# Economic and social changes

### I. Introduction

Tunisia, which has been independent since 1956, is approaching the new millennium in an international economic environment characterized by major political, economic and social changes. Until 1986, the country's remarkable growth was achieved in a context of protection, which revealed a number of structural deficiencies, low domestic integration and competitiveness. Tunisia was thus led to reorient its development strategy in order to give more room to private sector, restoration of market forces, the emergence of a strong determination for better resource allocation, and the rehabilitation of economic efficiency.

First MENA country to sign an Association Agreement with the European Union, the government, however, recognizes that without significant action, many firms will not survive competition. It therefore launched in 1994/95 the upgrading program ("programme de mise niveau de l'industrie"). The Tunisian industrial restructuring program aims to provide financial support to upgrade about 2000 private firms between 1995 and 2005. Enterprises undergo an external audit focusing on finances and competitiveness; they should submit a complete self-conceived upgrading plan that could make them eligible for government financial support to modernize equipment, raise quality standards and strengthen balance sheets.

The objective of this work is to estimate the production frontier and technical efficiency levels of Tunisian manufacturing firms using recent nonparametric methods and to analyze the impact of the upgrading program on firms' performance. Generally speaking, the idea is to analyze how firms combine their inputs to produce in an efficient way the output. The maximal achievable level of output for a given level of inputs defines the production frontier. The technical efficiency of a particular firm is then characterized by the distance between its level of output and this optimal level it should produce if it were efficient. The use of nonparametric frontier like DEA (Data Envelopment Analysis) and FDH (Free Disposal Hull), to estimate the frontier is quite appealing because they rely on very few assumptions and the shape of the function is much less constrained than with parametric methods. However, one drawback of these approaches is that the results are more difficult to interpret in term of sensitivity of production to particular inputs (shape of production function, elasticity...) and moreover, the curse of dimensionality implies that large sample sizes are to be considered to get sensible results.

Therefore, in order to get rid of these problems, we present the latest nonparametric methods of Cazals, Florens and Simar (2002) and Aragon, Daouia and Thomas-Agnan (2005) which are more robust to outliers than traditional nonparametric methods and so more adapted to our database. The data used in this study has been assembled using a diversity of sources (national accounts from of the Tunisian National Statistic Institute (INS) and statistics coming from the Quantitative Economy Institute (IEQ)). We did so in order to allow the construction of an integrated database of industrial, labor market and trade statistics feasible. Thus we have a panel on 1440 manufacturing industries from 1997 to 2003.

In a second step, we propose to modelize technical efficiency level of firms. The idea is to relate efficiency measures to some external or environmental factors which might influence the production process but that are not under the control of the producers. Efficiency measurement is crucial in developing countries and in particular in Tunisia as internal financing is vital for firms. Labor and market imperfections, among others, force firms to use this kind of financing. Then measuring technical efficiency allows identifying obstacles to firms functioning and giving possible ways to enhance firms' performance and development.

We propose an explanatory model for the inefficiency of our database firms to modelize the heterogeneity between firms, using the idea from Simar and Wilson (2007) and Simar (2003). We then apply a two-stage estimation method: we estimate in a first step the productive efficiency using the results by Cazals, Florens and Simar (2002), and in a second step we regress them on environmental variables to account for exogenous factors that might affect firms' efficiency and to analyze the impact of the upgrading program on firms' performance. This subsequent stage is applied with a bootstrap procedure, as proposed by Simar and Wilson (2007). In our analysis, we pay a particular attention to the detection of outliers (see Simar 2003) and adapt the initial procedure to the nonparametric estimator of production frontier proposed by Cazals, Florens and Simar (2002).

The paper is organized as follows: in the next section, we describe the Tunisian experience of the upgrading program. In section 3, we present the estimation methods of the production frontier. In section 4, we apply them to our database and we develop the explanatory model to analyze the impact of the upgrading program on the technical efficiency levels of firms. Section 5 concludes.

