Abstract
This Selected Issues paper reviews Canada’s business tax system, looking at the incentive effects of the country’s business tax regime and their implications for output and employment. It presents estimates of marginal effective tax rates on corporate-source income in Canada and comparator countries across sectors, asset classes, means of finance, and asset ownership. The paper also examines labor markets in Canada. It notes that unemployment rates in Canada have risen across all demographic groups, industries, and regions, although young and less-educated workers and workers in agriculture and primary industries have been most severely affected.
IV. Developments in Productivity Across Industries in Canada1
A. Introduction
1. Since the mid-1970s, real output and productivity growth in Canada have slowed (Chart 1). From 1962 to 1973, real GDP grew at an average annual rate of 5.4 percent, and labor productivity grew by 3.3 percent. However, from 1973 through 1995, average annual real GDP and labor productivity growth have decreased to 2.6 percent and 1.1 percent, respectively. Previous studies on Canadian growth have inconclusively identified some causes for the slowdown, including intersectoral shifts of output and labor toward services and other industries with lower productivity growth, a lack of technological progress in several mature industries, an increase in the obsolescence of capital due to the regulatory environment and structural changes in the economy, and a reduction in the benefits from increasing scale.2 Also, the rate of growth of the capital-labor ratio has decreased in Canada.
CANADA AND UNITED STATES: GDP, LABOR PRODUCTIVITY, AND CAPITAL-LABOR RATIOS
Citation: IMF Staff Country Reports 1997, 020; 10.5089/9781451806847.002.A004
Sources: Statistics Canada; Bureau of Economic Analysis, U.S. Department of Commerce; and Bureau of Labor Statistics, U.S. Department of Labor.2. Slower growth has not been limited to Canada. Most OECD countries have experienced similar phenomena. In the United States, for example, average annual real GDP and labor productivity growth have declined, respectively, from 4.2 percent and 3.1 percent in 1962–1973 to 2.5 percent and 1.2 percent in 1973–1995 (see Chart 1). Studies of the U.S. economy have attributed the slowdown to similar causes as in Canada. An over hiring of labor (relative to other industrial countries) due to a falling real minimum wage has also been cited as a factor in the United States.3 In addition, Griliches (1994), Gordon (1996), and Slifman and Corrado (1996) emphasize that measured output and productivity growth may be biased downward, and therefore, the slowdown may not be as large as suggested by the data.4 This may be the case in Canada as well.
3. One significant difference between the two countries has been productivity in the manufacturing sector. In the United States, manufacturing labor productivity growth decreased in the 1970s but has increased subsequently and returned to levels close to those observed in the 1960s. In Canada, however, the slowdown in the manufacturing sector has not been reversed.
4. This paper examines the recent growth performance of the Canadian economy at various levels of aggregation. In particular, it focuses on the slowdown in aggregate productivity growth that began in the mid-1970s and examines whether this slowdown has continued in recent years and is common across industries. The paper also assesses the extent to which the rapid increase in the share of services in the economy has contributed to reduced aggregate productivity growth and discusses whether the measured slowdown in services indicates an actual slowdown or problems in accurately measuring real output in that sector.
5. The rest of the paper is organized as follows. Section B discusses the issues and difficulties with measuring productivity and describes the methodology used in this paper to measure its growth. Section C presents the results for the aggregate economy and various levels of disaggregation. Section D offers some concluding remarks.
B. Measuring Productivity Growth
Measurement Issues
6. Productivity should reflect the efficiency of combining resources to produce output. It is usually measured by calculating the ratio of a weighted index of output to a weighted index of inputs. In a simple economy where there is one type of output and one type of input, productivity could be computed as the ratio of output to input. However, in an economy with heterogeneous output and inputs, there are several ways to compute productivity depending on the weights applied to each type of output and input.
7. The usual way to handle the heterogeneity of output is to construct an index of real output, where the physical units of output are weighted by their “real value,” computed by adjusting market values for inflation. One difficulty with this procedure arises in making the adjustment for inflation. In a modern, diverse economy, it becomes a difficult task to keep track of the prices of all products, especially given continuing quality improvements, product innovation, and outlet substitution. Therefore, various price indices are used to deflate nominal prices. For example, the consumer price index (CPI) and its components are used to deflate the final purchases of consumer goods and services (which are a large component of GDP). Gordon (1996) argues that the CPI is biased upwards, and, therefore, real output is improperly measured.5
8. A second difficulty arises when market prices for products do not exist. Examples of such products are output produced by the government and nonprofit institutions, services gained from owner-occupied dwellings, and goods produced for own consumption. In general, the prices for these products are computed based on the cost of their inputs or are imputed from prices of similar products.6 The use of the cost of inputs to measure real output (which is the method commonly used to measure government output) implies that productivity growth is zero.
9. There are several ways to handle the heterogeneity of inputs. For example, productivity can be measured as labor productivity, which is defined as output per employee or hours worked. In this case, labor (assumed to be homogenous) is the only input. Although this measure may be relatively easy to calculate and may be useful for studying real wage or per capita growth, it has a major limitation: namely, it measures output per unit of labor instead of output per unit of all inputs combined. As a consequence, growth in labor productivity includes growth in output due to the improved efficiency of all inputs (including labor) and the increased use of other productive inputs (including physical capital) relative to that of labor. Furthermore, if labor is defined as total employment, growth in labor productivity would also include growth in average hours worked.
10. An alternative measure of productivity is total factor productivity (TFP), which, in principle, attempts to take into account contributions from all inputs. In practice, however, aggregate measures of TFP include only contributions from labor and physical capital (measures which generally exclude land, natural resources, and other inputs).
11. One problem in computing TFP comes from measuring inputs. Generally, labor is considered homogenous, while physical capital is valued at its deflated book or constant- dollar replacement value. When labor is not differentiated by skill level, TFP measurements implicitly include relative growth in human capital in the estimates of productivity growth. When physical capital is valued by deflating book or replacement values, biases from mis- measured price indices can alter the estimates of productivity. Furthermore, during a recession, if firms do not adjust factors immediately (because of the fixed nature of capital or labor hoarding), some of the change in productivity growth should be attributed to underemployed resources. Another problem in computing TFP comes from determining the appropriate weights for different inputs. If constant returns to scale and perfectly competitive markets are assumed, then the weights for these aggregate factors are their shares in total factor payments. Alternatively, the weights can be estimated as the input elasticities of the factors.
