Mª Mar Salinas Jiménez Universidad de Extremadura
Mª Jesús DelgadoRodríguez Universidad Rey Juan Carlos
Inmaculada Álvarez Ayuso Universidad Complutense de Madrid
Reference: Received 04th April 2005; Published 22th July 2005. ISSN 15791475
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Resumen
 El objetivo de este artículo es analizar el crecimiento de la productividad laboral y la convergencia de los 15 en la UE entre los años 1980 y 1997. Adoptando un modelo de producción frontera, el crecimiento de la productividad laboral se descompone en componentes atribuibles al cambio de eficiencia, al progreso tecnológico y a la acumulación de capital. Asimismo, analizamos la dinámica de distribución de la productividad laboral, atendiendo al enfoque de Quah. Nuestros resultados muestran que la acumulación de capital físico y humano parece ser la principal fuerza conductora del crecimiento de la productividad laboral y de los procesos de convergencia experimentados por las economías europeas durante estos años. Por otra parte, observamos que aparecen algunos problemas en la Europa de los 15 en lo que respecta al crecimiento del Factor Total de Productividad (FTP).
Abstract

The aim of this article is to analyse labour productivity growth and convergence in the EU15 countries between 1980 and 1997. Adopting a production frontier approach, labour productivity growth is broken down into components attributable to efficiency change, technological progress and capital accumulation. Furthermore, in the spirit of the Quah´s approach, the dynamics of the distribution of labour productivity is also analysed. Our results show that physical and human capital accumulation appears to be the main force driving the labour productivity growth and convergence processes experienced by the European economies during these years. On the other hand, we observe that some problems appear in the EU15 in terms of Total Factor Productivity (TFP) growth.

1. Introduction
The literature on economic growth and convergence typically starts from an aggregate production function in which the total output depends on the productive inputs and the current level of technology, being the growth rate determined by the accumulation of the productive factors and the rate of technological progress. Assuming that all units of production operate efficiently, traditional growthaccounting exercises decompose economic growth into contributions due to factor accumulation and total factor productivity (TFP) growth, which is identified with technological progress1 . On the other hand, studies in the tradition of a production frontier approach consider the possible existence of inefficiencies (being inefficient behaviour measured by the difference between the actual level of production and the maximum possible level defined by the frontier). This in turn allows decomposing TFP growth into efficiency change, represented by movements of the economy towards or away from the frontier, and technological progress, represented by shifts of the production frontier2 .
Some recent studies have focused on the decomposition of TFP growth into efficiency change and technological progress, analysing their contribution to economic growth and, to a lesser extent, to economic convergence3 . In the context of this literature, the aim of this article is to analyse labour productivity growth and convergence in the EU15 countries during the period 198097 by adopting a production frontier approach. Under this approach, labour productivity growth is broken down into components attributable to efficiency change, technological progress and capital accumulation. Nonparametric techniques of linear programming (Data Envelopment Analysis) are used to estimate a common production frontier and TFP is decomposed by means of Malmquist productivity indices. With regard to capital accumulation, we analyse the contribution of private capital to productivity growth and, additionally, we consider both a broad measure of physical capital introducing public capital as an additional input and human capital accumulation4 . Once the components of labour productivity growth are analysed, we shall focus on their relative contributions to convergence. A first approach to analysing convergence bases on the commonly used concept of convergence (introduced by Barro and SalaiMartin, 1992). Moreover, following Quah´s (1993, 1997) suggestion, the dynamics of the overall distribution is also analysed, both for the distribution of labour productivity and for each of its components.
The structure of this article is as follows. Section II describes the approach followed and the data used in this study. Section III discusses the estimates for the levels of efficiency and analyses the contribution of each of the components of labour productivity to the process of productivity growth experienced by the European economies. Section IV focuses on the contribution of these factors to economic convergence and analyses the evolution of the distribution of productivity in terms of this decomposition. Finally, Section V presents the main conclusions of this study.
