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OECD

Organisation for Economic Co-operation and Development

Organisation de Coopration et de Dveloppement Economiques

OCDE

STATISTICS DIRECTORATE

National Accounts Division

SECOND MEETING OF THE CANBERRA GROUP

ON CAPITAL STOCK STATISTICS

Chteau de la Muette, Paris

29 September - 1 October 1998

Beginning at 10 a.m. on the first day

Agenda item : 7Document number : 3

Title : Productivity Measurement Problems

Author(s) : W. Erwin Diewert - University of British

Columbia, Canada

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WHICH (OLD) IDEAS ON PRODUCTIVITY ARE READY TO USE ?

I. ACCOUNT FOR THE MAJOR CLASSES OF INPUTS AND OUTPUTS

(1) OUTPUTS

We require prices and quantities for all major outputs.

(2) INTERMEDIATE INPUTS

The major classes are:

materials

business services

leased capital.

The current input-output framework deals well with the flows of materials but not with

intersectoral flows of contracted labor services or rented capital equipment. This means thecurrent input-output accounts will have to be greatly expanded at considerable cost.

(3) DISAGGREGATED LABOR

We all agree that labor should be disaggregated but we are not quite certain what the

appropriate classification should be.

(4) REPRODUCIBLE CAPITAL

User costs are still not part of the National Income accounting framework.

Interest is still not accepted as a cost of production in the system of National accounts butinterest is productive; it is the cost of inducing savers to forego immediate consumption.

Capital gains are not accepted as intertemporal benefits of production in the system of

National Accounts but if resources are transferred from a period where they are less valuable to a

period where they are more highly valued, then a gain has occurred; i.e., capital gains are

productive.

However, interest and capital gains pose practical problems for statistical agencies: which

interest rate should be used?

an ex post economy wide rate of return which is the alternative used by Jorgenson?

an ex post firm or sectoral rate of return?

an ex ante safe rate of return like a Federal Government one year bond rate? or should the ex ante safe rate be adjusted for the risk of the firm or industry?

Similarly, should the capital gains term of user cost be an ex ante expected capital gain

(which is the right concept from the viewpoint of trying to model economic behavior) or should

it be an ex post actual observed capital gain (which is the right concept from the viewpoint of

attempting to measure ex post economic performance of the producing unit)?

The ex ante concept is not observable and hence the statistical agency will have to make

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somewhat arbitrary decisions in order to construct expected capital gains.

The ex post concept will lead to rather large fluctuations in user costs which in some

cases , will lead to negative user costs, which may be hard to explain to users.

The Jorgensonian distinction between depreciation (a decline in value of the asset over the

accounting period) and deterioration (a decline in the physical efficiency of the asset over the

accounting period) is now well understood but still has not yet crept into the latest version of thesystem of national accounts. Unfortunately, our empirical information on the actual efficiency

decline of assets is negligible! We do not even have good information on the useful lives of assets.

This lack of knowledge creates more problems for statistical agencies: the UK statistician assumes

equipment on average lasts 22 years while the Japanese statistician assumes equipment lasts on

average about 10 years. These problems are being addressed by the Canberra Group on Capital

Measurement but progress is slow. Finally, it is not generally recognized that if depreciation is not

declining balance ( a la Jorgenson), then vintage specific user costs have to be constructed and

there are some unresolved aggregation problems that need to be addressed.

A final set of problems associated with the construction of user costs is the treatment of

business income taxes: should we assume firms are as clever as Hall and Jorgenson and can work

out their rather complex tax-adjusted user costs of capital or should we go to the accounting

literature and allocate capital taxes in the rather unsophisticated ways that are suggested there?

There is very little empirical evidence that firms actually construct Jorgensonian tax adjusted user

costs but there is some evidence that unadjusted for taxes user costs are creeping into the business

literature.

(5) INVENTORIES

Because interest is not a cost of production in the National Accounts and the depreciation

rate for inventories is close to zero, most productivity studies neglect the user cost of inventories.

Of course, this leads to totally faulty productivity statistics for industries where inventories arelarge relative to output, such as retailing and wholesaling.

Diewert and Smith (1994) (The Journal of Productivity Analysis 5, 335-347) found large

productivity gains for her fathers distribution firm using an appropriate user cost accounting

framework

The problems of accounting for inventories are complicated by the way accountants and the

tax authorities treat inventories. These accounting treatments of inventories are very misleading

in periods of high or moderate inflation.

These accounting problems seem to carry over to the National Accounts in that for virtually

all OECD countries, there are time periods where the real change in inventories has the opposite

sign to the corresponding nominal change in inventories. This does not make any sense to me.

