Productivity Measurement: Alternative Approaches and Estimates

Mawson, Peter; Carlaw, Kenneth I; McLellan, Nathan Working Paper Productivity Measurement: Alternative Approaches and Estimates New Zealand Treasury Working Paper, No. 03/12 Provided in Cooperation with: The Treasury, New Zealand Government Suggested Citation: Mawson, Peter; Carlaw, Kenneth I; McLellan, Nathan (2003) : Productivity Measurement: Alternative Approaches and Estimates, New Zealand Treasury Working Paper, No. 03/12, New Zealand Government, The Treasury, Wellington This Version is available at: https://hdl.handle.net/10419/205517 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Productivity measurement: Alternative approaches and estimates Peter Mawson, Kenneth I Carlaw and Nathan McLellan N EW Z EALAND T REASURY W ORKING P APER 03/12 J UNE 2003 Treasury:494653v4 NZ TREASURY WORKING PAPER 03/12 Productivity measurement: Alternative approaches and estimates MONTH / YEAR June 2003 AUTHOR / S Peter Mawson The Treasury PO Box 3724 Wellington New Zealand Email Telephone Fax [email protected] 64-4-471-5288 64-4-499-0922 Kenneth I. Carlaw Department of Economics, University of Canterbury Private Bag 4800 Christchurch New Zealand Email Telephone Fax [email protected] 64-3-364-2846 64-3-364-2635 Nathan McLellan The Treasury PO Box 3724 Wellington New Zealand Email Telephone Fax [email protected] 64-4-471-5130 64-4-499-0992 ACKNOWLEDGEMENTS The authors would like to thank Bob Buckle, John Creedy, Kevin Fox, Katy Henderson and Grant Scobie for their helpful comments and suggestions on various drafts of this paper. NZ TREASURY New Zealand Treasury PO Box 3724 Wellington 6008 NEW ZEALAND Email Telephone Website [email protected] 64-4-472 2733 www.treasury.govt.nz DISCLAIMER The views expressed in this Working Paper are those of the author(s) and do not necessarily reflect the views of the New Zealand Treasury. The paper is presented not as policy, but with a view to inform and stimulate wider debate. WP 03/12 | Productivity measurement: Alternative approaches and estimates i Abstract This paper provides a review of conceptual and methodological issues in measuring productivity. Attention is given to the concept of productivity and the relationship between productivity and technological change. Different approaches to measuring productivity are surveyed and the results from a number of NZ productivity studies are summarised. The availability of appropriate input and output data is essential for the accurate measurement of productivity and therefore this paper also discusses some important data issues that influence productivity measurement. JEL CLASSIFICATION O30 – Technological change: General O47 – Measurement of economic growth; aggregate productivity KEYWORDS Productivity; measurement issues; New Zealand; technological change WP 03/12 | Productivity measurement: Alternative approaches and estimates ii Table of Contents Abstract...............................................................................................................................i Table of Contents ..............................................................................................................ii List of Tables......................................................................................................................ii List of Figures....................................................................................................................ii 1 Introduction ..............................................................................................................1 2 The concept of productivity ....................................................................................2 2.1 What is meant by “Productivity”?....................................................................................2 2.2 The relationship between TFP and technology..............................................................3 3 Approaches to measuring productivity..................................................................6 3.1 Growth accounting..........................................................................................................6 3.2 Index number approaches to measuring productivity.....................................................7 3.3 A distance function based approach ..............................................................................9 3.4 The econometric approach to productivity measurement ............................................15 4 New Zealand’s historical productivity record......................................................16 5 Data issues that influence productivity measurement and research................22 5.1 Capital .......................................................................................................................22 5.2 Labour .......................................................................................................................23 5.3 Output (GDP)................................................................................................................25 6 Conclusions............................................................................................................30 References .......................................................................................................................31 List of Tables Table 1: International comparisons of cumulated percentage growth, 1980-1996...........................29 List of Figures Figure 1: Production frontiers............................................................................................................11 Figure 2: A Malmquist productivity index ..........................................................................................12 Figure 3: Construction of a production frontier at time t....................................................................14 Figure 4: Trend aggregate TFP growth rates (percent per