August
, 2010Do alternative measures of capital services impact
productivity analysis?
By
Reitze Gouma
1Supervisor
Prof. Dr. Marcel P. Timmer
Abstract
This thesis is a contribution to the ongoing debate among statisticians and researchers on what method to use in order to estimate capital services for the benefit of productivity research. This paper focuses on two main approaches; the Ex Post method where the user cost of capital is derived employing an endogenous nominal rate of return, and the Ex Ante method, which applies an external rate of return to determine the user cost of capital. The central question addressed is: Does the choice for using an endogenous or exogenous approach affect the conclusions drawn from productivity analysis? It is shown that the alternative measures produce considerable differences in the estimates of capital services and multi factor productivity. Applying both methods in a specific comparative analysis between the EU and the USA shows that the conclusions do not radically differ. This is however, due to the comparative nature of the analysis, so the conclusion does not extend to other types of productivity analysis.
JEL codes: E01,O47
2 | P a g e
1 Introduction
The study of economic growth is an integral part of economics. Economists study the driving forces behind growth to answer a multitude of questions. Why do some countries experience high growth rates over prolonged periods of time, while other countries hardly grow at all? What is driving the high growth in countries like India and China in the last decades, and is it sustainable for an indefinite period of time? Understanding the factors that influence economic growth improves our ability to develop policies that stimulate economic growth. Economists define the growth of an economy as the growth in economic output (GDP) in a certain period of time. It can be separated into the growth of labour productivity and the growth in labour input.
Labour productivity determines how efficiently inputs can be transformed into outputs and is measured as output per unit of labour input, for example an hour worked. Productivity research studies the factors that contribute to this efficiency. Training and education is one of those factors. An employee who is new to the job will in general be less efficient than a worker with twenty years of experience. On the other hand, a worker’s productivity may decline due to old age. These are examples of the composition of the labour force which affects productivity. Another factor that contributes to efficiency of production is the input of capital. In a car factory, workers will be able to manufacture more cars in one day when a machine is installed which automatically welds parts of the chassis together requiring less labour input. Similarly an office clerk will become more efficient when a computer is installed which reduces the amount of paperwork the clerk has to process and eases communications via e-mail. These are examples of how investment in different types of capital assets can increase efficiency. However, simply adding capital units to the production process will not automatically lead to a higher labour productivity. Giving the office clerk two computers may make him somewhat more efficient than giving him one, but with each added computer the contributions to efficiency will be less. This suggests we cannot simply take the stock of capital to estimate the contribution of capital to efficiency since not every unit in the stock may be productive. In productivity research economists look at the developments of inputs and output over time. Labour productivity growth (LPG) can be decomposed into the growth contributions of three main components: The first is a measure for the composition of the labour force, which takes the above described heterogeneity of labour input into account. The second is the use of different types of capital assets. The third contributing factor to LPG is technological progress. Countries that have a higher level of technology are able to produce more efficiently than countries with lower levels of technology. This factor is important because it holds the key to sustainable growth since it does not depend on physical or depletable resources. The relative importance of technological growth to output growth or LPG is a matter of ongoing controversy (Hulten, 2000). This is mainly due to the way it is measured.
3 | P a g e from output growth. As such, the measurement of MFP is directly affected by changes in the measurement of the input contributions of capital and labour. This explains the controversy noted by Hulten concerning the relative importance of MFP in explaining output or labour productivity growth.
This study focuses on the way the contribution of capital assets to output growth is measured. Or more accurately, the contribution of capital services to output growth. As was noted, capital stocks do not provide an accurate measure of the productive capital input in the production process. Therefore it has been advocated by, amongst others, Jorgenson and Griliches (1967) to instead use the flow of capital services. Capital services are service flows that reflect the costs of, or returns to, employing a unit of capital in the production process in a given period. These services need to be measured indirectly. In order to do so rental prices of capital assets are needed. As Harper, Berndt and Wood (1989) have noted, these rental prices are usually not directly observable as a result of market transactions, therefore they have to be estimated. There are several methods to do this however, and economic theory does not provide a clear answer to what is the best approach. Capital input consists of many types of different assets and similar to the composition of labour, the capital services measure has to take this heterogeneity into account. As is shown in the literature section, measuring capital services is far from straightforward as there are many methods to choose from. The main problem in relating capital stocks to capital service flows lies in allocating the benefits of using a capital asset to a specific time period when the asset’s economic lifetime is more than one period (Diewert, 2001).
This paper explores the application of specific versions of two general methods of measuring capital services; the endogenous or Ex Post (XP) approach and the exogenous or Ex Ante (XA) approach. The first employs a realized nominal rate of return, which is based on realized revenues and expenditures, to estimate capital services. For the second method this paper uses an external constant real rate of return. This rate can be interpreted as the rate of return firms expect to receive prior to making an investment decision. Further details of these methods are laid out in the Literature and Models and Data section. The central question this thesis aims to answer is: Does the choice for an Ex-Post or an Ex-Ante method to measuring capital services affect the results from productivity analysis? In order to answer this question the following issues are explored:
Do we observe significant differences in the estimates of capital services between the Ex Post and Ex Ante approaches?
How do the alternative approaches affect the measured input contributions to labour productivity growth and MFP?
Do these changes affect the results from the productivity analysis done by Van Ark et al. (2008)?
Do we observe different effects between the countries included from changing the measurement of capital services?
4 | P a g e was stated, MFP contains technological growth, but it also contains measurement error since it is derived as a residual. The question is whether applying a different method to estimating capital services and doing growth accounting, still allows us to interpret MFP as technological change. It is important to know what it is we are measuring when MFP is considered as a contributing factor to output or labour productivity growth. Furthermore, the preferred approach may also depend on the type of analysis we wish to do with the resulting estimates. In order to establish the effects of the alternative measures on comparative productivity analysis, this study takes the Van Ark et al. analysis as an example of productivity analysis done within the growth accounting framework based on an Ex Post approach. It was published in 2008 in the Journal of Economic Perspectives and is widely cited. Its main conclusion is that the productivity slowdown in the second half of the 1990s and the first half of the 2000s in Europe compared to the United States was largely the result of slower multifactor productivity growth in market services. This paper will check whether this conclusion still holds when an Ex Ante method is applied. Finally, this thesis covers a set of 10 European countries and the United States. For the European area as a whole, estimates of capital services and input contributions to LPG are produced for the aggregate of the 10 EU countries included. These estimates for the aggregate are used to compare the effects of the alternative capital service measurements between the USA and the European region. Comparisons are also made at the level of individual countries.
This topic is also highly relevant in light of the discussion on the revision of the System of National Accounts (SNA). Recently SNA 2008 has been released. This updated version of the 1993 SNA now allows statistical agencies the possibility to include a breakdown of gross operating surplus (GOS) into the returns to specific asset types as supplementary accounts. However, measurement of capital services is still not an obligatory integral part of the official accounts. Hence, it is currently not possible to do this type of productivity analysis, taking into account the contribution of capital services, solely based national accounts data. The “Advisory Expert Group for the Update of the System of National Accounts, 1993” has advocated formal inclusion of capital services as an input in production. They recommend that countries may include a breakdown of gross operating surplus into the returns accruing to different assets. Schreyer et al. (2005) present a list of arguments in favour of this augmentation of the national accounts. However, the preferred method of measurement is not specified. At present some statistical agencies are already compiling KLEMS datasets for the purpose of productivity research2
This paper will proceed as follows; section 2 will cover the relevant literature regarding this topic and discusses the issues this paper will address. The third section will provide details on the models applied and the data used
.
