Analytical Studies Branch Research Paper Series
Technological Frontiers and Post-2000 Productivity Growth in Canada

by Jianmin Tang and Weimin Wang
11F0019M No. 438
Release date: January 17, 2020

Acknowledgements

This is an abridged version of a longer research paper by the same authors. The authors would like to thank Christopher O’Donnell, Giuseppe Nicoletti, Danny Leung, Larry Shute and Pierre Therrien for their insightful comments and suggestions. The opinions expressed in this paper are those of the authors alone and do not represent—in any way—the views of Innovation, Science and Economic Development Canada, Statistics Canada, or the Government of Canada.  

Abstract

To better understand the movements in productivity during the post-2000 period in Canada, this paper applies the stochastic frontier framework to decompose each firm’s multifactor productivity into two parts: its technological frontier and its technical efficiency. Change in the aggregate technological frontier refers to improvements in the productivity potential of the economy, or the maximum productivity of the economy if all firms are fully efficient. Aggregate technical efficiency reflects the economy’s capacity to achieve that potential. Given that the drivers of these two sources of productivity growth are different, the decomposition sheds light on the factors that can account for changes in productivity. The empirical results show that changes in productivity since 2000 were mainly attributable to changes in the technological frontier. While an association is found between investments in research and development (R&D) and changes in the technological frontier, R&D accounts for only a small fraction of the change in the technological frontier over time. 

Keywords: productivity slowdown, stochastic frontier, productivity frontier, technical efficiency

Executive summary

Multifactor productivity (MFP) declined in Canada from 2000 to 2009 and then recovered after. The movements in productivity since 2000 have attracted great attention from researchers and policy makers because productivity is important both for economic growth and for improvements in living standards.

This paper applies the stochastic frontier framework to decompose each firm’s MFP into two parts: its technological frontier and its technical efficiency. Change in the aggregate technological frontier refers to improvements in the productivity potential of an economy, i.e., the maximum productivity of an economy if all firms are fully efficient. Aggregate technical efficiency reflects the economy’s capacity to achieve that potential. The results of this decomposition can show whether the movements in productivity after 2000 in Canada were mainly the result of changes in the technological frontier and productivity potential or of changes in the technical efficiency.

This study uses the National Accounts Longitudinal Microdata File, which is a rich analytical dataset derived from various administrative sources. It contains major variables that are considered to be important for productivity analysis, including measures of gross output, labour input, physical capital (including information and communications technology capital), intangible capital (including research and development [R&D] and organizational capital), capacity utilization and intermediate inputs.

The results show that changes in productivity in Canada since 2000 were mainly attributable to changes in the technological frontier, and these changes cannot be largely explained by the factors most commonly associated with enabling greater productivity potential (e.g., investments in R&D).

To better understand changes in the technological frontier, the firms were divided into three groups: firms with higher-than-average MFP levels from 2000 to 2002, firms with lower-than-average MFP levels from 2000 to 2002 and firms that entered after 2002. Empirical results show that the overall movements of the technological frontier were mainly associated with the firms in the 2000-to-2002 cohort with high MFP levels.

1 Introduction

Multifactor productivity (MFP) in Canada started to decline in 2002, and the decline continued until 2009, with some recovery afterwards (Chart 1). This decline is not unique to Canada: it is widespread across many member countries of the Organisation for Economic Co-operation and Development, including other G7 economies. The productivity growth slowdown was dramatic and has attracted great attention from researchers and policy makers, as it has important implications for economic growth and prosperity. 

However, despite extensive research, the causes of the productivity slowdown are still subject to debate (Murray 2017). Various arguments and counterarguments on both supply and demand sides have been put forward. On the supply side, Gordon (2012) argues that the productivity growth deceleration is the result of a slowdown in important innovation and diminishing returns from the innovation process. Consistent with Gordon’s view is the suggestion that the decline is attributable to a waning of the productivity boom related to information and communications technology (ICT), which took place in the second half of the 1990s (e.g., Remes et al. 2018). However, Gordon’s pessimistic view has been challenged (Sichel 2016). Byrne, Oliner and Sichel (2015) provided evidence that ICT-related technological progress has continued at a rapid pace since 2000. According to Syverson (2013), there has been no evidence that ICT-related productivity improvements have been exhausted. 