annum)..................................................18 Figure 5: (cont’d): Trend aggregate TFP growth rates (percent per annum)....................................19 Figure 6: Trend aggregate labour productivity growth rates (percent per annum)...........................20 WP 03/12 | Productivity measurement: Alternative approaches and estimates 1 Productivity measurement: Alternative approaches and estimates 1 Introduction This paper provides a review of conceptual and methodological issues in measuring productivity. Attention is given to the concept of productivity and the relationship between productivity and technological change. The paper also surveys four approaches to measuring productivity growth and reports productivity estimates for the New Zealand economy. The availability of appropriate input and output data is essential for the accurate measurement of productivity and therefore this paper also discusses some important data issues that influence productivity measurement. Economists and policy makers are interested in productivity measurement for several reasons. First, although TFP does not measure technological change, it is related to technological change to the extent that it measures free lunches associated with technological progress.1 Second, even though productivity measures may imperfectly measure the free lunches associated with technological change, they still exhibit persistent and systematic time series properties. These properties point to relationships that are not yet independently measured in the growth accounting methodology and therefore suggest that current understanding of what drives economic growth requires refinement. Third, productivity numbers provide information about how much measured output is being produced in an economy relative to measured inputs. This is an indication of how the economy is performing in terms of its productive efficiency with respect to available resources. Fourth, growth accounting, growth theory and productivity measures form an intellectual paradigm that has engaged a vast number of researchers who are trying understand the growth process (Hulten, 2000). Productivity analysis has been a core of this research agenda and discovering what it does not measure has been as important as determining what it does measure. Taken together with other indicators of economic activity (including independent measures on R&D and technological investment and diffusion), economists and policy makers can use productivity measures to develop an idea of how well or poorly an economy is doing in terms of the return it is obtaining on its investments. Uniform measures taken across 1 However, as a number of authors have argued, TFP appears to be an imperfect measure of these free lunches (see for example, Carlaw and Lipsey (2003) Lipsey and Carlaw (2002), Hulten (2000), Basu and Fernald (1997), Hall (1988), and Jorgenson, Gallop and Fraumeni (1987)). WP 03/12 | Productivity measurement: Alternative approaches and estimates 2 time, and to the extent possible across production units, can be used to examine whether productivity is rising or falling. These numbers can then be compared with other measures of economic performance, including per capita output growth, and direct measures of technological change to determine what are the correlations between measured productivity, output growth and technological change. What is probably of most importance in terms of the research agenda on productivity is an answer to Prescott’s (1998) call for a theory of productivity. Working out the causal linkages from fundamentals such as technological change through to measures such as GDP per capita growth and productivity change will provide economists and policy makers with a clearer picture of how productivity measures relate to underlying economic change and growth. To this end, research into productivity and its measurement are essential. The paper is organised as follows. Section 2 discusses the concept of productivity and its relationship to technological change. Section 3 surveys four different approaches to productivity measurement. Historical productivity estimates for the New Zealand economy are reported in Section 4. Given data issues that complicate the construction of accurate productivity series, Section 5 discusses data issues in productivity measurement and research. Section 6 concludes. 2 The concept of productivity This section discusses conceptual issues surrounding productivity. Subsection 2.1 outlines the concept of productivity, including the distinction between partial productivity measures, such as labour and capital productivity, and total factor productivity (TFP). Because TFP is often (erroneously) seen as a measure of technological change, Section 2.2 outlines several reasons why TFP cannot be equated with technological progress. 2.1 What is meant by “Productivity”? When economists refer to productivity, at the broadest level they are referring to an economy’s ability to convert inputs into outputs. Productivity is a relative concept with comparisons either being made across time or between different production units.2 For example, if it is possible to produce more output in period 2, when using the same amount of inputs that were used in period 1, then productivity is said to have improved. In other words, productivity is higher in the second period compared to the first. Different types of input measure give rise to different productivity measures. For example, labour productivity measures involve dividing total output by some measure that reflects the amount of labour used in production. The total number of worker hours is one such measure, although some studies have used total numbers employed.3 Capital productivity is measured by dividing total output by a measure reflecting the total amount of physical capital used in the production process. Productivity measures, such as labour productivity and capital productivity, that only relate to one class of inputs are known as partial productivity measures. Caution needs to be 2 For example, a comparison of productivity between two firms in an industry, between two industries within or between countries, or between countries. 