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Different measures of economic activity: Physical quantity, current dollars, and volume

by D. Wyman ¹ 

Overview

Most indicators of economic activity are physical quantity, current dollar, or volume measures. ²  Of the three, physical quantity data are the most common and the easiest to understand, counting the number of vehicles sold, bushels of wheat harvested, or barrels of oil exported. ³  Quantity measures provide a quick gauge of whether demand or output for a particular product group is changing. These measures are widely produced, since simple counts can be done with limited resources and are available on a very timely basis. They work best for relatively homogeneous commodities as there is an inherent assumption in quantity data that the products included in the total are qualitatively similar.

Current dollar indicators measure the value of an economic activity. By using dollars as the common unit of measure, the values of products that are heterogeneous can be combined, an advantage over physical quantity data. Moreover, a current dollar aggregate improves upon quantity data by accounting for the different values of the array of products within the product group, such as the choice of a different grade of beef or brand of clothing. In physical quantity data, each steak or shirt is counted as one unit. In current dollar data, the variation in the respective values of these products is reflected in their different prices. Department stores collect data, for example, on their total sales of a wide range of products. Statistical agencies do the same when they combine the value of goods and services sold by all retail stores to calculate total retail sales.

Volume measures share many traits with their current dollar counterparts, incorporating the diversity both within and across product groups. However, the influence of prices is separated from the current dollar data in order to isolate a measure of the change in volumes. More complex conceptually and more difficult to calculate, volume data include the effect of shifts in "quantity, quality, and structure" ⁴  within the economy and have been developed largely within statistical agencies.

Each of these indicators has its place; when each should be used depends on the objective of the analysis, as no one measure is the correct one in all circumstances. In fact, as this article will show, it is often informative to compare trends in different measures, as long as the analyst understands their strengths and weaknesses. For example, a quantity measure such as the number of vehicles sold is a good starting point in identifying major shifts in overall auto demand. However, the number of vehicles sold does not capture the full diversity of the auto industry's numerous models and features. As a result, statisticians quickly resort to current dollar and volume measures of auto sales to account for this variety and how demand for vehicles changes over time. An analogy is that, while the number of barrels of crude oil is sufficient to highlight overall changes in output, shifts between heavy oil extracted from the oilsands and conventional light oil are accounted for only in the current dollar and volume measures of crude oil production.

This article will discuss the uses as well as the limitations of physical quantity, current dollar, and volume measures. Examples will be presented which illustrate when the measures are complementary and when one measure is preferred over the others.

Physical quantity data

Physical quantity data are frequently cited in the business press. The number of houses sold, autos produced, and bushels of grain harvested are three common examples.

Timeliness and simplicity are the main advantages of quantity data over the other two measures. ⁵  While current dollar and volume data often require several weeks to compile and release, quantities can be quickly assembled after the reference month, in as little as two days in the case of unit auto sales or two weeks in the case of housing starts. ⁶  Counts can be done through an association of companies sharing data or by analysts compiling publicly available information.

Quantity data are user-friendly. Within a product grouping, such as housing starts, they can be broken down into single homes, semi-detached homes, town homes, and condominiums by province and the values for these components sum to the total, a trait called additivity. As well, composition analysis can be done, such as calculating the contribution of trucks and cars to the change in total auto sales, or the share of cars or trucks in total vehicle sales.

Physical quantity measures are most useful when the products under study are very similar. The tonnage of coal exported from Canada is a good example. There are two types of coal produced in Canada: thermal coal, which is used for producing electricity; and metallurgical coal, which is "transformed into coke and fed with iron ore into a blast furnace for iron and steel production." ⁷  Canadian companies almost exclusively export metallurgical coal (imports, conversely, are made up almost entirely of thermal coal). As coal exports are a relatively homogenous product, the quantity data in isolation provides analysts with a good picture of demand and, in combination with their price, of revenues from coal exports.

As the homogeneity of the group of products being measured declines, the clarity of the message provided by quantity data fades. For example, on examining total coal production in Canada, which includes both thermal and metallurgical coal, it is uncertain whether an increase or decrease in tonnage is related to a change in electricity or steel demand.

Similarly, while the number of vehicles sold provides a rough guide as to the state of the auto industry, there are large differences in prices for compact and luxury vehicles. Having the sale of a compact car and the sale of a luxury car each count as one in total unit sales means that this measure is less informative about structural changes in the auto industry. The rich detail of the auto market's composition as reflected in the wide range of products and in the diversity of models and features is not captured in the simple count of the number of vehicles sold, but these quality differences are reflected in the current dollar measure.

