11 (2000) 491 – 506
A general equilibrium analysis of the evolution
of Canadian service productivity
Pierre Mohnen
a,*, Thijs ten Raa
b aDepartement des Sceinces Economiques,Uni6ersite´ du Que´bec a` Montre´al and CIRANO,C.P.8888,
Succ.Centre-Ville,Montreal,Quebec,Canada H3C3P8 bTilburg Uni
6ersity,Tilburg,The Netherlands
Received 4 January 2000; received in revised form 12 August 2000; accepted 30 August 2000
Abstract
Can the slowdown in total factor productivity (TFP) that we have experienced since the mid-seventies be ascribed to the increasing importance of services, or do we instead observe an improvement of productivity in the service sectors by way of learning-by-doing or specialization? We feel that such questions are best answered within a general equilibrium analysis of the whole economy, i.e. a structural view of the whole economy. We maximize the level of domestic consumption subject to commodity balances and endowment constraints. The Lagrange multipliers associated with the endowment constraints measure the marginal productivities of labor and capital. We declare these shadow prices to be the factor productivities. The main empirical contribution of this paper is a reexamination of the services paradox. In Canada, the sluggish productivity in services is limited to finance, insurance and real estate, and to business and personal services. Any attempt to resolve the services paradox may focus on these two sectors. Transportation, trade, and to a lesser extent communication are progressive sectors. © 2000 Elsevier Science B.V. All rights reserved.
Keywords:Solow residual; Equilibrium analysis; Canadian service productivity; Total factor productivity www.elsevier.nl/locate/strueco
1. Introduction
Services have long ago relegated manufacturing to second rank in the importance of an economy’s total activity. It is often argued that services suffer from the Baumol disease. More and more resources are devoted to services, where
productiv-* Corresponding author. Tel.: +1-514-9873000 ext. 3503; fax: +1-514-9878494.
E-mail address:mohnen.pierre@uqam.ca (P. Mohnen).
ity gains are limited. The whole economy thus drifts to a lower productivity performance, unless the growth of services is offset by input savings in manufactur-ing. Oulten (1997) shows how resource shifts to service sectors with sluggish productivity may increase aggregate productivity if it concerns intermediate (busi-ness) rather than final (personal) services. Can the slowdown in total factor productivity (TFP) that we have experienced since the mid-seventies be ascribed to the increasing importance of services, or has this drag been offset by big savings of other inputs in manufacturing? Have services suffered from the Baumol disease at all, or do we instead observe an improvement of productivity in the services sectors by way of learning-by-doing or specialization? We feel that such questions are best answered within a general equilibrium analysis of the whole economy, i.e. a structural view of the whole economy. Our approach does not belong to the class of general equilibrium models, which model supply and demand functions and aim at finding prices, which sustain observed data as equilibrium outcomes. Our position is to start from the fundamentals of the economy to establish the production frontier and its shift over time, and to compute competitive prices, which sustain that frontier. We do not capture the variations of the economy about its frontier in this paper. The full theory of fundamentals based productivity measurement is presented in ten Raa and Mohnen (2000). Also, in this paper we focus on the service sectors and assume that capital is sector specific and not differentiated by type.
The fundamentals are the usual ones — endowments, technology, and prefer-ences. Endowments are represented by a labor force and stocks of capital. Technol-ogy is given by the combined inputs and outputs of the sectors of the economy. Preferences are reflected by the pattern of domestic final demand. All the informa-tion can be extracted from input and output tables in real terms, that is constant prices. The productivities are determined as follows. We maximize the level of domestic consumption subject to commodity balances and endowment constraints. Now, as is known from the theory of mathematical programming, the Lagrange multipliers associated with the endowment constraints measure the marginal pro-ductivities of labor and capital — the consumption increments per units of additional labor or capital. In economics, these Lagrange multipliers are shadow prices that would reign under idealized conditions of perfect competition. We declare these shadow prices to be the factor productivities.
The paper is organized as follows. Factor productivities and TFP are defined by means of a linear program in the next section. In Section 3 we present the data of the Canadian economy from 1962 to 1991. In Section 4 we present our results. The last section concludes.