### II. The Tunisian experience of the upgrading program

### 1. The concept

Upgrading concept should be considered as a dynamic and a global process needed to cope with the openness of the economy, and requiring tailored policies. Upgrading program involves actions by enterprises to bridge gaps between current performance and what is required to become internationally competitive. These gaps emerge as a result of global changes in technology, organization, marketing, and factor prices. Industry, in turn, is prompted by policy, regulatory and institutional changes to improve its competitiveness. Experience shows that Upgrading program at the firm level will not take place automatically in response to macroeconomic policy changes or rapid shifts in global conditions.

Upgrading program is needed not only by those that were protected, but also by some exporters. In an ideally functioning market the financing is available when such Upgrading program is economically viable, otherwise the firm closes. But there are several reasons why a potentially viable firm may not be able to obtain the required financing for the Upgrading program. The first is that the viability of the firm depends as much on the problems of entrepreneurship, management, and organization issues as on the physical characteristics of the equipment and products. The owners frequently lack the capabilities for putting together a program to solve their problems. A case may be made for providing assistance to firms in the form of diagnosis, formulation of the firm's project, and training plans that could be presented to potential investors or bankers. Second, banks may be deterred by problems of collateral and arrears on bank loans. If banks were to finance upgrading program of these enterprises they would need to restructure their debt as well.

Upgrading program is a dynamic process: operations should respond explicitly to rapid changes in global markets and technology and to sharp shifts economic policies.

Global economic studies of the business environment provide the parameters for judging whether restructuring moves by enterprises are consistent with internationally competitive performance. A firm's ability to compete in world markets is a key. Increasingly, this ability depends not only on factor prices and scale economies but also on the firm's flexibility and policies for organizational, technological, and marketing strengths upgrading program. But Upgrading projects that deal primarily with physical aspects -without giving adequate attention to regulatory policy issues, ownership, and organization - have only a limited impact.

Upgrading operations should reinforce competitive pressures. Monopoly status of critical industries often has serious adverse effects on the competitiveness of user industries.

### 2. The Preconditions for the Upgrading program

Governments need to establish policies that facilitate resource movements in response to competition, promote institutions that are capable of filling information and capacity gaps and ensure that appropriate financing is available. Also, a business environment that rewards efficient performance is necessary if enterprises, sub-sectors and industries as a whole are to restructure to attain global competitiveness.

Successful upgrading program depend on:

- Removal of, or significant reduction in, barriers to entry, exit and expansion of industrial enterprises;
- Elimination of policy-induced public or private sector industrial monopolies. When domestic competition is inadequate to force efficiency in production, import competition is required;
- Elimination of, or major reductions in, subsidies, unilateral transfers, and special arrangements for certain enterprises;
- Introduction of market-oriented pricing policies: the most important way Tunisia can innovate and improve the quality of its products and services are through global linkages, mainly between private parties, rather than governments. Stronger competition from trade liberalization will promote higher productivity and encourage a much stronger outward orientation.
- It is required to offer to program of grants, loans and technical assistance intended to enhance existing enterprise performance, rather than promote new activities in non-tradable goods.
- The Upgrading of services is critical to the country's competitive performance in international markets. Tunisia proximity to Europe is a major advantage, but high transport costs and outdated communications and information technology reduce its competitive edge.

It is very important at this stage of our analysis to discuss the concept of competitiveness which is a central concept to the upgrading program objectives. Competitiveness means different things to different people. It is helpful to consider competitiveness at three different levels of aggregation: the firm, the industry or group of industries and the nation.

At each level of aggregation, there are different measures, or indicators of competitiveness. They vary in what they imply about the present and future economic success or well being of a firm, industry or nation. Some concepts of competitiveness are applicable at one level of aggregation but not at another.

### 3. Achievements of the upgrading program

The upgrading program was launched in 1995 as a pilot project encompassing some 109 enterprises. In 1996, the program was expanded to include other companies from the industrial sector. The number of upgrading plans which have been approved by the COPIL (the piloting committee) reached 242 companies, for a total investment level valued at 664 million dinars, of which 75 is destined for non-material investment. There are yet another 311 enterprises which have entered into the diagnosis stage. Counting the original companies in the pilot project, there are more than 630 enterprises which have completed or at one stage or another in their modernization process.