12. Sectoral productivity growth can be computed in several ways. Output can be measured as gross output, or it can be measured as value-added output (by industry, product, or a industry-product combination). Gross output is the market value of all output for an individual industry. Value-added output is gross output minus the purchases of goods and services used in production (also called intermediate consumption). Generally, sectoral labor productivity is computed using value-added output. For sectoral TFP, the set of inputs that are used depends on the measure of output. The appropriate group of inputs to employ when using gross output includes both primary factors and intermediate consumption, while the appropriate group when using value-added output is only the set of primary factors.
13. There are additional problems specific to measuring sectoral output and inputs. The first one arises because the output of some industries is the intermediate consumption of others. Therefore, for example, if real value-added output in one industry is underestimated, then real value-added output and productivity of other downstream industries will be overestimated.7 Griliches (1994), Gordon (1996), Maclean (1996), and others suggest that real service-sector output is underestimated relative to real goods-sector output because service output is often intangible and cannot easily be defined in terms of quantifiable units. Therefore, to the extent that services are the intermediate consumption of the goods sector, some of the productivity gains in the service sector may be incorrectly measured as productivity gains for the goods sector.8 Furthermore, as goods-producing firms increase their demand for intermediate services due to outsourcing, this misallocation is exacerbated.
14. Assigning inputs to sectors presents another problem for sectoral productivity measurement. For example, in the finance, insurance, and real estate sector, capital owned is high, but much of this capital is leased out to other sectors. Because the capital stock is measured in terms of ownership, inputs into this sector tend to be overestimated, and as a consequence, TFP is underestimated.
Methodology
15. Labor productivity is calculated as the ratio of value-added GDP to homogenous labor hours, while TFP is calculated as the ratio of valued-added GDP to a weighted index of homogenous labor hours and physical capital Therefore, the measure of labor productivity growth includes growth due to changes in inputs other than labor, while the measure of TFP growth includes changes in productivity due to changes in inputs (including human capital, land, and natural resources) other than labor and physical capital. Furthermore, the biases due to improper measurement of real output and/or real physical capital appear in labor productivity and TFP.
16. To calculate TFP, the method suggested and employed by Christensen, Jorgenson, and Lau (1973), Gollop and Jorgenson (1980), Young (1992), and Young (1994) is followed. As a second-order approximation for any given production function, the translog (or transcendental logarithmic) production function is used:
where Y, K, H, and t are, respectively, output, capital, labor, and time. When there are constant returns to scale, the parameters satisfy the following conditions:
If equations (2) and (3) are satisfied, equation (1) can be simplified by differencing to provide a measure of the causes of growth across discrete time periods:
where α is capital intensity, β is labor intensity, and ΔTFP provides a measure of the amount that the log of output would have increased had all inputs remained constant between the discrete time periods. With constant returns to scale,
When there are perfectly competitive markets and firms maximize profits, β is also the labor share of total output and can be calculated by dividing labor compensation by output. In this case, a is the capital share of total output and can be calculated as 1-β. This method for calculating TFP growth is usually called growth accounting because output growth can be allocated to growth in inputs and growth in productivity.
17. However, if the assumption of constant returns to scale is incorrect, then the calculated residual (i.e., TFP growth) will include changes due to changes in scale. Therefore, as an alternative to growth accounting, the coefficients for α and β in equation (4) can be estimated.
18. Initially, the productivity residual using growth accounting is estimated for each sector of the Canadian economy assuming constant returns to scale and profit maximization.9 Subsequently, these assumptions are tested by estimating equations (1) and (4) and testing the parameters from these estimates against the conditions in equation (2), (3), and (5).10 Labor productivity by sector is also estimated.
19. The data used to measure labor productivity and TFP growth were provided by Statistics Canada and include nominal and real value-added GDP, nominal labor compensation, hours of labor worked, and the real gross capital stock from 1961–1992 for the total economy, the business sector, the nonbusiness sector, goods-producing industries, service-producing industries and small (S) level industry aggregates. For many of the sectors, capacity utilization estimates for 1962–1992 were available, and the capital stock estimates were adjusted accordingly.11
C. Productivity at the Aggregate and S Industry Level
20. Estimates of labor productivity growth for the S level industries and various aggregates are presented in Table 1. The first column of growth rates contains averages for the entire period (1962–1992), while the second, third and fourth columns provide average growth rates from 1962–73, 1973–81 and 1981–92, respectively.12 Labor productivity growth slowed down in most of the sectors and the aggregate economy after 1973, and it has remained relatively low. In fact, only two sectors (fishing and trapping and construction) have growth rates during 1981–92 that are higher than during 1962–73. For three other sectors (mining, quarrying, and oil well; communication; and finance, insurance, and real estate), growth rates have decreased by less than one half percent. In contrast, for the other sectors and the five aggregates, the slowdown in labor productivity growth ranges from around 1 percent to more than 5 percent. For example, in manufacturing, the labor productivity growth rates are about the same in the 1970s and 1980s but more than 2 percent below the rates in the 1960s.
