Analyzing firm performance in non-life insurance industry--parametric and non-parametric approaches.

Chakraborty, Kalyan ; Dutta, Anirban ; Sengupta, Partha Pratim 等

Abstract

This study investigates productive efficiency and total factor productivity growth for Indian non-life insurance industry after deregulation. The empirical analysis uses seven years panel data from twelve leading non-life insurers that accounts for above ninety-five per cent of the business in the industry. Productive efficiency estimates are based on Battese and Collie (1995) Stochastic Frontier inefficiency-effect model and Fixed Effect Stochastic Frontier model. Dynamic productivity index (Malmquist index) is estimated using data envelopment analysis (DEA). The study found differences in efficiency scores obtained from parametric (regression) and nonparametric (DEA) methods. Regression analysis found net claims, operating expenditure, and total investment are positively related to net premiums earned. Dynamic productivity analysis found eight out of twelve firms achieved gain in total factor productivity growth.

Keywords: Stochastic, Malmquist, Productivity, Frontier, Nonlife

JEL Code: G22; C14; G14

INTRODUCTION

Over the last decade insurance industry is moving toward the developing countries where the governments are actively pursuing deregulation and liberalization policies. Financial liberalization acts as incentive and draws foreign domestic investment (FDI) leading to a free flow of insurance services across the national boundaries. Between 1997 and 2004 insurance sector in emerging markets grew by 52 per cent compared to 27 per cent in the industrialized nations (UNCTD, 2007). Although the global financial crisis in 2007-09 made a dent on the flow of FDI worldwide, according to a recent report by the United Nations survey of transnational corporation (TNC) (WIPS, 2010) the FDI flow will reach USD 1.5 trillion in 2011 and USD 2.0 trillion in 2012 which is close to pre-crisis level. Surprisingly, the survey found that in the post-crisis recovery era for the first time the emerging countries like India, China, and Russian Federation are the top recipients of FDI investor countries in 2012. The growth of non-life insurance premium in 2010 in emerging markets is 22 per cent compared to 1.0 per cent for the industrialized countries and 2.1 per cent for the world (Swiss Re, 2010). A major part of the FDI flow in India is expected in the financial services sector, the non-life insurance industry in particular. India's insurance industry is one of the fastest growing markets in the global insurance industry.

The non-life insurance (property/casualty and health) premium in India for the year ended 31st March 2011 grew 28 per cent over the previous year (Towers, 2011). Unfortunately for India the insurance density (ratio of premiums to total population) and insurance penetration (ratio of premiums to GDP) numbers for non-life insurance are among the lowest in Asia. This implies there is a significant room for growth potential (Table 1). As India's GDP is expected to grow by 8.0-8.5 per cent for 2011 and 8.3-8.8 per cent for 2012, the role of insurance services as provider of risk transfer and indemnification and a promoter of growth will increase in the future (S & P, 2011). Studies have found that with the growth in national income both insurance density and penetration increase, more-so for the life than for nonlife since life insurance is more income elastic (Beck et al. 2010). With changing population demographics such as, increasing income and fast urbanization the demand for vehicles, increased awareness for health care, and customized sophisticated risk products would increase the demand for non-life insurance significantly in the near future. The deregulation and liberalization of insurance industry in 2000 and de-tariffing of the general insurance sector in 2007 is assumed to have improved the operating efficiency of the existing domestic companies through increased competition and by bringing in new techniques, skills, training procedures, and product innovations The number of non-life insures increased from 11 (2000) to 26 (2011), 4 being public and 22 private. Considering the fast growth of the Indian non-life insurance sector in recent years there is a lack of systematic research studies analyzing the efficiency and productivity of the non-life insurers. Table 1 reports a snap-shot for insurance density and penetration for life and non-life insurance in India, Japan, and selected South-Asian Nations: Insurance density is measured as a ratio of premiums to total population and expressed in US$. The insurance penetration is measured as a ratio of premiums to GDP.

The objective of the current study is to measure the productive efficiency and dynamic productivity of the nonlife insurers using data envelopment and stochastic frontier models and explore the causes of inefficiency. By comparing the efficiency scores across firms and over time this study will provide beneficial impact of deregulation in a highly competitive market. The study will also provide an understanding of the dynamic behavior of the insurance firms by analyzing the changes in total factor productivity and its various components using seven years panel data. Several studies in the insurance literature suggest that both parametric and non-parametric approaches should be employed for efficiency measurement because each uses different set of underlying assumptions on the construction of the frontier (Weill, 2004; Cummins and Zi, 1998; Hussels et al. 2006). In conformity with the suggestions the efficiency measure in this study follows both parametric (DEA) and non-parametric methods (fixed effect stochastic frontier model and Battese and Coellie, 1995 inefficiency effects model).

The empirical analysis uses seven years panel data (2004-10) from twelve leading non-life insurers which accounts for ninety-five per cent of the business in the industry. The productive efficiencies are measured using (i) data envelopment analysis (DEA); (ii) Fixed Effect Stochastic Frontier model (SFM); and (iii) Battese and Coellie (1995) Stochastic Frontier inefficiency-effect model (BC-95). Further, dynamic productivity index (Malmquist index), also known as total factor productivity and its various components are also measured. The study found that efficiency scores from the DEA model are higher than the econometric models. There are slight differences in efficiency score rankings for individual firms obtained from two econometric models, whoever they are consistent and is mainly due to the differences in the structure of the models. Among others, regression analysis found that net claims, operating expenditure, and total investment are positively related to net premium earned. The results from dynamic productivity analysis found eight out of twelve firms achieved gain in total factor productivity growth, ICICI Lombard leading the group with a 6.9 per cent annual growth during the study period (2004-2010).

The remainder of this paper is organized as follows. In section two a brief overview of the literature on efficiency measure in insurance industry is provided. Section three discusses the choice of input and output variables followed by section four on the methodology. Section five discusses the dataset and empirical results are discussed in section six. The summary and conclusions are in section seven.