Enterprises undergo an external audit focusing on finances and competitiveness; they should submit a complete self-conceived upgrading plan that could make them eligible for the upgrading program. The total cost of the program for the period 1996 to 2005 was estimated at TND 2.5 bn.

### III. Non parametric frontier analysis

In frontier analysis, most of the nonparametric approaches (DEA, FDH) are based on envelopment ideas, which suppose that with probability one, all the observed production units belong to the attainable set. These nonparametric deterministic frontier models are very appealing because they rely on very few assumptions[1] . Nevertheless, by construction, they are very sensitive to extreme values and to outliers, which is a crucial point for our database.

Therefore, in this part, we present two alternative robust nonparametric estimators of production [2] frontiers, robust to these extreme values. Moreover these two estimators are based on quite easy practical computations and benefited from a relatively high rate of convergence. Both methods can be applied in multivariate settings for multi-inputs multi-output technology. For sake of simplicity, and to be closer to our empirical work, we will only present the case of a single output produced from several inputs. In this section, we will note { (Xi,Yi) | i =1,...,n } the data sample of size n, where Xi denotes vector of input levels used by firm i and Yi vector of production level of firm i.

### 1. Robust nonparametric frontier estimator

### 1.1. The expected frontier of order-m

This estimator, proposed by Cazals, Florens and Simar (2002), is defined as follows. Consider a fixed integer m. For a given level x of inputs, define the expected value of the maximum of m random variables , drawn from the conditional distribution of the output Y , given X =x.

This expected maximal production function of order m can be interpreted as the expected maximum production among a fixed number of m firms using less than an input level x. A natural estimator is then given by:

where represents the empirical distribution function. In practice, this formula is approximated by the following Monte-Carlo method[3] :

- For a given level of input x, draw a sample of size m with replacement among those such that,
- Compute,
- Redo steps [1] and [2] for b =1,..., B, where B is sufficiently large,
- Then compute the empirical mean among the B samples:.

The bootstrap parameter B helps to adjust approximation quality. However appears to be quite reasonable for most empirical applications.

The asymptotic properties have been extensively studied by Cazals, Florens and Simar. They show in particular that for a fixed value m, the rate of convergence ofto the true solution is in, which is a very nice result since it reaches the usual parametric rate.

### 1.2. The quantile based frontier of ordre-

This estimator was recently proposed by Aragon, Daouia and Thomas-Agnan (2005). Its main advantage is that it is a bit less sensitive to extreme values than the expected order-m estimator.

### 2. Explaining Efficiencies

For many years, researchers have sought to explain differences in estimated efficiencies across firms. Often, researchers have in mind a set of environmental factors that might be related to efficiency differences; these factors might reflect differences in ownership type or structure, regulatory constraints, business environment, competition, etc. among the firms under analysis. Typically, such factors are viewed as possibly affecting the production process, but not under the control of firms' managers. Understanding how such factors might be related to efficiency is important for determining how firms' performances might be improved. In addition, from a public policy perspective, understanding these relationships is important for assessing the costs of regulation.

In our analysis, we adapt the two-stage method proposed by Simar and Wilson (2007) and use the expected frontier of order m as initial estimator for the first step. Then, in a second step, we regress the associated efficiency measure on environmental variables to account for exogenous factors that might affect firms' performance. This subsequent stage is applied with a bootstrap procedure, as proposed by Simar and Wilson (2007). We pay a particular attention to the detection of outliers (see Simar (2003)) and adapt the initial procedure consequently, as detailed below.

### 2.1. Two-stage approach

Let us focus particularly on the second stage. The dependent variable used is the estimated level of inefficiency defined by the nonparametric estimator of the production frontier. In what follows, we consider the associated level of inefficiency.

