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Productivity and energy price differentials
Regional Science and Urban Economics 15 (1985) 477489. North-Holland
PRODUCTIVITY
AND
ENERGY
PRICE
DIFFERENTIALS
Dean C. MOUNTAIN* Ontario York
Hydro,
University,
Toronto, Downsoiew,
Ontario Ontario
M5G M3J
1X6, IP3,
Canada Canada
Received September 1982, final version received January 1985 In taking account of the interrelationship between energy and other primary resources, labour and capital, this paper presents a methodology for quantifying regional efficiency differentials using Taylor series approximations to profit functions representing regional economies. The resulting formulation makes it possible to decompose labour productivity into its contributing factors which now include energy price differentials in addition to such traditional variables as differentials involving CapitaLemployee ratios and the quality of labour. This approach is applied to Canadian regional data from 1962 to 1978. On average, between 5.2% and 9.2% of Canadian regional productivity differentials can be attributed to regional energy price differentials.
1. Introduction
Since the birth of Canada as a nation there have always been large regional economic disparities. Significant divergences in efficiency levels and average labour productivity ratios customarily characterize such disparities. To explain these divergences this paper begins by presenting a methodology for quantifying these regional efficiency differentials based on Taylor series approximations to profit functions representing regional economies. A simple extenstion of the international literature devoted to labour productivity differentials would be to explain these divergences in terms of such traditional variables as capital-employee ratio and quality of labour differentials. However, with the aid of a profit formulation this paper is also able to quantify the contribution to productivity differentials of differing regional energy price differences. This concern stems from the recognition of energy as an important intermediate input in a region’s production process and the observance that energy prices have differed considerably across Canada. Annual Canadian regional data for the Atlantic region, Quebec, Ontario, the *In preparing this paper, valuable suggestions have been provided by Byron Spencer. In addition, the paper’s presentation has benefited significantly from suggestions made by Urs Schweizer and an anonymous referee. David Durfey’s extremely competent and diligent research assistance is gratefully acknowledged. 0166-0462/85/$3.30 0 1985, Elsevier Science Publishers B.V. (North-Holland)
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Prairies, and British Columbia will be used to examine these issues over the 196221978 period. A survey of the literature will show that in the industrial efficiency and productivity level comparisons the methodology has involved employing cost and gross production formulations and for international comparisons the economies are represented by value added production functi0ns.l In contrast, in order to take account of the impact of significant regional price differences of the intermediate input energy, this study outlines a procedure for comparing efficiency levels based on Taylor series approximations to indirect profit functions representing regional economies. Relative efficiency for region i will be defined in percentage terms as the ratio of real value added (RV’A) in region i to RV’A in reference region o, while controlling for the number of employees, capital services, energy prices, and quality of labour. This results in average labour productivity differentials being functions of differentials in energy prices in addition to differentials in capital-employee ratios and differentials in quality of labour. [Average labour productivity is here defined as regional real value added (RVA) per employee.] The paper starts with a profit specification which incorporates the price of energy in addition to quantities of labour and capital as ingredients in a regional economy’s production process. This section then proceeds to illustrate why this specification would suggest a modified efficiency differential. Using the theory of section 2 as groundwork, the third section then decomposes average labour productivity differentials into its ingredient components. Section 4 provides a brief digression into a discussion of the actual construction of quantity and price differentials, plus the quality of labour differentials. Section 5 provides the empirical results as applied to the Canadian regions from 1962 to 1978. Conclusions then follow. 2. A profit specification
To take account of energy’s role in explaining productivity and efficiency differentials a convenient starting point is to begin by specifying a relationship between regional economy i’s output at time s (Y(i,s)) and the primary resources labour (L(i,s)), capital (K(i,s)) and energy (EN(i,s)) plus a tech‘Recently there has emerged a literature devoted to making international comparisons of efficiency and productivity levels [see Jorgenson and Nishimizu (1978), Christensen, Cummings and Jorgenson (1980), and Caves, Christensen and Diewert (1982)]. As well, regional efficiency comparisons have recently been made for manufacturing in Canada [see Denny and Fuss (1980, 1981) and Denny, Fuss and May (1981)]. ‘The approach used in this paper to approximate a profit function is very similar to that employed by Denny, Fuss and May (1981) in their cost specification. However, this paper’s definition of efficiency differs slightly from that used by Denny, Fuss and May (1981). In the context of a cost function for manufacturing, they define the efficiency level as the relative total cost differential between regions after correcting for the effects of differing input prices and output levels.
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nology index (T(i, s)), Y(i, s) =F(L(i, s)), K(i, s), EN(i, s), T(i, s)).
(1)
Within EN(i,s) are both imported energy and regionally produced energy. The final output (Y) can either be consumed, invested or sold to pay for energy inputs. If in each region all producing units are maximizing profits, real value added at a regional level of aggregation is also maximized for L=L, K=R, max R VA = F(L, I?, EN, T) - PE . EN,
(2)
where PE is the real price of the input EN.3 This real value added specification, which is a regional real gross domestic product (GDP) formulation, is often used by other authors in examining the interrelationship between energy and an aggregate economy [e.g., Manne (1977), Sweeney (1979), Wright (1980), Peck and Solow (1982) and Burgess (1984)-J. The maximand of eq. (2) is the optimal level of the region’s real value added (R VA*(i, s)) which is an indirect function of L(i, s), K(i, s), and PE(i, s) and T(i,s). This means that RVA*(i, s) =II,[(L(i,
s), K(i, s), PE(i, s), T(i, s)].
(3)
It is assumed that the logarithms of the profit function are well approximated by a function of the logarithms of L(i,s), K(i,s), PE(i,s), T(i,s) and D -where D is a vector of dummy variables (D(i)), one for each region excluding the reference region. In R VA*(i, s) = In n(i, s) = G*[ln L(i, s), In K(i, s), In PE(i, s), T(i, s), D].
(4)
Notice that the assumption is made that the logarithms of the RVA function nis has become G* with a vector of dummy variables as one of its components. The common function G* indicates that there are identical components across regions but differences in formulation, however, are accounted for by including a vector of dummy variables in the profit function. This technique, in the context of a cost function, was first introduced by Denny, Fuss and May (1981). 3The price of energy is deflated by the region’s gross output price deflator (which is not the GDP price deflator). The resultant estimate of real value added is not the conventional measure of real GDP which uses double deflation techniques but instead a single deflated measure of output.
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Because the focus of this paper is to make inter-regional comparisons at one point in time (period s), from hereon the time index will be dropped. Therefore, In rc(i)= G*[ln L(i), In K(i), In PE(i), T(i), D(i)].
