'

0 PX2

Source: Jha, R. and Sahin, B.S. (1993)

Suppose a firm uses quantities of inputs, defined by point A , to produce a unit of output. The technical inefficiency of that firm could be represented by BA , which is the proportional reduction in all inputs that could theoretically be achieved without any reduction in level of output produced. This is usually expressed in percentage terms by

BA

the ratio . The technical efficiency (TE ) of a firm is then given by:

OA

OB

TE_i =

OA ......................................................................... (1)

It will take a value between zero and one, and hence provides an indicator of the degree of technical inefficiency of the firm. A value of one indicates the firm is fully technically efficient. For instance, at point B the firm is technically efficient because it lies on the efficient isoquant. Hence, points on the frontier are efficient points while those above the frontier are inefficient.

If the production frontier of the firm were known, the technical inefficiency of any particular firm could be assessed by comparing the position of the firm relative to the frontier. In practice, however, only observations of the input levels employed and the output levels achieved are available from which the production frontier must be empirically constructed. This leads to the measurements and associated econometric models for analyzing technical efficiency.

1.2 The Measurement of Technical efficiency

2.2.1 Frontier Approaches for Efficiency Measurement

Although there are different approaches² for measuring the efficiency of firms, frontier approaches are the widely applicable methods for efficiency measurement. Moreover, frontier production functions have been the subject of considerable econometric research during the last two decades. The development of frontier approach opened a wide range in the area of measure of efficiency (Forsund et al., 1980). The word frontier may meaningfully be applied either to the maximum possible output which can be produced from given quantities of a set of inputs or the minimum level of cost at which it is possible to produce some level of out put, given input prices or the maximum profit that can be attained given out put price and input prices. Currently, the frontier function is widely utilized to analyze efficiency for a variety of reasons. First, it is consistent with the underlying economic theory of optimizing behavior. Second, deviations from a frontier have a natural interpretation as a measure of the level of efficiency with economic units pursues their technical or behavioral objectives. Third, information about the structure of the frontier and about the relative efficiency of economic units has many implications (Bauer, 1990) (Cited in Awoke, 2001).

Frontier approaches are mainly composed of two components: deterministic and stochastic. Further, deterministic frontiers are sub-divided into non-parametric, parametric and statistical frontiers.

Deterministic Non-Parametric Frontiers

According to Forsund et al. (1980) the beginning point for any discussion of frontiers and efficiency is the work of Farrell (1957), who provided definitions and a computational framework for technical and allocative inefficiencies. Farrell’s approach is nonparametric in the sense that he simply constructs the free disposal convex hull of the observed input-output ratios by linear programming techniques. This is thus supported by a subset of the sample with the rest of the sample points lying above it. This procedure is not based on any explicit model of the frontier or the relationship of the observations to the frontier. The technical inefficiency of an observation is then measured relative to this frontier.

The principal advantage of this model is that no functional form is imposed on the data. However, it has two major weaknesses: First, its assumption of constant returns to scale is restrictive, and its extension to non-constant returns to scale technologies is cumbersome. Second, the frontier is computed from a supporting subset of observations from the sample, and is therefore particularly susceptible to extreme observations and measurement error (Forsund et al., 1980).

2

Other approaches include techniques like partial and total productivity, production function and profit function for efficiency measurement.

As a result, his approach is extended, proved and applied by Farrell and Fieldhouse (1962), Seitz (1970, 1971), Todd (1971), Afriat (1972), Dugger (1974) and Meller (1976) (cited in Forsund et al., 1980).

Deterministic Parametric Frontiers

Although the first Farrell’s non-parametric approach has won few adherents, a second approach which is also proposed by him was proved to be more fruitful. He proposed computing a parametric convex hull of the observed input-output ratios to determine a production function that obeys constant returns to scale. He recommended the Cobb-Douglas from for the sake of expressing the frontier in a simple mathematical form. Although the mathematical expression of the Cobb-Douglas from is simple, Farrell was aware of the unnecessary assumption of constant returns to scale. Unfortunately Farrell did not follow up on his own suggestions, and it was over a decade before anyone else did it.

Aigner and Chu (1968) were the first to follow Farrell’s suggestion. They specified a homogenous Cobb-Douglas production function and required all observations to be on or beneath the frontier. Their model is written as:

x

ln Y = ln f ) ( − U …………………………...……………. (2)

n

ln Y =α + _∑α ln X_i − U , U ≥ 0

0 i= 1

Where Y is the i -th firm output; f ( X ) is a suitable functional from (e.g. Cobb-Douglas

i

or translog) of inputs vector X for the i -th observation and of α is a vector unknown

i

parameters, and U is firm specific technical inefficiency which forces Y to be less than or

i

equal to f ( X ).

'

₀,The elements of the parameter vector α= (α α α ,..., α ) may be estimated either by

1^, 2 nlinear programming (minimizing the sum of the absolute values of the residuals, subject to the constraint that each residual be non-negative) or by quadratic programming (minimizing the sum of squared residuals, subject to the same constraint). Therefore, the technical efficiency of each observation can be computed directly from vector of residuals, sinceU represents technical inefficiency.

