Military-Madrasa-Mullah A Global Threat 1 Complex 1 Article
A Dynamic DEA Model for Indian Life Insurance Companies
Global Business Review 16(2) 1–12 © 2015 IMI SAGE Publications sagepub.in/home.nav DOI: 10.1177/0972150914564418 http://gbr.sagepub.com
Ram Pratap Sinha1 Abstract Efficiency studies relating to the Indian life insurance companies have so far used static one-period data envelopment analysis (DEA) models for the purpose of comparison of performance. A major weakness of the static framework is that the efficiency results are not inter-temporally comparable. In order to overcome this problem, the present study uses a dynamic slacks-based DEA model proposed by Tone and Tsutsui (2010) for performance evaluation of 15 in-sample life insurance companies for a seven-year period (2005–2006 to 2011–2012). The unique selling point (USP) of the present approach is that unlike the conventional static DEA models, the present framework, by using a link variable, connects the observed years and thereby creates a common benchmark. The results reveal significant fluctuations in mean technical efficiency over the period of observation. Keywords Dynamic DEA, life insurance, slacks-based measure
Introduction During the past one decade quite a number of new private life insurance companies have entered the Indian insurance market. While this undoubtedly resulted in market deepening, the insurance sector is undergoing a crisis due to a variety of internal and external factors. There are numerous efficiency studies relating to the insurance sector in India. However, majority of them used a static non-parametric framework for the purpose. Against this backdrop, the present study benchmarks the performance of 15 life insurance companies for the recent past (2005–2006 to 2011–2012) using a dynamic data envelopment analysis (DEA) model.
Organization The present study is organized in to four sections and proceeds as follows. The first section provides an overview of the Indian life insurance industry as it stands today. The second section traces the Associate Professor of Economics, Govt. College of Engineering and Leather Technology, Kolkata, L B Block, Sector – III, Salt Lake, Kolkata 700 098.
1
Corresponding author: Ram Pratap Sinha, Associate Professor of Economics, Govt. College of Engineering and Leather Technology, Kolkata, L B Block, Sector – III, Salt Lake, Kolkata 700 098. E-mail:
[email protected]
India Quarterly, 66, 2 (2010): 133–149
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Table 1. Trends in Life Insurance Density and Penetration (2006–2011) Year
2006
2007
2008
2009
2010
2011
Life Insurance Density Penetration (%)
33.2 4.1
40.4 4
41.2 4
47.7 4.6
55.7 4.4
49 3.4
Source: Author’s calculation.
evolution of non-parametric methodology for the measurement of efficiency and the advent of dynamic efficiency analysis. The third section discusses the results. The fourth section concludes.
Indian Life Insurance Market—An Overview Public sector giant, Life Insurance Corporation of India, had a monopoly control over the Indian life insurance market for a period of 43 years (1956–1999) which ended with the deregulation of entry in 1999. Between 2000–2001 and 2011–2012 the total number of life insurance companies operating in India increased from one to 24. As per the information provided by Swiss Re, India ranks tenth in terms of life insurance business out of a total of 156 countries. The level of development of the life insurance sector in a country is usually measured by two indicators: insurance density and insurance penetration. Insurance density is computed as the ratio of premium to population, that is, per capita premium. On the other hand, insurance penetration is calculated as the percentage of insurance premium to GDP. Table 1 provides the trend observed in respect of insurance density (measured in US dollars) and insurance penetration (in percentage terms) in the Indian life insurance market for the period 2006 to 2011. In the recent past, the Indian life insurance industry has been going through a crisis. Thus the (inflation-adjusted) real growth in premium was a negative 8.5 per cent in India for 2011–2012 while the same figure for the global insurance market was −2.7 per cent. During 2010–2011 and 2011–2012, the sale of life insurance policies dropped relative to the previous year. Moreover, between 2010 and 2012, the total number of offices of the life insurance companies operating in India has been reduced from 12,018 to 11,167.
