Estimation of Insurer’s Managerial Ability: A Goal Programming Approach

Abstract

Inter-firm performance differences are influenced by several contextual variables, and managerial ability is one important factor that enables some firms to gain leadership positions in the market and helps them to sustain the advantage over successive time periods. However, managerial ability is the cognitive capability which is not directly observable/measurable. In this article, an indirect estimate of managerial ability under a three-stage approach for 20 Indian general insurance companies based on 120 firm-year observations spread over the period 2012–2013 to 2017–2018 is provided. The three-stage estimation method for the measurement of firm-specific managerial ability includes data envelopment analysis (DEA)-goal programming, pooled regression, residual of the pooled regression, Ordinary Least Squares, and General Additive Model regression. Unlike other studies, in this study, DEA-goal programming method is considered to improve discriminatory power for proper classification of the Indian general insurance companies. The results indicate that the influence is statistically significant.

Keywords

Data envelopment analysis DEA-GP GAM regression managerial ability

Introduction

Managerial ability is an important catalyst in the transformation of enterprise resources into revenue streams. Managerial contributions are crucial in the context of operational and investment decision-making and therefore affect firm performance in both the short and long run. Further, managerial ability plays a pivotal role in the improvement of the firm performance. Considering the importance of managerial ability in the enterprise context, several research studies attempted to quantify this key factor in firm performance in several ways. Murthi et al.¹ estimated relative manufacturing and marketing efficiency of productive firms as surrogates for managerial skills. Bertrand and Schoar² found that manager fixed effects are significant for an array of corporate decisions. Chang et al.³ found that firm valuation and performance are positively related to the managerial ability. Demerjian et al.⁴ provided an empirical measure of managerial ability. The study showed that the efficiency of a firm is related to several contextual variables including managerial ability. Therefore, the measurement of managerial ability requires disentanglement of the managerial ability component from the other determinants of efficiency. This can be achieved by estimating the regression residual of efficiency scores on other contextual variables for the observed firms.

In the Indian context, managerial capability assumes special significance in the industries which experienced entry deregulation in past few decades leading to intensified price and non-price competition. The industry was deregulated in 1999 following the establishment of Insurance Regulatory and Development Authority which provided the requisite entry guidelines. The sector witnessed impressive growth in the past two decades due to the entry of new players in the market, relaxation of price controls, and growth in product variety. Thus, between 2012–2013 and 2017–2018, the number of general insurers including reinsurers has increased from 28 to 35. Further, insurer penetration (ratio of insurer premium to GDP) increased from 0.7 to 0.97 and insurer density (ratio of insurance premium to total population) from 11 to 19 during the same period (see Table 1).

Table 1.

Growth of General Insurance Industry in India

Particulars	2013	2014	2015	2016	2017	2018
Number of general insurance companies (including reinsurers)	28	29	29	30	31	35
Insurance penetration	0.80	0.70	0.70	0.77	0.93	0.97
Insurance density	11	11	12	13.2	18	19
Number of offices	8099	9872	10407	10803	10547	10425

Source: IRDA annual reports.

However, the insurer-specific growth rates have exhibited significant degree of variations across the insurers. In view of the above, the current study seeks to provide a measure of managerial ability for Indian general insurers for the six years period (2012–2013 to 2017–2018) based on the framework of Demerjian et al.^{4, 5} The present study seeks to contribute to the extant literature (in respect of scholarship and practice in two specific ways. First, the study provides a reasonable measure of managerial ability in the context of the Indian general insurance sector. While most of the managerial ability studies in the international context focused on the entire business sector, we have a sectoral focus. Second, instead of using Data Envelopment Analysis (DEA) for efficiency evaluation in the first stage of the analysis, we have used Goal Programming based DEA. This method is more suitable in our context (than DEA) as all reference Decision-making Units (DMUs) instead of a few. This study has four sections and proceeds as follows. The first section reviews the extant research literature. The second section introduces the research methodology. The third section includes data and variables and discusses the results. The fourth section concludes.

