Productivity Perspectives in Australia: Conclusions and Future Directions

Erwin Diewert,                                                                 January 20, 2005.
Department of Economics, 
University of British Columbia, 
Vancouver, Canada, V6T 1Z1.
Email: diewert@econ.ubc.ca

1. Introduction

As the last speaker at this conference, my task is threefold:

•	to list any conclusions that might have emerged from the papers that were presented;
•	to provide some future directions for improving the measurement of productivity in Australia and
•	to provide possible policy directions for improving Australia’s productivity performance.

However, before addressing the above topics, I would like to provide a few words of praise for the Australian Bureau of Statistics and the Productivity Commission.  The ABS produces all of the basic data on inputs and outputs that are required in order to compute Australia’s Labour Productivity (LP) and Total Factor Productivity (TFP).  The ABS does an excellent job and is internationally recognized as one of the best statistical agencies in the world.  On the other hand, the Productivity Commission educates the public about the importance of improving Australia’s productivity performance and it provides some very useful advice on how Australia’s productivity performance could be improved.  I would also like to praise Australia’s financial press, who do an excellent job of covering productivity and related policy issues.

The first task (to list any conclusions that might have emerged from the conference papers) will be discussed in section 2 below, where we will review some of the material presented by Eric Bartelsman (2004a) in his leadoff paper for this conference.  We will also review some of the literature that links productivity to investments in R&D.  The message that emerges from this section is that we should be cautious in making definitive conclusions on what factors can improve a country’s productivity performance for two reasons:

•	It is not a trivial exercise to measure productivity, particularly at the industry level (as opposed to the national level) and making cross country comparisons of productivity levels is particularly hazardous;
•	Even if the productivity of a sector has been accurately measured, it is not a trivial exercise to determine exactly what factors “explain” the sector’s productivity performance.

In view of the above uncertainties, I will not spend much time on my third task (to provide possible policy directions for improving Australia’s productivity performance) but I note that the papers by Bartelsman (2004a), Graeme Davis (2004), Steve Dowrick (2004), Sid Shanks (2004), Dean Parham (2004) and Jimmy Louca (2004) all provide some observations on productivity performance that may be of interest to policy makers.  

Most of this paper will focus on my second task: to provide some future directions for improving the measurement of productivity in Australia.  Thus in sections 3, 4 and 5 below, I follow in the footsteps of Carl Obst (2004) and focus on problem areas in the measurement of productivity for outputs (section 3), labour inputs (section 4) and capital inputs (section 5). 

There are some additional measurement difficulties that do not fit neatly into the above three categories.  Thus in section 6, we will discuss the problems involved in measuring inventory change.  In section 7, we discuss some of the problems associated with the quality adjustment of prices, while section 8 discusses some of the difficulties in measuring productivity when information on outputs and inputs is collected in different surveys.  Section 9 discusses some of the tricky issues that arise in the context of constructing industry productivity statistics: namely how should indirect taxes be treated in the productivity accounts?  Section 10 offers a few comments on how to measure the contribution to productivity growth of entering and exiting firms.  Section 11 concludes with some suggestions for future directions that the Australian Bureau of Statistics might want to consider.
 
2. Productivity: Some of the Main Issues

Eric Bartelsman (2004a) presented an overview of some of the main issues and controversies associated with the measurement of productivity and its policy implications and we will summarize part of his discussion of these issues in this section.  We will also treat the problem of measuring the contribution of investments in research and development (R&D) to productivity growth in some detail.
2.1 Approaches to the Measurement of Total Factor Productivity Growth

Total Factor Productivity Growth (TFPG) can be defined as the rate of growth of outputs for some collection of business enterprises divided by the rate of growth of inputs used by these enterprises.  In most economies, outputs grow faster than inputs and so TFPG contributes to increases in a country’s standard of living.

There are two broad approaches to measuring TFPG:

•	The growth accounting or index number approach and 
•	The econometric estimation approach.

The modern growth accounting approach to the measurement of TFPG dates back to the seminal contribution of Solow (1957), who used the assumption of a single output constant returns to scale production function with aggregate labour and aggregate capital as inputs. Using this framework, Solow was able to show that TFPG could be measured as a weighted average of output growth rates less a weighted average of input growth rates.  Jorgenson and Griliches (1967) (1972) improved upon Solow’s framework in several respects:

•	They generalized Solow’s one output and two input methodology to the case of many outputs and many inputs;
•	They used a more sophisticated index number formula (the Törnqvist Theil index) to aggregate inputs and outputs;
•	They realized that labour hours are not homogeneous and advocated using wage rates as price weights for different types of labour;
•	They introduced the idea of using rental prices or user costs of capital as price weights to aggregate the capital inputs and
•	They introduced the convention that indirect taxes that fall on outputs should be subtracted from output prices for productivity measurement purposes but that indirect taxes that fall on intermediate inputs should not be subtracted.

A recent very useful reference that describes in some detail the growth accounting approach to the measurement of Total Factor Productivity Growth is Schreyer (2001).  

The second approach to measuring TFP growth dates back to Jan Tinbergen (1942), who econometrically estimated an aggregate production function that had a time trend as an exogenous variable.  The coefficient on the time trend was interpreted as a measure of productivity growth.  Tinbergen’s approach is still in widespread use today.  

There are problems with both approaches to the measurement of productivity:

•	The growth accounting approach assumes a constant returns to scale technology and competitive price taking behavior.
•	The econometric approach is not subject to the above difficulties but has some severe difficulties of its own: namely, it cannot deal adequately with a large number of inputs and outputs and the results that the econometric approach generates are often fragile and are generally not reproducible.

