Estimating Efficiency at industrial aggregate level

Estimation of technical efficiency has been the subject of research in many empirical studies on industrial productivity, contributing to the theoretical development and empirical application of SFA at industry levels, with the purpose of screening out the external effects and statistical noise from the producer’s performance and achieving a more accurate efficiency measure. Empirical literature based on aggregate data, uses empirical models that are very similar to the work in this thesis, and are concerned with efficiency measurement for countries or regions in the European Union. Since the specific context of this thesis is on aggregate production functions and efficiency of industries/countries, relevant literature is that of western economies using aggregate rather than firm-level data, drawing reference to a recent literature that has spawned from Kumar and Russell (2002) using DEA and Kneller and Stevens (2006) using SFA. Other recent empirical contributions based on aggregate cross-country or cross-region data include: Koop (2001), Angeriz et al. (2006), Halkos and Tzeremes (2009), Ezcurra et al. (2009) and Bos et al. (2010), most of which focus on EU regions and countries. In addition, there are studies based on aggregate data focusing on specific EU countries: the UK (Driffield and Munday, 2001), Spain (Alvarez, 2007; Puig-Junoy and Pinilla, 2008) and Denmark (Bhattacharjee et al., 2009). All of these articles are based on aggregate data, use empirical models that are very similar to the work in this thesis, and are concerned with efficiency measurement for countries in the EU. This chapter, exploring the theory of Stochastic Production Frontiers, especially discusses thoroughly the literature on aggregate data and efficiency measurement for countries, drawing links to the theory used in later chapters to discuss how the results in the thesis are new or different, and thereby highlight where the contribution of the thesis truly lies.

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The process of output growth-either within countries or within industries within countries is still imperfectly understood. Standard economic models imply that the level of output by an economic entity should depend only on the inputs used. The new growth theory literature has emphasized factors such as technological spillovers, increasing returns, learning by doing, and unobserved inputs (e.g., human capital), whereas the empirical industrial organization literature (e.g., Caves and Barton 1990)

has emphasized the degree of openness of countries to imports and industry structure.

Another aspect of efficiency measurement literature focuses on estimating productive efficiency at aggregate data level. Since this thesis focuses on aggregate data level, this literature is rather important, both for estimations using Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA).

An enormous body of research has attempted to explain why some countries or industries produce more with their inputs than do others. The empirical economic growth literature [Levine and Renelt (1992), and Persson and Tabellini (1994)]

typically carried out cross-country regressions that attempt to explain economic growth using different sets of explanatory variables, both usimg DEA and SFA analysis.

The seminal paper that applied DEA to the aggregate economy was Färe et al. (1994).

Fare et al. (1994) use data envelopment analysis (DEA) to examine country-specific inefficiency in a subset of the OECD countries. In this paper, the aforementioned decomposition into the two components, noted above, is used to examine productivity growth in 17 Organization of Economic Cooperation and Development (OECD) countries in the post-war period. What is more, Färe et al. (1994) first applied production-frontier methods to empirical international economic growth.

Koop, Osiewalski, and Steel (1999) carry out a similar efficiency analysis. However, neither article includes data on different industries within a country, and thus they are unable to approach the issues raised by this article. Furthermore, these articles assume a common world production frontier for real GDP. Given the large differences in the composition of GDP across countries, this assumption is at best a crude approximation. Caves and Barton (1990) use industrial data for manufacturing industries within the United States, but do not allow for ties between industries or for cross-country comparisons. Bernard and Jones (1996) use industrial data for OECD countries that are similar to those used in this thesis. The focus of Bernard and Jones (1996) article is on convergence of productivity and it is worth noting that the authors find striking differences across industries. The assumption of a common frontier is, in principle, testable (Durlauf and Johnson, 1995). But given the paucity of data and the

flexible specification adopted, such tests would have little power in the present case.

From an economic point of view, the frontier is deterministic. However, factors such as measurement error exist and hence add an error term to the model. The addition of this error term makes the frontier stochastic, and the latter terminology is adopted to distinguish such models from those which assume that measurement error does not exist.