Related Research Literature

The observable output of a company is the result of several important variables including managerial skills. In fact, managerial quality properties have a great impact on the firm performance and there are numerous research studies which focus on measuring managerial ability. Ability, as an element of performance, is an essential concept in the theoretical literature. Another approach is to consider the efficiency of the observed firm as the indicator of managerial skill/ability. Murthi et al.¹ assessed managerial efficiency by measuring relative marketing and production efficiencies. Relative marketing efficiency is a performance measure to describe the relation between two outputs including return on investment and market share, and five managerial inputs. Relative production efficiency, on the other hand, is measured by the return on investment performance, as the output, relative to procurement and production costs, as the inputs. Then, these efficiency scores were used to control the managerial skills in establishing the effect of first-mover advantage on market share. A well-known rating to evaluate a bank’s health is based on Capital adequacy, Asset quality, Management quality, Earnings ability, and Liquidity position, which is CAMEL rating. Based on this rating, two bank failure prediction models were developed to assess the efficiency and the results indicated that Management quality is significant for the survival of a bank, Barr and Siems.⁶ Management style affected the performance of managers in their decision-making and this attribute leads to change the corporate behaviour and performance, Bertrand and Schoar.²

The most interesting approach concerning managerial ability was introduced by Demerjian et al.⁴ First, applying Data DEA, relative efficiency of the firms was computed and the authors formed an efficient frontier in terms of managerial observed ability to generate revenue relative to the quantity and mix of resources deployed by the firms. Then, to eliminate the impact of other effective variables on the efficiency of the firms, the authors removed the effects of firm size, firm age, time, market share, positive free cash flow, the variation of the firm’s operations, and industry effects so that the managerial ability factor could be recognized. Moreover, validation tests were performed to ensure that managerial ability was indicated by residual measure. In another study, Demerjian et al.⁵ analysed the linkage between quality of earnings and managerial ability. Through their study, they showed that managers influence the quality of the judgments that leads to earnings formation. In a study, DEA methodology applied to examine the efficiency of Malaysian public-listed software companies to convert intellectual capital, Public,⁷ as input variables, to corporate values (represented by Tobin’s Q and return on equity). The three input variables of this study were Capital Employed Efficiency, human capital efficiency, and Structural Capital Efficiency.⁸ Skill of mutual fund managers was analysed by Berkand Van Binsbergen,⁹ due to its importance to add value to the manager’s fund from financial markets. The authors increased the power of their analysis by including all actively managed USA mutual funds and revealed that, the managerial skill had a great impact on the fund size. In a new study, Demerjian et al.¹⁰ investigated the probability of doing stable earnings management by managers with higher abilities. The study provided strong evidence that managers with higher ability level are expressively more likely to involve in intentional smoothing of earnings and this is connected with upcoming enhanced operational performance. Also, the relation between managerial ability and productivity of workers in USA firms during 1980–2013 was analysed. Managers with more ability had more productive workers based on a study done by Ghosh et al.¹¹ As mentioned previously Demerjian et al.⁴ proposed a three-stage approach for analysing managerial ability based on DEA. A discussion was done by Banker and Park¹² to scrutinize several issues in the three-stage approach such as the reasons to select DEA as a method for evaluating the managerial ability, how to provide the method as a reliable estimator, and suggest best practices for researchers, and some other detailed options that are essential for the academics to make in the proposed three-stage approach.

Managers with less ability are the cost of a firm’s failure. In order to investigate management’s impact on this cost, revenue and cost efficiency of property-liability insurance companies in the United States were measured by Leverty and Grace.¹³ According to the findings, they specified the impact of CEO-specific effects on such efficiency. Measuring the managerial ability in the insurance sector still has been an appealing field of research and provided valuable insights into the dynamics of the managerial ability in different environments. In a study done by Banker et al.,¹⁴ by considering managers’ success as a measure, they found out managers’ success is positively linked with return on assets and CEOs with higher ability increase the return on asset. In another study, Cvetkoska et al.¹⁵ found that CEO duality, board size, board composition, gender diversity, and CEO gender as the measures had insignificant impact on the managerial ability. However, the diversity of nationalities had a positive and significant impact on managerial ability.

The above discussion shows that the enquiry about managerial ability is important in the context of the business sector as by assessing managerial ability, firms can make an evaluation of the relative strength and weaknesses of their human resource pool and initiate appropriate corrective measures. However, the extant Indian literature did not go beyond efficiency evaluation. The present study seeks to remove this research gap.