(5)
One of the purposes of this paper is to provide a measure of inter-regional efficiency differentials having netted out differences in capital-employee ratios, prices of energy, and quality of labour. Moreover, to put into perspective the influence of energy price differences on labour productivity differences, one must obtain a good estimate of the efficiency differentials. To derive a discrete approximate to these efficiency differentials the procedure begins by taking a Taylor series degree one expansion of lnrc(i) about the vector X(o) which is defined as [ln L(o), lnK(o), lnPE(o), T(o), D(o)] and a degree one expansion of lnrc(o) about X(i).” If we subtract the latter from the former and divide by 2 we have In n(i) -In 71(o) =1/2x=LxK r~(~ln7r~alnX~,+aln~/alnX~,)~(lnX(i)-lnX(o)) 1,
(6)
The relative efficiency for region i is defined in percentage terms as the ratio of RVA in region i to RVA in reference region o, while controlling for the levels of labour, capital services and prices of energy in the two regions. Therefore, the inter-regional efficiency differential (0,,) is defined as Rio= 1/2(aln~/dD~i+alnn/aD~,)(D(i)-D(o)).
(7)
The relative efficiency between two regions (E,) is defined as the exponential of 8, normalized to 100 if efficiency levels in the regions are identical: Ei,= exp(B,J. 100. In order to attach numbers to eq. (7), Hotelling’s (1932) lemma will be used. This lemma implies that the expenditure shares for region s (s=i,o) MY(s) (for Y =L,K) and ME(s) are alnrc(s)/aln Y(s) and - d In rc(s)/a In PE(s), respectively. Furthermore, since efficiency differentials are calculated at a particular point in time (T(i) = T(o) for all i), the 4For a similar usage of the discrete variable D, see Denny and Fuss (1980) where they show that the discrete variable D can be treated as a continuous variable when applying Diewert’s (1976) quadratic lemma.
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between region i and region o can be calculated using
f3,=A7r(i)-l/2~[MY(i)+MY(o)]AY(i) Y
+ 1/2[ME(i)
+ ME(o)] APE(i),
(8)
where Y = L, K and AX(i) = [ln X(i) -In X(o)] for any variable X. The conventional unmodified efficiency differential (0%) would exclude the energy price differential? f3$= Arc(i)-l/27
[MY(i)+MY(o)]
AY(i),
(9)
for Y=L,K. 3. The decomposition of average labour productivity
differentials
The analysis of gross domestic product (GDP) or real value added per employee is often an item of interest to government policy planning departments. The intention of this section is to outline how to decompose labour productivity differences into its explanatory components. Unlike the double deflated measure of output computed by government statistical agencies, the measure of real value added used in this paper is a single deflated measure of output. To be precise, average labour productivity (ALE(s)) is defined as regional real value added per employee. ALE(s) = n(s)/E(s)
for
implying that
AALE
s = 0, i, = An(i) - A-E(i).
(10)
Nevertheless, this latter measure is sufficiently similar in size and concept to that computed by government statistical agencies and by the DenisonKendrick methodology. To compare average labour productivity or output per employee (ALE(s)) across regions, and to explain the differences in terms of differences in capital intensity, quality of labour, efflcikncy, and particularly the influence of differences in energy prices, it is necessary first to define the quality of labour differential. sThe assumption that the energy price differentials are equal to zero is implicitly made in studies of intercountry efficiency differentials [see Christensen, Cummings and Jorgenson (1980), and Jorgenson and Nishimizu (1978)]. Therefore, the efficiency differential shown in eq. (9) is identical to their estimate.
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The quality of labour in region i at a particular point in time is an index which transforms the number of employees (E(i)) into an index of labour services L(i): QL(i) =L(i)/E(i)
implying that
dQL(i) = AL(i) -dE(i).
(11)
Then, using eq. (lo), (11) and rearranging eq. (8) and assuming linear homogeneity6 in L and K, it follows that the average productivity differential between region i and region o can be expressed as the weighted sum of capital intensity, quality of labour, and energy prices: dALE(i) = 1/2(MK(i)
+MK(o))
+ ML(o))dQL(i)
* d(K(i)/E(i)) + 1/2(ML(i)
- 1/2(ME(i) + ME(o))dPE(i)
+ BiO.
(12)
4. The construction of price, quantity, and quality of labour differentials
Before analyzing the empirical results arising from the above formulation, this section will digress and discuss explicity the construction of the differential found in eq. (12). A first step is to construct real value added, capital services, labour services and energy price differentials. Essentially Tornqvist indexes were evaluated. Data sources are in the appendix. For instance, consider the g components which enter the construction of the real value added differential. For each of the components, data is available on value (Vn(i, r)). Deflating these values by gross output price deflators associated with these components produces output components n(i,r). The real value added differential (Arc(i)) between region i and region o is then 437(i) = l/Zr$r (Src(i,r) + Src(0,r))(ln n(i, r) -In 7c(o,r)),
(13)
where Sn(s,r)=Vn(s,r)/(&
V7c(s,r))
for
s=i,o.
Similarly for the quantity differentials of labour and capital
6When RVA is linearly homogeneous with respect alnRVA/alnK= 1 [see Diewert (1974)]. The indirect underlying production function (F’) displaying constant ML(s) + MK(s) = 1 for s = o, i.
to inputs, K and L, alnRVA/aln profit function RVA corresponds returns to scale. The implication
L+ td an is that
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AX(i)= l/2rEI (SX(1’,r)+SX(o,r))(lnX(i,r)-lnX(o,r))
483
(14)
for X = L, K and where
and similarly for the energy price differential dPE(i)=1/2
i (SE(i,r)+SE(o,r))(lnPE(i,r)-lnPE(o,r)) *=l
(15)
for
For constructing the quality of labour index the initial assumption is that in each sectior i of the economy the flow of labour services (L(s,r)) is proportional at each point in time to the number of employees (E(s,r)). The constant of proportionality is QL(r). L(s, r) = QL(r) *E(s, r).
(16)
Thus, the aggregate labour services differential between regions is a weighted sum of employee differentials: (17) The aggregate quality of labour in region s, QL(s) is defined as the ratio of labour services L(s) to the number of employees E(s) =ci= 1E(s, r): QL(s) = L(s)/E(s).
(18)
Therefore the quality of labour differential is QL(i) =.iI
(SL(i, r) +SL(o, r))(lnL(C r) -1n L(o, r))
-[lnE(i)-lnE(o)].
