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

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.. The l

UNIVERSITY OF ECONOMICS INSTITUTE OF SOCIAL STUDIES

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

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

TABLE OF CONTENT

Page

LIST OF TABLES 4

LIST OF FIGURES 4

LIST OF CHARTS 4

CHAPTER I: INTRODUCTION 5

1 Introduction 5

2 Research objectives 7

CHAPTER II: LITERATURE REVIEW 8

1 Efficiency measurement 8

2 Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) 9

3 The cross-sectional Stochastic Frontier Model 12

4 Stochastic frontier model with panel data 15

4.1 Time-invariant models 16

4.1 Time varying models 19

CHAPTER III: METHODOLOGY 25

1 Overview of Vietnamese metal manufacturing industry 25

2 Analytical framework 27

3 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

1 Empirical result 37

1.1 Cobb-Douglas functional form 37

1.2 Translog functional form 42

2 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

LIST OF TABLES:

Table 3-1Output and Input deflators 31

Table 3-2Descriptive statistic of key variables 35

Table 3 – 3 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 9

Figure 2-2 Output-oriented efficiency 9

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

CHAPTER I: INTRODUCTION

1 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

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), Bravo-Ureta 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

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

2 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

CHAPTER II: LITERATURE REVIEW

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

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 2 – 1: Input-oriented efficiency

Figure 2 – 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

2 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)

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:

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:

with 𝑌𝑖 is output of firm i, 𝑋𝑖 is the vector of inputs, 𝛽 is the vector of parameters, which is to be estimated The last two factors: 𝑣𝑖 and 𝑢𝑖 are the two error terms 𝑣𝑖 is the random statistical noise and is assumed to have a normal distribution with zero mean 𝑢𝑖 is a non-negative term indicating inefficiency, which keeps firm far from producing on its frontier There are different assumptions about 𝑢𝑖’s distribution such as half normal distribution (Aigner et al., 1977), exponential distribution (Meeusen & Broeck, 1977), gamma distribution (Greene, 1990) or a non-negative truncation of 𝑁(𝑚𝑖𝑡, 𝜎2) (Battese & Coelli, 1988, 1992, 1995)

c Trade-off between DEA and SFA

Being different in approaching method, DEA and SFA have their own advantages and drawbacks This implies that when choosing between DEA and SFA, researchers must make some trade-offs Being a non-parametric method, DEA is a deterministic approach without the specification of the production function while SFA is a stochastic technique using econometric (parametric) tools and requires a model specification (Ray & Mukherjee, 1995) From that key difference, DEA is considered to be non-statistical, which assumes that the data have no noise Data noise can come from measurement errors or random factors which can be controlled by firms This restrict seems

to be stubborn in realistic situation SFA is statistical, so it allows and takes into account statistical noise In other words, it is more flexible with real world data, in which random factors and error

in collecting is unavoidable But using SFA requires assumptions about the specification of the model, functional forms, distribution of parameters and error terms (Wagstaff, 1989) In DEA, every factor that keeps the firm away from its frontier is regarded inefficiency While in SFA, the residual will be decomposed into two components One part, which is not under the control of the firm itself, is accounted to be the noise and has the zero mean The other part, which is known as the inefficiency, is the weakness of the firm which makes it produce below the frontier So, generally, the efficiency measured from SFA will be higher relatively (Ferrier & Lovell, 1990)

DEA has the advantages with the ability to be applied in various complicated condition of production Without the requirement of a definite production function, it helps simplifying the linkage from inputs to outputs of a production process Without statistical properties, no test can

be used to test DEA’s goodness of fit or specification In spite of having troubles with model specification, SFA still has econometric tools to test whether the model is suitable or not The most beneficial advantage of SFA is the capability of dealing with statistical noise Generally, for industries that the production processes are controlled strictly, DEA seems to be the better choice

of measuring efficiency This is because the random fluctuation in these industries is minimized and the production process is very stable (from a given amount of inputs, the number and quality

of outputs is likely to be determined precisely) Meanwhile, SFA tends to be suitable for industries

in which noise is inevitable Firms in those industries have to bear the impacts from random fluctuations In the case of this thesis, firms in metal manufacturing industries are influenced by from the markets of both inputs and outputs, both domestic and abroad and changes in policies For those natures of the industries the thesis analyzed, SFA is the better model to be applied The next part discusses in detail SFA method, both cross-sectional and panel data models