II. BRIEF OVERVIEW OF THE LITERATURE

Efficiency measurement using frontier methodology is a fast growing research field in the insurance literature. Eling and Luhnen (2009) surveyed of 95 studies on efficiency measurement in the insurance industry and found that the recent studies used refined methodologies, addressed new topics, and extended the geographic coverage from Europe and U.S to Southeast and East Asia. The most common technique for efficiency measurement in the insurance literature is to assume the insurance firms as production units that produce 'value added' outputs using a set of inputs. In that respect the efficiency of an insurer is its ability to produce a given set of outputs (i.e., premium and/or investment income) using a set of inputs (i.e., commission and sales expenses, capital, and labor). (Diacon, 2001; Cummins and Weiss, 2001; and Cummins and Zi, 1999)

Contrary to this line of research, Brockett et al. (2004, 2005) argue that a production approach that uses premiums, investment income, supplied capital, and labor costs as inputs and probably uses losses paid as an output ignores the fact that loss maximization is not the primary objective of a firm. The authors argue, for example, when these losses increase abnormally due to hurricane, earth quake, tsunami, or from a terrorist attack a firm making this loss payments without corresponding increase in inputs, would become insolvent, not efficient. For property liability insurance companies the authors contend that efficiency measure should use 'intermediary approach' rather that 'production approach' (Berger and Humphrey, 1997; Staking and Babble, 1995; Lai and Witt, 1992). In a financial intermediary approach an insurance company provides a basket of services to the stake holders, and each has its own concern for the overall success of the company. For example, solvency can be a main concern for the regulators for the insurance companies, claims paying ability can be a primary concern for the policy holders, and return on investment can be a primary concern for the investors. Hence solvency, financial returns, and claims paying ability can be considered as outputs for nonlife insurance firms for efficiency analysis. Jeng et al. (2007) used both 'value added' approach and 'financial intermediary' approach and measured efficiency for life insurers before and after demutualization using data from Taiwan. The study found no efficiency improvement after demutualization relative to stock control insurers. However, use of financial intermediary approach improved efficiency related to mutual control insurers.

Efficiency measurement using frontier methodology is fast expanding in the insurance literature. In frontier efficiency the performance of a firm is relative to the 'best practice' frontier which is determined by the most efficient firms in the industry. The efficiency score being equal to 1 is the most efficient and 0 being the least efficient firm. Two alternative approaches are available to identify the 'best practice' frontier - the econometric approach (stochastic frontier approach, SFA) and the mathematical programming approach (data envelopment approach, DEA). Both approaches have their advantages and disadvantages. Studies that considered both approaches found higher correlated results when firms were ranked according to their efficiency scores (Berger and Humphrey, 1997; Cummins and Zi, 1998; Hussels and Ward, 2006; Cummins and Weiss, 2000). However, for the European banking sector, Weill (2004) found significant differences in efficiency measurement between parametric (SFA) and non-parametric methods (DEA). In a comprehensive analysis of 95 studies conducted in the last decade Eling and Luhnen (2009) found 55 studies used DEA and 22 used SFA and 10 both.

As a methodological improvement over the conventional DEA model Kao and Hwang (2008) (termed as two-stage DEA) assumed the production process from non-life insurance industry can be divided into two sub-processes--premium acquisition and profit generation. The efficiency from the first stage measures the performance in marketing the services of the insurance and the efficiency in the second stage measures the performance in generating profit from premiums. The product of efficiencies from two sub-processes is the efficiency of the whole process. Compared to the volume of studies directed toward the measurement of efficiency of the insurance industry around the world, studies on Indian insurance industry are very limited. Except for a few studies analyzing efficiency of the life insurance firms (Tone and Sahoo, 2005; Sinha, 2007; Sinha and Chatterjee, 2009; and Chakraborty et al. 2010) there is only one study (known to the authors), Singh (2005) that measured technical efficiency for four public sector nonlife insurers. Considering the lack of studies analyzing the performance of nonlife insurers in India after its deregulation in 2000, the current study will provide a valuable input to the regulators, the insurers, and the customers in the nonlife insurance market.

III. DEFINING INPUT AND OUTPUT VARIABLES

Unlike a manufacturing firm using physical inputs to produce physical outputs it is difficult to measure the inputs and outputs of a financial intermediary i.e., an insurance firm. The choice of inputs and outputs are vital to the measure of efficiency however, the literature is fairly long and controversial on the appropriate choice of input and output variables (Cummins and Rubio-Misas, 2002; Hussels and Ward, 2006; Leverty, Lin, and Zhou, 2004). Brockett et al. (2005) suggested when considering a particular variable as input or output researchers should evaluate, remaining all other things constant, whether an increase in the quantity is 'desirable or undesirable' for the validity of the study. For insurance studies, one of the problems in finding appropriate proxies for the insurance output is the lack of simultaneity between the use of inputs and the production of outputs. For example, the property and casualty insurance inputs are used in advance, 'premium payments' but the production and delivery of output 'claims paid' are contingent at some uncertain future (Brockett et al. 2004). Further, financial intermediation services provided by the insurers enable them to make institutional investments in corporations, which generates income and can also be used as outputs.

There are also disagreements in the literature it premiums used as a proxy for output, should it be calculated as cash flow (written) or accrued (earned) basis because, for long-tailed nonlife businesses there are considerable delay between collection of premium and payment of claims (Browne, 2000). Cooper et al. (2000) suggest efficiency scores should reflect a firm's choice of smaller inputs and larger outputs, but in reality for insurers providing financial services it is hard to measure the appropriate proxies for those intangible outputs.

Unlike the measures of output, input measures in nonlife industry are in general agreement because they are more tangible and observable. Most of the studies use labor (administrative, managerial, sales) and capital but instead of units of labor operating and selling costs are also used as proxies. Eling and Luhnen (2009) found most of the studies in their survey used at least labor and capital as inputs in addition to some form of business services. The current study uses net premiums earned and income from investment as outputs and net claims incurred, operating expenditure, equity capital, total investment, fixed assets, claims-ratio, and market share as inputs.

IV. THE METHODOLOGY: THE MEASUREMENT OF EFFICIENCY AND TOTAL FACTOR PRODUCTIVITY

This study uses three different models for estimating firm level efficiency and uses Malmquist productivity index for measuring total factor productivity. The first model uses non-parametric output oriented DEA method, the second model uses fixed effect stochastic frontier approach (SFA), and the third model uses Battese and Coellie (1995) technical inefficiency effects stochastic frontier model (BC-95).

