(4. Methodological Frameworks

4.1. Measurement of Technical, Pure Technical, and Scale Efficiencies: CCR and BCC DEA models

As noted above, we intend to apply the technique of DEA for computing the measures of technical, pure technical, and scale efficiencies for individual PSBs. In general, DEA is referred to as a linear programming technique that converts multiple incommensurable inputs and outputs of each decision making unit (DMU) into a scalar measure of operational efficiency, relative to its competing DMUs. DEA identifies ‘peer’ DMUs for an individual DMU and then estimates the efficiency of the DMU by comparing its performance with that of the best practice DMUs chosen from its peers. Note that the idea here of best practice is not some theoretical and possibly unattainable concept, but the DMU(s) performing best amongst its (their) peers, which is assigned an efficiency score of 1. These units constitute the referrals ‘standards’ and ‘envelop’ the other units and, thus, form the efficient frontier. DEA involves solving a linear programming problem for each DMU. The solution to the linear programming problem consists of information about the peers of the DMU and the efficiency of the DMU relative to its peer group.

In DEA, technical efficiency (TE) can be viewed from two perspectives. First, input- oriented TE focuses on the possibility of reducing inputs to produce given output levels. Second, output-oriented TE considers the possible expansion in outputs for a given set of input quantities. A measure of TE for a DMU o can be defined as

Page | 42 EJBE 2008, 1(2)

An Examination of Technical, Pure Technical, and Scale Efficiencies in Indian …..

θ output = Actual output / Maximum possible output in output-oriented context, ooo

or θ input = Minimum possible input / Actual input in input-oriented context. To ooo

quantify a measure of TE, we need to find out the divergence between actual production and production on the boundary of the feasible production set. This set summarizes all technological possibilities of transforming inputs into outputs that are available to the organization. A DMU is technically inefficient if production occurs within the interior of this production set. A measure of scale efficiency (SE) can be obtained by comparing TE measures derived under the assumptions of constant returns-to-scale (CRS) and variable returns-to-scale (VRS). As noted above, the TE measure corresponding to CRS assumption represents overall technical efficiency (OTE) which measures inefficiencies due to the input/output configuration and as well as the size of operations. The efficiency measure corresponding to VRS assumption represents pure technical efficiency (PTE) which measures inefficiencies due to only managerial underperformance. The relationship SE = OTE / PTE provides a measure of scale efficiency. For the one- output and one-input case, the derivation of the concepts of technical, pure technical, and scale efficiency under DEA approach is illustrated in Figure 2.

EJBE 2008, 1(2) Page | 43)

writer can choose the easiest technical way to have saudi arabia insurance market

( portugal copy have to take from *15-16-17-18*)(4. Methodological Frameworks

4.1. Measurement of Technical, Pure Technical, and Scale Efficiencies: CCR and BCC DEA models

As noted above, we intend to apply the technique of DEA for computing the measures of technical, pure technical, and scale efficiencies for individual PSBs. In general, DEA is referred to as a linear programming technique that converts multiple incommensurable inputs and outputs of each decision making unit (DMU) into a scalar measure of operational efficiency, relative to its competing DMUs. DEA identifies ‘peer’ DMUs for an individual DMU and then estimates the efficiency of the DMU by comparing its performance with that of the best practice DMUs chosen from its peers. Note that the idea here of best practice is not some theoretical and possibly unattainable concept, but the DMU(s) performing best amongst its (their) peers, which is assigned an efficiency score of 1. These units constitute the referrals ‘standards’ and ‘envelop’ the other units and, thus, form the efficient frontier. DEA involves solving a linear programming problem for each DMU. The solution to the linear programming problem consists of information about the peers of the DMU and the efficiency of the DMU relative to its peer group.

In DEA, technical efficiency (TE) can be viewed from two perspectives. First, input- oriented TE focuses on the possibility of reducing inputs to produce given output levels. Second, output-oriented TE considers the possible expansion in outputs for a given set of input quantities. A measure of TE for a DMU o can be defined as

Page | 42 EJBE 2008, 1(2)

An Examination of Technical, Pure Technical, and Scale Efficiencies in Indian …..

θ output = Actual output / Maximum possible output in output-oriented context, ooo

or θ input = Minimum possible input / Actual input in input-oriented context. To ooo

quantify a measure of TE, we need to find out the divergence between actual production and production on the boundary of the feasible production set. This set summarizes all technological possibilities of transforming inputs into outputs that are available to the organization. A DMU is technically inefficient if production occurs within the interior of this production set. A measure of scale efficiency (SE) can be obtained by comparing TE measures derived under the assumptions of constant returns-to-scale (CRS) and variable returns-to-scale (VRS). As noted above, the TE measure corresponding to CRS assumption represents overall technical efficiency (OTE) which measures inefficiencies due to the input/output configuration and as well as the size of operations. The efficiency measure corresponding to VRS assumption represents pure technical efficiency (PTE) which measures inefficiencies due to only managerial underperformance. The relationship SE = OTE / PTE provides a measure of scale efficiency. For the one- output and one-input case, the derivation of the concepts of technical, pure technical, and scale efficiency under DEA approach is illustrated in Figure 2.

EJBE 2008, 1(2) Page | 43)

writer can choose the easiest technical way to have saudi arabia insurance market

( portugal copy have to take from *15-16-17-18*)