(6) LAND

The current system of National Accounts has no role for land as a factor of production,

perhaps because it is thought that the quantity of land in use remains roughly constant across time

and hence it can be treated as a fixed unchanging factor in the analysis of production. However,

the quantity of land in use by any particularfirm or industry does change over time. Moreover,

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the price of land can change dramatically over time and thus the user cost of land will also change

over time and this changing user cost will, in general, affect correctly measured productivity. For

the period 1955-1987, the price of land (nonreproducible tangible assets) in Japan grew

approximately 16% per year. Inserting an appropriate user cost of land into the aggregate

productivity formula for Japan (versus just omitting land from the computation) leads to a .5%

per year increase in Japanese total factor productivity! Thus it is important not to neglect the roleof land when computing the total factor productivity of a producer unit.

Land ties up capital just like inventories (both are zero depreciation assets). Hence, when

computing ex post rates of return earned by a production unit, it is important to account for the

opportunity cost of capital tied up in land. Neglect of this factor can lead to very biased rates of

return on financial capital employed.

Property taxes that fall on land must be included as part of the user cost of land. It may not

be easy to separate the land part of property taxes from the structures part. Note that in the

National Accounts, property taxes (which are input taxes) are lumped together with other indirect

taxes that fall on outputs! This is another shortcoming of the current system of accounts.

(7) RESOURCES

Examples of resources are:

depletion of fishing stocks, forests, mines and oil wells; these are resource inputs;

improvement of air, land or water environmental quality; these are resource outputs if

improvements have taken place and are resource inputs if degradation has occurred.

Statistics Canada is developing statistics for forest, mining and oil depletion.

The correct prices for these resource depletion inputs are the gross rents (including resource

taxes) that these factors of production earn. Note that resource rents are usually not linked up

with the depletion of resource stocks in the National Accounts.

The pricing of environmental inputs/outputs is much more difficult: from the viewpoint of traditional productivity analysis based on shifts in the

production function, the correct environmental quality prices are marginal rates of

transformation while from a consumer welfare point of view, the correct prices are

marginal rates of substitution; see the Gollop and Swinand paper presented at the

Conference: Total Resource Productivity: Accounting for Changing Environmental

Quality.

The environmental situation is somewhat analogous to the case of a government

enterprise that is told to provide services at prices well below marginal cost. In this case,

it is useful to have an addendum to the Accounts that revalues the subsidized goods and

services at market (i.e., at consumer) prices and this treatment would also be very usefulin the case of environmental goods and services. The problem with environmental goods

is that it is much more difficult to estimate the appropriate consumer or producer

environmental prices than in the case of say state subsidized housing.

Engineering studies may be able to determine appropriate producer environmental

prices.

Epidemiological studies may be able to determine appropriate consumer environmental

prices.

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Econometric and statistical techniques will also be useful in determining these producer

and consumer environmental prices.

(8) KNOWLEDGE CAPITAL

What is knowledge and innovation?

A local market area is characterized by a list of establishments or production units.

Each establishment produces outputs and uses inputs during each period that it exists.

Establishment knowledge is the set of input and output combinations that a local

establishment could produce during a given time period t. It is the economists period t

production function or period t production possibilities set.

Establishment innovation is the set of new input-output combinations that an

establishment in the local market area could produce in the current period compared to the

previous period; i.e., it is the growth in establishment knowledge or the increase in the size of the

current period production possibilities set compared to the previous periods set. Since thestatistical agency cannot know exactly what a given establishments production possibilities is at

any moment in time, it will be difficult to distinguish between substitution of one input for another

within a given production possibilities set versus an expansion of the production possibilities set;

i.e., it will be difficult to distinguish between substitution along a production function versus a

shift in the production function.

Both process and product innovations are included in the above definition of establishment

innovation. Product innovations lead to additions to the list of outputs, which traditional index

number theory is not well adapted to deal with but the shadow price technique introduced by

Hicks (1940)Economica 7, 105-1401 and implemented by Hausman (1996)(1997) could be used.

Our definition of an establishment innovation includes all technology transfers from outside

the establishment. Thus a local innovation to a given establishment is not necessarily a globalinnovation in the usual sense of being the first use of a new technique or product anywhere in the

world. A global innovation developed somewhere in the world is useless to a local business unit if

the new technology is not transmitted or diffused to the local establishment. In our view, the

diffusion of a new product or process to the local economy is at least as important as the actual

creation of the new knowledge for the first time.

The connection of infrastructure and knowledge capital.