2. Productivities
competi-tive and non-competicompeti-tive imports (the latter are indicated by zeros in the make table). Domestic final demand comprises consumption and investment. Investment is merely a means to advance consumption, albeit in the future. We include it in the objective function to account for future consumption. In fact, Weitzman (1976) shows that for competitive economies domestic final demand measures the present discounted value of future consumption.
Productivity growth will be defined as the measure of the shift of the frontier. Suppose an economy with only two commodities. Instead of comparing observa-tions of the economy in subsequent periods (represented by the dots in Fig. 1), we will compare the projections on the respective frontiers (the arrows).
The frontier of the economy in a particular year is determined by the resolution of a linear program. The primal program reads
maxs,g,g(e
Tf+w0l)
g
(VT−U)s]fc+Jg=F
cjKjsj5Kj
Ls+lg5N
−pg5−pgt=D
s]0
where S is activity vector (c of sectors); g stands for level of domestic final
demand (scalar); G is the vector of net exports (c of tradeable commodities); E
denotes unit vector of all components one;Ý is transposition symbol;frepresents
domestic final demand (c of commodities);w0
is base year price for non-business
labor (scalar); l signifies non-business labor employment (scalar); V is the make
table (c of sectors by c of commodities)Uthe use table (c of commodities by
c of sectors); J is 0 – 1 matrix placing tradeables (c of commodities by c of
tradeables); F is the final demand (c of commodities); cj denotes capacity
utilization rate of sector j (scalar between 0 and 1); Kj stands for capital stock of
sectorj (scalar); Ldenotes labor employment row vector (c of sectors);Nis the
labor force (scalar);p denotes US row price vector (c of tradeables);gt is vector
of net exports observed at timet(c of tradeables); andDis observed trade deficit
(scalar).
The linear program determines the activity levels of the various sectors of the
economy (s), the expansion of final demand (y), and the net export vector (g) that
together maximize the expansion of final demand. Those are the endogenous
variables of the primal. The expression in front ofgin the objective function only
serves to normalize the commodity prices, which sustain the optimal solution (essentially around unity, as we shall see when we interpret the dual program). The
production structure of the economy is given by the net output matrix (VÝ−U),
the capital stock used in each sector (cjKj), and the labor used in each business
sector (Lj) and in the non-business sector (l). The structure of preferences is given
by the domestic final demand vectorf. The capital, labor and allowed trade deficit
endowments of the economy are given by the available capital stock in each sector
(Kj), the total labor force N, and the observed trade deficit D. The competitive
world prices are given by sectorp. Labor is supposed to be mobile across sectors
but capital is sector-specific. The sum of net imports for tradeable commodities valued at world prices may not exceed the observed trade deficit.
The program thus activates to a certain extent the various sectors of the economy, thereby producing a certain amount of all commodities, which is given by the observed sectoral production vectors blown up by the respective optimal
activity levels (sj). Likewise, the observed domestic final demand vector for all
commodities is multiplied by the expansion factor of domestic final demand. If the activity levels were unity, we would reproduce the observed resource allocation in the economy. The first constraint of the linear program forces production for each commodity to be sufficient to accommodate domestic final demand and the optimal net exports (in case of tradeable commodities). The second set of constraints simply limits the activity levels of all sectors to be smaller than the inverse of the sector capacity utilization rates. The labor constraint stipulates that the sum of the labor used in all sectors may not exceed the available labor force. Labor is perfectly mobile across sectors in the economy, but totally immobile across countries. The last constraint, before the positivity constraint of sectoral activity levels, puts a limit to total net imports.
It should be noted that we do not set up the problem in terms of input – output coefficients, because of rectangular input – output tables, but in terms of given sectoral production and total demand structures. If we had a square input – output matrix, we could write the first commodity balance constraint, the first constraint of
the primal, as [I−A]x]fc+Jg, whereAis the matrix of input – output coefficients
andxis the vector of sectoral gross output. The role ofxis played bysand the role
of Aby the pair (U, V).
Productivities are not measured using market prices, but are determined by the dual program, which, as is well-known, solves for the Lagrange multipliers of the primal program. The latter measure the marginal products of the objective value with respect to the constraining entities, unlike observed factor rewards with all
their distortions. The dual program reads, denoting a diagonal matrix,
minp,r,w,o]0rK+wN+oD
pf+wl=eÝf+w0l
pJ=op.