2. Methodology and data
The methodology used in this study bases on Kumar and Russell (2002), who decompose labour productivity growth into components attributable to changes in efficiency, technological progress and physical capital accumulation, and on Henderson and Russell (2004), who extend this decomposition by adding human capital accumulation. The key relation of these works decomposition is:
where is the relative change in the outputlabour ratio between periods t and t+1, which is decomposed into: i) efficiency change change of the distance from the bestpractice frontier, ii) technological progress representing the shifts of the frontier, and iii) capital accumulation lied either to the notion of movements along the frontier due to changes in the level of physical capital or to improvements in the quality of labour due to human capital accumulation.
Using a Data Envelopment Analysis (DEA) approach, we estimate a best practice frontier and the associated efficiency levels of individual countries (i.e. the distance of each country from the frontier). Measures of relative performance to this frontier are calculated by means of Malmquist productivity indices, which may be decomposed into technological progress and efficiency change5 . Once the productivity indices are estimated, one shall decompose labour productivity growth into technological change (shifts in the production frontier), efficiency gains (movements toward the frontier) and capital accumulation (movements along the frontier or improvements in the quality of labour).
Most of the data used in this study comes from New Cronos Data Base (Eurostat) which offers on CDROM information concerning the series of Gross Value Added in 1990 standard purchasing power parity (1990 PPS), labour and investment. Public and private capital stocks were estimated from investment data (1990 PPS) available since at least 1970, in many cases since 1960, by the standard perpetual inventory method (PIM)6 . As to human capital, we consider a human capital measure that attempts to present the investment effort that Public Administrations have carried out7 . Expenditure on education series (19602000) comes from OECD publications8 and human capital was estimated from educational expenditure, expressed in 1990 PPS, by using again the PIM approach9 .
3. Efficiency levels and labour productivity growth decomposition
For comparison purposes, we calculate the efficiency indices and the TFP growth estimates both without and with public and human capital. The average efficiency indices estimated for the EU15 countries in the period 198097 are presented in Table 1. When these indices are estimated by ignoring the role of public and human capital (panel a), the average efficiency level stands at 82%. Nevertheless, we observe significant differences among countries, Luxembourg being on the frontier all along the period and United Kingdom, the Netherlands and Belgium showing efficiency levels above 90% whereas countries such as Sweden and Finland get indices below 70%. However, part of this estimated inefficiency comes from the omission of other relevant inputs. When we consider a broad measure of physical capital, including public as well as private capital (panel b), or the human capital variable (panel c), the average efficiency level rise until 89% and achieve 92.6% when all these inputs are considered simultaneously (panel d). This increase in the estimated level of efficiency when introducing public and human capital is common to all EU15 countries and is specially significant in the cases of Ireland and Italy when introducing public capital, or in the cases of Greece, Portugal, Spain and Sweden when adding human capital.
Table 2 shows the decomposition of productivity growth into TFP change (which is in addition decomposed into efficiency change and technological progress) and physical capital accumulation, both without and with public capital, but ignoring the role of human capital accumulation. When only private capital is took into account we observe that, on average, 61% of output productivity growth is due to TFP growth, the other 39% being explained by capital accumulation. However, when public capital is introduced in the analysis as an additional input, the part of productivity growth explained by capital accumulation rise to 48%, showing that part of the previous estimated TFP growth was due to the omission of the public capital variable. In any case, it is worthwhile noting that the estimates for changes in efficiency lie below unity, reflecting adjustment problems in the European economies.
The contribution of capital accumulation to labour productivity growth is even greater when human capital is introduced in the analysis. Table 3 shows the productivity decomposition when this variable is also considered. It can be observed that capital accumulation is now the driving force of labour productivity growth, compensating the negative effect of TFP change. This reflect that the omission of the human capital variable lead to overestimate the contribution of TFP. Moreover, taking into account the effect of human capital accumulation one observes that a significant problem in terms of TFP for the European economies appears. Again, there are significant differences among countries. Whereas average TFP growth is negative, countries such as Austria, Belgium, Germany, Luxembourg, the Netherlands, and Denmark present a positive evolution of TFP. On the other hand, we find a significant contribution of (physical and human) capital accumulation to productivity growth in the four cohesion countries (especially in Greece and Portugal) and in Sweden.