3 Section 5.2 discusses issues associated with the measurement of the labour input. WP 03/12 | Productivity measurement: Alternative approaches and estimates 3 applied when using partial productivity measures as changes in input proportions can influence these measures. A simple substitution of capital for labour within the input mix of a firm or industry can also raise average labour productivity. This means that movements in the average labour productivity statistics do not always represent true changes in the underlying productivity of labour…. Dixon, 1990: 6 The level of TFP can be measured by dividing total output by total inputs. Total inputs are often an aggregation of only physical capital and labour, and may overlook inputs such as land.4 When all inputs in the production process are accounted for, TFP growth can be thought of as the amount of growth in real output that is not explained by the growth in inputs. This is why Abramovitz (1956) described the TFP residual as a ‘measure of our ignorance’. As TFP levels are sensitive to the units of measurement of inputs and outputs, they are rarely of primary interest. Rather, the measurement of TFP growth is of primary interest. Hence, it is common to use the notation “TFP” to refer to growth rather than levels, and this is the convention adopted in this paper. 2.2 The relationship between TFP and technology Lipsey and Carlaw (2002) stated that there are three main views as to what TFP measures in the economics literature. The first is that TFP measures the rate of technological change.5 The second is that TFP measures the “free lunches” associated with technological change, which it is argued are mainly associated with externalities and scale effects.6 The third view is that TFP does not really measure anything useful at all.7 Lipsey and Carlaw argue that TFP does not measure technological change.8 Rather, it is an imperfect measure of the “super-normal” gains that are associated with growth-creating technological change. These gains are similar, although not identical, to Jorgensen and Griliches’s (1967) concept of free lunches. They provide the following six reasons why TFP is an imperfect measure of these gains.9 The first is that different timings of the arrival of technological advances cause differences in measured TFP changes. Importantly these differences are more than just a different TFP time profile. When considering two different timings of a technological advance that both result in an identical final change in technology, costs and outputs, overall TFP growth may differ considerably between the two cases. 4 Consequently some authors prefer to define the resulting productivity measure as multifactor productivity (MFP) due to it including multiple inputs but not all possible (ie, total) inputs. 5 Lipsey and Carlaw (2002) argued that Krugman (1996), Young (1992), Law (2000) and Barro (1999) reflect the view that TFP measures the rate of technological change. 6 This view is reflected in Jorgenson and Griliches (1967) and Hulten (2000). 7 This view is reflected in Metcalf (1987) and Abramovitz (1956). 8 Solow (1957: 312) also noted that the term ‘technical change’ is a “shorthand expression for any kind of shift in the production function. Thus slowdowns, speedups, improvements in education of the labour force and all sorts of things will appear as ‘technical change’.” 9 For an overview of the issues raised by Lipsey and Carlaw see Carlaw and Lipsey (2003). WP 03/12 | Productivity measurement: Alternative approaches and estimates 4 The second reason why TFP is an imperfect measure of the supernormal profits associated with technological change is due to the treatment of research and development (R&D) investment in the national accounts of some countries. In some countries R&D is recorded on the input side of the accounts as a current cost with no direct increase being made to current output. Offsetting output only appears when R&D results in reduced costs or increased final output. Such treatment means that increased R&D activity may reduce measured TFP even though there is no technological regression and even when potential technological advancement may be occurring. Their essential point is that “[i]f the patents produced are sold abroad, the transactions are recorded as capital transfers and no income is ever recorded. Hence there is no TFP gain at any point in the process.” (Carlaw and Lipsey, 2003: 19-20) The third reason is that the omission of certain inputs, particularly natural resources, can bias measured TFP. When the quantity of the omitted variable used in the production process is growing slower than the measured inputs, TFP will be biased downwards. That is, the measured value of TFP growth will be lower than would result from a “true” measure that included accurate values for all inputs used in the production process. Conversely, if the quantity of omitted inputs is growing faster than the measured inputs, the bias will be upwards. The fourth reason is that the use of an aggregate production function to describe disaggregated activity causes TFP growth to under-measure the free lunches associated with technological change. The reason is that if the free lunch component of the productivity advance occurs at a lower level of disaggregation than is being employed in the measurement of productivity, the free lunch will be measured as increases in inputs rather than a free increase in output for a given level of inputs. The fifth reason is associated with the expenditure weights used to calculate the TFP index when markets are not in full equilibrium. If a technological change that confers a free