Canada: Growth in Labor Productivity for S Level Industries and Aggregates
(Annual averages, in percent)
Canada: Growth in Labor Productivity for S Level Industries and Aggregates
(Annual averages, in percent)
| Sectors | 1962–92 | 1962–73 | 1973–81 | 1981–92 |
|---|---|---|---|---|
| Agriculture and related industries | 2.66 | 4.51 | 1.48 | 1.68 |
| Fishing and trapping | −0.31 | −2.24 | −1.92 | 2.80 |
| Logging and forestry | 3.12 | 4.83 | 2.15 | 2.11 |
| Mining, quarrying, and oil well | 1.63 | 5.52 | −8.45 | 5.07 |
| Manufacturing | 2.61 | 4.15 | 1.64 | 1.77 |
| Construction | 1.19 | 0.07 | 4.08 | 0.22 |
| Transportation and storage | 2.78 | 5.29 | −0.10 | 2.37 |
| Communication | 5.74 | 5.60 | 6.84 | 5.09 |
| Other utilities | 2.48 | 5.65 | 0.69 | 0.60 |
| Wholesale trade | 2.00 | 2.55 | 1.56 | 1.78 |
| Retail trade | 1.35 | 2.72 | −0.66 | 1.44 |
| Finance, insurance, and real estate | 0.74 | 0.76 | 1.16 | 0.41 |
| Community, business, and personal services | 0.72 | 1.78 | 0.89 | −0.47 |
| Nonbusiness sector | 0.60 | 1.34 | 0.21 | 0.15 |
| Business sector | 2.26 | 3.76 | 1.40 | 1.38 |
| Goods-producing industries | 2.77 | 4.61 | 1.55 | 1.81 |
| Service-producing industries | 1.74 | 2.71 | 1.20 | 1.16 |
| Total economy | 1.95 | 3.31 | 1.20 | 1.13 |
Canada: Growth in Labor Productivity for S Level Industries and Aggregates
(Annual averages, in percent)
| Sectors | 1962–92 | 1962–73 | 1973–81 | 1981–92 |
|---|---|---|---|---|
| Agriculture and related industries | 2.66 | 4.51 | 1.48 | 1.68 |
| Fishing and trapping | −0.31 | −2.24 | −1.92 | 2.80 |
| Logging and forestry | 3.12 | 4.83 | 2.15 | 2.11 |
| Mining, quarrying, and oil well | 1.63 | 5.52 | −8.45 | 5.07 |
| Manufacturing | 2.61 | 4.15 | 1.64 | 1.77 |
| Construction | 1.19 | 0.07 | 4.08 | 0.22 |
| Transportation and storage | 2.78 | 5.29 | −0.10 | 2.37 |
| Communication | 5.74 | 5.60 | 6.84 | 5.09 |
| Other utilities | 2.48 | 5.65 | 0.69 | 0.60 |
| Wholesale trade | 2.00 | 2.55 | 1.56 | 1.78 |
| Retail trade | 1.35 | 2.72 | −0.66 | 1.44 |
| Finance, insurance, and real estate | 0.74 | 0.76 | 1.16 | 0.41 |
| Community, business, and personal services | 0.72 | 1.78 | 0.89 | −0.47 |
| Nonbusiness sector | 0.60 | 1.34 | 0.21 | 0.15 |
| Business sector | 2.26 | 3.76 | 1.40 | 1.38 |
| Goods-producing industries | 2.77 | 4.61 | 1.55 | 1.81 |
| Service-producing industries | 1.74 | 2.71 | 1.20 | 1.16 |
| Total economy | 1.95 | 3.31 | 1.20 | 1.13 |
21. Table 2 provides the average annual TFP growth rates using the growth accounting methodology. In general, these results confirm that there has been little or no recovery from the slowdown of the 1970s. However, there are differences between using labor productivity and TFP to measure productivity growth. For the goods sectors (except construction), the TFP measures show less of a slowdown between 1962–73 and 1981–92, while for the service sectors (except transportation and storage and finance, insurance, and real estate), using TFP magnifies the slowdown. This discrepancy is reconciled by noting that growth in the capital services to labor ratio slowed in the goods sectors (except for construction), but it increased in the service sectors (except for transportation and storage and finance, insurance, and real estate) between the two periods.13 Controlling for the change in the capital services to labor ratio by sector, the slowdown in productivity growth in the service-producing industries is larger than in the goods-producing ones. Therefore, it is possible that the sectoral shift in the economy towards services explains part of the aggregate slowdown in productivity growth.
Growth in TFP for S Level Industries and Aggregates
(Annual averages, in percent)
Growth in TFP for S Level Industries and Aggregates
(Annual averages, in percent)
| Sectors | 1962–92 | 1962–73 | 1973–81 | 1981–92 |
|---|---|---|---|---|
| Agriculture and related ndustries | 1.81 | 1.48 | −0.94 | 4.13 |
| Fishing and trapping | −0.07 | −2.35 | −1.80 | 3.47 |
| Logging and forestry | 3.26 | 3.87 | 2.57 | 3.17 |
| Mining, quarrying, and oil well | −0.41 | 1.88 | −9.94 | 4.22 |
| Manufacturing | 1.70 | 3.07 | 0.92 | 0.89 |
| Construction | 0.71 | −0.16 | 3.02 | −0.09 |
| Transportation and storage | 2.69 | 4.95 | 0.45 | 2.07 |
| Communication | 4.66 | 5.04 | 5.90 | 3.38 |
| Other utilities | 1.26 | 3.79 | 0.29 | −0.57 |
| Wholesale trade | 2.06 | 3.11 | 1.81 | 1.19 |
| Retail trade | 1.28 | 2.92 | −0.42 | 0.87 |
| Finance, insurance, and real estate | −2.30 | −2.54 | −2.13 | −2.18 |
| Community, business, and personal services | 0.63 | 1.79 | 1.09 | −0.85 |
| Nonbusiness sector | 0.57 | 1.33 | 0.09 | 0.15 |
| Business sector | 1.44 | 2.67 | 0.66 | 0.79 |
| Goods-producing industries | 1.53 | 2.90 | 0.12 | 1.20 |
| Service-producing industries | 1.29 | 2.44 | 1.13 | 0.27 |
| Total economy | 1.35 | 2.50 | 0.63 | 0.72 |
Growth in TFP for S Level Industries and Aggregates
(Annual averages, in percent)
| Sectors | 1962–92 | 1962–73 | 1973–81 | 1981–92 |
|---|---|---|---|---|
| Agriculture and related ndustries | 1.81 | 1.48 | −0.94 | 4.13 |
| Fishing and trapping | −0.07 | −2.35 | −1.80 | 3.47 |
| Logging and forestry | 3.26 | 3.87 | 2.57 | 3.17 |
| Mining, quarrying, and oil well | −0.41 | 1.88 | −9.94 | 4.22 |
| Manufacturing | 1.70 | 3.07 | 0.92 | 0.89 |
| Construction | 0.71 | −0.16 | 3.02 | −0.09 |
| Transportation and storage | 2.69 | 4.95 | 0.45 | 2.07 |
| Communication | 4.66 | 5.04 | 5.90 | 3.38 |
| Other utilities | 1.26 | 3.79 | 0.29 | −0.57 |
| Wholesale trade | 2.06 | 3.11 | 1.81 | 1.19 |
| Retail trade | 1.28 | 2.92 | −0.42 | 0.87 |
| Finance, insurance, and real estate | −2.30 | −2.54 | −2.13 | −2.18 |
| Community, business, and personal services | 0.63 | 1.79 | 1.09 | −0.85 |
| Nonbusiness sector | 0.57 | 1.33 | 0.09 | 0.15 |
| Business sector | 1.44 | 2.67 | 0.66 | 0.79 |
| Goods-producing industries | 1.53 | 2.90 | 0.12 | 1.20 |
| Service-producing industries | 1.29 | 2.44 | 1.13 | 0.27 |
| Total economy | 1.35 | 2.50 | 0.63 | 0.72 |
22. Several of the sectors have negative TFP growth for significant periods of time. For example, finance, insurance, and real estate has negative TFP growth in every period. As this seems unlikely, the negative growth may be the result of mis-measuring real output and inputs or the result of assuming constant returns to scale and profit maximization. Because labor productivity is positive for finance, insurance, and real estate in all three time periods, it appears possible that the real capital stock in that sector is overestimated.
