(UNOBSERVED) HETEROGENEITY Tommaso Agasist

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Department of Economics and Statistics, University of Salerno, Via Giovanni Paolo II, ... 1991; Archibald and Feldman, 2008) and Europe (especially in UK, see Johnes, ..... weighting by their degree classification: In all cases results are similar.
WORKING PAPER No 700

Società italiana di economia pubblica

novembre 2015

 

EVALUATING THE EFFICIENCY OF ITALIAN PUBLIC UNIVERSITIES (20082011) IN PRESENCE OF (UNOBSERVED) HETEROGENEITY

Tommaso Agasisti, Politecnico di Milano Cristian Barra, Università di Salerno Roberto Zotti, Università di Salerno

JEL Classification: I24, I23, C14, C67 Keywords: efficiency, unobserved heterogeneity, higher education

società italiana di economia pubblica c/o dipartimento di scienze politiche e sociali – Università di Pavia

Evaluating the efficiency of Italian public universities (2008-2011) in presence of (unobserved) heterogeneity Tommaso Agasisti1 Cristian Barra2 Roberto Zotti2

Abstract In assessing universities’ performances, the most recent literature underlined that the efficiency scores may suffer from the presence of incidental parameters or time-invariant, often unobservable, effects that lead to biased efficiency estimates. To deal with this problem, we apply a procedure developed by Wang and Ho (2010), for estimating the efficiency in Italian higher education through a multi-output parametric distance function. We show that models which do not consider unobservable heterogeneity tend to estimate higher efficiency scores; we also study the determinants of efficiency. The findings provide a clue towards the expansion of pro-competitive policies in the Italian higher education sector, consistently with the interpretation that when market forces operate, there are benefits for university efficiency. When exploring differences in universities’ performances, by geographical areas, we claim that maintaining State-level policies can be detrimental for overall efficiency, and instead special interventions for universities in the South should be designed. Keywords: Efficiency, unobserved heterogeneity, higher education JEL Codes: I24; I23; C14; C67

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Department of Management, Economics & Industrial Engineering, Politecnico di Milano, P.za Leonardo da Vinci, 32 – 20133 – Milano (MI) – Italy. E-mail: [email protected] 2 Department of Economics and Statistics, University of Salerno, Via Giovanni Paolo II, 132 - 84084 - Fisciano (SA) – Italy. Email: [email protected]; [email protected]

1.

Motivation and objectives

The analysis of universities’ costs is at the hearth of institutional and academic debates since when Cohn et al. (1989) identified these organizations as multi-output, thus posing the challenge of measuring their scale and scope effects. Following this seminal study, several papers attempted at measuring the productivity of Higher Education Institutions (HEIs) – defined as the ratio between costs and output – in the USA (see, for instance, de Groot et al., 1991; Archibald and Feldman, 2008) and Europe (especially in UK, see Johnes, 1997; Glass et al., 2006; Thanassoulis et al., 2011). As widely discussed by Johnes (2004b), the problem of assessing HEIs’ economic performances in also exacerbated by inefficiency in production; then, when modeling production and cost functions, it must be kept in mind that HEIs are likely to produce using their inputs in a suboptimal way. The method proposed by Johnes (2006d) for measuring the efficiency in this context is Data Envelopment Analysis (DEA), as it allows estimating non-parametrically the degree of suboptimal production, by benchmarking each institution against best performers in the sample. Nonetheless, recent extensions of “robust” non-parametric methods provide a bootstrap approximation to the asymptotic distributions of efficiency estimators (for an overview, see Daraio and Simar, 2007). The alternative to the use of non-parametric technique is employing econometric models for estimating the production or cost function. The approach for incorporating inefficiency into the estimation of production is the method named Stochastic Frontier Analysis (SFA), proposed by Aigner et al. (1977) and Meeusen and Van den Broeck (1977); SFA has been extensively applied in the literature for measuring efficiency in the higher education environment. Econometrically, the method assumes that the error term is composed by two components with different distributions (see Kumbhakar and Lovell (2000) for analytical details on stochastic frontier analysis). The first component, regarding the “inefficiency”, is asymmetrically distributed (typically as a semi-normal), while the second component, concerning the “error”, is distributed as a white noise. In this way, it is necessary to assume that both components are uncorrelated (independent) to avoid distortions in the estimates. Nowadays, the most widely applied SFA technique is the model proposed by Battese and Coelli (1995) to measure technical efficiency across production units. This approach is particularly suitable considering our context, as one of the main advantages of SFA is that statistical inference can be drawn, obtain information on the determinants of inefficiency and consequently the estimated parameters may attract the interest of regulators and decision makers towards the adoption of improving policies in the higher education sector. On a methodological ground, the most recent literature, which deals with panel data, emphasized the importance of separating inefficiency and fixed individual effects. Indeed, the efficiency scores may suffer from the presence of incidental parameters (number of fixed-effect parameters) or time-invariant effects, often unobservable, that may distort the estimates. For instance, students’ or researchers (average) innate ability may be an important determinant of their individual academic achievement and thus account for an important share of the heterogeneity in data when evaluating the efficiency of the institution in which they are studying or working. As Wang and Ho (2010) have underlined: “(…) stochastic frontier models do not distinguish between unobserved individual heterogeneity and inefficiency”, forcing “all time-invariant individual heterogeneity into the estimated inefficiency”. In the context of the use of efficiency models for policy-making, or managerial considerations, the problem of separating the three elements: (i) unobserved structural differences in underlying inputs, (ii) inefficiency and (iii) production process is of crucial importance. Indeed, the lack of judgment