lunch occurs in one sector of the economy but it takes several periods for the inputs in the economy to adjust, moving out of the relatively less productive sector into the more productive sector, then during this period of transition TFP calculated using an aggregating index such as the Divisia index will bias the measure of the free lunch depending on the returns to scale in the production function in each sector. The sixth reason is that TFP measures the difference between contemporary changes in costs and output and consequently misses spillovers that freely provide profitable opportunities that spread across the economy as well as over long periods of time. This is yet another reason why TFP growth and technological change are not the same thing. To illustrate the point that technological change does not necessarily show up as a change in TFP, Lipsey and Carlaw (2002) provided the following example where an upstream producer develops a piece of machinery that will allow a downstream producer to produce more output than did a previous machine. Assuming a development cost of w for the upstream firm, v representing the value of the marginal product for the downstream firm, and an initial TFP level of 1 (ie 0 00 Y TFP I = , where the output index, 0 Y, equals the input index , 0 I) , then TFP after the machine is developed is: 0 1 110 Yv Y TFP IIw + ==+ (1) WP 03/12 | Productivity measurement: Alternative approaches and estimates 11 Figure 1: Production frontiers A. Constant Returns to Scale Technology B. Diminishing Return to Scale Technology The term ),( ttt O Dyx in equation (13) is the output distance function based on the input and output vectors at time t. The subscript “O” signals that the distance function is an output distance function. The superscript ""t on the D is important as it signals which period’s reference technology (or production possibility frontier) the distance is being measured from. To calculate ),( ttt O Dyx , it is necessary to find the largest factor by which all the outputs in the output vector could be increased when making production as technically as efficient as possible, based on the input vector t x. ),( ttt O Dyx is then the reciprocal of this value. The closer the economy is to the production frontier the smaller the factor increase will be and consequently the larger the value of ),( ttt O Dyx . If the economy is operating on the frontier then ),( ttt O Dyx will take a value of 1. In contrast, when the economy is below the frontier ),( ttt O Dyx will be less than 1. In terms of Figure 1 (panel A), if the economy is operating at point (,) tt x y then it is producing output quantity ""a. In this case, (,) tt x y is technically inefficient. If production were on the frontier, then the output quantity *yb = could be produced. ab θ =, ie, b is θ times as large as a. Therefore /ba θ = and 1* (,) / / ttt t t O Dabyy θ − == =xy . Therefore the distance function is actual output divided by the frontier level of output. Caves, Christensen and Diewert (1982a and b) define a Malmquist productivity index as: ),( ),( 11 ttt O ttt O t D D Myx yx ++ = (14) ie, they define their productivity index as the ratio of two output distance functions which both utilise technology at time t as a reference technology. The numerator is the output distance function at time 1t+ based on period t technology. The denominator is the output distance function at time t based on period t technology. x y Production Frontier x y t =a y t* =b y (xt,yt) Production Frontier c xt WP 03/12 | Productivity measurement: Alternative approaches and estimates 12 Instead of using period 'ts technology as the reference technology it is possible to construct output distance functions based on period 1'ts + technology and consequently we may construct a Malmquist productivity index as: ),( ),( 1 111 1 ttt O ttt O t D D Myx yx + +++ += (15) Fare et al (1994) avoid choosing an arbitrary benchmark technology by specifying their Malmquist productivity change index as the geometric mean of the indexes shown in equations (14) and (15). That is: 2 1 1 11111 11 ),( ),( ),( ),( ),,,(                         =+ +++++ ++ ttt O ttt O ttt O ttt O tttt OD D D D Myx yx yx yx yxyx (16) Equation (16) can also be written as: 2 1 1111 1111 11 ),( ),( ),( ),( ),( ),( ),,,(                         ×= ++++ ++++ ++ ttt O ttt O ttt O ttt O ttt O ttt O tttt OD D D D D D Myx yx yx yx yx yx yxyx (17) Fare et al (1994) give the following interpretation to the two terms on the right hand side of equation (17): Efficiency change = ),( ),( 11 ttt O ttt O D D yx yx ++ Technical change = 2 1 1111 11 ),( ),( ),( ),(                         ++++ ++ ttt O ttt O ttt O ttt O D D D D yx yx yx yx Hence the Malmquist productivity index they derive is simply the product of the change in relative efficiency that occurred between periods t and 1t + , and the change in technology that occurred between periods t and 1t + . Figure 2: A Malmquist productivity index (xt,yt) y t =a b e, c f y t + 1 =d xt xt+ 1 y x (xt+1,yt+1) st st+1 WP 03/12 | Productivity measurement: Alternative approaches and estimates 13 Consider the following example based on Figure 2, which gives the necessary pieces of information to construct a Malmquist output based productivity index. Given two constant returns to scale production frontiers ( t s and 1t s + ) that describe the technology available in periods t and 1t+ and also information on the input/output combinations that were realised by the economy during periods t and 1t + . In period t, the economy used t x inputs to produce t ya= outputs. In period 1t + the economy used 1t x + inputs to produce 1t yd += outputs. To calculate the efficiency change component we need to construct two distance functions, ),( 111 +++ ttt O Dyx and ),( ttt O Dyx . These two functions tell us for each period, how close the level of output actually produced was to the frontier level of output for the