The principal advantages of the parametric approach over the non-parametric approach are the ability to characterize frontier technology in a simple mathematical form, and the ability to accommodate non-constant returns to scale. This does not that mean the parametric approach is free from limitations. It imposes a limitation on the number of observations that can be technically efficient. For instance, when the linear programming algorithm is used in a homogenous Cobb-Douglas case, there will in general be only as many technically efficient observations as there are parameters to be estimated. The other limitation is, as in the case of non-parametric approach, the estimated frontier is supported by a subset of the data and is therefore extremely sensitive to outliers.

The absence of statistical properties of the estimates produced by this approach is also another limitation. That is, mathematical programming procedures produce 'estimates' without standard errors, t-ratio, etc. This is because no assumptions are made about the regressors or the disturbances in (2), and without some statistical assumptions, inferential results cannot be obtained (Forsund et al., 1980).

Deterministic Statistical Frontiers

Deterministic parametric frontiers can be made amenable to statistical analysis by making some assumptions. It was Afriat(1972) who first explicitly proposed this model and he developed a deterministic statistical model as follows:

Y_i = f ( X )e^−U ....................................................................(3)

x

ln( Y_i ) = ln [ f ) ( ]− U

Where Y_i , f ( X ), X_i , and U_i ≥ 0 are as defined in (2). From U_i ≥ 0 it follows

0 ≤ e^−u ≤ 1.In this model the observations on U are assumed to be independently and identically distributed (iid) and X is assumed to be exogenous (independent of U ). It should be stressed that the choice of a distribution of U is important because the maximum likelihood estimates (MLE) depend on it in a fundamental way, i.e., different assumptions for the distributions lead to different estimates.

Different people have proposed different distributions for U . For instance, Afriat (1972) proposed a two-parameter beta distribution for U and that the model be estimated by the maximum likelihood estimation technique. Richmond (1974) and Schmidt (1976) have proposed a gamma distribution and an exponential distribution for U , respectively (cited in Forsund et al., 1980).

The use of maximum likelihood in the frontier setting is not without limitations. The major weakness with this estimation technique is that there do not appear to be good a priori arguments for any of the distributions stated above. The other problem related with maximum likelihood is that the range of the dependent variable (output) depends on the parameters to be estimated which violates one of the regularity conditions invoked to prove the general theorem that maximum likelihood estimators are consistent and asymptotically efficient.

An alternative method of estimation is provided by Richmond (1974) (cited in Forsund et al., 1980) which is based on the ordinary least squares method, called Corrected Ordinary Least Squares (COLS). This method provides consistent estimates by shifting the COLS constant parameter estimate upward until no residual is positive. The difficulty with COLS technique is that, even after correcting the constant term, some of the residuals may still have the ‘wrong’ sign so that these observations end up above the estimated production frontier. This makes the COLS frontier a somewhat awkward basis for computing the technical efficiency of individual observations. Another difficulty with the COLS technique is that the correction to the constant term is not independent of the distribution assumed forU .

In addition to the above mentioned difficulties related with estimation, deterministic statistical frontiers assume all firms share a common family of production, cost and profit functions, and all variations in firm performance is attributed to variations in firm efficiencies relative to the common family of frontiers. The notion of a deterministic frontier shared by all firms ignores the very real possibility of that a firm’s performance may be affected by factors entirely outside its control (such as poor machine performance, input supply breakdowns, and so on), as well as by factors under its control (inefficiency). Therefore, to lump the effects of exogenous shocks, both fortunate and unfortunate, together with the effects of measurement error and inefficiency in a single one-sided error term and to label the mixture ‘inefficiency’ is somewhat questionable.

Stochastic Frontiers

The stochastic frontier production function which was independently proposed by Aigner, Lovell and Schmidt (1977) and Meeusen and Van den Broeck (1977), involves unobservable random variable associated with the technical inefficiency of production of individual firms in addition to the random error in deterministic statistical frontiers (Battese and Coelli, 1995). The error term in the stochastic frontier models is composed of a systematic component which captures the effects of measurement error, other statistical ‘noise’ or random ‘shocks’ outside the control of the production unit and a one-sided error component which captures the effects of inefficiency relative to the ‘best’ stochastic frontier. The presence of the variable which captures a firm’s inefficiency solves the bounded-range problem encountered in frontier model and the presence of the statistical noise allows the frontier to be stochastic.

The stochastic model may be written as:

_i = f ( X ,α)exp( V − U ).......................................................................(4)

Where Y_i , X ,α,U_i ≥ ,0 f ( X ) as defined in (2) and V is the statistical 'noise'.

i

In this model the stochastic production function is f ( X )exp( V ), V having some

systematic distribution to capture the random effects of measurement error and exogenous shocks which cause the placement of the deterministic part f ( X ) to vary across firms. Technical inefficiency relative to the stochastic production frontier is then captured by the one-sided error component exp( −U ), U > 0 . The condition U > 0ensures that all observations lie on or beneath the stochastic production function.