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about the various parts would lead to a misleading (under)evaluation of estimated inefficiency. Such a topic has been systematically investigated by Greene (2005), who examined different ways to incorporate heterogeneity; his findings demonstrate that different models produce very different results. In particular, he analysed several extensions of the stochastic frontier that account for unmeasured heterogeneity as well as firm inefficiency (an application of these methods to the analysis of universities’ efficiencies is in Johnes and Johnes, 2009, and Agasisti and Johnes, 2010). A quite different approach is promoted by Wang and Ho (2010) who, in order to incorporate heterogeneity in panel data in the stochastic frontier model, show that first-difference and within transformation can be analytically performed on this model to remove the fixed individual effects, and thus the estimator is immune to the incidental parameters problem (the latter being somehow affecting the methods proposed by Greene, 2005). In other words, after transforming the model, the fixed effects are removed before the estimation. This paper’s main objective is to apply the procedure developed by Wang and Ho (2010) for estimating the efficiency of Italian HEIs through a multi-output, parametric distance function, using data over the four-years 20082011; this way, the estimated efficiency is net of the influence of unobserved heterogeneity. To the best of authors’ knowledge, this is the first paper that attempts at separating inefficiency from heterogeneity when assessing the performances of Italian universities, with the only notable exception of Agasisti and Johnes (2010), who however used the Greene (2005) method for this purpose. This paper is innovative because of two other reasons. Firstly, it tests the effects of assuming different functional forms of universities’ production (cost) functions. While the theoretical problem of identifying the “correct” functional form of HEIs’ production processes is discussed in the literature (see, for instance, Cohn and Cooper, 2004; Johnes, 2004a) the empirical tests about how different forms affect estimations are quite sparse. The topic itself is important in a managerial perspective; indeed, it is important to check whether the judgment about efficiency is affected by the assumptions behind the production process or not. In this paper, we conduct such tests systematically: we start the empirical analysis assuming a translog functional form for the output distance function, with and without input-output separability property. Furthermore, we also consider a Cobb-Douglas formulation (see Section 2 for a discussion in the different assumptions of the production process). To anticipate the findings, the functional form chosen seems to have a minor impact on main estimates, then we consider them empirically robust. Secondly, this paper directly investigates whether the efficiency of universities is influenced by some characteristics of the market structure in which they operate. More specifically, we look at the effect of variables like an indicator of market share (MK), the level of fees (FPS), and wealth – as measured through added value per capita (AV) - in the areas (Regions) where universities operate. This policy-oriented analysis is particularly relevant given that since the 1990s the Italian university system has been characterized by policy interventions that stimulate competition between universities (Agasisti, 2009)1. The paper is organized as follows. In the Section 2, we present the methodological approach; Section 3 illustrates the data, production set and model specification for the empirical analysis; Section 4 contains the main results.

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See Agasisti (2009), Potì and Reale (2005), Bini and Chiandotto (2003) and Buzzigoli et al. (2010) for a brief review of the university system in Italy.

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Finally, Section 5 discusses the managerial and policy implications of the main findings, together with concluding remarks.

2.

Empirical Methodology

The presence of a multidimensional nature of the production (i.e. multiple outputs) may represent a problem when estimating stochastic production models. To solve this issue, a distance function approach has been considered (Lovell et al., 1994; Coelli and Perelman, 2000). Moreover, this technique is particularly useful when no price information regarding inputs and outputs is available (Coelli, 2000). Specifically, and following Abbott and Doucouliagos (2003) and Johnes (2014), we choose to model the production set through an output distance function in a panel context. Furthermore, as already mentioned before, we are aware that the estimates of the frontier and then, consequently, the efficiency scores suffer by the presence of incidental parameters or time-invariant effects that may distort the estimates. In order to deal with this problem and to estimate the technical efficiency, we apply a procedure developed by Wang and Ho (2010), according to whom after transforming the model by either first-difference or within-transformation, the fixed effects are removed before estimation. More specifically, we impose to data a within transformation. As Wang and Ho (2010) specified, “by within-transformation, the sample mean of each panel is subtracted from every observation in the panel. The transformation thus removes the time-invariant individual effect from the model”. Following the notation in Wang and Ho (2010), the transformation employed in our model is (being 𝑤 any variable to be transformed): 𝑇

𝑤𝑖. = (1/𝑇) ∑ 𝑤𝑖𝑡 , 𝑤𝑖𝑡. = 𝑤𝑖𝑡 − 𝑤𝑖.

(1)

𝑡=1

The stacked vector of 𝑤𝑖𝑡. for a given i is: 𝑤 ̃𝑖. = (𝑤𝑖1. , 𝑤𝑖2. , … , 𝑤𝑖𝑇. )′

(2)

For simplicity, hereafter in our formulation does not include a subscript t. The baseline model associated to distance function after the transformation can be written as: 𝑓(𝑦̃𝑖. ) = 𝑓(𝑥̃1. , … 𝑥̃𝑛. ) + 𝜀̃𝑖.

(3)

where 𝑦̃ represents the conventional outputs, 𝑥̃ denotes the conventional inputs and 𝜀̃ denotes the disturbance term. With stochastic frontier analysis, a frontier is estimated on the relation between inputs and outputs. This can, for example, be a linear function, a quadratic function or a translog function. This paper uses both translog and a CobbDouglas function. However, there is no general consensus about which one has to be adopted in the higher education environment (for a discussion on the different function forms, see Cohn and Cooper, 2004 and Agasisti and Johnes,

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2009b). Firstly, concerning the structure of production possibilities, a more general functional form, that is, the transcendental logarithmic, or “translog”, could be considered for the frontier production function. The translog functional form may be preferred to the Cobb–Douglas form because of the latter’s restrictive elasticity of substitution and scale properties, it allows for non-linear causalities, compared with the more simple Cobb-Douglas function (see Agasisti and Haelermans, 2015, who use a translog function in order to compare the efficiency of public universities among European countries). On the other hand, the assumptions behind the use of Cobb–Douglas production functions are also plausible in view of the theoretical model which describes the human capital formation in the university system. It allows overcoming the multicollinearity problem associated to estimate a few number of parameters with respect to the translog function; therefore it is less susceptible to multicollinearity and degrees of freedom problems than the translog function (see Laureti, 2008, who uses a Cobb-Douglas function in order to model exogenous variables in human capital formation). Following common practice, we now assume a translog functional form for the output distance function: 𝑀

𝐾

𝑀

𝑁

𝐾

𝐿

1 ̃𝑖.𝑜 = ∑ 𝛼̃𝑚 𝑙𝑛𝑦̃𝑚𝑖. + ∑ 𝛽̃𝑘 𝑙𝑛𝑥̃𝑘𝑖. + [ ∑ ∑ 𝛼̃𝑚𝑛 𝑙𝑛𝑦̃𝑚𝑖. 𝑦̃𝑛𝑖. + ∑ ∑ 𝛽̃𝑘𝑙 𝑙𝑛𝑥̃𝑘𝑖. 𝑥̃𝑙𝑖. ] 𝑙𝑛𝐷 2 𝑚=1

𝐾

𝑘=1 𝑀

𝑚=1 𝑛=1

(4)

𝑘=1 𝑗=1

+ ∑ ∑ 𝛿̃𝑘𝑚 𝑙𝑛𝑥̃𝑘𝑖. 𝑦̃𝑚𝑖. 𝑘=1 𝑚=1

By within transformation, 𝛼𝑖 (intercept that changes over time according to a linear trend with unit-specific timevariation coefficients and that represents time-invariant effects) disappears from our specification. In addition, time dummies are also included in the model in order to capture exogenous factors that might affect the production set. Normalizing by 𝑦̃𝑖 2, that guarantees the linear homogeneity of degree 1 in outputs (∑𝑀 ̃ 𝑚 = 1) as suggested by 𝑚=1 𝛼