23. Table 3 displays the results of testing the hypothesis of constant returns to scale using equations (2) and (3) on the OLS estimated parameters of equation (1). This hypothesis can be rejected at a 5 percent level of significance for four industries (fishing and trapping; construction; retail trade; and finance, insurance, and real estate) and at a 10 percent level for the nonbusiness sector. These results question the validity of using growth accounting for all the sectors.
Canada: Testing for Constant Returns to Scale 1/
Null hypothesis: Restrictions in equations (2) and (3) hold.
D refers to degrees of freedom, which are 22 for agriculture and related industries; fishing and trapping; communication; and the nonbusiness sector and 21 for the other industries.
Parmeters are unstable at the 10 percent level of significance.
Canada: Testing for Constant Returns to Scale 1/
| S Level Industries and Aggregates | F(4, D)Statistic 2/ | P-value |
|---|---|---|
| Agriculture and related industries | 2.030 | 0.125 |
| Fishing and trapping | 2.862 | 0.048 |
| Logging and forestry | 0.723 | 0.586 |
| Mining, quarrying, and oil well | 1.777* | 0.171 |
| Manufacturing | 0.419 | 0.793 |
| Construction | 31.122 | 0.0 |
| Transportation and storage | 0.512 | 0.728 |
| Communication | 1.401 | 0.266 |
| Other utilities | 0.095 | 0.983 |
| Wholesale trade | 1.423 | 0.261 |
| Retail trade | 6.283 | 0.002 |
| Finance, insurance, and real estate | 6.940 | 0.001 |
| Community, business, and personal services | 0.782 | 0.549 |
| Nonbusiness sector | 2.681* | 0.058 |
| Business sector | 1.580* | 0.216 |
| Goods-producing industries | 0.074 | 0.989 |
| Service-producing industries | 0.936 | 0.462 |
| Total economy | 0.904 | 0.479 |
Null hypothesis: Restrictions in equations (2) and (3) hold.
D refers to degrees of freedom, which are 22 for agriculture and related industries; fishing and trapping; communication; and the nonbusiness sector and 21 for the other industries.
Parmeters are unstable at the 10 percent level of significance.
Canada: Testing for Constant Returns to Scale 1/
| S Level Industries and Aggregates | F(4, D)Statistic 2/ | P-value |
|---|---|---|
| Agriculture and related industries | 2.030 | 0.125 |
| Fishing and trapping | 2.862 | 0.048 |
| Logging and forestry | 0.723 | 0.586 |
| Mining, quarrying, and oil well | 1.777* | 0.171 |
| Manufacturing | 0.419 | 0.793 |
| Construction | 31.122 | 0.0 |
| Transportation and storage | 0.512 | 0.728 |
| Communication | 1.401 | 0.266 |
| Other utilities | 0.095 | 0.983 |
| Wholesale trade | 1.423 | 0.261 |
| Retail trade | 6.283 | 0.002 |
| Finance, insurance, and real estate | 6.940 | 0.001 |
| Community, business, and personal services | 0.782 | 0.549 |
| Nonbusiness sector | 2.681* | 0.058 |
| Business sector | 1.580* | 0.216 |
| Goods-producing industries | 0.074 | 0.989 |
| Service-producing industries | 0.936 | 0.462 |
| Total economy | 0.904 | 0.479 |
Null hypothesis: Restrictions in equations (2) and (3) hold.
D refers to degrees of freedom, which are 22 for agriculture and related industries; fishing and trapping; communication; and the nonbusiness sector and 21 for the other industries.
Parmeters are unstable at the 10 percent level of significance.
24. Table 4 shows the results of OLS regressions of equation (4) for the S level industries and aggregates. The regressions for agriculture and fishing and trapping have extremely low R-squared, and therefore, the subsequent hypothesis tests are not very meaningful. The poor fit may be the result of excluding significant inputs in those sectors, namely, land and natural resources. Furthermore, the Durbin-Watson statistics for several of the regressions are quite poor. So the results must be viewed with some caution.
Testing for Constant Returns to Scale, Profit Maximization and Parameter Stability 1/ S Level Industries and Aggregates
Regression (t statistics in parenthesis): Δlny = g + α ΔlnK + β ΔlnL. Chow reports the p-values for the null hypothesis of parameter stability, CRS reports those for the null hypothesis of constant returns to scale, and Profit reports those for the null hypothesis of β is equal to labor share of output.