3. In the fourth section results are presented and section five concludes.
2 For an example at Statistics Netherlands see De Haan et al. (2005).
5 | P a g e
2 Background and literature
2.1 The user cost of capitalWhen doing growth accounting, the need to use capital service flows instead of capital stocks arises from the fact that the analysis underlying MFP measurement is based on the economic theory of cost and production, relating flows of inputs to flows of outputs (Harper, Berndt and Wood, 1989). Diewert (2001) notes that the main problem in relating capital stocks to capital service flows lies in allocating the benefits of using a capital asset to a specific time period when the asset’s economic lifetime is more than one period. Capital compensation (CAP) is used as weights to aggregate the growth rates of each asset’s capital stock. This results in the growth of aggregate capital service flows. Capital compensation is calculated by multiplying the stock of an asset by a rental rate which covers all costs of using the unit of capital in a given time period. Therefore this rental rate is also called the user cost of capital. According to Balk (2008) these expenses include a nominal rate of return on the asset which can be viewed as the opportunity cost of buying the asset, depreciation costs, and capital gains or losses i.e. the revaluation of the asset over time. Ideally allowance must also be made for taxes since these can affect the costs to the producer of using the asset. In the absence of taxes it is derived as follows:
𝑝𝑘,𝑡𝐾 = 𝑝
𝑘,𝑡−1𝐼 𝑖𝑡− �𝑝𝑘,𝑡𝐼 − 𝑝𝑘,𝑡−1𝐼 � + 𝛿𝑘𝑝𝑘,𝑡𝐼
where 𝑖𝑡 denotes the nominal rate of return, 𝛿𝑘the depreciation rate of asset type 𝑘, and 𝑝𝑘,𝑡𝐼 the investment price of asset type 𝑘. The first two terms on the right-hand side correspond to the nominal rate of return or the opportunity costs and the capital gains mentioned by Balk. The last term in the equation denotes the costs due to asset depreciation. Harper, Berndt and Wood (1989) note that rental prices of capital assets are usually not directly observable as a result of market transactions, therefore they must be estimated. Had there been a market where firms could rent any type of capital assets for the duration of a production period, economists would be able to simply observe the market price. For some asset types these markets do exist; firms rent office space or lease cars, sometimes combined with service contracts. However for many other asset types such as machinery firms choose to purchase an asset and use it over multiple production periods. This raises the question how to measure the rental price for one period (Diewert, (2001).
In determining the appropriate rental rate, or user cost of capital, the nominal rate of return and the capital gains components can be calculated using various methods, depending on the assumptions that are made. Since economic theory does not provide a clear cut answer to what should be the preferred approach, there is a broad body of literature covering this topic. To date there are two main approaches that can be identified and these will be discussed next.
2.2 The Ex Ante and Ex Post approach
6 | P a g e only as an aggregate of capital compensation for all asset types, this procedure yields an industry specific internal rate of return that fully exhausts CAP, which is the same for all assets. This ensures that, for each industry, capital and labour compensation (LAB) add up to output measured as value added (VA), such that there are no residual profits. This is important because the compensation of capital and labour are used as the cost share weights of these respective inputs when doing growth accounting to determine the contributions of capital labour and MFP to output growth. Underlying the Ex Post approach are a number of neo-classical assumptions including: 1) Technology exhibits constant returns to scale (CRS), 2) input and output markets are fully competitive, 3) firms show optimizing behaviour, and 4) economic agents possess perfect foresight with respect to movements in asset prices (Balk, 2008). This last assumption is used in the calculation of the capital gains term, which is derived retrospectively from realized movements in asset prices. The main appeal of this approach is that it ensures complete consistency between income and production accounts and that it is rooted in neo-classical production theory.
The alternative is the Ex Ante or exogenous approach. This method takes the nominal rate of return from external sources instead of the endogenously derived internal rate of return in determining the user cost of capital. This affects the estimates of capital compensation by asset type which are used as weights to aggregate over the growth rates of the capital stock for each asset type to measure the growth of capital services. As Schreyer (2004) and Balk (2008) have shown, using an exogenous rate of return causes the calculated value of total capital compensation to be different from CAP from the national accounts. Therefore it allows the possibility of residual profits, that is, calculated capital compensation plus labour compensation may no longer add up to value added. These residual profits in part reflect the returns to unmeasured capital inputs, such as land, inventories or intangible assets. It also includes profits due to non-constant returns to scale and market power. The Ex Ante method comes at a cost however; the internal consistency between income and production accounts is lost. The possibility of residual profits also may change the cost share weights, measured as labour compensation plus the total of calculated capital compensation, when doing growth accounting; this will have a separate effect on the measured contributions of capital, labour and MFP to output growth, apart from the change in measured capital services. The Ex Ante approach can be combined with fully anticipated capital gains as in the Ex Post method, assuming economic agents have perfect foresight. However, Oulton (2007) argues that investment decisions have to be made in advance of knowing the asset inflation that will be realized, so an expected or required rate or return is more appropriate than a realized rate of return. Another possibility is to opt for a constant real rate of return which incorporates the nominal rate of return and the expected capital gains.
2.3 Pros and cons
Both methods have been criticized on both theoretical and empirical grounds. First the theoretical arguments, and second the empirical problems when applying either method are discussed.
Theoretical arguments
7 | P a g e endogenous method. However there is no theory underlying this approach. By measuring capital gains Ex Ante there is the question of how we should measure expectations. Berndt and Fuss (1986) argue that when doing growth accounting we are interested in what the contribution of capital actually was, not what it was expected to be. This suggests that for the purpose productivity analysis rental prices should be measured Ex Post.
Empirical arguments
Schreyer (2004) shows that, in the Ex Post approach, if the internal rate of return fully exhausts capital income from the national accounts no asset types contributing to production may be omitted. If there are unobserved asset types, such as land, inventories or intangible assets, the internal rate of return for each asset type used in the industry will be overstated. Since Ex Ante the nominal rate of return is set in line with financial market data, no such overstatement occurs, regardless of the number of assets included. Studies have shown that rental prices resulting from this endogenous method are often highly volatile over time and can even become negative which is inconsistent with economic theory (Harper et al., 1989; Diewert, 2001). Furthermore studies have shown that the real rental rates resulting from an Ex Post approach are much higher than can be expected based on financial market data, such as risk premiums (Inklaar, 2010). The Ex Ante method does not have this problem because it is based on financial market data.
2.4 Sensitivity studies
Many variations to the Ex Post and Ex Ante models described here are possible. There are multiple ways of constructing nominal rates of return from external data. How to measure expected asset price inflation is also subject to debate and there have been several studies that address these issues. Harper et al. (1989) examine the implementation of five alternative measures of asset rental prices, each with their own set of assumptions. The authors distinguish between forward looking models, which employ expected measures of capital gains and backward looking models which assume capital gains are perfectly anticipated. Furthermore they experiment with an external nominal rate of return derived from the Moody Baa bond rate. They also employ a model using a constant real rate of return. The authors focus on the volatility and plausibility of rental prices and show that models utilizing an endogenous rate of return show considerable variability in rental prices. The external rate of return and fixed real rate of return models produce rental rates that are much more stable. The authors conclude that measurement procedures have a significant impact on the resulting estimates of capital services.
Diewert (2001) follows and extends on this study and compares the Ex Ante and Ex Post approach, as well as the effects of various assumptions regarding capital gains expectations and depreciation rates. In total Diewert estimates 12 models and concludes that the assumptions made about the nominal interest rates and the treatment of anticipated price changes are the most important. Furthermore his findings corroborate the findings of Harper et al. that in general Ex Ante models produce more stable results with respect to rental rates. Diewert notes two advantages of using a constant real interest rate versus using an Ex Ante nominal rate combined with a moving average of the capital gains term; the resulting rental prices tend to be smooth and the estimates are easily reproducible by other statisticians.