̃ Lovell et al. (1994), and imposing the linear (∑𝑀 ̃ 𝑚𝑛 = 0 and ∑𝑀 𝑚=1 𝛼 𝑚=1 𝛿𝑘𝑚 = 0) and suitable symmetry restrictions (𝛼̃𝑚𝑛 = 𝛼̃𝑛𝑚 and 𝛽̃𝑘𝑙 = 𝛽̃𝑙𝑘 ), the output oriented distance function becomes: 𝑀

𝐾

𝑀

𝑁

𝐾

𝐿

̃𝑖.𝑜 𝐷 ∗ ∗ ∗ 𝑙𝑛 ( ) = ∑ 𝛼̃𝑚 𝑙𝑛𝑦̃𝑚𝑖. + ∑ 𝛽̃𝑘 𝑙𝑛𝑥̃𝑘𝑖. + 1/2[ ∑ ∑ 𝛼̃𝑚𝑛 𝑙𝑛𝑦̃𝑚𝑖. 𝑙𝑛𝑦̃𝑛𝑖. + ∑ ∑ 𝛽̃𝑘𝑙 𝑙𝑛𝑥̃𝑘𝑖. 𝑥̃𝑙𝑖. ] 𝑦̃𝑖. 𝑚=1

𝑘=1

𝐾

𝑚=1 𝑛=1

(5)

𝑘=1 𝑗=1

𝑀

∗ + ∑ ∑ 𝛿̃𝑘𝑚 𝑙𝑛𝑥̃𝑘𝑖. 𝑙𝑛𝑦̃𝑚𝑖. 𝑘=1 𝑚=1

∗ ∗ where 𝑦̃𝑚𝑖. = 𝑦̃𝑚𝑖. /𝑦̃𝑖. , 𝑦̃𝑛𝑖. = 𝑦̃𝑛𝑖. /𝑦̃𝑖. and thus 𝑦̃𝑖. = 1. In addition, the time dummies are also taken into account in

order to capture exogenous or business cycle effects that can influence the production process of the decisioñ𝑖.𝑜 ) is not observable. Then, in order to solve this problem, we making units (i.e. universities). It’s obvious that 𝑙𝑛(𝐷 ̃𝑖.𝑜 /𝑦̃𝑖. ) = 𝑙𝑛(𝐷 ̃𝑖.𝑜 ) - 𝑙𝑛(𝑦̃𝑖 . ). Thus, we transfer 𝑙𝑛(𝐷 ̃𝑖.𝑜 ) to the residuals, i.e. on the right and side of can re-write 𝑙𝑛(𝐷 2

Since they are mathematically equivalent, the choice of the normalizing variable is innocuous (see Restrepo-Tobon and Kumbhakar, 2013, p. 16). Then, we normalize by grants for research.

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the equation (5), and ue −𝑙𝑛(𝑦̃𝑖. ) as dependent variable (Coelli and Perelman, 2000). In our case, we follow Paul et al. (2000), i.e. imposing 𝑙𝑛(𝑦̃𝑖 ). The equation (5) thus becomes: 𝑀

𝐾

𝑀

𝑁

𝐾

𝐿

∗ ∗ ∗ 𝑦̃𝑚𝑖. 𝑦̃𝑚𝑖. 𝑦̃𝑛𝑖. 𝑙𝑛(𝑦̃𝑖. ) = ∑ 𝛼̃𝑚 𝑙𝑛 ( ) + ∑ 𝛽̃𝑘 𝑙𝑛𝑥̃𝑘𝑖. + 1/2[ ∑ ∑ 𝛼̃𝑚𝑛 𝑙𝑛 ( ) 𝑙𝑛 ( ) + ∑ ∑ 𝛽̃𝑘𝑙 𝑙𝑛𝑥̃𝑘𝑖. 𝑥̃𝑙𝑖. ] 𝑦̃𝑖. 𝑦̃𝑖. 𝑦̃𝑖. 𝑚=1

𝑘=1

𝐾

𝑀

𝑚=1 𝑛=1

∗ 𝑦̃𝑚𝑖.

+ ∑ ∑ 𝛿̃𝑘𝑚 𝑙𝑛𝑥̃𝑘𝑖. 𝑙𝑛 ( 𝑘=1 𝑚=1

𝑦̃𝑖.

(6)

𝑘=1 𝑗=1

) + 𝑣̃𝑖 − 𝑢̃𝑖

Where 𝑣̃ is the vector of random variables assumed to be i.i.d. 𝑁(0, 𝜎𝑣̃2 ) and independent of the 𝑢̃ term which stands for inefficiency component. In particular, 𝑢̃ is assumed to be heteroschedastic and, in particular, distributed as 𝜎̃̃2 =

(𝑧̃𝑖 ̃ ) following a half-normal distribution, i.e. 𝑁 + (0,1), where 𝑧̃𝑖 is a vector of environmental variables

employed to explain determinants of inefficiency, and ̃ denotes a vector of unknown coefficients. In this analysis, we do not impose the “scaling property” (for more details see Wang and Schmidt (2002), in the context of crosssectional data, and Alvarez et al. (2006), in the panel data context); indeed, as underlined by Wang and Ho (2010), “whether the scaling property holds in the data is ultimately an empirical question”. In other words, we assume changes not only in scale but also in the shape of the inefficiency distribution. The validity of the heteroschedastic assumption is tested using a LR test which allows us to identify the fit of the model and to confirm the imposition of some explanatory factors in the variance of the inefficiency term. As already said, we estimate the function above described in a panel context, employing within transformation as recently suggested by Wang and Ho (2010) in order to eliminate the incidental parameters from our estimation, under the hypothesis of efficiency variability over time. Once singled out the best practice frontier from translog output distance function model, we compute the efficiency scores as deviations from this frontier. For comparison, we model the last equation with (i) no input-output separability; (ii) input-output separability and (iii) Cobb-Douglas formulation. The rationale for employing three different functional forms relies upon the opportunity of verifying how these are affecting the efficiency estimates (i.e. whether the assumptions about the specific combination of inputs in producing the outputs influence the efficiency scores). The coefficients 𝛼̃, 𝛽̃ , 𝛿̃, ̃ and technical efficiency are estimated through a maximum likelihood estimator (MLE) using the STATA 12 software. 3.