Testing for Constant Returns to Scale, Profit Maximization and Parameter Stability 1/ S Level Industries and Aggregates
| Sectors | g | α | β | R-squared | DW | CRS | Profit | Chow |
|---|---|---|---|---|---|---|---|---|
| Agriculture and related industries | 0.0146 (0.64) |
0.101 (0.28) |
−0.004 (0.01) |
0.003 | 2.62 | 0.209 | 0.424 | 0.960 |
| Fishing and trapping | 0.0044 (0.24) |
0.092 (0.50) |
0.203 (1.15) |
0.066 | 2.37 | 0.003 | 0.029 | 0.583 |
| Logging and forestry | 0.0321 (3.61) |
0.387 (3.94) |
0.495 (2.96) |
0.775 | 1.22 | 0.314 | 0.067 | 0.051 |
| Mining, quarrying, and oil well | 0.0012 (0.09) |
0.631 (3.82) |
−0.354 (−1.32) |
0.370 | 1.10 | 0.002 | 0.017 | 0.131 |
| Manufacturing | 0.0090 (1.27) |
0.558 (2.93) |
0.718 (3.21) |
0.790 | 1.25 | 0.066 | 0.876 | 0.463 |
| Construction | −0.0072 (−2.27) |
0.670 (14.88) |
−0.061 (−0.94) |
0.922 | 1.84 | 0.000 | 0.000 | 0.001 |
| Transportation and storage | 0.0269 (3.33) |
0.461 (2.36) |
0.484 (2.09) |
0.306 | 1.31 | 0.843 | 0.317 | 0.054 |
| Communication | 0.0504 (6.10) |
0.436 (2.62) |
0.306 (2.11) |
0.330 | 1.36 | 0.207 | 0.059 | 0.425 |
| Other utilities | 0.0011 (0.12) |
1.125 (7.10) |
0.036 (0.44) |
0.651 | 0.57 | 0.380 | 0.006 | 0.002 |
| Wholesale trade | 0.0230 (3.18) |
0.177 (1.85) |
0.733 (4.15) |
0.519 | 1.45 | 0.601 | 0,907 | 0.181 |
| Retail trade | 0.0218 (3.28) |
0.051 (0.53) |
0.475 (2.30) |
0.195 | 1.08 | 0.029 | 0.085 | 0.047 |
| Finance, insurance, and real estate | 0.0168 (2.87) |
0.188 (2.24) |
0.319 (3.71) |
0.518 | 2.05 | 0.001 | 0.851 | 0.030 |
| Community, business, and personal services | 0.0124 (1.30) |
0.159 (3.40) |
0.704 (1.60) |
0.469 | 2.17 | 0.465 | 0.582 | 0.304 |
| Nonbusiness sector | 0.0043 (0.97) |
0.336 (2.46) |
0.704 (5.72) |
0.644 | 1.56 | 0.802 | 0.120 | 0.000 |
| Business sector | 0.0138 (3.97) |
0.477 (5.32) |
0.413 (2.77) |
0.801 | 1.05 | 0.319 | 0.164 | 0.000 |
| Goods-producing industries | 0.0052 (1.02) |
0.675 (6.01) |
0.375 (2.36) |
0.809 | 1.57 | 0.668 | 0.120 | 0.145 |
| Service-producing industries | 0.0206 (4.85) |
0.176 (2.48) |
0.634 (4.36) |
0.679 | 1.12 | 0.123 | 0.933 | 0.000 |
| Total economy | 0.0144 (4.34) |
0.388 (4.93) |
0.492 (3.00) |
0.770 | 1.59 | 0.353 | 0.274 | 0.000 |
Regression (t statistics in parenthesis): Δlny = g + α ΔlnK + β ΔlnL. Chow reports the p-values for the null hypothesis of parameter stability, CRS reports those for the null hypothesis of constant returns to scale, and Profit reports those for the null hypothesis of β is equal to labor share of output.
Testing for Constant Returns to Scale, Profit Maximization and Parameter Stability 1/ S Level Industries and Aggregates
| Sectors | g | α | β | R-squared | DW | CRS | Profit | Chow |
|---|---|---|---|---|---|---|---|---|
| Agriculture and related industries | 0.0146 (0.64) |
0.101 (0.28) |
−0.004 (0.01) |
0.003 | 2.62 | 0.209 | 0.424 | 0.960 |
| Fishing and trapping | 0.0044 (0.24) |
0.092 (0.50) |
0.203 (1.15) |
0.066 | 2.37 | 0.003 | 0.029 | 0.583 |
| Logging and forestry | 0.0321 (3.61) |
0.387 (3.94) |
0.495 (2.96) |
0.775 | 1.22 | 0.314 | 0.067 | 0.051 |
| Mining, quarrying, and oil well | 0.0012 (0.09) |
0.631 (3.82) |
−0.354 (−1.32) |
0.370 | 1.10 | 0.002 | 0.017 | 0.131 |
| Manufacturing | 0.0090 (1.27) |
0.558 (2.93) |
0.718 (3.21) |
0.790 | 1.25 | 0.066 | 0.876 | 0.463 |
| Construction | −0.0072 (−2.27) |
0.670 (14.88) |
−0.061 (−0.94) |
0.922 | 1.84 | 0.000 | 0.000 | 0.001 |
| Transportation and storage | 0.0269 (3.33) |
0.461 (2.36) |
0.484 (2.09) |
0.306 | 1.31 | 0.843 | 0.317 | 0.054 |
| Communication | 0.0504 (6.10) |
0.436 (2.62) |
0.306 (2.11) |
0.330 | 1.36 | 0.207 | 0.059 | 0.425 |
| Other utilities | 0.0011 (0.12) |
1.125 (7.10) |
0.036 (0.44) |
0.651 | 0.57 | 0.380 | 0.006 | 0.002 |
| Wholesale trade | 0.0230 (3.18) |
0.177 (1.85) |
0.733 (4.15) |
0.519 | 1.45 | 0.601 | 0,907 | 0.181 |
| Retail trade | 0.0218 (3.28) |
0.051 (0.53) |
0.475 (2.30) |
0.195 | 1.08 | 0.029 | 0.085 | 0.047 |
| Finance, insurance, and real estate | 0.0168 (2.87) |
0.188 (2.24) |
0.319 (3.71) |
0.518 | 2.05 | 0.001 | 0.851 | 0.030 |
| Community, business, and personal services | 0.0124 (1.30) |
0.159 (3.40) |
0.704 (1.60) |
0.469 | 2.17 | 0.465 | 0.582 | 0.304 |
| Nonbusiness sector | 0.0043 (0.97) |
0.336 (2.46) |
0.704 (5.72) |
0.644 | 1.56 | 0.802 | 0.120 | 0.000 |
| Business sector | 0.0138 (3.97) |
0.477 (5.32) |
0.413 (2.77) |
0.801 | 1.05 | 0.319 | 0.164 | 0.000 |
| Goods-producing industries | 0.0052 (1.02) |
0.675 (6.01) |
0.375 (2.36) |
0.809 | 1.57 | 0.668 | 0.120 | 0.145 |
| Service-producing industries | 0.0206 (4.85) |
0.176 (2.48) |
0.634 (4.36) |
0.679 | 1.12 | 0.123 | 0.933 | 0.000 |
| Total economy | 0.0144 (4.34) |
0.388 (4.93) |
0.492 (3.00) |
0.770 | 1.59 | 0.353 | 0.274 | 0.000 |
Regression (t statistics in parenthesis): Δlny = g + α ΔlnK + β ΔlnL. Chow reports the p-values for the null hypothesis of parameter stability, CRS reports those for the null hypothesis of constant returns to scale, and Profit reports those for the null hypothesis of β is equal to labor share of output.
