Measurement of Government Output∗

Kam Yu†

Lakehead University

October 13, 2004

Abstract

Direct measurement techniques have recently been employed by some sta-tistical agencies for the government output components in the SNA. Thesemethods use proxies and indictator for outputs due to the inherent lack ofmarket valuations. This article investigates the pros and cons of these newapproaches and compares them with the traditional input method. This leadsus to take a deeper look at the purposes, objectives, and uses of the SNA. Thecurrent method can be justified from a collective household point of view, butthe lack of direct output data frustrates students of productivity analysis. Bytaking the economic approach in index number theory, some direct measure-ment methods can be compatible with the cost-of-living approach in the CPI.

JEL Classification: C43, H50, O47, P44Keywords: system of national accounts, public sector productivity, direct mea-surement, volume index, quantity index

1 Problems in Measuring Government Output

Evaluation of government output in the System of National Accounts (SNA) hasbeen subjected to debate for a long time by economists. The arguments range fromwhether government output should be included in the SNA, what activities should beincluded, to how to measure them. The debate involves fundamental and conceptualissues concerning the purposes, meanings, interpretation, and uses of the informationon economic activities of a country. Marketed goods and services are measured bytheir market values. The current dollar values are deflated with the appropriate

∗Forthcoming in Erwin Diewert, Bert Balk, Kevin Fox, and Alice Nakamura (eds), Essays onPrice and Productivity Measurement, Vol. 3, Victoria: Trafford Publishing.

†Department of Economics, Lakehead University, Thunder Bay, Ontario, Canada, P7B 5E1.Phone: 807-343-8229, Fax: 807-346-7936, E-mail: Kam.Yu@lakeheadu.ca.

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price indices to obtain constant dollar values, which are effectively quantity indices.A large portion of government services, however, is provided collectively free ofcharge or at heavily subsidized prices. The lack of market values poses seriousmeasurement problems. Moreover, quantities of government services are not easilydefined and quality of the services can vary across regions and over time. For mostindustrialized countries, the outputs of the public sector are taken as the sum offactor inputs. This implies that productivity growth for this sector is always zero.For this reason the Inter-Secretariat Working Group on National Accounts ([33],p. 402)1 and Eurostat [23] recommended direct measurement of non-market outputswhenever feasible. A few countries such as the U.K., Australia, and the Netherlandshave already implemented the recommendations in their SNA. They differ, however,on the methods of measuring the direct output. The purpose of this article is toreview the conceptual and practical issues in measurement of output in the publicsector. In the sections that follow we shall examine the purposes of the SNA, the roleof government outputs in the SNA, measurement problems, and recent developmentsin direct measurement methods. Our goal is to initiate further research in this areato improve the SNA in Canada.

2 What is the SNA Supposed to Measure?

The purpose of the national accounts has been a subject for debate by economistsfor a long time. Hicks [28] first raised the conflicting goals of measuring the welfareof the nation as a whole and the study of productivity of the economy. For the firstgoal Hicks suggests two solutions. First, if we prefer to measure consumers’ welfarein the strict sense, then goods and services provided by the government at no chargeshould be excluded. The reason is that prices reflect the consumers’ marginal utilitiesof the goods and services. Forte and Buchanan ([25], p. 116-7) support this view byarguing that any attempt to include a free government service in the SNA wouldcreate an overestimation of welfare and is inconsistent with our treatment of marketgoods. For example, the number of hours of sunshine is a service provided by theenvironment free of charge. Even though our marginal utility of sunshine is notzero it is not included in the SNA.2 In a strict sense this seems to be an acceptableargument but if we examine the nature of publicly provided services the conceptmay not cover the whole spectrum. SNA93 (p. 101) classifies government servicesinto three groups:

1. Services consumed collectively such as national defence, external affairs, andenvironment protection due to market failure,

1Hereafter referred to as SNA93.2This means that we want more sunshine than the weather permits. The analogy is a bit far

fetched since the provision of sunshine does not involve any economic activity but governmentservices do.

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2. Services provided to individuals at no cost or at prices that are not economicallysignificant such as health care and education,

3. Transfers paid to individuals for income redistribution and subsidies paid tofirms.

Group 3, for accounting purposes should be excluded. It is well-known in publiceconomics literature that if we rely on market mechanism for the provision of publicgoods in group 1, those services will be under-provided due to free-rider problems.For efficiency, the government is supposed to provide the services to the publiccollectively so that the marginal social benefit equals the marginal social cost. This,however, does not imply that the marginal social benefit is zero. For analyticalpurposes, services in groups 1 and 2 can be classified into two subgroups. Thefirst is those services that are provided free but individual consumers are activelychoosing the amount they consume. For example, public broadcasting, highways,and recreational parks are provided free but each consumer decides how often shetunes in the public channels or visit a park using the highways. If these services areprovided in ‘unlimited’ quantities, the marginal utility of the service is indeed zero.3

The second subgroup is for those services that are consumed inelastically such ashealth care and high school education. Figure 1 illustrates the supply and demandof hospital emergency services. For practical purposes it is not unrealistic to assumethat the demand curve D is vertical.4 The supply curve S represents the marginalcost curve. If ER services are provided by a competitive market as in some countries,the value will be equal to the sum of areas B and C, which is equal to pmqm. If,however, the services are provided free by the government, the marginal evaluation isexactly the same. Therefore it seems unacceptable to exclude the item in the SNA.