The endogenous variables in the dual program are shadow prices — p of
commodities, r of capital (c of sectors), w of labor and o of foreign debt (the
exchange rate). Since the commodity constraint in the primal program has a zero
bound, p does not show up in the objective function of the dual program. The
commodity pricesp are normalized by the second dual constraint, essentially about
unity. They are not deflatiors that convert nominal values into real values, but a price vector that sustains the optimal allocation of resources in the linear program. We now introduce the concept of productivity growth. Since labor productivity
is the Lagrange multiplier or shadow price associated with the labor constraint,w,
labor productivity growth is the growth ofw, w; =dw/dt. Similarly, ris the vector
of marginal productivities for each sectoral capital stock and o the marginal
productivity of the trade deficit1. TFP-growth is obtained by summing all factor
productivity growth figures over endowments, r;K+w;N+o;D, and normalizing by
the level of productivity, rK+wN+oD. Formally,
Definition.TFP-growth=(r;K+w;N+o;D)/(rK+wN+oD).
Remark. Replacement of (f, l) by (lf, ll) in the primal program with l\0 yields
solution (s,g/l, g). The value of the objective function is not affected. By the main
theorem of linear programming, rK+wn+oD is not either. In fact, the
productiv-ities are unaffected, as is, by extension, TFP-growth. The replacement does affect the commodity prices, as to preserve the identity between national product and national income, which we present next.
This straightforward definition of TFP-growth is now related to the commonly used Solow residual (SR). By the main theorem of linear programming, substituting the price normalization equation, we obtain the macro-economic identity of na-tional product and income (apart from the net exports on either side):
pfg+wlg=rK+wN+oD.
By total differentiation:
TFP-growth=[(pfg+wlg):−rK: −wN: −oD: ]
(pfg+wlg) .
To establish the link with the Solow residual (SR), focus on the numerator, substituting the assumed binding labor and balance of payment constraints:
(pF−pJg+wlg):−rK: −w(Ls+lg):+o(pg):.
Differentiating products, rearranging terms, and using the second dual constraint
and the definition of F presented in the primal program
pF: −rK: −w(Ls):−pJg;+o(pg):+p;(F−Jg)+(wlg):−w(lg):
=pF: −rK: −w(Ls):+op;g+p;fg+w;lg.
Now normalize again, dividing by rK+wN+oD. Then the first term yields the
technical change effect or Solow residual. It corresponds to the traditional Solow residual, except that here it is evaluated at shadow commodity prices and optimal
sectoral activity levels. The second term, with numeratorop;g, is the terms-of-trade
effect. Proportional changes in p are offset by a change in o. Only relative
international price changes matter. The last two terms are the preference-shift
effect. By the remark, pf+wl may be held constant, so that the preference-shift
effect reads −(pf:+wl:)g. If demand (f,l) shifts to commodities with low
opportu-nity costs, it is relatively easy to satisfy domestic final demand and TFP gets a boost. The terms-of-trade and preference-shift effects disappear when there is only
one commodity and no non-business labor. Under these circumstances,p is unity
and p also by the second dual constraint, hence their derivatives vanish. In other
words, in a macro-economic setting, TFP-growth reduces to the Solow residual. It should be mentioned, however, that a tiny difference remains in the denominators.
We divide by pfg+wlg=pF−pJg+wlg=pF−opg+wlg=pF+oD+wlg. In
other words, we account for the deficit and non-business labor income.
2.1.Remarks
1. The TFP measure used in Mohnen et al. (1997) is confined to the Solow residual without the terms-of-trade and preference-shift effects. There is also a slight
normalization difference. In this paper, we normalize with respect torK+wN+
oD=pfg+wlg, whereas Mohnen et al. (1997) normalize with respect to pF=
pfg+pJg.
2. In discrete time, the differentials are approximated using the identity xtyt−xt– 1
yt– 1=x˜txtyt+y˜txtyt, where x˜t=(xt−xt– 1)/xt and xt=(xt+xt– 1)/2, and
simi-larly for y˜t and yt.
3. By Domar’s aggregation we can decompose the aggregate Solow residual into
sectoral and group-sectoral Solow residuals. Let j index the sectors, i the
commodities, andkthe sector groups. Define the Solow residual of group-sector
k as.
