For example, if agricultural production increases by $1 million, the effect on each industry is calculated from column 1 of the final demand multipliers in Table 1. In this case, revenue in industries providing services to primary industries would rise by $20,000 (.02x$1 million), mining by $40,000 (.04x$1 million), manufacturing by $280,000 (.28x$1 million), and so on. The higher output reflects both greater demand directly from farmers and also indirect increases: the $280,000 gain for manufacturing reflects both higher demand for farm machinery from farmers and the indirect increase arising from the transportation system needing more rail cars to carry the additional farm production. Finally, increased farm output would feed back into a $190,000 increase in demand for its own output (the difference between 1.19 and 1.00 in column 1, row 1 of the matrix), mostly from grain required to feed animals. Summing up all these direct and indirect impacts yields the total multiplier of 1.97 at the bottom of column 1. That is, every $1 of additional agricultural output generates another $0.97 of gross revenue throughout the economy, the largest multiplier of any industry (the multiplier is the ratio of the total change – 1.97 in this case - to the initial change of $1).

Other goods-producing industries account for three of the next four highest multipliers, including forestry, construction and manufacturing. Forestry and construction both have strong links to manufacturing; construction also triggers more demand for professional services (such as architects and legal services) as well as mining (including concrete, gypsum, etc). Manufacturing also uses a number of business services as well as other manufactured goods.

Accommodation and food has the largest multiplier (1.78) among service industries. Nearly one-third of its demand for other industries is for manufacturing. It also has the largest impact on farming of any industry, which it requires to feed its clients, as well as the second-largest impact on finance and real estate (after retail trade). Tourism also requires extensive transportation and distribution of people and goods.

Transportation and recreation (including arts and entertainment) both have above-average multipliers of over 1.60. Transport’s strongest impact is on itself, partly reflecting how goods may arrive by one mode of transport before being shifted to another (containers shipped by boat from Asia are then carried by rail, while goods arriving by air are delivered by truck to their final destination). Transport also has strong linkages to manufacturing and finance. Recreation, especially gambling, draws on manufacturing and retailing.

Mining and utilities have the lowest multipliers in the goods sector at 1.41 and 1.30. Utilities, especially electric power, are relatively self-contained systems; while using some construction and manufactured goods, they have the lowest link with transportation, since utilities deliver power over their own grids. Mining requires lots of manufactured goods and finance for its capital-intensive production process, but buys few other services.⁷

While finance, insurance and real estate (FIRE for short in the tables and finance in the rest of this text) is a critical input for many industries, it uses relatively few inputs from other industries. In fact, excluding its demands on other financial firms, it has the smallest linkages with the rest of the economy. It consumes the fewest manufactured goods as a share of inputs and also requires little transportation or other services.

The two business services industries (professional, scientific and technical; and administrative and management) are virtually identical, which is why they are grouped together in this analysis. Their overall multipliers are about 1.50, with the largest input coming from within their own industries as well as finance.

Government (or public administration) services have a slightly larger multiplier at 1.48 than education and health care, but most of this difference reflects purchases from the health system. Government is unique in having health care as its largest input. It also has a relatively strong link to manufacturing.

Education and health care have two of the lowest multipliers at about 1.40, reflecting the self-contained nature of production in these sectors. Nearly half of the inputs they purchase from outside their own industry come from manufacturing and finance.

Retailing shows some surprising results. Its strongest impact is on finance, reflecting the role of credit in financing purchases. But its linkages to business services (0.09 points) are larger than to manufacturing (0.07), which in the IO system is no more important an input for retailers than government services. This is because retail trade in the IO calculation is a net measure of the retailing service: the costs of goods purchased for resale are subtracted from the value of retail sales. But then, buying these goods is not outsourcing of the production process by retailers, which is what the IO tables are used for in this paper.

The predominance of goods-producing industries with large multipliers reflects their high degree of interdependence with other industries, notably with each other and services such as transportation and finance. For example, manufactured goods are usually made of several standardised parts, which lends itself to outsourcing. As noted by Paul Krugman “the trend in manufacturing has been to slice up the value chain–to produce a good in a number of locations, adding a little bit of value at each stage”.⁸ This decomposition of production automatically raises their multiplier value. As well, these firms have led the way in contracting out services they need, ranging from advertising to building maintenance and even payroll systems. Similar results were found for the US, with manufacturing and other goods having the highest multipliers.⁹

Conversely, services tend to have low revenue multipliers, reflecting either a simpler production process with fewer linkages to other industries or a less standardised product.¹⁰ More health care and education, for example, triggers less additional demand for transportation and distribution than most goods do.