(19)
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5. Results
For all computations, Ontario is chosen as the reference region, primarily because it is the largest of the regional economies. Eq. (10) is used for comparing productivity per worker among regions in Canada.’ The relative productivity levels (normalized to 100) are shown in the sixth row of table 1. Eq. (8) is used for comparing efficiency levels among regions in Canada.* The relative efficiency (expressed as a percent) is listed for the sub-periods in the fourth row of table 1. If the relative efficiency is greater than 100, then regional value added is inherently higher in region i than region o, after adjusting for differences in quantities of labour and capital, the quality of labour and the prices of energy. A list of the relative levels of these latter factors along with the unmodified efficiency levels [see eq. (9)], are also found in table 1. If one does not take into account energy price differentials, Table 1 Relative indexes of contributors to productivity differentials. Differentials
Year
Atlantic
Quebec
Ontario
Prairies
British Columbia
Capital: employee exp [d(K(i)/E(i))] . 100
1962-1968 1969-1973 1974-197s 1962-1978 1962-1968 1969-1973 1974-1978 1962-1978 1962-1968 1969-1973 1974-1978 1962-1978 1962-1968 1969-1973 1974-1978 1962-1978 1962-1968 1969-1973 1974-1978 1962-1978 1962-1968 1969-1973 1974-1978 1962-1978
84.0 97.4 102.4 93.4 103.3 106.7 104.5 104.7 132.7 144.8 123.0 133.4 77.6 73.6 79.8 77.1 75.1 71.9 78.3 75.1 73.2 75.0 81.4 76.1
94.1 95.5 108.0 98.6 101.2 99.1 102.4 100.9 88.6 87.9 88.9 88.5 84.1 84.2 87.6 85.2 84.8 84.9 88.4 85.9 84.1 83.3 90.1 85.6
100.0 100.0
158.8 173.3 153.1 161.4 96.7 100.0 97.7 98.0 95.2 86.2 91.8 91.6 84.0 81.0 105.2 89.4 84.5 81.7 105.6 89.9 96.2 96.7 120.1 103.4
120.8 121.9 117.8 120.2 92.6 94.8 96.8 94.5 116.6 99.9 88.4 103.4 104.1 100.7 106.1 103.7 103.0 100.7 107.0 103.5 103.6 102.4 109.1 104.9
Quality of labour exp [AQ.L(i)]. 100 Price of energy exp [APE(i)]. 100
Efficiency exp [&,] ,100 Unmodified efficiency exp [e&l. 100
Average labour productivity exp [d ALE( i)] . 100
100.0
100.0 100.0
100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
‘A multilateral comparison of average labour productivity between regions i and k k)“) can be defined as AALE(i, k)“= dALE(i, o) -AALE(k, 0). ‘The multilateral efficiency differential between regions i and k can be defined [as suggested by Denny, Fuss and May (1981)] as 0;= &,-8,,. (dALE(i,
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conventional differential analysis dictated by eq. (9) would imply lower relative efficiency levels for the Atlantic region and higher efficiency levels for Quebec and the Prairies. Table 2 describes the relative importance of the aforementioned factors in explaining regional average productivity differentials. The contribution of each factor is defined as the weighted logarithmic differential in the factors divided by the logarithmic differential in average productivity. All numbers are expressed as percentages. A negative number indicates that the direction of contribution is opposite to the average productivity differential. In table 2, it is evident that for the Atlantic region and Quebec, .most of the lower labour productivity is due to the lower efficiency level. The higher quality of labour in these regions has generally helped narrow productivity differentials. In the Atlantic region, approximately 9.2% of the lower productivity differentials were due to the higher energy prices. In contrast, Quebec’s lower energy prices have helped narrow the differential, particularly in the 19741978 period where the energy price differential contribution grew to a share of 8.1%. For the Prairies and British Columbia in the 1974-1978 period, the Table Contribution
Contributing
factor
of factor
Years
differentials
Atlantic
2 to productivity
Quebec
differentials
(%).
Prairies
British Columbia
Capital: employee A [K(i)/E(i)]/d ALE(i)
1962-1968 1969-1973 1974-1978 1962-1978
15.8 2.3 -2.4 6.5
9.5 6.5 - 1.7 5.3
- 390.4 - 500.8 79.4 - 284.8
164.7 236.5 49.6 151.9
Quality of labour dQL(i)/dALE(i)
1962-1968 1969-1973 1974-1978 1962-1978
-7.4 - 17.0 - 16.5 - 12.9
-4.9 3.6 - 16.7 -5.9
56.8 -0.3 -8.7 20.7
- 148.9 - 166.0 -27.1 -118.1
Price of energy dPE(i)/dALE(i)
1962-1968 1969-1973 19741978 1962-1978
10.3 8.1 8.8 9.2
-4.0 -3.9 -8.1 -5.2
-6.8 -21.5 2.9 -8.3
-28.9 -0.4 9.7 -9.1
Efficiency B,,/AALE(i)
1962-1968 1969-1973 19741978 1962-1978
81.4 106.5 110.1 97.2
99.5 93.8 126.5 105.8
440.4 622.7 26.8 372.4
113.2 29.9 67.8 75.3
Average productivity (exp [dALE(i)] . 100)
1962-1968
100.0 (73.2) 100.0 (75.0) 100.0 (81.4) 100.0 (76.1)
100.0 (84.1) 100.0 (83.3) 100.0 (90.1) 100.0 (85.6)
100.0 (96.2) 100.0 (96.7) 100.0 (120.1) 100.0 (103.4)
100.0 (103.6) 100.0 (102.4) 100.0 (109.1) 100.0 (104.9)
1969-1973 1974-1978 1962-1978
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two largest contributing factors are the capitalemployee ratio and the relative efficiency level. The third most important factor contributing to the heightening of the productivity in these two regions is the relatively lower level of energy prices (2.9% share contribution in the Prairies and 9.7% in British Columbia). 6. Conclusions When quantifying regional efficiency differentials, instead of only taking account of differences in capital-employee ratios and differences in quality of labour, this study has also factored energy price differentials into the calculation. By starting with a regional production relation which models regional output as a function of all primary resources, which includes energy as well as labour and capital, an indirect profit function emerged which forms the basis of a modified efficiency computation. A Taylor series approximation to the profit representation of real value added was used to quantify the relative importance to differences ,in average labour productivity of energy price differentials in addition to capital-employee and quality of labour differentials. This technique also provided a consistent time series of regional efficiency in Canada. ’ By being able to trace these efficiency and average productivity levels through time, one is able to see which regions are improving their lot. In fact, on both counts, all regions have improved their lot relative to Ontario. Admittedly the contribution of energy price differentials to productivity differences are not of the magnitude of efficiency differentials but in any given time period can be of greater relative importance than either the quality of labour or capital-employee ratio contributions. Depending on the region and time period we found both over- and under-estimates of efficiency differentials if energy prices are not accounted for. Appendix This section will summarize the data sources employed. The primary sources of data were Statistics Canada, Revenue Canada, the Conference Board of Canada, and Energy, Mines, and Resources. Annual data relating to output, labour, capital and energy were collected for each of live regions (the Atlantic provinces, Quebec, Ontario, the Prairies, and British Columbia) from 1962 to 1978. With respect to output, it is necessary to obtain regional measures of real gin a report prepared for the Economic Council of Canada, Auer (1979) examines regional labour productivity differences using average industry data for the 197&1973 period. However, he does not examine the changes in relative productivity levels and efficiency levels through time.
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value added by sector. Whereas, indirect business taxes such as retail sales taxes and excise taxes are not included, indirect business taxes which would be components in payments for factor services (such as property taxes) will be included.” The output components used in estimating the output differential [see eq. (13)] are the agriculture, forestry, fishing, mining, construction, manufacturing, and services sectors. l1 Nominal value added (including relevant local taxes) in these sectors is created by employing the Statistics Canada publications, Survey of Production (61-202), and the ProvinciaZ Economic Accounts (13-213) plus data furnished by the Local Government Section of the Public Finance Division of Statistics Canada. Regional indexes of real value added by the categories already listed can be found in the Conference Board of Canada’s (1980) publication, The Provincial Economies 1961-1979.