In short, we observe that TFP growth and physical capital accumulation have contributed to productivity growth in the European economies, but part of the estimated TFP growth is in fact due to human capital accumulation10 . When human capital is also introduced in the productivity decomposition we observe that the contribution of TFP tend to be negative. However, one should soften this result by noting that the contribution of TFP change is positive in most of the European central economies whereas the Mediterranean countries suffer from problems in TFP. Labour productivity growth in these later countries has however been positive as the result of the capital accumulation process undergone by these economies.
4. Relative contributions to convergence
Given the existence of significant differences in the levels of efficiency and in the factors driving labour productivity growth in the EU15, one could wonder how these variables influence the process of convergence among the European economies. Regarding the differences in efficiency levels, a first question to answer would be whether a process of technological catchup has taken place among the European economies11 . In the approach followed in this article, a common technology is assumed for all countries and, consequently, technological catchup is identified with movements toward the bestpractice frontier. In order to analyse whether a process of technological catchup took place among the EU economies between 1980 and 1997, Figure 1 shows the results of the nonparametric regression between the efficiency growth rates and the initial levels of efficiency. This information is presented for the complete period under study (198097) and by subperiods (198085; 198592; and 199297) and both efficiency change and initial levels of efficiency are normalised with respect to the EU15 mean.
On average, the less efficient regions of 1980 underwent greater efficiency gains than the more efficient ones, what indicates the existence of a process of technological catchup in these years. Most of this convergence in efficiency levels took place between 1992 and 1997. In the period 198085 there were also a tendency towards convergence in efficiency, even when the dispersion of efficiency change from the mean was reduced. On the contrary, the period 198592 showed a tendency towards divergence since the less efficient economies presented a less favourable evolution in terms of efficiency change.
This convergence in efficiency levels, however, does not mean that technological catchup tends to reduce the differences in labour productivity. Countries with relatively high labour productivity could present significant levels of inefficiency and consequently take advantage of efficiency gains as much as countries with relatively low levels of productivity per worker. Likewise, one should also study whether countries with initially lower levels of labour productivity present greater rates of TFP growth and capital accumulation, with these factors contributing to convergence in output per worker. Figure 2 shows the dependence of the growth rate of labour productivity, and each of its components (efficiency gains, technological change and capital accumulation), on the initial levels of output per worker. Again, both the growth rates and initial levels of productivity are normalised with respect to the EU15 mean.
As can be observed, the less productive economies tend to grow slightly faster than the more productive ones, leading to a weak process of convergence in labour productivity between the EU economies. However, in analysing the relationship between efficiency change and the initial levels of productivity, we observe no clear pattern, suggesting that efficiency gains benefited the relatively more productive countries as much as the relatively less productive ones. Thus, although the European economies observed a catchup process during these years, it is noteworthy that efficiency change does not appear to be a source of convergence (or divergence) in labour productivity. Related to technological progress, we observe that this variable tend to contribute to divergence of labour productivity: the positive regression slope between output per worker and technological change suggests that the more advanced countries benefited more from technological progress than the less productive economies. In contrast, capital accumulation seems to have contributed positively to labour productivity convergence. Physical and human capital accumulation, that played an important role in explaining output per worker growth, also appears to be the main force driving labour productivity convergence since one observes a strong inverse relationship between capital accumulation and the initial levels of labour productivity.
The above analysis bases on regressions of average growth rates and aims at explaining the behaviour of the conditional mean. However, it provides little information about the crosssectional distribution of labour productivity and its evolution. In the spirit of Quah´s approach (Quah, 1993, 1997), we shall now turn to study the dynamics of the convergence process by analysing the entire distribution of labour productivity and efficiency levels of the European economies between 1980 and 1997. To this end, we use nonparametric kernel estimates of the density12 . Furthermore, in order to discount the common growth tendency, we focus on mean preserving variations in the distribution, so that estimated densities are normalised for the mean being equal to one. Figure 3 shows the distributions of output per worker and efficiency levels of the EU15 countries. The estimated densities of labour productivity show that the dispersion of the economies in the distribution remained relatively stable throughout the period. However, one observes a slight tendency towards convergence as the probability mass tends progressively to concentrate closer to the European mean. With regard to the distributions of efficiency levels, it is noteworthy the evolution from an initial bimodal distribution to a unimodal one, a transformation which took place between 1992 and 1997. Bimodal distributions appear during the eighties and the beginning of the nineties, with a tendency towards divergence between 1985 and 1992, increasing the dispersion in efficiency levels as the low mode shifted away from the mean. During the nineties, however, there is a tendency towards convergence in efficiency levels, driving to a final distribution that is clearly unimodal.