8 | P a g e factor productivity growth (MFPG) between the models employing an Ex-Ante and Ex-Post approach are industry wise largest for the UK and the US. However at the aggregate the differences are small. Oulton (2007) proposes a hybrid solution that combines the Ex Ante approach to the measurement of capital services with using the Ex Post determined capital compensation as weights to estimate the contribution of capital services to GDP or value added growth. In order to estimate the nominal rate of return, use is made of an Ex-Ante required rate of return calculated as an average of Ex Post determined rates from previous periods. The assumption is that in the long run Ex Ante rates of return should be equal to Ex Post rates of return. Oulton and Rincon-Aznar (2009) show that the number of negative rental rates is greatly reduced when using the hybrid approach compared to a purely endogenous approach. Since the contribution of capital services to value added growth are weighted with Ex Post determined weights, there are no residual profits when this method is used. In a study done for the U.S. Inklaar (2010) explores the sensitivity of capital services and MFPG to alternative methods of measurement. He concludes that many theoretical refinements matter only little when applied empirically, such as adjustments to the capital gains term. It is important however to take account of the heterogeneity of assets and their prices. Inklaar notes that estimates of endogenously determined nominal rates of return are difficult to reconcile with economic fundamentals such as the relative risk of industries or the cost of capital in financial markets. Hence the internal rate of return will only be economically useful if capital is measured correctly and includes all relevant capital assets, which is unlikely in practice. Oulton’s Hybrid approach does not solve this problem according to Inklaar and he argues for an Ex-Ante approach.
2.5 Issues addressed in this paper
The studies discussed in this section provide valuable insights into the theoretical issues as well as empirical problems in the estimation of capital services and applying the growth accounting framework. The sensitivity studies have shown that there can be considerable differences in estimates of capital services, the input contributions to output growth and MFP depending on the method applied. Furthermore, these studies show that a choice in the nominal rate of return matters most for the empirical results, compared to other refinements of the models. The role of taxes and depreciation in determining the rental rate so far has not been discussed extensively. This study takes the geometric depreciation rates directly from EU KLEMS. Using geometric depreciation rates is relatively common practice and has been shown to be consistent with empirical studies on asset types (Diewert, 2001). While taxes can be of influence (Inklaar, 2010; Erumban, 2008) they are beyond the scope of this thesis.
9 | P a g e
3 Data and Models
This section starts off by briefly discussing the EU KLEMS database as the main source of data for this paper. It continues to outline the standard growth accounting framework and the alternative models to measure capital services. This section follows the notation and methodology outlined by Timmer et al. (2010, Chapter 3). This study employs the value added production function, which gives the quantity of value added as a function of only capital, labour and technology. Hence, in this study we ignore the role of intermediate inputs and focus instead on capital and labour. This approach is taken since the decomposition of intermediate inputs, while interesting, is not essential to the current analysis of capital services and MFP. Finally the alternative models to capital services measurement are presented and the research questions are discussed.
3.1 EU KLEMS database
This database4 was originally constructed to enable researchers to do empirical and theoretical
research in the area of economic growth, and more specifically to do growth accounting. It has already been used by many researchers in this field, as well as in the studies by Erumban, Inklaar, Oulton, and Van Ark et al. discussed in the previous section. This database includes measures of inputs and output at a detailed industry level. The input measures include various categories of capital (K), labour (L), energy (E), material (M) and service inputs (S). The measures are developed for 25 individual EU member states, the US, Japan, Korea, Canada and Australia and cover the period from 1970 to 2007. For a detailed description of the variables and methodology see O’Mahony and Timmer (2009). Currently efforts are being undertaken to also produce consistent KLEMS databases for countries such as Russia, China, Indonesia, Taiwan, and a number of countries in Latin America.5
3.2 Basic growth accounting methodology
This dataset provides a standardized set of data for a wide variety of countries specifically designed to do this type of research. All data used in this paper are taken from the November 2009 release and are publically available at http://www.euklems.net. Use is made of data from output and capital input files for industries at the most detailed level, presented in appendix table A2. Aggregations are done by this author, using Törnqvist aggregation for volume data and growth rates, as is used in the EU KLEMS database. Table A1 in the appendix presents a list of the available asset types in the database. Appendix table A3 shows the countries included in this thesis with their acronyms.
Growth accounting allows the researcher to decompose output growth into the growth of various inputs and the growth of productivity or MFP. As the point of departure we take the standard ex Post framework. The value added production function for industry 𝑗 is given by:
𝑍𝑗 = 𝑔𝑗(𝐾𝑗, 𝐿𝑗, 𝑇) (1)
Where 𝑍𝑗 denotes output in terms of value added (VA), 𝐾𝑡 is an index of capital service flows, 𝐿𝑗 an index of labour service flows, and 𝑇 is the level of technology. All variables are also indexed by time but the subscript 𝑡 is suppressed whenever possible to facilitate exposition.
4This research was supported by the European Commission, Research Directorate General as part of the 6th Framework Programme, Priority 8, ‘Policy Support and Anticipating Scientific and Technological Needs’ and is part of the ‘EU KLEMS project on Growth and Productivity in the European Union’. The project was carried out by a consortium of 24 research institutes and national statistical institutes.
10 | P a g e Under Ex Post assumptions of perfectly competitive markets, full input utilization and constant returns to scale (CRS), multifactor productivity (𝐴𝑍) can be defined as:
∆ 𝑙𝑛 𝐴𝑗𝑍 ≡ ∆𝑙𝑛 𝑍𝑗− 𝑣̅𝐾,𝑗𝑍 ∆𝑙𝑛 𝐾𝑗−𝑣̅𝐿,𝑗𝑍 ∆𝑙𝑛 𝐿𝑗 (2)
where ∆𝑙𝑛 𝑥 = 𝑙𝑛 𝑥𝑡− 𝑙𝑛 𝑥𝑡−1 denotes the logarithmic growth rate from period t-1 to t. 𝑣̅ is the period average share of the input’s compensation in the total value of nominal output where the shares are derived as follows:
𝑣𝐿,𝑗𝑍 = 𝑝𝑗𝐿𝐿𝑗 𝑝𝑗𝑍𝑍 𝑗 and 𝑣𝐾,𝑗 𝑍 =𝑝𝑗𝐾𝐾𝑗 𝑝𝑗𝑍𝑍 𝑗 (3)
The period average shares are derived as:
𝑣̅𝐿,𝑗𝑍 = 0.5 ∗ (𝑣𝐿,𝑗,𝑡𝑍 + 𝑣𝑙,𝑗,𝑡−1𝑍 ) and 𝑣̅𝐾,𝑗𝑍 = 0.5 ∗ (𝑣𝐾,𝑗,𝑡𝑍 + 𝑣𝐾,𝑗,𝑡−1𝑍 ) (4)
Throughout this paper the weight of a subcomponent (subscript) in its relevant aggregate (superscript) is referred to by using subscripts and superscripts on weights 𝑣. A bar on a variable always indicates period averages. Since Ex Post returns to scale are assumed to be constant, the input cost shares add up to unity (𝑣𝐿,𝑗𝑍 + 𝑣𝐾,𝑗𝑍 = 1). Rearranging equation (2) yields the standard growth accounting decomposition of output growth as the cost share weighted growth of inputs and multifactor productivity growth:
∆𝑙𝑛 𝑍𝑗= 𝑣̅𝐾,𝑗𝑍 ∆𝑙𝑛 𝐾𝑗+𝑣̅𝐿,𝑗𝑍 ∆𝑙𝑛 𝐿𝑗+ ∆ 𝑙𝑛 𝐴𝑗𝑍 (5)
The right-hand side elements reflect the growth in value added accounted for by the growth in labour, capital and MFP which represents technical change and is measured as a residual.
Aggregate labour input 𝐿𝑗 is defined as a Törnqvist volume index of hours worked by individual labour types as follows:
∆𝑙𝑛 𝐿𝑗 = � 𝑣̅𝑙,𝑗𝐿 𝑙
∆𝑙𝑛𝐻𝑙,𝑗 where weights are
given by: 𝑣𝑙,𝑗𝐿 =𝑝𝑙,𝑗 𝐿 𝐻
𝑙,𝑗 𝑝𝑗𝐿𝐿
𝑗 (6)
where ∆𝑙𝑛𝐻𝑙,𝑗 indicates the growth in hours worked for labour type 𝑙 and weights are given by the period average shares of each type in the value of total labour compensation, such that the shares of all labour types sum to unity. The resulting labour input index (LAB_QI) is directly taken from the EU KLEMS output files. The EU KLEMS database covers 18 labour type categories, consisting of three age groups, three classes of educational attainment and two gender types, thus this index takes into account the heterogeneity of labour inputs.