For the above reasons, Hicks [28] recommended that government provided goodsand services should be evaluated at costs. He argued that since no market price isavailable, the benefit of the services is at least as good as their costs. Kuznets [36],[37], [38] agreed with Hicks in principle but raised the question of double counting.Kuznets emphasized that the SNA should measure the net contributions of economicactivities that have positive effects on the welfare of the consumers. A large portionof government activities are engaged in the production of intermediate goods andservices, which contribute indirectly to the final products. For example, in evalu-ating the welfare of the consumers, market goods are taken at the prices faced bythe buyers, which include all indirect taxes. If the tax revenues are used by thegovernment to finance activities that contribute to the consumption of the goods(such as food inspection to ensure public safety), then the costs of those activitiesare already included in taxes and should not be duplicated.5

3This may not be true if we take into account time constraint.4The same argument can be applied to fire fighting and other rescue operations.5Hicks [29] later takes the same position.

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This raises an interesting question: where do we put those government outputsin our social record of economic activities? In defending the position of the U.S.Department of Commerce, Gilbert et al [26] note that the purpose of the SNA isbroader than just a measure of consumers’ welfare. Final products, accordingly,should be defined as all purchases by consumers, nonprofit organizations, and gov-ernments that are not resold in the market. Moreover, government expenditures arenot solely financed by indirect taxes. On the practical side, it is sometimes diffi-cult to distinguish between services provided to business for intermediate inputs anddirect services to consumers (for example highways usage). Another problem asso-ciated with Kuznets’ idea is the exact definition of intermediate goods and services.Kuznets ([38] p. 156-157) contends that the product account in the SNA shouldinclude only those goods and services that are directly beneficial to the ultimateconsumer. Health care and education are examples of such services. Policing andnational defence are, on the other hand, ‘antecedent and indispensable costs of main-taining society at large,’ and do not provide final economic goods. These services,together with all services provided to the business sector, should be excluded fromthe product account. This raises the question of what exactly the definition of in-termediate products is. If policing and national defense are not final services, thesame argument can be applied to highways and education. The former are means toget us to our final destination when travelling, unless any one would enjoy the purepleasure of driving. The latter can be seen as investment in human capital. To put itto the extreme, medical care is an antecedent and indispensable cost of maintainingour health so that we enjoy other ‘final’ consumption.6

While Kuznets emphasizes the net final products of the economy, other authorsthink that the SNA does not cover all aspects of economic activities. For example,Peskin and Peskin [48] recommend including net environmental effects to industry,government, and household. Others present extended national accounts that includehousehold production, leisure time, environmental pollution, investment in humancapital, imputed rental on land, durables, and inventories for the government, etc.Many of these alternative measures of SNA are reviewed in a comprehensive surveyby Eisner [17].

Okun [46] supports the Department of Commerce position by arguing that grossnational product (GNP) does not measure social welfare, and should not attemptto do so. The SNA, in Okun’s opinion, should measure ‘output resulting frommarket-oriented activity’. In addition to economic welfare, social welfare includes,among other things, peace and security, freedom, social justice, equality, leisure,and environmental amenity. Therefore the general principle for a national accountstatistician is that, in Okun’s words, ‘if market behavior doesn’t tell you how muchsomething is worth, you have no way to tell.’ ([46], p. 132)

6This line of argument is often called the consumption of regrettable necessities.

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The debates are summed up by Mamalakis [42]. He defines total production in aneconomy as the sum of economic production and free production. The latter is prod-uct and services we obtain from the environment free of charge such as air, water,sunshine, and leisure time. Economic production is further divided into SNA marketproduction and non-SNA non-market production. Examples of the latter are house-hold production, illegal drugs, etc., which are excluded from the SNA. Correspondingto these definitions of production are the concepts of total welfare, economic welfare,free welfare, SNA welfare, and non-SNA welfare. Each welfare type is the resultof the corresponding production type. Under this framework, SNA is a measure ofSNA production. It is never ‘intended to be anything more than an indicator ofmarket based and oriented production.’ (p. 295) Therefore, what the SNA measuresis the quantities of goods and service produced by the market. It is not a directmeasurement of social welfare. This is indeed the position taken by SNA93 (p. 14).The SNA is ‘intended for purposes of economic analysis, decision-taking and policy-making. It is a multi-purpose system designed to meet the requirements of differentkinds of users: governments, businesses, research institutes, universities, the pressand the general public.’ Mamalakis’s [42] idea of SNA production as an indicatorof SNA welfare, which is in turn part of the total welfare is reflected by empiricalstudies in labour productivity. Some European countries such as Belgium, France,and Norway have higher labour productivity measured in GDP per hour workedthan the U.S. But all these countries have lower GDP per worker.7 This means thatalthough these European workers are more productive than their American fellows,they work fewer hours and enjoy more of their leisure time. In other words, theyhave lower SNA welfare but higher free welfare.