In the following subsection, we will look in more detail at some of the difficulties associated with the econometric approach to the measurement of productivity.  In particular, we will look at the econometric literature on estimating the effects of investments in R&D on productivity growth.

2.2 The Effects of Investments in R&D on Productivity Growth  

To illustrate some of the problems with econometric techniques, consider the evidence on spillovers cited by Dowrick (2004) on the social returns to R&D.  Dowrick’s (2004) review of the R&D and spillovers literature finds social rates of return to R&D investments in the 20% to 85% range.  An early paper in this econometric literature is Bernstein and Nadiri (1988), who found that private rates of return to investments in R&D in five U.S. manufacturing industries over the years 1961-1981 averaged 16.7% per year compared to rates of return on physical capital that averaged 9.6% per year.  However, Bernstein and Nadiri (1988; 433) found that when they took into account the effects of spillovers, social rates of return to R&D investments in these five industries averaged an astounding 50.0% per year.  These rates of return on R&D investments perhaps seem high but they are typical of the rates that are found in this econometric literature. 

These econometric estimates of private and social rates of return to investments in R&D are almost surely much too high.  These high rates of return are obtained by estimating a production function (or a factor requirements function) where an output measure is regressed on measures of labour, capital and an R&D stock variable.  There is no time trend in the regression so the R&D stock variable picks up not only the output augmenting effects of investments in R&D (which is entirely appropriate) but also the effects of other methods of improving the efficiency of the economy or industrial sector (which is inappropriate).  Some of the other productivity improving effects that generally trend with time are the effects of industry annual meetings and trade fairs where successful business practices are diffused into the general population.  Business consultants and benchmarking experts also diffuse best practice techniques into general use.  A general increase in the education levels of the population could also be a source of productivity gains.  Experience or learning by doing is another source of gains.  In summary: investments in R&D probably account for only a fraction of the improvements in productivity that occur through other channels but by neglecting these other factors (which are often difficult to measure) in the econometric model, virtually all of the industry’s productivity improvement is incorrectly attributed to R&D investments.

In the following subsection, we look more closely at some of the accounting problems associated with investments in R&D (and other intangible asset investments).

2.3 Are Private Sector R&D Investments the Same as Investments in Plant and Equipment?

There is another problem with the econometric literature on measuring the benefits of investments in R&D: R&D investments are treated in a manner similar to investments in physical capital.  Thus the econometrician forms nominal dollar estimates of R&D investments in the industry or firm or other production unit under consideration by time period, deflates these investments into constant dollar investments, assumes a depreciation rate (usually between 10 and 15 percent per year) and forms an R&D capital stock in a manner that is analogous to forming a structures capital stock.  This R&D capital stock is then used as an exogenous variable in the regression of output on input.  Aside from the arbitrariness of the assumption about the magnitude of the R&D depreciation rate, this model of the effects of R&D seems wrong. R&D is not like other depreciable assets which gradually wear out through use; rather R&D can be viewed as the creation of new technologies.  These new technologies may just reduce the cost of producing an existing commodity or they may create entirely new goods and services (process versus product innovation).  In either case, the R&D “asset” is not like a “normal” reproducible capital asset that depreciates with use.  The expenditures incurred in creating the R&D asset are sunk costs and they have no resale value as is the case with a purchase of a reproducible asset.  However, a successful private sector R&D venture has created a new product or process that will give rise to a stream of profits in future periods.  In many cases, the new technology can be licensed and the rights to use the new technology can be sold.  Thus in the case of successful private R&D ventures, a new asset has been created: the rights to a (monopoly) stream of future incremental revenues.  However, once a new successful technology has been created, expiry of patents, diffusion of knowledge about the innovation, even newer innovations by competitors and changing tastes all combine to reduce the stream of monopoly profits over time.  Note that the effects of these factors, which reduce the value of the R&D asset over time, are difficult to forecast.

To summarize the above discussion: a private sector R&D asset is much more complicated than a typical reproducible capital asset (like a structure or machine).  There are actually two “assets” associated with an R&D venture:

•	The first cost asset is the cumulated costs of the R&D project and
•	The second revenue asset is the discounted value of the incremental profits that the R&D project is expected to generate.

For any individual R&D project, it is unlikely that the R&D cost “asset” is equal to the R&D incremental revenue asset but, over a large population of R&D projects, we could expect to see the value of the cost assets to be approximately equal to the value of the revenue assets.

As defined above, the cost and revenue assets are defined in terms of nominal dollars.  It is relatively straightforward to obtain a constant dollar counterpart to the nominal cost asset, provided that deflators are available for the important components of nominal expenditures on R&D projects, such as scientific and engineering personnel, structures, materials and instruments.  However, it is not straightforward to obtain constant dollar estimates for the revenue asset.  Since the discounted incremental revenues that the project is expected to yield are in units of today’s dollar, the simplest approach to obtaining a constant dollar estimate for the revenue asset would be to deflate the current expected discounted profits estimate by a current general index of inflation.  

As was mentioned above, the cost asset is not really an asset: it is a sunk cost.  In the present system of national accounts, SNA 1993, privately funded R&D expenditures are regarded as intermediate business expenses and are written off as they occur.  This point of view is defensible, particularly for unsuccessful R&D ventures.  However, for successful R&D ventures, it could be argued that it is “unfair” to write down current period income by these expenditures since these expenditures will eventually be recovered in future periods as the project’s incremental revenues pour in to the firm.  Hence, from this point of view, it makes sense to capitalize these R&D expenditures into an “asset” and depreciate this “asset” in a proportional manner to the future period incremental revenues.  From this point of view, the problem is to determine how to allocate the cumulated cost of an R&D project over future periods.  This accounting problem has a different character than the usual problems involved in depreciating reproducible capital stock investments, where information on used assets can be used if an opportunity cost approach to depreciation is used.  For an R&D cost “asset”, the problem is one of matching current costs with future expected revenues, which is a rather daunting task!

