A Dynamic DEA Model for Indian Life Insurance Companies

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 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.

Table 1.

Trends in Life Insurance Density and Penetration (2006–2011)

Year	2006	2007	2008	2009	2010	2011
Life Insurance Density	33.2	40.4	41.2	47.7	55.7	49
Penetration (%)	4.1	4	4	4.6	4.4	3.4

Source: Author’s calculation.

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 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, …, x_k). 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.

Psxyyx

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: x⁰⁰

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 Y_f). In the presence of technical inefficiency X⁰ ≤ X* where X* represents optimal input. Technical efficiency of the firm is XX⁰

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: ^–(1)_l_l⁰⁺_k_k⁰x⁰Xs^–y⁰Ys⁺^–⁺X⁰X⁰₁X⁰₂X⁰_rY⁰Y⁰₁Y⁰₂Y⁰_m

The important properties of the slacks-based measure of efficiency are as under:

The measure is invariant with respect to the units of data.

The measure is monotone decreasing in each slack in input and output.

The measure is dependent only on the values attributable to the decision-making units included in the reference set of the DMU concerned.

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:

\frac{1}{m} [{(x_{i}^{0} s^{})/ x_{i}^{0}}] 1 / n [{(y_{i}^{0} s^{})/ y_{i}^{0} {}]}^{1}

(2)

The first term on the right hand side, that is, 1/m[∑{(x_i⁰ − s^–)/x_i⁰}] 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, that is, input inefficiency. In an analogous manner, the second term in Equation 2, $\frac{1}{n}$ [∑{(y_i⁰ + s⁺)/y_i⁰}] ^–1measures output inefficiency.

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}^{n} x_{oit}_{jt} (i 1, 2 . . . ., m; t 1, 2, . . . ., T)

y_{oit}_{j 1}^{n} y_{ijt}_{jt} (i 1, 2 . . . ., s; t 1, 2, . . . ., T)

z_{oit}_{j 1}^{n} z_{ijt}_{jt} (i 1, 2 . . . ., n; t 1, 2, . . . ., T)

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 \frac{1}{T}_{t 1}^{T} w^{T} [1 \frac{1}{s n} (_{i 1}^{n} \frac{w_{i}^{} s_{it}^{}}{y_{iot}}_{i 1}^{n} \frac{s_{it}^{}}{z_{iot}})]

The output-oriented overall technical efficiency θ* = 1/μ.

Figure 1.

Source: Tone and Tsutsui (2010).

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 Article

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 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.

Table 2.

Descriptive Statistics of Technical Efficiency of the In-sample Life Insurance Companies (Output-oriented Model)

Particulars	2005–2006	2006–2007	2007–2008	2008–2009	2009–2010	2010–2011	2011–2012	Overall
Mean Technical Efficiency	0.7146	0.5206	0.6499	0.6233	0.5269	0.6238	0.6173	0.5595
Standard Deviation	0.306	0.2766	0.2474	0.2653	0.3183	0.2613	0.2643	0.2519
Coefficient of Variation (%)	42.82	53.13	38.07	42.56	60.41	41.89	42.82	45.02

Source: Author’s calculation.

Figure 2.

Source: Drawn by the author.

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 3.

Company-wise Technical Efficiency

Company	2005–2006	2006–2007	2007–2008	2008–2009	2009–2010	2010–2011	2011–2012
Aviva	0.4669	0.2829	0.4820	0.7051	1.0000	0.5914	0.5390
Bajaj Allianz	0.6791	0.3302	0.5990	0.5932	0.0679	1.0000	1.0000
Birla Sunlife	1.0000	0.5426	0.7183	0.5618	0.5077	0.5054	0.5054
HDFC Standard Life	0.8471	0.4627	0.5832	0.3096	0.4103	0.5271	0.5243
ICICI Prudential	1.0000	0.4942	0.7364	0.6089	0.5191	0.7841	0.7778
ING Vysya	0.3847	0.2313	0.3192	0.2521	0.3910	0.2642	0.2635
Kotak Life Insurance	1.0000	0.5266	0.6102	0.6082	0.3890	0.5079	0.5079
LIC	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
Max New York Life	0.4530	0.3830	0.4028	0.4003	0.3365	0.3436	0.3367
Met Life	0.2131	0.2556	0.4003	0.5307	0.3077	0.5058	0.5058
Reliance	0.2238	0.2946	0.4896	0.4204	0.3131	0.4059	0.3773
SBI Life	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
Sahara	0.9160	0.6764	1.0000	1.0000	1.0000	1.0000	1.0000
Shri Ram Life	1.0000	1.0000	1.0000	1.0000	0.4955	0.5041	0.5041
TATA AIG	0.5360	0.3298	0.4070	0.3586	0.1661	0.4174	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 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.

Table 4.

Mean Factor Efficiency Indices

Particulars	2005–2006	2006–2007	2007–2008	2008–2009	2009—2010	2010–2011	2011–2012
Sum Assured	0.8559	0.7905	0.8762	0.8353	0.5587	0.9018	0.8976
Premium	0.9426	0.8404	0.8539	0.8573	0.8991	0.9014	0.8907
Investment	0.9002	0.8489	0.8502	0.8097	0.9491	0.8221	0.8221

Source: Author’s calculation.

Figure 3.

Source: Drawn by the author.

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.

Footnotes

Appendix

Table A3.

Insurer-wise Factor Efficiency Index (Indicator–Investment)

Company	2005–2006	2006–2007	2007–2008	2008–2009	2009–2010	2010–2011	2011–2012
Aviva	0.4956	0.4076	0.4223	1	1	0.4455	0.4455
Bajaj Allianz	0.6301	0.3488	0.5205	0.4196	1	1	1
Birla Sunlife	1	0.5792	0.6274	0.4025	0.7118	0.3327	0.3327
HDFC Standard Life	0.8337	0.5584	0.5121	0.1900	0.8651	0.3688	0.3688
ICICI Prudential	1	0.8010	0.9197	0.4988	1.2165	0.6768	0.6768
ING Vysya	0.3473	0.2511	0.3063	0.1519	0.4961	0.1511	0.1511
Kotak Life Insurance	1	0.4918	0.5479	0.5786	0.6293	0.3315	0.3315
LIC	1	1	1	1	1	1	1
Max New York Life	0.2825	0.2949	0.2698	0.2978	0.4202	0.2038	0.2038
Met Life	0.1230	0.2783	0.3735	0.5899	0.7522	0.3317	0.3317
Reliance	0.1846	0.4016	0.6094	0.4499	0.8841	0.3146	0.3146
SBI Life	1	1	1	1	1	1	1
Sahara	0.8908	1	1	1	1	1	1
Shri Ram Life	1	1	1	1	4.1135	0.3619	0.3619
TATA AIG	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 article. The usual disclaimers apply.

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