3 The Index Number Problem

Consider one of the most important identities in index number theory:

P (p1, p2, q1, q2)Q(p1, p2, q1, q2) =p2Tq2

p1Tq1. (1)

P is the price index function of four vectors, namely, p1 is the price vector of Ngoods and services in period 1 (base period), p2 is the prices in period 2 (comparisonperiod), q1 and q2 are the corresponding quantity vectors. Superscript T denotesthe transpose of a matrix or vector. Thus pTq =

∑Ni=1 piqi is the inner product of

the vectors p and q. Q is the quantity index function. The right hand side of (1)is the ratio of the total values of the N products in the two period. This identityis sometimes called the product test. It requires the product of the price indexand the quantity index to be equal to the total value ratio. If there is only one

7See [41] and [55].

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product, that is, N = 1, then the price index P is simply p21/p

11 and quantity index

Q = q21/q

11. Identity (1) is trivially satisfied and there is no index number problem.

For N > 1, we have to find a way to sum up the prices and quantities of differentgoods so that the resulting indices will satisfy (1). In other words, we try to compareapples with oranges, and then add them up together. Mathematically speaking wedecompose the value ratio into two factors P and Q. In the economic approach toindex numbers literature, P is interpreted as a cost of living index. It compares thecost of consuming the N goods and services to achieve the same standard of livingin both period [35]. Q, on the other hand, measures the change in the standardof living. Recently there has been a lot of discussion about adapting the economicapproach in the construction of the consumer price index (CPI).8 Some countriessuch as the U.S. have adopted the concept as the objective of the CPI.

Although the objectives and goals of the CPI may be different from those ofthe SNA, the economic approach can provide a theoretical foundation for both. Asdiscussed in section 2, the goal of the SNA is to measure the quantities of goodsand services produced and consumed in the economy, which then serves as a partialsocial welfare indicator. In principle this objective is compatible with the conceptualframework of a cost-of-living price index. For example, if Q in (1) is the constantdollar GDP per capita, then it can be interpreted as the SNA-economic welfareindicator as defined in section 2. Consequently, identity (1) stipulates that theimplicit GDP deflator P is indeed a cost-of-living index. In addition, the economicapproach does not conflict the other purposes of the SNA in economic analysis,decision-taking, and policy-making.

In practice we often deflate the current dollar value of a product (or a productgroup) with a proper price index to obtain a constant dollar volume index.9 Thatis, on a subindex level, we implicitly defined the Konus quantity index as

QK =1

PK

p2Tq2

p1Tq1(2)

where

PK =C(u, p2)

C(u, p1)

and

C(p, u) = minq

{∑i

piqi : U(q) ≥ u

}PK is the Konus cost-of-living (sub)index. It is defined as the ratio of the costfunctions in periods 2 and 1 when a consumer faces prices p2 and p1. The consumer

8A detailed discussion justifying the economic approach is given in [53].9The name volume index is used interchangeably with the term quantity index. See SNA93,

p. 381.

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is supposed to maximize her utility U(q) in both periods. The cost function C isthe minimum amount of money the consumer needs to achieve the same referencestandard of living or utility u in both periods. The choice of u is of course veryimportant because PK and consequently QK depend on it. It can be shown, however,that there exists a utility level u∗ between the utility levels of the consumer in periods1 and 2 such that PK lies between the values of the Laspeyres price index PL andthe Paasche price index PP . That is, there is a u∗ = λu1 + (1− λ)u2 for 0 ≤ λ ≤ 1such that10

PP ≤ PK ≤ PL orPL ≤ PK ≤ PP .

(3)

In fact the implicit Konus quantity index is a special case of a more general index,known as the Allen index:

QA(q1, q2, p) =C(U(q2), p)

C(U(q1), p). (4)

Here we directly compare the cost function of the utility or standard of living inperiods 2 and 1, using a reference price vector p. In the literature of cost benefitanalysis, C(U(q), p) is called a money metric measure of quantity vector q. Anothercommonly used theoretical index is the Malmquist quantity index:

QM(q1, q2, q) =D(U(q), q2)

D(U(q), q1)(5)

whereD(u, qt) = max

k

{k : U(qt/k) ≥ u, k > 0

}is called a distance or deflation function. D measures the maximum value that candeflate the quantity qt such that the resulting utility level is at least as high as u. In(5) q is a reference quantity vector that defines the reference utility level u = U(q).And QM is the ratio of the deflators for q2 and q1 with respect to U(q).

So far we have defined three theoretical quantity indices. In principle if theconsumer’s utility function is known or can be estimated, all three indices can becomputed using duality theory. In practice, of course, this is seldom done. These in-dices are used to derive simple non-parametric index formulae. A natural question iswhich one should be used to develop our quantity index in practice. It turns out thatif we make further assumptions about the utility function, the three indices becomethe same. In particular, if we assume that consumers’ preferences are homothetic,then

QK = QA = QM = U(q2)/U(q1).

Technically, a homothetic preference structure means that the utility function is anincreasing transform of a linearly homogeneous function. That is, U(q) = f(U(q))

10For a proof and other discussions on economic approach to index number see [13].

