CHAPTER 3 – EFFECT OF INFORMATION AND COMMUNICATION
3.6 ICT and technical efficiency
Where yi is the vector of log output, xi, is a vector of all the explanatory variables in
(3.2), while is the vector of estimated parameters, and u is a vector of residuals.
While
Q
( y / x )
i i represents the th conditional quantile of y, given the xi. The thregression quantile, 0 < < 1, solves the follow problem:
' '
i i n ' ' 1 1 n i i i n i i 1Min
(1
) y
x
Min
(u )
i i i i:y x i:y xy - x
(3.7)Where the check function is (.) and is defined as:
i i i i i u if u 0 (u ) (1- )u if u < 0 (3.8)
The th regression quantile as stated, ranges from zero to one and by changing continuously any quantile of the distribution of yi conditional on xi can be obtained. Least squares assumes that parameter estimates are the same at all points on the conditional distribution due to the independent and identically distributed (i.i.d) assumption, however under quantile regression as changes from zero to one this assumption is relaxed.
3.6 ICT and technical efficiency
Production frontier functions have been widely used in estimating technical efficiency and in this regard we use both the Cobb-Douglas and Translog production
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functions in exploring the relationship between ICT equipment/facilities and technical efficiency of the firm. It must however be emphasised that the traditional econometric estimation techniques (for example OLS) used to measure the production frontier fail as they allow some of the observed output bundles produced by a given set of inputs to be greater than the estimated maximal producible output (Arestis et al. 2006). Several techniques of estimating the firm’s technical efficiency of production have been suggested, both parametric and nonparametric. Seiford (1996) indicates that the choice of technique is a major of source of debate among researchers, with no clear view on which is best. This is due to the fact that each approach has its own merits and demerits. One major advantage of using a non- parametric estimation technique such as Data Envelopment Analysis (DEA) is that there is no need for fundamental assumptions underlying the functional form to be estimated. Shao and Lin (2002), opine that DEA does not require any explicit assumptions regarding inefficiency, an assertion also stressed by Odeck (2007). A major limitation of the non-parametric approach according to Odeck (2007) is that it is impossible to determine whether the source of inefficiency is actually due to technical inefficiency or statistical noise in the dataset. Another limitation of the DEA is that it has non-stochastic frontier with no probability distribution, however the efficiency of producers relative to the frontier might be probabilistic.
However, the parametric techniques in comparison with non-parametric techniques are based fundamental assumptions, regarding the functional form and also an explicit distributional assumption for the inefficiency term. Unlike the non- parametric approach, the parametric method uses econometrics methods to estimate the parameters of the production function and the technical efficiency. Econometric techniques accounts for stochastic noise, a limitation in using non-parametric approaches. Parametric approach also enables the statistical testing of the production structure and the extent of technical inefficiency. The determinants of technical inefficiencies are identified in a one stage approach, when parametric techniques are used rather than the traditional two stage approach. Technical inefficiency measures difference between a firm’s actual output and the maximum possible output. It estimates the ability of a firm to produce the optimal output, given its resources. ICT effect is measured by its contributions towards enhancing the efficiencies in the utilization of existing factor inputs and technology.
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It is important to determine the best production function specification that must be used in parametric approach of estimating technical efficiency. We estimate both Cobb-Douglas and Translog functional forms and test the null hypothesis that the Cobb-Douglas function adequately represents the dataset.
The Cobb–Douglas stochastic production frontier comprises of three inputs, capital (K), labour (L) and raw materials (RM). The general form of the Cobb-Douglas stochastic frontier production model for firm i is specified as,
(3.9)
Where ic is in reference to the ith firm located in country c. Taking logs on both sides, equation (3.9) can be rewritten as:
(3.10)
Where, lower case letters denote the corresponding logarithmic values and multifactor productivity variable. The random error denoted by is assumed to be independent and identically distributed (i.i.d.) with zero mean and constant variance . As specified in the previous section there are restrictions, such as fixed returns to scale and unitary elasticity of substitution, which are imposed on the
Cobb–Douglas production frontier. In this regard the chapter tests the Cobb-Douglas
production frontier against a three input Translog stochastic production frontier specified as,
(3.11)
Again the lower case letters are defined as the logarithmic values of capital (k), labour (l) and raw materials (rm). The value in both Cobb-Douglas and Translog production frontiers is assumed to be a non-negative random variable which represents the technical inefficiency of the production process and is assumed to be independently but not identically distributed and truncated at zero28. It measures the gap between the maximum possible output and what is actually produced; this is the “efficiency gap”.
28 The distributional assumption necessary for determining the inefficiency term requires the use of a
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Technical efficiency takes the value one only if the estimated potential output gap is equal to zero and otherwise it is less than one, implying the absence of technical inefficiency in the production process. If is equal to zero, and the firm produces at its maximum potential output; it is technically efficient in production. While less than zero implies the presence of technical inefficiency in the production process of the firm, indicating that the firm produces less than the potential maximum output level.
To estimate the effect of ICT on the technical efficiency of the firm there is the need for a second set of explanatory variables assumed to determine the level of efficiency at which the firm converts inputs into output. The literature on technical efficiency theory fails to designate specific variables that influence technical efficiency of the firm as it is an empirical issue and as such the set of independent variables are selected based on economic intuition (Carroll et al, 2007). Given data availability, the variables included in the second set of explanatory variables are types of ICT equipment or facility available to the firm ) and other firm characteristics such as firm size, ownership structure, management style, firm owner educational attainment, industrial sector of the firm, firm’s age and also the formality of firm (formal, informal or semi-formal sector firm). The inefficiency equation to be estimated from both Cobb-Douglas and Translog production frontiers is specified as:
(3.12)
Where represents whether firm i operating in country c has access to a particular type of ICT equipment or facility, say equipment/facility h and it also captures the total ICT capital in the firm, with representing the age of firm i in country c. Educational attainment of firm i’s owner in country c is represented by and represents the formality level of firm i in country c. The ownership structure of the firm i in country c is denoted by with and denoting the management style and industrial sector of firm i operating in country c. While represents the random variable term, which is defined by the truncation of the normal distribution with zero mean and variance, , such as . The set is the set of explanatory variables specified in the technical inefficiency equation (3.12). The ICT variable is added to the technical inefficiency equation so
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as to establish the relationship that exists between ICT and efficiency at the firm level. If the estimated parameter of ICT turns out to be significant and negative this will suggest that there is empirical evidence that the ICT equipment or facility has a positive effect on the technical efficiency of the firm.
Test for the present of technical inefficiency
The maximum likelihood estimation of the stochastic production frontier gives estimates of the variance parameters of the likelihood function, which is given in
terms of and , as well as . If =0 it implies
that technical inefficiency effects are relevant in determining the levels and
variations in the production of firms (Battese and Coelli, 1992). Further, if =0, it
supports the point that technical inefficiency effects are significant in explaining the variation in the dependent variable.
4 Estimation Results
This section is divided into three sub-sections. The first sub-section presents results of OLS estimation using both Cobb-Douglas and Translog production function forms. The sub-section also presents results of a meta-regression analysis. Finally, the sub-section presents results of an instrumental variable estimation of the Cobb- Douglas production function. The second and third sub-sections present results of the quantile and the stochastic production frontier estimations, respectively.