Comparison of Performance: The Methodological Issues Benchmarking of Productive Systems In the context of a multi-input multi-output production system, Shephard’s (1953, 1970) distance function provided a functional characterization of the production technology. The input set of the production technology is characterized by the input distance function which gives the maximum amount by which the producer’s input vector can be radially contracted. The output set, on the other hand, is characterized by the output distance function, which gives the minimum amount by which the producer’s output vector can be deflated and yet remains feasible for a given input vector. Farrell (1957) laid the foundation for new approaches to efficiency and productivity studies at the micro level, providing invaluable insights on two issues: defining efficiency and productivity, and the calculation of the benchmark technology and the efficiency measures. The fundamental contribution of Farrell included the following: (a) introduction of efficiency measures based on radial uniform contractions or expansions from inefficient observations to the frontier; (b) specification of the production
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frontier as the most pessimistic piecewise linear envelopment of the data; and (c) construction of the frontier through solution of the systems of linear equations. Farrell’s definitions of efficiency had close connections with the concepts of distance function since the reciprocal of the input distance function can be considered as the radial measure of input-oriented technical efficiency whereas the radial measure of output-oriented technical efficiency coincides with the output distance function. In their 1978 seminal paper, Charnes et al. (1978) provided a generalization of Farrell’s single-input single-output technical efficiency measure to the multiple-output multiple-input case and their contribution resulted in the genesis of DEA. The methodology originally developed by Charnes et al. (1978) was later further extended by Banker et al. (1984). DEA enables the construction of a production frontier in the context of a multiple input–output framework with minimal prior assumption on input– output relationship. The DEA approach constructs the efficiency frontier of productive units out of piecewise linear stretches thereby forming a convex production possibility set. In the DEA frontier, efficient observations are those for which no other decision-making unit or linear combination of units has as much or more of every output (given inputs) or as little or less of every input (given outputs). It envelops data sets and therefore makes no room for noise. Once DEA identifies the efficient frontier the performance of inefficient decision-making units (DMUs) is improved by either increasing the current output levels or decreasing the current input levels. In the presence of undesirable outputs, however, such an exercise is likely to give erroneous results. This is because, in such cases undesirable/bad outputs are to be decreased while good outputs are to be increased. The problem with the standard DEA model is that decreases in outputs are not allowed and only inputs are allowed to decrease (similarly, increases in inputs are not allowed and only outputs are allowed to increase).
The BCC Model for Data Envelopment Analysis The Banker–Charnes–Cooper (1984) model introduced performance benchmarking of productive entities based on local technology. In order to provide an extremely brief review of the model, let us consider a productive firm which produces a scalar output Y from a bundle of k inputs x = (x1, x2, …, xk). Let (xi, yi) be the observed input-out bundle of firm i (i = 1, 2, …, n). The technology used by the firm is defined by the production possibility set. Ps = {(x, y) : y can be produced from x} An input–output combination (x0, y0) is feasible if and only if (x0, y0) !Ps We assume the firm to be input minimized given the level of output(s). The firm’s optimization exercise can be written as: Min i Subject to: i x0 ≥ Xm , y0 ≤ Ym, em = 1, m ≥ 0 If we write the production function as: Y = f(X) → X = f–1(Y). Let X* represent the minimum input corresponding to a given level of output (say Yf). In the presence of technical inefficiency X 0 ≤ X* where X* represents optimal input. Technical efficiency of the firm is
Optimal input usage/Actual input usage = X*/X 0 = 1/i
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A characteristic feature of the BCC envelopment model is that the technical efficiency varies between 0 and 1. This is because the data set which is used to evaluate the observed firm includes the firm’s data also.
Input/Output Slacks in the Radial DEA Models The linear program mentioned above gives us a radial measure of technical efficiency. However, a major weakness of the radial approach is that it cannot reflect all identifiable potential for expansion of output and contraction of input. A firm is not efficient in the economic (Paretian) sense if output can be increased (without increasing input usage) or input usage can be reduced(without affecting output). When positive output and input slacks are present at the optimal solution of a Charnes et al. (1978) or Banker et al. (1984) linear programming problem, the corresponding radial projection of an observed input-output combination is unable to meet the criterion of Pareto optimality and will not qualify as an efficient point.
