Rating Liberalization and Efficiency: Evidence from the Property-Liability Insurance Industry

Abstract

The property-liability insurance market in Taiwan has implemented three-stage deregulation on rate-making since 2002. This research investigates whether the rating liberalization brought about improvements in efficiency and productivity of the property-liability insurance market. Using data on property-liability insurers in Taiwan over 2001 to 2019 and employing data envelopment analysis, we show that technical, cost, and revenue efficiencies have improved after rating liberalization. Post-liberalization productivity has improved as well, and the decomposition of productivity change demonstrates that change in technology contributes most to productivity improvement at the inception of liberalization, and the contribution of efficiency improvement follows when rating controls are further released. Further analyses reveal that technical and revenue efficiency rose in the third stage of liberalization and cost efficiency improved in the second and third stages. Our findings suggest that the removal of price controls creates an operating environment with less restrictions and thus favors progress in efficiency of the property-liability insurance market.

1. Introduction

The financial services industry is traditionally highly regulated because its soundness is intimately associated with a nation’s economic and social development. To promote competition and improve market efficiency, and partly because of the wave of globalization, deregulation or liberalization in the financial services industry (e.g., opening markets or releasing controls in operation) has continuously taken place worldwide. Investigations on the effect of regulation change on market efficiency or corporate operations have therefore proceeded continuously, yet there are no uniform conclusions (Hussels & Wald, 2007; Reyna & Fuentes, 2018; Turchetti & Daraio, 2004; Cummins & Rubio-Misas, 2006; Jeng & Lai, 2008; Weiss & Choi, 2008; Rees & Kessner, 2002; Boonyasai et al., 2002). Whether deregulation or liberalization does improve efficiency of the financial services market is thus a very popular topic in the related literature.

The insurance industry is regulated in many dimensions of business as well as financial operation such as policy design, rate-making, reserve requirement, investments, and so on. Restrictions imposed by the authorities may restrain insurers from operating more efficiently, e.g., setting more competitive prices or pursuing more profitable investments. As such, relieving controls should be beneficial for insurers’ operation because insurers can select more advantageous or efficient avenues when they have more discretion in operational activities. In terms of rate-making, the removal of restrictions in premium determination allows insurers to set prices more properly based on their operational results, which could reduce the distortion of prices and promote insurers to seek more efficient operating mode. Operating more efficiently may in turn enable insurers to set more competitive premiums, which could enlarge their market share. Moreover, the removal of rate-making controls may increase market competition, which could bring two possible results. On the one hand, increased market competition may elevate insurers’ operating pressure and adversely affect their performance if insurers cannot react properly to the fierce competition. On the other hand, intense competition may stimulate insurers to actively pursue operational improvements, resulting in a rise in performance. Thus, the effect of rate-making deregulation on insurers’ performance is indeterminate.

This research delves into whether price deregulation improves efficiency as well as productivity of the property-liability insurance market in Taiwan. This market has implemented rating liberalization since 20021, proceeding in a three-stage process that gradually releases controls in rate-making. The action in the first stage released restrictions on loading charge2, a relaxation of the risk premium to a certain extent was adopted in the second stage, and complete liberalization in rate-making was applied in the third stage. The rating liberalization in Taiwan’s property-liability insurance market provides an ideal laboratory for examining the influence of removing controls on efficiency or productivity of a highly regulated industry because the deregulation process proceeds in a step-by-step mode. The deregulation was divided into three stages, and therefore we are able to explore the evolvement in efficiency or productivity across phases. Studies have documented that different degrees of deregulation have divergent effects on insurers’ performance (Rees & Kessner, 2002; Boonyasai et al., 2002), and therefore the deregulation process of Taiwan’s property-liability insurance market provides an excellent opportunity for us to observe how efficiency and productivity differ under various degrees of control relaxation. Furthermore, we could also differentiate sources of productivity improvement in different phases by analyzing productivity change. Our study can thus advance knowledge in the deregulation and efficiency nexus of the insurance sector.

Using data on property-liability insurance firms in Taiwan over 2001 to 2019 and employing data envelopment analysis (DEA), this study computes technical, cost, and revenue efficiency scores and observes the evolvement of these scores across different phases of rating liberalization. The results show that technical efficiency diminished in the beginning of the rating liberalization, but improved later after rating controls were further released. Cost and revenue efficiencies also presented a similar pattern. Moreover, technical and revenue efficiencies generally rose with further relaxation of rating controls, while cost efficiency did not. Regression analyses demonstrate that insurers significantly had better technical and revenue efficiency in the third stage and cost efficiency in the second as well as third stages.

We also employ the Malmquist productivity index to analyze productivity changes brought by rate-making deregulation. The results reveal that the productivity of property-liability insurers improved after rating liberalization. The decomposition of productivity change displays that the post-liberalization productivity gains were attributable to improvements in pure technical efficiency, scale efficiency, and technology in different stages, respectively. Technological progress contributed most to productivity gain in the first stage, advancement in pure technical efficiency contributed most in the second stage, and the three components had a roughly equal contribution in the third stage. The findings imply that regulation change brings about innovation in the technical frontier, and that the effect of regulation change on efficiency improvement is not instant. There is statistical significance in productivity difference in some pairs between different phases.

The findings in this paper echo Turchetti and Daraio (2004), Cummins and Rubio-Misas (2006), and Jeng and Lai (2008) who documented a favorable effect of deregulation or liberalization on productivity improvement of the insurance industry. Turchetti and Daraio (2004) and Cummins and Rubio-Misas (2006) showed that deregulation constitutes a key component of efficiency or productivity improvement in Italy’s motor insurance industry and in the Spanish insurance industry, respectively. The two studies documented the positive effect of deregulation on insurers’ performance in developed economies, while this article demonstrated that the performance of the property-liability insurance industry improves after deregulation in Taiwan, suggesting that deregulation benefits the insurance sector in an emerging economy as well. Our study thus makes a contribution by enhancing academics’ and practitioners’ knowledge in this subject. On the other hand, Jeng and Lai (2008) explored the influence of a multi-stage liberalization of market entry on efficiency and productivity in Taiwan’s life insurance industry, while we look at property-liability insurers’ efficiency and productivity after liberalization of rate-making. Our study thus complements that of Jeng and Lai and promotes deeper understanding of Taiwan’s insurance market.