Figure 3.1 shows the recent trend in the number and current dollar value of new vehicles sold from 2008 to 2010. ⁸  A steep drop in unit auto sales occurred in the fall of 2008, marking the onset of the recession in consumer spending. Sales bottomed out in December 2008 and then rose steadily throughout 2009. During such periods of rapid change, quantity data are a useful measure of shifting demand. However, quantity data do not reveal more subtle movements, which are captured by examining current dollar data. For example, the numbers of units sold fell more (-31%) than nominal new vehicle sales (-22%) during 2008; this smaller drop in nominal sales indicates that there was a shift in the mix of cars sold toward more expensive vehicles as the recession deepened. The recovery of sales early in 2009 also was more clearly delineated in current dollars than in units, as consumers continued to buy more expensive vehicles, notably trucks.

Another limitation of quantity data is that products with different units of measure cannot be aggregated. For example, in order to examine not just coal but all energy exports, products such as barrels of oil, cubic metres of natural gas, litres of gasoline, and megawatt hours of electricity need to be added together. Combining production or sales numbers for a variety of diverse products requires moving beyond unit data for barrels, cubic metres, litres and megawatt hours to a common measure, usually dollars. ⁹  While quantity measures are well-suited to show broad trends in demand for a group of similar products, current dollar and volume measures are employed for measuring and analyzing more heterogeneous data. The task of capturing the complexity of the energy and auto markets and of aggregating these activities with other goods and services produced and consumed in Canada is carried out by means of economy-wide current dollar and volume indicators such as retail sales and GDP.

Current dollars

Tax revenues, stock market capitalizations, and department store sales are examples of current dollar data. While more complex than quantity measures, current dollar data measure the value of an economic activity at current prices and can be compiled as long as values (or quantities and prices) can be measured. ¹⁰  Total exports, retail sales, corporate profits and nominal GDP are examples of those compiled within statistical agencies.

The main benefit of current dollar (or 'nominal') measures is that heterogeneous groups of goods and services can be added together to form a single dollar value that reflects the diversity of these products and their prices. Current dollar energy exports provide analysts with the total earnings of a wide range of energy products. This can be aggregated with the value of all other exported goods. In compiling total exports, the heterogeneity of products is captured, reflecting their brand, features, design, and construction.

In addition, current dollar data can be summed from their most detailed component to the highest aggregate and can then be decomposed, resulting in a versatile analytical tool for economy-wide measures such as retail sales, tax revenues, exports and imports, or GDP. For example, within energy exports, current dollar exports of crude oil, natural gas, refined petroleum, coal, and electricity can be examined to understand their contribution to total energy exports. As well, energy exports can be combined with exports of metals, fertilizers, forestry, and agricultural products in order to examine overall natural resource exports.

Despite these advantages over physical quantity data, current dollar data have their own limitations. The main one is that they do not separate the total change between price and volume effects. For example, to understand whether the rise in current dollar energy exports between 2002 and 2007 resulted from higher volumes or higher prices or from a combination of the two, the best indicator shifts from current dollar to the volume of exports.

Volume

Volume data are the more sophisticated cousins of physical quantity data. They capture the diversity among product groups, such as heavy and light crude oil, and across them, in combining crude oil, coal, natural gas, gasoline, and electricity into total energy exports. Volume data provide a single aggregate measure for any variety of products. While simple quantity data provide quick indicators for individual commodities, and while current dollar data provide values of the full spectrum of goods and services sold at current prices, volume data offer a measure for this entire spectrum excluding the effect of prices changing over time (they are sometimes called 'real' data).

Within the price effect, there are two forces at work: the first is the impact of price changes for the same product over time, while the second is the change in the composition of products or markets. When a product improves its quality, it is equivalent in the statistical world to a reduction in price. As the volume measure is the current dollar measure with this price effect removed, it reflects changes in product quality, market composition "and, ultimately, changes in the composition of the economy." ¹¹ 

The integration of quality changes into a volume measure is best explained using an example. As shown in Figure 3.2, between 1993 and 2008, auto sales volumes doubled, from about $35 billion in 1993 to $70 billion in 2008. In contrast, the number of autos sold increased by only 40%, from 1.2 million units sold in 1993 to nearly 1.7 million units sold in 2008. ¹² 

Changes in quality and composition reconcile these quantity measures and volume measures of auto sales in Figure 3.2. It is clear from the quantity data that 40% of the increase in sales volumes from 1993 to 2008 was attributable to the rise in the number of autos sold. The remaining 60% growth in volumes was accounted for by the change in the mix of vehicles sold in that period and by the proliferation of features embedded in autos during that period, including safety features such as ABS brakes, child-proofing, and air bags, as well as entertainment and mapping systems like GPS, DVD, and MP3 stereos. A vehicle purchased in 1993 was without these features and was therefore of a lower quality than those produced in 2008. As well, consumer tastes shifted from cars to more expensive trucks and SUVs between 1993 and 2008, raising sales volumes.