The basic assumption of the model is that V and U are independent and X is exogenous. Using this assumption we can obtain direct estimates of the stochastic production frontier model using either maximum likelihood or COLS methods (Forsund et al., 1980). It is important to note that whether the model is estimated by maximum likelihood or by COLS, the distribution of U must be specified. Aigner et al., (1977) and Menusen and Van den Broeck (1977) considered exponential and half-normal distributions for U and Stevenson (1980) has shown how the half-normal and exponential distributions can be generalized to truncated normal and gamma distributions, respectively (cited in Forsund et al., 1980).

Many empirical studies involving both cross-sectional and time-series data have assumed that the firm effects have half-normal distribution (i.e., µ= 0 ). If the value of µ is zero or negative, then the distribution of the firm effects is such that there is highest probability of obtaining firm effects in the neighborhood of zero. In this case, the majority of firms would have high technical efficiencies. However, if the value of µ is positive, then a

relatively larger number of firms would have firm effects which were significant positive values and such firms would have smaller values of technical efficiencies.

Until the early 1980's the major criticism towards stochastic frontiers was that there was no way of determining whether the observed performance of a particular observation compared with the deterministic frontier is due to inefficiency or to a random variation in the frontier. In other words, it was not possible to decompose individual residuals into their two components and to estimate technical inefficiency by observation. However, after the appearance of the paper by Jondrow, et al. (1982) a solution was suggested for the problem mentioned above. They suggested that the conditional distribution of U given E_i can be used to obtain an estimator of U_i since contains information about

i ^Ei

U . They further suggested that either the mean or the mode of this distribution can be

i

used as a point estimator on U and they showed how to derive these estimators given the

i

distributions of U and V (Battese et al., 1989).

ii

Stochastic frontier models have been applied to a variety of data sets because of their advantages over the deterministic frontiers through incorporating the two error components. Further more, the main attraction of the stochastic frontier model is the possibility it offers for a richer specification, particularly in the case of panel data. The model also allows for, among other things, a formal statistical testing of hypothesis and the construction of confidence intervals. Because of all these aspects, this model seems most attractive and the study employed the model using firm’s panel data to predict technical efficiency.

2.2 Production Frontiers and Panel Data

The majority of previous empirical studies which used frontier models have been using cross-sectional data because of the assumption that error terms are independently distributed across observations. Also, with cross-sectional data it is required to make parametric assumptions about the distribution of the residual and the inefficiency term in order to separate the residual from inefficiency. Schmidt and Sickles (1984) indicated that stochastic frontier models using cross-sectional data suffer from three serious difficulties.

First, the technical inefficiency of a particular firm (observation) can be estimated but not consistently. We can consistently estimate the (whole) error term for a given observation, but it contains statistical noise as well as technical inefficiency. The variance of the distribution of technical inefficiency, conditional on the whole error term, doesn’t vanish when the sample size increases.

Second, the estimation of the model and the separation of technical inefficiency from statistical noise require specific assumptions about the distribution of the technical inefficiency term(e.g., half-normal) and the statistical noise (e.g., normal). It is not clear how robust one’s results are to these assumptions. Another way to emphasize this point is to note that the evidence of technical inefficiency is skewness of the production function error, and not anyone will agree that skewness should be regarded as evidence of inefficiency.

Third, it may be incorrect to assume that inefficiency is independent of the regressors. If a firm knows its level of technical inefficiency, for example, this should affect its input prices.

All the three problems are potentially avoidable if one has panel data; sayT observations on each of N firms. The technical inefficiency of a particular firm can be estimated consistently as T →∞ . This is because adding more observations on the same firm yields information not attainable by adding more firms. The other advantage of panel data is that one need not make such strong distributional assumptions as are necessary with a single cross-section. Panel data also permits the simultaneous investigation of both technical change and technical efficiency change overtime, given that technical change is defined by an appropriate parametric model and the technical inefficiency effects in the stochastic frontier model are stochastic and have the specified distribution. As a result, more recently attention has been made to apply frontier production functions in the analysis of panel data on firms involved in production.

Different people have developed various types of panel data models in relation to stochastic frontier production functions. Among them, Schmidt and Sickles (1984) specified a model to measure stochastic frontier production function using panel data assuming the inefficiency to be time-invariant. Their model is written as:

_it =βi + _∑βXj+ V ........................................................(5)

j it it

j

β=β − U_i

i 0

Where i i = 2 ,1 ,..., N ( ),

( t t = 2 ,1 ,..., T )and j( j = 2 ,1 ,..., K ) represents firm, time and input respectively; Y is log of output, X is vector of log of inputs, V is the white noise

itit it

component and U_i is the non-negative time-invariant technical inefficiency. The assumption of constant efficiency overtime presumes that weaknesses that are attributable to firms themselves are inherently in their very nature and their impact is invariant with time. The model can be estimated using the within estimator treating U ≥0 as fixed. A dummy variable for each firm can be introduced to the model or OLS can be applied to the within transformed data. During this, the intercept will be recovered as the means of the residuals to each firm. The within estimator allows U_i and X to be correlated. The

estimator of β then can be obtained as the max (β) . From this, it is apparent that

0i

U_i (U_i =β−β) will be zero at point where β=βand the corresponding firm in the

0 i 0 i

sample is fully efficient.

