A comparison of pre- and post-crisis efficiency of OECD countries: evidence from a model with temporal heterogeneity in time and unobservable individual effects.

• Author: Matkovskyy, Roman
• Position: Report

1. Introduction

   The importance of taking measures of efficiency and productivity, as well as their further benchmarking to improve the performance of any economic system, is recognised. These measures are success indicators and performance metrics (Fred et al, 2008, p.7-15). In general, to estimate efficiency one can compare observed performance (values) to some optimal values, or to some maximum potential output obtained from the available input. Optimum values can be defined in terms of the production possibilities of countries. Although "true" potential is unknown, it is possible to observe best practice, its evolution over time and its variation among countries. Thus, it refers to an operation on a best-practice "frontier" that leads to the identification of countries with the best performance, and further benchmarking performance of the rest against those of the best. Efficiency in this case is derived as the evaluation of observed outputs as compared to maximum potential outputs obtainable from the given inputs. This defines efficiency as technical efficiency.

   Technical efficiency, or its opposite term--inefficiency, is a heterogeneous phenomenon and varies both over time and across countries. According to Kose et al. (2008), heterogeneity across countries matters, despite the common evolution of business cycles. Macro factors largely drive heterogeneities since they define initial conditions for business and ways in which economies absorb shocks. Nowadays, economies are increasingly interconnected and integrated in all areas of economic activity. The literature has already highlighted the role of heterogeneity and interdependency in economic development (e.g., Chaserant and Harnay, 2013; Tamborini, 2014). The significant role of interdependency was also demonstrated during the recent global financial crisis (e.g. Dallago, 2013; Vollmer and Bebenroth, 2012). It is possible to assume that an estimation of efficiency on a macro level is sensitive to heterogeneity. Ignoring heterogeneity on a macro level may cause estimates to become highly biased which may lead to misinterpretations. This, therefore, is the motivation behind a study of technical efficiency on a macro level with respect to heterogeneity in various dimensions.

   Classical approaches to heterogeneity are based on panel models, which try to account for heterogeneity, including unobserved heterogeneity, by using dummy variables or structural assumptions on an error term (Baltagi, 2005; among others). Nevertheless, this approach has limitations, because unobserved heterogeneity is assumed to be constant over specified time. Extending classical models with a factor structure is one of the effective ways to deal with unobserved time-varying heterogeneity. This approach can provide a parsimonious specification which identifies the effects of unobserved heterogeneity on the outcomes of interest, allowing for access to time-varying technical efficiency.

   This paper focuses mainly on shifts in technical efficiency of OECD countries that are caused by the global financial crises, heterogeneity and interdependencies. The motivation for this is instigated by the great variety in the initial economic conditions and development of OECD countries on the one hand, and their high integratability, on the other hand. In this study OECD countries are analyzed as production units. Their outputs are real GDP and export of goods and services. Whilst inputs are limited to labor (the number of employed), capital (gross fixed capital formation) and import of goods and services. Thus, a dataset is formed for 34 OECD countries (1), including the abovementioned 2 outputs, 3 inputs, and covering the 2000Q1-2014Q4 period.

   This paper contributes to previous literature by computing and comparing technical efficiency in terms of productivity growth for each OECD country taking into consideration an arbitrary temporal heterogeneity through time to minimize bias and improve inference. For this purpose, the estimation of parameters and residuals of the panel model that has temporal heterogeneity through a time and factor structure (a model with unobservable individual effects) is based on a novel semi-parametric approach developed by Bai (2009) and Kneip et al. (2012). Another issue that is addressed in this paper is the one of missing values, which is the endemic problem for researchers working with economic indicators for a set of countries. Since the dataset should be balanced for heterogeneity estimation, a bootstrapping-based algorithm in the spirit of King et al. 2001, Honaker and King 2010--allowing for trends in time series across observations within cross-sectional units--is applied for multiple imputations. This keeps all OECD countries within the analysis.

   The results received help to shed light on current issues that have gained growing attention from researchers and practices in terms of comparative studies of different economies, and they contribute to the attempt to develop tools for better understanding of unobserved factors that drive fluctuation in economic development across countries, including OECD countries.