Data, the production set and model specification

3.1. Data and production set The dataset refers to Italian public universities from years 2008 to 2011 and it has been constructed using data which are publicly available on the National Committee for the Evaluation of the University System (CNVSU) website. We exclude all private sector universities, owing to the absence of comparable data on academic research variables;

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this leaves us with a sample of 53 universities 3, each of which yields data over the four year period, so we have a total of 212 observations. Referring to the literature on this subject, the production technology is specified, with three inputs: 1 – number of academic staff; 2 - percentage of enrolments with a score higher the 9/10 in secondary school; 3 - total number of students. More specifically, the first input is the number of academic staff (ACAD STAFF). It is a measure of a human capital input and it aims to capture the human resources used by the universities for teaching activities 4 (see Johnes, 2014; Agasisti and Dal Bianco, 2009). The second inputs is the percentage of enrolments with a score higher the 9/10 in secondary school (ENRHSG) with respect to the total number of students enrolled (a similar measure is used in Agasisti and Dal Bianco, 2009). Indeed, among the inputs that are commonly known to have effects on students’ performances there is the quality of the students on arrival at university. There is strong evidence that pre-university academic achievement is an important determinant of the students’ performances (Boero et al., 2001; Smith and Naylor 2001; Arulampalam et al., 2004; Lassibille 2011). The underlying theory is that ability of students lowers their educational costs and increases their motivation (DesJardins et al., 2002). Thus this input aims to capture the quality of students on arrival at university (i.e. it is a proxy of the knowledge and skills of students when entering tertiary education). The third and last input is the total number of students (STUD) in order to measure the quantity of undergraduates in each university (Agasisti and Dal Bianco, 2009)5. Two measures of outputs are included in the model reflecting the teaching and research functions of HEIs 6: 1 – number of graduates; 2 – research grants. The first output is the number of graduates weighted by their degree classification (GRADMARKS), in order to capture both the quantity and the quality of teaching 7 (see Worthington and 3

Which is very representative of the higher education system in Italy, corresponding to almost 90% of the total number of public universities in the country. 4 The variable ACADSTAFF indicates the number of total academic staff adjusting for the respective academic position. Specifically, the academic staff has been disentangled in four categories, namely professors, associate professors, assistant professors and lectures. In order to take into account this categorization, we assign weights to each category according to their salary and to the amount of institutional, educational and research duties the academic staff has to deal with (see Madden et al. 1997) and assuming that a professor is expected to produce more research and teaching work than an associate professors and so on (see Carrington et al. 2005). We follow Halkos et al. (2012) where professors are assigned with 1, associate professors with 0.75, assistant professors with 0.5 and lecturers with 0.25. They basically choose weights so that the distance between two ranks is 1/4=0.25. Thus, we use the following aggregate measure of human capital input: Equivalent personnel (EP)=1*professors+0.75*associate professors+0.50* assistant professors +0.25* lectures. Unfortunately, we do not have information on the auxiliary staff such as the administrative staff. 5 The second input (ENRHSG) is used as percentage in order to avoid a double counting problem due to presence of the total number of students (STUD) among the inputs. In this way we are able to measure the quantity of undergraduates in each university (through STUD) and include in the production process, at the same time, important information regarding the quality of the students enrolled in each university (ENRHSG). 6 Unfortunately, due to the unavailability of data, we are not able to consider what is known to be the third function of the universities such as knowledge transfer to industry and links of HEIs with industrial and business surroundings. 7 For the readers who are not familiar with the characteristics of the Italian higher education system, in Italy students can graduate obtaining marks from 66 to 110 with distinction. This grade is calculated mainly according to the average grades students have obtained in the exams; then a certain number of points is added after the final dissertation has been graded. In order to weight the graduates according to their degree marks, we apply the following procedure: GRAD MARKS =1* graduates with marks between 106 and 110 with distinction +0.75*graduates with marks between 101 and 105 + 0.5*graduates with marks between 91 and 100+0.25*graduates with marks between 66 and 90. The weights have been chosen so that the distance between two ranks is 1⁄ = 0.2 . For robustness, we also further test how alternative weights given to the GRAD MARKS variable, to avoid a severe discounting of the students earning less than top marks, would change the results as follows: GRAD MARKS=1*graduates with marks between 106 and 110 with distinction+0.75*graduates with marks between 101 and 105+0.5*graduates with marks between 91 and 100+0.50*graduates with marks between 66 and 90. We’ve also used just the number of graduates without weighting by their degree classification: In all cases results are similar.

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Lee, 2008; Johnes 2006c; Madden et al., 1997). The second output is a measure of research performances of the universities. Academic research is the most controversial output and different proxies have been used in the literature such as bibliometric indicators and peer review (De Groot et al., 1991), weighted indexes of publications (Athanassoupoulos and Shale, 1997; Johnes and Johnes, 1993; Tyagi et al., 2009; Johnes and Yu, 2008; Halkos et al., 2012). Information on the number of publications is not available to us, thus we use research grants (RES) as a second output and as a proxy of research outputs (see Abbott and Doucouliagos, 2003; Agasisti and Johnes, 2010; Kao and Hung, 2008; Agasisti and Johnes, 2009a; Agasisti et al., 2012; Worthington and Lee, 2008). According to Agasisti and Johnes, 2010, “Grants represent a measure of the market value of research done, and so provides a neat conflation of the quantity and quality of research effort. They also provide a measure of research output that is less retrospective than bibliometric analyses”. Research grants reflect the market value of the research conducted and can, therefore, be considered as a proxy for output (Cave et al., 1991; Tomkins and Green, 1988). Specifically, in our case, it represents the amount that the government is willing to pay the universities for the research they produce. We are aware that the use of grant income might raise some problems related to the presence of a lag between the publication of research output and the generation of that research; however, according to Hashimoto and Haneda (2008) this is more important when using citation counts or number of patents than research income measure. Moreover, according to Johnes (2014), the use of research grants as an output “is also an attractive measure of research in that it provides an up-to-date picture of research activity and output in the current academic year”. Thus, also considering that there are no clear criteria for deciding on the appropriate length of lag (Emrouznejad and Thanassoulis, 20058) and following Johnes (2014) we use a static model in our analysis. See also Frey and Rost (2010) for a discussion on the appropriate measures of research quality and quantity. When looking at the descriptive statistics (Table 1), it is interesting to notice that, considering the four geographical areas in which we have aggregated the universities and taking into account the inputs, the Southern area shows the lowest number of academic staff and, interestingly, the highest percentage of enrollments with a score higher than 9/10 in secondary school. The number of students is, instead, more stable across the areas. Considering the performances (output side) by geographical areas, again the North-Central areas outperform the Southern area both considering the number of graduates weighted by their degree marks and the grants received for the research activities. [Table 1] around here

3.2. Explaining (in)efficiency: the role of market competition It seems inadequate to assume that the variability of the efficiency behaviour is the same for each university. Therefore, given that several exogenous variables are available, the use of a heteroschedastic stochastic frontier 8

They develop a dynamic DEA model to capture the inter-temporal aspect, comparing the results of the dynamic model with those derived from a static (or conventional) DEA model in the context of higher education, and find considerable overall agreement between the efficiencies produced from the two approaches.