SRk=
%jk%ipi(sj6ji):
%jk%ipi6jisj −
%jk%ipi(sjuij):
%jk%ipi6jisj −
%jkw(sjLj):
%jk%ipi6jisj −
%jkrjK: j
%jk%ipi6jisj
.
Notice that ifk=j, we get the Solow residual for sector j. Also notice that it is
inputs. It can be shown that our aggregate Solow residual expression can be written as a Domar weighted average of sectoral Solow residuals (with weights adding to more than unity, see ten Raa, 1995):
SR=
%k%jk%ipi6jisj
%ipiFi
SRk.
In continuous time this is exact. In discrete time one must involve full employ-ment of labor at the frontier point. Otherwise a slack change term emerges that cannot be allocated to the sectors. With capital there is no such complication, since we assume it is sector specific.
3. Data
We use the input – output tables of the Canadian economy from 1962 to 1991 at the medium level of disaggregation, which has 50 industries and 94 commodities. The constant price input – output tables have been obtained from Statistics Canada in 1961 prices from 1962 to 1971, in 1971 prices from 1971 to 1981, in 1981 prices from 1981 to 1986, and in 1986 prices from 1986 to 1991. All tables have been converted to 1986 prices using the chain rule. For reasons of confidentiality, the tables contain missing cells, which we have filled using the following procedure. The vertical and horizontal sums in the make and use tables are compared with the reported line and column totals, which do contain the missing values. We select the rows and columns where the two figures differ by more than 5% from the reported totals, or where the difference exceeds $250 million. We then fill holes or adjust cells on a case by case basis filling in priority the intersections of the selected rows and columns, using the information on the input or output structure from other years, and making sure the new computed totals do not exceed the reported ones.
The gross capital stock, hours worked and labor earnings data are from the KLEMS dataset of Statistics Canada, described in Johnson (1994). In particular, corrections have been made to include in labor the earnings of the self-employed, and to separate business and non-business labor and capital. The total labor force figures are taken from Cansim (D767870) and converted in hours using the number of weekly hours worked in manufacturing (where it is the highest). Out of the 50 industries, no labor nor capital stock data exist for sectors 39, 40, 48, 49, 50, and no capital stock data for industry 46.
rate for total non-farm goods (excluding energy) producing industries, the most encompassing capacity utilization rate available. The capacity constraints on con-struction has been lifted as it can be supplemented by US capacity, as suggested on the Service Sector Productivity and the Productivity Paradox pre-conference.
The international commodity prices are approximated by the US prices, given that 70% of Canada’s trade is with the United States. We have used the US producer prices from the US Bureau of Labor Statistics, Office of Employment Projection. They are made relative prices using final demand shares to define the price level. The 169 commodity classification has been bridged to Statistics Canada’s 94 commodity classification. To convert US prices to Canadian equiva-lents, we have used, whenever available, unit value ratios, (UVRs, which are industry specific) computed and kindly provided to us by de Jong (1996). The UVRs are computed using Canadian quantities valued at US prices. For the other commodities, we have used the purchasing power parities computed by the OECD (which are based on final demand categories). The UVRs establish international price linkages for 1987, the PPPs for 1990 in terms of Canadian dollars per US dollar. We hence need two more transformations. First, US dollars are converted to
Canadian dollars using the exchange rates taken from Cansim (series 0926/B3400).
Second, since the input – output data are in 1986 prices, we need the linkage for 1986, which is computed by using the respective countries’ commodity deflators — the producer price index for the US (see above) and the total commodity deflator from the make table (except for commodities 27, 93 and 94, for which we use the import deflator from the final demand table) for Canada.
Commodities 13, 44, 70, 71, 72, 79, 81, 82, 88, 91 and 92 are considered as non-tradeable, for which no trade shows up in the input – output tables for most of the sample period. For computational reasons and similar output composition, we have aggregated the nontradeable commodities 70 – 72 (residential, non-residential and repair construction). Due to the absence of labor,capital stock and intermediate inputs for industry 39 (government royalties on natural resources), it has been aggregated with industry 5 (crude petroleum and natural gas). In the end, we are thus left with 49 industries and 92 commodities, which are listed in Tables 1 and 2. A more detailed documentation of the data and their construction is available from the authors upon request.