The rest of the paper is as follows: Section 2 states rating liberalization in Taiwan’s property-liability insurance market and reviews related literature. Section 3 describes data and methodology. Section 4 presents empirical results. Section 5 concludes the study.

2. Background and Related Literature

2.1. Rating Liberalization in Taiwan’s Property-Liability Insurance Market

The property-liability insurance market in Taiwan had undertaken mandated rates over a long period of time. Insurers have to follow rates approved by the authority when determining a product price, and thus they are not able to set the price competitively according to their operating performance. Under such a circumstance, efficiently performing insurers cannot acquire more advantages from the market owing to their good operational outcomes, and mandated rates are therefore equivalent to providing a protective umbrella for insurers with an inferior performance. This may be unfavorable for the healthy development of the market.

To promote market development, the insurance authority of Taiwan decided to deregulate rate-making of property-liability insurers starting in 2002. Rating liberalization was divided into three phases that gradually released controls in rate determination. The first phase was effective from 1 April 2002 to 31 March 2005. In this stage, the focus was on the relaxation of loading charge, except for policy-based insurance like compulsory automobile liability insurance and household earthquake insurance, while the risk premium was still rate-regulated. To be specific, insurers were allowed to determine freely, under a total amount control, the loading of major lines of business such as voluntary automobile insurance, household fire insurance, and commercial fire insurance, while mandated rates were still applied to the risk premium. In reviewing new products and corresponding rates, prior approval was adopted for personal lines, and a use and file procedure was applied to commercial lines.

The second phase became effective from 1 April 2005 to 31 March 2009. In this stage, in addition to maintaining measures in the first phase, restrictions on determination of risk premium were relaxed moderately. Although mandated rates of major lines were not completely discarded yet, insurers were allowed to set a risk premium that deviated from the mandated rates within a range of 10–30% based on their actuarial as well as statistical data. The review of new products and corresponding rates adopted a use and file procedure in principle, unless the authority deemed that prior approval should be taken.

Since 1 April 2009, the property-liability insurance market in Taiwan has formally entered the third phase of rating liberalization. All mandated rates were basically canceled, though there were still reference rates established by the Taiwan Insurance Institute. Insurers can determine rates freely without prior approval from the authority, except for policy-based insurance such as compulsory automobile liability insurance and household earthquake insurance.

After rating liberalization, property-liability insurers in Taiwan can determine product prices based on their loss and expense experiences. A less restrictive environment might be beneficial for insurers to increase their performance. As rating liberalization in the Taiwan property-liability insurance market is a multi-step process, we explore differences in efficiency and productivity under different degrees of control release.

2.2. Related Literature

From a theoretical or intuitive perspective, stringent regulation should exert an adverse impact on insurers’ efficiency performance as regulative actions may bind insurers’ hands in the pursuit of profitability activities. Extant studies, however, have not empirically documented a uniformly deterrent effect of stringent regulation such as capital on insurers’ efficiency. Regarding the influence of capital regulation on efficiency, for instance, Ryan and Schellhorn (2000) showed that a more stringent capital regulation did not exert an adverse influence on life insurers’ efficiency in the 1990s in the United States, while Lim et al. (2021) documented that efficiency and productivity of conventional insurers deteriorate after the implementation of new regulative measures in the Malaysian insurance market. The evidence reveals that regulation exerts a divergent effect on insurers’ efficiency across different jurisdictions.

In contrast, whether deregulation benefits the rise in insurers’ performance remains inconclusive. Deregulation covers a wide range of control-releasing measures, e.g., the removal of rate-making control or the entry barrier. On the one hand, deregulation may favor insurers’ performance as the relaxation of regulative measures could grant insurers with more space to operate in more efficient ways. On the other hand, deregulation may result in a more competitive environment, which may be disadvantageous for insurers to increase performance. Some studies showed that competition did rise after deregulation (Sinha, 2024; Zheng et al., 2022). Regarding insurers’ efficiency performance after deregulation, although some studies did not find a significant association between deregulation and insurers’ efficiency or productivity (Hussels & Wald, 2007; Reyna & Fuentes, 2018), more researchers found that deregulation improves insurers’ performance (Turchetti & Daraio, 2004; Cummins & Rubio-Misas, 2006; Jeng & Lai, 2008; Weiss & Choi, 2008; Rees & Kessner, 2002; Boonyasai et al., 2002). Moreover, the impact of deregulation on insurers’ efficiency performance varies as well depending on the extent of deregulation. For instance, Rees and Kessner (2002) found that deregulation has a positive effect on life insurers’ efficiency, whether the market is highly or only lowly regulated. Boonyasai et al. (2002) showed that the extent of deregulation affects life insurers’ operational efficiency, with a higher magnitude of deregulation resulting in more improvement of efficiency. The studies above covered different economies and showed that the effect of deregulation differs across countries, suggesting that how deregulation impacts insurers’ efficiency or productivity may depend on country-specific environments.

Studies regarding the efficiency of Taiwan’s insurance market mostly focused on the life insurance sector. Jeng and Lai (2008) demonstrated that deregulation and liberalization improved life insurers’ productivity and that the change in the extent of liberalization and deregulation over different periods had a differential effect on insurers’ efficiency and productivity. Boonyasai et al. (2002) yet found that liberalization alone did not significantly improve the efficiency of life insurers in Taiwan. The studies above revealed that deregulation or liberalization does not uniformly exert a positive influence on efficiency or productivity of the insurance industry. Even for identical countries, inconsistent findings were achieved because of different sample periods. This implies that there might be a time-variant association between deregulation or liberalization and insurers’ performance.