Analogously the aggregate capital service input 𝐾𝑗 is defined as a Törnqvist volume index of individual capital assets:
∆𝑙𝑛 𝐾𝑗= � 𝑣̅𝑘,𝑗𝐾 𝑘
∆𝑙𝑛𝐾𝑘,𝑗 where weights are
given by: 𝑣𝑘,𝑗𝐾 =𝑝𝑘,𝑗 𝐾 𝐾
𝑘,𝑗 𝑝𝑗𝐾𝐾
11 | P a g e Where ∆𝑙𝑛𝐾𝑘,𝑗 indicates the volume growth of capital asset 𝑘 and weights are given by the period average shares of each type in the value of total capital compensation, such that the sum of shares over all capital types sum to unity.
To analyze the impact of ICT and non-ICT capital, a breakdown of the contribution of capital to output growth is also provided. Capital assets are divided into two groups of assets; ICT assets (indicated by ICT), which covers asset types that are classified to the ‘information and communications technology’ category, and non-ICT assets (indicated by N) which includes all other asset types, such that:
∆𝑙𝑛 𝐾𝑗 = 𝑣̅𝐼𝐶𝑇,𝑗𝐾 ∆𝑙𝑛𝐾𝑗𝐼𝐶𝑇+ 𝑣̅𝑁,𝑗𝐾 ∆𝑙𝑛𝐾𝑗𝑁 (8)
with 𝑣̅𝐼𝐶𝑇,𝑗𝐾 the period-average share of ICT capital compensation in total capital compensation in industry 𝑗 at time t, and similarly for non-ICT assets. The volume growth of ICT and non-ICT capital is defined as: ∆𝑙𝑛𝐾𝑗𝐼𝐶𝑇 = � 𝑣̅ 𝑘,𝑗𝐼𝐶𝑇 𝑘𝜖𝐼𝐶𝑇 ∆𝑙𝑛𝐾𝑘,𝑗 and ∆𝑙𝑛𝐾𝑗𝑁 = � 𝑣̅𝑘,𝑗𝑁 𝑘𝜖𝑁 ∆𝑙𝑛𝐾𝑘,𝑗 (9)
where 𝑣̅𝑘,𝑗𝐼𝐶𝑇 denotes the period average share of the asset 𝑘’s capital compensation in total ICT capital compensation for industry 𝑗, and analogously for the non-ICT shares. Each set of weights will sum to unity. Substituting the decomposed input growth measures into equation (5) yields:
∆𝑙𝑛 𝑍𝑗= 𝑣̅𝐼𝐶𝑇,𝑗𝑍 ∆𝑙𝑛 𝐾𝑗𝐼𝐶𝑇+𝑣̅𝑁,𝑗𝑍 ∆𝑙𝑛 𝐾𝑗𝑁+ 𝑣̅𝐿,𝑗𝑍 ∆𝑙𝑛 𝐿𝐶𝑗+ 𝑣̅𝐿,𝑗𝑍 ∆𝑙𝑛 𝐻𝑗+ ∆ 𝑙𝑛 𝐴𝑗𝑍 (10)
which shows that value added growth can be decomposed into the contribution of ICT capital, non-ICT capital, labour composition, labour input in hours worked, and technical change in the use of labour and capital. From equation (10), equation (11) can be derived for the decomposition of labour productivity (value added per hour worked) by subtracting ∆𝑙𝑛 𝐻𝑗 from both sides of the equation. Let 𝑧 be labour productivity such that 𝑧 = 𝑍/𝐻, and 𝑘 the ratio of capital services to hours worked , 𝑘 = 𝐾/𝐻, then;
∆𝑙𝑛 𝑧𝑗= 𝑣̅𝐼𝐶𝑇,𝑗𝑍 ∆𝑙𝑛 𝑘𝑗𝐼𝐶𝑇+𝑣̅𝑁,𝑗𝑍 ∆𝑙𝑛 𝑘𝑗𝑁+ 𝑣̅𝐿,𝑗𝑍 ∆𝑙𝑛 𝐿𝐶𝑗+ ∆ 𝑙𝑛 𝐴𝑗𝑍 (11)
This expression shows four different sources of industry labour productivity growth; changes in labour composition, ICT capital deepening, non-ICT capital deepening and MFP growth. When employing the Ex Post method, the input shares in (10) and (11) are derived as the compensation of the input divided by total value added. Since full competition and constant returns to scale are assumed capital and labour compensation exhaust value added, and the shares will sum to unity. Alternatively, cost shares can be used to weight the input contributions to output or labour productivity growth. This method is relevant as an alternative when Ex Ante capital compensation is considered as weights. Defining 𝐶 as total input compensation, calculated as Ex Ante measured capital compensation plus the compensation of labour, equation (11) becomes:
12 | P a g e This is the approach taken by Schreyer (2004). It uses cost shares in total observable inputs i.e. the share of the input’s compensation in total measured input compensation. If residual profits are present, this will also change the weight given to the input of labour since the total of input compensation changes.
3.3 Measuring capital services
As has been explained in the literature section, in order to create a measure of capital services, we need capital compensation by asset type to use as weights to aggregate the growth rate of capital stocks by asset type, calculated by (8) and (9). Capital compensation by asset type is derived by multiplying a rental rate which covers the cost of employing the unit of capital with the asset’s capital stock. This rental price reflects the price at which the investor is indifferent between buying the asset and selling it at the end of the period or renting the capital good for a one-year lease in the rental market. The cost-of-capital equation shows this relationship in the absence of taxes:
𝑝𝑘,𝑡𝐾 = 𝑝𝑘,𝑡−1𝐼 𝑖𝑡+ 𝛿𝑘𝑝𝑘,𝑡𝐼 − �𝑝𝑘,𝑡𝐼 − 𝑝𝑘,𝑡−1𝐼 � (13)
where 𝑖𝑡 denotes the nominal rate of return, 𝛿𝑘the depreciation rate of asset type 𝑘, and 𝑝𝑘,𝑡𝐼 the investment price of asset type 𝑘. Ideally taxes should also be included. However, tax rates are not included in the EU KLEMS database; therefore the inclusion of taxes is beyond the scope of this paper. This expression shows that the rental rate is determined by a nominal rate of return, asset specific capital gains and the rate of economic depreciation. The rental price can also be redefined to express it as a function of depreciation and the real rate of return which includes the capital gains and the nominal rate of return, given by:
𝑝𝑘,𝑡𝐾 = 𝑟
𝑘,𝑡𝑝𝑘,𝑡−1𝐼 + 𝛿𝑘𝑝𝑘,𝑡𝐼 (14)
where 𝑟𝑘,𝑡 is the real rate of return.6
𝑖𝑗,𝑡=𝑝𝑗,𝑡 𝐾𝐾
𝑗,𝑡+ ∑ �𝑝𝑘 𝑘,𝑗,𝑡𝐼 − 𝑝𝑘,𝑗,𝑡−1𝐼 �𝑆𝑘,𝑗,𝑡− ∑ 𝑝𝑘 𝑘,𝑗,𝑡𝐼 𝛿𝑘𝑆𝑘,𝑗,𝑡 ∑ 𝑝𝑘 𝑘,𝑗,𝑡−1𝐼 𝑆𝑘,𝑗,𝑡
In the EU KLEMS database the Ex Post nominal rate of return is calculated for each industry as an internal rate of return using the following formula:
(15)
where 𝑆𝑘,𝑗,𝑡 is the capital stock of asset type 𝑘 in industry 𝑗 at time t and 𝑝𝑗,𝑡𝐾𝐾𝑗,𝑡 is the capital compensation in industry 𝑗, which can be derived under constant returns to scale as value added minus labour compensation. This nominal rate of return is the same for all assets, but it is industry specific. These rates are taken from the EU KLEMS capital input files. Geometric asset depreciation rates are also given in the capital input files; these are assumed to be the same for all countries. As has been noted in the literature section, several empirical as well as theoretical problems are associated with this approach.