25. The last three columns of Table 4 report the results from tests of various hypotheses for these sectors. The column labeled “CRS” displays the results of the test for constant returns to scale, while the column labeled “Profit” shows the results of the test for profit maximization.14 The last column shows the results of Chow tests which compare the stability of parameters between 1962–73 and 1974–92.
26. For the 16 sectors and the aggregates (excluding the two sectors for which the regressions fit poorly), the estimates generally confirm the results of testing constant returns to scale for the translog production function. They also show mixed evidence for profit maximization and provide relatively strong evidence of a structural break around 1973. Constant returns to scale are rejected for four of the sectors at the 5 percent level of significance, and one other at the 10 percent level. The scale results match those of Table 1, except in two sectors: mining, quarrying, and oil well and manufacturing. For mining, quarrying, and oil well, Chow tests show parameter instability when estimating the translog production function, while for the manufacturing sector, the estimates of labor and capital intensity point to increasing returns to scale. For the other four sectors (mining, quarrying, and oil well; construction; retail trade; and finance, insurance, and real estate), the parameter estimates point to decreasing returns to scale.
27. Profit maximization is rejected for 3 of the 16 sectors at the 5 percent level of significance and for 3 others at the 10 percent level. It is interesting to note that for all five aggregate measures, both constant returns to scale and profit maximization are not rejected at the 5 percent or 10 percent levels. This result provides some evidence to support using growth accounting at least for the aggregates. For the 11 S level industries, profit maximization or constant returns to scale is rejected for 5 of the sectors (mining, quarrying, and oil well; construction; other utilities; retail trade; and finance, insurance and real estate) at the 5 percent level and for 3 others (logging and forestry; manufacturing; and communication) at the 10 percent level. Only for three industries (transportation and storage; wholesale trade; and community, business and personal services) can neither assumption be rejected at the 10 percent level of significance. These results suggest that the TFP estimates made using growth accounting for the S level industries should be viewed with caution.
28. For 8 of the 16 sectors, Chow tests reject stable parameters at the 5 percent level of significance and for 2 other sectors at the 10 percent level. These results confirm the notion that there was a structural change in the economy occurring around 1973. However, it is interesting to note that manufacturing is one of the sectors for which parameter stability is not rejected.
29. Table 5 shows the results of estimating equation (4) while allowing TFP growth (g) to vary or g, α, and β to vary between 1962–73 and 1974–92.15 These regressions make it possible to control for parameter instability and scale (while not assuming profit maximization). Once g is allowed to vary, Chow tests cannot reject α and β remaining the same between periods for all sectors but construction. Essentially, the change in measured output growth is explained by changes in TFP growth for these sectors.
Controlling for Scale and Parameter Instability 1/
Regression (t statistics in parenthesis): Δlny = g + α ΔlnK + β ΔlnL, allowing g, α and/or β to vary between time periods 1962–73 and 1974–92). Chow reports the p-values for the null hypothesis of parameter stability. For sectors other than construction, only g varies. For construction, all three parameters vary.
Controlling for Scale and Parameter Instability 1/
| Allow g α and/or β to vary | |||
|---|---|---|---|
| S Level Industries and Aggregates | g | Δg | Chow |
| Agriculture and related industries | 0.0301 (0.72) |
−0.0214 (−0.44) |
0.999 |
| Fishing and trapping | −0.0165 (−0.53) |
0.0340 (0.86) |
0.881 |
| Logging and forestry | 0.0222 (1.36) |
0.0157 (0.73) |
0.147 |
| Mining, quarrying, and oil well | 0.0375 (1.77) |
−0.0526 (−2.12) |
0.804 |
| Manufacturing | 0.0192 (1.86) |
−0.0148 (−1.34) |
0.930 |
| Construction | 0.0029 (0.77) |
−0.0164 (−3.32) |
0.999 |
| Transportation and storage | 0.0509 (4.11) |
−0.0354 (−2.42) |
0.642 |
| Communication | 0.0584 (5.92) |
−0.0128 (−1.43) |
0.927 |
| Other utilities | 0.0325 (3.40) |
−0.0368 (−4.63) |
0.966 |
| Wholesale trade | 0.0355 (3.27) |
−0.0175 (−1.51) |
0.619 |
| Retail trade | 0.0431 (4.75) |
−0.0313 (−3.05) |
0.979 |
| Finance, insurance, and real estate | 0.0221 (2.78) |
−0.0060 (−0.98) |
0.109 |
| Community, business, and personal services | 0.0261 (2.24) |
−0.0194 (−1.89) |
0.978 |
| Nonbusiness sector | 0.0251 (5.23) |
−0.0182 (−5.64) |
0.941 |
| Business sector | 0.0280 (7.23) |
−0.0195 (−4.88) |
0.664 |
| Goods-producing industries | 0.0190 (2.64) |
−0.0171 (−2.50) |
0.998 |
| Service-producing industries | 0.0345 (7.67) |
−0.0189 (−4.47) |
0.110 |
| Total economy | 0.0285 (8.31) |
−0.0192 (−5.53) |
0.315 |
Regression (t statistics in parenthesis): Δlny = g + α ΔlnK + β ΔlnL, allowing g, α and/or β to vary between time periods 1962–73 and 1974–92). Chow reports the p-values for the null hypothesis of parameter stability. For sectors other than construction, only g varies. For construction, all three parameters vary.