The Slacks Based Measure Model Tone (2001) introduced the slacks-based measure model in which the efficiency of DMU with activity indicated by (x0,y 0) is estimated by the following fractional linear program: Min Ω = (1 – 1/m∑s–l/xl0)/(1 + 1/n∑s+k/yk0)(1) s.t. x0 = X m + s– y0 = Y m – s+ m ≥ 0, s– ≥ 0, s+ ≥ 0 X 0 = (X 01, X 02, …, X 0r) and Y 0 = (Y 01, Y 02, …, Y 0m) The important properties of the slacks-based measure of efficiency are as under: 1. The measure is invariant with respect to the units of data. 2. The measure is monotone decreasing in each slack in input and output. 3. The measure is dependent only on the values attributable to the decision-making units included in the reference set of the DMU concerned. 4. The slacks-based measure of efficiency has an additive structure, that is, it removes input and output slacks through addition and subtraction from their respective inequalities. The slacks-based measure of in efficiency can be interpreted as a product of output and input inefficiencies. For this, we write Equation 1 as:
1 Ω = m [∑{(xi0 – s–)/xi0}] × 1/n [∑{(yi0 + s+)/yi0}] –1
(2)
The first term on the right hand side, that is, 1/m[∑{(xi0 − s–)/xi0}] can be interpreted to evaluate the relative reduction rate of input i and hence the first term corresponds to the mean reduction rate of inputs, 1 that is, input inefficiency. In an analogous manner, the second term in Equation 2, n [∑{(yi0 + s+)/yi0}] –1 measures output inefficiency.
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Dynamic DEA Models The methodologies cited above compute technical efficiency on a standalone basis implying that the benchmarks used for the evaluation of efficiency are period-specific. The contributions of Fӓre et al. (1994) and Klopp (1985) permitted researchers to consider inter-temporal efficiency changes. However, neither of the two aforementioned approaches could connect the activities of successive time periods through link variables. The first formal attempt to consider inter-connected activities in a dynamic DEA framework was by Fӓre et al. (1996). Subsequent notable contributions in this field include Emrouznejad and Thanassoulis (2005), Nemoto and Goto (2003), Park and Park (2009) and Sueyoshi and Sekitani (2005). In 2010, Tone and Tsutsui (2010) introduced a slacks-based measure model for dynamic DEA which, by incorporating carry-over activities into the model, is capable of linking the activities of successive time periods (see Figure 1). In the present study a less general version of the Tone and Tsutsui (2010) model is considered. Accordingly, a truncated version of their model is provided below. Let us consider n DMUs for a period of T years (t = 1, 2, …, T). For each year DMUs have common m inputs, s outputs and a link variable z linking the time periods (t = 1, 2, …, T). The production possibilities are defined by the following inequalities:
x oit $ | j = 1 x oit m jt (i = 1, 2…., m; t = 1, 2, …, T)
y oit # | j = 1 y ijt m jt (i = 1, 2…., s; t = 1, 2, …, T)
z oit # | j = 1 z ijt m jt (i = 1, 2,…., n; t = 1, 2, …, T)
n
n
n
We assume that the goal of an observed DMU is to make inter-temporal maximization of output. Thus given the production possibilities set, the objective of an observed DMU is: Max n =
+ + 1 T 1 e n w i s it T :1 + | | w i = 1 y iot s+n T t=1
The output-oriented overall technical efficiency i* = 1/n.
Figure 1. Dynamic Characterization of Production System Source: Tone and Tsutsui (2010).
s
| ni = 1 z iotit oG
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Factor Efficiency Index In the present model, it is possible to compute a Factor Efficiency Index (FEI) in the following manner: FEI = (Actual Data/Projection). If an output/link/input is efficient, the factor efficiency index is 1. In case of output inefficiency it is less than one. On the other hand, for input inefficiency it is greater than one. Note that Tone and Tsutsui (2010) have taken a slightly different indicator: Actual Data/Projection – 1.
