Profit Efficiency of Indian General Insurance Companies: A Ratio-Based Approach

Abstract

While there are several studies regarding the technical efficiency of Indian general insurance companies, the field of profit efficiency remained relatively unexplored. The present study seeks to fill this gap. In the present article, two alternative ratio-based approaches have been adopted for the estimation of profit efficiency of Indian general insurers. The profit efficiency scores so derived are then decomposed in to revenue and cost efficiency components. In the final stage, the impact of several contextual variables on the efficiency scores are analysed. The data set for the present study includes information pertaining to 15 general insurance companies for the period 2011–12 to 2016–17. The outcome shows that the public sector insurers have done well in terms of revenue efficiency but needs to be concerned about cost efficiency. Further, the application of pooled ordinary least squares regression show that solvency ratio is an important explanatory variable of profit efficiency. Significance of the impact of return on equity on profit efficiency is, however, contingent on the model chosen.

JEL Classification: C-61, D-22, G-23

Keywords

General insurance profit efficiency return on equity solvency ratio

1. Introduction

General insurance (alternatively called non-life insurance) encompasses property, liability, health and personal insurance. In a globalised economy with rising complexities and health care costs, the importance of a well-developed general insurance sector cannot be undermined. In fact, the presence of a strong and well-developed non-life insurance sector is one of the key infrastructural prerequisites of rapid economic growth of the country.

The general insurance industry in India has a rich heritage. Modern form of general insurance business was established in 1850. India had more than hundred general insurance companies when the industry was nationalised in 1973, which led to the formation of 4 state-sponsored general insurance companies through the amalgamation of 107 private general insurance companies. Until the deregulation of the general insurance sector in 1999, which allowed private sector entry in the insurance business, Indian general insurance business was controlled by four public sector insurer (and one reinsurer). In the 1990s, India embraced an open market economy with greater role for the private sector. Financial sector reform was an integral part of the reform process that was initiated with banking sector reform involving deregulation of private sector entry and introduction of prudential regulations of banking operations. At the same time, the Government of India set up (in 1993) a High-Powered Committee on the Indian Insurance Sector (headed by Shri R. N. Malhotra) for examining the then existing scenario and recommend appropriate measures for boosting competitive efficiency and strengthening regulatory framework. The structural and regulatory changes undertaken in respect of the Indian insurance sector since 1999 were a fall out of the Committee recommendations.

In the post-liberalisation phase, the sector underwent important regulatory and structural changes during the last two decades leading to a rapid growth of the industry. Thus, during the period 2011–12 to 2016–17, gross direct premium increased by 2.4 times (from ₹545,780 million to ₹1,309,710 million). Total number of new policies issued annually from 8,570 million policies to 15,250 million. Total asset under management increased from ₹992,680 million to ₹2,223,440 million. Total number of offices expanded from 7,050 to 11,141.

The changing role of the general insurance sector in the Indian economy has attracted the attention of researchers and during the last few years, several research studies attempted to estimate the efficiency and productivity performance of the industry by adopting non-parametric methods. However, there is no study of profit efficiency performance of the general insurance companies in India as yet. The present study seeks to fill this gap as it tries to measure the profit efficiency performance of 15 major general insurance companies in India for the period 2011–12 to 2016–17. The present study has taken a two-stage approach. Thus, in the first stage, we have used value based approaches for estimating profit efficiency. In the second stage, the impact of several contextual variables (including solvency, return on equity and return of asset) on the efficiency scores is assessed using censored regression.

The remainder of the article has four sections and proceeds as follows. Section 2 provides a brief review of the cross-country efficiency literature related to the non-life insurance industry. Section 3 reviews the profit efficiency methodology and describes the two-stage approach adopted in the present study. Section 4 describes the variables and discusses the results. Section 5 concludes.