Since in the previous section labour productivity growth was decomposed into TFP growth and capital accumulation, one could analyse the dynamics of the distribution of labour productivity in terms of its components (efficiency change, technological progress and capital deepening). On the basis of our labour productivity decomposition, we carry out a simulation in order to assess how efficiency change, technological progress and capital accumulation contribute to the evolution of the labour productivity distribution. To answer the question of what the labour productivity distribution would have been in 1997 if the labour productivity of each country had changed due only to one of its components, we have to calculate the theoretical productivity corresponding to each country by isolating that component. Rewriting the labour productivity growth decomposition as:
we observe that the labour productivity in 1997 may be constructed by multiplying the initial labour productivity by all the components of labour productivity growth. Similarly, one can construct counterfactual distributions by introducing just one of these three components, thus isolating its effect from those of the other components (i.e. if one constructs the variable one isolates the effect of changes in efficiency, assuming a stationary production frontier and no capital accumulation). We shall now estimate the mean preserving densities of these counterfactual distributions. Figure 4 shows the initial distribution of output per worker and the densities estimated by isolating the effect of each component (estimated densities for initial and final years are also presented for comparison).
From Figure 4 we observe that the overall evolution of the labour productivity distribution cannot be explained by any of the three components of productivity change separately. However, efficiency change appears to be the main factor in explaining the concentration of the labour productivity distribution around the mean, while the tendency of technological change and capital accumulation is to increase the dispersion of the distribution. Thus, even when efficiency change did not appear to be a source of convergence in labour productivity, it stands out as the driving force in the change of the labour productivity distribution.
5. Conclusions
In this paper we analysed the labour productivity growth and convergence processes experienced by the EU15 economies during the period 198097. By taking into account the existence of inefficiencies in the behaviour of the European economies, labour productivity growth was decomposed into TFP growth which was additionally decomposed into technological progress and efficiency changes and capital deepening.
Focusing on this decomposition, it was found that physical and human capital accumulation appeared to be the major source of labour productivity growth in the EU15 during the 80´s and 90´s. When only physical capital accumulation was considered, labour productivity growth was explained by both capital deepening and TFP growth. However, part of the estimated TFP growth was in fact due to human capital accumulation. Thus, when the human capital variable was introduced in the analysis we observed that the contribution of TFP tended to be negative, reflecting a significant problem in terms of TFP for the European economies. It is also worthwhile noting the existence of significant differences among the European countries with regard to the factors driving productivity growth. In this sense, we observed that the contribution of TFP growth to labour productivity was positive in most of the European central economies. On the other hand, there were mainly the Mediterranean countries which suffered from problems in TFP, with labour productivity growth being positive as the result of the intense process of capital accumulation undergone by these economies.
Regarding the convergence process, a slight tendency toward convergence among the European economies was found during these years. We observed a process of technological catchup (or convergence in efficiency levels) since, on average, the less efficient countries in 1980 underwent greater efficiency gains than the more efficient ones. Nevertheless, efficiency change did not appear to be a source of convergence in terms of labour productivity, even when it seemed to be the main factor explaining the overall evolution of the labour productivity distribution. On the other hand, technological progress tended to contribute to divergence, whereas physical and human capital accumulation appeared to be the main force driving the process of convergence in labour productivity, with a strong inverse relationship between capital deepening and the initial levels of output per worker.
Given that labour productivity growth and convergence in the EU15 countries is largely driven by physical and human capital accumulation, public investment in these types of capital might constitute an appropriate instrument of development and cohesion policy. However, with regard to TFP, our results indicate that some European countries (and especially the Mediterranean ones) are suffering from problems in TFP growth. Therefore, policies aimed at promoting TFP growth in the European countries (i.e. policies promoting macroeconomic stability in order to improve efficiency levels, or R+D activities encouraging technological progress) should also be strongly supported.