Framework of Present Study and Results Approach of the Present Paper A number of research studies have attempted to evaluate the performance of life insurance companies of various regions/countries. In the international context, the notable contributions include Cummins and Zi (1998), Gardner and Grace (1993), Hao and Chou (2005), Mahlberg and Url (2010), Yuengert (1992), etc. In the Indian context important studies include Dutta (2013), Sinha (2007, 2012), Sinha and Chatterjee (2011) and Tone and Sahoo (2005). The present article benchmarks the performance of 15 life insurance companies operating in India (on a continuous basis) for the time span 2005–2006 to 2011–2012 using a dynamic DEA model. While many other new life insurance companies commenced operation in the later stage of the aforesaid period, they could not be included in the present study because of their non-existence in the earlier part of the time span. Unlike the approach followed by some other researchers, the present sample does not include non-life insurance companies because the businesses undertaken by life and non-life companies are vastly undertaken and consequently are not comparable.
Selection of Output and Input: The Conceptual Issues The outputs of financial service firms are measured according to three main approaches: the asset (intermediation) approach, the user-cost approach, and the value-added approach (refer Berger and Humphrey, 1992). The asset approach treats financial service firms as pure financial intermediaries which borrow funds from their customers which are invested, and thus transformed into assets. Interest payments are paid out to cover the time value of the funds used. Applying the asset approach would mean that only the intermediation services provided by life insurance firms are taken into account without any regard to the risk-pooling and risk-bearing services rendered by them. The user-cost approach was developed by Hancock (1985). It determines whether a financial product is an input or an output by analyzing if its net contribution to the revenues of an insurance firm is positive or negative. According to that, a product is considered an output, if its financial return exceeds the opportunity costs of funds or if the financial costs of a liability are lower than the opportunity costs. Otherwise, the financial product would be classified as an input. This method would require precise information on product revenues and opportunity costs which cannot be obtained for the Indian life insurance firms. The value-added approach differs from the asset approach and the user-cost approach as it considers all asset and liability categories to have some output characteristics. Those categories which have
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substantial value added are then used as the important outputs. The remaining categories are treated as rather unimportant outputs, intermediate products or inputs. An important advantage compared to the user-cost approach consists in the fact that the value-added approach uses operating cost data rather than determining the costs implicitly or using opportunity costs. The value added approach is considered to be the most appropriate method to measuring output of financial firms and is widely used in recent insurance studies. The present article follows a hybrid path and considers one input (operating expenses and commissions), two outputs (premium collected and sum assured) and one free link: investments.
Data Source Data relating to the inputs and outputs used in the study have been collected from the Insurance Regulatory and Development Authority (IRDA) website. The data so collected have been appropriately deflated to make performances comparable over time.
Descriptive Statistics of Technical Efficiency Table 2 presents the descriptive statistics of technical efficiency scores for the 15 in-sample life insurance companies. The table provides information on mean technical efficiency and standard deviation of technical efficiency. The third measure (coefficient of variation) is derived from the first two: CV = (Mean/Standard Deviation) * 100%. A graphical comparison of mean technical efficiency and standard deviation for the observed years is made in Figure 2.
Company-wise Technical Efficiency Table 3 provides the company-wise technical efficiency scores for the period under observation. The figures presented in the table show that during the period under observation, only two companies, that is the Life Insurance Corporation of India (LIC) and SBI Life Insurance were technically efficient for all the years. Among the other companies, Sahara Life Insurance also performed reasonably well.
Table 2. Descriptive Statistics of Technical Efficiency of the In-sample Life Insurance Companies (Output-oriented Model) Particulars Mean Technical Efficiency Standard Deviation Coefficient of Variation (%)
2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012 Overall 0.7146
0.5206
0.6499
0.6233
0.5269
0.6238
0.6173
0.5595
0.306
0.2766
0.2474
0.2653
0.3183
0.2613
0.2643
0.2519
42.82
Source: Author’s calculation.
53.13
38.07
42.56
60.41
41.89
42.82
45.02
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Figure 2. Mean Technical Efficiency and Standard Deviation Source: Drawn by the author.