2. Review of Related Literature and Motivation for the Study

2.1. International Studies on Non-Life Insurance Sector Efficiency

Toivanen (1997) estimated the economies of scale and scope for the non-life insurance companies of Finland for the three period 1989–91. Empirical evidence obtained from the study suggested that the creation of a branch network is important for acquiring market power or informational advantages. Fukuyama and Weber (2001) estimated technical efficiency and productivity growth of the Japanese non-life insurance companies based on the information for the period 1983–94. The study revealed that between 1983 and 1990 productivity improvement (mainly contributed by technological change) was significant followed by a stagnation during the next three years. Ennsfellner, Lewis and Anderson (2004) examined the production efficiency of the Austrian insurance market for the time period 1994–99 using a Bayesian stochastic frontier for estimating aggregate and firm specific efficiency of the in-sample insurance companies. The study found that the process of deregulation of the Austrian insurance market had influenced productive efficiency of the insurers in a positive manner. Choi and Weiss (2005) examined the linkage between firm performance, market structure and efficiency of the U.S. property-liability insurers during 1992–98 using a stochastic frontier approach. Yang (2006) made use of a two-stage DEA (data envelopment analysis) model for estimating the production and investment efficiency of Canadian life and health (L&H) insurance industry. Kao and Hwang (2008) applied a two-stage DEA model to evaluate the marketing and investment efficiency of 24 non-life insurance companies of Taiwan input and output data for 2001 and 2002. Barros, Nektarios and Assaf (2010) applied a two-stage robust estimation framework for efficiency estimation of 71 Greek life and non-life insurance companies. The first stage results of the study indicated significant divergence in efficiency performance exhibited while the second stage regression results showed that competition is a major influencing factor of efficiency in the Greek insurance industry. Mahlberg and Url (2010) examined the impact of market unification project of the European Commission on the efficiency and productivity change of 202 German insurance companies for 1991–2006. The outcomes provide a mixed picture regarding the convergence of performance among the observed insurance companies. Cummins and Xie (2013) examined efficiency, productivity and scale economies in the U.S. property-liability insurance industry. The results indicated that the insurers below median size mostly exhibited increasing returns to scale, while the insurers above median size mostly exhibited decreasing returns to scale. Jarraya and Bouri (2014) investigated profit efficiency and optimal production targets of the European non-life insurance industry for 2002–08 using directional distance and Lagrangean function. Alhassan and Biekpe (2015) estimated efficiency, productivity and returns to scale for the non-life insurance market in South Africa for the time span 2007–12.The study applied truncated bootstrapped and logistic regression techniques for identifying the determinants of efficiency and the probability of operating under constant returns to scale. Ferro and Leon (2017) applied stochastic frontier analysis for estimating the technical efficiency of Argentine non-life insurance companies for the period 2009–14. The results of his study indicated a low average of technical efficiency for the observed insurers, a stagnated efficiency level during the later phase of the observed time period and a technical regress.

2.2. Indian efficiency studies

In the last few years, several research studies estimated efficiency of general insurance companies. Mandal and Ghosh Dastidar (2014) estimated the performance of 12 general insurance companies in India between 2006–07 and 2009–10 using DEA and tried to assess the impact of global economic slowdown on the performance of the in-sample insurers. Sinha (2017a) used a dynamic DEA framework for estimating the dynamic efficiency performance of Indian general insurance companies. In another study, Sinha (2017b) estimated efficiency of Indian general insurance companies for 2013–14 using the conditional performance benchmarking method. Ilyas and Rajasekharan (2019a, 2019b) evaluated the efficiency and total factor productivity of Indian non-life insurance industry during the period 2005–16. The second study by Ilyas and Rajasekharan (2019b) used Fare-Primont index for the computation of total factor productivity found that the non-life insurance sector exhibits very low level of productivity. Sinha (2021) estimated a Farrell-type profit frontier of the Indian general insurance companies.

2.3. Motivation for the Present Study

As indicated in the beginning, the general insurance industry plays a pivotal role in the economy as a facilitator of industrial investment. On one hand, the presence of a robust insurance sector is important as it can provide the very essential risk coverage to the physical infrastructure as well as the labour force (against ill-health). The ongoing COVID pandemic has brought to the fore the necessity of having a good medical insurance system that our country still lacks. On the other hand, the insurance sector has a crucial role to play as the supplier of long-term finance to the government and the business sector for facilitating the growth of public and private infrastructure in India. From this stand point, analysis of the financial performance of the sector is of paramount importance as the future growth possibilities hinges on the present financial fundamentals of the sector.

3. Methodology of First Stage and Second Stage Estimation

3.1. The Concept of Profit Function

In a market economy, business firms produce goods and services for the market with the ultimate objective of generating profit. The assumption of profit maximisation in neoclassical microeconomics presupposes the existence of a maximum/potential level of profit corresponding to the state of technology and input resources deployed by it. Optimality of profit requires that the profit function reaches a maximum at some point and declines thereafter. A firm’s ability to realise the level of profit depends partly on internal management as well as on the degree of competition and various other external factors such as the regulatory environment. Thus, the profit function is essentially a restricted profit function. From the conceptual stand point, this is ensured by imposing restrictions on the profit function. Mcfadden (1978) introduced the concept of restricted profit function followed by Lee and Chambers (1986), Chambers, Chung and Färe (1998), Portela and Thanassoulis (2005), Cherchye, Kuosmanen and Leleu (2010) and Färe et al. (2019). Proceeding with the restricted profit function, maximum profit is obtained by a firm when the profit function is tangential to the technology set. Beyond the maximum profit level, the profit function exhibits decreasing returns to scale. The implicit assumption is that the production possibilities are constrained by physical or economic environment or by the existence of prior contracts relating to input procurement/output delivery (Mcfadden 1978). Färe et al. (2019) mentioned some additional constraints like requirement of minimum employment, input availability limits, budget constraints, etc.

