(Luận văn) stochastic frontier models review with applications to vietnamese small and medium enterprises in metal manufacturing industry

t to UNIVERSITY OF ECONOMICS HO CHI MINH CITY VIETNAM INSTITUTE OF SOCIAL STUDIES THE HAGUE THE NETHERLANDS ng hi ep w VIETNAM - NETHERLANDS PROGRAMME FOR M.A IN DEVELOPMENT ECONOMICS n lo ad ju y th yi pl al n ua STOCHASTIC FRONTIER MODELS REVIEW WITH APPLICATIONS TO VIETNAMESE SMALL AND MEDIUM ENTERPRISES IN METAL MANUFACTURING INDUSTRY n va ll fu oi m nh at A thesis submitted in partial fulfilment of the requirements for the degree of z MASTER OF ARTS IN DEVELOPMENT ECONOMICS z om l.c gm NGUYEN QUANG k jm ht vb By Dr TRUONG DANG THUY an Lu Academic Supervisor: n va ey t re th HO CHI MINH CITY, NOVEMBER 2013 Page | ABSTRACT t to Metal manufacturing industry has an important role in the economy due to the high demand of metal ng products, especially steel and iron in daily life, production and, mostly construction To help maintain and hi develop the benefit from this industry, it is necessary to have an analysis into the technical efficiency level ep of small and medium enterprises (SMEs) which takes about 97% of the number of Vietnamese enterprises This study aims to estimate the technical efficiency level of Vietnamese SMEs using an unbalanced panel w n dataset in three years: 2005, 2007 and 2009 with stochastic frontier model Besides, because of divergent lo literatures of panel-data stochastic frontier model, this paper also makes a review of popular ones in order ad to choose the suitable model for the case of Vietnamese metal manufacturing industry The result shows y th different technical efficiency levels while using different models due to the divergence among identifications ju yi of technical efficiency concept pl n ua al n va ll fu oi m at nh z z k jm ht vb om l.c gm an Lu n va ey t re th Page | TABLE OF CONTENT t to Page ng LIST OF TABLES hi LIST OF FIGURES ep LIST OF CHARTS CHAPTER I: INTRODUCTION w n Introduction lo ad Research objectives y th CHAPTER II: LITERATURE REVIEW ju Efficiency measurement yi Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) pl The cross-sectional Stochastic Frontier Model 12 al n ua Stochastic frontier model with panel data 15 va 4.1 Time-invariant models 16 n 4.1 Time varying models 19 fu ll CHAPTER III: METHODOLOGY 25 m Overview of Vietnamese metal manufacturing industry 25 oi nh Analytical framework 27 at Research method 26 z 3.1 Estimating technical inefficiency 26 z ht vb 3.2 Variables description 30 jm 3.3 Data source 34 k CHAPTER IV: RESULT AND DISCUSSION 37 gm Empirical result 37 l.c 1.1 Cobb-Douglas functional form 37 om 1.2 Translog functional form 42 an Lu Discussion 44 2.1 Models without distribution assumption 44 BIBLIOGRAPHY 54 Page | th CHAPTER V: CONCLUSION 50 ey 2.4 Identification issue 48 t re 2.3 Technical inefficiency and firm-specific effects 46 n va 2.2 The distribution of technical inefficiency 45 t to ng LIST OF TABLES: hi ep Table 3-1 Output and Input deflators 31 Table 3-2 Descriptive statistic of key variables 35 w Table – Real outputs and material costs value of different-sized firms 35 n lo ad Table 4-1 Time invariant models with Cobb – Douglas function 37 ju y th Table 4-2 Time varying models with Cobb – Douglas function 39 Table 4-3 Determinants 41 yi pl Table 4-4 Time invariant models with Translog function 43 al ua Table 4-5 Time varying models with Translog function 44 n Table 4-6 Value of μ in models with truncated distribution 46 n va ll fu oi m LIST OF FIGURES Figure 2-1 Input-oriented efficiency nh at Figure 2-2 Output-oriented efficiency z z Figure 2-3 various types of technical inefficiency distribution 14 k jm ht vb LIST OF CHARTS l.c gm Chart 3-1 Firm size and ownership type 36 Chart 3-2 Firm location 36 om an Lu n va ey t re th Page | CHAPTER I: INTRODUCTION t to ng Introduction hi ep The rising demand of metal products (especially iron and steel) in daily life, production and, mostly, construction sector makes the role of metal manufacturing industry important According w to