Alternatively an exogenous or Ex Ante nominal rate of return can be used, based on financial market data. The option applied in this paper is to set the real rate of return from equation (14) equal to a constant rate. Following Diewert (2001) and Erumban (2008), in this thesis a constant real rate of
13 | P a g e return of 4% is used, which suits OECD long term empirical evidence. This yields the following Ex Post and Ex Ante rental price formulations:
Ex Post 𝑝𝑘,𝑡𝐾 = 𝑝
𝑘,𝑡−1𝐼 𝑖𝑡− �𝑝𝑘,𝑡𝐼 − 𝑝𝑘,𝑡−1𝐼 � + 𝛿𝑘𝑝𝑘,𝑡𝐼 (16)
Ex Ante 𝑝𝑘,𝑡𝐾 = 𝑝
𝑘,𝑡−1𝐼 ∗ 4% + 𝛿𝑘𝑝𝑘,𝑡𝐼 (17)
3.4 Research questions
In the introduction the main research question was stated as: Does the choice for an Ex-Post or an Ex-Ante method to measuring capital services affect the results from productivity analysis? In order to answer this question, four sub questions were formulated. This section will detail the answers to these questions that may be expected based on the models described in this section.
The first question is concerned with the alternative estimates of capital services derived by equation (7). Studies have shown exogenous real rates of return to be more stable and generally lower than endogenously determined rates of return. This will also lead to lower estimates of capital compensation. However, since this is the case for all asset types, this need not affect the estimates of capital services. If asset capital compensation is proportionately lower for all asset types, this does not affect the weights in equation (7); hence the capital services index will be the same. Only if the asset’s shares in total capital compensation change will we see an effect in the capital services index. The second question regards effects of the alternative methods on the results from growth accounting. This will be dependent on two factors; firstly it will depend on whether the estimates of capital services have changed as was also discussed in the first question; secondly it depends on whether the cost-share weights have altered which are used for weighting the input growth contribution. In the case of ICT capital services shares in equations (11) and (12) that is whether 𝑣̅𝐼𝐶𝑇,𝑗𝐶 is different from 𝑣̅𝐼𝐶𝑇,𝑗𝑍 . If considerable residual profits exists this will certainly be the case. Positive residual profits deduct from capital compensation (CAP) as measured from the national accounts resulting in a lower measured CAP. This means that the share of CAP in total input compensation will also decline as labour compensation remains unaffected. This will have a depressing effect on the contributions of capital services to output or labour productivity growth, raising MFP. If residual profits are negative, the converse is true.
The third sub-question is concerned with the application of the alternative methods to comparative productivity analysis. The main conclusion drawn by Van Ark et al. (2008) is that the productivity slowdown in the second half of the 1990s and the first half of the 2000s in Europe compared to the United States was largely the result of slower multifactor productivity growth in market services. The effects of the different methods applied to measuring capital services and growth accounting on the results of this analysis is explored. A change in this result can be expected if the impact from applying either the Ex Post or Ex Ante method is different in each region. From a theoretical viewpoint it is not clear that this should be the case. Lastly the differences between the individual European countries are explored.
3.5 Other data issues
14 | P a g e files, use is made of 1997 purchasing power parities (PPP) which are also available on the website of EU KLEMS. Volume data and growth rates are first Törnqvist aggregated over countries at the highest level of industry detail, and then Törnqvist aggregated over industries to create sectoral sums. The EU KLEMS database provides no capital input file for Belgium. Therefore only Ex Post capital services are available. Since Belgium is relatively small compared to the total of the ten European countries (approximately 2.5% of gross output), this is not likely to greatly affect the results. For Germany only data from 1991 onwards is available. Therefore the data is linked to West Germany to produce full period estimates and to create the aggregation of EU15ex. The asset type Residential Structures (RStruc) in the EU KLEMS database is not considered in the analysis. As Van Ark et al. (2008) noted, residential capital does not contribute in any direct way to productivity gains. The same approach was taken in the sensitivity studies discussed in the literature section.
In the System of National Accounts (SNA), Value Added (VA) is the aggregate of the compensation of employees (COMP), gross operating surplus (GOS) and taxes less subsidies on production (TXSP). In order to have a proper measure of the compensation of labour, the compensation of the self-employed needs to be added to the compensation of employees. In the EU KLEMS database this is done by dividing the compensation of employees by the hours worked by employees, and multiplying it by the hours worked by the self-employed. The resulting variable is called labour compensation (LAB) and capital compensation (CAP) is derived as VA-LAB, which now incorporates GOS adjusted for labour compensation of the self-employed and taxes less subsidies. Thus it is implicitly assumed that the self-employed have the same hourly compensation as employees. For some industries such as the agricultural industry (AtB) this assumption in many cases leads to an overestimation of LAB and therefore it understates CAP. This has an effect on the endogenously derived nominal rate of return, calculated by (15). The effects of this will be discussed in the results section.
15 | P a g e
4 Empirical results
This section presents the results from applying the Ex Post and Ex Ante methods detailed in the previous section. It follows the order of the four research sub-questions stated in the introduction. Section 4.5 will present a brief overview of the main results.
4.1 Capital Services
The first research question is concerned with the effects of the alternative measurement methods on the resulting estimates of capital services. To provide an overview of the resulting difference between the Ex Post and Ex Ante methods to measuring capital services, table 1 shows the difference in the average annual growth rates. Three periods are distinguished and a split between capital services from ICT and Non-ICT assets is shown. The difference for total (TOT) capital services are presented as well.
Table 1
From table 1 it can be observed that the growth in ICT capital services is much higher than Non-ICT capital services growth. Also, it is higher in the USA than in the EU. This confirms the results of, amongst others, Van Ark et al. (2008) who also found higher growth rates in ICT capital services for the USA compared to the EU. Comparing the Ex Ante and Ex Post results reveals that the Ex Ante method produces capital services that grow slower than the Ex Post procedure does. Recall that the capital services index is measured as an aggregate of capital stock growth rates weighted by the period average shares in asset capital compensation (equations (7)). Since the same stocks are used in both methods, the difference in the aggregate index arises from the difference in the capital compensation weights. Capital compensation is measured by multiplying the Ex Ante or Ex Post derived rental rate by the capital stock. From table 1 it can be concluded that the Ex Ante capital compensation weights are lower for asset types with higher growth rates in stocks, resulting in a lower aggregate index.
This is confirmed in table 2 which shows the percentage change in the average shares of the asset’s capital compensation in the total of capital compensation over all assets, between Ex Post (X) and Ex Ante (XA) approach. Furthermore the growth of the capital stock is presented, which is the same for both methods used. The percentage change in the average share shows to what extent the growth
Period average growth rates of capital services in the Market Economy
XP XA difference XP XA difference 1980-1995 TOT 3.9% 3.2% 0.7% 3.9% 3.2% 0.7% ICT 12.5% 11.6% 0.9% 16.8% 14.7% 2.1% Non-ICT 2.8% 2.3% 0.5% 2.4% 1.8% 0.6% 1995-2007 TOT 3.8% 3.2% 0.6% 4.6% 4.5% 0.1% ICT 11.3% 10.2% 1.1% 13.7% 12.7% 1.0% Non-ICT 2.3% 2.1% 0.3% 2.0% 2.1% -0.1% 1980-2007 TOT 3.9% 3.2% 0.7% 4.6% 4.1% 0.5% ICT 12.0% 11.0% 1.0% 15.4% 13.8% 1.6% Non-ICT 2.6% 2.2% 0.4% 2.3% 2.0% 0.3%
Annual average logarithmic growth rates.
16 | P a g e rates’s weight has increased or decreased. Table 2 shows that indeed asset types with higher growth rates decline the most in terms of shares in capital compensation, when using an Ex Ante instead of an Ex Post approach.
Table 2
Interestingly, this finding is at odds with the results of Schreyer (2004) and Inklaar (2010), who find that moving from an endogenous to an exogenous rate of return leads to a rise in the observed measure of capital input, calculated by equation (7). This difference is explained by the fact that in the calculation of the Ex Ante rental rate (equation (16)), these studies employ a constant nominal rate of return and use a dynamic capital gains component based the movement in asset prices, instead of a constant real rate of return as is done in this study (equation (17)). Fixing the capital gains component lowers the rental rate for asset types which have high inflation rates, such as the ICT assets. Therefore, the weights of these asset types are lower than in the studies done by Inklaar and Schreyer. Since these asset types generally have higher growth rates in capital stocks, this will lead to a lower capital services index.