Appendix
Let be the technology of production at period t (t=1,...T):
where are the vectors of inputs and outputs, respectively.
Following Shephard (1970), the distance function at period t is defined as13 :
which allows a perfect characterization of the technology, since if, and only if,
In order to define the Malmquist productivity index, we need to relate the input and output vectors at period t to the technology of the next period,
Similarly, one could define , where the input and output vectors at period t+1would be related to the period t technology.
On the basis of the above concepts, Färe et al. (1994) define the following Malmquist productivity index:
As it can be observed, this index is the geometric mean of two Malmquist indices, the first related to the technology of period t, and the second to the technology of period t+114 .
This is in fact an index of productivity change between period t and t+1 and can be decomposed into efficiency change (EFF) change in relative efficiency between periods t and t+1 and technological change (TECH) the geometric mean of the shift in the frontier between these two periods:
In order to estimate the component distance functions of the Malmquist index, we use the data envelopment analysis (DEA)15 nonparametric technique of linear programming. By assuming constant returns to scale16 and exploiting the fact that the distance functions can be estimated as reciprocals of Farrell efficiency measures17 , the specific problem to calculate can be expressed as:
The other three distance functions are calculated similarly, substituting the appropriate period index (i.e. t or t+1).
Footnotes
1 Under this approach TFP is calculated residually and it is often referred as the "Solow residual".
2 Raa and Mohnen (2002) offer a theoretical framework that encompasses both the neoclassical growthaccounting and the frontier approaches.
3 From an international perspective, see for example the works by Färe et al. (1994), Perelman (1995), Taskin and Zaim (1997), Maudos et al. (1999), Kumar and Russell (2002) or Henderson and Russell (2004).
4 It is worth noting that the omission of relevant inputs (i.e. public and/or human capital) could lead to overestimate the levels of inefficiency. Similarly, TFP growth could be overestimated since part of this growth would be in fact the result of the accumulation of those omitted inputs.
5 Malmquist productivity indices and their decomposition are formally presented in the Appendix.
6 See OECD (1993) for a detailed explanation of this procedure.
7 Wö mann (2003) offers a good survey and discussion of the human capital literature and drawbacks of the different measures of this variable.
8 Educational Statistics in OECD Countries (1981), Public Educational Expenditure, Costs and Financing: An Analysis of Trends 1970/1988 (1992) and Education at a glance (several years).
9 See Alvarez and Delgado (2002) for a detailed explanation of the public, private and human capital estimation procedure.
10 In order to test empirically the significance of the public and human capital variables we used the Banker test, which indicated that both variables are statistically significant. Therefore, afterwards we centre on TFP estimates considering human and public capital as additional productive factors.
11 The notion of catchup bases on the idea of diffusion of the technology and was first discussed by Abramovitz (1986).
12 The kernel estimator for the value of the density function of a variable at a point will be given by , where is the socalled kernel function, and h is the bandwidth (or smoothing parameter) which controls the regularity of the estimated curve. In our study we used Gaussiantype kernel functions in all the calculations, and chose the bandwidth on basis of the leastsquares crossvalidation (LSCV) criterion.
13 The subscript o refers to output based distance functions. See Färe (1988) for a discussion of input and output distance functions.
14 A similar productivity index, based on Malmquist (1953), was proposed by Caves et al. (1982). However, these authors assumed to be equal to unity, so that technical inefficiencies were not considered.
15 Method developed by Charnes et al. (1978), based on Farrell (1957) technical efficiency measures.
16 GrifellTatjé and Lovell (1995) show that the Malmquist index may not be an accurate measure of TFP change when nonconstant returns are assumed. Furthermore, the constant returns to scale assumption is sufficient condition to guarantee that the optimization problem has a solution.
17 Specifically, where, is the Farrell output based measure of technical efficiency.
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About the AuthorsAutor: Mª Mar Salinas Jiménez Dirección: Universidad de Extremadura
Autor: Mª Jesús DelgadoRodríguez Dirección: Universidad Rey Juan Carlos Coerreo Electrónico: mariajesus.delgado@urjc.es
Autor: Inmaculada Álvarez Ayuso Dirección: Universidad Complutense de Madrid

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