2.4 How Should Public Sector Investments in R&D be Treated?

The above analysis is applicable for a profit motivated firm, which makes R&D investments.  However, a substantial fraction of R&D expenditures in all market economies is usually funded by governments and often the fruits of government funded R&D are made freely available to all potential users.  In the case of government funded R&D projects, the situation is much more complicated than was indicated above for the case of privately funded R&D projects.  In the case of a government funded R&D project, there are again two “assets” associated with the venture:

•	The first cost asset is again the cumulated costs of the R&D project and
•	The second utility asset is the discounted value of the incremental increases in utility that the R&D project is expected to generate for a reference population.

For a government funded R&D project, the treatment of the cost “asset” is conceptually similar to the case of a privately funded R&D project, except that the matching problem is more complex; i.e., instead of amortizing cumulated R&D costs in a manner proportional to expected future incremental revenues, the government should amortize the costs in a manner proportional to expected future incremental utility flows that will accrue to inhabitants of the country (present and future!) as a result of the project.  It can be seen that in the case of government funded R&D projects, the measurement problems are much more severe:

•	How should the utility of each household in the reference population be cardinalized?
•	How can the expected incremental increases in reference population utilities that are generated by the project be estimated? 

The above questions are not simple to answer!

For both a successful private or government funded R&D project, a new set of techniques of production (or input-output coefficients) is created.  Typically, there will be no traditional depreciation associated with the project; i.e., typically the new process or product will not be forgotten and so the effects of the innovation in adding to society’s stock of blueprints is more or less permanent.  But yet the incremental utility value of the project will generally decline over time due to the following factors:

•	Even more efficient processes are invented which render an existing process obsolete.
•	In the case of a product innovation, over time consumer tastes may shift away from the new product or a new product is invented which renders the existing product obsolete.

Hopefully, the above discussion will convince the reader that an R&D asset is rather different than a typical tangible asset like a machine, building, inventory component or plot of land.  Trying to work out the contribution of an R&D project to production and welfare is indeed a very complicated task.

We turn now to a brief (and incomplete) review of methods that have been suggested in the literature to determine the contribution of an R&D project to production and welfare.

2.5 The Patent Renewal Fee Method for Assessing the Benefits of R&D Investments

One method for determining how fast the stream of incremental revenues generated by an R&D project that is patented declines is to look at patent renewal fees; see Pakes and Shankerman (1978) (1986) for such an approach.  Nadiri and Prucha endorsed their approach and commented on their approach as follows:

“The estimates for both private and social rates of return in R&D investment have been very high in most industries (see Bernstein and Nadiri (1991)).  The private rate of return in R&D investment is affected by the rate of decay of the private revenues accruing to industrially produced knowledge.  However, except for the two studies by Pakes and Shankerman (1978) (1986), there are few estimates for the rate of decay of knowledge capital.  Pakes and Shankerman correctly emphasize that the conceptually appropriate rate of depreciation of knowledge is the rate at which the appropriable revenues decline.  The rate of decay in the revenues does not arise from any decay in productivity of knowledge but from reduction in market valuation, which arises due to inability to appropriate the benefits from the innovations and the obsolescence of original innovations by new ones.  Pakes and Shankerman employed data on patent renewal fees to estimate the decay rate for knowledge capital for several European countries.  Their estimates are shown in Table III.  In their first study, their reported point estimate for the rate of decay was about 0.25 with a 95 percent confidence interval between 0.18 and 0.36.”  M. Ishaq Nadiri and Ingmar R. Prucha (1996; 51).  

Thus the Pakes and Shankerman rates of incremental revenue decay for patented innovations ranged from 11% to 36% per year.  Of course, there are two problems with these estimates:

•	Their estimated range of revenue decay rates is rather wide and 
•	Not all innovations are patented and so the Pakes and Shankerman results do not cover all R&D investments.

Given the fact that the patent renewal fees method for assessing the benefits of R&D investments is necessarily incomplete, we turn to the second method that has been used.

2.6 Econometric Methods for the Determination of the Rate of Revenue Decay for R&D Investments

Nadiri and Prucha (1996) took a rather different approach to the problem of estimating rates of revenue decay for R&D investments.  They first criticized the “traditional” approach to the estimation of R&D depreciation rates as follows:

“Very little effort has been made, except for Pakes and Shankerman (1978) (1986), to measure the depreciation rates of the stock of R&D.  Researchers doing applied work typically assume an arbitrary depreciation rate of 0.10 to 0.15 to construct the stock of R&D capital using the perpetual inventory method.  M. Ishaq Nadiri and Ingmar R. Prucha (1996; 43).   
   
They then noted correctly that R&D investments should act as mechanism for shifting outward society’s production possibilities frontier but in their empirical work, they chose instead to treat R&D in the same manner as a reproducible capital stock component:

“As in many studies the stock of R&D may be considered to represent a technological index that shifts the production frontier.  Alternatively, given that the technology satisfies appropriate curvature conditions, the stock of R&D may be viewed as a factor input.”  M. Ishaq Nadiri and Ingmar R. Prucha (1996; 44).   

Nadiri and Prucha followed their suggested alternative route and assumed that R&D investments depreciated at the rate , where  is a depreciation rate between 0 and 1.  Hence, given an estimate of the initial stock of R&D at the beginning of period 0, say K0, the stock at the beginning of a subsequent period t is equal to:

(1) Kt  It1 + (1) It2 + (1)2 It2 + …+ (1)t I0 + (1)t+1 K0 ;      t = 1,2,… 

where It is (real) R&D investment in period t.  Now assume that aggregate output in period t, Yt, is related to aggregate input (excluding R&D inputs), Xt, and the R&D stock Kt by a production function F so that:

(2) Yt = F(Xt,Kt) ;                                                                                    t = 1,2,….