The within estimator will not provide the estimated values of time-invariant regressor coefficients. The generalized least squares (GLS) and maximum likelihood estimator (MLE) methods give the estimates assuming the U , with some specific distribution, are

i

random and uncorrelated to the regressors.

Cornwell et al., (1990) extended the generalized Schmidt and Sickles (1984) approach to relax the assumption of time-invariant on U by allowing time-varying efficiency for each

i

firm. The model can be written as:

Within estimator, GLS or MLE methods can be applied to estimate the model. Firm specific effects, β, are regressed on a constant, time and time-squared. Their estimates

itwill be consistent as T gets larger. The model allows the frontier intercept to vary overtime and the efficiency level to vary over firms and over time.

A more flexible formulation of technical inefficiency model for panel data was proposed by Kumbhakar (1990). It is written as:

_it =β+_∑β_jX +V_it −U_it ...............................................(7)

it jit j

−1

_it =γ) (

U t _i =1( +exp( bt +ct ²)) U_i

Where the firm effects are represented as a product of a deterministic part, γt

) (, which is an exponential function of time and a time-invariant random effect, . Appropriate

^Ui distributional assumption on the technical inefficiency component is needed in order to get the required estimates using MLE methods. The need for a restrictive distributional assumption on the technical inefficiency component is considered as the main disadvantage of the model.

Battese and Coelli (1992) developed a stochastic frontier production function model for panel data by expressing firm effects as a product of exponential function of time and time-invariant, U_i , as follows:

_it =β + _∑β _jX + V_it − U_it .......................................….... (8)

0 jit j

_it =η U_i = (exp( −η (t − T ))) U

it i

Whereη is an unknown parameter to be estimated and U_i , i = 2 ,1 ,..., N , is independently and identically distributed non-negative random variable, obtained by truncation (at zero)

2

of the normal distribution with unknown mean, µ , and unknown variance δ .

The advantage of this model is that if η> 0 , then as t increases U_it will decrease

monotonically which means that as the firm proceeds overtime, its inefficiency level monotonically decreases and the firm proceeds towards the frontier. Similarly, if η< 0, then inefficiency increases overtime. Therefore, the testable hypothesis offered by the

model is that efficiency monotonically decreases or increases overtime. However, the hypothesis of fluctuating efficiency cannot be tested in this model.

In a similar approach, Battese and Coelli (1995) defined the technical inefficiency effect, U_it , in stochastic frontier model as:

_it = Z_it δ+ W_it ..................................................................... (9)

Where Z_it is a (1 X M) vector of explanatory variables associated with technical inefficiency of production of firms overtime; δ is an (M X 1) vector of unknown coefficients; and are unobservable random variables, which are obtained by

it

2

truncation of the normal distribution with mean zero and unknown variance, δ , such that the point of truncation is, − Z_it δ i.e., W_it − ≥ Z_it δ . These assumptions are consistent with

( ,²_it being a non-negative truncation of the Z N _it δ δ ).

This model is used in the study for the simultaneous estimation of the parameters of the stochastic frontier and the model for technical inefficiency effects using maximum likelihood estimation technique.

1. Data and Methodology

2. Source of Data and Coverage

The study uses firm level data on large and medium scale industries and the main source of data is the annual survey of large and medium scale manufacturing industries conducted by Central Statistical Authority (CSA). Both raw data and data from various statistical bulletins published by the authority are used in the study. Since the raw data set is in terms of value at current price, it is converted to constant price by deflating using appropriate deflators. An implicit sectoral deflator is used to deflate gross value of production, wages and salaries and industrial cost, while investment deflator is used to deflate capital (or fixed assets). The study covers those large and medium scale manufacturing industries at national level during the survey period 1998-2002.

In this study among the manufacturing industries that are categorized under different industrial groups, nine industrial groups are considered in the study which constitute about 89 percent of the total manufacturing industries in country. These industries together employed around 94 percent of the workers in the manufacturing sector. In terms of gross value of production, they produce around 88 percent of the total production in the sector. Furthermore, 99 percent of the capital of the sector is also employed in these industries (CSA, 2003). The grouping of the industries is based on two-digit ISIC (International Standard Industrial Classification) although the survey report of CSA follows both the two-digit and four-digit classifications.