4. Results
comparable phases of the business cycle2. Canada hit recessions from January to
March 1975, from May to June 1980, from August 1981 to November 1982, and from April 1990 to March 1991, according to Bergeron et al. (1995). Over the next
business cycle (1974 – 1981), TFP-growth fell to −1.63%. It recovered to −0.72%
per annum in the 1980s (1981 – 1991). The preference-shift effect was nearly zero in the first and last periods and positive in the middle period, when consumers apparently switched their patterns of demand towards commodity bundles with lower contents of expensive factors. The technical change effect explains the lion’s share of TFP-growth — the Solow residual fell far below zero after 1974, but then recovered in the 1980s. The terms of trade effect played a minor role and followed a similar pattern as technical change. At the optimal terms of trade and trade balance, relative world prices moved so as to increase our purchasing power before 1970 and to decrease it afterwards. The three effects add up to TFP-growth.
From its definition, TFP-growth can also be decomposed into its constituent marginal productivity growth rates. We then get a second accounting identity. The numbers, at the bottom of Table 3, are slightly different because of rounding. We see that the contribution of labor productivity declined on average by 1.68% per year in 1962 – 1974 and by 0.73% per year in 1981 – 1991. During the turbulent period of the oil shocks (1974 – 1981), it actually increased on average by a strong 4.19% per annum. Capital productivity growth followed the same pattern as TFP-growth reflecting the predominant value of capital in the value of output. The contribution of the productivity of the trade deficit, i.e. the increased consumption permitted by a marginal increase in the allowed deficit was small throughout.
The primary sector very much determines the aggregate evolution in Canadian productivity. It was mostly struck by the slowdown in the 1970s, but also led to the recovery in the 1980s. Manufacturing and construction are average sectors, follow-ing the economy-wide Solow residual. Of the remainfollow-ing service sectors the first three are surprisingly healthy. Transportation, trade, and to a lesser extent commu-nication, all perform above the economy-wide average. Last and least, FIRE and B&P services drag the economy.
Table 4 lists the annual productivity growth figures giving a more precise timing of the up- and downturns of productivity growth. As is well-known and also very apparent here, TFP-growth fluctuates a lot. The primary sector, manufacturing and construction feature as many negative as positive Solow residuals over time. Transportation, communication and trade report predominantly solid positive Solow residuals confirming their status as progressive sectors. Last and least, FIRE and B&P services have a negative performance. It is interesting that shadow price based Solow residuals fluctuate to the extent that not a single year reports economy-wide positive values.
We have checked the sensitivity of our results to the use of net instead of gross capital stocks. The solutions to the linear programs are unaffected, so are the
Table 1
List of commoditiesa
Grains
Hunting and trapping products 6
Iron ores and concentrates 7
Other metal ores and concentrates 8
Services incidental to mining 13
17 Fruits and vegetables preparations
Feeds 18
Flour, wheat, meal and other cereals 19
20 Breakfast cereal and bakery products
Sugar
26 Cigarettes and tobacco manufacturing
Tires and tubes
Leather and leather products 30
31 Yarns and man made fibres
Fabrics 32
Other textile products 33
34 Hosiery and knitted wear
Clothing and accessories
Other wood fabricated materials 38
Furniture and fixtures 39
Pulp 40
Newsprint and other paper stock 41
Paper products 42
Printing and publishing 43
44 Advertising, print media
Iron and steel products 45
Aluminum products 46
47 Copper and copper alloy products
Nickel products 48
Table 1 (Continued)