The aforementioned studies mostly focused on the life insurance sector, and relatively few studies have been devoted to investigating the efficiency performance of the property-liability insurance industry after deregulation. Given the difference in the operational attribute between life and property-liability insurance, the property-liability insurance sector should not be neglected. This study explores property-liability insurers’ efficiency and productivity after deregulation in rate-making and thus can enhance the understanding of the academic community in this subject.

3. Data and Methodology

This paper focuses on domestic property-liability insurance firms of Taiwan because branches of foreign insurance firms only account for a tiny share of the market and many of them have left Taiwan in recent years. Moreover, the number of domestic property-liability insurers decreased as well after several mergers or acquisitions. Our final sample consists of 13 domestic insurers over 2001 to 2019. The market share of the 13 firms in terms of premium income during the sample period ranged between 83% and 98% in a roughly increasing trend with the share uniformly higher than 95% since 2008. Therefore, our sample can virtually represent the property-liability insurance market in Taiwan. We refer to efficiency studies on the insurance industry below to determine output as well as input factors.

3.1. Outputs and Output Prices

When evaluating outputs of financial institutions, three approaches are commonly utilized: financial intermediation, user cost, and value-added (Berger & Humphrey, 1992). Among them, the value-added approach is more consistent with traditional measures of insurers’ performance (Leverty & Grace, 2010) and is predominantly adopted in efficiency research on the insurance industry.3 As such, this article utilizes the value-added approach to choose insurers’ outputs. Based on such an approach, insurers mainly offer three types of services: risk pooling/bearing, financial services, and financial intermediation (Cummins & Xie, 2013). For property-liability insurers, losses incurred are an appropriate proxy related to risk pooling/bearing and financial services, and the value of invested assets is a proper proxy for the intermediation function (Cummins & Rubio-Misas, 2006; Berger et al., 1997). We thus adopt incurred losses and invested assets as the output factors. Incurred losses are defined as claims plus additions to reserves. Invested assets are investments in various financial instruments as presented on a balance sheet, including marketable securities, real estate, loans, and so on.

For output prices, the price of losses incurred can be defined as the ratio of the difference between premiums earned and losses incurred to losses incurred (Färe et al., 1992; Hussels & Wald, 2007; Jeng & Lai, 2005). We follow this definition by estimating the price of losses incurred by subtracting losses incurred from premium earned and dividing the difference by losses incurred. The return on invested assets is usually taken as the price of invested assets. We gauge the price of invested assets by dividing net investment income by invested assets. Data on outputs and output prices come from Insurance Year Book of Taiwan and annual reports of insurance firms.

3.2. Inputs and Input Prices

Insurance inputs are commonly assessed in the literature with three items: labor, business services, and capital (Cummins & Rubio-Misas, 2006; Eling & Luhnen, 2010; Berger et al., 1997; Cummins & Nini, 2002; Cummins & Xie, 2008, 2013; Berger et al., 2000; Cummins et al., 2004; Jeng & Lai, 2005; Tone & Sahoo, 2005; Jeng et al., 2007). Following related studies and depending on data availability, we chose an adequate proxy for these input factors. Labor input is measured by the number of employees. We measure business services by dividing operating expenses that exclude employees’ total salaries by the price index of the service industry. Capital input is measured by equity capital, which is proxied by shareholders’ equity. For input prices, we measure the labor price by total annual salaries, which equal the average monthly salary of the property-liability industry in Taiwan multiplied by the number of employees and twelve. The price of business services is gauged by the price index of the service industry, and the price of capital input is evaluated by the ratio of net income to shareholders’ equity.

We obtain data on the number of employees from “The largest corporations in Taiwan” published by China Credit Information Service, Ltd. and Taiwan Economic Journal (TEJ) database. Data on other inputs and outputs come from multiple sources, including Insurance Year Book of Taiwan, firms’ annual reports, and Directorate-General of Budget, Accounting and Statistics of Taiwan. To account for any difference in price levels across time, we convert all monetary amounts into 2016 monetary units using the Consumer Price Index of Taiwan.

3.3. Efficiency and Productivity Estimation

Both parametric and non-parametric approaches can be adopted for efficiency estimation. The parametric approach is implemented on an econometric basis that requires specifications in the objective function as well as the error terms, while the non-parametric approach follows a mathematical programming basis with less specification imposed. This study adopts data envelopment analysis, a non-parametric approach, to estimate the efficiency of property-liability insurers because this method is not plagued by any misspecification issue usually suffered in the econometric approach. Moreover, as this study also analyzes productivity change over time using the Malmquist approach that is usually carried out on the DEA basis, the DEA allows us to perform an evaluation in a consistent manner.

Efficiency evaluation adopted herein employs the frontier efficiency concept that measures a firm’s efficiency by its relative performance to “best practice” efficiency frontiers of the industry. Efficiency scores range between 0 and 1, where a score of 1 represents full efficiency and a score less than 1 signifies inefficiency. We compute technical, cost, and revenue efficiencies for each firm of our sample and observe the overall evolvement of these efficiencies over time.

In efficiency assessment, there are different assumptions regarding the types of production scale such as constant returns to scale (CRS), variable returns to scale (VRS), and non-increasing returns to scale (NIRS). The CRS assumption implies that all firms are operating at an optimal scale. However, Coelli et al. (2005) indicate that the attainment of the optimal scale may be hindered by frictions such as imperfect competition, regulations, and financial constraints. They note that the CRS specification may confound technical efficiency with scale efficiency when the condition of all firms’ achieving optimal scale is not accomplished, and the VRS assumption is more appropriate in such a circumstance. Although deregulation in rate-making may improve insurers’ operation owing to more pricing flexibility, there are still other regulative measures that may confine insurers’ capability to attain the optimal scale. Therefore, we adopt the VRS assumption in the estimation of efficiencies.