This underscores that multipliers do not necessarily reflect the complexity of the production process in an industry. Some industries are very complex operationally, but because they provide much of the work in-house, their contractual relationship with the rest of the economy is simpler and they have smaller multipliers. Multipliers are a guide to which industries are the most integrated with others, not which are the most valuable or productive.

Table 2 ranks the industry multipliers purely by their impact on other industries. Subtracting the feedback within the same industry gives a clearer appreciation of which industries have the strongest linkages to the rest of the economy.

The top and bottom rankings are essentially unchanged—primary industries, construction and accommodation and food lead the way, while finance, utilities, health and education trail. But there are some large shifts elsewhere. Notably, manufacturing tumbles 12 spots from fourth to sixteenth place. This reflects how increased manufacturing demand draws more output mostly from other factories and also leads other industries to order more manufactured goods. Information and culture drops seven places, partly because broadcasters buy extensively from each other. Transportation also slips five spots, but still remains above-average. No one industry moves up sharply in the rankings; most services rise two or three places, with the notable exceptions of the professional and technical and information industries.

Which industries supply the most inputs

Conventionally, multiplier analysis concentrates on inputs called forth from other industries–the sum of the vertical columns in Table 1. But summing across the rows is also a useful analytical tool, providing a rough measure of which industries are the most affected when other industries change output. Manufacturing and finance have the largest potential linkages. However, the actual number (over 3.0 in the case of these two industries) of the rows lacks the precise interpretation of multipliers, since it is unlikely that demand for more inputs from one particular industry will actually increase from every other industry at the same time and that demand would be evenly spread across all industries.

It is revealing to rank these industry inputs from other industries for every industry. Manufacturing and finance are the first or second largest input into almost all other industries. Only three out of 22 industries do not have manufacturing and finance ranked first or second (this excludes intra-industry relationships). The three exceptions are construction (which uses professional and technical services more than finance); finance (construction is ahead of manufacturing); and government (health care is ahead). And even in these three instances, manufacturing and finance are still in the top three.

Professional and technical services are needed nearly as ubiquitously as manufacturing and finance. They are consistently among the third or fourth largest input, with the exception of the primary sector. This reflects “the commoditisation of simple business services” such as tax preparation, human resources administration and especially information technology.¹¹

Other industries that consistently rank high as inputs include mining, transportation and wholesale trade. Mining’s links are confined to other goods, notably utilities, construction and manufacturing. Wholesale trade and transport also have strong connections to goods, reflecting their role in moving natural resources and manufactured goods to final users such as retailers and export markets.

Table 2: Revenue Multipliers With and Without Same-Industry Effects

Changes since 1986

Fifteen of the 22 industries increased their use of inputs from other industries between 1986 and 2002, most by a significant amount (see Table 3). For example, the multiplier for wholesalers rose from 1.41 to 1.56, which means that every $1 million in additional wholesale output generates $150,000 more revenue for other industries. Business services, information, retailing and utilities also posted sizeable increases. Of the six industries showing declines, two were insignificant (0.01). The largest declines were in education and the non-profit sector. Only two private sector industries posted decreases, and they were small changes.

Table 3: Revenue Multipliers, 1986 and 2002

The pervasive trend to higher multipliers suggests most private sector industries are specialising in their core area of expertise and purchasing other inputs. This is hardly a new phenomenon—it was Adam Smith’s major insight into the division of labour back in the 18th century.¹² This parallels a similar trend in international trade, with every sector of the economy using more imports in the production of exports.¹³ Indeed, the slight drop in domestic multiplier values for manufacturing appears to reflect this industry’s preference for more imported parts, not for in-house production: for example, nearly half of auto and electronic output is assembled from imported parts.