The main criteria employed in delineating divisions and groups (the two-digit and four digit categories) include the characteristics of the activities producing units which are strategic in determining the degree of the units and certain relationships in an economy. The major aspects of the activities considered are the character of the goods and services produced, the uses to which the goods and services are put, the inputs, the process and the technology of production. In delineating the divisions of ISIC, attention was also given to the range of kinds of activities frequently carried out under the same ownership or capital control and to potential differences in scale and organization that exist between enterprises. Additional criteria used in establishing divisions and groups were the pattern of categories at various levels of classification in national classifications (UN, 1990).

Based on this United Nations criteria the Ethiopian large and medium manufacturing industries are divided into different industrial groups of which 9 of them are included in this study as stated earlier. These include food processing, beverages, textile, leather, wood & furniture, paper & printing, chemical, rubber & plastics and non-metallic mineral industries. The selection of firms within each sub-sector is based on balanced panel data requirement such that those firms with complete observation and which are operational in the study period are covered.

As depicted in Table 1 among the industrial groups in the study 84 food processing industries are included which constitute about 23 percent of the total manufacturing industries in the study. 58 wood & furniture manufacturing industries are also included in the study which make 16 percent of the total manufacturing in the study. Around 12 percent of the total manufacturing industries are the 43 non-metallic mineral industries followed by 39 paper & printing industries constitute around 11 percent of the manufacturing industries. The textile industries included in the study are similar to those of the paper & printing industries whereby 38 industries are included which also make around 11 percent of the total manufacturing industries in the study.

Source: Author’s Computation

Among the total 361 manufacturing industries 32 of them are chemical industries which accounts for 9 percent of the total manufacturing followed by 30 leather industries which constitute around 8 percent of the total manufacturing industries. The rest of the manufacturing industries that are included in study are rubber & plastics and beverage industries. As shown in the table 4.1, these industries are relatively small in their number whereby the industries are 37 in total and they together constitute only 10 percent of the total manufacturing industries in the study.

3.2 Methodology

The panel data model developed by Battese and Coelli (1995) is used for measuring the technical efficiency of firms using a stochastic frontier production function. Provided the inefficiency effects are stochastic, the model also permits the estimation of both technical change in the stochastic frontier and time-varying technical inefficiencies. Moreover, the parameters of the stochastic frontier and the inefficiency models can be estimated simultaneously, given appropriate distributional assumptions associated with cross-sectional data on the firms included in the study.

They formulated the stochastic frontier production model as follows:

_it = f ( X _it : β) + E ...............……........................…………… (10)

it

Where Y_it denotes the production at t-th observation (t = 2 ,1 ,...,5) for the i-th firm (i = 2 ,1 ,.., N ) , X is (1XK )vector of values of known functions of inputs of production

it

and other explanatory variables associated with the i-th firm at the t-th observation, β is a (KX 1)vector of unknown parameters to be estimated, E_it is specified as

_it = V_it − U_it where V_it is the statistical noise and U_it is technical inefficiency.

In the above model f ( X : β ) represents a certain production technology which could be

it specified as Cobb-Douglas (C-D), constant elasticity of substitution (CES), translog, etc. Nowadays, flexible functional forms such as the translog form are usually recommended rather than the restrictive Cobb-Douglas form. Furthermore, the translog function is the only one of the flexible functional form which is readily used for direct estimation of the production function.

In fact, this study will not merely focus on the explanation of the pros and cons of the two functional forms given above. Rather the likelihood ratio test³ is performed to identify which production technology will better represent the technology of each of the industrial group included in the study⁴. Therefore, the empirical models that we used for estimation of technical efficiency of manufacturing industries in the study are both C-D and translog frontier production functions which are given as follows:

5

ln Y_it =α + _∑α ln X + E_it ……………............................…..........(11)

0 i it i= 1

5

ln Y_it =α + _∑α ln X _it + 2 1 _∑∑β ln X + E_it ..........................................(12)

0 i ij jt i= 1 j

Where Y_it is Gross Value of Production (in Birr) for the i-th firm, ( i = 2 ,1 ,.., N ) , in the t

th observation ( t = 2 ,1 ,...,5) ; X _it and X _jt are vectors of inputs such as capital (in Birr),

labour in terms of wages and salaries paid, and industrial cost (in Birr) for the i-th firm in the t-th year of observation; α 's and β _ij's are unknown parameters to be estimated; and

E is as defined in (10).

it

The likelihood ratio statistic, λ , is defined as follows:

(( ((

λ=− ln 2 [ H L ) H L ₁ )]= 2[ ln H L )− ln H L )]

0 10

((

Where H L ) and H L ) are the maximum values of the likelihood function over the null and

mixed χ with K degrees of freedom where K is the number of restrictions imposed by the null

hypothesis. The restrictions imposed by the null hypothesis are rejected when λ exceeds the critical value (Samad and Patway, 2003).

See section 4 for the test whether C-D or translog production function better represents the technology of each industrial group in the study.