The Labour Division of Statistics Canada provided wage income data for the employment categories of agriculture; forestry; mining; manufacturing; communications and other utilities; trade; construction; transportation, finance, insurance and real estate; commercial services; community, business and personal service; and public administration. Wage data for the military was obtained from the Provincial Economic Accounts (13-213). Imputed wage rates for unpaid labour were calculated and supplementary labour income was allocated across sectors. Employment data by sector was obtained from Statistics Canada’s publications, The Labour Force (71-001 and 71-201) and Estimates of Employees by Province and Industry (72-008 and 72-516). Capital in this study was confined to reproducible capital.12 This meant developing a time series of capital stocks for 10 asset classes: residential structures; inventories; and structures, machinery, and durable equipment found in the manufacturing; primary; transportation, communication and utilities; trade; finance; commercial services; institutional; and government services sector. The residential capital stocks were furnished by the Construc“This is similar to Christensen, Cummings and Jorgenson’s (1978) formulation. “Because of the difficulties in estimating the services producing sectors’ outputs the services producing sector is not disaggregated. Included in this sector are utilities, transportation and communication; wholesale and retail trade; finance insurance and real estate; community, business and personal service; and public administration and defence. [This categorization is consistent with that found in Christensen, Cummings and Jorgenson (1978).] See the United Nations Economic and Social Council’s (Statistics Commission) publication, Country Practices in National Accounting at Constant Prices, 1974, (1974) for a discussion of the methods used to estimate real domestic product in a variety of countries. “There is an ongoing debate concerning what should be in the capital stock aggregate. Diewert (1980) summarizes the issues involved and unlike Christensen, Cummings and Jorgenson (1978) recommends the exclusion of consumer durables because of the inconsistencies with the definition that a capital good is employed to produce other goods and services [see Creamer (1972, p. 61)]. Land and natural resources have been left out in this study because of the lack of data concerning acquisition prices and valuations. The definition of capital in this paper is slightIy narrower than Diewert’s but wider than studies of Canadian productivity by Auer (1979) and Sims and Stanton (1980) who omit inventories and residential capital stocks.
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tion Division of Statistics Canada. The Manufacturing and Primary Industry Division, Industry Statistics Branch and the Agriculture Statistics Dvision of Statistics Canada provided the inventory estimates. Real capital stock estimates for the remaining categories were obtained using investment series found in Fixed Capital Flows and Stocks (13-211) plus provincial data provided by the Construction Division of Statistics Canada. Geometric depreciation rates were used in the construction of the capital stock. The value of capital services by sector was defined as the sum of expenditures on federal and provincial corporation taxes, municipal taxes, the present value of acquisition costs and depreciation less capital gains. The price index of capital services is the value divided by the capital stock.13 Corporation taxes have been calculated using Revenue Canada’s publication, Taxation Statistics (1960--1970), and Statistics Canada’s publications, Corporation Taxation Statistics (61-208), Principal Taxes and Rates (68-201) and Local Government Finance (68-203). In constructuring the energy price differentials [see eq. (15)] regional energy prices and quantities were gathered for coal, electricity, natural gas, and oil products. The prices of the energy components, excluding retail and distribution margins and quantities were constructed using data from Statistics Canada’s Electric Power Statistics WZume II (57-202) and from data furnished by Energy, Mines, and Resources. r3This conforms to the user price of capital introduced by Griliches and Jorgenson (1966).
References Auer, L., 1979, Regional disparities of productivity and growth (Economic Council of Canada, Ottawa). Burgess, D.F., 1984, Energy prices, capital formation, and potential GNP, The Energy Journal 5, l-27. Caves, D.W., L.R. Christensen and W.E. Diewert, 1982, Multilateral comparisons of output, input and productivity using superlative index numbers, Economic Journal 92, 73-86. Christensen, L.R., D. Cummings and D.W. Jorgenson, 1978, Productivity growth 1947-73: An international comparison, in: W.G. Dewald, ed., The impact of international trade and investment on employment (Government Printing Office, Washington, DC). Christensen, L.R., D. Cummings and D.W. Jorgenson, 1980, Relative productivity levels, 19471973: An international comparison, Discussion paper no. 773 (Harvard Institute for Economic Research, Harvard University, Cambridge, MA). Conference Board of Canada, 1980, The provincial economies 1961-1979 data (The Conference Board of Canada, Ottawa). Creamer, D., 1972, Measuring capital input for total factor productivity analysis: Comments by a sometime estimator, Review of Income and Wealth 18, 55-78. Denny, M. and M. Fuss, 1980, Intertemporal and interspatial comparison of cost efficiency and productivity, Institute for Policy Analysis working paper no. 8018 (University of Toronto, Toronto). Denny, M. and M. Fuss, 1981, Intertemporal changes in the levels of regional labour productivity in Canadian manufacturing, Institute for Policy Analysis working paper no. 8131 (University of Toronto, Toronto).
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Denny, M., M.Fuss and J.D. May, 1981, Intertemporal changes in regional productivity in Canadian manufacturing, The Canadian Journal of Economics XIV, 390408. Diewert, W.E., 1974, Applications of duality theory, in: M.D. Intrilligator and D.A. Kendrick, eds., Frontiers of quantitative economics, Vol. II (North-Holland, Amsterdam) 106171. Diewert, W.E., 1976, Exact and superlative index numbers, Journal of Econometrics 4, no. 2, 115-145. Diewert,W.E., 1980, Aggregation problems in the measurement of capital, in: D. Usher, ed., The measurement of capital (The University of Chicago Press, Chicago, IL) 433-528 Griliches, Z. and D.W. Jorgenson, 1966, Sources of measured productivity change: Capital input, American Economic Review 56, 50-61. Hotelling, H., 1932, Edgeworth’s taxation paradox and the nature of demand and supply functions, Journal of Political Economy 40, 577-616. Jorgenson, D.W. and M. Nishimizu, 1978, U.S. and Japanese economic growth, 1952-74: An international comparison, Economic Journal 88, 707-726. Manne, A.S., 1977, Eta-macro: A model of energy economy interactions, in: C.J. Hitch, ed., Modelling energy-economy interactions: Five approaches (Resources for the Future, Washington, DC) 145. Peck, S.C. and J.S. Solow, 1982, Domestic energy: A forgotton factor in simple energy-economy models, The Energy Journal 3, 39-53. Revenue Canada, 1960-1970, Taxation statistics, RV44, (Revenue Canada, Ottawa). Sims, H. and J. Stanton, 1980, Recent changes in patterns of productivity growth in Canada (Department of Finance Canada, Ottawa). Statistics Canada, 19261979, various issues as listed in appendix (Ottawa). Sweeney, J.L., 1979, Energy and economic growth: A conceptual framework, in: B. Kursunoglu and A. Perlmutter, eds., Directions in energy policy: A comprehensive approach to energy resource decision making (Ballinger, Cambridge, MA) 115-140. United Nations Economic and Social Council, 1974, Country practices in national accounting at constant prices, 1974 (Statistical Commision, New York). Wright, B., 1980, The cost of tax-induced energy conservation, The Bell Journal of Economics 11, no. 1, 84-107.