Empirical contributions based on aggregate cross-country or cross-region data, most of which focus on EU regions and countries, include Koop (2001) who relates to aggregate production functions and efficiency of industries/ countries. Koop (2001) uses data from 11 countries for 19 years to investigate the forces driving output change in 6 manufacturing industries. A flexible model is adopted that allows for the decomposition of output changes into three types of change: technical, efficiency, and input. This framework allows, among other things, for the investigation of:

the relative roles of the three components of output growth in each industry, the manner in which efficiency change moves over the business cycle, and potential technical spillovers from one industry to another.

The use of industrial data implies that Koop (2001) article has a different focus. Koop (2001) develops a modeling strategy and presents empirical evidence that sheds light on some of the points raised in both these literatures. A structural methodology is adopted that allows for the decomposition of output change into efficiency, technical, and input change using data on 6 manufacturing industries for 11 OECD countries.

All these countries reasonably can be assumed to have access to the same technology in each industry, so for each industry, each country can be thought of as fac-ing the same production frontier. Koop (2001) considers a model that assumes independence across industries, but the general modeling strategy advocated allows for the possibility that production frontiers in the 6 industries move together. For the latter case, the degree to which technical change in one industry spills over to another industry can be measured. Data from 1970-1988 are available and examine patterns of efficiency change and technical change over time.

Koop (2001) aims to shed light on issues such as convergence and catch up and answer important questions such as, "What is driving output growth in an industry?"

"What happens to efficiency over the business cycle?" "Is openness to trade an important factor in forcing economic efficiency?". Empirical results indicate: (1) non constant returns to scale seem to be present, (2) the marginal product of capital tends to be lower than the marginal product of labor, (3) technological change involves the marginal products of capital and labor changing over time, and (4) the various industries exhibit completely different production technologies. With regard to the decomposition, on average, positive technical change is found to play a key role in explaining output growth in all industries. Negative input change plays an important part in the stagnation of textiles and metals industries. On average, efficiency change has little role to play. However, these cross-country averages hide many interesting special cases that are discussed in detail.

Koop (2001) article begins with a stochastic production frontier model where industrial output Y is a function of capital K and labor L and then seeks to determine what insights can be gained through the use of careful statistical techniques. In statistical terms, interest in this article centers on the conditional distribution of industrial Y given K and L, and economic theory guides the construction of the distribution. In other words, Koop (2001) imposes economic regularity conditions and assume inefficiency to have a one-sided distribution. The decomposition of output growth into components due to input, technical, and efficiency growth provides a convenient way of thinking about model extensions. For any new possible explanatory variable, one can ask whether it should affect: (1) the input component and thus should enter as an input, (2) the technical change component and thus should affect the frontier parameters directly, or (3) the efficiency component, in which case it should enter the efficiency distribution. This approach is in contrast to the cross-sectional regression articles that consider a myriad of possible additional explanatory variables. Statistically, this translates into consideration of the distribution of Y conditional on K, L, and many other variables. However, the investigation of such a complicated distribution typically involves select-ing only a few out of a potentially enormous number of conditioning variables. Given the restrictiveness of such a statistical model and the lack of robustness in cross-country growth regressions (see

Levine and Renelt 1992), Koop (2001) argues that the present approach is, at the very least, a reasonable alternative. It is worth noting that the present approach can be thought of as using economic theory to move one step away from reduced-form regression approaches. The existence of a best practice technology that is non decreasing in inputs is the only economic theory used. Some theories of industrial organization (see Caves and Barton 1990), for example, imply that increased openness to imports should increase efficiency in an industry. This means that the openness variable should enter the efficiency distribution and not the production frontier itself.

However, much of the empirical economic growth literature assumes constant returns to scale. For instance, the growth accounting literature typically imposes constant returns to scale and sets the marginal products of labor and capital equal to their shares in total income (Barro and Sala-I-Martin, 1995). Econometric approaches with constant returns to scale (Romer, 1994) also exist. A rough summary of the findings of both these approaches is that they impose constant returns to scale and find the marginal product of capital to be around 0.4, at least for the OECD countries (Barro and Sala-I-Martin, 1995). Furthermore, Koop, Osiewalski, and Steel (1999, 2000), using different data sets and models, find results that are consistent with those of Koop (2001).