Similar to the supply-side debate, the debate from the demand side has also gained significant traction. It has been asserted that weak aggregate demand, great uncertainty and financial market disruption because of the financial crisis, which led to the underutilization of production capacity and lower investments in productivity-enhancing activities (e.g., ICT and research and development [R&D]), could lead to a reduction in productivity (e.g., Remes et al. 2018). However, Fernald (2014) indicates that it is not likely that the post-2000 productivity slowdown was driven by demand, given that the decline started several years before the financial crisis. Some researchers even suggest that reverse causality might actually be at play, i.e., the expectation of lower future productivity and economic growth might cause weak demand (Blanchard, Lorenzoni and L’Huillier 2017).

Productivity is commonly measured as the Solow residual. It measures technological progress, but also reflects measurement errors in both output and inputs and captures any unmeasured factors that are important to productivity. As such, some commentators suggest that mismeasurement associated with the digital economy might play a role in the productivity slowdown. It has been suggested that current output estimates do not fully capture the services provided through ICT and other related technologies. However, subsequent research has shown that the measurement issue was not as important of a factor (e.g., Byrne, Fernald and Reinsdorf 2016; Ahmad and Schreyer 2016; Syverson 2016; Gu 2018). 

Chart 1 Multifactor productivity in the Canadian business sector, 1990 to 2016

Data table for Chart 1 
Data table for Chart 1
Table summary
This table displays the results of Data table for Chart 1 Multifactor productivity, calculated using index (2000=100) units of measure (appearing as column headers).
Multifactor productivity
index (2000=100)
1990 92.92
1991 90.38
1992 91.04
1993 92.01
1994 94.44
1995 94.76
1996 93.81
1997 95.03
1998 95.60
1999 97.85
2000 100.00
2001 99.92
2002 100.97
2003 100.22
2004 99.86
2005 99.87
2006 99.06
2007 97.95
2008 95.70
2009 93.25
2010 94.92
2011 96.34
2012 95.77
2013 96.42
2014 97.81
2015 96.83
2016 96.91

There has been no strong empirical evidence of what caused the slowdown in productivity growth after 2000. This paper continues to search for answers. The National Accounts Longitudinal Microdata File (NALMF)—a rich analytical dataset derived from various administrative sources—was used to systematically study the causes of the productivity slowdown in Canada. Major factors that are considered to be the most important for productivity were considered simultaneously, including firm age; foreign ownership; industry structure; capacity utilization; and investments in R&D, ICT and intangibles.

Unlike most of the literature that focuses on actual productivity directly and implicitly assumes that all firms are efficient, this paper applies the stochastic frontier production framework to decompose productivity into the components of technological change and technical efficiency. Technological change measures productivity potential (or the maximum level of productivity under full efficiency), while technical efficiency reflects the ability and capacity to achieve that potential. Variations in efficiency could arise because of variations in capacity utilization over the business cycle or because of differences in managerial practices across firms that are influenced by incomplete markets; asymmetric information; different management incentive payment systems; and different cultural beliefs, traditions and expectations. In addition, they may be the result of firm-level differences in investments in efficiency-enhancing technologies, such as ICT.

Importantly, this decomposition facilitated an analysis to help better understand the determinants of actual productivity. The factors that affect the technological frontier are different from those that influence technical efficiency. This separation makes it possible to link factors directly to one of the two components. 

The rest of this paper is organized as follows: Section 2 describes the stochastic frontier model, the factors that are important for technological change and technical efficiency, and the data. Empirical results and implications are discussed in Section 3. Section 4 examines trends in the technological frontier of high- and low-productivity firms in the 2000-to-2002 cohort and in that of firms that entered after 2002. Section 5 concludes.