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where f is a single-variable increasing function, i.e., f ′ > 0, and U(αq) = αU(q)for all α > 0. It implies that a consumer has constant expenditure share for eachcommodity even when total expenditure varies. Although this assumption is veryrestrictive, it provides us with a guideline for the search of the index formulae. Forexample, a frequently used utility function in economic analysis is the Cobb-Douglasfunction

U(q) =N∏

i=1

qαii

where∑N

i=1 αi = 1. It is easy to show that for this utility function

QK = QA = QM =N∏

i=1

(q2i

q1i

)αi

.

That is, the three theoretical indices all equal to the weighted geometric mean of thequantity ratios, which is often called the weighted geometric index. In this case wesay that the weighted geometric index is exact for the Cobb-Douglas utility function.This example shows that different assumptions on the utility function give rise todifferent index number formulae. In applied economic analysis a group of functionscalled flexible functional forms is often used for empirical estimation of demandand supply functions. The advantage is that they approximate an arbitrary utilityfunction to the second degree in a Taylor expansion. For example, the square rootquadratic utility function defined as

U(q) = (qTAq)1/2, (6)

where A is a symmetric N × N square matrix of coefficients, is a commonly usedflexible functional form. It can be shown that the Fisher quantity index, which isthe geometric mean of the Laspeyres index and the Paasche index, is exact for thesquare root quadratic function. An index which is exact to a flexible functionalform is called a superlative index. Critics of superlative indices often argue thatthe homotheticity assumption is too restrictive and unrealistic.11 This argumentis misleading in light of (3) because the result does not invoke the homotheticityassumption. Being a geometric mean of PL and PP , the Fisher price index is goodapproximation for PK .

All these are fine and well. In fact some countries like the U.S. and Canadahave adopted the Fisher formula in the SNA. An important advantage of the Fisherquantity index is that the implicit price index (or GDP deflator) implied by (1) isthe Fisher price index. This provides a consistent approach for both the CPI andthe SNA. In measuring government outputs, however, there are no prices, quantitiesare difficult to define, and some products and services undergo constant quality

11See, for example, [30].

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change. Moreover, some government services such as national defence and generaladministration are passively consumed by all citizens. The level of consumptionis not decided by the consumers and so the economic approach in index numbercollapses. Nevertheless, the value of government services has to be estimated andthen added to the value of marketed goods to get the GDP. How we add apples tooranges when oranges have no price tag has long been a vexing problem for economicstatisticians.

4 A Tour of Current Methodology

In applied welfare economics, government projects are often evaluated using tech-niques from cost-benefit analysis. These methods, however, are complex and timeconsuming so that they are not practical for the purpose of measuring outputs on aquarterly basis. In this section we explore current practices and recent developmentsin direct measurement of government outputs.

We first begin with some practical concepts in output measurement. An eco-nomic process can be roughly divided into four stages, namely, factor inputs, activ-ities, outputs, and outcomes. Factor inputs are labour, capital consumption, andintermediate products used in the production process. Activities are intermediatesteps or components that constitute a final product. Outputs are the products andservices that the consumers purchase from the producers. Outcomes are the effectson the consumers as the results of consuming the products. Hospitals hire physi-cians, nurses, and surgeons; invest in medical equipment; and construct buildings asinput factors. Activities can be the number of patients admitted, number of daysin hospital per patient, or number of different operations or treatments performed.Outputs are number of heart attacks cured, different types of cancer removed, num-ber of babies delivered, or cases of diabetes treated. And finally, outcomes are thephysical well-being of the citizens. In a market economy, it is the outputs that weaim to measure, although sometimes the distinctions between activity and outputare not always clear. For example, when measuring health care outputs, should wetake the number of days in hospital plus other treatment costs as the quantity or thenumber of heart attack patients treated? If we take the former, an improvement inbypass surgery technique may result in reduction in the length of hospital stay, andconsequently a decrease in output. But this will miss the productivity gain from theimproved technology. From the patients’ point of view, a shorter hospital stay fortreatment of the same disease is actually a quality improvement. For the same totalcosts price should go down and quantity should go up. Therefore the definition of aproduct or service has important consequences for the price and quantity indices.

When prices are not available, quantities have to be measured either directly orindirectly. Traditionally, total input factor costs have been used as government out-put. In recent years there has been much new research work on direct measurement

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of outputs. These methods are largely based on counting activities as a proxy foroutputs, although some research has been carried out to measure effects instead. Weshall examine the results of these works in some details and their implications onthe SNA.

4.1 Input Costs as Output

The most convenient way to include non-market government output in the SNA isto add up the total factor costs. From the welfare point of view, Hicks [28] arguesthat free government services are at least at good as they cost. Therefore the sumof direct and indirect taxes and government borrowing (negative if surplus) minusin-kind transfers serves as a lower bound to the value government outputs. From thenational account statistician’s point of view these products and services are not resoldanywhere in the market so they should be counted as final consumption. Critics ofthis approach point out that producers’ productivity changes and returns in capitalinvestment of government sectors are always zero. Note that productivity change isdifferent from the question of whether government sectors are inefficient.12 A sectorcan be inefficient but it still can undergo productivity change over time.

