annual - C$ and K$). But these pre-1997 estimates are less detailed and have never been revised to be consistent with SNA-2008. Moreover, they likely never will be.