2 Methodology and data

This paper decomposes actual productivity into technological change and technical efficiency based on the stochastic frontier model that was pioneered by Aigner, Lovell and Schmidt (1977).Note  Technological change refers to improvements in the productivity potential of the economy, i.e., the maximum productivity of the economy if all firms are fully efficient. In the stochastic frontier framework, this maximum productivity is called the technological frontier. The technological frontier is mainly driven by internal technological or innovative capacity, which feeds on a firm’s own past and current investments in R&D (Aghion and Howitt 1992). Therefore, after external factors are controlled for, the technological frontier of a firm reflects its past and current internal R&D. Some other variables may also have an impact on the technological frontier of a firm—the first being foreign ownership. Generally, foreign-controlled firms in Canada are significantly more productive than Canadian-controlled firms after other factors are controlled for. The foreign ownership productivity advantage is real and significant in Canada. It is generally believed that this advantage arises because foreign-controlled firms in Canada have access to the advanced technologies and superior management practices of their parent firms (Rao, Souare and Wang 2009; Tang and Rao 2003). The second factor is industry–year dummies. Industry–year dummies are introduced to control for all time-variant and time-invariant industry-specific effects. For example, they capture industry-specific demand shocks, spillover effects (such as those from external R&D) and effects from changes in the business environment, including competition and business dynamism (e.g., entry and exit).

Technical efficiency reflects the economy’s ability to be at the technological frontier. Technical efficiency has to be maintained or enhanced through the adoption of technology and investments in firm-specific human, knowledge and business organizational capital. Technical efficiency can also be affected by changes in the utilization rate of inputs when demand conditions fluctuate. In this paper, technology adoption was measured by investments in ICT, including software. The adoption of ICT allows firms to more efficiently organize their inputs, manage their inventories and conduct international business activities (Biagi 2013).

Investments in skills and better management practices are represented by investments in intangible, firm-specific human, knowledge and business organizational capital. Intangible capital enables efficient business execution (e.g., Battisti, Belloc and Del Gatto 2012). Corrado, Hulten and Sichel (2009) showed that these intangibles played a significant role in economic growth in the United States. Likewise, Baldwin, Gu and Macdonald (2012) obtained similar results for Canada. Furthermore, Ilmakunnas and Piekkola (2014) also linked investments in intangibles to higher productivity performance in Finland.

Firm-specific skills and organizational capital may also be improved through learning by doing, especially for young firms or start-ups. Therefore, a dummy variable is used to reflect the potential efficiency deficit facing young firms. Young firms are generally believed to be less efficient than established firms, as it takes time for young firms to learn their markets, establish supplier and distribution networks, and develop scale. According to Liu and Tang (2017), entrants take about five years to become as productive as incumbents.

Capacity utilization is used to capture the influence of changes in demand conditions on technical efficiency. An unexpected change in demand conditions affects the utilization of production capacity as firms are unable to adjust installed machines or even their workforce to suit the new demand. For example, a significantly lower demand than expected will lead to the underutilization of production capacity, which means that workers may not work to their full capacity and machines may sit idle more often than before. This leads to inefficiency. Basu and Kimball (1997) showed that changes in capacity utilization could explain up to 60% of short-run economic fluctuation. Baldwin, Gu and Yan (2013) showed that the Canadian manufacturing sector experienced excess capacity after 2000, with a decline in capacity utilization in 16 of the 20 manufacturing industries. This suggests that the development of excess capacity was mainly attributable to the large decline in exports as a result of the change in the trade environment during that period.

The stochastic frontier regression model can be written as

ln ( gross output ) = α 0 + α L ln ( labour ) + α K ln ( capital ) + α M ln ( intermediate ) + β R ln ( R&D ) + β Z Z + v u ,        with    u = γ 0 + γ X X (1) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaaciGGSb GaaiOBaiaacIcacaqGNbGaaeOCaiaab+gacaqGZbGaae4Caiaabcca caqGVbGaaeyDaiaabshacaqGWbGaaeyDaiaabshacaGGPaGaaCjaVl abg2da9iabeg7aHnaaBaaaleaacaaIWaaabeaakiabgUcaRiabeg7a HnaaBaaaleaacaWGmbaabeaakiGacYgacaGGUbGaaiikaiaabYgaca qGHbGaaeOyaiaab+gacaqG1bGaaeOCaiaacMcacqGHRaWkcqaHXoqy daWgaaWcbaGaam4saaqabaGcciGGSbGaaiOBaiaacIcacaGGJbGaai yyaiaacchacaGGPbGaaiiDaiaacggacaGGSbGaaiykaiabgUcaRiab eg7aHnaaBaaaleaacaWGnbaabeaakiGacYgacaGGUbGaaiikaiaacM gacaGGUbGaaiiDaiaacwgacaGGYbGaaiyBaiaacwgacaGGKbGaaiyA aiaacggacaGG0bGaaiyzaiaacMcaaeaacqGHRaWkcqaHYoGydaWgaa WcbaGaamOuaaqabaGcciGGSbGaaiOBaiaacIcacaqGsbGaaeOjaiaa bseacaGGPaGaey4kaSIaaCOSdmaaBaaaleaacaWGAbaabeaakiaahQ facqGHRaWkcaWG2bGaeyOeI0IaamyDaiaabYcacaqGGaGaaeiiaiaa bccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabEhacaqGPbGaae iDaiaabIgacaqGGaGaaeiiaiaabccacaWG1bGaeyypa0Jaeq4SdC2a aSbaaSqaaiaaicdaaeqaaOGaey4kaSIaaC4SdmaaBaaaleaacaWGyb aabeaakiaahIfaaaaa@9A17@