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model is particularly suitable for our analysis, to adequately measure the effects of exogenous characteristics on university inefficiency. Specifically, the market structure of the HEIs could play an important role in calculating the efficiency; indeed, as suggested by Agasisti (2009), “theoretical predictions in the economics of education are that a major increase in competition in the higher education sector must lead to greater efficiency, both from an allocative point of view (the choice of students will be more coherent with their utility function) and from a productive one (universities will obtain better performance without increasing costs, by managing more efficiently their resources)” even though there are not many empirical studies testing the effects of competition in tertiary education9 and most of them regard the US context (see for instance Allen and Shen, 1999; Brewer et al., 2002; Dill, 2003; Hoxby, 2000). It is also true that the character of competition among higher education institutions is complex to be analysed even though there are increasing calls for deregulating universities so that they can better compete in the global market for higher education. In order to study the determinants of inefficiency, we include in the variance of the inefficiency component the following three explanatory variables: market share (MK) measured as the ratio between the number of enrolments at university 𝑖 and the total number of enrolments in the universities located in the same region, included for capturing the potential effects due to the presence of more concentration or competition between universities; added value per capita (AV) corresponding to the difference between the production value of goods and services created by individual productive branches and the value of the intermediate goods and services consumed by them, with the aim of controlling for the growth of the economic system in terms of new goods and services made available to the community for final use10; fees per student (FPS) calculated as the ratio of the amount of income received by the university from the fees pays by the students over the total number of students, in order to take into account the services offered by the institution (more specifically, it corresponds to the fee income received from undergraduates students). We also included time trend (YEAR), which captures the influence of technical change leading a shift in the output over time. These factors are modeled as variables, which directly influence the variability of the inefficiency term. In other words, they affect the efficiency with which inputs are converted into outputs. We measure AV, FPS at regional level and MK at university level. See Table 2 below for a summary of the model implemented in the paper. [Table 2] around here 4.

Results

4.1. Efficiency scores The estimated parameters of the stochastic education distance frontier, as specified through our baseline model, are presented in the Table 311. From a methodological perspective, the null hypothesis that there is no heteroscedasticity in the error term has been tested and rejected, at 1% significance level, using a Likelihood Ratio Test (LR), giving 9

For a contribution on the role of competition on high school performances, see Harrison and Rouse (2014). This measure can be intended as an alternative indicator for GDP per capita, measured at regional level. 11 We rely on the routines provided in STATA software (version 12) by Wang and Ho (2010) in order to make a within transformation to data using the “sf_fixeff” command. 10

9

credit to the use of some exogenous variables, according to which the inefficiency term is allowed to change. In other words, the validity of heteroscedastic assumption has been confirmed, leading to the significance of the inefficiency term. The coefficients show that all the inputs variables have a positive and statistically significant effect on the various outcomes of the universities; the value of such coefficients are quite stable across all the specifications (translog with and without separability – respectively Table 3, Columns a and b, Cobb-Douglas – Table 3, Column c) and their statistical significance is not majorly affected by clustering the production function at regional level (Table 3, Columns a, b and c present the results with standard errors not clustered; Table 3, Columns d, e and f present the results with standard errors clustered at regional level). In this sense, the stability of coefficients, as well as the high correlations between efficiency scores derived through the different models, suggest that the functional form of the production (cost) educational function of the Italian universities is not affecting the quality of final judgments. [Table 3] around here When looking at the (average) technical efficiency scores by geographical area (Table 4), the estimates reveal that institutions in the Central-North area (North-Western, North-Eastern and Central) outperform those in the Southern area; this result is consistent with previous evidence, as for instance that reported by Agasisti and Dal Bianco (2006). This difference exists for all the four years and is quite constant over time; taking the average across years into consideration, the estimated gap of efficiency scores is in the order of 20%. Therefore, depending on the functional form, the average efficiency of Northern universities is estimated around 93% - in other words, the output can be expanded by 7% using the same amount of inputs, an increase that is substantial but not radical. Southern universities’ efficiency, instead, is around 75% - thus, their inputs can be used more efficiently for producing 25% more outputs. What is stunning is that the big difference between efficiencies of universities in different geographical areas is not only in the mean, but more importantly in the distribution (see the three boxplots – one for each efficiency model – in the figure 1): while on average all universities in Northern and Central Italy are similarly efficient, in the South very efficient institutions coexist with very inefficient ones. This point would be of extreme importance when discussing potential implications for regional-level policies in the field. [Table 4 and Figure 1] around here This gap in efficiency requires some explanation, that can be useful for defining consistent policies that can improve the productivity of the overall HE system – indeed, the second-stage analysis is deemed at this specific objective. Before going into that, on a policy ground it is interesting to notice that technical efficiency levels are increasing over time, i.e. the average efficiency of the whole HE system is improving in the four years under scrutiny (this is true across all the geographical areas, on average). Such finding is not only detectable from the average efficiency scores, but is reinforced by the estimation of the parameters T_1, T_2 and T_3 – the negative sign associated to the coefficients indicates that inefficiency is decreasing over time, with a more pronounced magnitude in the first year after the baseline one (2008) – see, also, the time trend’s estimation. A graphical representation of the evolution of

10

efficiency over time is in figure 2, and indicates that such a positive evolution of efficiency scores is detectable, irrespective of the functional form assumed for the production function – the subsequent figures show also the positive trend in all the geographical areas, with a tendency towards catch-up effect (albeit slow) for universities located in Southern Italy. The statistical correlations between the efficiency scores obtained through the various models are reported in tables 5 and 6 (Pearson and Spearman correlation indexes, respectively); overall, they suggest strong concordance both in terms of estimated efficiency levels and rankings, and they are also coherent in describing efficiency levels in the geographical areas. Summing up these generals findings about the universities’ efficiency scores, they are stable and consistent across various specifications and confirm the gaps across geographical areas; in other words, the functional form does not influence the general picture about the efficiency of HEIs in Italy. [Tables 5 and 6; Figure 2] around here With the aim of providing an idea about how much the lack of consideration for unobserved heterogeneity would bias the results (i.e. if the Wang and Ho 2010 model is not used), we re-estimate the model through the Greene (2005) approach, by specifying two different settings: (i) one in which dummies for geographical macro-areas are included into the calculation of efficiency frontier, and (ii) one in which the dummies are instead considering single regions, not macro-areas. The results of this sensitivity tests are reported in the tables 7 and 8. While the correlation indexes across all the models are high, it can be noted that the models that do not consider unobservable heterogeneity tend to estimate higher efficiency scores, meaning that they fail to attribute inefficiency correctly to the various universities. This bias is higher for the universities operating in Southern Italy (see that, in some cases, they receive efficiency scores not far from those of universities in other areas), and leads to underestimate the degree of inefficiency in their operations. In light of these results, the efficiency estimates reported by Agasisti and Johnes (2010) should be interpreted as somehow upward biased. [Tables 7 and 8] around here 4.2. Efficiency scores’ determinants: the role of market competition When considering the explanatory factors included in the analysis, our findings show that the variables used to control for the different competitive environment in which institutions live have an important role in describing the variance of the inefficiency term. Specifically, inefficiency is U-shaped relationship with respect to the measure of market competition (MK), showing a negative and statistically significant relationship between inefficiency and market share while, instead, a positive and statistically significant relationship between inefficiency and (squared) market share has been found. In other words, the increase in concentration does not lead to a linear change in efficiency; instead, at low values of concentration, having additional students has a negative effect on inefficiency (i.e. universities are more efficient, maybe because they are able to obtain benefits from scale of operations). At some point, the effect becomes positive, and the quadratic shape means that the inefficiency of HEIs with respect to the measure of market concentration is increasing as concentration increases (i.e. universities are less efficient), and