Now substitute (1) into (2), assume a functional form for the production function F, add an error term to (2), and we have a nice econometric model where the parameters of the production function plus the depreciation rate for R&D capital, , can be estimated, given data on outputs, Yt, non R&D inputs Xt and the R&D investments It. 

A second econometric framework can be obtained by assuming that producers face the period t price for non R&D inputs, wt, and competitively minimize the (variable) cost of  producing the period t output, Yt, given the R&D stock Kt.  Denote the resulting variable cost function as C(wt,Yt,Kt).  Then by Shephard’s (1953; 11) Lemma, the cost minimizing input demand is equal to the partial derivative of the cost function with respect to the input price:

(3) Xt = C(wt,Yt,Kt)/w ;                                                                          t = 1,2,….

Now substitute (1) into (3), assume a functional form for the cost function C, add an error term to (3), and we have an econometric model where the parameters of the cost function plus the depreciation rate for R&D capital, , can be estimated, given data on outputs, Yt, non R&D inputs Xt, input prices wt and the R&D investments It.

A third econometric framework can be obtained by assuming that producers face the period t price for non R&D inputs, wt, the period t price for output pt and they competitively maximize the (variable) profits, given the R&D stock Kt.  Denote the resulting variable profit function as (pt,wt,Kt).  Then by Hotelling’s (1932; 594) Lemma, the profit maximizing output supply and (minus) the input demand is equal to the partial derivatives of the profit function with respect to the output and input prices:

(4) Yt = (pt,wt,Kt)/p ;                                                                          t = 1,2,….
(5) Xt = (pt,wt,Kt)/w ;                                                                       t = 1,2,….

Now substitute (1) into (4) and (5), assume a functional form for the profit function , add error terms to (4) and (5), and we have an econometric model where the parameters of the profit function plus the depreciation rate for R&D capital, , can be estimated, given data on outputs, Yt, non R&D inputs Xt, output prices pt, input prices wt and the R&D investments It.  This third econometric framework, while leading to more degrees of freedom, has the disadvantage of assuming competitive behavior with respect to the pricing of outputs.  In the context of R&D investments, which are very much concerned with creating monopolies, the assumption of competitive pricing of outputs is somewhat suspect and thus this framework is probably not suitable for estimating R&D depreciation rates.

As mentioned above, Nadiri and Prucha (1996; 48) used a variant of the cost function approach to estimate depreciation rates for R&D and reproducible capital for the U.S. total manufacturing sector.  Their estimated depreciation rate for R&D capital turned out to be 12% per year.  However, their econometric model attributed all technical progress to R&D investments, which is almost surely not correct, and hence, their estimates cannot be accepted as being definitive.  Moreover, their econometric model was based on the assumption that R&D capital depreciated in much the same manner as reproducible capital; recall (1) above.  But as we have explained above, knowledge investments are not at all like investments in structures and machines, which wear out through use.  Instead, knowledge investments change the production function in an irreversible manner, allowing additional output to be produced from the same amounts of inputs.  As explained above in sections 2.3 and 2.4, tracing out the consequences of these shifts in the production frontier is a very complex process, possibly involving changing tastes and obsolescence.  It may be that treating R&D investments like investments in machines can provide a reasonable approximation to a more complete applied general equilibrium model that traces out the consequences of knowledge investments in a more realistic manner, but this has not yet been demonstrated.

The final approach to estimating amortization rates for R&D investments is due to Lev and Sougiannis (1996) (1999).  Their model can be very roughly described as follows: suppose that the gross value added of a firm in year t, Vt,  is related to the amount of tangible or reproducible capital that it has available at the beginning of year t, Kt, and its real investments in R&D for the past 7 years, Rt1, Rt2, … , Rt7.  The relationship between value added in year t to the firm’s tangible capital stock and past investments in R&D is assumed to the following one:

(6) Vt = 0 + 1 PKtKt + 1 PRt1Rt1 + 2 PRt2Rt2 +…+ 7 PRt7Rt7 + t ;

where the ’s and the ’s are unknown parameters to be estimated, PKt is the purchase price of a unit of tangible capital at the beginning of period t, PRt1 is the price of a unit of R&D for the firm in year t1, …., PRt7 is the price of a unit of R&D for the firm in year t7 and t is an error term.  Given information on the firm’s annual value added, value of tangible capital and past R&D investments, the unknown parameters in (6) can be estimated using regression techniques.

However, if there is inflation in the economy, it can be seen that the past R&D investments that appear on the right hand side of (6) are expressed in value units of varying purchasing power.  Moreover, Vt on the left hand side of (6) is also expressed in (different) varying units of purchasing power as t changes.  These problems with the model can be mitigated under some circumstances.  Assume that the firm produces Yt units of output in year t and sells this amount of output at the price pt and that it uses Xt units of labour and intermediate inputs and purchases units of this variable input at the price wt.  Assume also that the firm in year t faces the user cost ut for a unit of tangible capital.  Then the firm’s year t modified profits, t, can be defined as follows:

(7) t  ptYt  wtXt  utKt . 