3.2. Measures of Profit Efficiency

The construction of profit frontier and evaluation of profit efficiency needs a clarity regarding the definition of profit. Nerlove (1965) defined gross profit as the difference between total revenue and total variable cost of the firm. Thus, the profit earned by a firm depends on the technology and the input and output prices. He introduced two concepts of profit efficiency. The first measure introduced by him was a ratio measure that compares observed and optimal profit levels. The second measure is an additive measure reflecting the difference between optimal and observed profits. Varian (1990) used an incremental measure that indicates the incremental profit that may be earned by an observed firm by selecting the optimal input–output bundle instead of the observed one. Chambers et al. (1998) introduced a directional distance function approach based measure of profit efficiency using the profit distance function. Portela and Thanassoulis (2005, 2007) used the Geometric Distance Function (GDF) for estimating profit efficiency. The GDF is defined as the ratio of input and output related indices. The input index is measured as the ratio of target and observed levels of inputs and the output index as the ratio of observed and target levels of output. The two studies used geometric averages for finding out the average levels of input and output targets and actuals. Portela and Thanassoulis (2007) decomposed this measure in to technical and allocative components. Cherchye et al. (2010) examined the short run profit maximising behaviour of productive firms. The study reviewed the alternative profit efficiency measures provided by Nerlove (1965) and Varian (1990). The study identified Varian’s measure of profit efficiency as the preferred measure of short run profit efficiency. Further, they showed that the gauge function introduced by Mcfadden (1978) can be represented as Varian’s measure of profit efficiency at the shadow prices and it provides an upper bound for the measure of profit efficiency, which applies for any system of market prices. Cherchye, De Rock and Walheer (2016) defined a multi-output profit function and provided a composite measure of profit efficiency. Färe et al. (2019) introduced a Farrell type distance function and provided a measure of profit efficiency, which is based on the ratio of incremental profit (difference between optimal and observed profit) and observed revenue plus unity.

3.3. Formal Presentation of the Profit Function and Maximum Profit

For providing a formal presentation of the profit function, it is essential to specify the technology that relates inputs with outputs. Let us consider a technology $P_{T}$ given by $P_{T} = {(x, y) ∣ x$ can produce $y}$ , where $x \in R_{n}^{+}$ represent a vector of inputs $(x_{1}, x_{2}, \dots, x_{n})$ and $y \in R_{m}^{+}$ represents a vector of m outputs $(y_{1}, y_{2}, \dots, y_{m})$ . Let $p_{y 1}, p_{y 2}, \dots, p_{y m}$ represent the output prices and $w_{x 1}, w_{x 2}, \dots, w_{x n}$ represent the input prices. Let ύ represent the profit arising out of the productive activity. Then, we can relate the total profit with the input and output quantities and prices in the following manner: $π = \sum_{i = 1}^{m} p_{y i} y_{i} - \sum_{j = 1}^{n} w_{x j} x_{j}$ .

Fare and Primont (1995) showed that (a) the profit function is non-negative, non-increasing in input prices (w) and non-decreasing in output prices (p), (b) it is homogenous of degree one in input and output prices and (c) the function is convex and continuous in positive prices.

For the estimation of profit efficiency, it is essential to define maximum profit formally. In the present context, we may define the maximum(potential) profit as $π^{\max} (p, w) = \max {p y - w x : (x, y) \in T_{S}}, p \in R_{m}^{+} and w \in R_{n}^{+}$ . A firm is profit efficient if it is able to realise the potential profit.

3.4. Approach of the Present Study

In the present study, we have used DEA, which is a non-parametric method for the estimation of efficiency. DEA is based on the twin assumptions of free disposability of inputs and outputs and convexity of the technology. DEA constructs production frontier on the basis of observed data for all the productive units (for which we have information) and uses the so constructed frontier for estimating the relative performance of the observed decision-making unit (DMU).

Application of DEA in the context of profit frontier, however, involves comparison of benchmark and observed levels of profit and these are derived from revenue and cost indicators. In this case, benchmark values can deviate from the observed values because of the following two reasons: deviation of observed and benchmark physical units and deviation in prices. Estimation of profit efficiency is problematic when input and output prices are not same across all the observed DMUs and unit prices of inputs/outputs are not available.

Tone (2002) pointed out that when prices are not equal across the observed firms, the application of the quantity-based allocation model can lead to erroneous efficiency-based ranking of firms. Cross and Fare (2008) pointed out that the two models (value based and quantity based) coincide only when the prices are the same across the firms. In the event of the existence of price differences across firms, Cross and Fare (2008) decomposed the difference in to technology and firm related components and found the impact to be material affecting the relative ranking of firms.

A second problem of estimation of profit efficiency relates to data negativity. Unlike input and output quantities, profits can be negative. This problem is quite common in the context of Indian general insurance companies.

In view of the above, we have used two estimation methods that are based on values of inputs and outputs and uses the revenue–cost ratio as the profit indicator. The first model (Model 1) is by Tone (2002). As per this approach, the profit distance function (Shephard 1953, 1970) can be written as $D_{π} = \min [μ : π_{o} (y, x) / μ (y, x) \in P_{T}]$ . For an observed firm r, the DEA program for profit maximisation (in the radial framework) for the firm can be written as follows:

M a x π_{r} = \sum_{i = 1}^{m} p_{y i r} y_{i r} - \sum_{j = 1}^{n} w_{x j r} x_{j r}

Subject to x_{r} \geq λ X, y_{r} \leq λ Y, λ \geq 0, \sum λ = 1.