4.2 Rates of return
As the previous section has shown there are clear and observable differences between the endogenous and exogenous capital services estimates at the market economy level. These differences arise from the estimates of capital compensation by asset type, which are being used as weights. These in turn are based on the alternative measures of the rental rates. In the literature section a number of empirical issues have been raised when using Ex Post estimates of capital services. Empirically the main concern is the volatility and level of the rental prices. Oulton and Rincon-Aznar (2009) show the number of negative rental prices by country and asset type. Negative rental prices are put to zero when calculating capital compensation, which means they lower the estimates of capital services. Table A4 in the appendix provides these statistics on an asset as well as an industry basis. The table covers the period 1980-2007 for 26 industries, so in total there are 728
Average annual (logarithmic) growth rates of capital stock at market economy level (1980-2007)
AUT DNK ESP FIN FRA GER* ITA NLD UK USA
K_IT 23% 22% 17% 19% 13% 17% 21% 22% 24% 24% K_Soft 14% 14% 12% 7% 8% 7% 11% 13% 7% 13% K_CT 5% 9% 7% 14% 5% 4% 5% 4% 13% 7% K_Other 2% 0% 3% 1% 2% 4% 3% 3% 3% 5% K_TraEq 3% 2% 5% 0% 4% 4% 3% 3% 1% 2% K_Omach 1% 2% 3% 1% 2% 2% 3% 2% 2% 2% K_Ocon 1% 2% 4% 2% 1% 1% 2% 1% 3% 2%
Difference in asset share Ex Ante vs EX Post at the market economy level (1980-2007)
AUT DNK ESP FIN FRA GER* ITA NLD UK USA
CAP_IT -38% -37% -4% -42% -13% -33% -47% -18% -18% -23% CAP_Soft -3% -5% 15% -3% 13% 9% 4% 15% 27% 11% CAP_CT -4% -4% 8% -31% -9% -27% 0% 14% -6% 11% CAP_Other 61% -9% 6% 55% 90% 23% 12% -14% 22% 3% CAP_TraEq 14% 49% 26% 28% 2% -15% 6% 29% 39% 19% CAP_OMach 5% 3% 9% -8% 5% 9% -6% -4% 5% 3% CAP_OCon -5% -7% -16% 6% -8% 4% 10% -3% -19% -11%
* Germany for the period 1991-2007
No capital stock s data is available for Belgium
17 | P a g e observations for each country, except for Germany which only has data for 1991-2007. The Ex Ante method applied in this thesis did not produce any negative rental rates.
As was noted in the models and data section, the table confirms that negative rental rates are most frequently observed for the asset type Other Construction, which corresponds to non-residential buildings, for both the EU and the USA. Furthermore in the agricultural sector (AtB), where the labour compensation adjustment for self-employed people tends to be overstated, a great number of negative rental rates are Ex Post measured in the EU countries. Overstatement of labour compensation leads to understatement of capital compensation by industry, diminishing the internal rate of return and rental prices, calculated by equation (15). Since for the EU the agricultural sector has so many instances of negative rental rates, Ex Ante values of calculated capital compensation (CAP_GFCF) can be expected to be higher than Ex Post values in this industry.
Table A5 in the appendix shows the industry ranking of the differences in CAP_GFCF for the EU and the USA. As expected most of these differences are negative, indicating that the Ex Ante method produces lower estimates CAP_GFCF than the Ex Post method does, due to its use of a constant real rate of return. However for industries and assets that have negative Ex Post rental rates, capital compensation is zero. In these cases the Ex Ante approach produces higher capital services at the aggregate. For the EU this is clearly the case in the agricultural sector. The USA does not show many negative rental prices and it has a positive difference between the Ex Ante and Ex Post CAP_GFCF for only two industries, Mining (C) and Transport and Storage (60t63). The latter also ranks high for the EU. This industry does not have many negative rental rates (zero for the USA). However the fact that Ex Ante CAP_GFCF is higher than Ex Post indicates that the Ex Post real rate of return for this industry is below 4 percent. Verifying this reveals that this industry has an Ex Post average real rate of return of 1.1% for the EU and 2.1% for the USA over the 1980-2007 period.
These results of negative Ex Post rental rates and the discrepancies in the CAP_GFCF values between the Ex Ante and Ex Post method show that the Ex Post method is sensitive to negatives in the rental rates. This can be considered an argument to use an Ex Ante approach to measuring capital services, since this method does not produce negative rental rates and therefore will produce positive capital compensation weights where the Ex Post produces zeros.
18 | P a g e
Figure 1
This data is implicitly derived at the market economy level.
This variability in the real rate of return also affects the volatility of the rental price. This means that capital compensation that is used as weights to calculate capital services with equation (7) will also be more volatile, and therefore capital services will be affected. As Schreyer (2004) has noted, when not all asset types are taken into account, an internally derived nominal rate of return will be overstated. Considering the level of these real rates of return this is an indication that indeed the Ex Post measured nominal rate of return is overstated. Furthermore the degree to which asset types are omitted will vary overtime, generating additional fluctuations in these rates of return. Figure 1 suggests that the Ex Post rates of return are indeed subject to this bias, making the argument for using an Ex Ante real rate of return stronger.
A related problem described by Inklaar (2010) is that using an Ex Post approach can yield widely different rental rates for the same asset across industries. To test this Oulton and Rincon-Aznar provide charts depicting the mean real rates of return by branch. Following this approach table 6 shows the real rates of return for ICT and Non-ICT assets for four industry aggregates within the market economy. 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 1980 1985 1990 1995 2000 2005
Ex Post Real rate of Return, EU-USA
Ex Ante RR USA EU 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 1980 1985 1990 1995 2000 2005
Ex Post Real rate of return; EU countries
19 | P a g e
Table 3
The table shows that the mean real rates of return by asset type show a considerable spread across the sectors in the market economy, confirming the concerns expressed by Inklaar. Admittedly, part of the difference between sectors can be caused by the fact that a different mix of assets is used, since these indicators are aggregated over asset types. However, these rates are averaged over 28 years. It seems hard to believe that in the USA over such a long period of time the real returns to non-ICT assets can be more than twice as high in the manufacturing (excluding electrical machinery) (MexElec) than in the Electrical machinery, Post and telecom (ELECOM) sector. In the EU this difference is reversed, although they are much closer. Furthermore, all of these rates are considerably higher than the 4% real rate of return taken by OECD as being consistent with long term averages, supporting the view that the Ex Post real rates of return are overstated due to the omission of asset types such as land, inventories and intangible assets in the EU KLEMS data. Clearly firms have made investments in these types of assets.
4.3 MFP estimates
It has been shown that the Ex Ante and Ex Post approach yield considerable differences in the estimates of capital compensation and services. This section is concerned with the use of these capital services as an input in the growth accounting framework described in the models and data section. Growth accounting decomposes output growth in the growth contributions of inputs and MFP. Figure 2 shows the MPF estimates for the market economy in the EU and the USA. The results are presented in index form where 1980 is set to 100 for the period 1980-2007.
The first thing that stands out from the upper-left and upper-right graphs in figure 2 is the ranking of the alternative approaches. The Ex Ante method produces much higher growth rates of MFP for both the EU and the USA. This is in part due to the lower exogenous estimates of capital services. Furthermore, since Ex Ante capital compensation is generally lower than Ex Post (appendix table A4), capital gets a lower weight in calculating the input contributions to output growth; hence, Ex Ante, MPF growth as a residual will be higher. A second thing to note is that although there is a clear difference in the level of growth rates, MFP growth follows a similar pattern. There are no observable breaks in the trends between the different methods. In the lower-left and -right graphs the Ex Post and Ex Ante MFP indices for the EU and the USA are compared. Average EU MFPG is slightly higher than in the USA roughly between 1980 and the first half of the 1990s. In the second half of the 1990s MFPG starts to pick up for the USA and overtakes Europe, however this pattern seems to be reversing after 2005. There is not much difference between the methods, although Ex Ante the lines depict more overlap in the early period which indicates that the MFP growth rates are, on average, closer than in the Ex Post case for this period.