Output Oriented DEA Approach

In DEA the performance of each decision-making unit (DMU) is compared to the best reference technology constructed from the observed inputs and outputs for all DMUs and for all years. Following Fare et al. (1994) output distance functions are used in this study to measure efficiency and productivity.

Let [x.sup.t], ..., [x.sup.t.sub.n]) [member of] [[Real part].sup.N.sub.+] be a vector of n inputs producing [y.sup.t] = ([y.sub.t.sub.1] ,..., [y.sup.t.sub.m] [member of] [[Real part].sup.M.sub.+] a vector of m outputs in period t. If we define the production possibility set for [x.sup.t] as P([x.sup.t]) then it gives all possible combinations of [y.sub.t] that can be produced from input vector [x.sub.t]. Hence, the output distance function is defined as:

[D.sup.t.sub.o] ([x.sub.t], [y.sup.t]) = min [[theta].sup.t] subject to [y.sup.t] / [[theta].sup.t] [member of] P([x.sup.t)] (1)

Ignoring the time superscripts, if we denote column vector x and y as input and output vectors and K be the number of firms in the sample, then ([x.sup.k], [y.sup.k] represents the input-output vector or the activity of the k th firm. We denote X as (N, K) matrix of observed inputs and Y as (M, K) matrix of observed outputs for K different firms. Assuming inputs and outputs are non-negative, the piecewise linear output reference satisfying the properties of constant returns to scale and strong disposability of inputs and outputs (C, S), can be formed from X and Y as:

L([x.sup.k] | C, S) = {[y.sup.k]: [y.sup.k] [less than or equal to] Y [z.sub.k], X [z.sub.k] [less than or equal to] [x.sup.k], [z.sub.k] [member of] [[Real part].sup.K.sub.+]}, [x.sub.k] [member of] [[Real part].sup.N.sub.+], (2)

Where [z.sub.k] is the intensity vector identifying to what extent a particular activity ([x.sup.k], [y.sup.k]) is utilized. The assumption of strong disposability of inputs and outputs as a feature of technology implies that the same input vector can produce lesser outputs and a higher input vector can produce the same outputs. Given the technology in the above specification, the Farrell's (1957) output oriented measure of technical efficiency for activity k is obtained by maximizing the reciprocal of the distance function [D.sup.t.sub.o] ([y.sup.k], [x.sup.k]) in equation (1).

Max [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Subject to [[delta]y.sub.km] [less than or equal to] [K.summation over (k=1)] [z.sub.k] [y.sub.km], m = 1,2, ..., M;

[K.summation over (k=1)] [z.sub.k] [x.sub.kn] [less than or equal to] [x.sub.kn], n = 1,2,..., N; [z.sub.k] [greater than or equal to] 0, k = 1, 2, ..., K.

Hence, [D.sup.t.sub.o] ([y.sup.k], [x.sup.k]) =1 implies producer k is the most efficient and lies on the production frontier and any value less than 1.0 implies the firm is operating below the production frontier. Technical efficiency can be decomposed into a measure of scale efficiency and a measure of pure technical efficiency. If a farm is not operating in the range of constant returns to scale (CRS), then it could conceptually increase output without increasing inputs if CRS is realized. The measure of technical efficiency using variable returns to scale (VRS) is called pure technical efficiency. Scale efficiency is measured as the ratio between CRS and VRS technical efficiencies. The efficiency scores are obtained using linear programming technique.

Malmquist Productivity Index (MALM) and Total Factor Productivity

Over time an increase in efficiency may cause an upward shift in the production frontier leading to growth in productivity. Improvement in total factor productivity could be due to either improvement in technical efficiency or improvement in technology. This study calculates Malmquist Productivity Index as a measure of changes in total factor productivity. The Malmquist Productivity Index is defined as output produced per unit of input. In order to calculate Malmquist productivity index Fare et al. (1994) used an output distance function, which is a reciprocal of Farrelrs (1957) measure of output based technical efficiency. The Malmquist Productivity Index for ith farm in t+1 period can be further decomposed as the product of an efficiency change index and technological progress. A productivity index is constructed by examining the outputs in period t and t+1 relative to technology available in period t and t+1 using geometric mean. The expression for MALM:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Superscript t and t + 1 represent the current and the next period, respectively. The function [E.sup.t+1] (.) represents the productivity change arising from changes in technical efficiency, which is measured by the ratio of two distance functions at two different points in time. The function [T.sup.t+1] (.) represent changes in productivity due to a technological progress. This is composed of distance functions, which mix technology from one time period with observations from another time period, which are then averaged geometrically. For example, the mixed period distance function [D.sub.o.sup.t+1] ([x.sup.t], [y.sup.t]), computes the largest possible contraction of inputs observed in time period t so that the level of output in that period can be produced using technology from time period t + 1. The technology index captures the shift in technology between period t and t+1 evaluated at two different data points ([x.sup.t], [y.sup.t] and [x.sup.t+1], [y.sup.t+1]). An increase in the Malmquist Productivity Index implies technical progress towards the final year if it is the last year in the reference technology. Two linear programs associated with the estimation of [T.sup.t+1] (.) are similar to the one in equation (3) are produced in the appendix.

Stochastic Frontier Production Function Approach (SFM)

The basic idea behind the stochastic frontier model is that the error term is composed of two parts: (1) the systematic component (i.e., a traditional random error) that captures the effect of measurement error, other statistical noise, and random shocks; and (2) the one-sided component that captures the effects of inefficiency. Several extensions of the stochastic frontier models have been proposed over the years (Battese and Coelli, 1992; 1995; Kumbhakar and Lovell, 2000; Greene, 2001, 2002a, 2002b). In the stochastic frontier model, a nonnegative error term representing technical inefficiency is subtracted from the traditional random error in the classical linear model.

Following Green (2009) the general formulation for a fixed effect stochastic model is:

[y.sub.it] = [[alpha].sub.i] + [beta]'[x.sub.it] + [v.sub.it] - [u.sub.it] (6)

where [y.sub.it] denotes the output of the ith firm in the t th time period, [x.sub.it] represents a (1xk) vector of inputs and other explanatory variables for the i th firm at t th time, [beta] is a (kx1) vector of unknown parameters to be estimated, [v.sub.it] ~ N(0, [[sigma].sup.2.sub.v]) and [u.sub.it] ~ | N(0, [[sigma].sup.2.sub.u])|, [u.sub.it] [greater than or equal to] 0, and the [u.sub.it] and [v.sub.it] are assumed to be independent. The term [v.sub.it] allows for randonmess across firms and captures the effect of measurement error, other statistical noise, and random shocks outside the firm's control. The component [u.sub.it] captures the effect of inefficiency (Forsund et al. 1980). The equation is estimated using maximum likelihood method.