The whole idea of studying government productivity changes is based on theassumption of the government being a producer. Walk into any government de-partment and we see that it hires professional staff, administrators, clerks, janitors,and invests in capital goods like building structures, computers, and office furniture.Its organization structure is not very different from business corporations. The onlydifference is its products and services are not sold in the market. Under this assump-tion, taking the total input cost as output is certainly not appropriate because anyvalue added (or subtracted) is neglected. If we look at it from another perspective,however, the cost approach can have some merits. Let us consider again the oldeconomic joke about a bachelor marrying his cook. For political correctness reasonwe modernize the story a little bit. Suppose a single young executive, who has nospare time preparing her suppers, first eats out in a restaurant every evening. Ofcourse the SNA registers all her dining bills as outputs. After a while she finds outshe has put on some weight as a result of eating out everyday. She decides to hire acook at home in order to serve her home-cooked healthy meals. This causes a changein the GDP that now her dinner costs include the salary of her newly hired cook, allthe ingredients and kitchen utensils her cook buys in the market, and the extra elec-tricity charge for the home cooking. Since the cost of hiring a cook is quite high, thetotal cost is higher than eating out in restaurants and GDP goes up. Eventually, asthe story goes, the young executive falls in love with her cook and they get married.Her husband decides to stay home and prepare their dinners. As a result GDP goesdown because she no longer pays her husband a salary. From the national account

12For the latter topic see, [47].

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statistician’s perspective, the restaurants where the young executive used to have hersupper are producers of the services. Transactions occur after the final products, i.e.meals, are produced. After she hires the cook, production shifts home and the SNAcan only record the total cost of the meals as output. Finally, after their marriagethe labour component of production disappears in the SNA altogether.

For the sake of argument, we can treat a whole country as a large extendedfamily. The family hires its own guards and installs alarm systems for security(national defense); employs a family doctor full time for their illness (health care);hires contractors to build houses (public works); and even has its own school for theyoung members of the family (education). Governments, in this sense, are analogousto the second stage of the young executive’s search for her dining solution. Hernewly hired cook could suggest to her that she should renovation her kitchen toresemble that of a restaurant so that she could invite business partners and friendshome for formal dinners. The only difference is that the prepared meals are notsold in the market. This raises the question of household production [39]. If wetreat governments as producers, should we include household activities such as mealpreparation, child rearing, and even driving to work, which are the counterparts ofthe catering, day care, and transportation sectors in the market economy respectively,in the SNA? In fact this is exactly what some economists suggest.13 One mayobject that government decisions do not necessary reflect the wills of the citizens,so that this extended family analogy breaks down. Whether the democratic systemcan induce the government to act on the citizens’ collective preferences, or moreimportantly such a collective preference exists or not is outside the scope of thispaper.14 But governments are not unlike households since household decisions, basedon the collective preferences of all the members, and so face problems similar to thoseof governments if the number of household members exceeds three, the minimumnumber of voters for the Arrow Impossibility Theorem to apply.

The cost approach is also justifiable even if we see the government as a producer.15

Conceptually, we can assume the government produces a vector of goods and servicesq with a cost function C(w, q) where w is the input price vector. Then the appropriateoutput prices will be the vector of marginal costs, p = ∇qC(w, q). If there areconstant returns to scale in production, then qT∇qC(w, q) = C(w, q) and so costwill be the ‘correct’ value for government outputs. The vector of marginal costsenable us to split the value into price and quantity components.

Although the cost approach is justifiable, for policymaking and political reasonswe still want to measure productivity in the public sector. For example, Baumol

13See [17] [18]. In fact, using the household production approach, Hulten [31] has developed aneconometric model for estimating government productivity without measuring outputs. His resultsshowed that U.S. state-local government productivity growths over the period 1959-1979 are zeroor negative.

14See [1], [47], [27], and [43].15The author wants to thank Professor Erwin Diewert for this point.

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[6] argues that productivity of labour intensive sectors such as governments remainstagnant, while that of capital intensive sectors keep rising. Wages in equilibrium,however, rise across all sectors. As a result, government expenditure will eventuallyrun out of control. Among other reasons, Diewert and Fox [15] found that produc-tivity growth rates in 18 OECD countries dropped from an average of 3.25% in theperiod 1961-1973 to 1.09% in 1974-1992. Incidentally, the latter period coincideswith an era of rapid expansion in government expenditure. Furthermore, there ex-ists political pressure from time to time for the government ‘to do more with less’.Therefore a measure of efficiency of government operations is necessary. For thisend, there exist tools in the operations research literature for the measurement ofefficiency. The most popular method is the data envelopment analysis (DEA).16 Thebasic principle behind DEA is the use of linear programming techniques to map outthe production function of an industry. It does not need any price information anduses input and output quantity data from different production units. The result isa single index of relative efficiency among the production units. For example, therelative efficiencies of hospitals across a region can be assessed and compared withoutany price information. This technique, however, relies on the fact that the output ofthe production units can be directly measured.