Profit efficiency of the firm can be computed as $\frac{π_{r}}{π_{\max}}$ .

Since we are using the ratio approach, the DEA program for the observed firm becomes the following:

M a x π_{r a t i o} = \frac{\sum_{i = 1}^{m} Y_{v i o}}{\sum_{j = 1}^{n} X_{v j o}}

Subject to x_{v_{o}} \geq λ X_{v}, y_{v_{o}} \leq λ Y_{v}, λ \geq 0, \sum λ = 1.

Ratio-based profit efficiency of the firm can be computed as $\frac{π_{O}}{π_{*}}$ , where π_* is the optimal revenue–cost ratio. Thus, it can be decomposed in to revenue efficiency and cost efficiency components:

$\frac{π_{O}}{π_{*}} = (\frac{R_{O}}{R_{*}}) \times (\frac{C_{*}}{C_{O}})$ , where $(\frac{R_{O}}{R *})$ represents revenue efficiency and $(\frac{C_{*}}{C_{0}})$ represents cost efficiency.

The second model (Model 2) is based on directional distance function. For the technology set $P_{T} = {(x, y) ∣ x$ can produce $y}$ , the directional technology distance function can be defined as $D_{T π} (x, y, g_{x}, g_{y}) = \max [β \in R : {(x - β g_{x}), (y + β g_{y})} \in T_{S})$ , where $(g_{x}, g_{y})$ is a non-zero direction vector in $R_{+}^{n} \times R_{+}^{m}$ . The corresponding directional technology profit distance function is $D_{π} (p_{x} x, p_{y} y_{2} g_{x}, g_{y}) = \max {β \in R: p (y + β g_{y}) - w (x - β g_{x}) - \leq π (p, w)} = π (p, w) - (p y - w z) .$ Here, $(p, w)$ represents the price vector. However, this measure is not invariant to proportional price changes unless it is subjected to price normalisation. In the present context, however, we overcome this problem by using a ratio form directional distance-based profit function aiming to maximising the ratio of revenue to cost. Thus, we have used a Generalised Directional Distance Function (GDDF) introduced by Cheng and Zervopoulos (2014). The optimisation program for the observed DMU can thus be written as follows:

M a x \frac{1 + \frac{1}{m} \sum_{1}^{m} β \frac{p_{y i} g_{y i}}{y_{i}}}{1 - \frac{1}{n} \sum_{1}^{n} β \frac{w_{x j} g_{x j}}{x_{j}}} .

Subject to p_{x o} x_{o} - β p_{x o} x_{g} \geq λ P X and p_{y o} y_{o} + β p_{y o} y_{g} \leq λ P Y, λ \geq 0, \sum λ = 1.

When $g_{x} = p_{x o} x_{o} and g_{y} = p_{y o} y_{o}$ (the direction vectors are equal to the observed costs and revenues) then the directional distance function is equal to a radial model. In this case also we can decompose the overall profit efficiency in to revenue efficiency and cost efficiency.

3.4. Regression of Efficiency Scores on Contextual Variables

In the second stage analysis, we need to regress the profit efficiency scores obtained from the application of both the approaches on the contextual variables, which influence efficiency performance. Since the profit efficiency scores are bounded from below and above (the lower and upper bounds being 0 and 1, respectively), the problem can be countered either by resorting to data transformation (such as logarithmic or box-cox transformation) or by imposing restrictions (setting lower and upper bounds) on the dependent variable. While the Tobit Model is quite popular as the second stage method, there are reservations among the researches regarding the use of the approach. Hoff (2007) found that in most cases, ordinary least squares (OLS) can replace Tobit regression as the second stage method. Mcdonald (2009) pointed out that the second stage regression should be carried by a method that expresses the dependent variable in terms of fractional data. In view of the above, we have applied OLS regression of profit efficiency scores on the contextual variables.

4. Variables, Results and Discussion

4.1. Description of Variables

Efficiency evaluation of the general insurance companies requires the identification of inputs, outputs and prices of the insurance sector. However, specification of variables (and price parameters) in the context of an insurance industry is relatively complex due to the presence of several alternative approaches for the description of the insurer productive activities.

Eling and Luhnen (2010) found three major types of inputs, which are used in the insurance industry: labour (including agents and office staff), business services (including items such as travel, communications and advertisement) and capital (including debt and equity capital). Leverty and Grace (2010) mentioned three alternative approaches for choosing outputs: the financial intermediation approach, the user cost approach and the value-added approach. Insurance service providers as intermediaries collect premium from the insured and, in turn, provide risk coverage against unforeseen events. The user cost approach (Hancock 1985) treats an item as an input or output of the insurance industry depending on whether the net revenue contribution of the item is negative or positive.