Socio-economic factors include geographical and industrial features (Aigner and Chu, 1968; Timmer, 1971; and Aly et al., 1990), firm size (Wu, Devadoss, and Lu, 2003; Salinas-Jimenez, 2003)[5], ownership (Nguyen Thang, 2000), managerial structure of firms, such as age of workers, education, management policy, capital structure, and capital-labor ratio, and transitions in economic policies of a nation and a region (Pustay, 1978).

We use in our analysis the simple bootstrap method developed by Simar and Wilson (2007) with a linear regression model. The bootstrap procedure is used to take into account the correlation between the dependent variables. Moreover, in their article, Simar and Wilson (2007) discussed the opportunity to implement truncated models or Tobit models instead of linear regression models. It makes sense when considering the variable defined by DEA or FDH methods, which is defined on [1; +8 [. In this case, is a variable left-censored in 0. With the expected of order m method, the variable can take negative values and a linear regression model is then more justified.

Let recall now the simple bootstrap method proposed by Simar and Wilson (2007) and adapted to our own problem:

However we can question these results as the analysis of technical efficiency indexes, estimated by Cazals et al. (2002) raised two main issues. First, the data cloud is relatively sparse as efficiency indexes of firms located above the estimated frontier can be quite high. Second, for a non-negligible proportion of firms, efficiency index is artificially equal to unity, as these firms are located exactly on the frontier.

Hence we detail in the next two parts both points. The first one will be analyzed through the Simar (2003) method of outliers detection, the resolution of the second problem will rely on a detection method of "spurious" efficient observations.

### 2.2. Detecting Outliers

Estimation of individual technical efficiency levels by expected order-m frontier techniques leads to an efficiency indexes cloud with high variance. In particular, efficiency measures of "super-efficient" firms are really higher than the ones of inefficient firms. Detection of outliers allows to lessen disparity between indexes and to better justify the use of regression linear method.

Let present the detection method proposed by Simar (2003)[6]. The basic idea is to use the robustness property to outliers of the expected frontier estimator to detect eventual outliers.

Hence, as noted previously, the Cazals et al. (2002) method is by definition less sensitive to extreme values than other nonparametric methods. Simar (2003) proposes to use this method beforehand frontier estimation by a deterministic method (FDH, DEA or corrected OLS). Note however that our motivation is quite different: we use this detection method beforehand linear regression of inefficiency functions.

According to expected frontier definition, some observations are located above the estimated frontier, even for large values of m. Even so, being located above the frontier did not necessarily define an extreme value: one has to fix a threshold value in order to do not dismiss observations that are above but somehow close to the frontier. In practice two issues emerge: which values of m one must choose and from which threshold value observations can be considered as outliers? The Simar method does not offer straight answers and relies on a sensibility analysis of results.

The first analytical tool, practical in small sample cases, is a table which resumes for each observation the estimated efficiency index, the precision[7] of the Monte-Carlo approximation[8], and the proportion of observations using less input than the observation considered. The analysis of this table should allow detecting potential outliers.

Yet, the analysis of this table can reveal to be fastidious in large sample cases, and Simar (2003) proposes the following "semi-automatic" method. First, one must choose some arbitrary threshold values. For each value, the proportion of observations for which efficiency index is superior to 1+threshold value is evaluated. The graphical representation of this proportion for each threshold and for various values of m must enable to detect extreme observations. If the sample exhibits no extreme values then this proportion must be linearly decreasing with m values. Hence any deviation from the linear form, or the presence of an "elbow", can reveal the presence of potential extreme values. This allows to identify suspect observations and eventually to return to the previous table and to the data. The deviation nature of these points can then be analyzed: super efficient firms, measurement errors, data capture errors etc. As an extreme value can hide another ("masking effect"), Simar (2003) advises to repeat the analysis on the sample apart from detected outliers.

### IV. Empirical application

### 1. Database

The data used in this study has been assembled using a diversity of sources (national accounts from of the Tunisian National Statistic Institute (INS) and statistics coming from the Quantitative Economy Institute (IEQ)). We did so in order to allow the construction of an integrated database of industrial, labor market and trade statistics feasible. Thus we have a panel on 1440 manufacturing industries from 1997 to 2003.

