Stochastic frontier models review with applications to Vietnamese small and medium enterprises in metal manufacturing industry

UNIVERSITY OF ECONOMICS HO CHI MINH CITY VIETNAM INSTITUTE OF SOCIAL STUDIES THE HAGUE THE NETHERLANDS VIETNAM - NETHERLANDS PROGRAMME FOR M.A IN DEVELOPMENT ECONOMICS STOCHASTIC FRONTIER MODELS REVIEW WITH APPLICATIONS TO VIETNAMESE SMALL AND MEDIUM ENTERPRISES IN METAL MANUFACTURING INDUSTRY A thesis submitted in partial fulfilment of the requirements for the degree of MASTER OF ARTS IN DEVELOPMENT ECONOMICS By NGUYEN QUANG Academic Supervisor: Dr TRUONG DANG THUY HO CHI MINH CITY, NOVEMBER 2013 Page | ABSTRACT Metal manufacturing industry has an important role in the economy due to the high demand of metal products, especially steel and iron in daily life, production and, mostly construction To help maintain and develop the benefit from this industry, it is necessary to have an analysis into the technical efficiency level 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 dataset in three years: 2005, 2007 and 2009 with stochastic frontier model Besides, because of divergent literatures of panel-data stochastic frontier model, this paper also makes a review of popular ones in order to choose the suitable model for the case of Vietnamese metal manufacturing industry The result shows different technical efficiency levels while using different models due to the divergence among identifications of technical efficiency concept Page | TABLE OF CONTENT Page LIST OF TABLES LIST OF FIGURES LIST OF CHARTS CHAPTER I: INTRODUCTION Introduction Research objectives CHAPTER II: LITERATURE REVIEW Efficiency measurement Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) The cross-sectional Stochastic Frontier Model 12 Stochastic frontier model with panel data 15 4.1 Time-invariant models 16 4.1 Time varying models 19 CHAPTER III: METHODOLOGY 25 Overview of Vietnamese metal manufacturing industry 25 Analytical framework 27 Research method 26 3.1 Estimating technical inefficiency 26 3.2 Variables description 30 3.3 Data source 34 CHAPTER IV: RESULT AND DISCUSSION 37 Empirical result 37 1.1 Cobb-Douglas functional form 37 1.2 Translog functional form 42 Discussion 44 2.1 Models without distribution assumption 44 2.2 The distribution of technical inefficiency 45 2.3 Technical inefficiency and firm-specific effects 46 2.4 Identification issue 48 CHAPTER V: CONCLUSION 50 BIBLIOGRAPHY 54 Page | LIST OF TABLES: Table 3-1 Output and Input deflators 31 Table 3-2 Descriptive statistic of key variables 35 Table – Real outputs and material costs value of different-sized firms 35 Table 4-1 Time invariant models with Cobb – Douglas function 37 Table 4-2 Time varying models with Cobb – Douglas function 39 Table 4-3 Determinants 41 Table 4-4 Time invariant models with Translog function 43 Table 4-5 Time varying models with Translog function 44 Table 4-6 Value of μ in models with truncated distribution 46 LIST OF FIGURES Figure 2-1 Input-oriented efficiency Figure 2-2 Output-oriented efficiency Figure 2-3 various types of technical inefficiency distribution 14 LIST OF CHARTS Chart 3-1 Firm size and ownership type 36 Chart 3-2 Firm location 36 Page | CHAPTER I: INTRODUCTION Introduction 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 to World Steel Association, at the end of 2011, Vietnamese steel market was the seventh largest in Asia with the growth rate in tandem with economic expansion There are still huge potentials from this industry due to the growing income and an expanding trend of construction As reported by Viet Nam chamber of Commerce and Industry (VCCI), at the end of 2011, 97% of the number of enterprises in Viet Nam are small and medium sized which employ more than a half 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, this industry is now facing challenges due to outdated technology and the heavy dependence on import materials From the reasons above, an analysis into the technical inefficiency level of Vietnamese small and medium enterprises (SMEs) in metal manufacturing industry is necessary to maintain and develop the benefit from this industry Technical efficiency is the effectiveness with which the firm uses a given set of inputs to produce outputs The set of highest amounts of output that can be produced from given amounts of inputs is the production frontier Technical efficiency reflects how close a firm can reach this border: firms producing on this frontier are technically efficient, while those far below from the frontier are technically inefficient A technical efficiency analysis is often conducted by constructing a production-possibility boundary (the frontier) and then estimating the distance (the inefficiency level) of firms from that boundary There are two approaches to measure technical efficiency: deterministic and stochastic The deterministic approach, called Data Envelopment Analysis (DEA), was first introduced in Charnes, Cooper, and Rhodes (1978) which use linear programming with the data of inputs and outputs to construct the frontier The advantage of this method is that it does not require the specification of the production function However, for being deterministic, this method assumes that there is no statistical noise in data The stochastic approach, called Stochastic Frontier 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 | production function and allows data to