same level of inputs based on the technology available in the period under consideration. These two measures describe the relative efficiency of production in each period and both will take values between 0 and 1. Based on Figure 2, b a Dttt O=),( yx as the level of output was t ya=, whereas had production be technically efficient, output would have been b. f d Dttt O= +++ ),( 111 yx and thus efficiency change equals a b f d b a f d =. To calculate the technical change component we need to use the two distance functions calculated above as well as ),( 11 ++ ttt O Dyx and ),( 1ttt O Dyx +. ),( 11 ++ ttt O Dyx measures how close the level of output actually produced in period 1t + is to the maximum level of output that could have been produced with 1t x + inputs had period 'ts technology been available. In Figure 2, e d Dttt O= ++ ),( 11 yx . Note that ),( 11 ++ ttt O Dyx can exceed 1 (and does in this case) if technological advancement has occurred. ),( 1ttt O Dyx + measures how close the level of output actually produced in period t is to the maximum level of output that could have been produced from period 'ts inputs, had period 1'ts + technology been available. c a Dttt O= +),( 1yx . Thus in this example technical change equals 2 1 2 1       =                               b c e f c ab a f de d To compute distance functions the researcher needs to know the production technology of or production frontier at all time periods under consideration. Fare et al (1994) who looked at productivity growth in 17 OECD countries, produced a world production frontier nonparametrically using an approach known as activity analysis or Data Envelopment Analysis (DEA). They then compared their 17 countries to the “world” production frontier calculated from data for the 17 countries. Fare, Grosskopf and Margaritis (1996) (hereafter, FGM) followed this approach but used sector level input and output data for New Zealand to produce an aggregate production frontier for the New Zealand market sector. Individual sectors are then compared to this frontier. The basic approach used in both these studies involved having data for 1,2,...,kK= countries (or sectors in the case of FGM). Each of these countries (or sectors) uses 1,2,...,nN=inputs tk n x, at each time period t, to produce 1,2,...,mM = outputs tk m y, (in WP 03/12 | Productivity measurement: Alternative approaches and estimates 14 FGM each sector produced one output so 1m = ). The production frontier or technology can be constructed under the assumption of constant returns to scale:      ===≥≤≥= ∑∑ == K k K k tkt n tk n tkt m tk m tkttt CRS KkMmNnzxxzyyz 11 ,,,,, ,..1,,...,1,,...,1,0,,,:),( yxS (18) where tk z, is an intensity variable. It is possible to allow for different returns to scale by adding restrictions involving the intensity variable. For example it is possible to relax the assumption of constant returns to scale by adding the restriction shown in equation (19) which allows for non-increasing returns to scale: 1 1 ,≤ ∑ = K k tk z (19) Figure 3 illustrates the construction of a production frontier, for a particular period, based on equation (18), in the simple case where we have one input and one output.14 Figure 3: Construction of a production frontier at time t In Figure 3 there are three different output-input combinations ( A, B and C), which could relate to three countries or three sectors depending on the level at which the analysis is being undertaken. If the restriction shown in equation (19) is imposed, that the sum of the intensity variables must be less than or equal to 1, then the production frontier is the line 0AB and the horizontal extension from B . If instead constant returns to scale is imposed (ie, the formulation given in equation (18)), the production frontier is given by the ray from the origin passing through A. In the variable returns to scale case, the production frontier will consist of the line A X AB and the horizontal extension from B . A number of economists have expressed scepticism about the practical merit of the DEA approach to identifying an economy-wide or world production frontier. For example, Diewert and Lawrence (1999) stated in relation to FGM’s study: 14 This discussion and figure 2.3 is based on Fare et al. (1994). B A Out p ut In p ut C 0 X A WP 03/12 | Productivity measurement: Alternative approaches and estimates 15 Evidently, they just used a variant of DEA analysis, assuming that the value added outputs of each industry can be produced by every other industry. This seems to be a rather untenable assumption to say the least and hence we suspect that their measures of efficiency change and technical progress are essentially worthless. Diewert and Lawrence, 1999: 98 Carlaw and Lipsey (2003) had similar concerns noting that the underlying assumption when using this technique to construct an economy’s production frontier from industry level data is that all the industries have the same aggregate production function.15 Given what we know about technological complementarities and the need to adapt technologies for specific uses, identical production functions across industries is not an acceptable assumption. For example, it is difficult to believe that the application of electricity to communications technologies can be considered to be the same production technology as the application of electricity to mining or machining? Carlaw and Lipsey, 2003: 10 3.4 The econometric approach to productivity measurement The econometric approach to productivity measurement involves estimating the parameters of a specified production function (or cost, revenue, or profit function, etc). Examples of the approach using New Zealand data include Grimes (1983), Szeto (2001) and Razzak (2002). Often the production function is expressed in growth rate form and then estimated to yield an estimate of the parameter that reflects the growth in technological progress, which is typically