The evolvement of efficiency scores over time can be used to observe progress or regress of efficiency, but it cannot be applied to inspect productivity growth because the shift in the frontier is not taken into account (Cummins & Rubio-Misas, 2006). We utilize Malmquist productivity analysis to tackle this issue. The Malmquist index of total factor productivity is often applied to explore productivity change, which can further be decomposed into different components such as changes in technical efficiency, technology, as well as scale efficiency.4 The estimation regarding efficiency and productivity mentioned above are all obtained using the FEAR software package compiled by Wilson (2008). To check the statistical significance of the difference in efficiency and productivity change between different liberalization phases, we adopted the Wilcoxon signed rank test, which is a non-parametric statistical approach, due to the small sample.

3.4. Regression Analysis

After estimating efficiency scores, we explore the association between rating liberalization and efficiency through regression analysis. To deeply examine the impact of the extent of control removal in rate-making on efficiency, we specify the following models:

$${ES}_{it}={\alpha }_0+{\alpha }_{1}LIBER+{\alpha }_m{X}_{it}+{\epsilon }_{it}$$

(1)

$${ES}_{it}={\beta }_0+{\beta }_{1}Phase\_I+{\beta }_{2}Phase\_II+{\beta }_{3}Phase\_III+{\beta }_m{X}_{it}+{\epsilon }_{it}$$

(2)

$${ES}_{it}={\gamma }_0+{\gamma }_{1}Phase\_II+{\gamma }_{2}Phase\_III+{\gamma }_m{X}_{it}+{\epsilon }_{it}$$

(3)

$${ES}_{it}={\delta }_0+{\delta }_{1}Phase\_III+{\delta }_m{X}_{it}+{\epsilon }_{it}$$

(4)

where ES denotes efficiency scores, including technical, cost, and revenue efficiency; LIBER is a dummy variable equal to 1 for the liberalization period from 2003 to 2019 and 0 otherwise; Phase_I is a dummy variable equal to 1 for the first stage liberalization spanning from 2003 to 2005 and 0 otherwise; Phase_II is a dummy variable equal to 1 for the second stage liberalization spanning from 2006 to 2009; Phase_III is a dummy variable equal to 1 for the third stage liberalization spanning from 2010 onward; X_it is a vector of control variables; ε_it is random error term, and the subscript i denotes insurance firm and t stands for the time period. Referring to the literature and accounting for data completeness, this paper selects firm age, firm size, the ratio of premiums to equity, and whether the insurer is a member of a financial holding company as control variables. Firm age is the age of the insurance firm, firm size is proxied by the natural logarithm of firm’s total assets, and a dummy variable is utilized to identify insurer’s affiliation.

In the two-stage estimation of the impact of environmental variables on efficiency scores estimated by data envelopment analysis, Banker et al. (2019) demonstrated that ordinary least squares (OLS) performs relatively better as compared to other estimation methods such as tobit or truncated regression. Therefore, we adopt OLS in parameter estimation of liberalization dummies as well as control variables. A significantly positive α₁ in Equation (1) signifies that the removal in rate control raises insurers’ efficiency. A significantly positive β₁, β₂, or β₃ in Equation (2) represents that different extent of control removal in rate-making can favor the rise in efficiency as compared with regulatory rates because the base group is the pre-liberalization period. The specification of Equations (3) and (4) renders us to further examine the impact of step-by-step rating liberalization because the effect of removing control may not appear apparently at the earlier stage. A significantly positive γ₁ or γ₂ in Equation (3) indicates that insurers’ efficiency performs better in the second or third stage of rating liberalization as compared to the pre-liberalization and the first stage. A significantly positive δ₁ in Equation (4) represents that it is the third stage of liberalization that noticeably heightens insurers’ efficiency.

4. Results and Discussion

This section presents the results on efficiency and productivity changes across years and different phases of rating liberalization. We also test if there is a statistically significant difference in efficiency as well as productivity changes between different phases. We first look at the contents of output and input items for efficiency and productivity computation.

Table 1. Descriptive statistics of outputs and inputs and corresponding prices.

	Whole Period	Pre-L	Phase I	Phase II	Phase III
Output (million NT dollars)
Loss incurred	3591	2318	3008	3421	4088
Invested assets	10,094	6808	8342	8796	11,797
Output prices
Loss incurred	0.77	0.50	0.67	0.70	0.88
Invested assets	0.06	0.10	0.07	0.08	0.04
Input
Labor	1071	869	978	1062	1142
Business services (million NT dollars)	1099	762	959	1099	1208
Equity capital (million NT dollars)	6771	6606	6612	5284	7447
Input prices
Labor (million NT dollars)	774	596	692	727	845
Business services	0.96	0.91	0.91	0.94	0.99
Equity capital	0.10	0.06	0.09	0.10	0.11
Number of firms	13	13	13	13	13

Notes: The table reports averages of output, output price, input, and input price for different periods. Monetary variables are expressed in 2016 monetary values based on Taiwan’s consumer price index. Pre-L denotes the period before rating liberalization, the period of Phase I is from 2003 to 2005, the period of Phase II is from 2006 to 2009, and the period of Phase III is from 2010 to 2019.

reports summary statistics of outputs and inputs.

The results of outputs and inputs, except for equity capital, reveal an increasing tendency across phases, indicating that property-liability insurance firms in Taiwan enlarged their operation over time. The decrease in equity capital in the second stage might be caused by the global financial tsunami during 2008 and 2009. Output and input prices, except for the price of invested assets, also present a rising trend. The price for losses incurred did not diminish with the rating liberalization. One possible explanation is that insurers can adjust premiums correspondingly and quickly reflect losses when they have more discretion in price determination.

4.1. Efficiency Analyses

Table 2. Efficiency scores across years.

Year	Technical Efficiency	Cost Efficiency	Revenue Efficiency
2001	0.9471	0.7969	0.8914
2002	0.9661	0.7809	0.9334
2003	0.9506	0.7143	0.8567
2004	0.9437	0.7684	0.9296
2005	0.9372	0.8896	0.9072
2006	0.9731	0.8838	0.9321
2007	0.9602	0.8893	0.8823
2008	0.9618	0.9401	0.9197
2009	0.9853	0.9112	0.9195
2010	0.9914	0.8644	0.9570
2011	0.9788	0.8262	0.9567
2012	0.9906	0.8458	0.9612
2013	0.9729	0.8275	0.9451
2014	0.9512	0.8052	0.9286
2015	0.9776	0.8223	0.9451
2016	0.9835	0.8483	0.9500
2017	0.9635	0.9082	0.9343
2018	0.9737	0.9301	0.9684
2019	0.9820	0.9298	0.9763

Note: The table reports average efficiency scores across years calculated by data envelopment analysis with variable returns to scale.

presents technical, cost, and revenue efficiency scores across years assessed based on variable returns to scale (VRS). The results show that technical efficiency was high and remained stable during the sample period, suggesting that property-liability insurers in Taiwan had operated at a technical level close to the best practice. High technical efficiency scores were similar to those in Jeng and Lai’s (2008) study for life insurance insurers in Taiwan. The technical efficiency scores in the post-liberalization period were mostly higher than those of the pre-liberalization period, suggesting that insurers experienced a slight improvement in technical efficiency after rating liberalization. The improvement was more apparent in cost efficiency where the efficiency scores in the post-liberalization period, except for 2003 and 2004, were higher than those of the pre-liberalization period. The better cost efficiency suggests that deregulating rate-making makes it more efficient for insurers to control the operational cost. Revenue efficiency reveals that the post-liberalization revenue efficiency scores were generally higher than the pre-liberalization ones after 2009. The improvement in revenue efficiency suggests that more discretion in rate-making could render insurers to offer more competitive premiums and therefore increase insurers’ revenues. The results overall indicate that a release of price control could increase flexibility of insurers’ operations and therefore improve their operating efficiency.

To explore efficiency difference under various degrees of liberalization, we compute average efficiency scores in different phases and examine the statistical significance. The results appear in

Table 3. Efficiency scores across phases of rating liberalization.

Panel A: Mean efficiency scores across different phases
Phase	Technical efficiency	Cost efficiency	Revenue efficiency
Pre-L	0.9566	0.7893	0.9106
Phase I	0.9438	0.7887	0.8970
Phase II	0.9701	0.9036	0.9129
Phase III	0.9765	0.8607	0.9523
Phase III a	0.9869	0.8445	0.9584
Panel B: Wilcoxon signed rank test for efficiency differences between phases
Pre-L vs. Phase I	0.6750	–	–
Pre-L vs. Phase II	1.0000	–	–
Pre-L vs. Phase III	0.9057	–	–
Pre-L vs. Phase III a	0.4017	–	–
Phase I vs. Phase II	0.3525	–	–
Phase I vs. Phase III	0.4772	–	–
Phase I vs. Phase III a	0.1422	–	–
Phase II vs. Phase III	1.0000	–	–
Phase II vs. Phase III a	0.1056	–	–

Notes: The table reports efficiency across phases and tests of difference in efficiency between different phases. Panel A reports average efficiency scores in different phases calculated by data envelopment analysis with variable returns on scale, and Panel B presents p-values of the Wilcoxon signed rank test for efficiency differences between phases. Pre-L denotes the period before rating liberalization, the period of Phase I is from 2003 to 2005, the period of Phase II is from 2006 to 2009, and the period of Phase III is from 2010 to 2019. Phase III ^a denotes the period from 2010 to 2012. We did not perform the Wilcoxon signed rank test for a paired sample for cost and revenue efficiency due to unbalanced data.

. Panel A of Table 3 shows that technical efficiency scores in the first stage are on average lower and those in the second and third stage are higher than the pre-liberalization scores. This suggests that technical efficiency diminished in the beginning of the rating liberalization but improved when the rate control was further released compared to the pre-liberalization period. Similar results are observed in cost and revenue efficiencies. Moreover, technical and revenue efficiencies rose stably with further relaxation in rate control, while cost efficiency did not, though it still performed better than the pre-liberalization period. This implies that cost control might be a concern when property-liability insurers in Taiwan are granted more discretion in price determination.

As each of the early two stages consisted of a roughly three-year period and there are more observations in the third stage in our sample, we also computed average efficiency scores for the first three years of the third stage to make a comparison. As can be seen, the technical and revenue efficiency are higher than those of the early two stages when we only observe the first three-year period of the complete rating liberalization. The cost efficiency in the first three-year period of the third phase is higher than those of the pre-liberalization period and of the first phase. The results overall suggest that rating liberalization did improve the operating efficiency of property-liability insurers in Taiwan. Panel B of Table 3 presents paired sample testing results of the Wilcoxon signed rank test. The results show no statistically significant difference in efficiency between different phases. We further examined the impact of different phases on efficiency later.

4.2. Productivity Analyses

The efficiency analyses above are able to capture the “catching-up” of insurers’ operation to the efficiency frontier, but cannot evaluate if an innovation (e.g., technological change) brings about productivity change. In this sub-section, we utilize the Malmquist productivity index to analyze productivity change brought by deregulation in rate-making. In the evaluation of sources of productivity change, Färe et al. (1992) decomposed productivity change into changes in efficiency and technology. Färe et al. (1994) further decomposed efficiency change into alterations in pure efficiency and scale efficiency, and thus productivity change can virtually be decomposed into three aspects: pure technical efficiency, scale efficiency, and technology.

To conduct a thorough observation, we adopt the methodology proposed by Färe et al. (1994) to decompose productivity change into alterations in pure technical efficiency, scale efficiency, and technology. Indices with numbers greater than one represent progress and those less than one represent regress. We first look at productivity indices across years.

Table 4. Malmquist productivity indices across years.

Index	TFP Change	Change in Pure Efficiency	Change in Scale Efficiency	Change in Technology
2002	0.9689	1.0263	0.9660	0.9793
2003	1.0443	0.9944	1.0133	1.0438
2004	1.0898	0.9923	1.0240	1.0751
2005	1.0911	0.9924	1.0233	1.0853
2006	1.0736	1.0557	1.0172	0.9516
2007	1.0496	0.9858	0.9878	1.0785
2008	1.0716	1.0012	1.0099	1.0625
2009	0.9336	1.0322	0.9954	0.9083
2010	0.9965	1.0068	1.0212	0.9710
2011	0.9289	0.9861	0.9903	0.9485
2012	1.0468	1.0150	1.0123	1.0187
2013	0.9449	0.9817	0.9842	0.9786
2014	1.0460	0.9750	1.0045	1.0695
2015	1.0541	1.0356	0.9955	1.0227
2016	1.0305	1.0064	1.0094	1.0130
2017	0.9625	0.9783	1.0090	0.9747
2018	1.0104	1.0143	0.9774	1.0213
2019	0.9979	1.0100	0.9968	0.9921

Notes: The table reports total factor productivity changes across years. The Malmquist productivity index and its components are calculated and decomposed based on the procedure proposed by Färe et al. (1994).

shows that total factor productivity did grow when rating liberalization came into play in 2003, and it continued to grow year by year during the first phase, i.e., from 2003 to 2005. Productivity also improved in most years after liberalization. The results thus suggest that rating liberalization could advance productivity of property-liability insurers. Further looking at components of the Malmquist index, we find that productivity improvement was derived from thet change in pure technical efficiency, scale efficiency, and technology that arose in different years, respectively. This implies that the relaxation of price control changes the operating environment of the insurance market, and that a more flexible pricing mechanism increases flexibility of insurers’ operations, in turn improving their productivity.

To observe if the productivity change across different phases presents any significant difference, we calculate the average Malmquist index and its components in different phases and perform a paired sample test using the Wilcoxon signed rank test. The results are presented in

Table 5. Malmquist productivity indices across phases of rating liberalization.

Index	TFP Change	Change in Pure Efficiency	Change in Scale Efficiency	Change in Technology
Panel A: Mean productivity indices across different phases
Pre-L	0.9689	1.0263	0.9660	0.9793
Phase I	1.0751	0.9930	1.0202	1.0681
Phase II	1.0321	1.0187	1.0026	1.0002
Phase III	1.0018	1.0009	1.0001	1.0010
Phase III a	0.9907	1.0027	1.0079	0.9794
Panel B: The Wilcoxon signed rank test for productivity differences between phases
Pre-L vs. Phase I	0.0479 **	0.5294	0.0423 **	0.0398 **
Pre-L vs. Phase II	0.3757	0.6750	0.2240	0.6355
Pre-L vs. Phase III	0.3396	0.2863	0.1467	0.3757
Pre-L vs. Phase III a	0.6355	0.2945	0.0185 **	1.0000
Phase I vs. Phase II	0.1465	0.4469	0.1698	0.0215 **
Phase I vs. Phase III	0.0046 ***	1.0000	0.0653 *	0.0005 ***
Phase I vs. Phase III a	0.0002 ***	1.0000	0.6891	0.0002 ***
Phase II vs. Phase III	0.4973	0.2361	0.5049	0.2163
Phase II vs. Phase III a	0.6848	0.6750	1.0000	0.9460

Notes: The table reports total factor productivity changes across phases and tests of differences in productivity indices between phases. Panel A presents the Malmquist productivity index and its components, and Panel B presents the p-values of the Wilcoxon signed rank test for productivity differences between phases. The Malmquist productivity index and its components are calculated and decomposed based on the procedure proposed by Färe et al. (1994). Pre-L denotes the period before rating liberalization, the period of Phase I is from 2003 to 2005, the period of Phase II is from 2006 to 2009, and the period of Phase III is from 2010 to 2019. Phase III ^a denotes the period from 2010 to 2012. *** denotes a significance level of 1%, ** denotes a significance level of 5%, and * denotes a significance level of 10%.

. The second column in Panel A of Table 5 displays that pre-liberalization productivity experienced regress, and the productivity improved during the post-liberalization period, although the average growth rate decreased from 7.51% in the first phase to 0.18% in the third phase. As the early two stages of liberalization consisted of a roughly three-year period, we compute the productivity index for the first three years of the third phase (i.e., from 2010 to 2012) to make a comparison. The results show that productivity declined at a rate of 0.93%, meaning that productivity fell in the beginning of full liberalization in rate-making. For this outcome, we speculate that because rate control in Taiwan’s property-liability insurance market was loosened step-by-step, the impact of liberalization should be most apparent at its initiation and might then decrease gradually with an increase in competitive intensity.

With respect to components of productivity change, columns 3 to 5 in Panel A of Table 5 reveal that the post-liberalization productivity gains are attributable to improvements in pure technical efficiency, scale efficiency, and technology, among which some patterns could be observed. In the first stage of liberalization, technological progress contributed most to productivity gain. For this, we conjecture that regulation change would alter the operating environment and therefore bring about innovation in the technical frontier. The regress in pure technical efficiency also reflects a relatively lower technical efficiency score in the first stage, as presented in Table 3.

In the second stage, the productivity gain was derived from the three components in which the advancement in pure technical efficiency contributed most and the contribution of technological innovation, compared to the first stage, diminished materially. For this outcome, one possible explanation is that improvement in operating efficiency might not appear instantly at the inception of liberalization. In the third stage of full liberalization, the three components all contributed to productivity progress as well, although the extent was lower compared to the prior two stages. The last row of Panel A shows that the productivity regress in the first three years of the third stage was attributable to technological regress. We speculate that this is because the marginal effect of regulation change on the technical frontier might diminish gradually through a multi-stage process. As a whole, the results support that deregulation in rate-making favors property-liability insurers’ operation.

Panel B of Table 5 presents paired sample testing results of the Wilcoxon signed rank test. To explore whether there is a difference in the effect of liberalization on productivity change under a step-by-step process, we perform tests between different phases. The results show that pre-liberalization productivity change has a statistically significant difference at the 5% significance level only with the productivity change in the first stage. This is consistent with our speculation above that changes in insurers’ operation induced by regulative alteration would be most apparent at its inception. It also reveals that the difference in productivity change resulted mainly from the difference in change in scale efficiency and technology. The difference in productivity change between the first and third phases is statistically significant as well at the 1% significance level, and the difference took place mainly in technical change. As the two stages are characterized by a least and complete liberalization, respectively, it suggests that the difference in magnitude of regulative release brings about various degrees of technical innovation.

4.3. Regression Results

The aforementioned analyses reveal that insurers’ technical, cost, and revenue efficiencies improved after the control in rate-making was further loosened during a step-by-step deregulating process, though the improvement did not take place at the inception of deregulation. In this section, we examine whether different stages of rating liberalization do exert divergent impacts on efficiency through regression analyses. Different models are specified to identify the association between liberalization and efficiency.

Table 6. Regression for technical efficiency.

	Model 1	Model 2	Model 3	Model 4
LIBER	0.017
	(0.023)
Phase_I		−0.011
		(0.028)
Phase_II		0.017	0.024
		(0.024)	(0.015)
Phase_III		0.033	0.039 ***	0.028 ***
		(0.024)	(0.015)	(0.010)
Firmage	−0.000 *	−0.000 *	−0.000 *	−0.000
	(0.000)	(0.000)	(0.000)	(0.000)
Firmsize	−0.006	−0.017 **	−0.017 **	−0.013 **
	(0.007)	(0.007)	(0.007)	(0.007)
PmSurplus	0.000	0.000 *	0.000 *	0.000 *
	(0.000)	(0.000)	(0.000)	(0.000)
Affiliated	0.047 ***	0.053 ***	0.053 ***	0.051 ***
	(0.008)	(0.009)	(0.009)	(0.008)
Constant	1.047 ***	1.219 ***	1.216 ***	1.162 ***
	(0.118)	(0.116)	(0.115)	(0.115)
Observations	246	246	246	246
Adi-$R^2$	0.059	0.084	0.087	0.081

Notes: LIBER is a dummy variable that equals 1 for rating the liberalization period of 2003 to2019 and 0 otherwise. Phases I, II, and III are a dummy variable that equals 1 for the period from 2003 to 2005, from 2006 to 2009, and from 2010 afterwards, respectively, and 0 otherwise. Firmage denotes the age of the insurance firm; Firmsize is the natural logarithm of total assets of the firm; PmSurplus is the ratio of direct premiums written to equity; Affiliated is a dummy variable that equals 1 if the insurance firm is a member of a financial holding company and 0 otherwise. Robust standard errors in parentheses. *** significant at the 1% level; ** significant at the 5% level; * significant at the 10% level.

presents the results of regressing technical efficiency on liberalization as well as control variables. In Model 1, where the dummy variable of rating liberalization only separates the pre-liberalization and liberalization period, the result shows that rating liberalization is not significantly correlated with insurers’ technical efficiency. Therefore, the effect of liberalization on technical efficiency is not observed when the extent of relieving rate control is not taken into account. When liberalization is broken down into different stages, some link of the extent of control relief with technical efficiency arises. Although Model 2 shows that the coefficients of all liberalization phases are still insignificant, the difference emerges in other specifications. In Model 3, where the base group covers the period of pre-liberalization and the first stage liberalization, the result shows that the coefficient for the third stage of liberalization is positive and statistically significant. In Model 4, in which the base group covers the period of pre-liberalization, the first and second stages of liberalization, the result also displays that the coefficient of the third stage of liberalization is significantly positive. The findings overall indicate that technical efficiency of property-liability insurers in Taiwan improved in the third stage of rating liberalization, suggesting that a complete removal of rate control is beneficial for the rise in insurers’ technical efficiency.

Table 7. Regression for cost efficiency.

	Model 1	Model 2	Model 3	Model 4
LIBER	0.074 **
	(0.032)
Phase_I		0.034
		(0.038)
Phase_II		0.146 ***	0.124 ***
		(0.032)	(0.021)
Phase_III		0.064 **	0.043 **	−0.014
		(0.032)	(0.021)	(0.016)
Firmage	−0.003 ***	−0.003 ***	−0.003 ***	−0.003 ***
	(0.001)	(0.001)	(0.001)	(0.001)
Firmsize	0.005	0.001	0.002	0.019
	(0.014)	(0.012)	(0.012)	(0.013)
PmSurplus	−0.001 ***	−0.001 ***	−0.001 ***	−0.001 ***
	(0.000)	(0.000)	(0.000)	(0.000)
Affiliated	0.110 ***	0.111 ***	0.110 ***	0.102 ***
	(0.018)	(0.016)	(0.016)	(0.018)
Constant	0.985 ***	1.061 ***	1.067 ***	0.819 ***
	(0.250)	(0.228)	(0.229)	(0.248)
Observations	228	228	228	228
Adi-$R^2$	0.346	0.406	0.405	0.324

Notes: LIBER is a dummy variable that equals 1 for rating the liberalization period of 2003 to2019 and 0 otherwise. Phases I, II, and III are a dummy variable that equals 1 for the period from 2003 to 2005, from 2006 to 2009, and from 2010 afterwards, respectively, and 0 otherwise. Firmage denotes the age of the insurance firm; Firmsize is the natural logarithm of total assets of the firm; PmSurplus is the ratio of direct premiums written to equity; Affiliated is a dummy variable that equals 1 if the insurance firm is a member of a financial holding company and 0 otherwise. Robust standard errors in parentheses. *** significant at the 1% level; ** significant at the 5% level.

presents regression results for cost efficiency. Model 1 shows that the coefficient on rating liberalization is positive and statistically significant at the 5% level, suggesting that property-liability insurers had better cost efficiency after the rate control was removed in Taiwan. After differentiating liberalization phases, as Models 2 to 4 show, we find that cost efficiency rose in the second and third stages of liberalization. The results reveal that rating liberalization exerts a quicker impact in the rise in cost efficiency than that of technical efficiency. Concerning revenue efficiency,

Table 8. Regression for revenue efficiency.

	Model 1	Model 2	Model 3	Model 4
LIBER	0.018
	(0.036)
Phase_I		−0.012
		(0.042)
Phase_II		−0.004	0.003
		(0.039)	(0.028)
Phase_III		0.046	0.053 **	0.052 ***
		(0.037)	(0.025)	(0.019)
Firmage	−0.001 ***	−0.001 ***	−0.001 ***	−0.001 ***
	(0.000)	(0.000)	(0.000)	(0.000)
Firmsize	0.024 **	0.008	0.008	0.009
	(0.011)	(0.012)	(0.012)	(0.011)
PmSurplus	0.000 **	0.000 **	0.000 **	0.000 **
	(0.000)	(0.000)	(0.000)	(0.000)
Affiliated	0.071 ***	0.079 ***	0.080 ***	0.079 ***
	(0.014)	(0.014)	(0.014)	(0.014)
Constant	0.515 ***	0.766 ***	0.762 ***	0.755 ***
	(0.183)	(0.194)	(0.194)	(0.194)
Observations	236	236	236	236
Adi-$R^2$	0.092	0.113	0.117	0.120

Notes: LIBER is a dummy variable that equals 1 for rating the liberalization period of 2003 to 2019 and 0 otherwise. Phases I, II, and III are a dummy variable that equals 1 for the period from 2003 to 2005, from 2006 to 2009, and from 2010 afterwards, respectively, and 0 otherwise. Firmage denotes the age of the insurance firm; Firmsize is the natural logarithm of total assets of the firm; PmSurplus is the ratio of direct premiums written to equity; Affiliated is a dummy variable that equals 1 if the insurance firm is a member of a financial holding company and 0 otherwise. Robust standard errors in parentheses. *** significant at the 1% level; ** significant at the 5% level.

reveals that the influence of rating liberalization on revenue efficiency presents a similar pattern to technical efficiency. The coefficient for the third stage of liberalization is positive and statistically significant in Models 3 and 4 of Table 8, suggesting that insurers had better performance in revenue efficiency in the third stage of liberalization as compared with pre-liberalization as well as other stages.5

The overall results above demonstrate that removing rate control does favor the rise in property-liability insurers’ efficiency, including technical, cost, and revenue dimensions, and the advancement seems more apparent in cost efficiency than in technical and revenue efficiency. The findings also reveal that the rating liberalization in the third stage had a more apparent effect for all three efficiency dimensions of property-liability insurers, suggesting that a greater degree of deregulation in rate-making resulted in a better performance of insurers, including overall operation, cost control, and revenue increase. This implies that deregulation exerts a favorable impact on multiple aspects of insurers’ operation. The authorities should thus relieve regulative controls as much as possible to promote insurers’ performance.

With regard to other control factors, the coefficients on affiliation are uniformly positive and statistically significant across all models, suggesting that insurers affiliated with a financial holding company have better efficiencies, possibly because of the advantage of resource sharing. Firm age is significantly and negatively correlated with efficiency scores in most models, suggesting that operational efficiencies decrease as an insurers age.

5. Conclusions

The property-liability insurance market in Taiwan has implemented rating liberalization since 2002 that was divided into three stages, relieving controls in rate-making through a step-by-step manner. Using data on Taiwan’s property-liability insurance firms over 2001 to 2019 and employing data envelopment analysis as well as the Malmquist productivity analysis, this paper studies whether liberalization in rate-making brought about improvements in efficiency and productivity. Empirical results show that technical, cost, and revenue efficiencies diminished in the beginning of rating liberalization but improved in later phases compared to the pre-liberalization period. Further analyses show that technical and revenue efficiency rose mainly in the third stage of liberalization and cost efficiency improved in the second as well as third stages.

We also find that productivity improved when insurers had more discretion in rate-making during the post-liberalization period. The decomposition of productivity change components revealed that the post-liberalization productivity gains were attributable to improvements in pure technical efficiency, scale efficiency, and technology in different phases. Productivity advancement was derived mainly from technical progress in the first stage, from a rise in pure technical efficiency in the second stage, and from improvements with a roughly equal extent in all three components in the third stage. The findings as a whole support that the removal of rate controls favors property-liability insurers’ operating efficiency and productivity growth.

Although the issue of rate-making deregulation studied in this article is different from other deregulation aspects explored in previous studies, consistent conclusions are reached that deregulation favors insurers’ efficiency or productivity. Our findings display that the removal of rate-making controls can increase insurers’ space in determining more competitive prices and may drive insurers to improve operation to confront elevated market competition. Consequently, to promote better development of the insurance industry, the authorities should relieve various control measures as much as possible under the prerequisite of maintaining the order of the insurance market.