World Steel Association, at the end of 2011, Vietnamese steel market was the seventh largest n lo in Asia with the growth rate in tandem with economic expansion There are still huge potentials ad from this industry due to the growing income and an expanding trend of construction y th ju As reported by Viet Nam chamber of Commerce and Industry (VCCI), at the end of 2011, 97% of yi the number of enterprises in Viet Nam are small and medium sized which employ more than a half pl ua al of the domestic labor force and contribute more than 40% of GDP This dynamic group of firms have become have become an important resource for economic growth in Viet Nam However, n n va this industry is now facing challenges due to outdated technology and the heavy dependence on fu import materials From the reasons above, an analysis into the technical inefficiency level of ll Vietnamese small and medium enterprises (SMEs) in metal manufacturing industry is necessary m oi to maintain and develop the benefit from this industry nh at Technical efficiency is the effectiveness with which the firm uses a given set of inputs to produce z z outputs The set of highest amounts of output that can be produced from given amounts of inputs vb is the production frontier Technical efficiency reflects how close a firm can reach this border: ht jm firms producing on this frontier are technically efficient, while those far below from the frontier k are technically inefficient A technical efficiency analysis is often conducted by constructing a gm production-possibility boundary (the frontier) and then estimating the distance (the inefficiency om l.c level) of firms from that boundary an Lu There are two approaches to measure technical efficiency: deterministic and stochastic The deterministic approach, called Data Envelopment Analysis (DEA), was first introduced in Analysis (SFA), was mentioned first in Aigner, Lovell, and Schmidt (1977) and Meeusen and Broeck (1977) This method, contrary to DEA, requires a specific functional form for the Page | th that there is no statistical noise in data The stochastic approach, called Stochastic Frontier ey specification of the production function However, for being deterministic, this method assumes t re outputs to construct the frontier The advantage of this method is that it does not require the n va Charnes, Cooper, and Rhodes (1978) which use linear programming with the data of inputs and production function and allows data to have noises SFA is used more often in practice because t to for many cases, the noiseless assumption are unrealistic ng hi Since its first appearance in Aigner et al (1977) and Meeusen and Broeck (1977), the literature of ep technical efficiency has been widely developed through many studies such as Pitt and Lee (1981), Schmidt and Sickles (1984), Battese and Coelli (1988, 1992, 1995), Cornwell, Schmidt, and w n Sickles (1990), Kumbhakar (1990), Lee and Schmidt (1993) and Greene (2005) (see Greene (2008) lo ad for an overview of those) Being able to deal with various production processes, this method has y th become a popular tool to analyze the performance of production units such as firms, regions and ju countries Those applications can be found in Battese and Corra (1977), Page Jr (1984), Bravo- yi Ureta and Rieger (1991), Battese (1992), Dong and Putterman (1997), Anderson, Fish, Xia, and pl ua al Michello (1999) and Cullinane, Wang, Song, and Ji (2006) n Despite the fact that a rich literature of this matter has been developed over a long time, researchers va n at times find it difficult to choose the most appropriate model to estimate the technical efficiency ll fu level or determining its sources The earliest versions of these models were built to deal with cross oi m sectional data (Aigner et al., 1977; Meeusen & Broeck, 1977) These models need assumptions nh about technical inefficiency distribution and its uncorrelatedness with other parts of the model Pitt at and Lee (1981) and Schmidt and Sickles (1984) criticized that technical inefficiency cannot be z z estimated