The value-added approach (Berger, Hanweck and Humphrey 1987) considers those activities as outputs that contributes significant value added as assessed using operating cost allocations. Broadly speaking, the value-added approach assumes that the insurers provide the following three major services: risk-pooling and risk bearing, real financial services and intermediation. The present study seeks to estimate profit efficiency and consequently we need to identify the major activities that contribute to insurer revenue as well as the principal contributors of cost. Since we do not very detailed information on various elements of operating costs, total operating expenses is considered as the proxy input for capturing operational activities. The expenses on account of claims is considered as the second input. We did not include equity capital as input as we are interested in profit measure prior to the distribution of profit. On the output side, we have considered net premium income and income from investments as the two outputs. Thus the input and output measures are broadly in conformity with Kao and Hwang (2008). For all the inputs and outputs, price is taken as unity Table 1 provides an overview of inputs, outputs and the prices.

Table 1.

Inputs, Outputs and Prices.

Description	Input	Output	Price
Operating expenses	√	-	Unity
Claims incurred	√	-	Unity
Net premium income	-	√	Unity
Investment income	-	√	Unity

Source: Author’s own selection.

The current study is based on the observations for fifteen general insurance companies for six consecutive financial year: 2011–12 to 2016–17. The in-sample general insurance companies include eleven private sector and four public sector general insurance companies. The relative data have been collected from the following two main sources: Annual Reports of IRDA for the respective years and the Handbook on Indian Insurance Statistics published by IRDA for the years 2012–13, 2014–15 and 2016–17. The audited accounts of the in-sample insurers have also been consulted where found necessary. Estimation has been made the assuming that the insurance companies operate under variable returns to scale.

4.2 Results and Discussion

4.2.1. Descriptive Statistics of Efficiency

Tables 2 and 3 present the descriptive statistics of efficiency scores of the observed general insurers obtained from Models 1 and 2 for the period under observation. The number of efficient units has fluctuated between 4 and 8 during the in-sample period. The insurer wise profit, revenue and cost efficiency scores for the six years under observation are included in Tables A1 –A6 for Model 1 and 2.

Table 2.

Descriptive Statistics of Efficiency Scores for Model 1.

Particulars	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Mean efficiency score	0.9244	0.9404	0.9564	0.9611	0.9552	0.9272
Standard deviation	0.0876	0.0582	0.0532	0.0517	0.0671	0.0833
Maximum	1	1	1	1	1	1
Minimum	0.7300	0.8499	0.8841	0.8692	0.7874	0.7328
No of efficient DMUs	7	5	7	8	7	4

Source: Calculated.

Table 3.

Descriptive Statistics of Profit Efficiency Scores for Model 2.

Particulars	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Mean efficiency score	0.7847	0.7890	0.8602	0.8009	0.8185	0.7668
Standard deviation	0.2216	0.2019	0.1570	0.2123	0.2004	0.2489
Maximum	1	1	1	1	1	1
Minimum	0.4173	0.3902	0.5082	0.3271	0.3677	0.3622
No of efficient DMUs	7	6	7	6	6	7

Source: Calculated.

It is to be noted that in the present study, efficiency scores have been computed relative to the year wise profit frontiers constructed on the basis of sample data and consequently efficiency scores are not comparable across time periods. However, the mean efficiency scores and the related standard deviation do provide us an idea about the performance variability relative to the economic (profit) frontier. Efficiency estimate for Model 1 (Table 2) exhibits convergence in performance (as indicated by upward movement in mean efficiency and decline in standard deviation) during the first four in-sample years. However, the mean efficiency scores have declined during the last two years under observation. The insurer wise profit, revenue and cost efficiency scores are presented in Tables A1 –A3. Among the observed insurers, Shri Ram General Insurance, New India Assurance, SBI General Insurance and Bajaj Allianz occupied the top four positions under both the models.

Table 3 provides the descriptive statistics of profit efficiency scores estimated by applying the GDDF. The trend obtained from the application of directional distance function shows that mean efficiency score increased every year from 2011–12 to 2013–14 but showed fluctuations thereafter. Thus, the trend observed here is quite similar to that encountered in Model 2. The insurer wise profit, revenue and cost efficiency scores relative to second model are included in Tables A4 –A6.

4.2.2. Decomposition of Profit Efficiency

The profit efficiency performance estimated from the two models can be decomposed in to two components: revenue efficiency and cost efficiency. Table 4 provides the mean revenue and cost efficiency estimates obtained from Model 1 for the period under observation. It shows that between 2011–12 and 2015–16, mean revenue efficiency has improved between 2012–13 and 2014–15 and remained stationary for the next two years. On the other hand, mean cost efficiency has improved between 2011–12 and 2014–15 but declined thereafter. The degree of inefficiency is more pronounced in cost performance when compared to revenue performance.

Table 4.

Decomposition of Profit Efficiency for Model 1.

Particulars	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Mean revenue efficiency	0.9936	0.9692	0.9735	0.9878	0.9878	0.9878
Mean cost efficiency	0.9300	0.9704	0.9828	0.9731	0.9672	0.9391
Overall	0.9244	0.9404	0.9564	0.9611	0.9552	0.9272

Source: Calculated.