where Z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbeaeaaaaaa aaa8qacaWFAbaaaa@36FB@  is a vector of variables controlling for the effects of external factors on the technological frontier, v MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWG2baaaa@3711@  is a random error term reflecting the stochastic nature of the technological frontier, u MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWG1baaaa@3710@  is a measure of technical inefficiency or the distance to the production possibility frontier,Note  and X MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbeaeaaaaaa aaa8qacaWFybaaaa@36F9@  is a vector of the covariates that may affect technical efficiency.

The data used in this paper come from the NALMF. The data cover all industries from 2000 to 2014. The NALMF’s source data come from tax files (T2 Corporation Income Tax Return, T4 Statement of Remuneration Paid and PD7 Payroll Account Deductions); the Business Register; and the Survey of Employment, Payrolls and Hours. The T2 Corporation Income Tax Return form can be used to derive a firm’s gross output, physical capital stock and intermediate inputs, as well as its ICT capital stock, R&D investment and spending on intangibles. R&D capital stock and intangible capital stock are then derived using the perpetual inventory method. The other source data provide payroll and employment information, foreign ownership indicators, and the year a firm was founded.

Nominal variables need to be deflated for over-time comparisons. Because of the lack of deflators at the firm level, detailed industry-level deflators from the KLEMS database were used.Note  The deflator for R&D is the implicit price index for R&D investments derived from Statistics Canada table 36-10-0098-01.Note   

Tangible capital stock includes assets associated with machinery, equipment and buildings. It includes ICT stock, but excludes intangible assets and R&D stocks. The R&D stock for each firm is estimated from real R&D investments using the perpetual inventory method, assuming a capital depreciation rate of 15%. R&D expenditures were derived from the Scientific Research and Experimental Development Program data included in the T2 Corporation Income Tax Return. Following Corrado, Hulten and Sichel (2005, 2009), spending on intangible assets consists of non-scientific innovative properties (architect fees) and economic competencies that include organizational capital (20% of director and management salaries plus consulting fees), brand equity (60% of advertising) and firm-specific human capital (training). These six items were obtained directly from the General Index of Financial Information included in the T2 Corporation Income Tax Return. Nominal intangible spending was deflated using an industry-level implicit price deflator for intermediate inputs (from KLEMS). The perpetual inventory method was used for estimating intangible capital stock from real intangible spending, assuming a 15% depreciation rate. Total capital stock equals the sum of all tangible, intangible and R&D capital stocks.

A dummy variable was introduced to determine whether young firms were more or less efficient than established ones. According to Liu and Tang (2017), entrants in Canada take about five years to become as efficient as incumbents. Therefore, the dummy variable equalled 1 if a firm was less than six years old and equalled 0 otherwise. Lastly, capital use intensity was calculated with adjustment for the input substitution effectNote  as an indicator of capacity utilization.

For the estimation, the sample was restricted to include only firms with an average of 10 or more employees over the sample period. The average number of employees per firm was used instead of the number of employees in each year to avoid truncated observations for the firms in the sample. The restricted sample represents 88% and 83% of gross output and employment in Canada, respectively. With this restriction, there were nearly 1.9 million observations for the entire sample period (Table 1). 