interpreted as a measure of productivity growth. One advantage of the econometric approach is the ability to gain information on the full representation of the specified production technology. In addition to estimates for productivity, information is also gained on other parameters of the production technology. It is not possible to generate this additional information using the growth accounting or index number approaches. Moreover, because the econometric approach is based on using information on outputs and inputs, there is greater flexibility in specifying the production technology. For example, it is possible to introduce other forms of factoraugmenting technological change other than the Hicks-neutral formulation implied by the growth accounting and index number approaches, and to make allowance for adjustment costs and variation in input utilisation. Within the econometric framework it is possible to test the validity of assumptions that underpin the growth accounting and index number approaches because of the sampling properties of the production technology. For example, it is possible to test the assumption of constant returns to scale that is often used in the growth accounting approach to productivity measurement. The increased flexibility and the ability to test the validity of different assumptions of the econometric approach do not come without cost. The use of the econometric approach 15 Likewise when constructing a world frontier the assumption is that all countries have the same underlying aggregate production function. WP 03/12 | Productivity measurement: Alternative approaches and estimates 16 raises estimation issues that may call in to question the robustness of parameter estimates. For example, the parameter estimates for a specified technology may appear implausible (such as negative factor income shares for a Cobb Douglas production function), causing researchers to impose a priori restrictions on parameter values. Furthermore, when data samples are small, restrictions such as constant returns to scale are often imposed to preserve degrees of freedom. The use of more flexible function forms for the production technology often means that non-linear estimation techniques are required, which bring their own complications. Szeto (2001) provides a good example of the non-linear estimation issues that are often faced by researchers when using the econometric approach to estimate productivity. A further drawback of the econometric approach is the greater difficulty of explaining the econometric methodology to a range of users, as well as the difficulty in replicating and producing productivity estimates on an ongoing basis. This is why measuring productivity using the econometric approach is best suited to single, one-off studies. Hulten (2000) has pointed out that the econometric approach to productivity measurement should be viewed as complimentary to the growth accounting and index number approaches for several key reasons. First, index number techniques are often used to construct the output and input series that are used as variables in estimating productivity using the econometric approach, thus “the question of whether or when to use econometrics to measure productivity change is really a question of which stage of the analysis index number procedures should be abandoned” (Hulten, 2000: 23). Second, the relative simplicity of the growth accounting and index number approaches can be used to help interpret the richer results of the econometric approach. Finally, by merging the different approaches, econometrics can be used to help explain TFP. In summary the “potential richness and testable set-up [of the econometric approach] make them a valuable complement to the non-parametric, index number methods that are the normal tool for productivity statistics” (Schreyer and Pilat, 2001: 133). 4 New Zealand’s historical productivity record This section briefly summarises the results obtained in a number of studies that have attempted to measure productivity growth rates for New Zealand. Figure 4 summarises the growth rates found in studies that included measures of TFP growth, while Figure 5 summarises labour productivity growth rates. This section does not attempt to discuss the robustness of results obtained in any of the studies, rather it illustrates that a number of studies have attempted to measure productivity growth in New Zealand, albeit over different timeframes and by using a number of different measurement techniques. Diewert and Lawrence (1999) chapter 6 reviews more comprehensively a number of the studies featuring in Figures 4 and 5. In Figures 4 and 5, the timeframe to which the average productivity growth relates is shown by the placement and length of the horizontal bars. The number in the centre of the bar is the average annual growth rate for that period. Razzak (2002) used an OLS method that allows for either a deterministic or stochastic trend to produce a number of TFP estimates. Razzak argued that TFP measurement in New Zealand may be affected by several factors. The first factor is whether or not there exists a structural break in the data used. Second, is the nature of the trend. Third is whether the production function exhibits constant or increasing returns to scale. WP 03/12 | Productivity measurement: Alternative approaches and estimates 17 McLellan (2001) used a growth accounting approach to measure TFP and labour productivity over the classical business cycle using a peak-to-peak approach.16 This approach attempts to measure trend output growth by removing the cyclical component of growth. TFP was calculated using a Cobb-Douglas production function with labour’s share set equal to 0.65. The data used were quarterly production GDP, Labour full time equivalents (FTEs) from the Household Labour Force Survey (HLFS), with a weighting of 0.5 on part-time employment, and a capital stock measure calculated using