Table 5 provides a decomposition of profit efficiency computed with the help of GDDF (Model 2) in to revenue and cost efficiency components for the in-sample years. Model 2 exhibits a fluctuation in both mean revenue and cost efficiency after 2013–14 and a sharp drop in cost efficiency during the last observed year (2016–17) relative to the previous year (2015–16).

Table 5.

Decomposition of Profit Efficiency for Model 2.

Particulars	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Mean revenue efficiency	0.8141	0.8248	0.8712	0.8133	0.8242	0.8471
Mean cost efficiency	0.9553	0.9589	0.9858	0.9817	0.9910	0.8863
Overall	0.7847	0.7890	0.8602	0.8009	0.8185	0.7668

Source: Calculated.

4.2.3. Ownership and Efficiency

Finally, we are also interested to know how efficiency performance varies across ownership categories (private and public). Table 6 provides the relative information for Model 1. The table indicates that mean profit efficiency of the in-sample private insurers has improved after 2011–12 while the same for the public sector insurers has gradually declined over the observed period. For the public sector companies this was mainly due worsening mean cost efficiency. The private sector counterparts, on the other hand, showed much less variation in cost efficiency after 2011–12.

Table 6.

Efficiency Variations across Private and Public Sector General Insurers (Model 1).

Category &Efficiency Type	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Private sectorrevenue efficiency	0.9927	0.9637	0.9654	0.9845	0.9845	0.9845
Private sectorcost efficiency	0.9092	0.9862	0.9895	0.9811	0.9752	0.9701
Private sectorprofit efficiency	0.9030	0.9505	0.9549	0.9658	0.9599	0.9548
Public sectorrevenue efficiency	0.9960	0.9841	0.9957	0.9967	0.9967	0.9967
Public sectorcost efficiency	0.9871	0.9269	0.9646	0.9511	0.9452	0.8541
Public sectorprofit efficiency	0.9832	0.9126	0.9607	0.9481	0.9423	0.8513

Source: Calculated.

Table 7 provides the relative performance of the in-sample private and public sector general insurance companies for Model 2. The table shows that the observed private sector general insurance companies exhibited higher mean profit efficiency in comparison to the public sector companies for only two years. However, they have done better in terms of cost efficiency while the public sector insurers have mostly done better in terms of revenue efficiency.

Table 7.

Efficiency Variations across Private and Public Sector General Insurers (Model 2).

Category &Efficiency Type	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Private sectorrevenue efficiency	0.7662	0.8106	0.8459	0.8048	0.8090	0.8322
Private sectorcost efficiency	0.9395	0.9886	0.9940	0.9942	0.9944	0.8630
Private sectorprofit efficiency	0.7265	0.8005	0.8426	0.8028	0.8068	0.7367
Public sectorrevenue efficiency	0.9457	0.8664	0.9407	0.8365	0.8658	0.8881
Public sectorcost efficiency	0.9989	0.8774	0.9634	0.9473	0.9819	0.9505
Public sectorprofit efficiency	0.9448	0.7572	0.9086	0.7958	0.8507	0.8493

Source: Calculated.

4.3. Linkage of Efficiency with the Contextual Variables

Profit efficiency of the insurers is an indicator of financial performance and should have strong linkages with other financial indicators. In the present part of the study, we explored the relationship of profit efficiency (as computed from Model 1 and Model 2) with two important and widely accepted indicators of performance: return on equity and solvency ratio in terms of three approaches: pooled OLS, fixed effects model and random effects model. We have also included ownership dummy (0 for public sector and 1 for private sector) and insurer size (log of total asset) as control variables. For comparing pooled OLS with the fixed effects model, we have F-test and for comparing fixed effects model with random effects model, Hausman test has been used. The panel diagnostics outcome has been included in Table 8. The outcomes indicate that pooled OLS is the best alternative for carrying out regression of efficiency scores (derived from Model 1 and Model 2) on the contextual variables.

Table 8.

Panel Diagnostics-Regression of Efficiency Scores on the Contextual Variables.

Particulars	Test Name	Purpose	Test Statistic	Probability of Type 1 Error
Regression of Model 1 efficiency scores	F-test	Comparison of pooled OLS with fixed effects model	0.8115	0.6541
Regression of Model 1 efficiency scores	Hausman test	Comparison of fixed effects model with random effects model	7.3571	0.1182
Regression of Model 2 efficiency scores	F-test	Comparison of pooled OLS with fixed effects model	0.5284	0.9083
Regression of Model 2 efficiency scores	Hausman test	Comparison of fixed effects model with random effects model	1.4221	0.8403

Source: Calculated.