This sample is representative of the Tunisian manufacturing sector with regard to control variables such as employment, gross fixed capital formation and output.

Our sample is distributed as follows across industries: 14,029% belong to agriculture and food products (IAF), 8,332% to the materials construction, ceramics and glass (CMCG), 15,765% to the metal and electrical industries (MEI), 9,581% to the chemical industry (CI), 39,932% to the textile, clothing and leather (TCL) and finally 12,361% to other manufacturing industries (OMI).

Output level matrix Y is evaluated by sales values, corrected by stock variations. The matrix X refers to the 2 inputs used: K (capital) and L (labor). Labor is evaluated as the total number of hours worked in the firm per week. Capital definition is made on a permanent inventory base.

### 3. Technical efficiency levels

Individual technical efficiency levels associated to the expected frontier of order m are evaluated by a Monte-Carlo method (where B = 200), individual technical efficiency levels associated to the quantile frontier of orderare simply evaluated as the ratio between observed production and estimated frontier.

In order to compare the two measures, we determine the value of m such as the proportion of observations below the frontier is almost the same than the one obtained with a quantile frontier of order =0.995. We found that for proportions are roughly the same. A small table helps to represent these proportions: for the two cases, proportions of observations above and on are of 53.12% for and 52.94% for =0.995. Moreover proportions of firms strictly under are not so far. However more than a third of the firms are located on : this comes directly from the definition of the quantile frontier.

With regard to the evolution of the mean technical efficiency during 1997-2003 in the figure 1, we note that the mean technical efficiency of the Tunisian manufacturing firms is increasing over the time. We note also that the upgrading program enhance firm's technical efficiency because technical efficiency of the Tunisian manufacturing firms adapting the upgrading program is larger than technical efficiency of the Tunisian manufacturing firms no adapting the upgrading program .

### 4. Determinants of technical efficiency

### 4.1. Factorial effect Variables

Socio-economic factors that might affect firms' performance include geographical and industrial features (Aigner and Chu, 1968; Timmer, 1971; and Aly et al., 1990), firm size (Wu, Devadoss, and Lu, 2003; Salinas-Jimenez, 2003)[9], ownership (Nguyen Thang, 2000), managerial structure of firms, such as age of workers, education, management policy, capital structure, and capital-labor ratio, and transitions in economic policies of a nation and a region (Pustay, 1978). So that, we have adapted these variables described below:

- DPMNi, a dummy variable, is equal 1 if firm i is adapted the PMN program and DPMNi is equal to 0 otherwise. In the sample, there are 288 firms adapted the PMN program, accounting for 20% of the sample.
- Dop,i , an ownership dummy variable, is equal to 0 if firms are foreign-owned-firms and 1 otherwise.
- Firm size (li) is the average number of workers of firm i.
- Capital-labor ratio (k2li) is equal to total capital divided by total workers.
- External cost ratio (tytrong) is equal to costs that are not involved in production process divided by total cost.
- Per capital income (wl) is the average wage that a worker is paid annually.
- Dopwl,i is a variable of cross-section effect between , Dop,i and wl.

Three variables l2 and k2l2 are l, k2l, and squared respectively (Kim [2003] and Gumbau-Albert [2000] argued that capital-labor ratio and firm size might affect technical efficiency quadratically).

### 4.2. Explaining technical efficiency levels

We present here estimation results of linear regression models in three particular cases: efficiency levels measured with a FDH frontier[10], with the expected frontier of order m = 150 and with the quantile based frontier of order a = 0.995.

The bias correction of the variance-covariance matrix generated few modifications in decisions in parameters significance tests. However, as corrected confidence intervals are tighter, conclusions on the impact of the socio-economic variables on efficiency can be too optimistic, if the bias, generated by the correlation of efficiency index, is not corrected.