When calculating (7), we need to exclude expenditures on R&D from Xt.  Thus the modified profits t for firms engaging in R&D should be positive and these positive modified profits are equal to pure profits plus the period t profits that can be attributed to past R&D investments.  We can adjust period t modified profits for price change by constructing a value added price index that adjusts the year t prices to the level of prices prevailing in a prior year 0, say P(p0,w0,u0; pt,wt,ut; Y0,X0,K0; Yt,Xt,Kt), and then we can use this value added price index to deflate t into common units that are free from inflationary effects.  Using these definitions, our suggested inflation adjusted version of the model (6) is (8) below:

(8) t/P(p0,w0,u0; pt,wt,ut; Y0,X0,K0; Yt,Xt,Kt) 
                                                                        = 0 + 1 Rt1 + 2 Rt2 +…+ 7 Rt7 + t ;

where 0 and 1, 2, … , 7 are unknown parameters to be estimated.  The above model essentially says that if we make a real R&D investment in year 0 of size R then in year 1, it will contribute the amount 1R to real profits; in year 2, it will contribute the amount 2R to real profits; … and in year 7, it will contribute the amount 7R to real profits.  Once the ’s have been estimated, we can follow the example of Lev and Sougiannis (1996; 117) and normalize these coefficients into the amortization coefficients, k, defined as follows:

(9) k  k/[1+ 2 +…+ 7] ;                                                              k = 1,2,…,7.

Thus if an R&D investment is made by the firm this year, then it should be capitalized and using the matching principle in accounting, 1R should be written off or amortized next year, 2R should be amortized in the following year, and so on.

There is one important aspect of the model defined by (8) that should be mentioned: namely, the coefficients 0, 1, 2, …, 7 should all be nonnegative.  This is a straightforward observation for the ’s but what about the parameter 0?  We argue that this constant term in the regression (8) should be nonnegative since it represents all of the omitted variables in the regression that increase the firm’s productivity in each period in addition to the firm’s R&D investments.  A similar comment applies to the original model of Lev and Sougiannis, (6) above.

One problem with the models (6) and (8) is that because Vt and t are defined as differences of economic variables that are subject to a considerable amount of measurement error, the measurement error in Vt and t could be very large, leading to inaccurate estimates of rates of return to R&D investments and to inaccurate amortization terms.  Another problem with the model (8) is that it does not fully capture the complexities mentioned sections 2.3 above about modeling how the monopoly profits of a firm that undertakes R&D are eroded over time due to the diffusion of knowledge about the R&D induced innovations and changing consumer tastes.  Our conclusion at this point is that none of the suggested econometric methods for estimating the effects of R&D investments are completely satisfactory.      

Bartelsman (2004a) asked what do we really know about the effects of R&D investments on productivity performance?  As can be seen from the above discussion, the existing econometric evidence on this question seems, at least to this reader of the evidence, to be unreliable and inconclusive.  Hence, at this stage, I do not think that there is much reliable advice that we can give to policy makers on this topic.

2.7 Time Series versus Cross Sectional Comparisons of Productivity

Bartelsman (2004a) also looked at the convergence literature and cross country comparisons of productivity levels.  He correctly noted that it is much more difficult to make cross country comparisons of productivity compared to making time series comparisons.  The increased difficulties are due to the fact that it is much more difficult to make cross country comparisons of prices than it is to make time series comparisons for the same country or industrial sector.  National price statisticians are usually obligated to construct consumer price indexes but they are not obligated to compare prices in their country with the prices of comparable products in other countries and hence accurate information on cross country comparisons of prices is generally not available.  Thus in making cross country comparisons of per capita real GDP or of the productivity of a particular industry, there is bound to be much more measurement error than when one compares the productivity performance of a particular sector over time in the same country.  Hence policy makers should be very cautious in drawing any policy conclusions whatsoever from cross country comparisons of productivity levels in particular industries for two reasons:

•	It is much more difficult to measure productivity at the sectoral level than at the national level and
•	It is much more difficult to construct accurate price indexes that compare price levels across countries than it is to construct intertemporal price indexes for the same production unit within a country.

Bartelsman (2004a) noted that growth accounting measures of productivity growth do not tell us anything about the sources of this growth.  However, these growth accounting measures of TFP growth are used as the dependent variable in thousands of regressions that attempt to find causal factors for the growth.  Needless to say, these regressions are not entirely convincing and of course, they are bound to be somewhat contradictory.  Again, these regressions are not reliable enough for policy makers to make important decisions based on them.

2.8 Factors that Affect a Country’s Productivity Performance

There is a large literature on factors that tend to improve a country’s productivity performance.  My own summary of some of the factors is given below:

In summary, factors that will tend to augment TFP growth are:

•	Rapid investment growth (in reproducible or physical capital).
•	Rapid growth in investments in education, training and human capital.
•	Rapid growth in primary inputs will tend to lead to an even more rapid growth of output due to increasing returns to scale in production.  The main drivers of increasing returns to scale are: the existence of indivisibilities; the laws of geometry and physics; the existence of fixed costs and the laws of statistics.
•	Increases in TFP are associated with increased specialization, which in turn is driven by growth in the size of the market.  In brief: big tends to be better!
•	Improvements in the functioning of markets, which could occur in a variety of ways, including: (i) improvements in personal security; (ii) improvements in property rights; (iii) reductions in trade barriers; (iv) improvements in telecommunications (in particular, the growth of internet driven markets) and (v) improvements in transportation and infrastructure.
•	Access to new knowledge about the development of new commodities and processes.  Recall our discussion about the importance of business consultants, trade associations and benchmarking to diffuse knowledge about best practices.

Factors which will tend to reduce the growth of Total Factor Productivity (in addition to the negative of the above factors) are:

•	High taxes.  In theory, this factor should just have one time level effects on economic efficiency but it is likely that high taxes have dynamic effects as well, tending to reduce investments in physical and human capital and retarding the formation of specialized markets.
•	High inflation.  High or unpredictable rates of inflation tend to increase uncertainty about the real interest rate and future prices and hence lead to a misallocation of investment and a reduction in productive efficiency.
  