Methodology for the Estimation of Managerial Ability

Estimation of Firm Efficiency

Estimation of managerial ability involves a three-stage approach where firm-wise efficiency is computed in the first stage. In the second stage, the efficiency scores obtained from the first stage of efficiency analysis are regressed on the environmental variables which influence the efficiency performance of the productive units. In the final stage, an indicator of managerial ability is computed which is the residual of the regression estimate performed in the second stage.

While the first estimation of firm-level efficiency scores could be obtained from either parametric (stochastic frontier analysis) approach or non-parametric (DEA) approach. In the present case, we have adopted the second approach because of two specific advantages of DEA over stochastic frontier analysis. First, DEA can handle multiple outputs in the context of efficiency evaluation. Second, it is not required to make a priority assumption of a specific parametric relationship between the inputs and outputs of the production process.

For explaining the efficiency evaluation process (undertaken in the present study) let us consider a technology P_T relating outputs of the transformation process with the inputs. The technology is represented as:

P_{T} = {(X, Y) | X c a n p r o d u c e Y}

Where X $\in R_{k + l}^{+}$ represents the vector of k inputs used by the productive system, X = (x₁, x₂…. x_K,) and Y $\in R_{k + l}^{+}$ represents the vector of the outputs produced, Y = (y₁, y₂…. y_l,). The production possibility set comprises both output and input sets. The output set O(Y) $\in P$ corresponds to the set of feasible outputs for each input vector while the input set I(X) includes the input vectors that are feasible with each output vector. The technology is assumed to exhibit free disposability of inputs and outputs and convexity of technology. We may specify them as:

Free disposability: if (X,Y) $\in P_{T}$ , then (x_a,Y) $\in P_{T}$ where x_a ≥ X. Similarly (X, X_a) $\in P_{T}$ , provided y_a ≤ Y. The inequalities between the (input and output) vectors are understood component wise.

Convexity: Convexity implies that if (X_a,Y_a) and (X_b,Y_b) $\in$ then (X_c,Y_c) $\in P_{T}$

Where, X_c = ω X_a + (1–ω) X_b and Y_c = ω Y_a + (1–ω) Y_b and ω ϵ [0,1]

The technology as described above can be represented in terms of transformation function as follows: T = {(X, Y): F (–X, Y) ≤ 0}. The function is called an implicit production function in the single output case and a transformation function when there are multiple outputs. If the system is fully efficient then we have T = 0. In the presence of inefficiency, T < 0.

Now, since there are k inputs and l outputs (in the present case) we can rewrite the transformation function as:

T = - \sum_{i = 1}^{k} x_{i} \frac{\partial F}{\partial x_{i}} + \sum_{j = 1}^{l} y_{i} \frac{\partial F}{\partial y_{i}} \leq 0

Rearranging, we get $\frac{\sum_{j = 1}^{l} y_{i} \frac{\partial F}{\partial y_{i}}}{\sum_{i = 1}^{k} x_{j} \frac{\partial F}{\partial x_{j}}} \leq 1$

Charnes et al.¹⁶ replaced $(\frac{\partial F}{\partial y_{i}}, \frac{\partial F}{\partial x_{j}})$ with (u_i, v_j) where u and v represent weights corresponding to the output and input vectors respectively. The optimal input and outputs for each productive unit could be found for each observed DMU by using the following mathematical programme (corresponding to the input-oriented approach)

M a x E_{0} = \frac{u_{0} y_{0}}{v_{0} x_{0}} \leq 1

(1)

Subject to: –VX + UY ≤ 0, U ≥ 0, V ≥ 0

Where (x₀, y₀) represents the input and output vectors of the observed DMU and (u₀, v₀) represent the weights attached to them.

In the context of estimation scenarios with limited number of sample observations, estimation of input and output weights by the application of DEA has an important weakness. In such circumstances, DEA often lacks the desired discriminatory power for proper classification of the DMUs in to efficient and inefficient groups. This is mainly due to the inappropriate weighting scheme embedded in DEA where the optimal weights for many inputs and outputs are found to be 0.

Model (1) can be solved by the application of Multi-criteria Decision-making (MCDM) techniques. MCDM techniques are used for evaluating multiple conflicting criteria in decision-making. The objective of MCDM is to identify the optimal alternative or rank the alternatives or identify a small number of efficient alternatives based on the preferences of the decision-maker. Because of this ability, several research studies have integrated DEA and MCDM for estimating efficiency performance of DMUs.^17–24 An MCDM method applies a common set of weights (CSWs) which reflects a decision maker’s preferences.