11

the results can be due to the finishing incentives in becoming efficient when concentration arises indeed. Overall, these findings suggest that differences in performances might be due to the market structure of higher education, in the direction that a more competitive environment could lead to higher efficiency. We also find a negative and statistically significant on the FPS variable; this indicates that the higher levels of fees per capita are associated with higher levels of universities’ efficiency. This finding is also consistent with the interpretation that when market forces operate, there are benefits for HEIs’ efficiency – an analogous finding about the positive association between efficiency and fees of Italian universities is in Agasisti and Wolszczak-Derlacz (2015). They underline that this result could depend on the fact that those universities “are more responsive towards students’ needs and use the money in a more efficient way (for instance, on teaching services that are able to help “producing” more graduates)”. The potential explanation for this general result resides in the traditional economic argument that competition can stimulate the ability of institutions of maximizing the outputs for any available input level; the series of reforms that, since 1990s, provide incentives to Italian universities in this direction, can be then judged as potentially useful in improving the efficiency of the overall HE system. A negative and statistically significant coefficient has been found on the variable value-added (AV), meaning that the higher is the value added per capita the lower is the technical level of inefficiency; operating in more economically developed areas is associated, on average, with higher efficiency. Given that there is a gap in economic development between Northern and Southern Italy, this result raises serious social issues under the equity profile. Indeed, all else equal, HEIs that are operating in South Italy are required to provide extra-effort to produce the same level of output; the empirical evidence that they are not able to do that (i.e. the inefficiency gap is still evident) should raise concerns about the effectiveness of policies that in the past allocated more (public) money to universities in the South for closing the performance gap. Taken together, our results suggest the promotion of pro-competitive policies, which in turn can foster universities’ efficiency. Nevertheless, the implementation of such actions would not reducing the gap between universities operating in the North and South of Italy, a topic that remains at the edge of the policy debate. 5.

Concluding remarks and lesson learned

This papers estimates the efficiency of the Italian higher education system through a multi-output parametric distance function, using data over the four-years 2008-2011. Italy is a very interesting case of analysis as substantial reforms have been taken place in the last years in the tertiary education system with the aim of reaching higher standards quality; public funds to higher education institutions are now related to performance indicators according to which evaluate their management and productivity. Borrowing an expression made in an OECD report (OECD 2008), which fits very well to describe also the situation the Italian universities started to deal with, “higher education institutions have become increasingly accountable for their use of public funds and are required to demonstrate value for money” and “the university becomes responsible for decisions on the composition of its teaching personnel”; moreover, “formal linkages between the performance assessment and the resource allocation have been settled up” (Potì and Reale, 2005). As a consequence the need of measure efficiency of HEIs has never been more actual.

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A very important issue, when estimating of decision making units’ economic performances, is that the efficiency scores may suffer from the presence of incidental parameters or time-invariant, often unobservable, effects; indeed, do not separate inefficiency and fixed individual effects and thus do not distinguish between unobserved individual heterogeneity and inefficiency, forcing all time-invariant individual heterogeneity into the estimated inefficiency, would distort the estimates. Thus, the first contribution of the paper is to apply a procedure developed by Wang and Ho (2010) imposing to data a within transformation such that the sample mean of each panel is subtracted from every observation in the panel and the estimated efficiency is net of the influence of unobserved heterogeneity. The coefficients show that all the inputs variables have a positive and statistically significant effect on the various outcomes of the universities and their statistical significance is not majorly affected by clustering the production function at regional level. Furthermore, consistently with previous evidence (Agasisti and Dal Bianco, 2006), the findings show that institutions in the Central-North area (North-Western, North-Eastern and Central) outperform those in the Southern area. More importantly, the empirical evidence suggests the importance of removing timeinvariant individual effects from the model; indeed, when we replicate the analysis without taking into account the above mentioned unobserved heterogeneity, a bias is found in our estimation, meaning that the efficiency scores calculated might be over-estimated. More specifically, when bias corrected efficiency estimates are taken into account, the differentials between geographical areas (especially between Southern and Northern Italy) tend to be reduced. Important managerial considerations could be drawn in using these efficiency models for policy-making; our main claim is that maintaining State-level policies in the field can be detrimental for overall efficiency, and instead special interventions for universities in the South should be designed. The second contribution of the paper is analyzing whether and how some characteristics of the marketplace in which the higher education institutions operate affect their inefficiency. The empirical evidence reveals the validity of the heteroscedastic assumption, giving credit to the use of such variables according to which the inefficiency is allowed to change; indeed, the results show that inefficiency is U-shaped relationship with respect to the measure of market competition in favor of a more competitive environment in order to reach higher efficiency. Moreover, the higher is the level of fees per capita the lower is the universities’ inefficiency as well as that the higher is the value added per capita the lower is the technical level of inefficiency. Again, as for the inputs variables used in the production function, the statistical significance of the exogenous variables is not majorly affected by clustering the production function at regional level. These findings should provide a clue towards the expansion of pro-competitive policies in the Italian HE sector, for example stimulating the students’ freedom of choice through additional grants, loans and vouchers. Indeed, these results are in line with the realization of both a decentralization of powers from the State to the universities and of the following attempts to set up an evaluation system, as a result of the implementation of a series of reforms the Italian university system has gone through since the beginning of the 1990s. These interventions led to a concession of a certain degree of autonomy to the universities by letting them having their own statutes, allocating the central funding and creating new faculties and courses, encouraging a higher degree of autonomy in management of resources and in the teaching processes. The higher education institutions are now allowed to autonomously allocate the funding from the central government and work a more performanceoriented system of resources allocation, in which each university is in competition with others for the assignment of