3 The cross-sectional Stochastic Frontier Model:

The cross-sectional stochastic frontier model in Aigner et al (1977) can be describe as:

with 𝑣𝑖 is the random noise and 𝑢𝑖 is technical inefficiency (𝑢𝑖 ≥ 0) To distinguish these two components of residual, some assumptions are necessary The first assumption is about the distribution of 𝑢𝑖 while 𝑣𝑖 follows a symmetric normal distribution For the reason that 𝑢𝑖represents the distance from the frontier which keeps firms below the frontier, its value is non-negative As mentioned above, the distribution that is suggested includes half normal distribution (Aigner et al., 1977), exponential distribution (Meeusen & Broeck, 1977), gamma distribution (Greene, 1990) or a non-negative truncation of 𝑁(𝑚𝑖𝑡, 𝜎2) (Battese & Coelli, 1988, 1992, 1995)

Both two main estimation methods of econometric can be used to deal with technical inefficiency calculation – Ordinary Least Squares (OLS) and Maximum Likelihood (ML) But for the fact that the error term 𝜀 includes two components, that is: 𝑢 with an asymmetric distribution and 𝑣 with a symmetric distribution, so 𝜀 will not have normal distribution Since 𝜀 = 𝑣 − 𝑢 then 𝜇𝜀 = −𝜇𝑢 This makes the intercept in OLS bias downward To clarify, we consider a regression with just the intercept 𝛼: 𝑦 = 𝛼 + 𝜀, then the estimator for 𝜀 will be 𝑦̅ From the equation above, 𝑝𝑙𝑖𝑚(𝑦̅) =

𝛼 + 𝜀, which does not equal to 𝛼 Winsten (1957) suggested an method called Corrected Ordinary Least Squares (COLS), Afriat (1972) and Richmond (1974) offered the method of Modified Ordinary Least Squares (MOLS) to solve this bias problem Those two methods correct or modify the intercept upward by add up the maximum or average value of OLS residuals COLS and MOLS have some problems, such as non-statistical meaning estimates (Mastromarco, 2007) ML, however, has some asymptotic properties and is able to deal with asymmetrically distributed residual, is used frequently than OLS

With technical inefficiency (𝑢) following a half-normal distribution i.e 𝑢~𝑁+(0, 𝜎𝑢2) (Aigner et al., 1977) the log-likelihood function is:

Log-likelihood function with exponential distribution can be described as:

Figure 2 – 3: Distribution of technical inefficiency

Figure (2 - 3) illustrates the probability density function of four types of distribution of 𝑢 visually Obviously, there are restrictions with gamma, exponential and half-normal distribution With these distributions, because most observations locate in the area has low value of u (technical inefficiency), one can conclude that the level of efficiency of firms is rather high (the inefficiency level is low) Put differently, most firms are highly efficient This can be untrue with many industries, in which high efficiency is not realistic Truncated normal distribution is more flexible when it allows the allocation of inefficiency to almost positive point Therefore it can be used to describe 𝑢 better

Consider a Cobb-Douglas production function as:

𝑚𝑖 = 𝛿0+ 𝑍𝑖𝛿 + 𝜔𝑖 (2.3.7)

With 𝑍𝑖 is the vector of determinants of 𝑚𝑖 and 𝛿 is the vector of parameters that need to be estimated The distribution of 𝜔𝑖 is the truncation of the normal distribution 𝑁(0, 𝜎2) (Battese & Coelli, 1995) This is called Technical Inefficiency Model and can be estimated simultaneously with the Stochastic Frontier

4 Stochastic frontier model with panel data

There are three problems arising while we use stochastic frontier model with cross sectional data (Schmidt & Sickles, 1984) The first is the inconsistency in estimating technical inefficiency Most studies in this field uses the method in Jondrow, Lovell, Materov, and Schmidt (1982) to predict the technical inefficiency level for each firm in the sample The formula is:

where 𝑓 and 𝐹 are the standard normal density and cumulative density function respectively, 𝜇∗ =