50 Boilers, tanks and plates
51 Fabricated structural metal products
52 Other metal fabricated products
53 Agricultural machinery
54 Other industrial machinery
55 Motor vehicles
56 Motor vehicle parts
57 Other transport equipment
Appliances and receivers, household 58
59 Other electrical products
60 Cement and concrete products
Other non-metallic mineral products 61
62 Gasoline and fuel oil
Other petroleum and coal products 63
Industrial chemicals 64
Fertilizers 65
66 Pharmaceuticals
67 Other chemical products
Scientific equipment 68
69 Other manufactured products
Construction 70
71 Pipeline transportation
Transportation and storage 72
73 Radio and television broadcasting
74 Telephone and telegraph
Postal services 75
76 Electric power
77 Other utilities
78 Wholesale margins
79 Retail margins
80 Imputed rent owner ocpd. dwel.
81 Other finance, insurance, real estate
82 Business services
83 Education services
Health services 84
85 Amusement and recreation services
86 Accommodation and food services
Other personal and misc. services 87
88 Transportation margins
Supplies for office, lab. and cafetaria 89
Travel, advertising and promotion 90
Non-competing imports 91
92 Unallocated import and exports
Table 2
List of industriesa
Agricultural and related services industries 1
2 Fishing and trapping industries Logging and forestry industries 3
4 Mining industries
5 Crude petroleum, natural gas, government’s royalties on natural resources Quarry and sand pit industries
6
Service related to mineral extraction 7
11 Rubber products industries Plastic products industries 12
Leather and allied products industries 13
Primary textile and textile products industries 14
Clothing industries 15
Wood industries 16
17 Furniture and fixtures industries Paper and allied products industries 18
Printing, publishing and allied industries 19
20 Primary metal industries
Fabricated metal products industries 21
Machinery industries 22
Transportation equipment industries 23
Electrical and electronic products 24
25 Non-metallic mineral products industries 26 Refined petroleum and coal products
Chemical and chemical products industries 27
31 Pipeline transport industries Storage and warehousing industries 32
Communication industries 33
34 Other utility industries Wholesale trade industries 35
Retail trade industries 36
Finance and real estate industries 37
Accommodation and food service industries 43
Amusement and recreational services 44
45 Personal and household service industries Other service industries
46
Operating, off., cafet. and lab. Sup. 47
48 Travel, advertising and promotion Transportation margins
49
Table 3
Average annual growth rates and TFP decomposition at shadow prices and optimal activity levels (%)
1962–1974 1974–1981 1981–1991
Solow residual
−7.46
−0.42
Primary sector 1.46
0.57
Manufacturing −0.22 −1.11
−0.19
Construction −1.11 0.00
2.60
Transportation −0.04 0.38
−0.96
Communication 1.85 −0.21
1.13
Trade −0.04 0.29
FIRE −2.49 −1.89 −3.81
B&P services 0.32 −2.50 −2.01
TFP decomposition
−1.59
Solow residual 1.09 −0.67
−0.08
−0.14
Terms of trade 0.22
0.02
Preference shift −0.04 0.10
−0.72
TFP-growth 1.26 −1.63
Marginal producti6ity growth contributions
−1.68 4.19
Labor −0.73
−0.02
3.17 −6.28
Capital
0.05 0.49
Trade deficit −0.21
−0.70
−1.59
TFP-growth 1.28
optimal shadow wage rates. The only difference is in the shadow prices of capital, which adjust to the new capital stock measures so as to yield zero profit conditions. It is like a scaling problem. All that matters in our model for the expansion to the efficiency frontier are the rates of capacity utilization. The choice of measurement for the capital stocks would only matter if capital from various sectors was substitutable. TFP-growth rates differ because the marginal productivities of capital differ. But both qualitatively and quantitatively, the results are rather similar.
5. Conclusions and qualifications
P
Solow residual at shadow prices and optimal activity levels (%)
Transportation Construction
Period Primary sector Manufacturing Communication Trade (35–36) FIRE (37–39) B&P services (40–49)a
1964–1965 −0.30 2.08
2.23
1967–1968 0.66 1.33 1.30 1.80 2.64 −1.24 1.48 −3.79 0.34 1971–1972 2.13 1.93 −0.95
−2.93 1975–1976 −7.36 1.98 3.80
2.66 0.63 −1.31 −1.25 −3.84 1976–1977 −4.64 0.31 1.69
0.42 −2.41 −1.99
−5.93 2.03
−3.59 1977–1978 −3.79 0.51
−0.78 1980–1981 −26.92 0.74 2.12
−7.19
1982–1983 −0.13 4.14
0.74
1985–1986 −1.02 0.03
1.60 −5.72 −4.09 1990–1991 7.75 −2.40
outward shift of that efficiency frontier rather than changes in observed input – output ratios.