Table 1
Distribution of sample observations (firms with 10 or more employees in the businness sector)
Table summary
This table displays the results of Distribution of sample observations (firms with 10 or more employees in the businness sector). The information is grouped by NAICS industry (appearing as row headers), 2000, 2005, 2009, 2014 and 2000 to 2014, calculated using number of observations units of measure (appearing as column headers).
NAICS industry 2000 2005 2009 2014 2000 to 2014
number of observations
Crop and animal production 738 727 716 572 10,772
Forestry and logging 730 714 625 492 9,715
Fishing, hunting and trapping 61 77 77 68 1,096
Support activities for agriculture and forestry 358 423 426 406 6,148
Oil and gas extraction 204 226 216 178 3,139
Mining and quarrying (except oil and gas) 304 285 279 266 4,257
Support activities for mining, and oil and gas extraction 688 786 853 736 11,425
Utilities 147 219 186 182 2,840
Construction 11,625 12,986 13,608 13,968 197,518
Food manufacturing 2,139 2,084 1,959 1,856 30,174
Beverage and tobacco manufacturing 162 148 145 177 2,304
Textile and textile product mills 583 505 377 314 6,653
Clothing, leather and allied product manufacturing 1,217 947 624 411 12,071
Wood product manufacturing 1,586 1,571 1,443 1,251 22,150
Paper manufacturing 448 395 324 262 5,351
Printing and related support activities 1,180 1,135 1,011 837 15,693
Petroleum and coal product manufacturing 81 80 51 40 935
Chemical manufacturing 789 734 685 645 10,725
Plastics and rubber products manufacturing 1,202 1,176 1,074 1,026 16,783
Non-metallic mineral product manufacturing 716 741 676 616 10,409
Primary metal manufacturing 322 318 304 265 4,553
Fabricated metal product manufacturing 3,116 3,148 2,951 2,762 45,426
Machinery manufacturing 1,979 2,004 1,884 1,750 28,777
Computer and electronic product manufacturing 869 802 745 616 11,476
Electrical equipment, appliance and component manufacturing 461 459 425 385 6,561
Transportation equipment manufacturing 930 904 835 721 12,704
Furniture and related product manufacturing 1,334 1,384 1,261 1,100 19,418
Miscellaneous manufacturing 1,022 1,117 1,033 965 15,706
Wholesale trade 12,094 11,856 11,441 10,555 173,753
Retail trade 18,902 20,072 19,845 18,968 294,953
Transportation and warehousing 5,625 5,791 5,546 5,406 84,463
Information and cultural industries 1,963 1,954 1,891 1,952 29,269
Finance, insurance, real estate and company management 7,206 7,257 7,323 6,777 107,248
Professional, scientific and technical services 7,475 8,227 8,215 7,592 120,297
Administrative and support, waste management and remediation services 5,440 6,528 7,021 6,982 99,274
Arts, entertainment and recreation 2,400 2,879 2,920 2,844 42,100
Accommodation and food services 17,559 20,062 21,386 22,742 310,793
Other services (except public administration) 5,360 6,789 7,752 8,053 106,460
All industries 119,015 127,510 128,133 124,738 1,893,389

There are two reasons why small firms were excluded. First, the derivation of the major variables necessary for productivity analysis involves the use of fields in the source data that are not mandatory. For smaller firms with less economic activity, these data fields are often left blank. The second reason is technical—it is time consuming to use all firms for the estimation, as there were more than 9 million observations before the exclusion.Note 

Despite this exclusion, the estimates of aggregate MFP based on the sample used for the estimation of (1) track the movements of the official estimates of MFP for the business sector closely (Chart 2). The sample-based MFP measure aggregated firm-level MFP using Domar weights. These Domar weights were calculated as the ratio of a firm’s nominal gross output over the business sector’s nominal value added. The MFP at the firm level was calculated as a residual of gross output minus contributions from labour, capital and intermediate inputs. The output elasticities with respect to all inputs were obtained using ordinary least squares (OLS), controlling for industry–year dummies.Note 

Chart 2 Sample-based and official multifactor productivity estimates in the business sector