Statistics New Zealand’s productive capital stock data. The Diewert and Lawrence (1999) preferred TFP series (labelled DL Preferred Series in Figure 4) was constructed using data in the Diewert and Lawrence database. A total output index was formed by aggregating 49 output components and a total input index was formed by aggregating 13 input components, both using a chained Fisher index. All outputs and inputs are expressed in producers’ prices. Both indices relate to the market sector. Their database covered the period 1972 to 1998 (March years). Their database drew on labour times series presented in the OECD’s Economic Outlook and Census based hours worked per person by occupation data from Statistics New Zealand. Their (HLFS Hours) TFP series on the other hand used data derived from the HLFS rather than the Census. TFP numbers using the “Official” database were also constructed by Diewert and Lawrence. The database was based on Statistics New Zealand (SNZ) data and covered the period 1978 to 1998 (and consequently numbers were based on the System of National Accounts 1968 data). The official database included data on production GDP, labour and capital for 20 separate market sector industries. Chained Fisher TFP series were constructed using industry GDP data, industry hours worked data (drawn primarily from the HLFS, Quarterly Employment Survey (QES) and the Economic Survey of Manufacturing (ESM)), and industry net capital stocks for plant and equipment and building and construction, weighted by user costs with industry specific depreciation rates and asset lives based on Philpott (1992).17 16 The 1997 to 2001 period is not a full cycle but represented the most up-to-date period available at the time McLellan (2001) was written. McLellan (2001) also presented trough-to-trough measures. 17 See Diewert and Lawrence (1999), chapter 4 for more details. WP 03/12 | Productivity measurement: Alternative approaches and estimates 18 Figure 4: Trend aggregate TFP growth rates (percent per annum) 60 65 70 75 80 85 90 95 00 Author Methodology Estimates of TFP growth rates Razzak ( 2002 ) : OLS (Deterministic Trend) Econometric OLS (Stochastic Trend) Econometric Peak to Peak Growth Accounting McLellan ( 2001 ) : DL Preferred Series Index Number Diewert & Lawrence ( 1999 ) – Own Database Measures: DL (HLFS Hours) Series Index Number 3.1 1.79 0.89 0.97 0.82 -1.4 0.90 1.71 0.9 0.1 -0.35 1.26 1.80 0.07 1.47 -1.19 1.18 -0.15 1.17 0.95 0.36 0.81 0.76 0.12 1.19 1.09 1.46 1.56 2.38 1.35 1.12 1.32 0.33 -0.20 Diewert & Lawrence ( 1999 ) – “Official” Database Measures: Preferred Base Case Index Number HLFS Index Number A BS Equivalent for NZ Index Number Year WP 03/12 | Productivity measurement: Alternative approaches and estimates 19 Figure 5: (cont’d): Trend aggregate TFP growth rates (percent per annum) 60 65 70 75 80 85 90 95 00 Färe , Grossko p f , and Mar g aritis ( 1996 ) : Unweighted sectoral mean DEA Growth Accounting Hall ( 1996 ) : A ggregate TFP Growth Accounting Janssen ( 1996 ) : Phil p ott ( 1995 ) : Total Economy Growth Accounting 0.7 2.4 1.46 1.2 0.9 2.3 1.0 1.1 1956 1.25 0.88 2.5 0.8 0.1 1.5 1.0 AUSTRALIAN COMPARISONS: ABS MFP: 1.44 0.68 0.77 2.27 1.20 1.05 1.62 0.87 0.56 0.78 1.25 1.02 Diewert and Lawrence: Index Number Index Number Year Author Methodology Estimates of TFP growth rates WP 03/12 | Productivity measurement: Alternative approaches and estimates 20 Figure 6: Trend aggregate labour productivity growth rates (percent per annum) 60 65 70 75 80 85 90 95 00 Author Methodology Estimates of Labour Productivity growth rates Peak to Peak Growth Accounting McLellan ( 2001 ) : DL Preferred Series Index Number Diewert & Lawrence ( 1999 ) – Own Database Measures: DL “Official” data Series Index Number 6.2 -0.7 0.9 0.9 0.45 2.11 2.53 1.33 1.54 1.66 2.77 0.35 1.92 1.8 Hall ( 1996 ) : Growth Accounting 1.8 1.9 2.0 2.0 1.9 Year WP 03/12 | Productivity measurement: Alternative approaches and estimates 27 There is a direct relationship between the two MFP growth measures outlined in (23) and (25), with this relationship being shown below: GO VA VA MFP s MFP ∆=∆ % 1 % (26) where VA s is the nominal share of value-added in gross output. As 10 ≤ ≤ VA s, MFP growth measures based on value added will be greater than MFP growth measures based on gross output. How should these two different MFP measures be interpreted? When production technology is Hicks neutral the gross output based productivity measure is a valid representation of disembodied technical change, however this is not the case for the corresponding value added based measure. Technology change in the value-added based measure reflects the ability to translate technical change into income and into a contribution in final demand (OECD, 2001). This interpretation is dependent on equation (22) being a valid representation of the production process. If technological change only operates on primary inputs then this is no longer the case and the value-added based measure becomes the valid measure of technical change and the gross output measure loses its significance.23 When the unit of interest, such as a firm or industry, is subject to vertical integration and outsourcing, the gross output based TFP measure is usually considered superior as this measure gives a better indication of how much extra delivery to final demand per unit of primary inputs a firm or industry generates. Extrapolation In order for productivity measures to be valid it is important that price and quantity indices of output are constructed independently of price and quantity indices of inputs. An example of when this independence assumption is breached is when quantity indices of outputs are based on extrapolation of input series. From the perspective of productivity measurement, the independence of statistics on inputs and outputs is key. Input-based indicators that are used to deflate output series generate an obvious bias in productivity