From Adam Smith and Alfred Marshall, we know that the bigger the market, the more

1

Hicks later described these index number difficulties as follows: Gains and losses that result from price changes

(such as those just considered) would be measurable easily enough by our regular index-number technique, if we

had the facts; but the gains which result from the availability of new commodities, which were previously not

available at all, would be inclined to slip through. (This is the same kind of trouble as besets the modern national

income statistician when he seeks to allow for quality changes.) The variety of goods available is increased,

with all the widening of life that that entails. This is a gain which quantitative economic history which works with

index-numbers of real income, is ill-fitted to measure or even describe. John Hicks, pp. 55-56 in A Theory of

Economic History, Oxford University Press, 1969.

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establishments can specialize; i.e., create new local commodities.

Thus reduction of transportation costs within and without the local region can widen the

market and reduce the costs of importing knowledge.

Similarly, a reduction in communication costs can make international and interregional

knowledge more accessible to local establishments.

Thus it seems likely that regions that are large and have good infrastructure facilities willhave easier access to knowledge stocks. We shall return to infrastructure shortly.

How can we measure knowledge capital?

Given the way we have defined knowledge (as time dependent, firm specific potential

production possibilities sets), it is extremely difficult to measure knowledge and changes in

knowledge (innovation). Some of the possible input-output combinations that a production unit

can produce are imbedded in its capital equipment and the accompanying manuals; other possible

combinations of inputs and outputs might be imbedded in its patents or the unpublished notes of

the scientists that developed the patents and yet other combinations might be imbedded in the

brains of its workers. However, there are certain stocks that we can measure that will probably be

positively correlated with the size of local knowledge stocks. A science and technology statistical

system should concentrate on collecting information on these knowledge related stocks. Some

possible candidates for data collection are:

stocks of patents (how to value these and what depreciation rate to use?)

research and development expenditures (how to deflate these and what depreciation

rate?)

education and training undertaken in the firm (how to value this?)

trade fairs and professional meetings (in the local area only or do we also count the fairs

and meetings attended by local employees?)

availability of universities and research labs in the local region

stocks of books, journals, blueprints within the firm

availability of local libraries

local availability of trade magazines, newspapers, and how to do it books (i.e.,

availability of local bookstores)

availability of mail service

availability of internet services

ease of access to business consultants who can inform firms of what best practice

input-output coefficients look like and then help the business unit to achieve the best

practice technology

participation of the local community in business associations, clubs and societies which

facilitate best practice knowledge flows.

Obviously, it is very difficult to pin down exactly how knowledge flows into the local

economy. Government regulations can also cause valuable knowledge flows. For example, my

local building code now specifies that a layer of plastic insulation must be placed below ground

level concrete floors when a building is being constructed. This is relatively inexpensive but is

very valuable in preventing loss of heat through the floor. Also, local building contractors must be

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categories 7-10 are formidable, both from the practical and conceptual points of view.

II THE ORGANIZATION OF THE STATISTICAL SYSTEM

Every statistical agency uses differentsurveys to collect to collect information on the outputs

of an industry and on the various input components. Every statistical agency usesdifferentsurveys to collect information on prices and values.

These separate data collection surveys do not greatly impede the construction of reasonably

accurate price and quantity aggregates for the components of final demand for the economy as a

whole but they lead to extremely inaccurate estimates of price and quantity for industries or

smaller units such as firms or establishments. In particular, the firm or industry specific price

indexes that are applied to the firms or industrys value components (such as output, intermediate

input, labor input, etc.) will be very inaccurate. Hence I believe, that in most cases, the resulting

firm or industry productivity measures will be virtually useless.

In the U.S., the situation is even worse, with one or more agencies collecting value

information and another entirely separate agency collecting price information. The various

agencies have separate sampling frames and, at present, are not even allowed to exchange micro

information! To an outside impartial observer (i.e., myself), this situation cries out for reform. The

various statistical agencies should be reorganized and combined intoStatistics USA.

Statistics Canada, under the leadership of Phillip Smith, is instituting a new micro data

management plan to manage the data burdens for large firms. Each large firm will have its own

Statistics Canada representative who will act as the single point of reference for all survey

information that is to be collected from that firm. This will reduce respondent burden but it will

also ensure that the survey information is coherent so that, for example, price information is

matched up with the corresponding value information. It should also be mentioned that the

national tax authority in Canada (Revenue Canada) has introduced a single business number for

each firm in Canada and Statistics Canada will also use this number. I believe that every statisticalagency should monitor the outcome of this experiment, and if it is successful, plan to introduce a

similar plan.