Data table for Chart 2 
Data table for Chart 2
Table summary
This table displays the results of Data table for Chart 2 Sample estimates and Official estimates, calculated using index (2000=100) units of measure (appearing as column headers).
Sample estimates Official estimates
index (2000=100)
2000 100.00 100.00
2001 103.91 99.92
2002 104.21 100.97
2003 96.26 100.22
2004 97.54 99.86
2005 97.79 99.87
2006 94.45 99.06
2007 93.91 97.95
2008 92.54 95.70
2009 89.27 93.25
2010 93.82 94.92
2011 92.97 96.34
2012 97.04 95.77
2013 100.56 96.42
2014 102.07 97.81

The movements of the two series were generally consistent. The series based on the sample used for estimation was more volatile than the official one—both the decline after 2002 and the recovery after 2009 were more dramatic. The difference may be attributable to a number of factors. First, the elasticity of output with respect to inputs used in calculating MFP for the sample used in the estimation was regression-based and fixed over the estimation period, while that for the official estimates was based on growth accounting and was time varying. Second, small firms were excluded from the sample. Third, the MFP calculation for the sample used in the estimation did not adjust for capital quality and labour composition, while the official MFP estimates did. Lastly, the MFP calculation for the sample used in the estimation was Domar-aggregated at the firm level. The official estimates were Domar-aggregated from industry-level data. These industry-level data came from a greater number of data sources than are used in the NALMF.

3 Estimation results

The stochastic frontier estimation results are reported in Table 2. The first regression is for the whole sample period and for all firms with 10 or more employees. For the technological frontier, the results show that R&D investments and foreign ownership are important for raising productivity potential. For inefficiency, all variables were found to be negative and highly significant, meaning that firms with more investments in ICT and intangibles, as well as young firms, tend to be closer to their technological frontiers.Note  Furthermore, as expected, capacity utilization is positively associated with technical efficiency.

Interestingly, the estimated coefficients of all variables based on the stochastic frontier model (regression [1]) in Table 2) were similar to the results of some traditional regressions.Note  Implicitly, the similarity is a robustness check of the results from the stochastic frontier estimation.Note 

Regressions (2) and (3) in Table 2 are for the sub-periods from 2009 to 2014 and from 2000 to 2009, respectively. The purpose was to determine whether the effect of any of those factors changed significantly over these two sub-periods. Overall, there were no significant changes for R&D, foreign ownership, ICT and intangibles. However, the efficiency advantage of young firms over established firms was greater after the financial crisis. This is an interesting result, and may be because only high-efficiency and productive firms can enter the market after the financial crisis. 

Regressions (4) and (5) are for manufacturing and non-manufacturing firms, respectively. These two sets of results are generally similar. However, the impact of R&D and foreign ownership on manufacturing firms was smaller than on non-manufacturing firms. The same is true for the effect of ICT on technical efficiency. In addition, the efficiency advantage of young firms was larger in manufacturing than in non-manufacturing.

Given the general consistency across all columns in Table 2, the discussion and analysis to follow will be based on the estimation results in Column 1 of Table 2.


Table 2
Stochastic frontier estimation of the production function
Table summary
This table displays the results of Stochastic frontier estimation of the production function Regression 1, Regression 2, Regression 3, Regression 4 and Regression 5 (appearing as column headers).
Regression 1 Regression 2 Regression 3 Regression 4 Regression 5
All firms
2000 to 2014
All firms
2009 to 2014
All firms
2000 to 2009
Manufacturing firms
2000 to 2014
Non-manufacturing firms
2000 to 2014
Technological frontier
Labour (in log)
Coefficient 0.2780Note ** 0.2921Note ** 0.2699Note ** 0.2367Note ** 0.2821Note **
Standard error 0.0003 0.0005 0.0004 0.0007 0.0003
Tangible capital (in log)
Coefficient 0.0647Note ** 0.0623Note ** 0.0664Note ** 0.0716Note ** 0.0643Note **
Standard error 0.0002 0.0003 0.0002 0.0005 0.0002
Intermediate inputs (in log)
Coefficient 0.6455Note ** 0.6361Note ** 0.6500Note ** 0.6814Note ** 0.6410Note **
Standard error 0.0002 0.0004 0.0003 0.0005 0.0003
R&D stock (in log)
Coefficient 0.0049Note ** 0.0044Note ** 0.0053Note ** 0.0013Note ** 0.0068Note **
Standard error 0.0001 0.0001 0.0001 0.0001 0.0001
Foreign-owned
Coefficient 0.2025Note ** 0.2140Note ** 0.1960Note ** 0.1106Note ** 0.2279Note **
Standard error 0.0015 0.0021 0.0020 0.0021 0.0018
Industry dummy variables Yes Yes Yes Yes Yes
Year dummy variables Yes Yes Yes Yes Yes
Year by industry dummy variables Yes Yes Yes Yes Yes
Inefficiency
Ratio of ICT to total capital stock
Coefficient -0.2600Note ** -0.2564Note ** -0.2635Note ** -0.1418Note ** -0.2663Note **
Standard error 0.0018 0.0030 0.0022 0.0064 0.0019
Ratio of intangibles to total capital stock
Coefficient -0.2242Note ** -0.2279Note ** -0.2235Note ** -0.1974Note ** -0.2271Note **
Standard error 0.0013 0.0021 0.0016 0.0033 0.0014
Young firms
Coefficient -0.0087Note ** -0.0183Note ** -0.0039Note ** -0.0291Note ** -0.0056Note **
Standard error 0.0006 0.0011 0.0007 0.0013 0.0007
Capacity utilization
Coefficient -0.0408Note ** -0.0450Note ** -0.0385Note ** -0.0413Note ** -0.0410Note **
Standard error 0.0004 0.0008 0.0005 0.0008 0.0005
Constant Yes Yes Yes Yes Yes
Number of observations 1,893,389 764,016 1,257,506 277,869 1,615,520