Koop (2001) is related to the growth accounting literature (Maddison 1987), which decomposes output growth into two parts: one explained by input changes and the other the unexplained residual, or "technical change." Growth accounting techniques have been used in a wide variety of empirical studies, and many of these articles have increased the understanding of economic growth. However, the interpretation of the unexplained residual as technical change is unreasonable unless it is assumed that all industries in all countries are producing on their frontiers. In contrast, by making some reasonable assumptions, the model of this article allows me to give a structural interpretation to the unexplained residual. Koop (200d1) interprets this residual as a combination of inefficiency and measurement error. Technical change is associated with the movement of the best-practice production frontier.

To conclude, Koop (2001) article is intended to be an empirical study of manufacturing output growth in OECD countries. However, it is also intended to develop and motivate new models and econometric techniques for working with industrial data. However, it is relevant to digress briefly to discuss more general modeling issues that might be relevant in other data sets.

Koop (2001) explores the driving forces of output growth in six manufacturing industries during the 1970s and 1980s, while Kneller and Stevens (2006) investigate the sources of inefficiency in nine industries over the same period. With the exception of Koop (2001), who estimates six frontiers for six industries, these studies all benchmark industries (countries) against a common production frontier. However, it may well be the case that not all industries share a single common frontier. Recent theoretical and empirical contributions (Basu and Weil, 1998; Los and Timmer, 2005) have stressed the ‘appropriateness’ of technology as industries (countries) choose the best technology available to them, given their input mix. Industries are members of the same technology club if their marginal productivity of labor and capital (the technology parameters that characterize the efficient production frontier) are the same for a given level of inputs. In other words, their input/output combinations can be described by the same production frontier (Jones, 2005). With the exception of a handful of studies that accommodate these technology clubs, therefore, allowing for parameter heterogeneity when estimating frontier or conventional production functions, the empirical (frontier) literature has largely ignored this issue.

Bos et al. (2010) investigate the forces driving output growth in a panel of manufacturing industries over the period 1980–1997. Relevant past studies typically assume that: (i) industries use resources efficiently and (ii) the underlying production technology is the same for all industries. Technical change is a crucial component for growth for industries, while input (capital, in particular) growth plays an important role. Policy makers generally agree that higher R&D spending is desirable and are willing to subsidize and/or give tax credits to industries that engage in R&D.

According to results, the effects of an increased R&D effort depend on the allocation of R&D tax credits/subsidies. Bos et al. (2010) also find some evidence of a positive relationship between R&D and efficiency. Therefore, a preliminary conclusion can be

that increasing the R&D effort facilitates the absorption of existing technologies.

However, increases in R&D effort do not always lead to increased technical growth.

Bos et al. (2010) allow for different production technologies, differing from past attempts, which mainly relied on ex ante divisions to classify industries into different technology clubs, by endogenizing the technology club allocation, augmenting the stochastic frontier production model with a latent class structure. A logit model is used to condition group membership probabilities on technological effort as measured by R&D. As a result, technology parameters depend on the effect of the technological effort on club membership probabilities. Production function parameters differ across clubs and are estimated simultaneously with membership probabilities. Based on club-specific production parameters, Bos et al. (2010) identify technical, efficiency and input growth for endogenously determined technology clubs, introducing further flexibility to the model by permitting industries to switch between technology clubs overtime. The efficiency of industries in different technology clubs is estimated simultaneously, but relative to each club’s specific frontier. Thus, the latent class stochastic frontier model avoids the imposed assumption of a common production function for all industries, while still yielding results that are comparable across industries at a given point in time.

Kumar and Russell (2002) suggest that economic growth convergence can be considered as the movements of countries toward a world production frontier. In Kumar and Russell (2002)analysis, the world production frontier is constructed using deterministic methods requiring no specification of functional form for the technology, nor any assumption about market structure or the absence of market imperfections. Then, using DEA analysis, they analyze the evolution of the cross-country distribution of labor productivity, decomposing labor-productivity growth.