Many firms have taken advantage of the low cost of computing and have detailed data on all

of their financial transactions (e.g., they have the value of each sale and the quantity sold by

commodity). This opens up the possibility of the statistical agency replacing or supplementing

their surveys on say, prices of outputs, by the electronic submission by firms to the statistical

agency of their computerized transaction histories for a certain number of periods. This

information would provide the industry/firm counterparts to the scanner data studies that have

proved to be so useful in the context of the Consumer Price Index. This information would also

lead to true microeconomic price and quantity indexes at the firm level and to accurate firm and

industry productivity indexes.

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III SYSTEM WIDE VERSUS SECTORAL PRODUCTIVITY MEASUREMENT

Individual firms or establishments could be operating efficiently (i.e., be on the frontiers of their

production possibilities sets) but yet, the economy as a whole may not be operating efficiently.

How can this be? The explanation for this phenomenon was given by Gerard Debreu in 1951

(Econometrica 19; 273-292)2

: there is a loss of system wide output (or waste, to use Debreusterm) due to the imperfection of economic organization; i.e., different production units, while

technically efficient, face different prices for the same input or output, and this causes net outputs

aggregated across production units to fall below what is attainable if the economic system as a

whole, were efficient. In other words, a condition for system wide efficiency is that all production

units face the same price for each separate input or output that is produced by the economy as a

whole. Thus, if producers face different prices for the same commodity and if production

functions exhibit some substitutability, then producers will be induced to jointly supply an

inefficient economy wide net output vector. What are sources of system wide waste?

industry specific taxes or subsidies that create differences in prices faced by production units

for the same commodity; e.g., an industry specific subsidy for an output or a tax on the output of

one industry where that output is used as an input by other industries (an example of the latter is agasoline tax);

tariffs on imports or subsidies or taxes on exports;

union induced wage differentials across firms for the same type of labor service;

monopolistic or monopsonistic markups on commodities by firms or any kind of price

discrimination on the part of firms;

a source of commodity price wedges that is related to the last source above is the difficulty

that multiproduct firms have in pricing their outputs, particularly when there are large fixed costs

involved in producing new (or old) products (see the work of Paul Romer (1994); Journal of

Development Economics 43; 5-38) and particularly when there is high inflation and historical cost

accounting techniques for pricing products break down (see Diewert and Fox (1998); CanMeasurement Error Explain the Productivity Paradox?, forthcoming in the Canadian Journal of

Economics);

imperfect regulation; it is very difficult for government regulators to set optimal prices for

the commodities that are regulated (recall our earlier discussion about the difficulties involved in

determining what the appropriate prices for environmental bads should be). If the regulators

are unable to determine the optimal prices for regulated commodities, then the other producers

that use the regulated outputs as inputs will generate system wide waste. Examples of imperfect

regulation might include:

marketing boards (should quota capital be included in the capital stock?);

telecommunications;

environmental protection and health and safety regulations;

regulation of labor markets including the collective bargaining framework;

2

Debreu (1951; 285) distinguished two other sources of waste in the allocation of resources: (a) waste due to the

underemployment of available physical resources (e.g., unemployed workers) and (b) waste due to technical

inefficiency in production. Obviously, the application of knowledge capital could be useful in diminishing waste

(b).Waste (a) results from market imperfections between the aggregate production sector and the household sector

of the economy.

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regulation of the radio/TV spectrum;

municipal zoning and building code regulations;

the patent system;

Another source of market imperfections between economic agents might be the legal system:

are property rights well defined and enforceable? If not, the resulting uncertainty prevents the

market from assigning a definite value to the asset or resource under dispute and this uncertainty

will generally prevent the asset from being utilized in its most profitable use;

A related source of price wedges between economic agents is the existence of widespread

bribery and corruption. A bribe has roughly the same effect as an uncertain tax on a transaction

and will create distortion wedges between business units;

A final source of Allais-Debreu intersectoral waste is the system of business income taxation

that is in place in most countries. The lack of indexation of depreciation allowances for inflation

causes a divergence between the value of a depreciable asset to the producer of the asset and the

value to the purchaser of the asset: in periods of high inflation, the discounted value of the

depreciation allowances allowed for tax purposes will be much less than the purchase price of the

asset and thus the using firm will have to charge itself a much higher price than the purchase pricefor the asset to overcome this tax induced penalty for using the asset. There are many other

distortions between sectors and assets that the typical system of business income taxation induces.