−𝜎𝑢2𝜀 𝜎⁄ 2, 𝜎∗2 = 𝜎𝑢2𝜎𝑣2⁄𝜎2 and 𝜎2 = 𝜎𝑢2+ 𝜎𝑣2 For the reason that 𝜇∗ and 𝜎∗ are unknown so their estimator 𝜇̂∗ and 𝜎̂∗ are used instead which leads to some sampling bias In principle, one must take into account this bias but it is very complicated to do This kind of bias disappears asymptotically and can be ignored with large sample However, essentially, technical inefficiency

is independent of sample size So the level of technical inefficiency level will be estimated inconsistently (Schmidt and Sickles, 1984) The second is the ambiguity in the distribution of 𝑢, which is necessary to guarantee an independence between technical inefficiency (𝑢) and statistical noise (𝑣) Without a stubborn distribution assumption, it is impossible to decompose the overall error term (𝜀) into inefficiency (𝑢) and statistical noise (𝑣) However, with cross-sectional data, the robustness of the assumption is hard to test The third problem is the assumption of the uncorrelatedness of u with other regressors in the model This problem of endogeneity causes biases in the model Schmidt and Sickles (1984) suggests that the endogeneity is unavoidable because in the long-run the firm realizes its inefficiency level and adjusts the use of inputs to be more efficient

Panel data models (with data from N firms in T periods) can help avoid these three weaknesses (Greene, 2008) Firstly, more observation overtime (the ideal case is when we have long enough

time series data T→∞) helps estimate the technical inefficiency more consistently Secondly, by isolation and treating technical inefficiency as fixed effect, the model using panel data is distribution free (the distribution assumption is now optional) (Greene, 2008) Finally, the assumption of uncorrelatedness is also relaxed because some panel models can take into account the effects of this correlation The next section describes in detail those panel data stochastic frontier models which have been developed over a long period since its first appearance

*Note: Schmidt and Sickles (1984) use a log-linear function

with 𝑣𝑖𝑡 is uncorrelated with 𝑋𝑖𝑡′𝛽 and 𝑢𝑖 The within estimator uses dummy variables to estimate separate intercepts for each firm which stand for its own technical inefficiency This method has advantages because it need neither an assumption about the uncorrelatedness between 𝑢 and other variables nor an assumption about 𝑢’s distribution After calculating, each firm’s effect is compared with the highest in the sample and inefficiency is estimated as 𝑢̂𝑖 = max(𝛼̂𝑖) − 𝛼̂𝑖 The authors suggests a large number of firms to have exact estimate of the most efficient firm in the sample (the ideal case is with an extensive number of firms over a considerable number of time periods) For the fact that this method is simply a fixed effects estimation using panel data, it includes in technical inefficiency the effects of time-invariant but firm-varying effects (as Schmidt and Sickles (1984) mentioned, it can be capital stock for example – if the value of capital stock stays unchanged overtime, fixed effects model will include it in the value of firm’s specific intercept) which cannot be considered as inefficiency

From the weaknesses of the within estimator mentioned above, the authors suggests assumptions about the uncorrelatedness of 𝑢 and 𝑋𝑖𝑡′𝛽, based on which we can conduct GLS estimation to estimate 𝑢 better The better point from this method comes from the ability to separate the time-invariant regressor which within estimator cannot However, the stubborn assumption needs to be

tested Given the matter of uncorrelatedness and distribution assumptions, the authors suggests other two methods The first is the estimation of Hausman and Taylor (1981) which relaxes the uncorrelatedness assumption and the second is the maximum likelihood estimation which are more advanced given a specific distribution of 𝑢

The two model considered above is two of some simplest approaches to the concept of technical efficiency With their criticism about the inconsistency in estimating technical inefficiency level, they suggest the use of fixed and random effects model which give more consistent estimate of technical inefficiency in case T is large with a given N However, the lack of a distribution makes

it hard to estimate the true inefficiency apart from other firm-specific factors Back in time in Pitt and Lee (1981), a half normal distribution with maximum likelihood estimation is described in the next section

b The model with time-invariant efficiency in Pitt and Lee (1981)

In this paper, the panel data from the Indonesian weaving industry was used to estimate technical inefficiency level and its sources The hypothesis of whether technical inefficiency is time-invariant or time-varying was tested using three different models Three cases were suggested by the authors The first case is when 𝑢 is fixed through time and only varies among individuals, which means it is indexed by 𝑖 only (𝑢𝑖) as described below:

*Note: Pitt and Lee (1981) use a linear function

In the second case, technical inefficiency is independent of time and among individuals, which leads back to the cross-sectional model as in Aigner et al (1977) That is:

With 𝐸(𝑢𝑖𝑡𝑢𝑖𝑡′) = 0 and 𝐸(𝑢𝑖𝑡𝑢𝑗𝑡′) = 0 for all 𝑖 ≠ 𝑗 and 𝑡 ≠ 𝑡′

The final case is the intermediate of these two when the technical inefficiency is assumed to be correlated with time That is:

With 𝐸(𝑢𝑖𝑡𝑢𝑖𝑡′) ≠ 0 and 𝐸(𝑢𝑖𝑡𝑢𝑗𝑡′) = 0 for all 𝑖 ≠ 𝑗 and 𝑡 ≠ 𝑡′

The first and second models are estimated using maximum likelihood method while the intermediate model is estimated with generalized least squares (for the reason that the maximum likelihood procedure for the last case is intractable) Comparing between two first models and model three is conducted by a 𝜒2 test which can be found in Jöreskog and Goldberger (1972) The test suggests that the last model is appropriate (which implies technical inefficiency is time varying) The measure of technical inefficiency for each firm is not mention in the paper, however, can be done by the method of Jondrow et al (1982) which infers the value of each 𝑢𝑖 from the value of each 𝜀𝑖

Although the last model is shown to be more precise, it does not take into account the distribution

of technical inefficiency Moreover, it supplies no measure of inefficiency Thus, generally, the idea proposed by Pitt and Lee (1981) hinges around a model with time-invariant inefficiency following half normal distribution and suggests further research into time varying inefficiency However, as mentioned above, a half normal distribution is sometimes unreasonable Battese and Coelli (1988) suggests a more general distribution of 𝑢 – the truncated normal distribution The model is discussed in detail in the next section

c The model with truncated normal distribution in Battese and Coelli (1988)

Battese and Coelli (1988) proposes a model in that technical inefficiency follows a truncated normal distribution which is developed in Stevenson (1980) for the estimation of stochastic production frontier For the availability of data (3 years), the authors make the assumption of time-invariant inefficiency The new distribution is 𝑁+(𝜇, 𝜎𝑢2) It is more general than the old ones (half normal, which is introduced in Pitt and Lee (1981) and Schmidt and Sickles (1984)) because when

𝜇 = 0, the distribution becomes half normal With development in calculating the likelihood function from Stevenson (1980), the model is estimated with maximum likelihood method The model can be described as:

*Note: Battese and Coelli (1988) use a Cobb-Douglas function

An extensive contribution of this paper to the field of stochastic frontier is its approach in estimating technical efficiency both in the industry level and firm level for the logarithmic case (the Cobb-Douglas functional form in the study) Instead of using the mean of technical inefficiency - 𝐸(𝑢) and calculating the efficiency level as 1 − 𝐸(𝑢) in Jondrow et al (1982), the

authors suggests that technical efficiency level should be attained in form of exp (−𝑢) in the logarithmic case The formula of technical efficiency level is then clarified with the properties of truncated distribution of 𝑢

A common suggestion from the studies mentioned above is the research direction into time varying characteristics of 𝑢 Pitt and Lee (1981) base on their empirical evidences to suggest further research about time varying technical inefficiency Schmidt and Sickles (1984) also state that firms will recognize their inefficiency level in the long-run and change themselves to be more efficient The lack of a long-period data makes Battese and Coelli (1988) assume 𝑢 to be fixed through time, however in their hint for future research, they also suggest other models that allow inefficiency to vary overtime To relax the inflexible assumption of time-invariant inefficiency, models with time varying inefficiency arise The next section considers those models

4.2 The time varying models

a The model of Cornwell et al (1990)

As mentioned above, the problems of technical inefficiency’s distribution and that whether it is uncorrelated with inputs are treated differently among researches Once those assumptions about uncorrelatedness and distribution are made, they easily look too stubborn and become a weakness

of the study Panel data can help relax those assumption but in the cost of treating technical inefficiency as fixed through time Once again, the assumption of a time-invariant efficiency is too strong (Cornwell et al., 1990) By regarding firm effect as a function of time with parameters alter across firms, Cornwell et al (1990) create a model that changes the fixed firm-effect into flexible firm effect which can be varied overtime The model can be described as:

*Note: Cornwell et al (1990) use a Cobb-Douglas function

with 𝛼𝑖𝑡 is time varying firm effects which follows a function of time The authors mentions a quadratic function of time with parameters vary across firms described as

which allows firm effects change across firms and overtime The model can be estimated by within estimator, GLS or efficient instrumental estimator The residuals after being estimated, are regressed on a quadratic function of time Firm specific temporal effect 𝛼𝑖𝑡 then is estimated using

the coefficients of the latter estimation Using the method similar to the one in Schmidt and Sickles (1984), the authors calculated firm specific temporal inefficiency level:

b The model of Kumbhakar (1990), Battese and Coelli (1992) and Lee and Schmidt (1993)

Kumbhakar (1990) considers the time varying inefficiency as a function of time and time invariant inefficiency The model can be described as:

*Note: Kumbhakar (1990) use a Cobb-Douglas function

with 𝑢𝑖𝑡 = 𝛾(𝑡)𝑢𝑖 where 𝑢𝑖 is fixed through time but varied across firms and 𝑢𝑖 follows a half normal distribution The suggested time function is:

The fact that 𝛾(𝑡) ≥ 0 makes 𝑢𝑖𝑡 always positive in the production

The values of 𝑏 and 𝑐 decide 𝛾(𝑡) to be monotonically increasing or decreasing and to be concave

or convex Thus, the data which is used to estimate the model can determine the time-behavior of 𝛾(𝑡) and also 𝑢𝑖𝑡 Then we can easily test the functional form of 𝛾(𝑡) by a LR test with the null hypothesis 𝑏 = 0, 𝑐 = 0 or 𝑏 = 𝑐 = 0 The model then is estimated by ML method with the likelihood function as given in the paper After estimating 𝛾̂(𝑡) and 𝑢̂𝑖, temporal technical inefficiency for each firm is calculated as 𝑢̂𝑖𝑡 = 𝛾̂(𝑡) × 𝑢̂𝑖

Having the same thought as in Kumbhakar (1990), the model in Battese and Coelli (1992) also considers the form of technical inefficiency as 𝑢𝑖𝑡 = 𝛾(𝑡)𝑢𝑖 with the form of 𝛾(𝑡) =exp[−𝜂(𝑡 − 𝑇)] and 𝑢𝑖 𝑖𝑖𝑑 |𝑁(𝜇, 𝜎𝑢2)| (truncated normal distribution at zero) The value of 𝜂

determine the time behavior of technical inefficiency When 𝑡 increases, 𝑢𝑖𝑡 will increase, remain constant or decrease if 𝜂 < 0, 𝜂 = 0 or 𝜂 > 0 repectively Thus the functional form of technical inefficiency can be decided by the data This approach, however is simpler and uses less parameters than the one in Kumbhakar (1990)

The model in Lee and Schmidt (1993) replace the time function in those two previous studies by

a set of dummy variables 𝜃𝑡 The model can be described as:

*Note: Lee and Schmidt (1993) use a linear function

with 𝑢𝑖 is firm’s time invariant technical inefficiency The authors suggest that by doing this, the time pattern is not restricted to a specific functional form of time However the number of parameters can be large (even though smaller than the one in Cornwell et al (1990)) in the case T

is large, thus the authors recommend this method in the case the time-series is not too long Since

it does not use any distribution of technical inefficiency, the method of within estimator and GLS

is applied to estimate the model

Generally, the three models mentioned above adapts well in dealing with time varying technical inefficiency and relax the strong time-invariance assumption However, they do not consider the matter of determinants of technical inefficiency This matter is first regarded in the study of Pitt and Lee (1981) with the purpose of finding the source of technical inefficiency This kind of model which is called as technical inefficiency effects model (TIEM) has been developed through the researches of Kumbhakar, Ghosh, and McGuckin (1991), Reifschneider and Stevenson (1991) and Huang and Liu (1994).The next section will describe the model of Battese and Coelli (1995), a popular model which includes both stochastic frontier model and technical inefficiency effects model

c The model of Battese and Coelli (1995) with technical inefficiency effects model

The model suggested in this paper includes a stochastic frontier model and a technical inefficiency effects model Theoretically, the stochastic frontier model estimates technical inefficiency of firms from the data of outputs and inputs and then the technical inefficiency effects model regresses 𝑢

on other variables which can be considered as explanatory factors associated with 𝑢 The formula

of stochastic frontier model for panel data can be described as:

𝑌𝑖𝑡 = exp(𝑥𝑖𝑡𝛽 + 𝑉𝑖𝑡− 𝑈𝑖𝑡) (2.4.13)

*Note: Battese and Coelli (1995) use a Cobb-Douglas function

with 𝑥𝑖𝑡 is a vector of value of a specific functional form, 𝑉𝑖𝑡 is symmetric normal distributed statistical noise 𝑈𝑖𝑡 follows a truncated normal distribution with mean 𝑧𝑖𝑡𝛿 and variance 𝜎2 with

𝑧𝑖𝑡 is a vector of explanatory variables which can be considered as sources of technical inefficiency

The two models are estimated simultaneously using maximum likelihood method given the truncated normal distribution of 𝑢 In this paper, Battese and Coelli use micro panel data of India villages to apply the model A time variable is included in the stochastic frontier model to take into account the technical progress (Hicksian neutral technological change) while a time variable is used in the technical inefficiency model to imply the time varying characteristic of 𝑢 (here is a linear correlation) With similar procedure in their papers in 1988, 1992 and 1993, the authors use

a log likelihood test to examine the existence of technical inefficiency, functional form of stochastic frontier model and technical inefficiency effects model

Having the ability to take into account the impacts of explanatory factors on technical inefficiency, the (Battese & Coelli, 1995)’s model is applied widely to analyze technical efficiency and its determinants This application is useful in the case of discovering factors that benefit firms in gaining efficiency Thus, become a powerful tool in policy recommendation However, the fact that technical inefficiency can be explained by other factors raises the problem of biases in estimating the whole model Greene (2005) seriously criticizes this matter and proposes a new approach which called “true” fixed effects model and “true” random effects model Those models are described in detail below

d “True” fixed effects model and “true” random effects model (Greene, 2005)

Greene (2005) mentions two shortcomings of those fixed effects and random effects approaches mentioned above The first is the strong assumption about the time pattern of technical inefficiency The model of Pitt and Lee (1981), Schmidt and Sickles (1984) and Battese and Coelli (1988) both assume a time invariant technical inefficiency This assumption becomes too strong, especially in the case of using panel data with large number of time periods Cornwell et al (1990) proposes a model to deal with this problem by using a time function with parameters change across firms By this way, the number of parameters is large and this makes the model inefficient Later

papers such as Battese and Coelli (1992), Lee and Schmidt (1993) and Kumbhakar (1990) solve the problem by adding a time behavior function 𝑔(𝑡) so 𝑢𝑖𝑡 = 𝑔(𝑡)𝑢𝑖 Despite the various functional forms of 𝑔(𝑡), the assumption that technical inefficiency follows a specific pattern of time, again, seems to be strong either (Greene, 2005)

The second matter is the assumption that 𝑢𝑖𝑡 is uncorrelated with other variables in the model The previous fixed effects model does not need this assumption By imposing a separate intercept for each firm, the “firm effect” now is not correlated with other variables However, Greene criticizes that by doing this, one can only compute technical inefficiency by comparing with the “best” firm

in the sample Besides, he also states that “firm effect” from this method includes heterogeneity that is not related to inefficiency In his view, technical inefficiency needs not contain time invariant effects and should vary freely through time (Greene, 2008) This kind of heterogeneity

is also considered in the study of Farsi, Filippini, and Kuenzle (2003) as factors beyond the control

of firms The authors give the examples of factors that belongs to business environment (for example: network effects in network industries) or relates to output characteristics such as the severity of illness in healthcare industry or the demand fluctuations in electricity utilities In healthcare industry, different hospitals must treat different kinds of disease with different severity level If we take number of lives saved by a hospital as the representative of output, then this number will be low in the hospitals which mainly treat minor diseases and vice versa Thus, those hospitals will be closer to the frontier than others with major diseases One can conclude that the hospitals treating minor diseases are more efficient than the hospitals treating major diseases If

we let them cure the same amount of patients that have the same level of severity, we cannot assure which group will save more Therefore, taking those effects into technical efficiency level is not reasonable From those ideas, Greene (2005) suggests “true” fixed and random effects model which separate that latent heterogeneity from inefficiency

“True” fixed model is described as:

with 𝛼𝑖 is the firm specific constant Greene also introduces a maximization method that can help estimating simultaneously all coefficients by maximum likelihood which uses a specific distribution of 𝑢 Meanwhile the “true” random effects model can be written as:

*Note: the functional form of production function in equation (2.4.14) and (2.4.15) are the ones that were used in Greene (2005) to introduce their model In their examples, they use the Cobb-Douglas form

with 𝑤𝑖 is a random constant term that varies across firms

As we can see, those panel data models mentioned above can be divided into two groups by types

of approach Those with fixed effects approach as the fixed effects model in Schmidt and Sickles (1984), Cornwell et al (1990), Lee and Schmidt (1993) and Greene (2005) do not require assumptions on the uncorrelatedness between technical inefficiency and other parts of the model Those with random effects approach such as the models in Schmidt and Sickles (1984) (random effects model), Pitt and Lee (1981), Battese and Coelli (1988, 1992, 1995), Kumbhakar (1990) and

“true” random effects model in Greene (2005) require technical inefficiency to be uncorrelated with the rest of the model People can also divide them into time invariant models and time varying models as mentioned above Coming from different points of view, they have their own strengths and weaknesses that make them suitable to different situations

The literature on cross-sectional data stochastic frontier model is quite consistent Its simplicity and weaknesses attract less attention When the need of a more careful analysis into the nature of firm’s efficiency arises and the data in panel form are now attainable widely, researchers tend to rely on panel data models despite their complicatedness Like what I mentioned about my intention for this thesis, I will only apply those models with panel data in my empirical process The purpose

is to compare them relatively to each other, to find out differences that make them more or less suitable in specific circumstances The methodology will be described particularly in the section

below

CHAPTER III: METHODOLOGY

1 Overview of Vietnamese metal manufacturing industry

Firms in the sample used in this study are divided into two categories: basic metal manufacturing firms and fabricated metal manufacturing (except machinery and equipment) firms according to their main products Details for this classification can be found in International Standard Industrial Classification of All Economic Activities (ISIC), Revision 4 Firms in the first group are involved

in the activities of smelting and refining ferrous and non-ferrous metals Those firms use metallurgic techniques with the materials from mining industry such as metal ore, pig or scrap Taking part in this industry need large investments in physical assets Thus, in this sample of small and medium enterprises, this group takes only 9% of the numbers of firms The second group manufactures structural metal products, metal container-typed objects and steam generators Producing more popular products, this group takes about 91% of the number of firms

The metal manufacturing industry in Viet Nam has many potentials due to the high demand of metal products for daily using, production and construction In Vietnamese young developing economy, metal manufacturing industry is still immature and most products are used for construction According to World Steel Association, about 80% of iron and steel materials are used for construction Besides, the domestic rising demand of metal materials of machinery, motor and automobile and other consumer goods manufacturing can also be considered as important condition of development of metal manufacturing industry However, along with the depressed situation of Vietnamese economy in the recent year, metal manufacturing industry also has many difficulties The investment cut in public construction due to government budget deficit strongly decreases the demand of metal materials for construction According to Vietnamese Steel Association, steel consumption fell about nine percent in 2012 The rising price of inputs such as electricity, water and labor cost also imposes many hardships on this industry

Due to the importance of metal manufacturing industry, this study is conducted with the objective

of analyzing technical efficiency level of firms in this sector However, most observations in this sample are micro and household firms (74.5%) and the number of medium sized firms take only four percent Moreover, due to the availability of data, the dataset used here is in the period of

2005 to 2009, during which economic conditions may be different from the current situation Because of those reasons, there should be high probability of sample bias if this study gives

conclusions about the industry (the population) Thus, as a reminder for readers about the precision

of the conclusions from this study, those results should be considered carefully while using for the

purpose of policy recommendation

2 Analytical framework

Panel-data stochastic frontier models presented in Chapter II are applied to estimate technical inefficiency level of Vietnamese SMEs in metal manufacturing industry Production function for the model is estimated with inputs and outputs data in two different functional forms – Cobb-Douglas and Translog For the case of technical inefficiency effects model in Battese and Coelli (1995), a firm-specific group of variables will be added into the model Those variables can be considered and sources or determinants of technical inefficiency The results, then, are compared among models to find out the impact of each assumption and model specification on the way technical efficiency is determined