PRODUCTIVITY
AND
ENERGY
PRICE
DIFFERENTIALS
Dean C. MOUNTAIN* Ontario York
Hydro,
University,
Toronto, Downsoiew,
Ontario Ontario
M5G M3J
1X6, IP3,
Canada Canada
Received September 1982, final version received January 1985 In taking account of the interrelationship between energy and other primary resources, labour and capital, this paper presents a methodology for quantifying regional efficiency differentials using Taylor series approximations to profit functions representing regional economies. The resulting formulation makes it possible to decompose labour productivity into its contributing factors which now include energy price differentials in addition to such traditional variables as differentials involving CapitaLemployee ratios and the quality of labour. This approach is applied to Canadian regional data from 1962 to 1978. On average, between 5.2% and 9.2% of Canadian regional productivity differentials can be attributed to regional energy price differentials.
1. Introduction
Since the birth of Canada as a nation there have always been large regional economic disparities. Significant divergences in efficiency levels and average labour productivity ratios customarily characterize such disparities. To explain these divergences this paper begins by presenting a methodology for quantifying these regional efficiency differentials based on Taylor series approximations to profit functions representing regional economies. A simple extenstion of the international literature devoted to labour productivity differentials would be to explain these divergences in terms of such traditional variables as capital-employee ratio and quality of labour differentials. However, with the aid of a profit formulation this paper is also able to quantify the contribution to productivity differentials of differing regional energy price differences. This concern stems from the recognition of energy as an important intermediate input in a region’s production process and the observance that energy prices have differed considerably across Canada. Annual Canadian regional data for the Atlantic region, Quebec, Ontario, the *In preparing this paper, valuable suggestions have been provided by Byron Spencer. In addition, the paper’s presentation has benefited significantly from suggestions made by Urs Schweizer and an anonymous referee. David Durfey’s extremely competent and diligent research assistance is gratefully acknowledged. 0166-0462/85/$3.30 0 1985, Elsevier Science Publishers B.V. (North-Holland)
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Prairies, and British Columbia will be used to examine these issues over the 196221978 period. A survey of the literature will show that in the industrial efficiency and productivity level comparisons the methodology has involved employing cost and gross production formulations and for international comparisons the economies are represented by value added production functi0ns.l In contrast, in order to take account of the impact of significant regional price differences of the intermediate input energy, this study outlines a procedure for comparing efficiency levels based on Taylor series approximations to indirect profit functions representing regional economies. Relative efficiency for region i will be defined in percentage terms as the ratio of real value added (RV’A) in region i to RV’A in reference region o, while controlling for the number of employees, capital services, energy prices, and quality of labour. This results in average labour productivity differentials being functions of differentials in energy prices in addition to differentials in capital-employee ratios and differentials in quality of labour. [Average labour productivity is here defined as regional real value added (RVA) per employee.] The paper starts with a profit specification which incorporates the price of energy in addition to quantities of labour and capital as ingredients in a regional economy’s production process. This section then proceeds to illustrate why this specification would suggest a modified efficiency differential. Using the theory of section 2 as groundwork, the third section then decomposes average labour productivity differentials into its ingredient components. Section 4 provides a brief digression into a discussion of the actual construction of quantity and price differentials, plus the quality of labour differentials. Section 5 provides the empirical results as applied to the Canadian regions from 1962 to 1978. Conclusions then follow. 2. A profit specification
To take account of energy’s role in explaining productivity and efficiency differentials a convenient starting point is to begin by specifying a relationship between regional economy i’s output at time s (Y(i,s)) and the primary resources labour (L(i,s)), capital (K(i,s)) and energy (EN(i,s)) plus a tech‘Recently there has emerged a literature devoted to making international comparisons of efficiency and productivity levels [see Jorgenson and Nishimizu (1978), Christensen, Cummings and Jorgenson (1980), and Caves, Christensen and Diewert (1982)]. As well, regional efficiency comparisons have recently been made for manufacturing in Canada [see Denny and Fuss (1980, 1981) and Denny, Fuss and May (1981)]. ‘The approach used in this paper to approximate a profit function is very similar to that employed by Denny, Fuss and May (1981) in their cost specification. However, this paper’s definition of efficiency differs slightly from that used by Denny, Fuss and May (1981). In the context of a cost function for manufacturing, they define the efficiency level as the relative total cost differential between regions after correcting for the effects of differing input prices and output levels.
D.C. Mountain,
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nology index (T(i, s)), Y(i, s) =F(L(i, s)), K(i, s), EN(i, s), T(i, s)).
(1)
Within EN(i,s) are both imported energy and regionally produced energy. The final output (Y) can either be consumed, invested or sold to pay for energy inputs. If in each region all producing units are maximizing profits, real value added at a regional level of aggregation is also maximized for L=L, K=R, max R VA = F(L, I?, EN, T) - PE . EN,
(2)
where PE is the real price of the input EN.3 This real value added specification, which is a regional real gross domestic product (GDP) formulation, is often used by other authors in examining the interrelationship between energy and an aggregate economy [e.g., Manne (1977), Sweeney (1979), Wright (1980), Peck and Solow (1982) and Burgess (1984)-J. The maximand of eq. (2) is the optimal level of the region’s real value added (R VA*(i, s)) which is an indirect function of L(i, s), K(i, s), and PE(i, s) and T(i,s). This means that RVA*(i, s) =II,[(L(i,
s), K(i, s), PE(i, s), T(i, s)].
(3)
It is assumed that the logarithms of the profit function are well approximated by a function of the logarithms of L(i,s), K(i,s), PE(i,s), T(i,s) and D -where D is a vector of dummy variables (D(i)), one for each region excluding the reference region. In R VA*(i, s) = In n(i, s) = G*[ln L(i, s), In K(i, s), In PE(i, s), T(i, s), D].
(4)
Notice that the assumption is made that the logarithms of the RVA function nis has become G* with a vector of dummy variables as one of its components. The common function G* indicates that there are identical components across regions but differences in formulation, however, are accounted for by including a vector of dummy variables in the profit function. This technique, in the context of a cost function, was first introduced by Denny, Fuss and May (1981). 3The price of energy is deflated by the region’s gross output price deflator (which is not the GDP price deflator). The resultant estimate of real value added is not the conventional measure of real GDP which uses double deflation techniques but instead a single deflated measure of output.
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Because the focus of this paper is to make inter-regional comparisons at one point in time (period s), from hereon the time index will be dropped. Therefore, In rc(i)= G*[ln L(i), In K(i), In PE(i), T(i), D(i)].