Whether outsourcing to other firms in Canada or offshoring to firms around the globe, the motivation is the same—to boost efficiency and lower costs. It is revealing that two of the six industries that did not outsource more were education and the non-profit sector, which are relatively insulated from the market forces pushing for more efficiency.¹⁴ The two public sector industries that did raise their use of other industries as inputs may have faced more pressure to do so because of downsizing of public administration in the 1990s and spiraling health care costs.

A side effect of these economy-wide changes was to narrow the gap between industries with extensive linkages and those with fewer. The six industries where multipliers shrank were all ranked in the top nine industries in 1986 with the most linkages to rest of the economy. The average decrease in multiplier values for industries with above-average linkages in 1986 was .05.

Conversely, 13 of the 14 industries with below-average multipliers in 1986 increased them over the next 15 years. These gains averaged 0.08 points, including the industries with the seven largest increases. The increase for information and culture was boosted by pay TV, while the rise for business services was widespread. One measure of the narrowing dispersion of multiplier values is the shrinking of the gap between the top and bottom from 0.81 to 0.67 points.

The increasing linkages between industries since 1986 were led by the growing use of business services. Summing up changes across the rows, they had a net gain of 0.54 points as an input into other industries, two-thirds of which was for professional and technical services. This reflects the emphasis on contracting out business-process operations (such as payroll administration) and computer services.¹⁵

Finance also posted a significant increase (.36 points). All industries except education used more business services and finance as inputs. Wholesale and retail trade also were purchased more often. Transportation was the only service industry that was used less as an input.

Some goods-producing industries were used less by other industries. Manufacturing fell the most (-.08 points), with nearly half the drop originating in education and manufacturing itself. Construction also saw a large drop in demand from education, presumably reflecting cuts to building and maintenance as demographic changes resulted in fewer students, triggering lower school capital budgets over this period. Utilities, forestry and fishing edged down (the latter two from already extremely low levels).

The increase in outsourcing also has implications for the analysis of industry shares in GDP. Industries such as manufacturing that have rapidly increased outsourcing (both here and abroad) will see their share of GDP decline as some work previously done in-house is transferred to other industries, especially services. Conversely, part of the growth of finance and business services in GDP in recent decades reflects this unbundling of work previously done in other industries, which is now contracted out. If the wholesale multiplier had not grown between 1986 and 2002 (and assuming all of the increase was due to outsourcing), GDP in wholesaling would have been $8.3 billion higher, equivalent to 0.7% of GDP.

While most industries have moved to more outsourcing, there is a limit to this trend. Firms are reluctant to contract out revenue-producing and strategic-planning activities. And many report growing dissatisfaction with their outsourcing experience.¹⁶

Revenue multipliers are often used to gauge the relative impact of different industries on overall GDP growth. This is misleading. Revenue multipliers show the linkages an industry has with others. Therefore, strategically placed industries—such a manufacturing, transport and finance—whose output is often used by others will have relatively high multipliers. But this does not mean that other industries, such as utilities and mining, do not make significant contributions to overall output. Manufacturers could not raise output without drawing more power from utilities. Utilities and mining also have among the largest value-added per employee in the economy. Therefore, increased output in these industries makes a large contribution to Canada’s overall output and productivity, even if their connections to other industries are relatively small. The next section on output multipliers captures these effects.

Output multipliers

Up to now, the focus has been on how output changes in one industry affect the revenues (or gross output) of all other industries. But what is the impact on overall GDP? Table 4 compares the conventional revenue multipliers with their GDP multipliers. The GDP multiplier reflects the increase in overall output in Canada from a change in output by a particular industry; the 0.77 value for agriculture means that $1 million in higher farming output would increase overall GDP by $770,000. The values are all less than 1.00 largely because of leakages to imports (shown in column 3). The $1 million rise in farming output, for example, boosts imports either directly (through higher imports of seed or farm machinery) or indirectly (increased demand by farmers for manufactured goods would increase imports used by factories). Unlike revenue multipliers, however, output multipliers do not show the interdependence between individual industries. They do show each industry’s use of imports.