This study uses firm-wise heteroscedesticity corrected and fixed effects in the variance of [u.sub.it] hence, the model estimated is written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

Battese and Coellie (1995) Technical Inefficiency Effects Model (BC-1995)

Following Battese and Coellie (1995) consider a generalize frontier production function for insurance is written as:

[y.sub.it] = exp([x.sub.it] [beta] + [v.sub.it] - [u.sub.it]) (8)

where [y.sub.it] and [x.sub.it] have same definition as the SFM model above, [v.sub.it] are assumed to be iid ~ N(0,[[sigma].sub.v.sup.2]) random variables and [u.sub.it] s are non-negative unobserved random variables associated with the technical inefficiency of production which is distributed independently (not identically) normally and truncated at zero such that,

[u.sub.it] ~ [N.sup.+]([m.sub.it], [[sigma].sup.2.sub.u]) where mit = [z.sup.it] [delta] + [c.sub.it] (9)

where [z.sub.it] is a (1xM) vector of explanatory variables associated with technical inefficiency effects; [delta] is a (Mx1) vector of unknown parameters and [c.sub.it] is non negative unobserved random variable obtained by truncation of the [c.sub.it] ~ [N.sub.+] (0, [[sigma].sup.2.sub.c]) such that [c.sub.it] [greater than or equal to] - [z.sub.it] [delta]. This is an alternative specification of [u.sub.it] being a non-negative truncation of the N([z.sub.it] [delta] [[sigma].sup.2]). Thus the means may be different for different firms and time periods, but the variances are assumed to be the same. For details please see Battese and Broca (1997) and Battese and Coellie (1995). The model is estimated using . maximum likelihood method.

V. THE DATASET

The data for this study are collected from the Annual Report of the Insurance Regulatory and Development Authority (IRDA) Government of India, for various years. Currently 26 nonlife insurers are operating in India not all of them started operation at the beginning of the study period i.e., 2004. Due to non-availability of a consistent balanced pane for entire study period (2004-2010) our panel data consist of 12 leading non-life insurers observed for seven years (8 private and 4 public) operating in India. Like most of the studies in financial services the data availability for this study is restricted to publicly available information submitted by the insurers in compliance with the regulatory authority. Since the data on direct measure for labor input is not available this study uses operating expenditure (expenditure on sales, administration, and managerial staff) as a proxy for labor input. Assuming insurance firms act as financial intermediaries, net income from investment from the policyholders and shareholders account is used as one of the two outputs in the DEA model for efficiency measure and for dynamic productivity analysis. Following Yang (2006), Diacon (2001), and Hussels and Ward (2006) the other output used for the DEA efficiency measure and productivity analysis is the net premium earned. (1)

Selection of outputs and inputs in this study is based on the past studies in the literature and examination of the raw data. A positive and strong relationship is observed between non-life investment and net premium earned (Fig. 4). No systematic relationship is observed between non-life premium earned and solvency ratio for all firms for 2010 (Fig. 3) hence, solvency ratio is not included as an input in this study. Raw data for 2010 also revealed that the two major components of non-life investment are approved investments (36 per cent) and government securities (25 per cent) (Fig. 1). As expected, the major source for non-life premium is motor (49 per cent) (Fig. 2). In summary, the DEA measure of productive efficiency and dynamic measure of productivity growth (TFP) use two outputs i.e., net premiums earned and income from investment and four inputs i.e., net claims, operating expenditure, equity capital, and fixed assets. Efficiency estimates from the SFM and BC-95 models use net premium earned as output; and net claims, operating expenditure, investment, fixed assets, claims ratio and market share as inputs.

It is hypothesized that claims ratio (proportion of claims to gross premium) and market share (proportion of the industry gross premium written by the firm) will be positively related to the efficiency measure and will capture the firm's unique characteristics. In consistency with the insurance literature all input and output variables are deflated to real terms using consumer price index (CPI) data for various years collected from the Ministry of Labor, Government of India website. Descriptive statistics of the variables used in this study are reported in Table 2.

VI. ANALYSIS OF THE RESULTS

Output oriented DEA efficiency scores under variable returns to scale for each year are obtained using Limdep (2009) and are reported in Table 3. The last column reports average for all years for each firm. It is evident that 3 out of 4 public insurers including two private insurers, BAJAJ ALLIANZE and TATA AIG is fully efficient (last column, Table 3). The lowest efficient firm is HDFC-ERGO which is 11.8 per cent inefficient. This implies the firm could produce same amount of outputs with 11.8 per cent less inputs and still be efficient. For inefficient firms the causes for inefficiency could be operating at an inappropriate size (scale inefficient) and/or misallocation of resources. Operating at an inappropriate size implies the firm is not taking advantage of the returns to scale, such as producing low output during the increasing returns to scale phase, or producing too much output during the decreasing returns to scale phase. Misallocation of resources refers to the use of inefficient input combinations. Review of annual average efficiency scored across firms shows insurers achieved highest efficiency score in 2007 (0.981) and then average score started decreasing for next 3 years but remained stable at 0.965in 2010 (Table 3, last row).

Table 4 reports parameter estimates from SFM model (equation 7) and BC-95 model (equation 8). A detail discussion on the parameter estimates is not the primary objective of this study hence, a brief discussion is provided. For efficiency estimate using stochastic frontier models coefficients do not have meaningful interpretations, except for the direction of change. For both models a log-linear functional form of Cobb-Douglas type are estimated. For BC-95 model coefficients on operating expenditure, investment, and fixed asset are insignificant but positive. Implying increased level for these variables will increase net premium. Negative and significant time variable ([z.sub.i] variables) implies that on average, efficiency decreases (inefficiency increases) over time. Negative and significant coefficient on claims ratio and positive and significant coefficient on market share imply that inefficiency increases(efficiency decreases) with the decrease (increase) in claims ratio and increases with the increase in market share. All diagnostic statistics for this model are significant implying our selection of stochastic frontier model is appropriate for this data.