   The plan of the paper is as follows. In second chapter a theoretical framework of the research is described. Attention is paid to a radial stochastic frontier, a Cobb-Douglas production function, and an arbitrary temporal heterogeneity in time panel model. The third chapter introduces empirical results and discussion. The fourth chapter contains a summary and concluding remarks.

2. Theoretical framework and model set-up

   In the last decade, a number of research projects have been developed to estimate and benchmark performance measures on a macro level by applying various approaches, e.g., Cherchye et al. (2004), Despotis (2005), Ravallion (2005), Yoruk and Zaim (2005), etc. Within the framework of the current study, methods which are well-established in the field of production theory are used. There are two fundamental ways to deal with efficiency estimation: the frontier approach that was introduced by Farrell (1957) and the non-frontier approach, initially developed by Solow (1957) and Griliches and Jorgenson (1966). As the main idea of this study is to compare the productivity growth across OECD nations the stochastic frontier approach, proposed by Aigner, Lovell and Schmidt (1977) and Meeusen and van cave Broeck (1977), and further developed by Schmidt and Sickles (1984), is chosen as a starting point. Furthermore, these models are particularly suitable when countries cannot entirely control their deviations from a production frontier due to external influences, e.g. crises. Thus, this study is based on the properties of the traditional micro-economic theory of production. A radial stochastic frontier and a Cobb-Douglas production function are used as back-bone models. Detailed reviews of these models are provided by Forsund et al. (1980), Kumbhakar and Lovell (2000), Kumbhakar (2006), and Greene (2008), among others. The application of these methods is done in the similar way, as in Matkovskyy (2015a, 2015b).

   Two main types of estimation techniques are discussed in the literature on technical efficiency analysis. The first one includes econometric techniques that represent a stochastic approach. The second one is mathematical programming techniques that are nonparametric methods of the estimation. Econometric techniques allow for incorporating statistical noise, which is an advantage in comparison to mathematical programming, which does not naturally produce these estimates. Therefore, in this paper econometric techniques are used in a semi-parametric way, which allows for arbitrary temporal heterogeneity in time with a factor structure.

   2.1. Stochastic Frontier Model

   Let us denote a vector of output as Y, and an input requirement set as X. Thus, a production process can be formalized as

   L(Y) = {X: (Y,X) is producible}.

   The production function can be defined in terms of the efficient subset as an isoquant (Y) = {X: X [memebr of] L(Y)}.

   Broadly speaking, productivity can be defined as the ratio of output to input. Efficiency means a comparison between observed and optimal values of its output and input. Thus, the optimum is defined in terms of production possibilities and efficiency is technical and can be estimated as a comparison between the observed output and maximum potential output obtainable from the given input.

   According to Debreu (1951) and Farrell (1957), a production function can be formalized as Y [less than or equal to] f (X). Since a country uses several inputs to produce several outputs, both the outputs and the inputs should be aggregated in some economically sensible way. Adams et al. (1999) proposed a persuasive m-output and n-input deterministic distance function for efficiency estimation, D(Y, X) [less than or equal to] 1, that estimates a radial measure of technical efficiency in the following way:

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

   where Y is an aggregated output, X is a given input, [[gamma].sub.j] and [[delta].sub.k] are weights of outputs and inputs that describe a country's technology, respectively.

   A stochastic frontier model can be specified as the Cobb-Douglas production function:

   [Y.sub.it] = f([X.sub.it]) - [u.sub.it] + [[epsilon].sub.it], (2)

   where (-[u.sub.it] + [[epsilon].sub.it]) represents a composed error term, where is statistical noise, and [u.sub.it] is a country's specific level of radial technological efficiency. Then, according to Lovell et al. (1994), Equation (1) can be rewritten as

   0 = [[summation].sup.m.sub.j=1] [[gamma].sub.j] ln [y.sub.j,it] - [[summation].sup.q.sub.k=1] [[delta].sub.k] ln [x.sub.k,it] + [v.sub.it] + [[epsilon].sub.it], (3)

   then

   ln [y.sub.j,it] = [[summation].sup.m.sub.j=1][[gamma].sub.j](- ln [[??].sub.j,it]) - [[summation].sup.q.sub.k=1] [[delta].sub.k](- ln [x.sub.k,it]) - [v.sub.i](t) + [[epsilon].sub.it], (4)

   where [y.sub.j,it] is the normalized...