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public funds. Indeed, universities have started to be funded according to their level of virtuosity and both quantitative and qualitative indicators were developed to accurately evaluate their productivity in research and teaching. All hints pointing at a development of a quasi-market in the provision of education where, as Agasisti and Catalano (2006) have underlined, students are free to choose the university to attend, institutions are allowed to compete for students, since public funding is associated with the number of students, control over financial resources is delegated to universities, all institutions have to meet the requirements of a national curriculum, but also have to leave their formative offer to be determined by market forces, freedom of entry into the market, universities’ freedom in the setting of fees and availability of relevant information. Finally, a third contribution of the paper regards the not secondary issue of of identifying the more appropriate functional form of higher education institutions’ production processes. We firstly consider a translog functional form for the output distance function with input-output separability; then, for robustness, we firstly relax the separability assumption by assuming a translog functional form without input-output separability property and secondly by considering a Cobb-Douglas formulation. The estimates are quite stable across all the specifications, suggesting that the functional form of the production (cost) educational function of the Italian universities does not affect the quality of final judgments. Although we are aware of the limit of external validity allowed by operating within a national higher education environment, the empirical evidence do offer an important instrument to the university and governance structures. It is very important being aware of the possible source of inefficiency in order to increase the university productivity and to make more accurate resource allocation decisions; indeed, as pointed out by Avkiran (2001), failing to make efficiency analysis a standard practice would certainly lead to less than efficient allocation of educational resources. Regulators operating in this sector might take advantage of these studies and make, through appropriate policy decisions (i.e. focusing on the distribution of available additional resources either among the more efficient units, as reward, or the more inefficient units, helping them to improve their efficiency), the tertiary education system more effective.

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Tables and Figures

Table 1– Definition of the variables and descriptive statistics – Mean values by geographical areas Mean values North-Western

North-Eastern

Central

Southern

1043.56 (648.21)

1026.32 (812.46)

1159.07 (891.37)

797.75 (641.73)

3.29 (0.96)

3.42 (0.67)

3.49 (1.02)

4.48 (1.05)

Inputs ACADSTAFF1 (X1)

# of academic staff (university level)

ENRHSG2 (X2)

% of enrolments with a score higher than 9/10 in secondary school (university level)

STUD (X3)

Total number of students (university level)

29147.55 (18022.32)

27666.63 (22397.37)

35612.70 (32268.32)

26882.18 (20765.05)

GRADMARKS (Y1)

# of graduates weighted by their degree classification (university level)

3082.15 (1951.83)

3114.63 (2595.89)

4013.856 (3589.95)

2435.71 (1962.20)

RES (Y2)

Research grants (university level)

1.17e+07 (7729784)

1.07e+07 (9462683)

1.18e+07 (9981867)

5808383 (5449196)

Output

Explaining the inefficiency MK

Market share (university level)

0.016 (0.010)

0.015 (0.012)

0.019 (0.018)

0.015 (0.011)

AV

Value added (regional level)

28.62 (2.43)

27.50 (1.25)

25.28 (1.75)

15.83 (1.57)

FPS

Fees per student (regional level)

1157.13 (248.55)

1175.73 (239.43)

844.25 (208.17)

588.47 (130.36)

44 40 40 88 Obs. Note: Authors calculation on data collected by the Italian Ministry of Education, Universities and Research Statistical Office. 1 In order to get an easy and comprehensible measure, the total number of academic staff is reported in the descriptive statistics. In the analysis, the total number of academic staff has been, instead, adjusted for their respective academic position (i.e. professors, associate professors and lectures). 1 Both ENRHSG and ENRLYC are percentages of the total number of students enrolled.

Table n. 2 – Specification of inputs, outputs and exogenous factors in SFA model Model Inputs

ACADSTAFF; ENRHSG; STU

Outputs

GRADMARKS; RES

Explaining the inefficiency

MK; AV; FPS

Notes: ACADSTAFF: # of academic staff ENRHSG: % of enrolments with a score higher than 9/10 in secondary

school STU: Total number of students GRADMARKS: # of graduates weighted by their degree classification

RES: Research grants MK: Market share AV: Value added FPS: Fees per student

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Table 3 – Parameters’ estimation, baseline model (a) (b) Translog Unrestricted Separable

(c) Cobb Douglas

(d) Unrestricted

(e) Translog Separable

(f) Cobb Douglas

X1 X2 X3 Y1 Y1*Y1 X1*X1 X2*X2 X3*X3 X1*X2 X1*X3 X2*X3 X1*Y1 X2*Y1 X3*Y1

0.263 (0.074) *** 0.132 (0.047) *** 0.627 (0.073) *** -0.848 (0.035) *** 0.150 (0.071) ** 1.260 (0.415) *** -0.301 (0.255) 1.195 (0.402) *** 0.628 (0.444) -2.275 (0.806) *** -0.898 (0.466) * 0.379 (0.133) ** -0.084 (0.122) -0.473 (0.143) ***

0.213 (0.074) *** 0.148 (0.047) *** 0.669 (0.072) *** -0.879 (0.033) *** 0.080 (0.067) 0.786 (0.387) ** -0.320 (0.273) 0.485 (0.347) 0.961 (0.353) *** -1.039 (0.719) -1.281(0.378) ***

0.213 (0.066) *** 0.162 (0.053) *** 0.743 (0.064) *** -0.870 (0.034) ***

0.263 (0.198) 0.132 (0.078) * 0.627 (0.166) *** -0.848 (0.068) *** 0.150 (0.113) 1.260 (0.946) -0.301 (0.336) 1.195 (0.974) 0.628 (0.659) -2.275 (1.919) -0.898 (0.631) 0.379 (0.302) -0.084 (0.140) -0.473 (0.329)

0.213 (0.178) 0.148 (0.068) ** 0.669 (0.133) *** -0.879 (0.045) *** 0.080 (0.110) 0.786 (0.746) -0.320 (0.369) 0.485 (0.646) 0.961 (0.501) * -1.039 (1.365) -1.281(0.458) ***

0.213 (0.181) 0.162 (0.071) ** 0.743 (0.165) *** -0.870 (0.078) ***

T_1 T_2 T_3

-0.098 (0.048) ** -0.037 (0.032) -0.025 (0.025)

-0.115 (0.042) *** -0.045 (0.031) -0.030 (0.027)

-0.133 (0.048) *** -0.061 (0.037) * -0.040 (0.033)

-0.098 (0.036) *** -0.037 (0.025) -0.025 (0.013) *

-0.115 (0.026) *** -0.045 (0.021) ** -0.030 (0.014) **

-0.133 (0.045) *** -0.061 (0.016) *** -0.040 (0.011) ***

MK MK2 AV FPS

-5.855 (1.286) *** 10.648 (2.767)*** -0.121 (0.042) *** -0.002 (0.0008) ***

-6.830 (1.346) *** 13.173 (2.929) *** -0.132 (0.043) *** -0.003 (0.0009) ***

-3.624 (1.334) *** 7.942 (3.061) *** -0.190 (0.067) *** -0.003 (0.001) ***

-5.855 (1.455) *** 10.648 (3.636)*** -0.121 (0.046) *** -0.002 (0.0012) **

-6.830 (1.112) *** 13.173 (2.755) *** -0.132 (0.054) ** -0.003 (0.001) ***

-3.624 (1.433) ** 7.942 (3.038) *** -0.190 (0.081) ** -0.003 (0.001) **

Time trend

-0.485 (0.202) **

-0.312 (0.197)

-0.189 (0.233)

-0.485 (0.307)

-0.312 (0.250)

Inefficiency effects 𝛿

Log Likelihood 101.6090 95.6993 73.1429 101.6090 95.6993 73.1429 Wald 4747.77 4179.14 3518.59 4747.77 4179.14 3518.59 Observations 212 212 212 212 212 212 (a)-(b)-(c): Standard errors not clustered; (d)-(e)-(f) Standard errors clustered at regional level. (a)-(b)-(d)-(e): results are obtained through a translog functional form for the output distance function, without and with input-output separability property. (c)-(f): results are obtained through a Cobb-Douglas functional form for the output distance function.