Given C-D and translog frontier production functions and the assumptions of each of the models, prediction of the technical efficiency of i-th firm at the t-th observation is based on the conditional expectation of U which is given by:

it

TE_it = exp (− U ) ………...............…………..................……(13)

it

Where U_it s are non-negative random variables, which are assumed to be independently

distributed with mean µ and variance δ².

it

To determine why some industries are less efficient than others, the technical inefficiency model for each industrial group is specified as follows:

µ =δ +δSIZ_it +δ SIZSQR_it +δ AGE_it +δ AGESQR_it +δ LOCT_it +δ OWNR_it

it 012 34 56

δ INCT_it +δTIM _it ……………………………………………………... (14)

78

Where µ is as defined above, δ 's unknown parameters to estimated and the variables

iti

(SIZ , AGE ,..., TIM )are as defined in the following sub-section.

The method of maximum likelihood is used for simultaneous estimation of the parameters of the stochastic frontier and the model for the technical inefficiency effects using the computer program, FRONTIER 4.1c, Coelli (1994). The likelihood function of

22

the model is expressed in terms of the variance parameters, δ =δ_V +δ and

U

2

γ= ^δU . The parameter, γ , measures the discrepancy between the frontier

22

δ +δ_U

V

attributable to technical inefficiency. It has a value between zero and one. The value of zero indicates that the non-negative random variable, U , is absent from the model while

it the value of one shows the absence of statistical noise or exogenous shocks from the model and hence low level of firm’s production compared to the best practice (the maximum output) of the other firm that is totally a result of firm specific technical inefficiency.

Definitions of Variables

Those variables that are included in equations 11, 12, and 14 are defined as follows: Gross Value of Production (GVP): is a combination of sales value of all products of the establishment, the net change between the beginning and end of the reference period in the value of finished goods and the value of work in progress, the value of industrial services rendered to others, the value of goods bought and resold without any transformation or processing and other receipts.

Fixed Capital (CAP): represents those assets of the establishments with a productive life of one year or more. It shows the net book value at the beginning of the reference year plus new capital expenditure minus the value of sold and disposed machineries and equipment and depreciation during the reference period.

Labour (LAB): in the frontier production function labour is proxied by the amount wages and salaries paid to the workers in each sub-sector. This is done because the heterogeneity of labour is not only in terms of biological make-up of the workers but also in terms different attributes like education and work experience. Therefore, wages and salaries are presumed to better consider such differences and better represents the extent of labour input use. This variable includes all payments in cash or in kind made to the workers during the reference year in connection with the work done for the establishments

Industrial Cost (INCT): includes the cost of raw materials, fuels, electricity and other supplies consumed and cost of industrial services rendered by other firms.

Size and Size Squared (SIZ and SIZSQR): in equation (22) size of the firm is proxied by the number of workers engaged in the reference year. Size squared is included in the model to allow for U-shaped relationship between firm size and technical efficiency in the sense that the marginal impact of increased size diminishes overtime.

Age and Age Squared (AGE and AGESQR): in the inefficiency model, firm age is included to capture the effect of experience on the technical efficiency of manufacturing industries. Like size squared, age squared is included in the model because of the strong diminishing returns in the learning-by-doing process so that the gains in technical efficiency from experience are eventually exhausted (Lundvall and Battese, 1999).

Location (LOCT): 1 if the firm is located around Addis Ababa, 0 otherwise. This variable is included in the inefficiency model to examine whether the location of a firm within each sub-sector matters in determining the technical efficiency of firms.

Ownership (OWNR): 1 if the firm is privately owned totally or partially, 0 if the firm is totally owned by the government. An inclusion of this variable will help us to consider if there is any difference on the impact of technical inefficiency due to the different types of ownership within each sub-sector.

Incentive (INCT): represents the amount of incentive paid to workers in the form of commissions, bonuses, professional and hardship allowances, food, lodging, and medical benefits, pension, life and causality insurance schemes, etc. the payment is either in cash or in kind during the reference period.

Time (TIM): Time (1, 2, 3, 4 and 5) is included in the inefficiency model to examine the effect of time on technical efficiency of firms in each sub-sector.

1. Empirical Results

2. Tests of Different Hypotheses

It is worthwhile to discuss some of the tests we carried out before we directly go to the discussion of our results. Four types of tests are undertaken and the first one is related to whether the technology of each industrial group included in the study is better represented by Cobb-Douglas or translog production functions.

Table 2 Hypothesis Testing on the Stochastic Frontier Cobb-Douglas and Translog Production Functions for each Industrial Group

Source: Author’s Computation

*

The critical values correspond to 5 percent level of significance

As shown in Table 2, given the specification of Cobb-Douglas or translog stochastic frontier production function, the null hypothesis that the Cobb-Douglas production technology is a better representation for the firms in each sub-sector is rejected for all sub-sectors, except for leather and chemical industries. The log-likelihood ratio tests indicate that the rest seven industrial groups (i.e., food processing, beverages, textile, wood & furniture, paper & printing, rubber & plastics and non-metallic mineral industries) are better represented by the translog production technology.