4.2 Measuring Activities

When outputs cannot be observed directly, we can examine the possibility of mea-suring activities or outcome. Recent developments in direct measurement mostly fallinto the former techniques. Statistical agencies in the U.K. and Australia have al-ready implemented direct measurement of activities in selected areas such as healthcare, education, and justice.17 These are services that are provided to individualsfor free. Pure public goods and services such as national defense are more difficultto quantify and therefore are not measured directly.

The general procedure for this technique are as follows:

1. Identify an area of services where activities are to be measured

2. List all activities of the area

3. Find a volume measure for each activity (number of incidents or cases, etc.)

4. Form a volume ratio for each activity between the comparison period and thebase period

5. Aggregate the volume ratios using cost shares as weights to produce a subindexfor the area

16See [10], [11], [4], [45], and [16].17See [8], [7], [49], [51], and [2] for the British developments and [12], [3], [44], and [57] for the

Australian efforts.

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The result is sometimes called a cost-weighted activity index (CWAI). For example,in the U.K., administration of justice is divided into six sub-areas, namely, prisons,legal aid, crown prosecution service, crown courts, county courts, and magistrates’scourts. Each sub-area is broken down into a number of activities. In legal aid, forexample, annual data are available for all ten types of cases. Each type of case iscounted and the volume ratios are cost weighted to form the subindex for legal aid.Like DEA, CWAI can be used as a tool for efficiency studies.

Eurostat [19] [20] [21] [22] has formed a number of task forces to study measuringprices and volumes for health, education, public administration, defence, and socialservices. Their results are incorporated in the Eurostat’s ([23], chapter 4) handbookon price and volume measures. The recommended methods in volume measures forthese areas are output indicator methods, which use activity or product counts asoutput indicators.

Using the activity approach, the U.S. Bureau of Labor Statistics [24] has carriedout a long term productivity study of the U.S. federal government from 1967 to 1994.A total of 2,500 indicators are used to measure activities of various departments. Costweights, however, are restricted to labour quantities and labour compensation only.Capital consumption and land uses are not included in the costs. Results show thataverage productivity growth for the departments studied are 1.5% per year for theperiod 1967-1982 and 0.6% for 1982-1994, with an overall average of 1.1% per year.For comparison, the average labour productivity growth of the private (non-farmbusiness) sector in the same period is 1.4% per year. On an output per employeebasis, the highest productivity growth is in the area of finance, with an average rateof 3.8% per year, while electric power production registers the lowest rate of -1.0%per year. Compensation per employee, on the other hand, increases at an averageannual rate of 6%. This seems to be a vindication of Baumol’s [6] prediction. Thelabour productivity growth rate for the private sector, however, is also much lowerthan the wage increase. Thus the differences must be due to other factors such as ashift of low-skilled workers to high-skilled workers. It is interesting to compare theseresults with those of Hulten [31], who uses the public household model to estimatetotal factor productivity growth rates of U.S. state and local governments from 1959to 1979. Hulten’s results show that the average growth rate is -0.50% per year.There is no reason to believe that productivity of the U.S. federal government grewfaster than that of the state and local governments. This reflects the possibility thatdifferent approaches in direct output measurement will give contradicting results.

Despite the endorsements by a number of statistical agencies, activity measureshave some drawbacks in implementation. First, the choice of an output indicator hasthe most important consequence on the volume measure. The example of measuringhospital output is discussed in the introduction of this section. Another example is inchoosing the output indicator for education. It can be the total number of students,total number of student hours, or total number of student days. These three choices

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will certainly give different results and may be subject to political manipulation byschool board administrators. In universities and research institutions, the choice ofthe research output indicator will certainly be controversial.18

Second, all direct measurement methods are data intensive. For marketed goods,quantities are obtained by deflating values with price indices. Collection of pricedata, however, is simpler than collection of quantity data, because prices of similargoods tend to have less variation so that small samples are adequate. Direct quantitydata, on the other hand, need to be exhaustive to cover all aspects of outputs. Thedata requirements are also very different from the existing input method. Theyrequire extensive revisions of the current data collection procedures and collaborationfrom government departments. Moreover, not all data are available and some areonly available on an annual basis. For the quarterly SNA some data have to beforecasted by time series techniques and later revised when the actual data areavailable.

Third, quality adjustment is often important for output measure comparisonsacross different regions and through time. For marketed goods and services, valuesare usually deflated by quality adjusted price indices. For activity measures, outputshave to be adjusted directly. In education, for example, there are suggestions touse inspection reports, standardized examination results, or student/teacher ratiosas the quality indicator. None of these, however, are satisfactory. Consistency ofinspection reports are questionable across regions and time. Examination resultscan be influenced by other environmental factors other than the quality of teaching.And student/teacher ratios do not necessary reflect the quality directly or in a simplemanner ([40] chapter 5). For these reasons, the British Office of National Statisticsdecided to impose a quality factor of 0.25% per year for schools ([51] p. 4).

Fourth, the way that quantity ratios are weighted can be misleading. A morevaluable product may sometimes cost less to produce than others. For example,Statistics Canada has a large budget for gathering and processing data from theagricultural sector, probably due to historical reasons. The relative size of this sectoris small compared with others and the number of users of agricultural data is alsosmall. On the other hand, the CPI is one of the most watched statistics producedby Statistics Canada and has an impact on every aspect of the economy. Thereforeusing the cost shares of production undermines the importance of the CPI relativeto most agricultural data.