In the present study, we have used Goal Programming for finding out the efficiency of the observed DMUs. Let us explain the method briefly. Since the weighted output of an observed DMU cannot exceed the benchmark output, u₀ y₀ ≤UY and similarly v₀ x₀ ≤VX. Let Z₀ represents the objective function and G₀ represents the goal of the observed DMU. Then we can convert Model (1) in to a single criterion problem and express it as follows:

M i n \sum_{r = 1}^{n} (d_{r}^{+} + d_{r}^{-})

(2)

Subject to: $Z_{0} - G_{0} = (d_{r}^{+} - d_{r}^{-}), d_{r}^{+}, d_{r}^{-} \geq 0, r = 1, 2, …, n$

Since by applying DEA, comparing DMUs in the framework of a common weight is not possible and the model is of low discrimination power. Moreover, to achieve the required efficiency, we need n times running the model for n DMUs. Therefore, in the present study by proposing common weights for the DMUs utilizing Goal Programming, the discrimination power for selecting efficient DMUs is improved and an integrated DEA and GP techniques are presented to evaluate the efficiency of DMUs. CSWs were introduced for the first time by Roll et al.²⁵ The focal point of attaining CSWs is to make a common base for classifying the DMUs.

Based on the above-mentioned, DEA-GP model is formulated as follows:

\begin{matrix} \min \sum_{r = 1}^{n} d_{r}^{+} + d_{r}^{-} \\ s . t . \end{matrix}

\frac{\sum_{r = 1}^{s} u_{r} y_{r j}}{\sum_{i = 1}^{m} v_{i} x_{i j}} + d_{r}^{-} - d_{r}^{+} = 1 r = 1, …, n

(3)

\begin{matrix} u_{i} \geq 0 i = 1, \dots, k \\ v_{j} \geq 0 j = 1, \dots, l \\ d_{r}^{+}, d_{r}^{-} \geq 0 r = 1, \dots, n \end{matrix}

Where all the goals equal 1 (the maximum amount of efficiency). By solving DEA-GP model (Model (3)), u_i* and v_i* are achievable as CSWs and the efficiency of all the DMUs could be calculated considering the CSWs.

Methodology of Second- and Third-stage Estimation

In the second stage of our analysis, we have chosen pooled OLS approach after checking panel diagnostics for three approaches-pooled OLS, Fixed Effects Model (FEM), and Random Effects Model (REM). Since the efficiency scores are bounded from below, we have used log of efficiency as the dependent variable. However, in the final stage, we have regressed Return on Equity on Managerial Ability measured using General Additive Model (GAM) which needs a brief introduction.

A GAM is a generalized linear model in which the dependent variable depends linearly on unknown smooth functions of some explanatory variables. Hastie and Tibshirani²⁶ originally developed GAM regression by combining properties of general linear models with additive models. If Y denotes the dependent variable and we have r explanatory variables Z₁, Z₂,…Z_r, respectively then we may write the GAM regression equation as:

Y = β_{0} + s (Z_{1}) + s (Z_{2}) + …. + s (Z_{r}) + U

Where b₀ represents the intercept and s(Z_i) represents the smooth functions of the explanatory variables to be estimated semi-parametrically.

Case Study and Results

Input, output, and contextual variables used in the first and second stages of analysis are outlined in this section and the results are discussed.

Description of Input, Output, and Contextual Variables

To measure the efficiency of the general insurers, inputs and outputs of the insurers are required. Basically, labour (agents and office staff), business services (travel, communications, and advertisement), and capital (debt and equity capital) are the main kinds of inputs in the insurance industry, Eling and Luhnen.²⁷ On the other hand, to select financial sector outputs in the insurance industry, there are three different methods. The first one is flow approach by considering financial service firms as intermediaries which match the requirements of demanders and suppliers of funds, Leverty and Grace.²⁸ User cost approach considers 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, Hancock.²⁹ Berger and Hanweck³⁰ and Berger and Humphrey³¹ introduced the final method which is value-added approach. Based on this method, outputs are those activities that have considerable added value and are measured by means of operating cost allocations. In some researches, premiums were represented as outputs. In this study, net premium was classified as the value-added for customer. On the contrary, others suggested earned profits and asset changes as the representation of outputs in the life insurance companies, Jarraya and Bouri.³²

In the present study, insurer-wise efficiency is measured with a particular emphasis on the ability of insurer to provide income. For the first stage, inputs, and outputs are determined. Then, descriptive variables are selected for the second-step analysis. Descriptive variables are insurer age, insurer size (log of total asset), solvency ratio, time series dummy (1 to 6 for the 6-year period), and diversification dummy (0 for the 4 in-sample health insurers and 1 for the 16 diversified insurers). Inputs/outputs and contextual variables are listed in Table 2.