Measurement and Sources of Technical Inefficiency in Ethiopian Manufacturing Industries____ Table 3 Hypothesis Testing on the Distribution of U

it

Source: Author’s Computation

*

The critical values correspond to 5 percent level of significance. Another test which checks whether the technical efficiency levels for the firms in each sub-sector are better estimated using a half normal or a truncated normal distribution of

is shown in Table 3. The table indicates that only the technical efficiency levels for

it

the firms in food processing industries are better estimated with the truncated normal distribution of U_it while the technical efficiency levels for those firms in other sub-sectors

are better estimated with half normal distribution of U_it . Table 4 Hypothesis Testing on Deciding Whether Technical Inefficiency is Absent

from the Model or not

Source: Author’s Computation

___________________________________________________________________________ 19 Daniel G/Hiwot

*

The critical values correspond to 5 percent level of significance

The null hypothesis that technical inefficiency in each sub-sector is absent from the model is also tested given either Cobb-Douglas or translog stochastic production function. The log-likelihood ratio tests shown in Table 4 for each sub-sector indicate that the null hypothesis that technical inefficiency is absent is rejected for all the sub-sectors. This result suggests the existence of technical inefficiency among the firms in Ethiopian manufacturing sector and thus the inappropriateness of the average production function which assumes all the firms are fully technically efficient.

Table 5 Hypothesis Testing on the Joint Significance of the Explanatory Variables Included in the Inefficiency Model

Source: Author’s Computation

*

The critical values correspond to 5 percent level of significance

Finally, as shown in Table 5 the null hypothesis that the inefficiency effects are not a function of the explanatory variables or factors which are attributable to the technical inefficiency existing among the Ethiopian manufacturing industries is rejected for all sub-sectors confirming that the joint effect of these variables on technical inefficiency is found to be statistically significant.

4.2 Production Function

As opposed to other production function models efficiency studies concentrate on the specification of the error term for prediction of technical efficiency while the estimation of elasticity as characteristics of production process is only secondary interest. Due to this, the maximum likelihood estimates of the coefficients of the production function are not of immediate interest to this study also. Therefore, we tried to give some explanations to the coefficients of the variables for both the Cobb-Douglas and translog stochastic production functions.

For those sub-sectors, i.e. leather and chemical industries, where the production technology is represented by Cobb-Douglas production function the relationship between the traditional input variables and the level of output turned out to have expected signs. However, the parameter estimates of all the production inputs are found to be statistically significant at 5 percent significance level only for leather industries whereas in chemical industries it was only industrial cost that is found to be significantly affecting the level of production. The other two input variables, capital & labour, are not statistically significant at the conventional 5 and 10 percent significance levels. On the other hand, in those sub-sectors where the production technology is represented by the translog stochastic production frontier, most of the parameter estimates are statistically significant at both 5 and 10 percent significance levels even though some parameter estimates are not found to be significant at both significance levels. From the parameter estimates that are found to be statistically significant, some of the coefficients turned out to have unexpected relationships with the level of output.

For instance, as shown in Table 6, in beverage industries the impact of labour on the level of output produced is found to be negative. This could be due to a large amount of labour that is employed on a relatively small amount of capital. Capital is also found to have a negative relationship with the level of production in paper & printing industries which could be as a result of old and technologically backward machineries used by the industry. In textile industries, industrial cost (or raw material) is observed to have an inverse relationship with the level of output produced. The possible explanation for this result could be an over commitment of raw materials to the production of different types of products in the industry.

In flexible functional forms, like translog production function, this kind of unexpected results could be observed also due to the multicollinearity problems often associated with such flexible functional forms. In a production function analysis, correlation between some of the explanatory variables is expected. Collinearity among economic variables is an inherent and age-old problem leading to problems of multicollinrearity. Some have, therefore, suggested that multicollinearity is not necessarily a problem unless it is very high (Gujarati, 1995). In efficiency estimation, since the primary interest is to predict the degree of technical efficiency, some degree of multicollinearity can be tolerable.

Table 6 Maximum Likelihood Estimates for the Parameter of the Cobb-Douglas or Translog Stochastic Frontier Production Functions for the Nine Industrial Groups

Inefficiency Model

Constant SIZ

SIZSQR AGE AGESQR LOCT OWNR INCT TIM

-12.31* (1.42) 0.013* (0.0025)

-0.00002* (0.000004) 0.57* (0.082) -0.0069* (0.001) -0.026 (0.21) 0.26 (0.25) -0.57* (0.08) 0.76* (0.093) -

0.033* (0.0088)

-0.00004* (0.000012) -1.49*

(0.36) 0.057* (0.019)

0.039

(0.65) -4.29*

(1.31) -2.89**

(1.46)

1.01* (0.327)

-

-0.092*

(0.002)

0.0000026* (0.0000006) 0.12* (0.047) -0.055* (0.002) -1.26* (0.44) -0.16 (0.48) -0.83* (0.27) -0.32* (0.11) -