Our model offers some explanation to productivity growth. Some inputs can earn high returns if they are in short supply. TFP-growth is nothing but a reflection of the evolution of marginal valuations of primary factor inputs. The modeling of existing constraints is very crucial in our approach. Another key role in our analysis is played by the levels of capacity utilization. Their construction is still controversial. No estimates are available for services. Proper measures of output and capacity utilization for services are problematic, but we urge Statistics Canada to devote resources to construct such measures. Our analysis would also be enriched if we could have data on sectoral use and total availability of labor disaggregated by level of qualification and of sectoral utilization and availability of capital disaggregated by type of capital. It would allow us to get a more precise picture of scarcities in the Canadian economy. By construction, the vintage structure of capital does not matter. To relax this assumption, we would need to make investment endogenous and switch to a dynamic model, which would lead to Hulten’s (1979) notion of a dynamic residual.
We must also admit that our assessment of productivity growth in services might be biased because of improper price measurements. New products and services or improved quality of existing ones are seldom measured in national accounts statistics. This problem is especially acute in services where output and prices are harder to measure than for manufacturing goods. The bias may show up in various places in the productivity formulas (see Oulten, 1997 for a related discussion). First, the optimal solution of the linear program, which determines the frontier of the economy, may differ if the underlying input and output quantities are different. For example, if a given commodity is actually larger than measured because of quality improvement (say computers), and if it is used heavily as an intermediate input in a sector with a high potential of being assigned a high activity level at the optimal solution of the linear program (e.g. because it has a low rate of capacity utilization and requires few other inputs), it may well happen that either the final demand can expand less or that the main sector producing that commodity must expand more. The shadow prices underlying the optimal solution may, therefore, change as well (different bottlenecks may show up) and hence the measured productivity figures will differ. Second, assuming for the sake of argument that the optimal solutions do not change, it can readily be seen from the TFP-growth decomposition that the Solow residual will increase if final demand increases, i.e. that the TFP-growth is underestimated, if growth in observed final demand is underestimated. It is unclear what the final bias in our sectoral TFP figure will be.
Acknowledgements
We thank Nathalie Viennot and Sofiane Ghali for their dedicated research assistance and Rene Durand, Jean-Pierre Maynard, Ronald Rioux and Bart van Ark for their precious cooperation in constructing the data. We are grateful to Carl Sonnen and other participants of the Service Sector Productivity and the Productiv-ity Paradox conference, Ottawa, April 1997, for their helpful comments. We are also grateful to Michael Landesmann and other participants of the Technical Change, Growth and International Trade conference, Eindhoven, October 1999, for their helpful comments. We acknowledge the financial support of the Social Sciences and Humanities Research Council of Canada, CentER, the Netherlands Foundation for the Advancement of Research (NWO), and the Association for Canadian Studies in the Netherlands.
References
Bergeron, L., Fauvel et, Y., Paquet, A., 1995. L’indicateur synthe´tique avance´ de l’e´conomie canadienne selon la me´thode de Stock et Watson, mimeo. Centre de recherche de l’emploi et des fluctuations e´conomiques, UQAM.
de Jong, G., 1996. Canada’s postwar manufacturing performance: a comparison with the united states. Research Memorandum, Groningen Growth and Development Center, GD-32.
Hulten, C.R., 1979. On the importance of productivity change. Am. Econ. Rev. 65, 956 – 965. Johnson, J., 1994. Une base de donne´es KLEMS de´crivant la structure des entre´es de l’industrie
canadienne. Statistique Canada, Division des Entre´es-Sorties, Cahier Technique c73F.
Mohnen, P., ten Raa, T., Bourque, G., 1997. Mesures de la croissance de la productivite´ dans un cadre d’e´quilibre ge´ne´ral: L’e´conomie du Que´bec entre 1978 et 1984. Can. J. Econ. 30 (2), 295 – 307. Oulten, N., 1997. Total factor productivity growth and the role of externalities. Natl. Inst. Econ. Rev.
161 (3), 99 – 111.
ten Raa, T., 1995. Linear analysis of competitive economies. In: LSE Handbooks in Economics. Harvester Wheatsheaf, New York.
ten Raa, T., Mohnen, P., 2000. Neoclassical Growth Accounting and Frontier Analysis: a Synthesis. CentER Discussion Paper 67.
Weitzman, W., 1976. On the welfare significance of national product in a dynamic economy. Q. J. Econ. 90, 156 – 162.