In the FDH case, few business variables are significant and the quality of regression is weak (less than 8%). The results of the two regressions based on robust technical efficiency indexes are quite similar. However, at significance level of 10%, socio-economic variables, which could affect technical efficiency, are capital-labor ratio, wage, ownership types and the PMN program. Table 7 provides some implications. Firstly, PMN program strongly affected technical efficiency. Secondly, firm size was not related to pure technical efficiency. This means that firms' number of workers did not make pure technical efficiency divergent. Thirdly, capital-labor ratio was quadratically related to efficiency. The signs prove such relation to be convex, who differs from recent empirical studies that held this relation, should be concave (making an optimal level of capital-labor ratio)[11]. Lastly, higher average wages (which imply higher quality of labor) were correlated with higher pure technical efficiency scores. Productivity, quality of labor, and pure technical efficiency were found to be positively related.

Then, we analyze both problems of detecting outliers and "Spurious" technically efficient firms. These two features are intimately linked to estimation methods and cannot be ignored in the analysis. They can be easily identified in Figure (3), where technical efficiency indexes 1/?i are represented. It appears that a significant proportion of firms has indexes superior to 2, for example, and that some firms, especially those which used low levels of inputs, exhibits unity indexes.

Hence we propose in the next two sub-sections to take into account these two points in our estimations. This allows us to compare our results after corrections with the one presented in Table (7) and to guess pertinence of detection methods in this case.

### 4.3. Detecting outliers

We identify a first elbow in m = 500 for ? = 0.1. This leads us to consider 21 observations as potential extreme values. This elbow can be determined from Figure (2) which represents, for different values of m, the proportion of observations located above the estimated frontier, given a threshold value ?.

### V. Conclusion

We have presented in this work an application of recent nonparametric production frontiers methods. They are more robust to outliers and have higher rate of convergence than classical nonparametric methods (FDH and DEA). The empirical work is performed on a survey of Tunisian manufacturing firms. Potential measurement errors and small sample size are arguments in favour of an application of these recent methods.

In a second step, we propose a modelling of technical efficiency levels of firms. This method is adapted from the one of Simar and Wilson (2007) and raises some interesting empirical problems as detection of outliers and "spurious" technically efficient firms. The Simar and Wilson method was developed for DEA indexes, and we have adapted it to the expected order m indexes.

Technical efficiency was found to be low; it was just around 53.1 percent. Human resource development policies and increasing labor quality were very important factors in improving efficiency. Capital-labor ratio was positively related to technical efficiency. Increasing the capital-labor ratio should be considered intensively to increase productivity and competitiveness for these firms. We note also that the upgrading program (PMN program) enhance firm's technical efficiency.

A drawback of nonparametric techniques is that, as no functional form is specified in nonparametric frontier methods, estimation of technological parameters is precluded. It is then possible to implement the parametric approximation method of nonparametric frontiers developed by Florens and Simar (2005). With this method technological parameters are identified from the boundary of the data cloud.