W. Erwin Diewert (2004a; 21-22). 

In the remainder of this paper, we concentrate on outlining some of the measurement problems that the ABS faces in constructing its estimates of Australian TFP.  In the following three sections, we follow the example set by Obst (2004) and outline some of the measurement problems associated with the measurement of outputs, labour input and capital input.

3. Output Measurement Problems

Australia is facing a problem that is similar to that faced by North American countries; namely, the industry classification system is changing, leading to hundreds of new service sector industries where price information on the major products produced by these new industries is at present not collected by most statistical agencies.  When the new classification system is implemented, many industries will lack adequate deflators for their major outputs.  Sixty years ago, services did not play such a large role in most economies and so industrial classification systems gave more importance to primary and manufacturing industries (and products).  It is only in the last decade or so that statistical agencies have started to devote more resources to measuring service sector outputs more accurately.  The ABS does have an impressive service industry price measurement program but even more resources could and should be devoted to this important task.

Many difficult conceptual problems are associated with the measurement of service sector prices and outputs.  We list below some general categories of difficult to measure service products:

•	Unique products.  If products are one of a kind, then obviously the prices of products produced in the present period cannot be compared with the price of the same product in a previous period. This is a pervasive problem in the measurement of the prices of services.
•	Complex products.  Many service products are very complicated; e.g., telephone service plans.
•	Tied products.  Many service products are bundled together and offered as a single unit; e.g., cablevision plans and banking services packages.  In principle, hedonic regression techniques could be used to price out these types of service products.
•	Marketing and advertising products.  This class of service sector outputs is dedicated to influencing or informing consumers about their tastes.  A standard economic paradigm for this type of product has not yet emerged.
•	Financial products.  What is the “correct” real price of a household’s monetary deposits?  Somewhat surprisingly, this question has not yet been resolved in a definitive manner.
•	Uncertain products.  What is the correct pricing concept for gambling and insurance expenditures?  What is the correct price for a movie or a record original when it is initially released?

Many of these measurement problems are theoretically quite challenging.  Hopefully, some of the academics and other researchers at this meeting will be stimulated to work on these measurement problems.

4. Labour Measurement Problems

The most comprehensive information on labour input by industry in Australia comes from the Labour Force Survey, which is a household survey.  Unfortunately, respondents to this survey may not provide very accurate answers to some of the questions asked; in particular, they may not know which industries family members work in or precisely how many hours they work.

Every country has some difficulty in determining precisely what the labour input of the self employed is.  The System of National Accounts 1993 puts the labour input of non employees into Gross Operating Surplus and so the contribution to output of the self employed is classified into this category, along with the contribution of any capital that the self employed might be using.  Since there is no international standard for extracting the labour contribution of the self employed from Gross Operating Surplus, different countries that have TFP programs estimate the labour input of the self employed in different ways, leading to a lack of international comparability.  Since self employment in many advanced countries has rebounded during the past decade (due to outsourcing and the continuing specialization of the labour market), the associated labour input measurement problems are not trivial.

The final labour measurement problem that we note in this section is that there are two alternative methods for calculating labour input.  The first method treats all labour hours by all types of worker are regarded as being equivalent.  However, as noted by Jorgenson and Griliches (1967), all labour hours are not equivalent.  Hence, the second method classifies labour inputs into relatively homogeneous types of labour and then normal index number theory is used to aggregate up the various kinds of labour.  The Australian Bureau of Statistics uses both methods but at present uses the first method in its headline series, possibly because it was able to construct this series back to 1964 whereas the weighted hours series could only be constructed back to 1984. It seems to me that the second method is the preferred one.
 
5. Capital Measurement Problems

The Gross Operating Surplus of a country (less the labour contribution of the self employed) should be decomposed into several components:

•	Depreciation;
•	A return to the financial capital employed;
•	A charge for any obsolescence of the capital employed;
•	Rents to land and resources;
•	Amortization of intangible capital components such as goodwill, R&D, trademarks, advertising, etc.;
•	A charge (or credit) due to changes in the prices of assets over the accounting period; and
•	Taxes paid to governments that do not fall on outputs, intermediate inputs or labour.

There are measurement difficulties associated with implementing each of the above decompositions:

•	What are the correct depreciation rates to use?
•	What is the correct opportunity cost of capital to use?  Should the chosen rate be an endogenous one that causes the value of inputs to equal the value of outputs or should it be an exogenous one? And if it is an exogenous one, how exactly should it be chosen?
•	How exactly is the obsolescence charge do be determined?  Should the obsolescence be foreseen?
•	What is the right opportunity cost rate of return to land?  Should we take into account the fact that historically, land appreciates in price in real terms and so some of the normal return to land is taken in the form of holding gains?
•	Should the capital gains or holding gains term be an expected one or an actual ex post one?  Should holding gains even be in the production accounts?  And if we want to allow consistently negative holding gains as an obsolescence charge (e.g., computers), how can we not allow consistently positive holding gains in the production accounts?
•	How exactly should the intangible capital items be amortized?
•	How exactly should the tax component be calculated?

Many of the above issues were discussed in the nice paper by Zheng (2004) but they are not easy to resolve in a definitive manner. 

There are a few more issues associated with the measurement of capital:

•	Are land stocks productive?
•	Are resource stocks productive?
•	Are inventory stocks productive?
•	Are intangible assets like R&D stocks productive?

Most productivity researchers, would agree that land, resource and inventory stocks are all productive and should be in the productivity accounts.  The ABS multifactor productivity measures do include land and inventory stocks and some components of resource stocks are also included in their balance sheets (tree plantations).  Presumably, other resource stocks will also be included at some stage in the productivity estimates when the data on resource stocks are refined.  

The inclusion of intangible assets such as R&D investments, expenditures on training, advertising and marketing expenditures, trademarks and franchises is more problematical.  From the perspective of capital theory, any current expenditure that yields benefits in future periods could be capitalized.  However, all of the intangible assets listed above have the character of sunk costs and so from the perspective of the firm’s expected discounted stream of future profits, it is immaterial whether these expenditures are capitalized or not.  But from the viewpoint of measuring the periodic (i.e., the period by period) income of the firm, it does make sense to capitalize these intangible expenditures and then amortize them over the future periods where the expenditures still generate benefits.  The practical problem facing the government statistician is: how exactly should these capitalized expenditures be amortized?  We considered this question in some detail in section 2 above for R&D investments and we suggested that the amortization amounts should be proportional to the incremental revenues generated by the investment.  But the practical problem for the ABS is how exactly are these future incremental revenues to be estimated?  In section 2, we suggested that the academic literature on this topic is not too helpful in answering this question.  Again, we leave this question as a challenging problem that academics and other researchers should address.

One problem with the treatment of inventories by most statistical agencies is that the treatment of inventory change in the national accounts is a real dog’s breakfast in the sense that at times, the real and nominal inventory change have opposite signs!  In the following section, we suggest a theoretical methodology that will eliminate this problem.

6. The Treatment of Inventory Stocks and Inventory Change

As was mentioned in the previous section, we need a theoretical framework to measure the contribution of an inventory stock to production.  We outline a possible framework taken from Diewert and Smith (1994).

Consider a firm that perhaps produces a noninventory output during period t, Yt, uses a noninventory input Xt, sells the amount St of an inventory item during period t and makes purchases of the inventory item during period t in the amount Bt.  Suppose that the average prices during period t of Yt, Xt, St and Bt are PYt, PXt, PSt and PBt respectively.  Then neglecting balance sheet items, the firm’s period t cash flow is:

(6) CFt  PYt Yt  PXt Xt + PSt St  PBt Bt.

Let the firm’s beginning of period t stock of inventory be Kt and let its end of period stock of inventory be Kt+1.  These inventory stocks are valued at the balance sheet prices prevailing at the beginning and end of period t, PKt and PKt+1 respectively.  Note that all 4 prices involving inventory items, PSt, PBt, PKt and PKt+1 can be different.  

The firm’s period t economic income is defined as its cash flow plus the value of its end of period t stock of inventory items less (1+rt) times the value of its beginning of period t stock of inventory items:

(7) EIt  CFt + PKt+1 Kt+1  (1+rt) PKt Kt

where rt is the nominal cost of capital that the firm faces at the beginning of period t.  Thus in definition (7), we assume that the firm has to borrow financial capital or raise equity capital at the cost rt in order to finance its initial holdings of inventory items.  This cost could be real (in the case of a firm whose initial capital is funded by bonds) or it could be an opportunity cost (in the case of a firm entirely funded by equity capital).

The end of period stock of inventory is related to the beginning of the period stock by the following equation:

(8) Kt+1 = Kt + Bt  St  Ut

where Ut denotes inventory items that are lost, spoiled, damaged or are used internally by the firm.  In the case of livestock inventories, there is a natural growth rate of inventories over the period so equation (8) is replaced by:

(9) Kt+1 = Kt + Bt  St + Gt

where Gt denotes the natural growth of the stock over period t.

Define the change in inventory stocks over period t as:

(10) Kt  Kt+1  Kt .

Using (10), both (8) and (9) can be written as:

(11) Kt+1 = Kt + Kt.

Now substitute (11) into the definition of economic income (7) and we obtain the following expression:

(12) EIt  CFt + PKt+1 [Kt + Kt]  (1+rt) PKt Kt
             = CFt + PKt+1 Kt  [rt PKt  (PKt+1  PKt) ]Kt.

Thus economic income is equal to cash flow plus the value of the change in inventory (valued at end of period balance sheet prices) minus the user cost of inventories times the starting stocks of inventories where this period t user cost is defined as 

(13) PIt  rt PKt  (PKt+1  PKt).

Note that the above algebra works for both livestock and ordinary inventory items.

Of course, there can be two versions of the user cost:

•	An ex post version where the actual end of period balance sheet price of inventories is used or
•	An ex ante version where at the beginning of period t, we estimate a predicted value for the end of period balance sheet price.

In practice, beginning of period inventory stocks should be estimated along with appropriate balance sheet prices.  When aggregating over a number of inventory stock items, normal index number theory can be used in order to decompose balance sheet values of inventory items into price and quantity components.  Then the change in stocks can be obtained by differencing the stock volume series and the end of period balance sheet price (or a predicted version of it) could serve as the flow price for the change in inventories.  Note that normal index number theory breaks down for value aggregates that can be either positive or negative over time.
      
What is new in this section is the development of a methodology that can deal with livestock inventories, where there is a natural biological growth rate associated with the stock.  What we have shown above is that a biological inventory stock can be treated just like any other inventory stock: what is necessary is the ability to estimate the size of the stock at the balance sheet dates (and of course, we have to keep track of any product flows that occur during the period such as sales and purchases of the inventory item or transformations of it into other products). 

7. The Problems of New Products and of Quality Adjustment

Increasingly, the world economy devotes more and more resources to the development of new goods and services.  This creates severe problems for statistical agencies when they attempt to measure real economic growth because their methodology to measure price change is based on the list of products remaining constant from period to period.; i.e., the price of a product produced in the present period is compared with the price of the same product produced in a prior period.  Obviously, this matched model methodology breaks down when what is being produced is constantly changing.

Two broad approaches to deal with this new goods problem have been suggested over the years:

•	The hedonic regression approach pioneered by Court (1939) and 
•	The reservation price approach pioneered by Hicks (1940; 114).

The reservation price technique has not caught on with statistical agencies but Hausman (1997a) (1997b) has implemented it for some forms of telecommunications services.  However, starting in the 1980’s, various statistical agencies have used hedonic regression techniques to quality adjust the prices of new products that have varying amounts of a given list of characteristics. 

There is little doubt that the use of the traditional statistical agency matched model pricing methodology leads to a substantial understatement of economic growth.  Our recommendation here is that the ABS have a systematic program in order to quality adjust the prices of commodities where there has been rapid technological change.  

8. Problems with How We Collect our Statistics

In this section, we discuss some of the difficulties in measuring productivity when information on outputs and inputs is collected in different surveys.

Eric Bartelsman (2004a) in his presentation noted that the best way to collect data for the purpose of measuring productivity is to collect data on output and input prices and quantities by firm or establishment in one big comprehensive survey.  Before the information technology revolution, this suggestion would have been impractical, due to respondent burden issues.  But increasingly, firms are collecting very detailed data on the prices and quantities of their outputs sold and their inputs used for their own internal management purposes.  This means that these firms could simply pass on their data files to the statistical agency with virtually no respondent burden.  It may be thought that this “one big survey” methodology is impractical but it is being adopted in Iceland on an experimental basis as they introduce a program for measuring producer prices.  However, it may be that the relatively small scale of the Icelandic economy makes such a program practical there but not in a larger economy.

The problem with the existing business survey methodology is this: labour input by industry is collected in two separate surveys, capital input by industry in another survey, and information on the prices and values of outputs and intermediate inputs is collected in two additional surveys.  This means that the estimated production statistics for any (small) firm and any industry are synthetic constructs which can contain a considerable amount of measurement error.  This also means that the statistics on productivity for the entire economy will be much more accurate than for any particular industry, since aggregate output, imports, labour and capital input are much more accurately estimated at the national level. 

As mentioned above, the most promising approach to improving industry productivity measurement will be to convince firms to share their internal data on prices and quantities with the national statistical agency.     

9. Problems with the Input Output Framework

Simon Zheng (2004) in his presentation at this conference raised the following issue: under what conditions will industry growth contributions add up to overall GDP growth?  This question was also raised by Moyer, Reinsdorf and Yuskavage (2004) in a recent contribution.  The answer to this question is complicated by the fact that overall GDP is measured at final demand prices whereas the productivity literature recommends that industry outputs be measured at prices that exclude indirect taxes that are paid for by final demanders and industry intermediate inputs should be measured at prices that include indirect taxes; see Jorgenson and Griliches (1972; 85).  However, recently Diewert (2004c) showed that industry growth contributions could be made to add up to overall GDP growth at final demand prices provided that a certain treatment of indirect taxes was followed and provided that either the Laspeyres, Paasche or Fisher index number formula is used in the aggregation.    

The analysis in Diewert (2004c) also has implications for constant dollar input output tables produced by statistical agencies.

10. Firm Dynamics

Bartelsman (2004b) in his second presentation at the conference reported on some of his research on how entering and exiting firms contribute to the overall productivity growth of a country.  This is an exciting new area of research in productivity analysis that is only a bit over 10 years old; see the pioneering contributions of Baldwin and Gorecki (1991) and Baily, Hulten and Campbell (1992).  Not only is this area of research of interest from a theoretical point of view, it appears to be extremely important empirically; see Haltiwanger (1997) (2000) and Bartelsman, Haltiwanger and Scarpetta (2004).

An open question in this area is the influence of the regulatory and institutional environment on firm dynamics.  No doubt, many interesting papers on this topic will be written in the future.

An unresolved issue in this literature on the contributions to productivity growth of entering and exiting firms is how exactly should we measure these contributions.  Various answers to this question have been proposed by Baldwin and Gorecki (1991), Baily, Hulten and Campbell (1992), Griliches and Regev (1995), Olley and Pakes (1996), Bartelsman and Doms (2000), Foster, Haltiwanger and Krizan (2001), Fox (2002), Balk (2003; 25-31) and Baldwin and Gu (2003).  No doubt future contributions on this topic will resolve this question.

The following section concludes with some suggestions for the ABS that might improve the measurement of productivity in Australia.  These suggestions follow from the discussion in the previous sections of this paper.  

11. Future Directions 

I have five suggestions for the ABS to improve its measurement of Australia’s Total Factor Productivity performance:

•	Institute a systematic program to measure the prices of service sector outputs.  This program will be required in order to provide measures of real output for the new service sector industries that will emerge from the new classification of industries for Australia and New Zealand.
•	Improve the measurement of labour input by dealing with the self employment problem and disaggregating labour input into reasonably homogeneous types of labour.
•	Put additional resources into the measurement of capital input.  For reproducible capital components, institute a capital retirements survey.  Improve the measurement of the contribution of inventories and land.  Implement several user cost concepts and make them available to users, with full documentation of methods used.  With respect to intangible assets, it might be wise to wait until some of the methodological problems mentioned in section 2 above have been solved before the ABS provides official estimates for stocks of intangible assets.
•	Experiment with computer intensive methods for collecting price and quantity data from firms in a cost effective manner.
•	Institute a systematic program for the quality adjustment of prices for goods and services that are subject to rapid technological progress.  Cooperate with other countries that have done hedonic regressions to profit from their experience.

The above suggestions for improving economic measurement apply to many countries and not just Australia!

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