Table 3. Company-wise Technical Efficiency Company Aviva Bajaj Allianz Birla Sunlife HDFC Standard Life ICICI Prudential ING Vysya Kotak Life Insurance LIC Max New York Life Met Life Reliance SBI Life Sahara Shri Ram Life TATA AIG
2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012 0.4669 0.6791 1.0000 0.8471 1.0000 0.3847 1.0000 1.0000 0.4530 0.2131 0.2238 1.0000 0.9160 1.0000 0.5360
0.2829 0.3302 0.5426 0.4627 0.4942 0.2313 0.5266 1.0000 0.3830 0.2556 0.2946 1.0000 0.6764 1.0000 0.3298
0.4820 0.5990 0.7183 0.5832 0.7364 0.3192 0.6102 1.0000 0.4028 0.4003 0.4896 1.0000 1.0000 1.0000 0.4070
0.7051 0.5932 0.5618 0.3096 0.6089 0.2521 0.6082 1.0000 0.4003 0.5307 0.4204 1.0000 1.0000 1.0000 0.3586
1.0000 0.0679 0.5077 0.4103 0.5191 0.3910 0.3890 1.0000 0.3365 0.3077 0.3131 1.0000 1.0000 0.4955 0.1661
0.5914 1.0000 0.5054 0.5271 0.7841 0.2642 0.5079 1.0000 0.3436 0.5058 0.4059 1.0000 1.0000 0.5041 0.4174
0.5390 1.0000 0.5054 0.5243 0.7778 0.2635 0.5079 1.0000 0.3367 0.5058 0.3773 1.0000 1.0000 0.5041 0.4174
Source: Author’s calculation.
Factor Efficiency Index Table 4 provides the mean factor efficiency indices (= data/projection) for the two output variables (Sum Assured and Premium) and one link variable—Investment. The table indicates fluctuating
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Sinha Table 4. Mean Factor Efficiency Indices Particulars
2005–2006
2006–2007
2007–2008
2008–2009
2009—2010
2010–2011
2011–2012
0.8559 0.9426 0.9002
0.7905 0.8404 0.8489
0.8762 0.8539 0.8502
0.8353 0.8573 0.8097
0.5587 0.8991 0.9491
0.9018 0.9014 0.8221
0.8976 0.8907 0.8221
Sum Assured Premium Investment
Source: Author’s calculation.
Figure 3. Mean Factor Efficiency Indices of Output and Link Variables Source: Drawn by the author.
performance of the in-sample insurance companies over the observation period. Figure 3 provides a graphical presentation of mean factor efficiency indices. The insurer-wise factor efficiency indices are provided in the three appendix tables: Tables A1 through A2.
Conclusion The efficiency studies relating to the Indian life insurance industry have so far used static one-period DEA models. Two major weaknesses of this type of analysis are that the successive time periods are not connected and the benchmarks constructed are time-period specific. The present study is free from both the drawbacks and consequently the technical efficiency scores are inter-temporally comparable. The study indicates that mean technical efficiency of the in-sample life insurance companies fluctuated significantly during the observed period implying oscillating divergence from the frontier. The recent slowdown in the life insurance industry is reflected in the decline in mean technical efficiency scores for 2009–2010 and 2011–2012 relative to 2008–2009 and 2010–2011.