(5)
One of the purposes of this paper is to provide a measure of inter-regional efficiency differentials having netted out differences in capital-employee ratios, prices of energy, and quality of labour. Moreover, to put into perspective the influence of energy price differences on labour productivity differences, one must obtain a good estimate of the efficiency differentials. To derive a discrete approximate to these efficiency differentials the procedure begins by taking a Taylor series degree one expansion of lnrc(i) about the vector X(o) which is defined as [ln L(o), lnK(o), lnPE(o), T(o), D(o)] and a degree one expansion of lnrc(o) about X(i).” If we subtract the latter from the former and divide by 2 we have In n(i) -In 71(o) =1/2x=LxK r~(~ln7r~alnX~,+aln~/alnX~,)~(lnX(i)-lnX(o)) 1,
(6)
The relative efficiency for region i is defined in percentage terms as the ratio of RVA in region i to RVA in reference region o, while controlling for the levels of labour, capital services and prices of energy in the two regions. Therefore, the inter-regional efficiency differential (0,,) is defined as Rio= 1/2(aln~/dD~i+alnn/aD~,)(D(i)-D(o)).
(7)
The relative efficiency between two regions (E,) is defined as the exponential of 8, normalized to 100 if efficiency levels in the regions are identical: Ei,= exp(B,J. 100. In order to attach numbers to eq. (7), Hotelling’s (1932) lemma will be used. This lemma implies that the expenditure shares for region s (s=i,o) MY(s) (for Y =L,K) and ME(s) are alnrc(s)/aln Y(s) and - d In rc(s)/a In PE(s), respectively. Furthermore, since efficiency differentials are calculated at a particular point in time (T(i) = T(o) for all i), the 4For a similar usage of the discrete variable D, see Denny and Fuss (1980) where they show that the discrete variable D can be treated as a continuous variable when applying Diewert’s (1976) quadratic lemma.
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481
between region i and region o can be calculated using
f3,=A7r(i)-l/2~[MY(i)+MY(o)]AY(i) Y
+ 1/2[ME(i)
+ ME(o)] APE(i),
(8)
where Y = L, K and AX(i) = [ln X(i) -In X(o)] for any variable X. The conventional unmodified efficiency differential (0%) would exclude the energy price differential? f3$= Arc(i)-l/27
[MY(i)+MY(o)]
AY(i),
(9)
for Y=L,K. 3. The decomposition of average labour productivity
differentials
The analysis of gross domestic product (GDP) or real value added per employee is often an item of interest to government policy planning departments. The intention of this section is to outline how to decompose labour productivity differences into its explanatory components. Unlike the double deflated measure of output computed by government statistical agencies, the measure of real value added used in this paper is a single deflated measure of output. To be precise, average labour productivity (ALE(s)) is defined as regional real value added per employee. ALE(s) = n(s)/E(s)
for
implying that
AALE
s = 0, i, = An(i) - A-E(i).
(10)
Nevertheless, this latter measure is sufficiently similar in size and concept to that computed by government statistical agencies and by the DenisonKendrick methodology. To compare average labour productivity or output per employee (ALE(s)) across regions, and to explain the differences in terms of differences in capital intensity, quality of labour, efflcikncy, and particularly the influence of differences in energy prices, it is necessary first to define the quality of labour differential. sThe assumption that the energy price differentials are equal to zero is implicitly made in studies of intercountry efficiency differentials [see Christensen, Cummings and Jorgenson (1980), and Jorgenson and Nishimizu (1978)]. Therefore, the efficiency differential shown in eq. (9) is identical to their estimate.
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The quality of labour in region i at a particular point in time is an index which transforms the number of employees (E(i)) into an index of labour services L(i): QL(i) =L(i)/E(i)
implying that
dQL(i) = AL(i) -dE(i).
(11)
Then, using eq. (lo), (11) and rearranging eq. (8) and assuming linear homogeneity6 in L and K, it follows that the average productivity differential between region i and region o can be expressed as the weighted sum of capital intensity, quality of labour, and energy prices: dALE(i) = 1/2(MK(i)
+MK(o))
+ ML(o))dQL(i)
* d(K(i)/E(i)) + 1/2(ML(i)
- 1/2(ME(i) + ME(o))dPE(i)
+ BiO.
(12)
4. The construction of price, quantity, and quality of labour differentials
Before analyzing the empirical results arising from the above formulation, this section will digress and discuss explicity the construction of the differential found in eq. (12). A first step is to construct real value added, capital services, labour services and energy price differentials. Essentially Tornqvist indexes were evaluated. Data sources are in the appendix. For instance, consider the g components which enter the construction of the real value added differential. For each of the components, data is available on value (Vn(i, r)). Deflating these values by gross output price deflators associated with these components produces output components n(i,r). The real value added differential (Arc(i)) between region i and region o is then 437(i) = l/Zr$r (Src(i,r) + Src(0,r))(ln n(i, r) -In 7c(o,r)),
(13)
where Sn(s,r)=Vn(s,r)/(&
V7c(s,r))
for
s=i,o.
Similarly for the quantity differentials of labour and capital
6When RVA is linearly homogeneous with respect alnRVA/alnK= 1 [see Diewert (1974)]. The indirect underlying production function (F’) displaying constant ML(s) + MK(s) = 1 for s = o, i.
to inputs, K and L, alnRVA/aln profit function RVA corresponds returns to scale. The implication
L+ td an is that
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dt@rentials
AX(i)= l/2rEI (SX(1’,r)+SX(o,r))(lnX(i,r)-lnX(o,r))
483
(14)
for X = L, K and where
and similarly for the energy price differential dPE(i)=1/2
i (SE(i,r)+SE(o,r))(lnPE(i,r)-lnPE(o,r)) *=l
(15)
for
For constructing the quality of labour index the initial assumption is that in each sectior i of the economy the flow of labour services (L(s,r)) is proportional at each point in time to the number of employees (E(s,r)). The constant of proportionality is QL(r). L(s, r) = QL(r) *E(s, r).
(16)
Thus, the aggregate labour services differential between regions is a weighted sum of employee differentials: (17) The aggregate quality of labour in region s, QL(s) is defined as the ratio of labour services L(s) to the number of employees E(s) =ci= 1E(s, r): QL(s) = L(s)/E(s).
(18)
Therefore the quality of labour differential is QL(i) =.iI
(SL(i, r) +SL(o, r))(lnL(C r) -1n L(o, r))
-[lnE(i)-lnE(o)].