consistently with cross-sectional data and suggested models that deal with panel data ht vb The literature of panel data models first come with the assumption of time-invariant technical jm inefficiency (Battese & Coelli, 1988; Pitt & Lee, 1981; Schmidt & Sickles, 1984) Researchers, k after that, claimed that it is too strict to assume technical inefficiency to be fixed through time and gm suggested models that allow its time-variation such as Cornwell et al (1990), Kumbhakar (1990), l.c Lee and Schmidt (1993) and Battese and Coelli (1992) Those models solved the problems by om imposing some time patterns Nevertheless, the assumption of an unchanged time behavior was an Lu also criticized too strict Then the model with technical inefficiency effects was created by Battese and Coelli (1995) which allows technical inefficiency to vary with time and other determinants with panel-data stochastic frontier models Besides, this study also reviews those panel data models of technical inefficiency analysis and gives some implication about model choice in this field This Page | th This thesis aims to estimate the technical efficiency level of Vietnamese metal manufacturing firms ey t re changing of inefficiency and separate it from other firm specific factors n va Greene (2005) introduces “true” fixed and random models which warrant the unrestraint time study uses an unbalanced panel dataset of firms in metal manufacturing industry in the year 2005, t to 2007 and 2009 which is withdrawn from Vietnamese SMEs survey The result shows different ng technical efficiency levels among those stochastic frontier models hi ep Research objectives w - To give a review of panel-data stochastic frontier models; n lo - To apply those models to investigate the technical efficiency of SME firms in metal ad manufacturing industry in Viet Nam ju y th yi pl n ua al n va ll fu oi m at nh z z k jm ht vb om l.c gm an Lu n va ey t re th Page | CHAPTER II: LITERATURE REVIEW t to ng Efficiency measurement hi ep The main economic function of a business can be expressed as a process which turns its inputs into outputs with a specific producing ability The ratio outputs/inputs indicates the productivity w of a specific firm (Coelli, Rao, O'Donnell, & Battese, 2005) Change in productivity reflects how n lo well a production unit operates, in other words, how efficient it is From economic perspective, ad growth in productivity or efficiency can be considered as the most popular proxy for firm ju y th performance yi The terms productivity and efficiency need to be discriminated in the context of firm production pl ua al On the one hand, productivity implies all factors that decide how well outputs can be obtained from given amounts of inputs It can be considered as “Total factor productivity - TFP” On the n n va other hand, efficiency relates to the production frontier This frontier shows the maximum output fu that can be produced with a level of input A firm is called efficient technically when it produces ll on this frontier Firm production cannot go beyond this frontier for this is the limitation of its m oi performing ability When the firm performs below this frontier, it is considered inefficient The nh farther the distance is, the more inefficient the firm is Changes in productivity can be due to the at z changes in efficiency (the firm becomes more or less efficient technically), a change in the amount z vb and proportion of its inputs (changing its scale efficiency), a change in technical progress (change jm ht in technology level over time) or a combination of all the above factors (Coelli et al., 2005) k Efficiency measurement can be approached from two sides, inputs and outputs Input-oriented gm measures relate to cost reduction (minimum amount of inputs to produce a given amount of l.c output) Output-oriented measure, on the other hand, makes use of the maximum level of output om produced from a given amount of inputs Figure 2-1 and 2-2 illustrate these two approaches Figure an Lu 2-1 demonstrates a firm with two inputs X1 and