Ex Post real rates of return by four major sectors in the Market Economy
Code Industry description EU USA EU USA
MARKT MARKET ECONOMY 15% 21% 6% 12%
ELECOM ELECTRICAL MACHINERY, POST AND COMM. SERVICES 12% 10% 10% 7% MexElec TOTAL MANUFACTURING, EXCLUDING ELECTRICAL 13% 28% 8% 18%
OtherG OTHER PRODUCTION 14% 16% 7% 7%
MSERV MARKET SERVICES, EXCLUDING POST AND TELECOMM. 17% 36% 5% 15%
Spread 5% 25% 5% 11%
The real rates of return are the mean of 1980-2007.
20 | P a g e
Figure 2
Indices of multi factor productivity in the market economy, 1980 = 100. 4.4 Growth accounting decomposition
A choice between an Ex Ante and Ex Post method affects the estimations of MFP in two ways; first the Ex Ante method lowers the estimates of capital services directly, and second the input contributions to output growth are being given new weights based on cost shares. This also has an effect on the contribution of labour inputs. In this section the decomposition of output growth is shown for both the Ex Ante and Ex Post method. Emphasis is placed on the input contributions to labour productivity growth (LPG) giving the input contributions the interpretation of contributions per hour, which is also called factor intensity (Van Ark et al. 2008).
Table 4 shows that moving from an Ex Post approach to the Ex Ante method works to reduce the contributions of capital and increases the importance of MPF as a contributing factor to labour productivity growth. This is the case in general for both periods and regions. Figure A1 in the appendix shows the residual profits as a percentage of total capital compensation derived from the national accounts for four sectors in the market economy. With the exception of market services in the EU up to 1987, residual profits are positive. They can be observed to run up to almost 50% of total capital compensation measured from the national accounts. This greatly reduces the weights
90 100 110 120 130 140 150 1980 1985 1990 1995 2000 2005 USA Market economy MFP
21 | P a g e assigned to capital services when using cost shares in the Ex Ante approach. Consequently capital’s contribution to LPG will decline.
Table 4
To test whether these differences will result in new insights in terms of productivity analysis we take the analysis by Van Ark et al. (2008) and replicate their results using both methods. In their study they concluded that the productivity slowdown in the second half of the 1990s and the first half of the 2000s in Europe compared to the United States was largely the result of slower multifactor productivity growth in market services. They based their results on Ex Post estimates. Indeed the results from this study show that for the USA 1.7% of the 2.7% LPG in the market economy was due to market services for the period 1995-2007. For the EU, LPG was 1.6% in the market economy of which 0.6% was contributed by market services. Table 5 below replicates the growth accounting results for Market Services from this article, and shows the results from the two approaches applied in this paper.
Table 5
Growth accounting comparison in the Market Economy
1+2+3+4 1 2 3 4 1+2+4 (1980-1995) European Union XP 2.5 0.3 0.4 0.8 1.0 1.7 XA 2.5 0.3 0.3 0.6 1.3 1.9 Difference 0.0 -0.1 -0.2 0.3 0.2 United States XP 2.0 0.2 0.7 0.3 0.7 1.7 XA 2.0 0.3 0.4 0.1 1.2 1.9 Difference 0.0 -0.3 -0.2 0.5 0.2 (1995-2007) European Union XP 1.6 0.2 0.5 0.4 0.5 1.2 XA 1.6 0.2 0.3 0.3 0.8 1.4 Difference 0.0 -0.2 -0.1 0.3 0.1 United States XP 2.7 0.3 0.9 0.3 1.2 2.4 XA 2.7 0.3 0.6 0.2 1.6 2.5 Difference 0.0 -0.3 -0.1 0.4 0.1 Contribution of the k nowledge economy to labour productivity Labour productivity contributions from
Labour productivity Labour composition ICT capital per hour Non-ICT capital per hour Multi factor productivity
Market Services growth accounting (1995-2007)
European Union XP 1.1 0.2 0.6 0.3 0.0 XA 1.1 0.2 0.4 0.2 0.4 Unites States XP 2.8 0.3 1.0 0.3 1.2 XA 2.8 0.4 0.6 0.2 1.7
Difference in (contributions to) labour productivity growth, USA minus EU
22 | P a g e Taking a closer look at the decomposition of LPG in market services in table 5, reveals that most of the LPG gap between the EU and the USA in market services is attributable to MFP in both the Ex Ante and Ex Post case. This was also the conclusion drawn in the study by Van Ark et al.. However, we do see some changes. Again the contributions of capital assets have diminished while MFP contribution increased. Since the effect had a similar magnitude in both countries on MFP the gap between the countries remains approximately the same, roughly 1.2%. Therefore, moving from an Ex Post to an Ex Ante approach does not change the overall picture in this case.
Table 6 below shows the decomposition of labour productivity growth for each of the EU-countries in the EU15ex aggregate as well as the aggregate and the USA for the period 1980-2007. By looking at the Ex Ante-Ex Post comparison by country, it can be seen whether the effects of the difference in the measurement of rental prices are different for each country. From this table it can be seen that the effects from using an exogenous real rate of return are uniform across countries. For all countries there is a decrease in the contribution of capital and an increase in the estimate of MFPG. The effects on the contributions of labour composition are very modest, but always positive. This is to be expected since the indices used in both approaches are the same and the effect is solely due to the Ex Ante reduction of total calculated capital compensation, giving labour compensation a higher relative cost share weight. Only for Spain is the difference in the growth contribution from Non-ICT assets higher than from ICT-assets.
Table 6
Contributions to labour productivity growth in the Market Economy (1980-2007)
AUT DNK FIN FRA GER* ITA NLD ESP UK EU** USA Labour productivity growth
2.5 2.1 3.5 2.5 1.7 1.3 1.6 1.9 2.8 2.1 2.3 Labour composition
Ex Post 0.2 0.1 0.4 0.4 0.0 0.1 0.3 0.3 0.4 0.3 0.3 Ex Ante 0.2 0.2 0.4 0.4 0.0 0.1 0.3 0.4 0.4 0.3 0.3 Difference 0.1 0.1 0.0 0.1 0.0 0.0 0.0 0.1 0.1 0.0 0.0 ICT capital per hour
Ex Post 0.4 1.0 0.5 0.3 0.5 0.2 0.5 0.4 0.6 0.4 0.8 Ex Ante 0.3 0.6 0.3 0.2 0.3 0.2 0.3 0.3 0.4 0.3 0.5 Difference -0.1 -0.4 -0.2 -0.1 -0.2 -0.1 -0.1 -0.1 -0.2 -0.1 -0.3 Non-ICT capital per hour
Ex Post 0.3 0.3 0.4 0.5 0.5 0.5 0.2 0.8 0.6 0.6 0.3 Ex Ante 0.3 0.4 0.4 0.4 0.4 0.5 0.2 0.5 0.3 0.5 0.1 Difference 0.0 0.0 0.0 -0.1 -0.2 0.0 0.0 -0.3 -0.2 -0.1 -0.1 Multi factor productivity
Ex Post 1.6 0.7 2.2 1.3 0.7 0.4 0.7 0.4 1.2 0.8 1.0 Ex Ante 1.7 0.9 2.3 1.4 1.0 0.5 0.8 0.7 1.6 1.1 1.4 Difference 0.1 0.2 0.1 0.1 0.3 0.1 0.1 0.3 0.4 0.3 0.4
23 | P a g e
4.5 Discussion of the results
Answering the first research question, it has been shown that the Ex Ante method employing a constant real rate of return produces lower capital services estimates than the Ex Post method. The origins of this have been traced back to lower capital compensation shares for relatively faster growing asset types in terms of capital stock. Considering evidence from other studies, this result is not general to models employing exogenous rates of return, but rather the effect from using a constant real rate of return, which is a special case of the Ex Ante method. In line with other sensitivity studies, this thesis has found considerable volatility in real rates of return. While they appear quite stable for the EU as a whole, looking at the real rates of return on a country by country basis considerable variability can be observed in the EU region as well. Levels of the Ex Post real rates of return are also shown to be well above the 4%, taken as the Ex Ante constant real rate of return. The concern of Inklaar (2010) that real rates of return for the same asset type differ greatly across industries has been corroborated. These observations confirm the empirical problem suggested in the literature section that the Ex Post method of calculating rental prices (equation (16)) does indeed overstate the rental price when asset types are omitted. This is further supported by the analysis of the negative rental rates.