The parameters estimates from the fixed effect heteroscedastic SFM model are also reported in column 4 and 5 of Table 4. Except for the investment and fixed assets, all other variables have expected signs and are significantly different from zero at 5 per cent of above level. It is noticeable that coefficients on claims ratio and market share variables although, significant have reverse signs when compared to BC-95 model. This is because these two variables are structured differently in two models. For example, in BC-95 model claims ratio and market share affect inefficiency component through the mean of the distribution of [u.sub.it] whereas, in SFM this two variables are used to correct the variance of distribution of [u.sub.it] for firm-wise heteroscedasticity. The signs of claims ratio and market share variables are contrary to our expectations. However, an intuitive explanation for negative market share could be that as insurers enter into price war offering price discounts to increase market share and do poor underwriting, that reduces net premium earned (S & P, Mar 2011) (2).

Table 5 reports efficiency scores from the SFM for all firms for all years. Average efficiency scores across years for all firms (last column) suggest that NEW INDIA and TATA AIG are the top two efficient firms with average efficiency scores being 0.990 and 0.979, respectively, the least efficient firm is RELIANCE (0.858). Review of yearly average efficiency scores across firms (last row) suggests that efficiency in non-life insurance industry increased over time from 0.876 (2004) to 0.956 (2010) for the SFM model.

Table 6 reports efficiency scores from the BC-95 model. Compared to overall efficiency for all firms across time this model estimates lower industry average score (0.889) than SFM model (0.921). The top two efficient firms are TATA AIG (1.000) and BAJAJ ALLIANZ (0.995) and the least efficient firm is CHOLAMANDALAM (0.781). It is interesting to note that TATA AIG is the most efficient firm (ranked 1) in BC-95 model and second most efficient firm (ranked 2) for SFM. Similarly, BAJAB ALLIANZ ranked second in BC-95 model and third in SFM. The results suggest that efficiency rankings for firms in two econometric models are not significantly different. A closer look at the last row in Table 6 reveals that on average, efficiency score were low at the beginning of the study period 2004 (0.871) reached the highest score in 2007 (0.938), and then decreased in 2010 (0.876).

Finally, Table 7 reports total factor productivity change index (Malmquist Index) and its various components. Malmquist productivity indices are decomposed into efficiency change (EFFCH), technological change (TECHCH), pure technical efficiency change (PECH), scale change (SECH), and total factor productivity change (TFPCH). The numbers reported are averages for the entire study period. The value of any of these indices if greater than one indicates improvement and less than one denotes deterioration in performance. Subtracting one from the values reported in any of the columns in Table 7 yields the average annual rate of change. The results indicate that the total factor productivity change index (TFPCH) across firms over the years increased at an average rate of 0.07 per cent (1.007-1.000* 100) per year. The improvement in productivity came from improvement in efficiency (EFFCH) 0.01 per cent and technological change (technical progress) 0.06 per cent. Technical progress is interpreted as the non-life industry uses less input on average to produce a given level of output in 2010 compared to 2004.

Further, for the industry the efficiency change index 0.01 per cent (EFFCH) is attributable to an increase in pure efficiency change (PECH) of 0.03 per cent and a decrease in scale efficiency index (SECH) by 0.02 per cent (0.01 = 0.03--0.02). Among the 12 non-life insurers total factor productivity decreased for 4 firms (index < 1) (TFPCH). Two fastest growing firms in terms of productivity growth are ICICI-LOMBARD and IFFCO-TOKIO. The former grew by 6.9 per cent and the later by 4.6 per cent annually. The review of EFFCH and TECHCH columns reveals that for both firms the major cause of productivity improvement is efficiency change, 4.1 per cent for ICICI-LOMBARD and 3.4 per cent for IFFCO-TOKIO. The empirical evidence form Table 7 suggests that insurance industry deregulation has an overall small but positive impact on the total factor productivity growth for nonlife insurers. Cummins el at. (1996) using Italian insurance data and Grifell-Tatje and Lovell (1996) using Spanish savings bank data found overall total factor productivity decreased due to deregulation in the industry. In a study of Japanese insurance firms Yoshihiro et al. (2004) found on average deregulation improved the efficiency of the firms however the productivity of the stock firms were higher than the mutual firms. The improvement in overall productivity for firms in the current study are driven mainly by the leading firms producing more output from the given resources than pushing out the frontier in each year under study.

VII. SUMMARY AND CONCLUSIONS

This study has analyzed efficiency measurement and dynamic change in efficiency for Indian non-life insurers and uses value measure of insurance inputs and outputs. Three main issues are explored--first, technical efficiency measures are produced using DEA model, stochastic frontier model (SFM), and Battese and Coellie model (BC-95). Second, the use of econometric models (SFM, BC-95) enabled us to explore the relationship between various inputs and output in the measurement of efficiency. Lastly, we measured the total factor productivity growth (Malmquist Index) and its various components.

We found the overall efficiency measures averaged over all firms for all years from DEA model (0.965) exceeds the scores from SFM model (0.921) and BC-95 model (0.889). This is consistent with the literature considering the underlying assumptions for efficiency measure using linear programming technique and econometric models. Past studied found that the DEA efficiency scores are biased upward (Cummins et al. 2007; Simar and Wilson, 2007). The overall efficiency scores from SFM and BC-95 models are very similar but vary across firms. The study found that Indian non-life insurance grew by 0.07 per cent per year between 2004 and 2010. Eight out of 12 firms showed annual productivity growth between 0.01 per cent (TATA AIG) and 6.9 per cent (ICICI LOMBARD).

One interesting result from this study is that the improvement in overall productivity for the non-life sector (0.07 per cent) is more driven by the technological improvement than by catch-up effects. As it is observed that industry level productivity gains are mostly driven by two firms, IFFCO and ICICI-LOMBARD due to improvement in efficiency change index (EFFCH) 3.4 and 4.1 per cent respectively, as opposed to underperforming firms struggling to decrease their inefficiency. Compared to other developing countries which introduced deregulation and liberalization policies in the insurance sector, the productivity growth for Indian non-life insurance industry is low. Studies in the literature found that insurance market activities, especially non-life promote economic growth in the developing countries and raise insurance density and penetration (Arena, 2008).