Elasticities of technological change or technical efficiency with respect to each factor were estimated to determine their sensitivity to control factors. The estimated elasticities are reported in Table 3. The results show that doubling R&D—for example—would lead to a 0.5% increase in the technological frontier. Furthermore, foreign-owned firms are—on average—20.3% more productive than a domestic firm. For technical efficiency, if the ratio of ICT to total capital and the ratio of intangibles to total capital are doubled, efficiency would increase by 1.8% and 2.7%, respectively. In addition, young firms have a 0.9% efficiency advantage over established firms, and a 10% increase in capacity utilization would increase efficiency by 0.4%. Given these elasticities, even when all firms doubled their R&D, ICT and intangible capital stock over the period from 2002 to 2009, the drop in MFP over the period can be reduced by 5 percentage points only, leaving a large portion of the decline unexplained. 


Table 3
Average elasticities of technological change or technical efficiency with respect to their factors
Table summary
This table displays the results of Average elasticities of technological change or technical efficiency with respect to their factors. The information is grouped by Factor (appearing as row headers), Elasticity, calculated using coefficient units of measure (appearing as column headers).
Factor Elasticity
coefficient
Technological change with respect to its factors
Research and development 0.0049
Foreign-controlled 0.2025
Technical efficiency with respect to its factors
Ratio of information and communications technology to total capital 0.0181
Ratio of intangibles to total capital 0.0272
Young firm 0.8698
Capacity utilization 0.0408

Changes in MFP, technological frontier and technical efficiency at the firm level were aggregated using Domar weights. The indexes of the business-sector MFP, technological frontier and technical efficiency are depicted in Chart 3, which shows that the movement of MFP was largely driven by the movement of the technological frontier, while technical efficiency was relatively stable over the whole period.

Chart 3 Multifactor productivity, technological change and technical efficiency in the business sector

Data table for Chart 3 
Data table for Chart 3
Table summary
This table displays the results of Data table for Chart 3 Multifactor productivity, Technical efficiency and Technological change, calculated using index (2000=100) units of measure (appearing as column headers).
Multifactor productivity Technical efficiency Technological change
index (2000=100)
2000 100.00 100.00 100.00
2001 103.29 97.45 105.99
2002 103.10 97.42 105.83
2003 95.37 97.83 97.49
2004 97.27 97.58 99.69
2005 97.32 96.88 100.46
2006 94.15 97.27 96.79
2007 93.22 97.97 95.15
2008 91.39 98.22 93.04
2009 87.11 95.78 90.95
2010 92.43 97.56 94.75
2011 91.32 96.74 94.39
2012 95.16 96.86 98.24
2013 98.66 97.87 100.81
2014 100.18 98.25 101.96

4 The movement of high-productivity and low-productivity cohorts

To shed more light on the productivity slowdown, firms in the 2000-to-2002 cohort were divided into two groups.Note  The high-productivity group consisted of firms with MFP levels higher than the corresponding industry averages over the period from 2000 to 2002, and all of the remaining firms in the cohort were in the low-productivity group. All firms that appeared after 2002 were considered new entrants. 