Tables 9 and 10 present the pooled OLS regression results corresponding to the efficiency scores obtained from the two models respectively. The results indicate that as per Model 1, the coefficients of both solvency ratio and return on equity are statistically significant at the 95% level of confidence. The coefficients of ownership dummy and log of total asset are, however, not significant. The results are, however, somewhat different for the second case (involving Model 2 efficiency scores). Table 8 shows that while the coefficients of solvency ratio and log of total asset are statistically significant at 90% and 95% levels of confidence respectively.

Table 9.

Regression of Efficiency Scores of Model 1 on the Contextual Variables.

Particulars	Coefficient	Standard Error	t-Ratio	Probability of Type 1 Error
Intercept	–0.2405	0.0730	–3.294	0.0014
Solvency ratio	0.0272	0.0079	3.443	0.0009
Ownership dummy	0.0169	0.0184	0.9162	0.3622
Return on equity	0.1750	0.0334	5.236	<0.0001
Log of total asset	0.0049	0.0076	0.6414	0.5230
R-squared	0.2926
Adjusted R-squared	0.2593

Source: Calculated.

Table 10.

Regression of Efficiency Scores of Model 2 on the Contextual Variables.

Particulars	Coefficient	Standard Error	t-Ratio	Probability of Type 1 Error
Intercept	–1.07271	0.292407	–3.669	0.0004
Solvency ratio	0.0593811	0.0316223	1.878	0.0638
Ownership dummy	0.0420794	0.133819	0.3145	0.7539
Return on equity	0.0692504	0.0738110	0.9382	0.3508
Log of total asset	0.0804803	0.0305045	2.638	0.0099
R-squared	0.1185
Adjusted R-squared	0.0070

Source: Calculated.

4. Concluding Observations

In the present study, we have applied two different models for the computation of profit efficiency. The results obtained from the two models are similar but not identical. This is because the estimation procedures are different. Model 1 allows estimation of efficiency through the possibility of radial expansion/contraction of revenue and cost. In the second model, the inefficiency in revenue/cost is calculated through the recognition of input and output slacks.

We now consider the similarities. For both the models, the results indicate that the public sector insurers have done relatively better than their private sector peers in terms of revenue efficiency (for most of the years under observation). However, they need to improve in terms of cost efficiency in order to enhance their level of cost efficiency. Secondly, one general insurance company, New India Assurance Company Limited is found to be efficient for all the in-sample years for both the models. Thus, it can be considered as the benchmark insurer for the peers in respect of profit efficiency. Finally, for both the models, application of OLS regression shows that profit efficiency is closely associated with solvency ratio. The empirical evidence regarding the linkage with return on equity, however, depends on the model chosen. Among the two control variables, the coefficient of log of total asset is significant in the second regression.

Future studies can extend the analysis in three directions. First, profit efficiency can be decomposed into technical and allocative components. Second, bootstrap DEA/stochastic DEA can be applied to obtain interval estimates of efficiency. Third, more contextual variables can be identified and considered for second stage regression analysis.

Annexure

Table A1.

Insurer Wise Profit Efficiency Scores (Model 1).

Insurer	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Bajaj Allianz	1	1	1	1	1	1
Cholamandalam	0.9114	0.9662	0.9297	1	1	0.9912
Future Generali	0.7908	0.9749	1	1	1	1.0001
HDFC Ergo	0.8700	0.9540	0.9124	1	1	0.8771
ICICI Lombard	1	0.8914	0.8841	0.8692	0.7874	0.8959
IFFCO Tokio	0.8485	0.9521	0.9617	0.9433	0.9894	0.9253
Reliance	0.7300	0.8487	0.8389	0.8721	0.8721	0.8693
Royal Sundaram	0.9084	0.8683	0.9766	0.9669	0.9856	0.9504
SBI General	1	1	1	1	0.9617	0.9997
Shri Ram General	1	1	1	1	1	1.0003
Tata AIG	0.8736	1	1	0.9722	0.9626	0.9937
National	1	0.8499	1	1	0.8549	0.8500
New India	1	1	1	1	1	1
Oriental	0.9330	0.8922	0.8920	0.8953	1	0.7328
United	1	0.9082	0.9508	0.8971	0.9143	0.8226

Source: Calculated.

Table A2.

Insurer Wise Revenue Efficiency Scores (Model 2).

Insurer	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Bajaj Allianz	1	1	1	1	1	1
Cholamandalam	0.9883	0.9883	0.9297	1	1	1
Future Generali	0.9749	0.9749	1	1	1	1
HDFC Ergo	0.9551	0.9551	0.9124	1	1	1
ICICI Lombard	0.9039	0.9039	1	0.9886	0.9886	0.9886
IFFCO Tokio	0.9860	0.9860	0.9617	0.9894	0.9894	0.9894
Reliance	0.8487	0.8487	0.8389	0.8721	0.8721	0.8721
Royal Sundaram	0.9442	0.9442	0.9766	0.9856	0.9856	0.9856
SBI General	1	1	1	1	1	1
Shri Ram General	1	1	1	1	1	1
Tata AIG	1	1	1	0.9937	0.9937	0.9937
National	0.9552	0.9552	1	1	1	1
New India	1	1	1	1	1	1
Oriental	0.9961	0.9961	0.9827	1	1	1
United	0.9849	0.9849	1	0.9869	0.9869	0.9869

Source: Calculated.