We believe that both technological improvement and efficiency change for the industry are needed to increase the total factor productivity levels for the firms. Possible solution might be improvement of underwriting performances which is weak over the last few years despite a strong growth in net premiums (S & P, 2011). Recently the non-life insurance industry in India has been downgraded from 'stable to negative' by the S & P (2011) based on its assessment of the 'combined ratio' for 2012 to be 121 per cent (claims over by 21 per cent than premiums received). The upside of this assessment is that there are significant scopes for improvement. One of the factors for slow productivity growth in the sector we found is that the industry's strong dependence on investment income (Fig. 1, and Fig. 4) rather than growth policies and risk management. Other areas for improvement could be efficient claims management, cost control, improved customer services and product innovations.

[FIGURE 3 OMITTED]

Appendix--1

Figure 1A, depicts the construction of an output distance function. Assume there are 3 firms represented by A, B, and N each using same input combinations [x.sup.A] = [x.sup.B] = [x.sup.N] but each produces different combinations of two outputs of [y.sub.1] and [y.sub.2]. The production possibility frontier (PPF) at time t is defined as the line bounded by GBDNH. Firm A is inefficient because it is below the PPF however, it could increase both of its outputs moving along OA up to point B, which is on the PPF. The measure of technical efficiency is q = OA/AB, which is the value of the output distance function and measured as the ratio of actual output to maximum potential output. The reciprocal of the distance function implies maximum proportional expansion of outputs given the county's level of input usage. A value equal to one implies the firm is fully efficient and operating on the frontier and a value less than one implies the county is inefficient.

[FIGURE 1a OMITTED]

Malmquist productivity index is constructed graphically using Figure 1A. Assume that at time t+1 Malmquist productivity index is constructed graphically using Figure 1A. Assume that at time t+1 the production frontier is defined by OJKFM, and the outputs produced by the same inefficient firm (firm A) are now at point E. The input-output vector for the same firm in period t evaluated relative to the technology available in time t+1 is denoted by the distance function [D.sup.t+1.sub.o] ([x.sup.t], [y.sub.t]) = OA/OC. Its input-output vector at t+1 evaluated relative to the technology available at t is denoted by the distance function, [D.sup.t.sub.o] ([x.sup.t+1], [y.sup.t+1]) = OE / OD. The value of the output distance functions at time t and t+1 are: [D.sup.t.sub.o] ([x.sup.t], [y.sub.t]) = OA/AB, and [D.sup.t+1.sub.o] ([x.sup.t+1], [y.sup.t+1]) = OE/OF, respectively. Substituting these distance functions in (4) the Malmquist productivity index reduces to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The first term in the above expression measures change in technical efficiency and the second term represent technological progress. The linear programs used to measure the output distance equations above equation (two of them) are presented below. Linear program for k th firm with (C, S) technology, with M outputs and N inputs at time t is written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (A1)

[z.sub.k] is an intensity vector that serves to form convex combination of outputs and inputs for the K firms in the sample. For each of the T time period equation (6) is solved K times to obtain the efficiency measure of each firm. Linear program for mix time period is solved running the following equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (A2)

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Notes

(1.) Yuengert (1993) argues that net premiums earned or written are a measure of insurer's revenue, as it is price times quantity, and is not a strict measure of output.

(2.) An effort was made to use solvency ratio as one of the firm characteristics for both models, but the variable did not appear significant and the signs were inconsistent with economic theory. Hence, it is not included in the final model. Diacon (2001) found that impact of solvency ratio on net premium earned is inconsistent in his multi-country efficiency analysis.

KALYAN CHAKRABORTY, School of Business, Emporia State University, 1200 Commercial Street, Box 4057, Emporia, KS, 66801, Email: kchakrab@emporia.edu

ANIRBAN DUTTA, NSHM Business School, NSHM Knowledge Campus-Durgapur. Arrah, Shibtala, Durgapur, WB. 713 212, E-mail: anirbandutta3@rediffmail.com

PARTHA PRATIM SENGUPTA, Department of Humanities and Social Science, National Institute of Technology (NITD), Mahatma Gandhi Avenue, Durgapur, WB, India, E-mail: pps42003@yahoo.com

Table 1
Insurance Density and Penetration for Life and Non-life Insurance
for India vis-a-vis Japan and Some of South Asian Nations in 2010

 Insurance Insurance
 Growth in Density (UD$) Penetration (%)

Country GDP Life Non-life Life Non-life

Japan 4.0 3472.8 917.4 8.0 2.1
Singapore 14.6 2101.4 722.1 4.6 1.6
India 8.4 55.7 8.7 4.4 0.7
Malaysia 7.3 282.8 138.3 3.2 1.6
Thailand 7.9 121.9 77.5 2.6 1.7
PR China 10.4 105.5 52.9 2.5 1.3
Sri Lanka 7.0 13.7 20.6 0.6 0.9
Philippines 7.3 14.3 8.4 0.7 0.4
Indonesia 6.1 30.9 14.9 1.0 0.5
Pakistan 4.1 3.2 2.9 0.3 0.3
Asia 7.0 208.1 73.5 4.5 1.6
World 4.0 364.3 263.0 4.0 2.9

Source: Swiss Re Sigma No. 2/2010

Table 2
Descriptive Statistics of the Variables Used in the DEA and
Stochastic Frontier Models (Values are in Lakhs of Rupees: l
Lakh = Rs.100,000) Firms = 12, Observations = 84

Variables 2003-04 2004-05 2005-06 2006-07

 Outputs (Lakhs of Rs.)

Net Premium Earned Mean 338211 260699 112976 73013
 Minimum 189889 205693 12730 9649
 Maximum 501927 335370 337339 168645

Income from Invest Mean 144787 94418 45115 8544
 Minimum 90795 63796 1334 1446
 Maximum 215099 131424 148408 20510

 Inputs (Lakhs of Rs.)