In answer to the second research question, we do indeed measure great differences in the contributions of capital and MFP when using the Ex Ante or Ex Post approach. This is in part due to the differences in the measured capital services. However, residual profits have been shown to be present for all countries and can be as high as 50% of capital compensation from the national accounts in some industries (appendix figure A1). This has a considerable diminishing effect on the cost share weights for capital used in the growth accounting exercise, which explains much of the difference in the contributions of MFP and capital to labour productivity growth.
24 | P a g e
5 Conclusions
This thesis has shed new light on the debate concerning what alternative rental price model to use in order to measure capital services and decompose labour productivity growth. The theoretical literature provides many options to estimate capital services and there is as yet still no consensus on what should be the preferred approach. This paper has applied and compared specific versions of the Ex Post and Ex Ante approach to measuring capital services, and growth accounting. In the literature a number of empirical concerns have been raised when employing the commonly used Ex Post method. Results from this study confirms these concerns.
Evidence has presented that the Ex Post approach indeed overstates the rate of return to asset types due to omission of investments in asset types such as land, inventories and intangibles. The Ex Ante approach largely resolves these problems and does not rely on some of the stringent neo-classical assumptions such as perfect foresight, competitive markets and constant returns to scale. The overall research question was stated to be: Does the choice for an Ex-Post or an Ex-Ante method to measuring capital services affect the results from productivity analysis? The answer is that it depends on the analysis. In the EU-USA comparison analysis done by Van Ark et al. (2008) it did not alter the conclusions. However MFP estimates have been shown to be considerably higher when using an Ex Ante Method. Therefore, analysis which aims to determine the origins of output or labour productivity growth is affected. This begs the question however of what we are actually measuring when we estimate MFP.
Ex Ante, unmeasured capital inputs no longer end up in the contributions of capital to output, however they do end up in the MFP measure. Whether this is a better way of measuring MFP also depends on the analysis. MFP as a residual is, according to Hulten (2000) a measure of our ignorance. In other words it includes all unknown contributions to output growth as well as the effects from technological progress. It can be argued that if exogenous rates of return are measured correctly, the Ex Ante procedure gives a more accurate measure of the contributions of capital to output or labour productivity growth. However, this does mean that the interpretation of MFP as technological progress becomes more questionable since it captures ‘pure’ technical change, the growth contributions of unobserved assets, and scale effects and the distribution of mark-ups, according to Schreyer (2004). Considering the level of residual profits, these unmeasured inputs can be considerable. However, Schreyer argues it is possible to further decompose MFP and isolate the effects of the non-observed inputs, this may be a fruitful avenue for further research.
25 | P a g e
6 References
Balk, B. M., “Measuring Productivity Change without Neoclassical Assumptions: A Conceptual Analysis,” Mimeo, 2008.
Berndt, E.R. and M.A. Fuss (1986), ‘‘Productivity Measurement with Adjustments for Variations in capacity Utilization and Other Forms of Temporary Equilibrium’’, Journal of Econometrics, vol. 33, pp. 7–29.
Diewert, E. (2001), ‘‘Measuring the Price and Quantity as Capital Services under Alternative Assumptions’’, Discussion Paper 01-24, Department of Economics, The University of British Columbia.
Erumban, A.A. (2009), “Rental Prices, Rates of Return, Capital Aggregation and Productivity: Evidence from EU and US”, CESifo Economic Studies, 54(3), pp. 499-533.
Haan, M. de, Bert M. Balk, Dirk van den Bergen, Ron de Heij, Hans Langenberg and Gerrit Zijlmans (2005), The Development Of Productivity Statistics At Statistics Netherlands, Paper presented at the OECD Workshop on Productivity Measurement, Madrid, October 2005.
Harper, M.J., E.R. Berndt and D.O. Wood (1989), ‘‘Rates of Return and Capital Aggregation Using Alternative Rental Prices’’, in D.W. Jorgenson and R. Landau, eds., Technology and Capital
Formation, MIT Press, Cambridge, MA, pp. 331-372.
Hulten, C.R. (2000), ‘‘Total Factor Productivity: A Short Biography’’, NBER Working Paper 7471. Inklaar, Robert (2010), “The Sensitivity of Capital Services Measurement: Measure All Assets and the
Cost of Capital”, Review of Income and Wealth, 56(2), pp. 389-412, June 2010
Jorgenson, D.W. and Z. Griliches (1967), ‘‘The Explanation of Productivity Change’’, Review of Economic Studies 34, 249–83.
O’Mahony, Mary and Marcel P. Timmer (2009, forthcoming), “Output, Input and Productivity Measures at the Industry Level: the EU KLEMS Database”, Economic Journal.
Oulton, N. (2007), “Ex post versus ex ante measures of the user cost of capital” Review of Income
and Wealth, vol. 53(2), pp. 295-317.
Oulton, N. and Ana Rincon-Aznar (2009), “Rates of Return and Alternative Measures of Capital Input: 14 Countries and 10 Brances, 1971-2005”, CEP Discussion Paper No 957
Schreyer, Paul (2004), “Measuring Multi-Factor Productivity when Rates of Return are Exogenous,” paper prepared for the SSHRC International Conference on Index Number Theory and the Measurement of Prices and Productivity.
Schreyer, Paul. W. Erwin Diewert, and Anne Harrison (2005), Cost of Capital Services and the
National Accounts. Issues paper for the July 21005 AEG meeting.
Timmer, M.P., Robert Inklaar, Mary O’Mahony and Bart van Ark (2010), ‘Economic Growth in
Europe, A comparative Industry Perspective’, Cambridge University, Chapter 3.
26 | P a g e
7 Appendix
7.1 Tables and figures
Table A1
List of EU KLEMS asset types
Full name Abbreviation
Total assets GFCF
ICT assets ICT
Computing equipment IT Communications equipment CT
Software Soft
Non-ICT assets Non-ICT
Residential structures Rstruc Non-residential structures OCon Transport equipment TraEq Other machinery and equipment OMach
Other assets (a) Other
Note: (a) Other assets include products of agriculture and other tangible and intangibles products not
elsewhere classified following the ESA 1995 (mainly mineral exploration and artistic originals).
Table A2
List of EU KLEMS industries, lowest nodes Code Description
TOT TOTAL INDUSTRIES
AtB Agriculture, hunting, forestry and fishing C Mining and quarrying
15t16 Food products, beverages and tobacco 17t19 Textiles, textile products, leather and footwear 20 Wood and products of wood and cork
21t22 Pulp, paper, paper products, printing and publishing 23 Coke, refined petroleum products and nuclear fuel 24 Chemicals and chemical products
25 Rubber and plastics products 26 Other non-metallic mineral products 27t28 Basic metals and fabricated metal products 29 Machinery, nec
30t33 Electrical and optical equipment 34t35 Transport equipment
36t37 Manufacturing nec; recycling E Electricity, gas and water supply F Construction
50 Sale, maintenance and repair of motor vehicles and motorcycles; retail sale of fuel 51 Wholesale trade and commission trade, except of motor vehicles and motorcycles 52 Retail trade, except of motor vehicles and motorcycles; repair of household goods H Hotels and restaurants
60t63 Transport and storage 64 Post and telecommunications J Financial intermediation 70 Real estate activities
71t74 Renting of m&eq and other business activities L Public admin and defence; compulsory social security M Education
N Health and social work