(19)
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5. Results
For all computations, Ontario is chosen as the reference region, primarily because it is the largest of the regional economies. Eq. (10) is used for comparing productivity per worker among regions in Canada.’ The relative productivity levels (normalized to 100) are shown in the sixth row of table 1. Eq. (8) is used for comparing efficiency levels among regions in Canada.* The relative efficiency (expressed as a percent) is listed for the sub-periods in the fourth row of table 1. If the relative efficiency is greater than 100, then regional value added is inherently higher in region i than region o, after adjusting for differences in quantities of labour and capital, the quality of labour and the prices of energy. A list of the relative levels of these latter factors along with the unmodified efficiency levels [see eq. (9)], are also found in table 1. If one does not take into account energy price differentials, Table 1 Relative indexes of contributors to productivity differentials. Differentials
Year
Atlantic
Quebec
Ontario
Prairies
British Columbia
Capital: employee exp [d(K(i)/E(i))] . 100
1962-1968 1969-1973 1974-197s 1962-1978 1962-1968 1969-1973 1974-1978 1962-1978 1962-1968 1969-1973 1974-1978 1962-1978 1962-1968 1969-1973 1974-1978 1962-1978 1962-1968 1969-1973 1974-1978 1962-1978 1962-1968 1969-1973 1974-1978 1962-1978
84.0 97.4 102.4 93.4 103.3 106.7 104.5 104.7 132.7 144.8 123.0 133.4 77.6 73.6 79.8 77.1 75.1 71.9 78.3 75.1 73.2 75.0 81.4 76.1
94.1 95.5 108.0 98.6 101.2 99.1 102.4 100.9 88.6 87.9 88.9 88.5 84.1 84.2 87.6 85.2 84.8 84.9 88.4 85.9 84.1 83.3 90.1 85.6
100.0 100.0
158.8 173.3 153.1 161.4 96.7 100.0 97.7 98.0 95.2 86.2 91.8 91.6 84.0 81.0 105.2 89.4 84.5 81.7 105.6 89.9 96.2 96.7 120.1 103.4
120.8 121.9 117.8 120.2 92.6 94.8 96.8 94.5 116.6 99.9 88.4 103.4 104.1 100.7 106.1 103.7 103.0 100.7 107.0 103.5 103.6 102.4 109.1 104.9
Quality of labour exp [AQ.L(i)]. 100 Price of energy exp [APE(i)]. 100
Efficiency exp [&,] ,100 Unmodified efficiency exp [e&l. 100
Average labour productivity exp [d ALE( i)] . 100
100.0
100.0 100.0
100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0
‘A multilateral comparison of average labour productivity between regions i and k k)“) can be defined as AALE(i, k)“= dALE(i, o) -AALE(k, 0). ‘The multilateral efficiency differential between regions i and k can be defined [as suggested by Denny, Fuss and May (1981)] as 0;= &,-8,,. (dALE(i,
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485
conventional differential analysis dictated by eq. (9) would imply lower relative efficiency levels for the Atlantic region and higher efficiency levels for Quebec and the Prairies. Table 2 describes the relative importance of the aforementioned factors in explaining regional average productivity differentials. The contribution of each factor is defined as the weighted logarithmic differential in the factors divided by the logarithmic differential in average productivity. All numbers are expressed as percentages. A negative number indicates that the direction of contribution is opposite to the average productivity differential. In table 2, it is evident that for the Atlantic region and Quebec, .most of the lower labour productivity is due to the lower efficiency level. The higher quality of labour in these regions has generally helped narrow productivity differentials. In the Atlantic region, approximately 9.2% of the lower productivity differentials were due to the higher energy prices. In contrast, Quebec’s lower energy prices have helped narrow the differential, particularly in the 19741978 period where the energy price differential contribution grew to a share of 8.1%. For the Prairies and British Columbia in the 1974-1978 period, the Table Contribution
Contributing
factor
of factor
Years
differentials
Atlantic
2 to productivity
Quebec
differentials
(%).
Prairies
British Columbia
Capital: employee A [K(i)/E(i)]/d ALE(i)
1962-1968 1969-1973 1974-1978 1962-1978
15.8 2.3 -2.4 6.5
9.5 6.5 - 1.7 5.3
- 390.4 - 500.8 79.4 - 284.8
164.7 236.5 49.6 151.9
Quality of labour dQL(i)/dALE(i)
1962-1968 1969-1973 1974-1978 1962-1978
-7.4 - 17.0 - 16.5 - 12.9
-4.9 3.6 - 16.7 -5.9
56.8 -0.3 -8.7 20.7
- 148.9 - 166.0 -27.1 -118.1
Price of energy dPE(i)/dALE(i)
1962-1968 1969-1973 19741978 1962-1978
10.3 8.1 8.8 9.2
-4.0 -3.9 -8.1 -5.2
-6.8 -21.5 2.9 -8.3
-28.9 -0.4 9.7 -9.1
Efficiency B,,/AALE(i)
1962-1968 1969-1973 19741978 1962-1978
81.4 106.5 110.1 97.2
99.5 93.8 126.5 105.8
440.4 622.7 26.8 372.4
113.2 29.9 67.8 75.3
Average productivity (exp [dALE(i)] . 100)
1962-1968
100.0 (73.2) 100.0 (75.0) 100.0 (81.4) 100.0 (76.1)
100.0 (84.1) 100.0 (83.3) 100.0 (90.1) 100.0 (85.6)
100.0 (96.2) 100.0 (96.7) 100.0 (120.1) 100.0 (103.4)
100.0 (103.6) 100.0 (102.4) 100.0 (109.1) 100.0 (104.9)
1969-1973 1974-1978 1962-1978
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two largest contributing factors are the capitalemployee ratio and the relative efficiency level. The third most important factor contributing to the heightening of the productivity in these two regions is the relatively lower level of energy prices (2.9% share contribution in the Prairies and 9.7% in British Columbia). 6. Conclusions When quantifying regional efficiency differentials, instead of only taking account of differences in capital-employee ratios and differences in quality of labour, this study has also factored energy price differentials into the calculation. By starting with a regional production relation which models regional output as a function of all primary resources, which includes energy as well as labour and capital, an indirect profit function emerged which forms the basis of a modified efficiency computation. A Taylor series approximation to the profit representation of real value added was used to quantify the relative importance to differences ,in average labour productivity of energy price differentials in addition to capital-employee and quality of labour differentials. This technique also provided a consistent time series of regional efficiency in Canada. ’ By being able to trace these efficiency and average productivity levels through time, one is able to see which regions are improving their lot. In fact, on both counts, all regions have improved their lot relative to Ontario. Admittedly the contribution of energy price differentials to productivity differences are not of the magnitude of efficiency differentials but in any given time period can be of greater relative importance than either the quality of labour or capital-employee ratio contributions. Depending on the region and time period we found both over- and under-estimates of efficiency differentials if energy prices are not accounted for. Appendix This section will summarize the data sources employed. The primary sources of data were Statistics Canada, Revenue Canada, the Conference Board of Canada, and Energy, Mines, and Resources. Annual data relating to output, labour, capital and energy were collected for each of live regions (the Atlantic provinces, Quebec, Ontario, the Prairies, and British Columbia) from 1962 to 1978. With respect to output, it is necessary to obtain regional measures of real gin a report prepared for the Economic Council of Canada, Auer (1979) examines regional labour productivity differences using average industry data for the 197&1973 period. However, he does not examine the changes in relative productivity levels and efficiency levels through time.
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value added by sector. Whereas, indirect business taxes such as retail sales taxes and excise taxes are not included, indirect business taxes which would be components in payments for factor services (such as property taxes) will be included.” The output components used in estimating the output differential [see eq. (13)] are the agriculture, forestry, fishing, mining, construction, manufacturing, and services sectors. l1 Nominal value added (including relevant local taxes) in these sectors is created by employing the Statistics Canada publications, Survey of Production (61-202), and the ProvinciaZ Economic Accounts (13-213) plus data furnished by the Local Government Section of the Public Finance Division of Statistics Canada. Regional indexes of real value added by the categories already listed can be found in the Conference Board of Canada’s (1980) publication, The Provincial Economies 1961-1979.