Net Claims Incurred Mean 288395 239771 93691 52408
 Minimum 152843 177346 8627 7013
 Maximum 451091 302614 292607 121866

Operating Mean 101679 84860 38565 25373
 Expenditure Minimum 69887 70310 6331 6190
 Maximum 152703 107119 101688 53398

Equity capital Mean 13529 9260 14073 13618
 Minimum 9168 8789 10555 9575
 Maximum 18768 9627 18726 22025

Total Investment Mean 1446090 933303 377567 88396
 Minimum 659095 619027 19836 13641
 Maximum 2303000 1246150 1181970 222490

Fixed Assets Mean 9898 7020 4157 4420
 Minimum 5539 5003 1082 1182
 Maximum 14251 9659 11054 13478

Claims Ratio (%) Mean 0.853 0.918 0.734 0.714
 Minimum 0.760 0.850 0.610 0.610
 Maximum 0.900 1.020 0.930 0.830

Market Share (%) Mean 20.739 15.743 6.077 5.208
 Minimum 13.540 12.970 1.560 1.950
 Maximum 29.750 20.650 14.630 8.330

Variables 2007-08 2008-09 2009-10

 Outputs (Lakhs of Rs.)

Net Premium Earned Mean 72436 43736 18693
 Minimum 7613 2294 3836
 Maximum 192727 123845 40631

Income from Invest Mean 12999 5235 2096
 Minimum 2030 1030 1091
 Maximum 49362 13096 4681

 Inputs (Lakhs of Rs.)

Net Claims Incurred Mean 56941 32551 13833
 Minimum 6744 2011 2987
 Maximum 167222 104211 34792

Operating Mean 27519 20230 9060
 Expenditure Minimum 7325 2556 3882
 Maximum 60509 51603 17046

Equity capital Mean 23968 14154 15846
 Minimum 11889 9572 11449
 Maximum 35948 26751 36474

Total Investment Mean 110920 50597 26879
 Minimum 21250 14560 14812
 Maximum 309649 121625 54815

Fixed Assets Mean 5388 2319 1367
 Minimum 1026 227 753
 Maximum 13979 5740 2507

Claims Ratio (%) Mean 0.720 0.743 0.715
 Minimum 0.540 0.540 0.560
 Maximum 0.890 0.900 0.990

Market Share (%) Mean 6.010 2.812 1.345
 Minimum 2.080 0.590 0.680
 Maximum 11.530 6.760 2.560

Values are in real numbers deflated by Consumer Price Index.
Operating expenses are the sum of expenditure on sales,
administration, and managerial staff, and commission. Claims
ratio is measured as proportion of claims to gross premiums, firm
size is measured as total assets and market share (share in the
total premium written).

Table 3
Output Oriented DEA Efficiency Scores Under Variable Returns
to Scale (Two-Outputs and Four-Inputs)

 2004 2005 2006 2007 2008

 1 New India 1.0000 1.0000 1.0000 1.0000 1.0000
 2 Oriental 1.0000 1.0000 1.0000 1.0000 1.0000
 3 National 1.0000 1.0000 1.0000 1.0000 1.0000
 4 United 1.0000 0.9982 1.0000 0.9910 1.0000
 5 Royal Sundaram 0.9550 0.9523 1.0000 1.0000 1.0000
 6 Bajaj Allianz 1.0000 1.0000 1.0000 1.0000 1.0000
 7 IFFCO Tokio 0.8213 0.9147 1.0000 1.0000 1.0000
 8 ICICI Lombard 0.7878 0.9081 0.9553 0.9294 0.9173
 9 Tata AIG 1.0000 1.0000 1.0000 1.0000 1.0000
10 Reliance 1.0000 0.8681 1.0000 0.8569 0.9172
11 Cholamandalam 1.0000 0.7543 0.7585 0.9924 0.9082
12 HDFC ERGO 0.8777 0.9822 1.0000 1.0000 0.8299
 Average 0.9535 0.9482 0.9762 0.9808 0.9644

 2009 2010 Avg

 1 New India 1.0000 1.0000 1.0000
 2 Oriental 1.0000 1.0000 1.0000
 3 National 1.0000 1.0000 1.0000
 4 United 1.0000 1.0000 0.9985
 5 Royal Sundaram 1.0000 1.0000 0.9868
 6 Bajaj Allianz 1.0000 1.0000 1.0000
 7 IFFCO Tokio 1.0000 1.0000 0.9623
 8 ICICI Lombard 0.9002 1.0000 0.9140
 9 Tata AIG 1.0000 1.0000 1.0000
10 Reliance 0.9818 0.9607 0.9407
11 Cholamandalam 0.9220 0.9450 0.8972
12 HDFC ERGO 0.7610 0.7191 0.8814
 Average 0.9638 0.9687 0.9651

Table 4
Parameter Estimates from Battese and Coellie Technical
Inefficiency Effects Model (1995) and Fixed Effect Stochastic
Frontier Model (SFM) (Dependent Variable = Ln(Net Premium
Earned)

 Battese and Coellie Model
 BC-1995

Variables Coefficient t-statistics

Constant 0.592 * 26.68
Ln(Net claims) 0.954 * 81.16
Ln(Operating expenditure) 0.019 1.00
Ln(Investment) 0.001 0.23
Ln(Fixed asset) 0.006 1.46
Constant -0.885 * -54.92
Claims Ratio -0.010 * -6.34
Market Share 1.375 * 46.27
Time -0.006 * -21.00
Sigma (2) 0.001 * 23.81
Gamma 0.001 * 8.21
LLF 196.42
LR for one sided error 268.9 *
Observations 84

 Stochastic Frontier Model
 SFM

Variables Coefficient t-statistics

Constant 1.173 * 8.01
Ln(Net claims) 0.718 * 19.05
Ln(Operating expenditure) 0.184 * 4.23
Ln(Investment) 0.006 0.34
Ln(Fixed asset) 0.036 1.53
Constant -6.44 * -10.46
Claims Ratio 18.78 * 1.91
Market Share -0.309 * -2.08
Time
Sigma (2) NA
Gamma NA
LLF 109.18
LR for one sided error NA
Observations 84

 * indicates coefficients are significant at 5 per cent or above
[Chi.sup.2] critical value for k=5, n = 84 is 11.5

Table 5
Technical Efficiency Scores from Fixed Effect Stochastic Frontier
Model (SFM) for All Firms