19

Table 4 - Technical Efficiency - Directional output distance efficiency scores by geographical areas Unrestricted (translog) Obs

2008

2009

2010

2011

All years

North-Western North-Eastern Central Southern

44 40 40 88

0.8539 0.9067 0.8941 0.7148

0.8990 0.9385 0.9091 0.7366

0.9326 0.9584 0.9249 0.7887

0.9484 0.9696 0.9392 0.8187

0.9085 0.9433 0.9162 0.7647

Total

212

0.8424

0.8708

0.9012

0.9190

0.8832

Geographical areas

Separable (translog) North-Western North-Eastern Central Southern

44 40 40 88

0.8965 0.9492 0.9104 0.7374

0.9254 0.9573 0.9199 0.7491

0.9459 0.9689 0.9306 0.7926

0.9533 0.9752 0.9402 0.8166

0.9303 0.9627 0.9249 0.7739

Total

212

0.8734

0.8879

0.9095

0.9213

0.8980

Cobb Douglas North-Western North-Eastern Central Southern

44 40 40 88

0.9660 0.9752 0.9383 0.7793

0.9691 0.9769 0.9444 0.7866

0.9760 0.9822 0.9509 0.8244

0.9792 0.9853 0.9585 0.8454

0.9726 0.9799 0.9478 0.8089

Total

212

0.9147

0.9193

0.9334

0.9421

0.9273

Table 5 - Pearson’s correlation

Central

Southern

All

0.9123 (0.0000)

0.9909 (0.0000)

0.9750 (0.0000)

0.9796 (0.0000)

0.7496 (0.0000)

0.9304 (0.0000)

0.9067 (0.0000)

0.8915 (0.0000)

0.8369 (0.0000)

0.8977 (0.0000)

0.9524 (0.0000)

0.9163 (0.0000)

0.9219 (0.0000)

44

40

40

88

212

North-Western a.

Unrestricted (translog) vs Separable (translog) 0.9615 (0.0000)

b.

Unrestricted (translog) vs Cobb Douglas 0.7540 (0.0000)

c.

Obs

North-Eastern

Separable (translog) vs Cobb Douglas

20

Table 6 - Spearman correlation

Central

Southern

All

0.9593 (0.0000)

0.9379 (0.0000)

0.9755 (0.0000)

0.9759 (0.0000)

0.8129 (0.0000)

0.8704 (0.0000)

0.9096 (0.0000)

0.8729 (0.0000)

0.8405 (0.0000)

0.8664 (0.0000)

0.9338 (0.0000)

0.9159 (0.0000)

0.9233 (0.0000)

44

40

40

88

212

North-Western a.

Unrestricted (translog) vs Separable (translog) 0.9763 (0.0000)

b.

Unrestricted (translog) vs Cobb Douglas 0.7992 (0.0000)

c.

North-Eastern

Separable (translog) vs Cobb Douglas

Obs

Table 7 - Technical Efficiency - Directional output distance efficiency scores by geographical areas – SFA with macro-area dummies in the frontier Unrestricted (translog) Obs

2008

2009

2010

2011

All years

North-Western North-Eastern Central Southern

44 40 40 88

0.9471 0.9760 0.9429 0.9179

0.9579 0.9783 0.9519 0.9240

0.9639 0.9814 0.9555 0.9269

0.9658 0.9817 0.9532 0.9327

0.9587 0.9794 0.9508 0.9253

Total

212

0.9459

0.9530

0.9569

0.9583

0.9535

Geographical areas

Separable (translog) North-Western North-Eastern Central Southern

44 40 40 88

0.9356 0.9724 0.9357 0.9014

0.9556 0.9753 0.9476 0.9145

0.9619 0.9804 0.9535 0.9224

0.9646 0.9816 0.9519 0.9315

0.9544 0.9774 0.9471 0.9171

Total

212

0.9362

0.9482

0.9545

0.9574

0.9490

Cobb Douglas North-Western North-Eastern Central Southern

44 40 40 88

0.9463 0.9708 0.9413 0.9482

0.9633 0.9760 0.9482 0.9502

0.9641 0.9810 0.9539 0.9582

0.9652 0.9807 0.9504 0.9650

0.9597 0.9771 0.9484 0.9554

Total

212

0.9516

0.9594

0.9643

0.9653

0.9601

21

Table 8 - Technical Efficiency - Directional output distance efficiency scores by geographical areas - SFA with Regional dummies in the frontier Unrestricted (translog) Obs

2008

2009

2010

2011

All years

North-Western North-Eastern Central Southern

44 40 40 88

0.9116 0.9585 0.9230 0.8585

0.9255 0.9641 0.9240 0.8650

0.9363 0.9685 0.9265 0.8769

0.9394 0.9723 0.9182 0.8820

0.9282 0.9658 0.9230 0.8706

Total

212

0.9129

0.9196

0.9270

0.9279

0.9219

Geographical areas

Separable (translog) North-Western North-Eastern Central Southern

44 40 40 88

0.9185 0.9652 0.9274 0.8571

0.9371 0.9684 0.9305 0.8670

0.9446 0.9731 0.9335 0.8805

0.9450 0.9759 0.9255 0.8868

0.9363 0.9706 0.9293 0.8729

Total

212

0.9170

0.9257

0.9329

0.9333

0.9272

Cobb Douglas North-Western North-Eastern Central Southern

44 40 40 88

0.8886 0.9322 0.9063 0.8666

0.9132 0.9396 0.9044 0.8718

0.9116 0.9486 0.9068 0.8860

0.9164 0.9529 0.8935 0.8926

0.9075 0.9433 0.9030 0.8792

Total

212

0.8984

0.9072

0.9132

0.9138

0.9082

22

Figure 1. Efficiency scores’ estimates, by macro-area (different functional forms)

Note: Central area: 40 observations; Northern area: 88 observation (44 in the North-Western and 40 in the North -Eastern area); Southern area: 88 observations.

Figure 2. Efficiency scores’ distribution over time, by macro-area (different functional forms)

Note: NW (North-Western area): 44 observation; NE (North-Eastern area): 40 observations; C (Central area): 40 observations; S (Southern area): 88 observations .