Fifth, although quantities are measured directly, in order to come up with con-stant dollar values, the volume indices must be multiplied by values from the baseperiod. Since there are no market evaluations, what values should we use? It seemsthat we are forced to use the total costs from the base period. But then this is

18Australia, for example, uses the Composite Research Index, which is a weighted index of thenumber of books, book chapters, articles in scholarly refereed journals, and conference papers. See[57] p. 15.

14

conceptually inconsistent when we add government outputs with market outputs.Figure 2 illustrates the supply and demand curves of a market product. The valueof the output is area B plus area C, while the total cost is area C only. Thereforewe still miss the producer surplus portions of the values. The discussion here has animportant implication when we compare health care expenditure in countries like theU.S. where it is privately provided, with public systems such as in Canada. There areother factors that contribute to the higher costs in the U.S. Malpractice litigations,for one thing, result in high insurance costs for doctors and hospitals. Also, medicalpractices in the two countries differ dramatically. For example, in 1991, Americanseniors are up to eight times more likely to get expensive operations such as bypasssurgery, coronary angiograms, and balloon angioplasties within 30 days after a heartattack than Canadian seniors do, with no impact on the mortality rates after oneyear [54]. A third possible reason is that U.S. medical expenditures include producersurpluses, while those in Canada are only measured at cost. How big area B is forthe U.S. health care sector remains an interesting empirical question.

Finally, the British experience shows that the implicit price indices (deflators)resulting from direct measurement of outputs can become erratic.19 When activitycounts are used as output indicators, the economic interpretation of the deflatorsis unclear and may not be suitable for analytical purposes. In fact Pritchard andPowell ([51] p. 7) concede that the new general government deflator is not a priceindex at all.

4.3 Measuring Outcomes

We saw in the last section that output indicators of activities do not capture theproducer surplus of marketed products. Also in some areas, quality of service isdifficult to adjust for. An alternative is to measure welfare of the consumers directly.This is exactly what the economic approach to quantity indices does. The Allenindex defined in (4) is the ratio of the money metric measure of utilities in twoperiods. The right hand side on identity (1) is the ratio of the sums of currentvalues, which are products of marginal evaluations (prices) and quantities. Thebeauty of the economic approach is that the decomposition of the value ratio intothe cost of living index P and standard of living index Q implies that Q comparesutilities rather than costs or marginal utilities. Consequently, if the money metricutilities of consuming government outputs can be measured directly, the resultingconstant dollar values are conceptually compatible with other marketed goods.

Unfortunately, research on direct measurement of outcomes is relatively rare anddata requirements are intensive. Furthermore, direct measurement of welfare is rarelypossible so proxies are often used instead. When proxies are used, the advantage ofcompatibility with marketed goods is lost. An example of this outcome approach

19See [7] p. 5.

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is in the measurement of police services. Using clear-up rates in reported crimesas the output proxy, Carr-Hill and Stern [9] and Levitt and Joyce ([40] chapter 12)compare outputs of police forces adjusted for external factors such as populationdensity, age distribution, income distribution, etc. Their technique involves a three-stage least squares econometric model with three simultaneous regression equations.The endogenous variables are size of police force per capita, recorded crime rate, andclear-up rate. The rationale behind the model is the perceived interactions betweenthe endogenous variables.

Another example of direct welfare measurement is in the area of the gamblingsector. Using a model developed by Diewert [14] based on non-expected utility the-ory, Yu [56] estimate the money metric output for Lotto 6/49 in Canada. Althoughgovernment lotteries are marketed products, currently the SNA uses the operationalcosts of the lottery corporations as outputs, which are in turn fixed proportions of thetotal sales. As risk takers, the estimated consumer utilities derived from buying lot-tery tickets are much higher than the operational costs. Other outcome approachesinclude the quality adjusted life year method, which uses psychometric analysis ofthe quality of life in accessing health care and police outputs.20

In addition to the complexity of the techniques involved, the outcome approachalso has its drawbacks.21 First, by measuring welfare directly in money terms, theincome account will be different from the expenditure account in the SNA. In thecase of lotteries, there will be a large consumer surplus which requires explanationin the new SNA. Second, using the clear-up rate as a proxy for police services ne-glects other functions of the police force. Police activities are not restricted to crimeinvestigation. Other important functions include crime prevention, public security,and participation in ceremonial activities. Finding output proxies for these otherfunctions is not all that straightforward and without controversy. Therefore it seemsthat some functions are better measured by the CWAI method. Third, a more solidtheoretical model has to be developed on the link between welfare and the proxy.Finally, desired consequences may change over time. For example, the goal of edu-cation changes progressively with the social and economic environments.22

4.4 The Deflator Method

The deflator method is used by Statistics Netherlands to calculate volume change ofgovernment services [34]. The basic assumption of the method is that long-run wagechange can be decomposed into two components, namely, compensation for inflationand compensation for productivity change.23 A good proxy for the first component

20See [40] p. 124 and 135.21See [52], chapter 3.22For the problem of changing preferences and its effects on index numbers see [5].23This is contrary to Baumol’s [6] assumption that labour productivity in government sector

stays unchanged, that is, wages compose of the first component only.