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Appendix Table A1. Insurer-wise Factor Efficiency Index (Indicator–Sum Assured) Company Aviva Bajaj Allianz Birla Sunlife HDFC Standard Life ICICI Prudential ING Vysya Kotak Life Insurance LIC Max New York Life Met Life Reliance SBI Life Sahara Shri Ram Life TATA AIG
2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012 0.3941 0.6974 1 1 1 0.4226 1 1 1 1 0.2470 1 0.8676 1 1
0.1753 0.2868 0.4877 0.3696 0.2979 0.2112 0.5355 1 0.6105 0.3025 0.2009 1 0.4260 1 0.3841
0.5161 0.7337 1 0.7060 0.5834 0.3434 0.6873 1 0.9017 0.5529 0.3590 1 1 1 0.5379
0.6427 0.9130 0.7759 0.4119 0.5859 0.3750 0.5692 1 0.5899 0.5199 0.2986 1 1 1 0.4227
1.0000 0.0240 0.3436 0.2215 0.2792 0.3192 0.1952 1 0.2301 0.1420 0.1384 1 1 0.2466 0.1816
0.7463 1 0.9288 0.6457 0.7500 0.4226 0.7529 1 0.5928 0.8175 0.3999 1 1 0.5177 0.5803
0.9343 1 0.9288 0.6559 0.7273 0.4247 0.7529 1 0.6248 0.8175 0.3281 1 1 0.5177 0.5803
Source: Author’s calculation.
Table A2. Insurer-wise Factor Efficiency Index (Indicator–Premium) Company Aviva Bajaj Allianz Birla Sunlife HDFC Standard Life ICICI Prudential ING Vysya Kotak Life Insurance LIC Max New York Life Met Life Reliance SBI Life Sahara Shri Ram Life TATA AIG
2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012 0.5347 0.7162 1 0.7450 1 0.3917 1 1 0.4801 0.2019 0.2540 1 1 1 0.4303
0.4089 0.3661 0.5706 0.5031 0.6823 0.2350 0.5566 1 0.3565 0.2067 0.3681 1 0.9190 1 0.3260
0.5213 0.5800 0.6317 0.5634 0.7859 0.3104 0.6111 1 0.3800 0.3323 0.5876 1 1 1 0.3611
0.5887 0.6332 0.6383 0.5004 0.8229 0.3773 0.6910 1 0.4096 0.4917 0.6395 1 1 1 0.4148
1 0.7093 0.6273 0.6092 0.8350 0.3962 1 1 0.4566 0.7262 0.8156 1 1 1 0.5433
0.6718 1 0.5396 0.6986 0.9851 0.4220 0.6404 1 0.4680 0.5904 0.5842 1 1 0.7956 0.5084
0.4442 1 0.5396 0.6733 0.9953 0.4143 0.6404 1 0.4162 0.5904 0.5794 1 1 0.7956 0.5084
Source: Author’s calculation.
Table A3. Insurer-wise Factor Efficiency Index (Indicator–Investment) Company Aviva Bajaj Allianz Birla Sunlife
2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012 0.4956 0.6301 1
0.4076 0.3488 0.5792
0.4223 0.5205 0.6274
1 0.4196 0.4025
1 1 0.7118
0.4455 1 0.3327
0.4455 1 0.3327
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Sinha Company HDFC Standard Life ICICI Prudential ING Vysya Kotak Life Insurance LIC Max New York Life Met Life Reliance SBI Life Sahara Shri Ram Life TATA AIG
2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 2010–2011 2011–2012 0.8337 0.5584 0.5121 0.1900 0.8651 0.3688 0.3688 1 0.8010 0.9197 0.4988 1.2165 0.6768 0.6768 0.3473 0.2511 0.3063 0.1519 0.4961 0.1511 0.1511 1 0.4918 0.5479 0.5786 0.6293 0.3315 0.3315 1 1 1 1 1 1 1 0.2825 0.2949 0.2698 0.2978 0.4202 0.2038 0.2038 0.1230 0.2783 0.3735 0.5899 0.7522 0.3317 0.3317 0.1846 0.4016 0.6094 0.4499 0.8841 0.3146 0.3146 1 1 1 1 1 1 1 0.8908 1 1 1 1 1 1 1 1 1 1 4.1135 0.3619 0.3619 0.4400 0.2919 0.3646 0.2787 0.0933 0.2859 0.2859
Source: Author’s calculation.
Acknowledgements The author is grateful to the anonymous referees of the journal for their extremely useful suggestions to improve the quality of the paper. The usual disclaimers apply.