measures: (labour) productivity growth will either be zero by construction or will reflect any assumption about productivity growth made by statisticians. Occurrences of input-based extrapolation are concentrated in activities where market output prices are difficult to observe. This may create a case for excluding from productivity measurement those industries that are characterised by a large share of non-market producers and thereby avoiding potential biases in output measurement. OECD, 2001: 33 This paper does not go into detail on how New Zealand output measures are constructed but it should be noted that extrapolation based on input measures is important for 23 The hypothesis that technology affects only the primary inputs has not usually held up to empirical verification. The calls into question the validity of the value-added based productivity measure. On the other hand, the gross output formulation of technical change has also not always been supported by econometric studies (OECD, 2001). WP 03/12 | Productivity measurement: Alternative approaches and estimates 28 measuring output in some industries. For example, the contribution to gross domestic product made by the government services industry involves extrapolation by an employment volume indicator. Terms of Trade Recent work by Kohli (2002), which examined the impact of terms of trade change on real GDP and real value added, found that real GDP tends to underestimate the increase in real value added and welfare when the terms of trade improve. Kohli found that an improvement in the terms of trade can be viewed as similar to technological progress in that it means, for a given trade balance position, a country can either import more for what it exports, or export less for what it imports. Consequently, an improvement in the terms of trade increases real income, real value added, and welfare. However, the benefits of an improvement in the terms of trade do not show up in the real GDP figures, which focuses on production per se, whereas technological progress does. Kohli notes an improvement in the terms of trade, holding all other prices constant, actually leads to a fall in real GDP due to the GDP deflator increasing. For example, consider the case in which real GDP is constructed using a Laspeyres index and the price of imports falls (corresponding to a terms of trade increase).24 Given the lower price of imports, it may be expected that the use of imports as inputs in the production process will increase. However, a Laspeyres index approach uses the earlier period’s prices of imported inputs as weights meaning that the value of inputs will be higher than in some other index approaches and consequently value added will be measured as being lower. The problem with the Laspeyres index is that it is the change in prices that results in a substitution effect but that the price prior to the change is used to construct the index. Kohli (2002) argued that: … real GDP can be a very misleading indicator of a country’s welfare in the face of changing terms of trade. It is therefore important to distinguish between real GDP, on the one hand, and real domestic income or real value added, on the other. Real GDP focuses on production possibilities, whereas real income and real value added stress consumption (or more generally absorption) possibilities and, ultimately, welfare. We show that real GDP systematically underestimates growth in real value added when the terms of trade improve. The distinction between real GDP and real value added implies differences between the corresponding price indexes. The implicit GDP deflator, which is obtained by dividing nominal GDP by real GDP, will point at higher inflation than the value-added deflator when the terms of trade improve. In fact, it turns out that a drop in the price of imports, holding all other prices constant, leads to an increase in the GDP deflator. Kohli, 2002: 2 24 Statistics New Zealand uses a chain weighted Laspeyres index to measure real GDP. WP 03/12 | Productivity measurement: Alternative approaches and estimates 29 Table 1: International comparisons of cumulated percentage growth, 1980-1996 Laspeyres Real GDP Implicit Törnqvist Real GDP Implicit Törnqvist Real value added United States 60.1 59.4 61.5 Canada 45.4 45.0 46.0 Mexico 35.7 35.5 25.6 Japan 65.2 68.2 68.9 South Korea 265.5 272.2 277.8 Australia 61.0 61.1 62.0 New Zealand 40.6 41.5 49.4 Austria 40.8 40.9 39.8 Belgium 29.7 29.4 32.8 Denmark 38.4 39.0 38.1 Finland 36.6 37.0 42.4 France 32.5 32.0 36.2 Germany 39.8 40.5 43.9 Greece 30.2 27.5 36.8 Iceland 42.5 41.6 39.0 Ireland 106.1 111.1 105.0 Italy 32.8 31.9 37.9 Luxembourg 107.7 107.6 96.5 Netherlands 42.2 43.0 41.6 Norway 59.5 59.2 39.7 Portugal 47.3 48.7 60.0 Spain 46.5 45.7 50.8 Sweden 26.5 26.4 26.6 Switzerland 22.0 22.1 34.5 Turkey 108.3 117.4 111.3 United Kingdom 41.6 40.9 41.3 Source: Table 1 in Kohli (2002). As shown in Table 1 Kohli found that real GDP severely underestimated growth in real value added for New Zealand, Greece, Italy, Portugal and Switzerland. These countries all experienced significant improvements in their terms of trade over the past two decades. New Zealand’s cumulative growth rates in both the Laspeyres and implicit Törnqvist Real GDP figures were around 41% whereas the implicit Törnqvist Real value added growth was quite a bit higher at over 49%. Real GDP overestimated real value added growth for Mexico, Luxembourg and Norway, which experienced a deterioration in their terms of trade. In the case of New Zealand, it should be noted that most of this effect arose between 1986 and 1991. Since then there has been no discernible trend in the terms of trade. WP 03/12 | Productivity measurement: Alternative approaches and estimates 30 6 Conclusions This paper has provided a review of conceptual and methodological issues in measuring productivity. 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