 Firm 2004 2005 2006 2007 2008

 1 New India (1) 0.9968 0.9955 0.9836 0.9920 0.9887
 2 Oriental (6) 0.9625 0.9042 0.9167 0.9546 0.9359
 3 National (5) 0.9492 0.9669 0.8433 0.9604 0.9200
 4 United (8) 0.9299 0.8610 0.8348 0.8769 0.8926
 5 Royal Sundaram (4) 0.8594 0.9209 0.9522 0.9794 0.9691
 6 Bajaj Allianz (3) 0.9217 0.9778 0.9621 0.9773 0.9869
 7 IFFCO Tokio (7) 0.7936 0.8639 0.9188 0.9520 0.9456
 8 ICICI Lombard (9) 0.7910 0.7987 0.8628 0.9246 0.9588
 9 Tata AIG (2) 0.9442 0.9824 0.9795 0.9875 0.9909
10 Reliance (12) 0.7909 0.7914 0.8652 0.8013 0.8655
11 Cholamandalam (10) 0.7910 0.7919 0.7920 0.9603 0.9499
12 HDFC ERGO (11) 0.7916 0.9080 0.9741 0.9698 0.7966
 Average 0.8768 0.8969 0.9071 0.9447 0.9334

 Firm 2009 2010 Avg

 1 New India (1) 0.9848 0.9887 0.990
 2 Oriental (6) 0.8744 0.9596 0.930
 3 National (5) 0.9127 0.9809 0.933
 4 United (8) 0.9853 0.9818 0.909
 5 Royal Sundaram (4) 0.9760 0.9825 0.948
 6 Bajaj Allianz (3) 0.9857 0.9868 0.971
 7 IFFCO Tokio (7) 0.9476 0.9752 0.914
 8 ICICI Lombard (9) 0.9240 0.9582 0.888
 9 Tata AIG (2) 0.9872 0.9819 0.979
10 Reliance (12) 0.9526 0.9368 0.858
11 Cholamandalam (10) 0.9220 0.9464 0.879
12 HDFC ERGO (11) 0.7951 0.7916 0.861
 Average 0.9373 0.9559 0.9217

Numbers in parenthesis are rank orders.

Table 6
Technical Efficiency Scores from Battese and Coellie Model (BC-9.5)
for All Firms

 2004 2005 2006 2007 2008

 1 New India (5) 1.0000 0.9999 0.8692 0.9586 0.8712
 2 Oriental (10) 0.9024 0.7905 0.8212 0.8223 0.7984
 3 National (11) 0.8229 0.8663 0.6760 0.8300 0.7576
 4 United (9) 0.8358 0.7654 0.7570 0.7906 0.7637
 5 Royal Sundaram (3) 0.9691 0.9999 1.0000 1.0000 1.0000
 6 Bajaj Allianz (2) 1.0000 1.0000 0.9863 1.0000 1.0000
 7 IFFCO Tokio (4) 0.9068 0.9850 0.9627 0.9470 0.8779
 8 ICICI Lombard (7) 0.7319 0.9435 0.9415 0.9474 0.9304
 9 Tata AIG (1) 1.0000 1.0000 1.0000 1.0000 1.0000
10 Reliance (8) 0.7136 0.8263 1.0000 0.9683 0.9050
11 Cholamandalam (12) 0.7318 0.8613 0.8583 1.0000 0.1000
12 HDFC ERGO (6) 0.8402 0.9997 1.0000 1.0000 0.8980
 Average 0.8712 0.9198 0.9060 0.9387 0.8252

 2009 2010 Avg

 1 New India (5) 0.8516 0.8445 0.914
 2 Oriental (10) 0.7003 0.8029 0.805
 3 National (11) 0.7129 0.8690 0.791
 4 United (9) 0.9382 0.8537 0.815
 5 Royal Sundaram (3) 1.0000 0.9910 0.994
 6 Bajaj Allianz (2) 0.9996 0.9757 0.995
 7 IFFCO Tokio (4) 0.8411 0.8957 0.917
 8 ICICI Lombard (7) 0.8499 0.8269 0.882
 9 Tata AIG (1) 1.0000 1.0000 1.000
10 Reliance (8) 0.9227 0.8319 0.881
11 Cholamandalam (12) 0.9660 0.9489 0.781
12 HDFC ERGO (6) 0.8480 0.6743 0.894
 Average 0.8859 0.8762 0.8890

Numbers in parenthesis are rank orders.

Table 7
Total Factor Productivity Index (Malmquist Index for 12 Firms
(2004-2010)

 Firm EFFCH TECHCH PECH SECH TFPCH

1 New India 1.000 0.997 1.000 1.000 0.997
2 Oriental 0.998 1.019 1.000 0.998 1.017
3 National 1.000 1.020 1.000 1.000 1.020
4 United 1.000 1.006 1.000 1.000 1.006
5 Royal Sundaram 1.011 1.010 1.000 1.011 1.021
6 Bajaj Allianz 1.000 1.028 1.000 1.000 1.028
7 IFFCO Tokio 1.034 1.012 1.000 1.034 1.046
8 ICICI Lombard 1.041 1.027 1.030 1.010 1.069
9 Tata AIG 1.000 1.003 1.000 1.000 1.003
10 Reliance 0.977 0.997 1.000 0.977 0.973
11 Cholamandalam 0.987 0.971 1.000 0.987 0.958
12 HDFC ERGO 0.967 0.989 1.004 0.963 0.956
 Average 1.001 1.006 1.003 0.998 1.007

This table reports Malmquist productivity indices and the
decomposition of these indices into efficiency change (EFFCH),
technological change (TECHCH), pure technical efficiency change
(PECH), scale change (SECH), and total factor productivity change
(TFPCH) over the sample period. TFPCH = FFFCH + TECHCH; EFFCH =
PECH + SECH

Figure 1: Share of Various Sectors in Non-life Total Asset, 2009-10

Housing & Loans to State Govt. for Housing & FFE 7%
State Govt. & Other Approved Securities 10%
Central Govt. Securities 25%
Other Investments 5%
Approved Investments 36%
Infrastructure Investments 17%

Note: Table made from pie chart.

Figure 2: Share of Various Sectors in Non-Life Net Premium, 2009-10

Health 22%
Others 15%
Fire 10%
Marine 4%
Motor 49%

Note: Table made from pie chart.

Figure 4: Net Premium Earned and Investments in Non-Life Insurance
Sector 2004-2010

 Net Premiums Earned Investment

2004-05 12,118 40,224
2005-06 13,710 57,122
2006-07 16,047 58,711
2007-08 19,289 70,805
2008-09 22,775 55,463
2009-10 25,521 79,122

Note: Table made from line graph.