Table 2.

Inputs, Outputs, and Contextual Variables

Description	Type of Variable
Operating expenses (related to insurance business), claims incurred	Input variables
Net premium income, income from investments	Output variables
Ownership dummy, insurer age, insurer size, solvency ratio	Contextual variables

Source: The authors.

Description of Case Study

Here, the case study includes totally 120 observations from 12 private sectors diversified general insurers, 4 public sectors diversified general insurers, and 4 private sector health insurers. To estimate the managerial ability, input/output data and descriptive variables were provided from two sources: IRDA Annual Reports published by the IRDA and Indian Insurance Statistics Handbook for the relevant financial years (2012–2018). The nominal data have been deflated for carrying out meaningful comparisons over time.

Description of Results

In this section, the three-stage approach for estimating the managerial ability and the relation between return on equity and the measure of managerial ability are done. The results are presented and described in the below subsections.

Efficiency Evaluation of the Observed General Insurers

Descriptive statistics of the efficiency scores for our case study are tabulated in Table 3. Mean efficiency measures for the case study including three groups (diversified private, diversified public, and specialized health insurers) as well as total number of general insurers are calculated. Based on the results, mean efficiency scores have an ascending trend during the observation period except for the period 2015–2016. The insurer-wise efficiency measures are represented in Table A1.

Table 3.

Descriptive Statistics of Efficiency Scores for the General Insurers (2012–2013 to 2017–2018)

Particulars	2013	2014	2015	2016	2017	2018
Mean efficiency	0.7585	0.9841	1.0229	0.9578	0.9995	1.0124
Standard deviation	0.3854	0.0698	0.2979	0.0974	0.0966	0.1014
Skewness	0.0151	–0.4940	3.2303	–0.1432	–0.2572	0.9919
Kurtosis	0.1642	0.9212	12.4870	–0.1755	0.3053	3.0349

Source: The authors.

Impact of Contextual Variables on Efficiency Scores

The efficiency scores generated from the application of DEA-GP model are bounded from below. Consequently, in the second stage of our study, log of efficiency is regressed on the mentioned contextual variables (ownership dummy, insurer age, insurer size, and solvency ratio). We have considered three alternative models for the purpose of regression: pooled Ordinary Least Squares (OLS), FEM, and REM for estimation. The results are then compared using F-test, Lagrange Multiplier test, and Hausman test. The outcomes of the three tests are provided in Table 4.

The results indicate favour of the pooled OLS model. The pooled OLS results are presented in Table 5. Table 5 displays the coefficients of three variables including ownership dummy, insurer age, and log of total asset and according to the computations they are statistically significant. However, the coefficient of solvency ratio is not significant statistically.

Table 4.

Panel Diagnostics (Pooled OLS, FEM, and REM)

Test Name	Purpose	Observed Statistic	Probability of Type I Error
F-test	Comparison of pooled OLS and FEM	1.4420	0.1259
LM test	Comparison of pooled OLS and REM	0.9301	0.3348
Hausman test	Comparison of FEM and REM	7.8781	0.0961

Source: The authors.

Table 5.

OLS Regression for Log of Efficiency on the Contextual Variables

Particulars	Estimate	Std Error	t-ratio	p-value of Type I Error
Intercept	−1.9990	0.4977	−4.017	0.0001
Ownership dummy	0.9202	0.2706	3.401	0.0009
Solvency ratio	−0.0835	0.0633	−1.318	0.1900
General insurer age	0.0200	0.0096	2.088	0.0390
Log of total asset	0.1337	0.0610	2.191	0.0305
R-squared	0.1639
R-squared (adjusted)	0.1348

Source: The authors.