Some references to the literature include: A. C. Harberger (1974),Taxation and Welfare, Boston:

Little, Brown and Co.; D. W. Jorgenson and K.-Y. Yun (1986), Scandanavian Journal of

Economics 88, 85-107 and 355-377; M. Feldstein (1978), Journal of Political Economy 86, 29-

51; C. Ballard, J. B. Shoven and J. Whalley (1985), American Economic Review, 78, 1019-1033;

J. B. Shoven and J. Whalley (1984), The Journal of Economic Literature 22, 1007-1051.

Note that the above sources of intersectoral waste are mostly induced by governments

(nonoptimal taxes and nonoptimal regulations and institutions) but some waste is induced by the

fixed costs of establishing new plants and developing new products and processes which in turnleads to monopolistic (or somewhat random) pricing of outputs on the part of business units.

However, it is difficult for governments to determine optimal taxes or optimal prices for the

outputs of regulated businesses and it is just as difficult for multiproduct firms that are constantly

developing new products or experimenting with new processes to price their products at the

socially efficient levels.

What are the implications of intersectoral waste for statistical agencies?

The current input-output system of industry accounts is 2 dimensional: current and constant

dollar value flows are classified by industry and by commodity. There is an urgent need to make

the classification 3 dimensional and add a table that lists taxes paid (or subsidies received) by

industry and by commodity. This would enable applied general equilibrium modelers to calculateestimates of the waste or excess burdens that are induced by the tax-subsidy wedges that are

pervasive in most economies. The present system of National Income Accounts just adds a row to

the usual input-output table that simply sums up all indirect commodity taxes paid by the industry

without telling users what the incidence of the taxes are by commodity.

For regulated industries, there is a need for statistical agencies to provide estimated marginal

costs (or producer prices) for the regulated commodities and estimated user values (or consumer

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prices) as well as quantities supplied. This is a somewhat utopian request given the limited

resources that statistical agencies have at their disposal at present and given the practical and

conceptual difficulties in constructing producer and consumer prices for regulated commodities.

Perhaps this is a fruitful area for the academic community to till.

IV ADDITIONAL PROBLEMS THAT STATISTICAL AGENCIES FACE

Statistical agencies face some increasingly difficult problems in providing indexes of real output

and input, which are the basic ingredients for computing both productivity and real consumption

growth rates.3

There is no doubt that the growth of knowledge has led to an increase in the dimensionality

of the commodity space. It is likely that the commodity space is expanding more rapidly now than

ever before. Traditional index number theory assumes that the set of commodities being

aggregated is constant and unchanging over time. Thus, strictly speaking, traditional index

number theory is not applicable to the current situation: there is a lack ofcomparability of the set

of commodities that exist in the current period with the set that existed in the previous period.

Most OECD economies are experiencing an increase in self employment and hence, there isan increase in the formation of new business units. The entrance of new firms and the exit of old

firms again creates problems for productivity statistics: the traditional methodology assumes an

unchanging set of business units. Thus, again there is a lack ofcomparability: the set of firms that

exists in this period is different from the set of firms that existed in the previous period.

When one examines the range of individual commodities produced by different firms in the

same industry, one is struck by the tremendous amount of heterogeneity in the composition of

these outputs. This heterogeneity makes comparisons of real output and productivity across firms

in the same industry somewhat dubious, since their outputs may not be comparable.

The existence ofseasonal patterns in the production of outputs and the utilization of inputs

again makes it difficult to compare this months output or productivity with the previous months.If a commodity was produced this month and was not produced at all in the previous month,

between month comparisons become meaningless. For more material on the difficulties that the

existence of seasonal commodities can create for National Income Accounting, see: P. Hill

(1996), Inflation Accounting: A Manual on National Accounting under Conditions of High

Inflation, Paris: OECD; W.E. Diewert (1998), Index Number Approaches to Seasonal

Adjustment, forthcoming in Macroeconomic Dynamics; and W. E. Diewert (1998), High

Inflation, Seasonal Commodities and Annual Index Numbers, forthcoming in Macroeconomic

Dynamics.

Thus, statistical agencies are increasingly facing the problem of a lack of comparability when they

construct their estimates of business real output, input and productivity. In addition, in the above3 sections, we saw that statistical agencies faced many difficult conceptual measurement

problems, where reasonable people could come up with quite different answers to these

3

A recent publication that makes the same point (and many others) is: Michael J. Boskin (1997), Some Thoughts

on Improving Economic Statistics to Make Them more Relevant in the Information Age , document prepared for the

Joint Economic Committee, Office of the Vice Chairman, United States Congress, Washington D.C.: Government

Printing Office, October, 22 pp.

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measurement problems. These difficulties mean it is becoming increasingly difficult for agencies to

construct reproducible estimates of real output, input and productivity4. Unfortunately, I do not

see any easy solutions to these measurement problems on the horizon.

4

The reproducibility testfor data construction states that every competent statistician would construct the same

aggregate given identical disaggregated information sets. The idea of this test dates back to the early accounting

literature.