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is an index of basic wage rates according to the union collective agreement (CAO-wages). With these assumptions, the following identity is readily obtained:

Lt = AtCtPt (7)

where Lt is the chain index of total amount of wages and salaries paid by the gov-ernment in period t, At is a chain index of paid employment, Ct is the chain indexof CAO-wages, and Pt is the chain index of labour productivity. Since Lt, At, andCt can be measured directly, Pt is calculated using (7). In practice a three-periodmoving average for Pt is used instead to smooth out volatility. In the Dutch SNA,provincial results are published first, and the final revised outputs are available withtwo and a half year lags. Government services are split into four subcategories:general administration, defence, education, and other government services so that aproductivity index for each subcategory can be published.

While technically simple and easy to implement, the deflator method criticallydepends on the assumptions that the index of basic wage rates is a true indicator ofcompensation for inflation only. In reality, the basic wage rate may include part ofthe labour productivity change. In addition, wages sometimes may depend on thebargaining power of the unions. The latter point is important since the objective ingovernment departments, unlike firms in the private sector, is not to maximize profitsor minimize costs. Therefore wages of government employees do not necessary equaltheir marginal products. Further research regarding this approach is necessary.

5 Welfare, Efficiency, and Productivity

We now return to the second goal of the SNA put forward by Hicks [28], that is, themeasurement of productivity. The topic has been studied by economists for decadesand has recently entered political debate in Canada.24 Figure 3 plots the total factorproductivity (TFP) growth rate against the proportion of government expenditure inthe GDP (GYR) in Canada from 1961 to 1992.25 A simple regression show that TFPis negatively related to GYR. The estimated slope coefficient is equal to -0.29 with at-ratio of -3.3 and a R2 = 0.26. This result is entirely logical given that governmentoutputs were valued at cost. Therefore on the surface it seems that measurementproblems in government outputs can explain about one quarter of the productivitydecline in Canada.

Productivity, simply defined, is the comparison of total outputs given the to-tal amount of inputs. It is therefore a measure of efficiency. Economists use theword efficiency in a variety of contexts. For example, allocation efficiency is about

24See the special issue in service sector productivity and the productivity paradox in the CanadianJournal of Economics, Volume 32, No. 2, April 1999 and [32].

25Data on TFP are from [15].

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distribution of public goods or welfare gains from trading in an exchange economy.An often used criterion is Parato-efficiency, which asks the question of whether wecan improve someone’s welfare without reducing that of others. Market efficiencygenerally refers to the impacts of taxes and subsidies on market equilibrium and thewelfare of consumers and producers. Technical efficiency concerns whether a produc-tion unit can produce more outputs with the given inputs. Government productivitythat we are discussing here, therefore, is about its technical efficiency as a productionunit. This does not imply, however, that allocation efficiency is not important in theproduction of publicly provided goods and services. In fact, one of the main goals inthe study of public economics is to decide how much public goods the governmentshould provide. The job of politicians is to reveal preferences of voters.

Olson [47] argues forcibly that inefficiency in the public sector is caused by thedifficulty of measuring the outputs of collective goods such as national defence andforeign affairs. When job performance of government employees cannot be basedon volumes of output, promotions are frequently given to those who adhere to theestablished policies of the organizations, are loyal to the conservative style, and donot ‘rock the boat.’ Hence it is ‘the consummate organization man who rises tothe top’ (p. 367). Therefore, switching to a direct measurement method in the SNAmay create some unintended political consequences. It can be a lose-lose situation forgovernment managers. They certainly do not want to find out that their departmentis inefficient. On the other hand, if productivity improves over time, they may seetheir budgets being cut.

6 Discussion and Recommendations

We have discussed the role of government outputs in the SNA, its measurementproblems, and some of the possible solutions. There are multiple objectives andgoals for the SNA, although the most important use is as an indicator for economicwelfare of a country. The conventional method of using total factor costs as outputsis unsatisfactory for the propose of measuring productivity growth. The practice,however, can be justified if we consider the government as a collective agent forpublic consumption. We collectively hire civil servants and invest in capital in thesame way households retain the services of accountants, lawyers, and plumbers andbuy durable goods such as cars and computers. Direct methods such as CWAIand the outcome approach measure proxies for outputs. Results generally dependon the method used, and it is not clear how well these proxies resemble the desiredconceptual ideal. But this is a circular question. Outputs of collective goods, in manyinstances, are difficult to define. The government GDP deflator may be difficult tointerpret and this may create confusion for SNA users. As Pritchard and Powell [51]point out, development of new approaches in the SNA is more than an academicresearch project. The required efforts will be similar to research in the problems of

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quality adjustment in price indices, where each sector or product has to be studiedindependently before the most appropriate method can be decided. The stakes arehigh because maintaining the reputation of our published numbers is of utmostimportance.

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Figure 3: Productivity Growth and Government Expenditure in Canada

24