Table 4: Revenue, GDP and Import Multipliers, 2002

The GDP multipliers are much lower—often only half the size of the revenue multiplier, and in the case of manufacturing just over one-third. This is because GDP multipliers take account of a number of additional factors. First, they remove all intermediate inputs included in the revenue multipliers. A major drawback of revenue multipliers is that while they correctly capture how an industry raising its output needs more inputs from a wide range of industries, they do not net out the purchases these industries subsequently make from each other. These intermediate inputs inflate the revenue multipliers by duplicating (or double-counting) inputs from one industry that are ultimately purchased from another. For example, higher auto output triggers more steel purchases which leads to increased demand for iron; without netting out these intermediate purchases, the value of the iron ore would be counted three times in the making of a vehicle.¹⁷

Second, output multipliers reflect the impact of higher output within each industry, and not just the ripple effect on other industries. This adjusts for the problem noted earlier that revenue multipliers are higher for industries with standardized production processes, which lend themselves to lots of linkages with other sectors (like manufacturing), and lower for industries that supply most of their inputs from within (such as mining and utilities).

While revenue multipliers do net out imports, GDP multipliers allow an explicit measure of the import content of production of each industry. This is especially important for manufacturing.

Table 5 compares the ranking of the 22 industries for revenue and output multipliers. For most, the difference is substantial, almost standing the results on their head. The seven industries with the largest revenue multipliers all tumble to the lower half for output multipliers. The largest drop is for agriculture, which plummets 20 places from first to twenty-first. Manufacturing slides from fifth to last place. Construction, forestry, and accommodation and food all post double-digit declines.

Figure 1

Conversely, a number of services industries move to the forefront for output multipliers. Finance and education jump from among the lowest revenue multipliers to the two largest output multipliers. Retail and wholesale trade and government follow close behind, compared with their mid-rank status for revenue multipliers. Administration and health care also rise nearly 10 places.

Utilities stands out among goods-producing industries, as its output multiplier ranked ninth versus its having the lowest revenue multiplier. Mining moved up slightly. While most services improved their standing, there were some exceptions. As noted earlier, accommodation and food fell 12 places. Recreation, information and transportation moved down about half a dozen spots.

Within manufacturing, computer and electronics had the lowest output multiplier of any industry, followed by motor vehicles (both are less than 0.4). This reflects the high import content of both industries. Several services have output multipliers above 0.9 (especially in finance and real estate), while oil and gas extraction is among the leaders for goods-producing industries at 0.9. These multipliers are particularly noteworthy in light of recent cutbacks by some auto firms and the rapid growth in the energy and financial sectors.

The GDP multipliers have fallen for 20 of the 22 industries over the last 15 years (education edged up while non-profit was unchanged). Most goods-producing industries posted slightly larger declines than services, perhaps because they can more easily use imports in their production. But the uniformity of declines is in striking contrast with the across-the-board increases for revenue multipliers. This adds weight to the idea that the increase in revenue multipliers was driven by a trend to outsourcing the provision of inputs to other firms in Canada.

Imports

A related factor is imports. Not only can manufacturers carve up their production process by purchasing from other firms in Canada, they can also import parts from abroad. As noted in our 2001 paper on the import content of exports, firms significantly increased this form of vertical dis-integration during the 1990s.

The import multiplier for each industry is shown in column 3 of Table 4. For example, every dollar that manufacturers raise output leads them to directly or indirectly import 37.7 cents more, sharply reducing their impact on Canada’s GDP. Most other goods-producing industries (construction, farming, forestry and fishing) have import multipliers of about 0.2. Conversely, mining and utilities have the lowest import content among goods at about 10%, below many services.

Finance and education have the smallest import content, at just 4% and 6% respectively. Other services with import content of only about 10% include health care, professional and technical services and wholesale and retail trade. There are a few services with a higher import content than the bottom-ranked goods, including transportation and accommodation and food (all around 15%).

Conclusion

This paper has demonstrated some of the different analytical uses of multipliers. Revenue multipliers show the inter-connections between industries at a micro level. Changes in these multipliers over time shed light on structural shifts in how firms are re-organizing their operations.

However, revenue multipliers exaggerate the importance of industries with complex contractual and production relationships with other industries. GDP multipliers take account of this problem, virtually reversing the ranking of which industries have the largest impact on other industries.

Multiplier analysis has its limitations. It does not take into account the macroeconomic determinants of overall output and employment, such as interest rates and the exchange rate, which could be affected by any significant change in output in major industries. Finally, multipliers do not take account of capacity constraints or consumption of capital.

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