The Labour Division of Statistics Canada provided wage income data for the employment categories of agriculture; forestry; mining; manufacturing; communications and other utilities; trade; construction; transportation, finance, insurance and real estate; commercial services; community, business and personal service; and public administration. Wage data for the military was obtained from the Provincial Economic Accounts (13-213). Imputed wage rates for unpaid labour were calculated and supplementary labour income was allocated across sectors. Employment data by sector was obtained from Statistics Canada’s publications, The Labour Force (71-001 and 71-201) and Estimates of Employees by Province and Industry (72-008 and 72-516). Capital in this study was confined to reproducible capital.12 This meant developing a time series of capital stocks for 10 asset classes: residential structures; inventories; and structures, machinery, and durable equipment found in the manufacturing; primary; transportation, communication and utilities; trade; finance; commercial services; institutional; and government services sector. The residential capital stocks were furnished by the Construc“This is similar to Christensen, Cummings and Jorgenson’s (1978) formulation. “Because of the difficulties in estimating the services producing sectors’ outputs the services producing sector is not disaggregated. Included in this sector are utilities, transportation and communication; wholesale and retail trade; finance insurance and real estate; community, business and personal service; and public administration and defence. [This categorization is consistent with that found in Christensen, Cummings and Jorgenson (1978).] See the United Nations Economic and Social Council’s (Statistics Commission) publication, Country Practices in National Accounting at Constant Prices, 1974, (1974) for a discussion of the methods used to estimate real domestic product in a variety of countries. “There is an ongoing debate concerning what should be in the capital stock aggregate. Diewert (1980) summarizes the issues involved and unlike Christensen, Cummings and Jorgenson (1978) recommends the exclusion of consumer durables because of the inconsistencies with the definition that a capital good is employed to produce other goods and services [see Creamer (1972, p. 61)]. Land and natural resources have been left out in this study because of the lack of data concerning acquisition prices and valuations. The definition of capital in this paper is slightIy narrower than Diewert’s but wider than studies of Canadian productivity by Auer (1979) and Sims and Stanton (1980) who omit inventories and residential capital stocks.
488
D.C. Mounta;,
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tion Division of Statistics Canada. The Manufacturing and Primary Industry Division, Industry Statistics Branch and the Agriculture Statistics Dvision of Statistics Canada provided the inventory estimates. Real capital stock estimates for the remaining categories were obtained using investment series found in Fixed Capital Flows and Stocks (13-211) plus provincial data provided by the Construction Division of Statistics Canada. Geometric depreciation rates were used in the construction of the capital stock. The value of capital services by sector was defined as the sum of expenditures on federal and provincial corporation taxes, municipal taxes, the present value of acquisition costs and depreciation less capital gains. The price index of capital services is the value divided by the capital stock.13 Corporation taxes have been calculated using Revenue Canada’s publication, Taxation Statistics (1960--1970), and Statistics Canada’s publications, Corporation Taxation Statistics (61-208), Principal Taxes and Rates (68-201) and Local Government Finance (68-203). In constructuring the energy price differentials [see eq. (15)] regional energy prices and quantities were gathered for coal, electricity, natural gas, and oil products. The prices of the energy components, excluding retail and distribution margins and quantities were constructed using data from Statistics Canada’s Electric Power Statistics WZume II (57-202) and from data furnished by Energy, Mines, and Resources. r3This conforms to the user price of capital introduced by Griliches and Jorgenson (1966).
References Auer, L., 1979, Regional disparities of productivity and growth (Economic Council of Canada, Ottawa). Burgess, D.F., 1984, Energy prices, capital formation, and potential GNP, The Energy Journal 5, l-27. Caves, D.W., L.R. Christensen and W.E. Diewert, 1982, Multilateral comparisons of output, input and productivity using superlative index numbers, Economic Journal 92, 73-86. Christensen, L.R., D. Cummings and D.W. Jorgenson, 1978, Productivity growth 1947-73: An international comparison, in: W.G. Dewald, ed., The impact of international trade and investment on employment (Government Printing Office, Washington, DC). Christensen, L.R., D. Cummings and D.W. Jorgenson, 1980, Relative productivity levels, 19471973: An international comparison, Discussion paper no. 773 (Harvard Institute for Economic Research, Harvard University, Cambridge, MA). Conference Board of Canada, 1980, The provincial economies 1961-1979 data (The Conference Board of Canada, Ottawa). Creamer, D., 1972, Measuring capital input for total factor productivity analysis: Comments by a sometime estimator, Review of Income and Wealth 18, 55-78. Denny, M. and M. Fuss, 1980, Intertemporal and interspatial comparison of cost efficiency and productivity, Institute for Policy Analysis working paper no. 8018 (University of Toronto, Toronto). Denny, M. and M. Fuss, 1981, Intertemporal changes in the levels of regional labour productivity in Canadian manufacturing, Institute for Policy Analysis working paper no. 8131 (University of Toronto, Toronto).
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Denny, M., M.Fuss and J.D. May, 1981, Intertemporal changes in regional productivity in Canadian manufacturing, The Canadian Journal of Economics XIV, 390408. Diewert, W.E., 1974, Applications of duality theory, in: M.D. Intrilligator and D.A. Kendrick, eds., Frontiers of quantitative economics, Vol. II (North-Holland, Amsterdam) 106171. Diewert, W.E., 1976, Exact and superlative index numbers, Journal of Econometrics 4, no. 2, 115-145. Diewert,W.E., 1980, Aggregation problems in the measurement of capital, in: D. Usher, ed., The measurement of capital (The University of Chicago Press, Chicago, IL) 433-528 Griliches, Z. and D.W. Jorgenson, 1966, Sources of measured productivity change: Capital input, American Economic Review 56, 50-61. Hotelling, H., 1932, Edgeworth’s taxation paradox and the nature of demand and supply functions, Journal of Political Economy 40, 577-616. Jorgenson, D.W. and M. Nishimizu, 1978, U.S. and Japanese economic growth, 1952-74: An international comparison, Economic Journal 88, 707-726. Manne, A.S., 1977, Eta-macro: A model of energy economy interactions, in: C.J. Hitch, ed., Modelling energy-economy interactions: Five approaches (Resources for the Future, Washington, DC) 145. Peck, S.C. and J.S. Solow, 1982, Domestic energy: A forgotton factor in simple energy-economy models, The Energy Journal 3, 39-53. Revenue Canada, 1960-1970, Taxation statistics, RV44, (Revenue Canada, Ottawa). Sims, H. and J. Stanton, 1980, Recent changes in patterns of productivity growth in Canada (Department of Finance Canada, Ottawa). Statistics Canada, 19261979, various issues as listed in appendix (Ottawa). Sweeney, J.L., 1979, Energy and economic growth: A conceptual framework, in: B. Kursunoglu and A. Perlmutter, eds., Directions in energy policy: A comprehensive approach to energy resource decision making (Ballinger, Cambridge, MA) 115-140. United Nations Economic and Social Council, 1974, Country practices in national accounting at constant prices, 1974 (Statistical Commision, New York). Wright, B., 1980, The cost of tax-induced energy conservation, The Bell Journal of Economics 11, no. 1, 84-107.