Chart 4 shows the trends in the technological frontiers of the three groups of firms. The technological frontier increased across the entire sample for the low-productivity cohort, but declined for the other two groups until 2009, implying that the retreat of the technological frontier was driven by the high-productivity cohort and the new entrants. As shown in Table 4, the aggregate technological frontier dropped by 7.0% from 2003 to 2009. The contributions of the high-productivity cohort, the low-productivity cohort and the new entrants were -8.4, 4.9 and -3.5 percentage points, respectively. The technological frontier fully recovered after 2009, and the corresponding contributions were 7.0, 4.2 and 0.7 percentage points. These results suggest that the retreat of the technological frontier was mainly driven by the high-productivity firms in the 2000-to-2002 cohort.


Table 4
Contribution of high-productivity and low-productivity cohorts and new entrants to growth in technological frontier
Table summary
This table displays the results of Contribution of high-productivity and low-productivity cohorts and new entrants to growth in technological frontier 2003 to 2009 and 2009 to 2014, calculated using percent and percentage points units of measure (appearing as column headers).
2003 to 2009 2009 to 2014
percent
Change in technological frontier -7.0 11.9
percentage points
Contribution
High-productivity cohort -8.4 7.0
Low-productivity cohort 4.9 4.2
Entrants after 2002 -3.5 0.7

Chart 4 Trends in the technological frontiers of high-productivity and low-productivity cohorts and new entrants in the business sector

Data table for Chart 4 
Data table for Chart 4
Table summary
This table displays the results of Data table for Chart 4 High-productivity cohorts, Low-productivity cohorts and New entrants, calculated using index (2003=100) units of measure (appearing as column headers).
High-productivity cohorts Low-productivity cohorts New entrants
index (2003=100)
2000 108.54 95.44 Note ...: not applicable
2001 116.64 99.34 Note ...: not applicable
2002 115.65 100.11 Note ...: not applicable
2003 100.00 100.00 100.00
2004 99.87 105.76 91.93
2005 99.15 109.78 84.55
2006 92.23 111.93 76.17
2007 94.33 107.19 69.07
2008 92.98 104.54 66.01
2009 83.73 113.35 64.35
2010 90.80 114.61 64.51
2011 88.18 115.52 66.58
2012 95.47 117.30 66.55
2013 98.67 119.97 67.50
2014 97.50 126.61 66.56

5 Conclusion

By decomposing actual productivity into technological frontier (or technology-related productivity potential) and technical efficiency, the empirical results of this study show that the decline in Canada’s productivity from 2000 to 2009 and the subsequent recovery were largely associated with changes in the technological frontier.

This paper shows that (1) R&D investments and foreign-controlled firms in particular played important roles in supporting the technological frontier, while industrial structure played a minor negative role; (2) ICT and intangibles played a positive role in supporting technical efficiency.

In addition, this study demonstrates that movements in productivity in Canada after 2000 were largely associated with the high-productivity firms in the 2000-to-2002 cohort. This evidence is consistent with the findings in the literature for the Canadian manufacturing sector. The post-2000 productivity decline in the Canadian manufacturing sector was mainly the result of a decline in the productivity of large firms (Tang 2017) or exporters (Baldwin, Gu and Yan 2013). However, Baldwin, Gu and Yan (2013) also claimed that at least half of the productivity decline was attributable to the pro-cyclical nature of productivity growth arising from capacity utilization, but this was not the case in this paper. A future study of the causes of the weak productivity performance of large and exporting firms may shed more light on the productivity slowdown in Canada.

It is important to note that technological frontier and frontier firm are different concepts. The former is associated with each firm’s technological potential, while the latter refers to high-productivity firms and is often used to examine the productivity dispersion between frontier and non-frontier firms.Note  Gu, Yan and Ratté (2018) found that the relative labour productivity level of frontier-to-non-frontier firms in Canadian manufacturing decreased from 2000 to 2005 and increased thereafter, implying that the aggregate productivity growth was mainly driven by frontier firms. This is generally consistent with the findings in this paper.

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