Volume data are usually calculated by estimating current dollar values and removing price changes. The level at which price changes are adjusted is pragmatic, intended to drill down to a level of detail in the data at which important product differentiation diminishes, such as between light crude oil obtained through conventional extraction methods versus heavy crude oil extracted from the oil sands. However, the statistical system is dynamic, and in its evolution a once acceptable level of detail can quickly become outdated and needs to be revised in order for the data to remain as valuable as before. For example, prior to the rapid growth of oilsands production in the Canadian crude oil market in 1990, ¹³  the price of crude oil was measured by the price of conventional crude oil. After 1990, the price of heavy crude oil had to be included.

Volume data are especially important when analyzing sectors in which prices are volatile, such as the energy sector, because it becomes difficult to use current dollar data as a measure of growth in demand. While the change in current dollar energy exports measures the growth in export receipts, for example, it does not reveal whether exporters received more dollars as a result of higher prices and higher volumes, higher prices and stable volumes, stable prices and higher volumes, or lower prices and even-higher volumes. It is the breakdown of current dollar data into its price and volume components that reveals these changes.

Analysts are not obliged to choose between current dollars and volume; they are often best used together. Canada's recent recession and subsequent recovery are more easily understood by examining both current dollar and volume data. Real GDP fell 3.6% between the third quarter of 2008 and the second quarter of 2009, less than most G7 countries. In current dollars, the drop was more pronounced, down 7.5%, led by a 30% drop in export earnings. This helps to explain the marked drop in spending in some sectors of domestic demand, notably business investment, which fell in tandem with profits as export prices plunged.

However, some analysis can be conducted only in current dollars or in volumes. For example, share analysis, such as the part of energy exports in total exports, can be carried out only with current dollars. Energy prices have risen sharply over the past decade. By 2006, energy exports accounted for nearly 20% of export receipts, compared to 7% in 1998. For volume data that rely on holding prices fixed to those of the base period (such as Laspeyres volumes, which will be discussed in the next section), the share of energy exports if prices were held constant at 2002 prices are different than that based on 1997 or 1992 prices. Share analysis is not done using Laspeyres volume data because the shares change depending on the base period selected. In the case of a chained volume measure (such as the chain Fisher), the problem is not the base period but rather that this data is not additive. Therefore, shares cannot be calculated.

Conversely, understanding the relationship of GDP and hours worked (a measure of the volume of labour demand) is best done using real GDP. As real GDP reflects the volume of goods and services produced in Canada, it is evident that the change in real output would be reflected in the change in the number of hours worked to produce those goods and services. The current-dollar GDP measure includes price movements and the volatility of these movements loosens its relationship to hours worked.

Different volume measures

While there are a variety of ways to calculate volumes, their interpretation as current dollar data with the price effect removed remains unchanged. Statistics Canada produces two different measures of volume, using the Laspeyres ¹⁴  and chain Fisher methodologies (each named for the individual responsible for its respective development). ¹⁵  While the Laspeyres and chain Fisher methodologies differ, they are somewhat overlapping. The main contrast between the Laspeyres and the chain Fisher measures is that the Laspeyres method uses a fixed base period against which all future price growth is compared while the chain Fisher reweights prices each period to more accurately reflect the changing structure of the economy. Several economic programs at Statistics Canada apply the chain Fisher method, primarily those that contribute directly to the measurement of GDP, while others use the Laspeyres method. ¹⁶  In some cases, both measures are provided, and it is left to the analyst to select the data that meet his or her needs.

When using the Laspeyres method, economic activity is valued in the prices of the base period (which is updated periodically, typically every five to ten years, and then chained to data using earlier base periods), currently in 2002 prices. For Laspeyres volumes, as the time frame moves further away from the base period (such as calculating 2010 volumes with a base period of 2002), there is an increased likelihood that the base period weights no longer accurately reflect relative prices. Relative prices refer to the price increases or decreases in different sectors of the economy in relation to each other. For example, in an economy comprised of high technology products and natural resources, if the prices of these two sectors move in tandem, relative prices are stable. However, when prices of technology products are falling as more advanced products are introduced to the market and rising global demand push up prices for resources rapidly, relative prices in these sectors shift, changing the importance or 'weight' of the sectors to the economy. Despite regular updates of the base period, accurately reflecting current economic conditions is a limitation of the Laspeyres measure, most evident during periods of rapid relative price changes.