Table A3.

Insurer Wise Cost Efficiency Scores (Model 1).

Insurer	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Bajaj Allianz	1	1	1	1	1	1
Cholamandalam	0.9114	0.9777	1	1	1	0.9912
Future Generali	0.8562	1	1	1	1	1.0001
HDFC Ergo	0.8700	0.9989	1	1	1	0.8771
ICICI Lombard	1	0.9862	0.8841	0.8792	0.7965	0.9062
IFFCO Tokio	0.8521	0.9656	1	0.9534	1	0.9352
Reliance	0.7300	1	1	1	1	0.9968
Royal Sundaram	0.9084	0.9196	1	0.9810	1	0.9642
SBI General	1	1	1	1	0.9617	0.9997
Shri Ram General	1	1	1	1	1	1.0003
Tata AIG	0.8736	1	1	0.9783	0.9687	1
National	1	0.8897	1	1	0.8549	0.8500
New India	1	1	1	1	1	1
Oriental	0.9483	0.8957	0.9077	0.8953	1	0.7328
United	1	0.9221	0.9508	0.9089	0.9265	0.8335

Source: Calculated.

Table A4.

Insurer Wise Profit Efficiency Scores (Model 2).

Insurer	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Bajaj Allianz	1	1	1	0.6954	0.8507	1
Cholamandalam	0.6865	0.3902	0.6900	1	1	0.5607
Future Generali	0.5939	0.6471	1	0.7328	0.7791	1
HDFC Ergo	0.6052	0.8474	0.8079	1	1	1
ICICI Lombard	1	1	0.5082	1	1	0.7440
IFFCO Tokio	0.4173	1	0.6869	0.3271	0.3677	0.4300
Reliance	0.5589	0.7180	0.7351	0.7502	0.6398	0.4068
Royal Sundaram	0.5998	0.5549	0.8404	0.4526	0.4838	0.6005
SBI General	1	1	1	1	1	1
Shri Ram General	1	0.6480	1	1	1	0.3622
Tata AIG	0.5304	1	1	0.8727	0.7538	1
National	1	0.6359	1	0.6596	0.7742	0.6927
New India	1	1	1	1	1	1
Oriental	0.7792	0.7136	0.7801	0.7785	0.7491	0.7045
United	1	0.6794	0.8542	0.7450	0.8793	1

Source: Calculated.

Table A5.

Insurer Wise Revenue Efficiency Scores (Model 2).

Insurer	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Bajaj Allianz	1	1	1	0.6954	0.8507	1
Cholamandalam	0.7802	0.3902	0.6900	1	1	0.6700
Future Generali	0.6812	0.6471	1	0.7328	0.7791	1
HDFC Ergo	0.6172	0.9317	0.8079	1	1	1
ICICI Lombard	1	1	0.5444	1	1	0.7981
IFFCO Tokio	0.4377	1	0.6869	0.3495	0.3921	0.7861
Reliance	0.6151	0.7444	0.7351	0.7502	0.6398	0.7169
Royal Sundaram	0.6741	0.5549	0.8404	0.4526	0.4838	0.7060
SBI General	1	1	1	1	1	1
Shri Ram General	1	0.6480	1	1	1	0.4775
Tata AIG	0.6238	1	1	0.8727	0.7538	1
National	1	0.6945	1	0.7373	0.8245	0.7969
New India	1	1	1	1	1	1
Oriental	0.7826	0.9690	0.8471	0.8305	0.7491	0.7553
United	1	0.7925	0.9158	0.7783	0.8895	1

Source: Calculated.

Table A6.

Insurer Wise Cost Efficiency Scores (Model 2).

Insurer	2011–12	2012–13	2013–14	2014–15	2015–16	2016–17
Bajaj Allianz	1	1	1	1	1	1
Cholamandalam	0.9694	0.9027	0.9305	1	1	1
Future Generali	0.8599	0.8944	0.9997	1	1	1
HDFC Ergo	0.9420	0.9662	0.9474	1	1	1
ICICI Lombard	1	1	1	1	1	1
IFFCO Tokio	1	1	1	1	1	1
Reliance	0.8676	0.9317	0.9114	0.9996	1	0.8313
Royal Sundaram	0.9295	0.8856	0.9146	0.9429	1	0.9021
SBI General	1	1	1	1	1	1
Shri Ram General	1	1	0.9641	1	1	1
Tata AIG	1	1	1	0.9992	1	1
National	1	1	1	1	0.8611	0.8165
New India	1	1	1	1	1	1
Oriental	0.8481	1	0.8195	0.7978	0.7932	0.6529
United	1	1	1	1	1	0.7929

Source: Calculated.

Footnotes

Author’s Note

An earlier version of the paper was presented at Econference-2020 organised by University of Burdwan during February 2020.

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author received no financial support for the research, authorship and/or publication of this article.

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