have noises SFA is used more often in practice because for many cases, the noiseless assumption are unrealistic Since its first appearance in Aigner et al (1977) and Meeusen and Broeck (1977), the literature of 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 Sickles (1990), Kumbhakar (1990), Lee and Schmidt (1993) and Greene (2005) (see Greene (2008) for an overview of those) Being able to deal with various production processes, this method has become a popular tool to analyze the performance of production units such as firms, regions and countries Those applications can be found in Battese and Corra (1977), Page Jr (1984), BravoUreta and Rieger (1991), Battese (1992), Dong and Putterman (1997), Anderson, Fish, Xia, and Michello (1999) and Cullinane, Wang, Song, and Ji (2006) Despite the fact that a rich literature of this matter has been developed over a long time, researchers at times find it difficult to choose the most appropriate model to estimate the technical efficiency level or determining its sources The earliest versions of these models were built to deal with cross sectional data (Aigner et al., 1977; Meeusen & Broeck, 1977) These models need assumptions about technical inefficiency distribution and its uncorrelatedness with other parts of the model Pitt and Lee (1981) and Schmidt and Sickles (1984) criticized that technical inefficiency cannot be estimated consistently with cross-sectional data and suggested models that deal with panel data The literature of panel data models first come with the assumption of time-invariant technical inefficiency (Battese & Coelli, 1988; Pitt & Lee, 1981; Schmidt & Sickles, 1984) Researchers, after that, claimed that it is too strict to assume technical inefficiency to be fixed through time and suggested models that allow its time-variation such as Cornwell et al (1990), Kumbhakar (1990), Lee and Schmidt (1993) and Battese and Coelli (1992) Those models solved the problems by imposing some time patterns Nevertheless, the assumption of an unchanged time behavior was 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 Greene (2005) introduces “true” fixed and random models which warrant the unrestraint time changing of inefficiency and separate it from other firm specific factors This thesis aims to estimate the technical efficiency level of Vietnamese metal manufacturing firms 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 | study uses an unbalanced panel dataset of firms in metal manufacturing industry in the year 2005, 2007 and 2009 which is withdrawn from Vietnamese SMEs survey The result shows different technical efficiency levels among those stochastic frontier models Research objectives - To give a review of panel-data stochastic frontier models; - To apply those models to investigate the technical efficiency of SME firms in metal manufacturing industry in Viet Nam Page | CHAPTER II: LITERATURE REVIEW Efficiency measurement 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 of a specific firm (Coelli, Rao, O'Donnell, & Battese, 2005) Change in productivity reflects how well a production unit operates, in other words, how efficient it is From economic perspective, growth in productivity or efficiency can be considered as the most popular proxy for firm performance The terms productivity and efficiency need to be discriminated in the context of firm production 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 other hand, efficiency relates to the production frontier This frontier shows the maximum output that can be produced with a level of input A firm is called efficient technically when it produces on this frontier Firm production cannot go beyond this frontier for this is the limitation of its performing ability When the firm performs below this frontier, it is considered inefficient The farther the distance is, the more inefficient the firm is Changes in productivity can be due to the changes in efficiency (the firm becomes more or less efficient technically), a change in the amount and proportion of its inputs (changing its scale efficiency), a change in technical progress (change in technology level over time) or a combination of all the above factors (Coelli et al., 2005) Efficiency measurement can be approached from two sides, inputs and outputs Input-oriented measures relate to cost reduction (minimum amount of inputs to produce a given amount of output) Output-oriented measure, on the other hand, makes use of the maximum level of output produced from a given amount of inputs Figure 2-1 and 2-2 illustrate these two approaches Figure 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 isoquant (the frontier), it will be technically efficient in an input-oriented way for the reason that the inputs amount of this firm is minimized The iso-cost line CC’ (which can be constructed when the input-price ratio is known) determines the optimal proportion of inputs in order to archive lowest cost Technical efficiency (TE) can be calculated by the percentage rate of OR/OP, allocative efficiency (AE) equals the percentage rate of OS/OR The multiplication of AE and TE Page | expresses the overall efficiency of the firm, called economic efficiency (EE) (i.e.𝐸𝐸 = 𝐴𝐸 × 𝑇𝐸) Figure 2-2, illustrate the case where the firm uses one input and produces one output, The f(X) curve determines the maximum output can be obtained by using each level of input X (the frontier) The firm will be technical efficient operating on this frontier In this situation, TE equals BD/DE Figure – 1: Input-oriented efficiency Figure – 2: Output-oriented efficiency Measurements and analyses of TE were conducted by a huge number of studies with two main approaches – Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) The next section briefly discusses these two methods Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) a Data Envelopment Analysis (DEA) DEA is a non-parametric method in estimating firm efficiency which was first introduced in Charnes, Cooper, and Rhodes (1978) with constant return to scale Later on, it was extended to allow for decreasing and variable return to scale in Banker, Charnes, and Cooper (1984) Specific instruction can be found in Banker et al (1984), Charnes et al (1978), Fare, Grosskopf, and Lovell (1994), Färe, Grosskopf, and Lovell (1985) and Ray (2004) Page | With n firms (called Decision Making Units – DMUs), each firm uses m types of inputs and produces s types of outputs, the model for DEA following an output-oriented measure is given by: max ℎ0 = ∑𝑠𝑟=1 𝑢𝑟 𝑦𝑟0 ∑𝑚 𝑖=1 𝑣𝑖 𝑥𝑖0 (2.2.1) Subject to: ∑𝑠𝑟=1 𝑢𝑟 𝑦𝑟𝑗 ≤1 ∑𝑚 𝑖=1 𝑣𝑖 𝑥𝑖𝑗 𝑢𝑟 , 𝑣𝑖 ≥ With: 𝑗 = 1,2, … , 𝑛; 𝑟 = 1,2, … , 𝑠; 𝑖 = 1,2, … , 𝑚; 𝑥𝑖𝑗 , 𝑦𝑟𝑗 are respectively the ith input and rth output of jth DMU; 𝑢𝑟 , 𝑣𝑖 are the weights of outputs and inputs which come from the solution of this maximization problem (Charnes et al., 1978) Using a piece-wise frontier from (Farrell, 1957) and linear programming algorithm in maximization mathematics, this method constructs a production frontier Then, the ratio between outputs and inputs will be brought into account and compared with the frontier to calculate the efficiency level of each firm Only being noticed from 1978, but, for many reasons, DEA has become a popular branch of efficiency analysis Wei (2001) described this growing progress by listing five evolvements in DEA researches Studies using DEA have been conducted in almost industries, both private and 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, such as additive model, log-type DEA model and stochastic DEA model Besides, the economic and management background of DEA have been analyzed more carefully and deeply, 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 theoretical improvements and empirical applications of this non-parametric method b Stochastic Frontier Analysis (SFA): Aigner et al (1977) and Meeusen and Broeck (1977) suggested the method of production stochastic frontier to measure firms’ efficiency The model can be described mathematically as below: 𝑌𝑖 = 𝑓(𝑋𝑖 , 𝛽)𝑒 𝑣𝑖 −𝑢𝑖 (2.2.2) Page | 10 1.2 Translog functional form a Time invariant model Table – shows the result from estimating time invariant models with Translog functional form Two first columns show the result for fixed and random effects models in Schmidt and Sickles (1984) respectively The result from estimating the model in Pitt and Lee (1981) is in the third column The last column is the result from the model in Battese and Coelli (1988) The random effects models in Pitt and Lee (1981), Battese and Coelli (1988) and Schmidt and Sickles (1984) (column [2], [3] and [4]) gives similar results but it is quite different to the one in the fixed effects model (column [1]) The variance of 𝑢𝑖 is small to the variance of 𝑣𝑖 and all their estimated technical efficiency levels are about 100% This implies the absence of technical inefficiency effects Obviously, when the technical inefficiency is absent or its value is fractional, differences among those random effects models’ result would be small The result from fixed effects model is quite divergent with the average technical efficiency level is about 51.78% and the range is 41.54% - 100% Coefficients estimated from three random effects models in Schmidt and Sickles (1984), Pitt and Lee (1981) and Battese and Coelli (1988) are similar in value and significant level Most coefficients are significant Fixed effects model in Schmidt and Sickles (1984) has just a few differences in the value and the significance of coefficients Generally, the form of production is quite consistent among those models b Time varying models Table – shows the result of time varying models with Translog functional form Three first columns are the result of the model in Kumbhakar (1990), Battese and Coelli (1992) and Lee and Schmidt (1993) respectively Columns [4] and [5] is the result form technical inefficiency effects model in Battese and Coelli (1995) with two cases: with and without determinants The last four columns are the result of the models in Greene (2005) Columns [8] and [9] are the general forms with variables standing for observable heterogeneity The time varying models in Kumbhakar (1990) and Battese and Coelli (1992) give quite equivalent results The technical efficiency level Page | 42 [1] lnK lnL lnM lnI lnK lnL lnK lnM lnK lnI lnL lnM lnL lnI lnM lnI lnK2 lnL2 lnM2 lnI2 const [2] [3] [4] [5] [6] [7] [8] KUMB90 BC92 FELS BC95 BC95w TRE TFE Genral TRE General TFE 0.095** 0.092** 0.237 0.087** 0.103*** 0.085** (0.040) (0.036) (0.232) (0.037) (0.035) (0.034) 0.219*** 0.221*** 0.503 0.190*** 0.209*** 0.231*** (0.062) (0.059) (0.057) (0.058) (0.063) 0.188** 0.176*** 0.153 0.238*** 0.214*** 0.230*** (0.073) (0.042) (0.040) (0.040) (0.040) 0.265*** 0.240*** 0.369 0.228*** 0.294*** 0.215*** (0.065) (0.054) (0.428) (0.051) (0.053) (0.053) 0.005 0.007 -0.013 0.013** 0.010** 0.011** (0.005) (0.005) (0.038) (0.005) (0.005) (0.005) (0.400) (0.340) -0.014*** -0.014*** -0.008 -0.018*** -0.016*** -0.017*** (0.004) (0.003) (0.027) (0.003) (0.003) (0.003) 0.004 0.004 0.006 0.009* 0.004 -0.107*** (0.004) (0.004) (0.035) (0.005) (0.004) (0.004) -0.109*** -0.107*** -0.118** -0.108*** -0.111*** -0.1*** (0.012) (0.007) (0.048) (0.007) (0.007) (0.007) 0.004 0.006 -0.01 0.004 0.004 0.002 (0.009) (0.009) (0.073) (0.010) (0.009) (0.009) -0.065*** -0.067*** -0.066 -0.062*** -0.065*** -0.064*** (0.007) (0.006) (0.057) (0.006) (0.006) (0.006) -0.001 -0.001 -0.002 -0.004** -0.002 -0.003** (0.002) (0.002) (0.011) (0.002) (0.002) (0.001) 0.057*** 0.053*** 0.066 0.052*** 0.056*** 0.052*** (0.007) (0.005) (0.043) (0.006) (0.006) (0.006) 0.100*** 0.100*** 0.104*** 0.099*** 0.101*** 0.099*** (0.005) (0.003) (0.003) (0.003) 0.027*** 0.029*** 0.028 0.024*** 0.025*** 0.026*** (0.005) (0.006) (0.006) (0.005) 3.272*** 2.642*** 3.200*** (0.003) (0.006) (0.028) (0.045) 2.994*** 3.230*** (0.413) (0.308) (0.303) (0.288) (0.317) 𝜎𝑢 or 𝜎𝑢2 𝜎𝑣 or 𝜎𝑣2 0.203 n/a 0.120 n/a 0.0006 0.0007 0.134 n/a 0.130 n/a 0.148 0.144 2005 90.54% 90.40% 92.87% 99.95% 99.94% 2007 100.00% 96.95% 93.55% 99.95% 99.94% 2009 100.00% 99.03% 93.80% 99.95% 99.94% n/a [9] Table – 5: Time varying models with Translog function KUMB90: model in Kumbhakar (1990); BC92: the model in Battese and Coelli (1992); FELS: the model in Lee and Schmidt (1993); BC95: the model in Battese and Coelli (1995); BC95w: BC95 with determinants; TRE: “true” random effects model; TFE: “true” fixed effects model Page | 43 is respectively 90.54% in average in 2005 and 100% in 2007 and 2009 with the model of Kumbhakar (1990) The technical efficiency level in Battese and Coelli (1992) model is 90.40% in 2005, 96.95% in 2007 and 99.03% in 2009 The result from the FRONTIER 4.1 shows that the model in Battese and Coelli (1995) has no effects of technical inefficiency in the case no determinant is included in the model When those determinants appear, the range of firms’ technical efficiency is widen (83.41% to 100%) True random effects give the result that all firms are efficient with the technical efficiency levels are about 99.95% True fixed effects models cannot give the result This implies a misspecification in the model In other words, technical inefficiency does not exist The estimated coefficients of inputs from the general form of “true” random effects model with Translog functional form is quite comparable to the result of the technical inefficiency effects model in Battese and Coelli (1995) Most determinants are more significant when being put in the production function than in the technical inefficiency effects model All determinants (age, size, location and ownership type) are shown to affects firm’s output STATA cannot compute the result for the general form of “true” fixed effects model in Greene (2005) This implies that the technical inefficiency is absent from this model The coefficient of inputs are quite consistent Most coefficients of labor, raw material and indirect costs are significant All F-tests reject the null hypothesis that inputs variables are absent from the model In other words, the specification of the production function is valid Discussion 2.1 Models without distribution assumption From the estimating result, the first and most obvious inference is that models without distributional assumption as those in Schmidt and Sickles (1984) and Lee and Schmidt (1993) give the result of wide-gap efficiency ranges and also lower average technical efficiency levels While all models with distributional assumption suggest the technical efficiency level more than 90%, the fixed effects model in Schmidt and Sickles (1984) gives the average of technical efficiency of 21.71% with the Cobb-Douglas function and 51.78% with the Translog function Although the random effects model cannot find technical inefficiency effects for the Translog function (this may be because Translog functional from has more ability in explaining the production function than Cobb-Douglas functional from), it still gives the average technical efficiency level of 63.25% with Page | 44 the Cobb-Douglas functional from The difference in technical efficiency level is also large in those results This result comes from the matter of what will be included in technical efficiency Without any assumption on the distribution of 𝑢, all firm specific factors will be considered in technical inefficiency value By doing this, the gaps in efficiency among firms are widen This also lowers the average level of technical efficiency Schmidt and Sickles (1984) considered this matter as a weakness of their models They claimed that the technical inefficiency estimated from those models include all fixed effects when some of those (in their example: capital stock) may not relate to technical inefficiency Also, by using these models, technical inefficiency can only be calculated by comparing with the best firm in the sample but not with an absolute standard Then sampling bias will arise With a sample what observations are similar, most of them will be efficient With a sample that a firm or a group of firm has extremely large specific value, most firms will have low efficiency and vice versa Those biases can makes conclusions and implications in efficiency analysis less confident 2.2 The distribution of technical inefficiency As mentioned above, different assumptions about the distribution of technical inefficiency can lead to different estimating results With half-normal and exponential distribution, most observations have the inefficiency level near zero Then most firms will be efficient Pitt and Lee (1981) support this idea by stating that over time, most firms will recognize their inefficiency level and change themselves to be more efficient Sometimes this assumption is too strong A truncated distribution with positive mean value can help us avoid that matter by allowing 𝑢 to gather around a positive particular value Thus, the level of technical efficiency is not necessary to be high How suitable an assumption of distribution is could depend on the nature of the industry Consider an industry with just a small amount of firms’ entry and exit Then most firms stay overtime and with the reason mentioned above, they become more efficient This situation fits the assumption of a half normal or exponential distribution With another industry where a large amount of firms enter and exit every year Then the average level of efficiency should not be so high for the reason that new firms tend to be less efficient than the old ones because they are lack of experience or small in scale However, as we mentioned above, the truncated normal distribution is more general than the others With the value of 𝜇 equals zero, it becomes a half-normal distribution When 𝜇 is Page | 45 not positive, its shape is not different from the others Thus, letting data decide the value of 𝜇, or, in other words, the type of distribution will reflect the nature of technical inefficiency better The 𝜇 value estimated from those truncated models above is all negative which implies that the distributions of 𝑢 in all case are similar to a half-normal one Cobb-Douglas function Translog function bc88 -9.17 -4.02 bc92 -0.136 -0.055 bc95 (without det.) bc95 (with det.) -0.05 -0.05 n/a -0.205 Table – 6: Value of 𝜇 in models with truncated distribution 2.3 Technical inefficiency and firm-specific effects The technical inefficiency model in Battese and Coelli (1995) shows different results between the case with determinants and the case without determinants (columns [5] and [6] in table – and – 5) The reason is, with the appearance of determinants of technical inefficiency in the log likelihood function, their parameters gain value from other parts of the model and contribute it to the value of technical inefficiency Thus, the more different the firms are, the greater value of 𝑢 will be estimated By adding more determinants that can makes firms’ characteristic more divergent, we can change the result For this reason, the use of this model needs careful considerations about the matter of what can be the determinants of technical inefficiency Previous literature has suggested many of them such as firm’s size (Mead and Liedholm (1998); Van Biesebroeck , 2005), firm’s age (Mueller, 1972; Jovanovic, 1982), location (Glancey, 1998; Devereux, Griffith, and Simpson, 2007; Vu, 2003), ownership (Bevan et al., 1999; Chaganti & Damanpour, 1991), export (Abdullayeva, 2010; Bigsten et al., 2000; Bigsten et al., 2004), innovation (Janz, Lööf, & Peters, 2003; Koellinger, 2008) The list has not been exhausted While firm-specific effects gain value for technical inefficiency in the model of Battese and Coelli (1995), it takes away the value of technical inefficiency in the model of Greene (2005) Greene suggests the “true” fixed and random model in order to separate technical inefficiency with unobserved heterogeneity between firms By doing this, the larger the firm-specific effects are, the smaller the value of 𝑢 is In our empirical result, the “true” random model, after separate out all firm specific effects, leaves just a fractional value for 𝑢 Therefore all firms are nearly 100% efficient The fact that “true” fixed effects cannot give the result can be expressed as, essentially, there is no technical inefficiency effects with a specific distribution, all factors that explain the difference between firms are those time invariant firm effects and random noise Page | 46 From the distinction above, there should be some comparisons about the nature of technical inefficiency in the points of those authors Battese and Coelli (1995) considers technical inefficiency as the combination of all factors that make production effectiveness different from a firm to another From this viewpoint, we can ascertain the determinants of technical inefficiency Moreover, some of those determinants can be influenced to help improve firm’s efficiency such as size, ownership and export Thus, the model in Battese and Coelli (1995) is helpful in studies which tend to give policy implication for firms and for governments in order to ameliorate technical efficiency The model in Greene (2005) considers inefficiency as a freely various over time factor which is random and uncorrelated with other parts of the model Thus, from Greene’s viewpoint, no firm specific factor can have impact on inefficiency The only characteristic that makes this random factor different from the random noise is a particular distribution Therefore, the technical efficiency level estimated from this model can hardly be used to give implication for firms to improve their efficiency It simply implies the distance from firms to the frontier Although the model in Greene (2005) cannot explain much about technical inefficiency, it can be used like a powerful tool in analyzing firm productivity and its sources Recall a general form of “true” fixed and random effects model as described below: “True” fixed effects model: 𝑦𝑖𝑡 = 𝛼𝑖 + 𝛽𝑋𝑖𝑡 + 𝛾𝑍𝑖𝑡 + 𝑣𝑖𝑡 − 𝑢𝑖𝑡 “True” random effects model: 𝑦𝑖𝑡 = (𝛼 + 𝑤𝑖𝑡) + 𝛽𝑋𝑖𝑡 + 𝛾𝑍𝑖𝑡 + 𝑣𝑖𝑡 − 𝑢𝑖𝑡 with 𝑣𝑖𝑡 is the random noise, 𝑢𝑖𝑡 is technical inefficiency (in the viewpoint of Greene), firm’s specific unobserved heterogeneity stored in 𝛼𝑖 and 𝑤𝑖 , 𝑋𝑖𝑡 is a vector of inputs value, 𝑍𝑖𝑡 is a vector of firm-specific observed factors, 𝛽 and 𝛾 are coefficients to be estimated There are three separate factors can be considered here The first is unobservable heterogeneity (𝛼𝑖 or 𝑤𝑖 ), which has impacts on firm production but cannot be measured by specific variables The second is observable heterogeneity (𝛾𝑍𝑖𝑡 ) which influences firm’s production and can be measured And the last is technical inefficiency (𝑢𝑖𝑡 ) which can change freely through time “True” fixed effects can separate them without any assumptions while the assumption of the uncorrelatedness between 𝑤𝑖𝑡 and other parts of the model is necessary in “true” random model The observable part can help us in making implication to improve efficiency So, the larger this part is, the better we can understand about firms The unobservable part stays in the form of “effect” However, gradually overtime, it can be observed Thus, potentially, this part can provide information about firm performance Page | 47 2.4 Identification issue With the objective of reviewing methods of estimating technical inefficiency with Stochastic Frontier Model using panel data, this thesis has tried to describe the divergence among different aspects of previous studies on this matter One general comment can be made at the moment is that over a long development of both theoretical and empirical researches, this field has been deeply and broadly analyzed in many aspects to solve different matters However, the viewpoints about technical inefficiency hardly come to a consensus Each model has inside itself strengths and weaknesses that make it suitable to only specific situations Thus, the matter of model choice depends on what definition of technical inefficiency is perceived and what assumptions that one is willing to make about its nature In other words, it depends on the identification of the technical efficiency There are some factors that influences the choice of models and assumptions that can be made They are the theory that one bases on, the reality of the industry or the sample being analyzed and the availability of data Models mentioned above are different in the way they perceive technical inefficiency The fixed effects theory in Schmidt and Sickles (1984), Cornwell et al (1990), Lee and Schmidt (1993) suggest that all firm effects are included in technical inefficiency With within estimator, they not require any assumption either about the distribution of 𝑢 or the correlation between 𝑢 and other parts of the model “True” fixed effects model in Greene (2005) separates technical inefficiency from observable and unobservable heterogeneity Also use within estimators, it requires only the distributional assumption Random effects model as in Schmidt and Sickles (1984) also suggests that all firm specific effects are involved in technical inefficiency but uses a random approach Therefore, it requires only the assumption of uncorrelatedness Those models in Pitt and Lee (1981), Battese and Coelli (1988, 1992, 1995), Kumbhakar (1990) and “true” random effects model Greene (2005) require both assumptions However, “true” random effects model separates technical inefficiency from those heterogeneities while other cannot that Generally, the perceptions of what factors are included in technical inefficiency and whether they have a correlation with other parts of the model are important factors in model choice The reality or the nature of the chosen sample also affects the way assumptions are imposed As mentioned above, each industry should be considered carefully when its distribution of 𝑢 is chosen (half normal, exponential or truncated normal) Consider an industry with all firms stay close to the frontier (an old industry in which firms are almost technically efficient) and new technology is Page | 48 not obtained through the survey (no shifting in the frontier) Normally, year by year, firms get nearer to the frontier But for the reason that the distance is now too small, the changes are not worth to consider For those cases, one can ignore the matter of time shifting in the level of technical inefficiency and use those time invariant models The evidence from the empirical results of this study shows little differences between the technical efficiency level estimated with time invariant models (Pitt and Lee (1981) and Battese and Coelli (1988) models) and time varying models (Kumbhakar (1990), Battese and Coelli (1992, 1995) models) Besides, the assumption on model specification also needs careful consideration when using the model in Battese and Coelli (1995) The matter of reality should be considered carefully in the use of the technical inefficiency effects model Like what has been mentioned above, the way we choose the form of this model influences the estimated result For example: to analyze the technical inefficiency of an industry with 100% products are sold domestically, the appearance of the variable related to exporting are necessary Thus, regarding the specific characteristic of the targeted sample help researchers in choosing the most parsimonious and suitable models Finally, the availability of data is also an important factor that alters the model choice in analyzing technical efficiency Battese and Coelli (1988) conducts their study with a panel dataset of only three year about the performance of Australian dairy farm then they are willing to assume technical inefficiency to be time invariant The model in Cornwell et al (1990) needs a long panel dataset (more than three year) to be able to estimate technical inefficiency Schmidt and Sickles (1984) stated that a panel dataset with small N (number of groups) and large T (number of time periods) then the within estimator (fixed effects) is relevant because the firm specific intercepts will be estimated consistently If N is large and T is small, those asymptotic properties of maximum likelihood estimation will be useful then one should choose those models that use this estimating method As a summary for this discussion sector, we suggest one should base on clear research objectives to choose the model that can be conducted with the availability of data and has theoretical base fits the practical situation of the targeted sample Page | 49 CHAPTER V: CONCLUSION Despite the fact that a rich literature of estimating technical inefficiency with stochastic frontier model has been developed over a long time, it is difficult to choose the most appropriate model to estimate the technical efficiency level or determining its sources Researchers always have to choose between models with different assumptions and those without, between different perceptions about what technical inefficiency includes, between time invariant and time varying models or between different time patterns of technical inefficiency This study aims to review popular panel-data stochastic frontier models from the first one in Pitt and Lee (1981) to those in Greene (2005) The findings can help in justifying which model is suitable in specific circumstances The application of those models in estimating technical efficiency level of Vietnamese SMEs in metal industry give evidences about the impacts of model choice on empirical results The result shows substantive differences between those models that include all firm effects in technical inefficiency and those that use a specific distribution to separate them Models in the former group give the result of a wide range and low average level of technical efficiency while those in the latter group suggest that efficiency levels of firms are quite similar and averagely high except the case of random effects model with Translog functional form Different assumptions about distribution of technical inefficiency give similar results when the means of truncated distribution are negative or close to zero, which give truncated distribution a similar shape compared with half normal or exponential distribution With specific distributional assumptions, the model in Battese and Coelli (1995) with determinants shows a wider range of technical efficiency than “true” random effects model and the case without determinants (although “true” random model use half normal distribution and technical inefficiency model use truncated distribution but those distribution are similar because the mean of truncated distribution is very close to zero) Once again this emphasizes that technical inefficiency level depends on what it includes even with a specific distributional assumption Generally, there are clear evidences on the way the differences in assumptions and identifications of technical inefficiency affect the estimated result From those results, the study suggests that panel-data stochastic frontier models should be chosen flexibly to solve specific matters of analyzing technical inefficiency Differences in theories, practical conditions and the availability of data are key factors that affect the choice of model in Page | 50 this field Various definitions from theories decide what will be included in and determines technical inefficiency Different industries may have different time patterns or determinants of technical efficiency Finally, data availability has its own role in deciding whether to choose between time invariant models and time varying ones or between different estimating methods However, as mentioned in the discussion sector 2.4 in Chapter IV, the general form of “true” fixed and random effects model is very useful for the purpose of analyzing firm production These kinds of stochastic frontier model have the advantages of a clear look into factors that influence firm production Those factors are technical inefficiency, unobservable heterogeneity and observable heterogeneity By separating them, researchers can exactly valuate the extent to which each of them affects the production process The model in Battese and Coelli (1995) also has the ability to analyze the impact of technical inefficiency determinants However, limiting their impacts on only technical inefficiency can be considered as an undervaluation As shown in our result, when determinants are put in the technical inefficiency model, the technical inefficiency level does not change much (most firms are still highly efficient technically) and very few of determinants have significant impacts The results from the general form of “true” random effects model show more significant impact of those determinants (almost determinants are significant) and a simple likelihood ratio test can prove the appearances of those variables in “true” random effects model are reasonable Moreover, the STATA command for “true” fixed and random effects models created by Belotti et al (2012) can also deal with the case where those factors have impacts on the mean technical inefficiency as in Battese and Coelli (1995) Thus, it allows those factors to shift the production function and also shift the mean of technical inefficiency level (it is even allowed to impact the variance of technical inefficiency and random noise which can be used to solve the problem of heteroskedasticity but those matters are beyond the scope of this study) This paper suggests the use of these “true” model in analyzing firm production process According to the results of the “true” random effects model, the average technical efficiency level of Vietnamese SMEs in metal industry is nearly 100% with both Cobb-Douglas and Translog function which implies that, separating from those firm heterogeneities, all firms are technically efficient However, the observable heterogeneity has large impacts on firm production process The results show that firm age has positive impacts on firm productivity In other words, old firms are more productive than new ones Firm size’s impact are significant in the case with Cobb-Douglas function but not in Translog function Both ownership type and location factors have significant impacts on firm productivity Page | 51 The high level of firms’ technical efficiency level from this study implies that most firms in the sample are fully efficient Thus, to promote the production process, we need a new technology or we need to change total factor productivity (TFP) A new technology can be expressed by a change in the functional form of production function or the coefficients of inputs while change in TFP is the variation of the other parts of the model that is not inputs and outputs The general form of “true” random effects model shows two groups of factors that can be considered TFP: observable and unobservable factors Absolutely, only those observable factors can be used in policy implication for the fact that we can recognize, measure and influence some of them According to the result of the general form of “true” random effects with Cobb-Douglas (the third column in table – 3), the coefficients of the dummy variables “micro” and “small” are negative and significant Thus, the result show that micro and small firms are less productive than bigger ones in the case of a Cobb-Douglas function However, a likelihood ratio test confirm that the Translog function where the effects of firm size is not significant is more appropriate than the Cobb-Douglas one Firms in private and partnership types have worse productivity than limited liability ones (the reference group) in both Cobb-Douglas and Translog functions Those results induce entrepreneurship of micro firms and limited liability firms Moreover, the fact that most location dummy are negative and significant suggests some advantages that firms in Ho Chi Minh City have over the ones in other locations Therefore, analyses on the way this location benefits small and medium firms should be conducted to help find out suitable policies about infrastructure development or firm locating However, as mentioned above, doubts on the representative ability of the sample restrict this study from implicating policy for broader scopes beyond this sample The study, however, has some limitation Firstly, it loses its confidence due to the weakness of data The fact that the dataset of Vietnamese SMEs in metal industry is not consistent in established year of firms and low value of average wage (about nine million dong in 2005 and 2007 and about 11 million dong in 2009) can be the evidences of data error However, for the fact that most observations are household which not have suitable tools for data recording and the situation of under-report in almost Vietnamese enterprises can explain for that Secondly, there are other matters related to technical efficiency that should be introduced such as location and scale effects, testing for model specification or confidence of technical efficiency statement But for the objective of model choice guiding, they are beyond the scope of this paper Besides, by conducting analysis with rather many model and production functions, the properties of those production function has not yet been tested Finally, we suggests use of the general forms of “true” model in Page | 52 Greene (2005) in future researches because of its usefulness in analyzing separate parts of TFP which greatly influence firm production process Page | 53 BIBLIOGRAPHY Abdullayeva, S (2010) Exports and Firm Performance Central European University Afriat, S N (1972) Efficiency estimation of production functions International Economic Review, 13(3), 568-598 Aigner, D J., Lovell, C A K., & Schmidt, P (1977) Formulation and estimation of stochastic frontier production function models Journal of Econometrics, 6(1), 21-37 Alvarez, R., & Crespi, G (2003) Determinants of technical 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