The chain Fisher index is calculated as an average (specifically, the geometric mean) of the Laspeyres and the Paasche indexes. It has a reference period (currently 2002), not a base period. A reference period is simply the "period for which the index series is expressed as equal to 100 [or the value of the time series for that year in order to express it in dollar terms]. The reference period can be changed by simply dividing the index series with its level in any period chosen as the new reference period." ¹⁷  The chain Fisher volume measure instead updates the indexes for each additional quarter (or month or year) to reflect the average weights over the two adjacent periods; then, the indexes are 'chained', by linking quarter after quarter (or months or years) like the loops of a chain to create a time series. In doing this, chain Fisher volumes reflect ongoing changes in the economy.

Data that contribute to the National Accounts calculation of GDP usually use the chain Fisher methodology, as a precise measure of growth is needed. Retail sales and international trade volume data are produced using both the Laspeyres and the chain Fisher methodologies; manufacturing sales are calculated only on a Laspeyres basis.

For energy exports, Paasche prices ¹⁸  and Laspeyres volumes are available at a relatively detailed level, broken down into crude oil, natural gas, gasoline, coal, and electricity. For each of these major groups within the energy sector, the price and volume effects are calculated for each month. Additivity means that the Laspeyres volumes of these major groups sum to the total volumes for the energy sector and that the sum of the export volumes of each sector – agriculture, energy, forestry, industrial goods, machinery and equipment, autos, and consumer goods – equals total export volumes as long as they have a common base period.

When using a volume measure deflated by a chain Fisher index, there is a loss of additivity among the components. For example, the sum of the components of GDP does not equal total GDP, nor do the components of sub-aggregates such as personal expenditure equal total personal expenditure. This is considered the main downside to the chain Fisher method. One way in which Statistics Canada facilitated analysis of chain Fisher volumes for data users was to create contribution-to-growth tables, which quantify for users the contribution of individual components to sectoral or overall GDP growth. As well, the sum of the Fisher volume and price effects does equal the change in nominal GDP, a feature called consistency. The Fisher index is the only index for which this is true. ¹⁹ 

Quarterly real GDP adopted the chain Fisher methodology in 2001 in order to maintain comparability with the US and other international agencies, and to ensure that GDP adjusted more rapidly to the ongoing changes to new products and the resulting changes occurring in relative prices. ²⁰  This move of GDP to a chain Fisher measure in 2001 proved to be prescient, as shifts in relative prices accelerated after 2002 as a result of the sharp rise in commodity markets, the appreciation of the Canadian dollar, and the ongoing declines in ICT prices.

In effect, there is a trade-off of simplicity and accuracy between the two measures. The greater complexity of working with the "computationally more difficult to use" ²¹  chain Fisher is accepted in order to achieve the most accurate measure of GDP growth. Even a small change in GDP can have a large impact on our understanding of the economy, with dating business cycles providing one example. During the 2008-09 recession, there are three quarters in which output clearly fell, while the quarters on either side of those posted gains of just 0.1% or 0.2%. The dates of the recession could change as a result of relatively minor revisions to GDP, so accurately measuring growth is important for business cycle analysis. More broadly, much attention is paid to exactly when the rapid contraction in trade began and when consumer spending recovered to understand the internal dynamics of how the economy moved from recession to recovery. In situations such as these, the difference of a few percentage points between the Laspeyres and chain Fisher volume measures become significant for the dating of a change in the economy. For other series and other purposes, such as examining Canada's exports of energy or imports of machinery and equipment, the Laspeyres measure remains widely-used, as users judge the loss of accuracy to be acceptable in return for the gain in accessibility and interpretability.

Conclusion

While physical quantity measures are widely used by industry and are accessible, both conceptually and in calculation, they are inadequate for statistical agencies to carry out their task of measuring economy-wide statistics. As a result, statisticians have developed an array of current dollar and volume data. These measures allow comparisons among heterogeneous products, an integral element to calculating the most important economic indicators, such as GDP. As well, in calculating GDP in current dollars and volumes, the complex diversity of each good and service is maintained in the measurement and can be compiled to offer an accurate portrayal of the depth of the Canadian economy.

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