More specifically, Kumar and Russell (2002) used production-frontier methods to analyze the evolution of the distribution of labor productivity in terms of decomposition into three components; technological change, technological catch-up, and capital accumulation. Labour-productivity growth is decomposed into technological change, technical efficiency change and a capital accumulation effect, and then they analyse the contribution of these components to convergence.

This approach originally employed by Kumar and Russell (2002) enables decomposing the growth of labor productivity growth into some components to empirically analyze economic growth, namely into efficiency change, technological change and capital deepening (Yamamura and Inyong, 2007):

technological catch-up (movements toward or away from the frontier):

technological catch-up does not seem to have been a force for convergence as relatively rich as well as poor countries have benefited from catch-up.

technological change (shifts in the world production frontier): Technological change has not been neutral, apparently benefiting rich countries more than poor.

capital accumulation (movement along the frontier): It is primarily capital deepening, as opposed to technological change or catch-up, that has contributed the most to both growth and bipolar international divergence of economies.

Kumar and Russell (2002) conducted not only regression analysis but also distribution hypothesis tests for examining the relative contribution of components of productivity changes to changes in the distribution of labor productivity. Through regression analysis, they examined how the initial output per worker has an effect upon these components. By using Penn World data, Kumar and Russell (2002) decomposed labor-productivity growth into the three components to construct a cross section dataset. They conduct a very simple regression model in which independent variables are the output per worker in 1965 and the dependent variables are the percentage change between 1965 and 1990 in output per worker, technology change, efficiency index, and the capital accumulation index. In spite of their long term analysis covering over 25-year period, the analysis of Kumar and Russell (2002) conducted a very simple regression model devoid of international time specific, countries’

specific, and any socioeconomic variables. Since the lack of these variables results in the omission of variable bias, they are generally included or controlled for in the micro economic analysis to reduce the bias. Kumar and Russell (2002) also recognized that there are caveats; potentially important variables (e.g., human capital and natural resources) are omitted, and long-run analysis has not taken short-run economic fluctuations into account. Kumar and Russell (2002) concluded that

technological change is decidedly non neutral and that both growth and bipolar international divergence are driven primarily by capital deepening. However, the major contribution of Kumar and Russell (2002) was that they built a bridge between the two streams of literature: macroeconomic convergence and technology frontier estimation. One of the main conclusions of their study was that: It is primarily capital deepening, as opposed to technological catch-up, that has contributed the most to both growth and bipolar international divergence of economies⁹³.

A major drawback of the Kumar and Russell (2002) work is that the results of their estimations are biased because they omitted country specific variables such as human capital, natural resources and the year specific variables capturing international time trends. The empirical results through a fixed effects regression model show that the initial level of productivity has a negative effect on the contribution of efficiency to productivity growth, which implies that technological catch-up has done much to cause economic convergence among countries. Moreover, they ignored the unobservable individual or time effects and did not pay attention to the possibility that their estimators suffered from an omission bias. Further, Badunenkoy and Zelenyukz (2004) found that, if year dummy variables are incorporated, the relation between the initial level of productivity and the change in capital accumulation is not negative but positive. These results are contrary to the assertion of Kumar and Russell (2002).

Using data envelopment analysis, Angeriz et al. (2006) calculate indices of total factor productivity (TFP), efficiency and technological change for the manufacturing industries of 68 European NUTS1 regions over the period 1986–2002. They subsequently examine these indices using exploratory spatial data analysis techniques, before considering tendencies towards convergence in both TFP and technical efficiency levels. While the analysis reveals significant spatial autocorrelation, the convergence analysis uncovers no tendency for regions with initially lower TFP to

93 During the period Kumar and Russell (2002) studied, between 1965 to 1990, fast growing countries (e.g. Asian Tigers) which have undergone heavy capital accumulation (Mankiw et al., 1992).

Noteworthy, the effect of computers on economic growth during that time was found to be negligible, but quite considerable during the 90's (Brynjolfsson and Hitt, 2000).