Estimation and Validation of Managerial Ability

Although regression of the log of efficiency on the contextual variables comprises some effective predictors of the efficiency, any indicator of managerial effort is not included as such effort is not directly observable. Therefore, the residual from the OLS regression represents the managerial ability factor. Descriptive measurements of the managerial ability for the intended period are provided in Table 6. The insurer-wise ability estimates for the years under observation are indicated in Table A2.

Table 6.

Descriptive Statistics of Managerial Ability

Particulars	2013	2014	2015	2016	2017	2018
Mean	–0.2734	0.1183	0.0950	0.0350	0.0183	0.0068
Median	0.0088	0.1337	0.0806	0.0100	0.0085	–0.0112
Standard deviation	0.6780	0.1280	0.2897	0.1735	0.1753	0.1634
Skewness	–1.5549	–0.6392	1.5916	1.1318	0.4859	0.8609
Kurtosis	2.6765	0.8109	5.0570	2.4009	–0.4939	1.1536

Source: The authors.

Finally, return on equity for the observed general insurers has been regressed on the measure of managerial ability, as a measure for validation testing of our managerial ability estimation. In order to provide a more robust estimate, GAM has been applied for capturing the linkage between return on equity and managerial ability. The relation between return on equity and managerial ability in this study is highly significant. The explanatory power of the regression relationship can be understood from the estimate of adjusted R-squared, generalized cross-validation score, and scale estimate presented in Table 7.

Table 7.

GAM Regression of Return on Equity on Managerial Ability

Particulars	Coefficient	Std Error	t-ratio	p-value
Intercept	0.0477	0.0125	3.811	.000228
Significance of smooth terms	edf	Ref edf	F-statistic	p-value
OLS residual (managerial ability)	8.459	8.912	8.658–	~.0000
R-squared (adjusted)	0.379
Deviance explained	42.3%
Generalized cross validation	0.0204
Scale estimate	0.0188

Source: The authors.

Conclusion

The degree of competition in the Indian general insurance market has increased considerably in the post-liberalization phase. In a highly competitive insurance market, the importance of managerial ability is immense. Our estimate of managerial ability in the context of the Indian general insurance sector seeks to identify this important driving force behind company growth. The results indicate that some insurers have maintained their position in the insurance market due to the presence of managerial talent in their resource pool while other insurers suffered from not having comparable managerial capability.

The present study has two main drawbacks which need to be mentioned. The small size of the general insurance market in India is a limitation of the current study. This market consists of few players compared to the advanced insurance markets. Further, most of them entered the market relatively recently, and consequently, our study is based on only a six-year time span. Consideration of only a few contextual variables in the second stage of analysis (due to limited data disclosure) is another weakness. Future studies can take care of these two drawbacks.

Footnotes

Declaration of Conflicting Interests

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

Funding

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

Appendix

References

Murthi

, Srinivasan

, Kalyanaram

. Controlling for observed and unobserved managerial skills in determining first-mover market share advantages. J Mark Res. 1996 Aug; 33(3):329–336.

Bertrand

, Schoar

. Managing with style: The effect of managers on firm policies. Q J Econ. 2003 Nov 1; 118(4):1169–1208.

Chang

, Dasgupta

, Hilary

. CEO ability, pay, and firm performance. Manag Sci. 2010 Oct; 56(10):1633–1652.

Demerjian

, Lev

, McVay

. Quantifying managerial ability: A new measure and validity tests. Manag Sci. 2012 Jul; 58(7):1229–1248.

Demerjian

, Lev

, Lewis MF, McVay

. Managerial ability and earnings quality. Account Rev. 2013 Mar; 88(2):463–498.

Barr

, Siems

. Bank failure prediction using DEA to measure management quality. In: Glover

(ed) Interfaces in computer science and operations research. Boston, MA: Springer, 1997, pp. 341–365.

Pulic

. VAIC™–an accounting tool for IC management. Int J Techno Manag. 2000 Jan 1; 20(5–8):702–714.

Kweh

, Chan

, Ting

. Measuring intellectual capital efficiency in the Malaysian software sector. J Intellect Cap. 2013 Apr 12; 14(2), 310–324.

Berk

, Van Binsbergen

. Measuring skill in the mutual fund industry. J Financ Econ. 2015 Oct 1; 118(1):1–20.

10.