### References

- Aly, M. and M. A. Chaudhry. (1990). ''Inter-regional Farm Efficiency in Pakistan's Punjab: A Frontier production Function Study''. J. of. Agr. Econ. 41: 62-74.
- Aragon, Y., Daouia, A., and Thomas-Agnan, C. (2005). "Nonparametric Frontier Estimation: a Conditional Quantile-based Approach". Econometric Theory,21, pp 358-389.
- Battese, G.E., and Coelli, T.J.(1995). "A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function and Panel Data", Journal of Empirical Economics, 20(2), 325-332.
- Cazals, C., Florens, J-P. and Simar, L. (2002) : "Nonparametric Frontier Estimation: a Robust Approach", Journal of Econometrics, 106, 1-25.
- Daouia, A. (2005).'' Asymptotic Representation Theory for Nonstandard Conditional Quantiles'', Journal of Nonparametric statistics, 17(2), 253-268.
- Daouia, A and Simar, L. (2005). '' Robust Nonparametric Estimators of Monotone Boundaries'', Journal of Multivariate Analysis, 96, 311-331.
- Fre, R. and V. Zelenyuk .(2003). ''On Aggregate Farrell Efficiency Scores'', European Journal of Operations Research 146:3, 615-620.
- Farrell, M. J. (1957). ''The Measurement of Productive Efficiency''. J. Roy. Stat. Soc., Series A., General, 120, Part 3: 253-281.
- Florens, J-P., and Simar, L. (2005). "Parametric Approximations of Nonparametric Frontiers", Journal of Econometrics,124, 91-116.
- Ghali, S. and P. Mohnen. (2003). "Restructuring and Economic Performance: The Experience of the Tunisian Economy", in Trade Policy and Economic Integration in the Middle East and North Africa: Economic Boundaries in Flux, (Hassan Hakimian and Jeffrey B Nugent, eds), London: Routledge-Curzon.
- Ghali, S. and P.Mohnen. (2004). "The Evolution and Determinants of Frontier Total Factor Productivity Growth in Tunisia", mimeo.
- Jeong, S.-O. (2004). ''Asymptotic distribution of DEA efficiency scores'', Journal of the Korean Statistical Society, to appear.
- Lakhoua, F, (1998), "The Tunisian experience of "Mise niveau": Conceptual issues and policy orientations", MDF II, World Bank, Marrakech, September.
- Lakhoua, F et Bouzaiane, L, (1998), "Quelles cibles pour le programme de mise niveau? ", Tunis, P.N.U.D/B.M.A.N, Janvier.
- Marcos, Ana Martin and C. S. Galvez, (2000), "Technical Efficiency of Spanish Manufacturing Firms: A Panel Data Approach", Applied Economics 32, 1249-1258.
- Park, B. L. Simar, and Ch. Weiner.( 2000). ''The FDH Estimator for Productivity Efficiency Scores: Asymptotic Properties'', Econometric Theory 16, 855 -877.
- Simar, L. (1992). ''Estimating Efficiencies from Frontier Models with Panel Data: a Comparison of Parametric, Non-parametric and Semi-Parametric Methods with Bootstrapping'', Journal of Productivity Analysis 3, 167-203.
- Simar, L. (2003). "Detecting Outliers in Frontier Models: A Simple Approach", Journal of Productivity Analysis, 20, 391-424.
- Simar, L. and P. Wilson.(1998). ''Sensitivity of efficiency scores: How to bootstrap in Nonparametric frontier models'', Management Sciences 44(1), 49-61.
- Simar, L. and P. Wilson . (2000 a). ''A General Methodology for Bootstrapping in Nonparametric Frontier Models'', Journal of Applied Statistics 27, 779-802.
- Simar, L. and P. Wilson . (2000 b). ''Statistical Inference in Nonparametric Frontier Models: The State of the Art'', Journal of Productivity Analysis 13, 49-78.
- Simar, L., and Wilson, P.W. (2003) : "Estimation and Inference in Two-Stage, Semi-parametric Models of Production Process", IAP (Universit Catholique de Louvain), Document de Travail 0310.

- Relative to stochastic frontier methods.
- Note that both methods can be applied to cost frontiers estimation.
- This procedure is preferred to the application of the exact formulae, which is more complicated.
- Deprins, Simar and Tulkens (1984) is the seminal paper on FDH estimation.
- These studies use different units as measurement of firm size. These units may be in number of workers, cultivated areas, total revenue, and total capital.
- Others methods have been developed (Wilson (1993-1995)) but their applications are heavier than this one, especially in large sample case.
- If the approximation precision is low then a higher Monte-Carlo parameter has to be chosen.
- where B is the Monte-Carlo parameter, technical level estimated by a Monte-Carlo procedure and technical efficiency level estimated on the bootstrapped sample b.
- These studies use different units as measurement of firm size. These units may be in number of workers, cultivated areas, total revenue, and total capital.
- The censored nature of the dependant variable raised doubt on the validity of the linear model in the FDH case. However we find interesting to present these results, as a kind of benchmark.
- A convex relation implies that there is the worst level of capital-labor ratio, at which firms should not be, since this level would minimize pure technical efficiency, holding other things equal.
- Note that, contrary at what figure (12) shows, the proportion of excluded firms exceed 3%, as we exclude all firms which have less than 10 firms at their "left".