Controlling for Scale and Parameter Instability 1/
| Allow g α and/or β to vary | |||
|---|---|---|---|
| S Level Industries and Aggregates | g | Δg | Chow |
| Agriculture and related industries | 0.0301 (0.72) |
−0.0214 (−0.44) |
0.999 |
| Fishing and trapping | −0.0165 (−0.53) |
0.0340 (0.86) |
0.881 |
| Logging and forestry | 0.0222 (1.36) |
0.0157 (0.73) |
0.147 |
| Mining, quarrying, and oil well | 0.0375 (1.77) |
−0.0526 (−2.12) |
0.804 |
| Manufacturing | 0.0192 (1.86) |
−0.0148 (−1.34) |
0.930 |
| Construction | 0.0029 (0.77) |
−0.0164 (−3.32) |
0.999 |
| Transportation and storage | 0.0509 (4.11) |
−0.0354 (−2.42) |
0.642 |
| Communication | 0.0584 (5.92) |
−0.0128 (−1.43) |
0.927 |
| Other utilities | 0.0325 (3.40) |
−0.0368 (−4.63) |
0.966 |
| Wholesale trade | 0.0355 (3.27) |
−0.0175 (−1.51) |
0.619 |
| Retail trade | 0.0431 (4.75) |
−0.0313 (−3.05) |
0.979 |
| Finance, insurance, and real estate | 0.0221 (2.78) |
−0.0060 (−0.98) |
0.109 |
| Community, business, and personal services | 0.0261 (2.24) |
−0.0194 (−1.89) |
0.978 |
| Nonbusiness sector | 0.0251 (5.23) |
−0.0182 (−5.64) |
0.941 |
| Business sector | 0.0280 (7.23) |
−0.0195 (−4.88) |
0.664 |
| Goods-producing industries | 0.0190 (2.64) |
−0.0171 (−2.50) |
0.998 |
| Service-producing industries | 0.0345 (7.67) |
−0.0189 (−4.47) |
0.110 |
| Total economy | 0.0285 (8.31) |
−0.0192 (−5.53) |
0.315 |
Regression (t statistics in parenthesis): Δlny = g + α ΔlnK + β ΔlnL, allowing g, α and/or β to vary between time periods 1962–73 and 1974–92). Chow reports the p-values for the null hypothesis of parameter stability. For sectors other than construction, only g varies. For construction, all three parameters vary.
30. The results are quite illuminating. For all five aggregate sectors, as well as five of the S level industries (mining, quarrying, and oil well; construction; transportation and storage; other utilities; and retail trade), the change in TFP growth between periods is significant at the 5 percent level For one other S level industry (community, business and personal services), the change is significant at the 10 percent level.
31. Three of the six S level sectors with a TFP growth slowdown are service industries. For these three sectors, this result agrees with the estimates of TFP growth calculated by growth accounting. However, the hypothesis that there has been no slowdown in TFP growth for the communication and wholesale trade sectors cannot be rejected, in contrast to estimates made using growth accounting. For finance, insurance, and real estate, both techniques show no change in TFP growth. Controlling for decreasing returns to scale, the TFP growth in that sector has been positive.
32. The slowdown for the goods-producing industries is driven by mining, quarrying, and oil well; construction; and other utilities. For the first of these sectors, the growth accounting result that TFP growth has rebounded is reversed after controlling for decreasing returns in that sector. For the other two sectors, the growth accounting estimation is confirmed. It is particularly interesting to note that for manufacturing, the hypothesis that TFP growth is unchanged cannot be rejected after controlling for increasing returns to scale. For the other three sectors (agriculture and related industries, fishing and trapping, and logging and forestry), there does not appear to be a slowdown of TFP growth.
D. Concluding Remarks
33. The results presented here confirm that there has been a slowdown in aggregate productivity growth and that this slowdown has occurred across several industries. This study also highlights the difficulty in defining an appropriate measure for productivity growth (whether it be labor productivity or total factor productivity) and determining the best procedure to calculate this measure. In particular, the assumption of constant returns to scale may not be valid for several industries, and therefore, the growth accounting methodology to calculate TFP may be inappropriate at the sectoral level. Furthermore, because some of the regressions have low R-squared and/or poor Durbin-Watson statistics, the results must be viewed with caution.
34. The study focuses on three potential explanations for the slowdown in aggregate productivity growth: the intersectoral shift of output and labor towards services, a reduction in the benefits from increasing scale in manufacturing, and a slowdown in capital accumulation (adjusted for capacity utilization) relative to labor force growth. The relative contribution of intersectoral shifts in the productivity slowdown can be measured by decomposing the estimated productivity growth into growth that would have taken place if the initial shares of the sectors had remained constant at their original levels and the rest, which basically reflects the effect of the changes in shares. The relative contribution of the reduced benefits from increasing scale in manufacturing can be calculated by comparing observed aggregate productivity growth to aggregate productivity growth if the manufacturing sector had continued to expand at its 1962–73 growth rates. The relative contribution of the slowdown in the growth of the capital services to labor ratio can be measured by multiplying this slowdown by the capital intensity coefficient or equivalently, by calculating the difference between labor productivity and TFP growth.
35. The results from these calculations show that intersectoral shifts account for 0.05 percent of the 2.15 percent slowdown in aggregate labor productivity growth between 1962–73 and 1974–92. The reduction in the benefits from increasing returns to scale in manufacturing accounts for 0.52 percent, and the reduction in the growth of the capital services to labor ratio accounts for 0.34 percent. The residual is 1.24 percent which can be attributed to a slowdown in technical progress or a variety of other factors.16 The slowdown in TFP growth (measured using growth accounting) between 1962–73 and 1974–92 is equivalent to the slowdown in aggregate labor productivity growth less the slowdown in the capital services to labor ratio or equal to 1.81 percent. For TFP growth, intersectoral shifts account for 0.04 percent and the reduction in benefits from increasing returns to scale accounts for 0.62 percent of the slowdown, leaving a residual of 1.15 percent.
36. The somewhat surprising result is that intersectoral shifts account for a very minor part of the slowdown in aggregate productivity. This occurs because the slowdown in productivity growth has taken place across many industries in Canada. There has been almost as much of a slowdown in the goods-producing sectors as in the service-producing sectors. Given the downward bias in measuring real output in the service sector, the part of the slowdown due to intersectoral shifts may in fact be overstated.