Demerjian

, Lewis-Western

, McVay

. How does intentional earnings smoothing vary with managerial ability? J Account Audit Finance. 2020 Apr; 35(2):406–437.

11.

Ghosh

, Huang

, Sun

. Managerial ability and employee productivity. In: Martin

J. R.

(ed) Advances in Management Accounting. Bingley: Emerald Publishing Limited, 2020 Sep 28.

12.

Banker

, Park

. Three-stage approach to analyze managerial ability. Data Envel Anal J. 2021 Jun 21; 5(1):27–54.

13.

Leverty

, Grace

. Dupes or incompetents? An examination of management’s impact on firm distress. J Risk Ins. 2012 Sep; 79(3):751–783.

14.

Banker

, Luo

, Oh

. Measuring managerial ability in the insurance industry. Data Envel Anal J. 2021 Jun 21; 5(1):115–143.

15.

Cvetkoska

, Eftimov

, . Measuring the Managerial Ability in the Insurance Companies in the Republic of North Macedonia, Croatia, Serbia, and Slovenia, and Identifying its Determinants. Int J Bank Risk Ins. 2022 Feb 8; 10(1).

16.

Charnes

, Cooper

, Rhodes

. Measuring the efficiency of decision making units. Eur J Oper Res. 1978 Nov 1; 2(6):429–444.

17.

Estellita

Lins MP

, Angulo-Meza

, Moreira da Silva

. A multi-objective approach to determine alternative targets in data envelopment analysis. J Oper Res Soc. 2004 Oct 1; 55(10):1090–1101.

18.

Makuei

, Alinezhad

, . A goal programming method for finding common weights in DEA with an improved discriminating power for efficiency. J Ind Syst Eng. 2008; 1(4):293–303.

19.

Alinezhad

, KIANI

. Practical common weights goal programming approach for technology selection. Math Sci. 2009; 3(2):201–212.

20.

Stewart

. Goal directed benchmarking for organizational efficiency. Omega. 2010 Dec 1; 38(6):534–539.

21.

Vaisi. The superiority of DEAGP in ranking decision making units over DEA-AHP method: Utilizing relative closeness to ideal decision making units. Manag Sci Lett. 2012; 2(8):2903–3908.

22.

Vaisi

Ebrahimi A

. Utilizing Computer Simulation and DEAGP to Enhance Productivity in a Manufacturing System. Int J Data Envel Anal. 2015 Nov 1; 3(4):857–866.

23.

Tavana

, Shabanpour

, . A hybrid goal programming and dynamic data envelopment analysis framework for sustainable supplier evaluation. Neural Comput Appl. 2017 Dec; 28(12):3683–3696.

24.

Vaisi

. Productivity improvement in a manufacturing system using computer simulation: A comparison between DEA and DEAGP. Recent Applications of Data Envelopment Analysis. 2017 Oct; 210.

25.

Roll

, Cook

, Golany

. Controlling factor weights in data envelopment analysis. IIE Trans. 1991 Mar 1; 23(1):2–9.

26.

Hastie

, Tibshirani

. Generalized additive models. Routledge; Chapman & Hall/CRC, 1990.

27.

Eling

, Luhnen

. Frontier efficiency methodologies to measure performance in the insurance industry: Overview, systematization, and recent developments. Geneva Pap Risk Insur: Issues Pract. 2010 Apr; 35(2):217–265.

28.

Leverty

, Grace

. The robustness of output measures in property-liability insurance efficiency studies. J Bank Financ. 2010 Jul 1;34(7):1510–1524.

29.

Hancock

. The financial firm: Production with monetary and nonmonetary goods. J Polit Econ. 1985 Oct 1;93(5):859–880.

30.

Berger

, Hanweck

, Humphrey

. Competitive viability in banking: Scale, scope, and product mix economies. J Monet Econ. 1987 Dec 1;20(3):501–520.

31.

Berger

, Humphrey

. Measurement and efficiency issues in commercial banking. In: Griliches

(ed) Output measurement in the service sectors. 1992 Jan 1. Chicago, IL: University of Chicago Press, 245–300.

32.

Jarraya

, Bouri

. Efficiency concept and investigations in insurance industry: A survey. Manag Sci Lett. 2013; 3(1):39–54. https://mpra.ub.uni-muenchen.de/53544/