References Banker, R., Charnes, A., & Cooper, W.W. (1984). Some models for estimating technical and scale efficiency. Management Science, 30, 1078–1092. Berger, A.N., & Humphrey, D.B. (1992). Measurement and efficiency issues in commercial banking. In Zvi Griliches (Ed.), Output measurement in the services sectors (pp. 245–279). National Bureau of Economic Research, Studies in Income and Wealth, Vol. 56. Chicago: University of Chicago Press. Charnes, A., Cooper, W.W., & Rhodes, E. (1978) Measuring efficiency of decision making unit. European Journal of Operational Research, 2(6), 429–444. Cummins, J.D., & Zi, H. (1998). Comparison of frontier efficiency methods: An application to the US life insurance industry. Journal of Productivity Analysis, 10(2), 131–152. Dutta, Anirban. (2013). Impact of privatization on productivity: A non-parametric analysis of Indian insurance sector. Global Business Review, 14(2), 297–314. Emrouznejad, A., & Thanassoulis, E. (2005). A mathematical model for dynamic efficiency using data envelopment analysis. Applied Mathematics and Computations, 160(2), 363–378. Färe, R., Grosskopf, S., & Brännlund, R. (1996). Intertemporal production frontiers: With dynamic DEA. Dordrecht: Kluwer Academic. Färe, R., Grosskopf, S., & Lovell, C.A.K. (1994). Production frontiers. Cambridge: Cambridge University Press. Farrell, M.J. (1957). The measurement of productive efficiency. Journal of The Royal Statistical Society, Series A, General, 120(3), 253–281. Gardner, L., & Grace, M.F. (1993). X-efficiency in the US life insurance industry. Journal of Banking and Finance, 17(2–3), 497–510. Hancock, D. (1985). The financial firm: Production with monetary and nonmonetary goods. Journal of Political Economy, 93(5), 859–880. Hao, James C.J., & Lin-Yhi Chou. (2005) The estimation of efficiency for life insurance industry: The case in Taiwan. Journal of Asian Economics, 16(5), 847–860. Klopp, G.A. (1985). The analysis of the efficiency of production system with multiple inputs and outputs. Ph.D. dissertation, University of Illinois, Industrial and System Engineering College, Chicago. Mahlberg, Bernhard, & Url, Thomas. (2010). Single market effects on productivity in the German insurance industry. Journal of Banking and Finance, 34(7), 1540–1548.
12
Global Business Review 16(2)
Nemoto, J., & Goto, M. (2003). Measuring dynamic efficiency in production: An application of data envelopment analysis to Japanese electric utilities. Journal of Productivity Analysis, 19(2–3), 191–210. Park, K.S., & Park, K. (2009). Measurement of multiperiod aggregative efficiency. European Journal of Operational Research, 193(2), 567–580. Shephard, R.W. (1953). Cost and production functions. Princeton: Princeton University Press. ———. (1970). Theory of cost and production functions. Princeton: Princeton University Press. Sinha, R.P. (2007). Operating efficiency of life insurance companies—An assurance region model. Artha Vijnana, 49(3–4), 305–320. ———. (2012). Are Indian life insurers cost efficient? Some recent empirical evidence, Prajnan, 41(3), 181–201. Sinha, R.P., & Chatterjee, B. (2011). Technical efficiency behaviour of life insurance companies—A dynamic panel approach. The Indian Economic Journal, 59(1), 150–165. Sueyoshi, T, & Sekitani, K. (2005). Returns to scale in dynamic DEA. European Journal of Operational Research, 161(2), 536–544. Tone, K. (2001). A slacks-based measure of efficiency in data envelopment analysis. European Journal of Operational Research, 130, 498–509. Tone, Kaoru, & Sahoo, B.K. (2005). Evaluating cost efficiency and returns to scale in the Life Insurance Corporation of India using data envelopment analysis. Socio-Economic Planning Sciences, 39(4), 261–285. Tone, Kaoru, & Tsutsui, Miki. (2010). Dynamic DEA: A slacks-based measure approach. Omega, 38(3–4), 145–156. Yuengert, A.M. (1993). The measurement of efficiency in life insurance: Estimates of a mixed normal gamma error model. Journal of Banking and Finance, 17(2–3), 483–496.