APPENDIX
Data
37. The Canadian System of National Accounts divides the total economy into the business and nonbusiness sectors. Within the business sector, industries are further divided into seven small (S) level goods-producing industries and six S level service-producing industries. The goods-producing industries are agriculture and related industries; fishing and trapping; logging and forestry; mining, quarrying, and oil well; manufacturing; construction; and other utilities. The service-producing industries are transportation and storage; communication; wholesale trade; retail trade; finance, insurance and real estate; and community, business, and personal services.
38. The general method used to calculate real value-added output is by double deflation, that is, subtract the deflated value of intermediate consumption from the deflated value of gross outputs. The double deflation method is only accurate under some restrictive conditions. For example, the double deflation technique distributes total real value-added according to base-year relative prices. Therefore, if relative prices change, double deflation allocates too much value-added to the industry with a decrease in its relative price. This misallocation leads to problems. For example, it makes it possible to have negative value-added or a negative gross operating surplus.
39. Capacity utilization data are available for many of the S level industries. When the data are not available, the capital stock estimates are adjusted using data from similar industries as a proxy. However, for four of the sectors (agriculture and related industries, fishing and trapping, communication, and the nonbusiness sector), the capital stock is not adjusted.
References
Baily, Martin N., 1982, “The Productivity Growth Slowdown by Industry,” Bookings Papers on Economic Activity, Vol. 2, pp. 423–459.
Christensen, Laurits R., Dale W. Jorgenson, and Lawrence J. Lau, 1973, “Transcendental Logarithmic Production Function Frontiers,” Review of Economics and Statistics, Vol. 55, pp. 28–45.
Daly, Michael J. P. Someshwar Rao, 1985, “Some Myths and Realities Concerning Canada’s Recent Productivity Slowdown and their Policy Implications,” Canadian Public Policy Vol. 11 No. 2, pp. 206–217.
Denny, M., J. Bernstein M. Fuss, L. Nakamura, and L. Waverman, 1992, “Productivity in Manufacturing Industries Canada Japan and the United States 1953–1986: was the ‘Productivity Slowdown’ Reversed,” Canadian Journal of Economics, Vol. 25 No. 3, pp. 584–603.
Fuess, Scott M. and Hendrik Van den Berg, 1995, “The Impact of Transactional Activities on Productivity Growth in Canada and a Comparison with the United States,” North American Journal of Economics & Finance, Vol. 6 No. 1, pp. 1–15.
Gollop, Frank M. and Dale W. Jorgenson, 1980, “U.S. Productivity Growth by Industry 1947–73 in Kendrick, John W. and Beatrice N. Vaccara (eds.) New Developments in Productivity Measurement and Analysis (Chicago: University of Chicago Press).
Gordon, Robert J., 1996, “Problems in the Measurement and Performance of Service-sector Productivity in the United States,” NBER Working Paper, No. 5519 (Cambridge Massachusetts: National Bureau of Economic Research).
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Prepared by Ranil Salgado.
For example, see Daly and Rao (1985), Denny et. al. (1992), Morrison (1992), Mullen and Williams (1994), and Fuess and Van den Berg (1995). Note that these papers generally focus on aggregate growth or growth at the major (one-digit) industrial level. Denny et. al. (1992) study manufacturing industries at the two-digit level.
For example, see Baily (1982), Morrison (1992), Griliches (1994), and Gordon (1996).
Griliches (1994) notes that the share of sectors in which output is easily measured (i.e., agriculture, mining, manufacturing, transportation, and utilities) has declined from 49 percent of U.S. GDP in 1947 to 31 percent of GDP in 1990. Gordon (1996) discusses the sources of bias in aggregate price indexes, as well as other measurement problems specific to industries, particular the service industries. Decomposing aggregate output by sector, Slifman and Corrado (1996) show that output and productivity growth have rebounded since the early 1980s to the level of the 1960s in all sectors other than nonfarm, noncorporate services. In fact for this sector, productivity growth has been negative while profitability has remained the same. They note that the kind of measured rapid relative price increases that reconcile these productivity and profitability trends appear unlikely and maybe due to difficulties in measuring prices in that service sector. All three papers conclude that real output growth is incorrectly measured and significantly underestimated.
The bias in the CPI stems from biases due to product quality changes, introduction of new products, outlet substitution, and product substitution. Although the upward bias in the CPI (using a fixed basket of products) need not be fully reflected in a downward bias in GDP (a variable basket of products), procedures for calculating real output ensure that part of the CPI bias gets transmitted to the measure of real output. For example, in Canada, real output in the banking sector is defined as the difference between the rate of return on assets and liabilities deflated by the CPI.
For example, services from owner-occupied dwellings are valued at the estimated rental prices of those dwellings.
When the intention is to measure TFP, using gross output does not avoid this problem as the error in measurement will show up in inputs (intermediate consumption).
Note that to the degree that services are intermediate rather than final consumption, this misallocation will not change aggregate productivity.
To be precise, profit maximization is assumed to hold only on average. Therefore, average labor share (rather than the actual labor share in each period) is used.
Estimating equation (1) in levels provides poor Durbin-Watson statistics. Therefore, the equation is estimated using first differences.
See appendix for more details. The rationale for adjusting the data for capacity utilization is to attempt to remove demand conditions as a contributing factor for changes in productivity. However, this adjustment may not completely purge the data of cyclical effects. In particular, labor hoarding and work effort effects remain.
The rationale for dividing the post-1973 period into two periods is to abstract from the demand-induced slowdown due to the energy-price shocks of the 1970s.
Capital services are calculated by multiplying the capital stock by capacity utilization.
In this model, given constant returns to scale, profit maximization implies that labor intensity equals the labor share of GDP.
For the construction sector, the table shows the regression which allows all three parameters to change (since the Chow test fails for the regression allowing only g to vary). For the other sectors, the table shows the regression allowing only g to change. Chow tests on parameter estimates for equation (4) during the period 1974–92 confirm parameter stability in this period (results not shown). Therefore, it does not seem necessary to separate this period further.
As mentioned before, these factors include relative changes in the average level of labor skills (or human capital accumulation), in the quality and quantity of land and natural resources, in the underutilization of resources (for example, due to labor hoarding, work effort effects, or incorrectly measuring capacity utilization), and in the obsolescence of capital.