X2, YY’ is an isoquant which shows every minimum set of inputs that could be used to produce a given output If a firm operates on this allocative efficiency (AE) equals the percentage rate of OS/OR The multiplication of AE and TE Page | th lowest cost Technical efficiency (TE) can be calculated by the percentage rate of OR/OP, ey the input-price ratio is known) determines the optimal proportion of inputs in order to archive t re the inputs amount of this firm is minimized The iso-cost line CC’ (which can be constructed when n va isoquant (the frontier), it will be technically efficient in an input-oriented way for the reason that expresses the overall efficiency of the firm, called economic efficiency (EE) (i.e.𝐸𝐸 = 𝐴𝐸 × 𝑇𝐸) t to Figure 2-2, illustrate the case where the firm uses one input and produces one output, The f(X) ng curve determines the maximum output can be obtained by using each level of input X (the frontier) hi ep The firm will be technical efficient operating on this frontier In this situation, TE equals BD/DE w n lo ad ju y th yi pl n ua al n va Figure – 1: Input-oriented efficiency ll fu oi m at nh z z jm ht vb Figure – 2: Output-oriented efficiency k Measurements and analyses of TE were conducted by a huge number of studies with two main gm next section briefly discusses these two methods a Data Envelopment Analysis (DEA) an Lu Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) om l.c approaches – Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) The (1994), Färe, Grosskopf, and Lovell (1985) and Ray (2004) Page | th instruction can be found in Banker et al (1984), Charnes et al (1978), Fare, Grosskopf, and Lovell ey allow for decreasing and variable return to scale in Banker, Charnes, and Cooper (1984) Specific t re Charnes, Cooper, and Rhodes (1978) with constant return to scale Later on, it was extended to n va DEA is a non-parametric method in estimating firm efficiency which was first introduced in With n firms (called Decision Making Units – DMUs), each firm uses m types of inputs and t to produces s types of outputs, the model for DEA following an output-oriented measure is given by: ng hi max ℎ0 = ∑𝑠𝑟=1 𝑢𝑟 𝑦𝑟0 (2.2.1) ep ∑𝑚 𝑖=1 𝑣𝑖 𝑥𝑖0 Subject to: w n lo ad ∑𝑠𝑟=1 𝑢𝑟 𝑦𝑟𝑗 ≤1 ∑𝑚 𝑖=1 𝑣𝑖 𝑥𝑖𝑗 y th ju 𝑢𝑟 , 𝑣𝑖 ≥ yi pl With: 𝑗 = 1,2, … , 𝑛; 𝑟 = 1,2, … , 𝑠; 𝑖 = 1,2, … , 𝑚; 𝑥𝑖𝑗 , 𝑦𝑟𝑗 are respectively the ith input and rth al ua output of jth DMU; 𝑢𝑟 , 𝑣𝑖 are the weights of outputs and inputs which come from the solution of n this maximization problem (Charnes et al., 1978) Using a piece-wise frontier from (Farrell, 1957) va n and linear programming algorithm in maximization mathematics, this method constructs a ll fu production frontier Then, the ratio between outputs and inputs will be brought into account and oi m compared with the frontier to calculate the efficiency level of each firm nh Only being noticed from 1978, but, for many reasons, DEA has become a popular branch of at z efficiency analysis Wei (2001) described this growing progress by listing five evolvements in z DEA researches Studies using DEA have been conducted in almost industries, both private and vb jm ht public sector Moreover, numerical methods and supporting computer programs have grown in both number and quality Over time, new models of DEA have been discussed and established, k gm such as additive model, log-type DEA model and stochastic DEA model Besides, the economic l.c and management background of DEA have been analyzed more carefully and deeply, om strengthening the base for the applications of this model Mathematical theories related to DEA have also been promoted by many mathematicians Those factors gave rise to the progress of both an Lu theoretical improvements and empirical applications of this non-parametric method va n b Stochastic Frontier Analysis (SFA): 𝑌𝑖 = 𝑓(𝑋𝑖 , 𝛽)𝑒 𝑣𝑖 −𝑢𝑖 (2.2.2) Page | 10 th below: ey stochastic frontier to measure firms’ efficiency The model can be described mathematically as t re Aigner et al (1977) and Meeusen and Broeck (1977) suggested the method of production