-0.018*

(0.0068)

0.000019* (0.000007) -0.20* (0.073) 0.014* (0.0042) 1.15 (0.80) -2.12** (1.09) -1.04* (0.40) 0.57* (0.23) -

-0.041*

(0.011)

0.00008* (0.00003) -0.063* (0.022) 0.0005* (0.00024) 0.69* (0.22)

(0.24) 0.00019 (0.00018) 0.28* (0.076)

Variance Parameters

22

δ =δ +δ

uv

2

22

γ=δ (δ +δ )

u

uv

Log-Likelihood Mean TE Observations

1.69* (0.156)

0.92* (0.012) -309.39 0.76 84 1.59*

(0.27) 0.96*

(0.0094) -39.86 0.76 16 1.14*

(0.15) 0.92*

(0.03) -159.85 0.62 38 1.12*

(0.26) 0.87*

(0.04) -111.35 0.74 30

0.52* (0.078)

0.82*

(0.04) -130.07 0.80 58

Cont

___________________________________________________________________________ 22 Daniel G/Hiwot

Table 6 Cont’d

Notes -Source: Author's Computation -Figures in Parentheses are standard errors.

* **

-Significance levels of 5 and 10 percents are indicated by and , respectively.

___________________________________________________________________________ 23 Daniel G/Hiwot

4.3 Prediction of Firm Level Technical Efficiencies

For all sub-sectors, the results of maximum likelihood estimates as shown in Table 6 indicate that, there are significant inefficiency effects associated with production, which is in line with the test presented in Table 4. This is evident from the estimates of the discrepancy parameter γ which are 0.92, 0.96, 0.92, 0.87, 0.82, 0.72, 0.95, 0.48 and 0.87

for food processing, beverages, textile, leather, wood & furniture, paper & printing, chemical, rubber & plastics and non-metallic mineral industries. This means that around 92, 96, 92, 87, 82, 72, 95, 48, and 87 percent of the discrepancies between the observed output and the frontier output levels are due to technical inefficiency. This implies that Ethiopian manufacturing industries are characterized by inefficient way of production. Moreover, the very high value of γ indicates that much of the shortfall of observed

output from the frontier output is due to technical inefficiency, i.e. due to those factors within the control of the firm rather than statistical ‘noise’ or external ‘shocks’. Furthermore, the significance of γ in the inefficiency model justifies the use of stochastic

frontier model and the associated method of maximum likelihood estimation.

Once it is proved that there exists a significant level of technical inefficiency among Ethiopian manufacturing industries, prediction of the level of technical efficiency for the firms in each sub-sector is found to be very important. Constructing an index of technical efficiency provides a good picture of the extent of variation in its level among firms which will have important implications for the industrial policy formulation in the country. Based on this, the frequency distribution of the predicted technical efficiencies for each industrial group or sub-sector is discussed with the help of Tables 7 to 15.

As shown in Table 7 below the predicted technical efficiency values for food processing industries vary from 14 to 94, 51 to 95, 6 to 95, 2 to 88 and 2 to 87 percent in 1998, 1999, 2000, 2001 and 2002, respectively. This indicates the existence of high variation in technical efficiency of firms in the sub-sector. It is also observed that the variation is increasing during the study period.

During the early periods of the study, some firms were able to operate at an efficiency level of 90 percent and above while at the end of the study period any of the firms in the industry fail to score this efficiency level. The number of firms which were operating at efficiency level of 40 percent and below have been increasing during the study period. This shows the increase in technical inefficiency of firms under the existing level of inputs and technology environment.

Table 7 Frequency Distribution of Technical Efficiencies in Food Processing Industries Percent of Firms (%)

Source: Author’s Computation

The sample averages of technical efficiencies for firms in food processing industries are found to be 80, 81, 74, 74 and 68 percent in 1998, 1999, 2000, 2001 and 2002, respectively. These figures also indicate that average technical efficiency of firms relative to the frontier level has been decreasing during the study period. A panel mean technical efficiency of 76 percent for food processing industries indicates that there exists a 24 percent difference between the observed level of output and the frontier output level that could have been obtained using the existing level of inputs and technology.

The predicted technical efficiency values for beverage industries vary from 40 to 76, 49 to 93, 5 to 89, 1 to 92 and 48 to 95 percent in 1998, 1999, 2000, 2001 and 2002, respectively. Table 8 shows a higher variation is observed in 2001 and low variation is observed in 1999. In 1999 and 2002 there was no firm which was operating at an efficiency level of 40 percent and below while 6.3 percent of the firms in both years were operating at an efficiency level of 91 percent and above. The converse is true in 1998 and 2000 where no firm has scored over 90 percent level of efficiency while 6.3 percent of the firms in beverage industry scored 40 percent and below in both years.

Table 8 Frequency Distribution of Technical Efficiencies in Beverage Industries Percent of Firms (%)