3 Research method

3.1 Estimating technical inefficiency:

Firm efficiency will be calculated with Stochastic Frontier Model As noted above, an important step of using Stochastic Frontier Model is choosing the suitable functional form to build up the frontier Some types of production function can be considered, such as Linear, Cobb-Douglas, Quadratic, Normalized Quadratic, Translog, Generalized Leontief and Constant Elasticity of Substitution (CES) forms (see Griffin, Montgomery, and Rister (1987) for a review of those) Coelli et al (2005) emphasizes that good functional form should be flexible, linear (in parameters),

regular, parsimonious An ith-ordered flexible functional form is the one that has enough parameters for ith-ordered differential approximation Among those function mentioned above,

Linear and Cobb-Douglas form is first-ordered flexible All the rest are second-ordered flexible Most of production function considered above is linear in parameters Cobb-Douglas and Translog function can become linear in parameters when we take the logarithm of both sides of the equation

A regular functional form is the form that satisfies economic regularity properties of production function with its own nature or with some simple restriction Finally, a parsimonious function can

be understood as the simplest function which can adequately solve the problem A flexible functions will less likely imposes assumptions or restrictions on the properties of the production

function while parsimonious functions will save the degree of freedom In choosing functional form, researchers always face the trade-off between flexibility and parsimony

Researchers usually choose Cobb-Douglas for its parsimony (and sometimes tractability), while choosing Translog for its flexibility Being less flexible, Cobb-Douglas functional form imposes constant production elasticity, and constant elasticity of factor substitution while Translog functional form does not So the Translog form makes properties of the production function testable Therefore, it is considered to be more realistic and less restrictive Nonetheless it still has some weaknesses The appearance of cross and squared terms in Translog model increases the number of parameters Correlation among those is highly potential Furthermore, if the number of observations is not enough, this increase in parameters reduces the degree of freedom For a comparison, the Cobb-Douglas function and Translog function can be described in specification with three inputs: capital (K), labor (L), material (M) and indirect cost (I) as below:

Cobb-Douglas functional form:

With the denominator i denotes firms, t denotes time periods; 𝑌𝑖𝑡 is output; 𝐾𝑖𝑡 is capital input; 𝐿𝑖𝑡

is labor input; 𝑀𝑖𝑡 is materials; 𝐼𝑖𝑡 is indirect costs, 𝑉𝑖𝑡 stands for statistical noise, which follows 𝑁(0, 𝜎𝑣2); 𝑈𝑖𝑡 stands for TE, which follows specific non-negative distribution mentioned above

Obviously, without squared and interaction terms, the Translog function becomes Cobb-Douglas function Cobb-Douglas functional form has constant proportionate returns to scale, constant elasticity of factor substitution, and all pairs of inputs are assumed to be complimentary Those assumptions make it more restrictive

A likelihood ratio test (LR) can be used to test for goodness of fit between these two functional forms with:

𝐻0: 𝛽5 = 𝛽6 = 𝛽7 = 𝛽8 = 𝛽9 = 𝛽10= 𝛽11= 𝛽12= 𝛽13= 𝛽14= 0;

𝐻1: otherwise where 𝐿(𝐻0) is the log-likelihood value for null model (𝐻0) and 𝐿(𝐻1) is the log-likelihood value for alternative model (𝐻1), the test is given by:

“xtfrontier” for panel data are those popular STATA commands to estimate technical efficiency

“frontier” can deal with models whose 𝑢𝑖 follows half normal, truncated normal, exponential or gamma distribution “xtfrontier” can treat the model in Battese and Coelli (1988) (time-invariant) and Battese and Coelli (1992) (time varying) With only those two commands, users face many troubles testing other models Fortunately, thanks for the very updated paper of Belotti, Daidone, Ilardi, and Atella (2012) and their contribution for building useful “sfcross” and “sfpanel” commands, STATA now grants us full capability of using those models mentioned above with simple syntaxes The second programs is FRONTIER 4.1 from Coelli (1996) which can deal with models in Battese and Coelli (1992) and Battese and Coelli (1995)

For those logarithm functional forms (Cobb-Douglas and Translog) Technical efficiency will be calculated from the value of 𝑢 following two different methods The first method is the one in Jondrow et al (1982) which give the formula: 𝑇𝐸 = exp[−𝐸(𝑢|𝜀)] The second method is the one

in (Battese & Coelli, 1988) which suggest the formula: 𝑇𝐸 = 𝐸[exp( − 𝑢)|𝜀] TE calculated from this equation will be a positive value less than one It is the ratio of actual output over the maximum level of output where there is no inefficiency: