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This study employs flexible Fourier unit root test proposed by Enders and Lee (2012) to examine the regional differences in life insurance market development in China. We find that property of stationarity for life insurance market development varies across different regions. Specifically, stationarity prevails in provinces with middle and low income, indicating characteristics of convergence and the possibilities to forecast future movements of life insurance activities based on past behavior, while 7 out of 10 provinces in high-income group show non-stationarity, suggesting unbound development in these regions and weak predictability. Justifications for the test results are presented from aspects of development of financial market, market structure of life insurance and business strategy of life insurance companies, and implications for policy-making are also given.

Since 1950, the global insurance industry has seen an annual growth rate of over 10%. For the period 1985–2007, the world's total written real insurance premiums have increased by approximately 5.5 times from US$0.63 trillion to US$4.13 trillion, and the life and non-life insurance premiums have increased by approximately 7.5 times and 3.9 times respectively. However, the insurance development in China encountered huge set-back during the planned economy era when “private insurance was neither much needed nor purchased” (Dorfman, 2008) because of the exaggerated use of public funds for coverage of losses, comprehensive social insurance and government ownership of the means of production. Most of the domestic insurance business was shut down before the starting of the policy of reform and opening in 1978. Since then, the economic reform of China has been a spectacular economic success which has generated rapid economic growth over last three decades and the country has moved from a centrally planned economy towards a market economy. Instead of being tightly controlled and centrally planned the economies become market-oriented. Privatization has been at the forefront of the economic transition process when insurance industry is considered. Privatization incentives the development of risk management and growth of insurance demand and at the same time insurance markets became more and more deregulated and liberalized. Insurance industry keeps growing at a high speed. In 2010, the Chinese insurance market had total gross written premiums of $214.3 billion, ranking 6th in the world insurance market, representing a compound annual growth rate (CAGR) of 26.7% between 2006 and 2010. Although domestic insurance markets are still modestly developed in terms of insurance density compared to their western counterparts, insurance premium growth in China has outpaced economic growth and China's insurance industry is playing an indispensable role in supporting reform, protecting economy, stabilizing society and benefiting people. Life insurance, which is thought to have significant function of financial intermediation compared to non-life insurance (Ward and Zurbruegg, 2000), has grown in quantitative importance as an integral part of the general development of the financial sector with more recently the emphasis increasingly being shifted to insurance sectors. When the scale of insurance market increases, the issues about structure are more and more concerned. The development of life insurance market was inferior to non-life insurance at the first stage of development in China. After the life insurance premium written surpassed non-life insurance in 1997, life insurance market left non-life insurance market far behind in subsequent years. In 2010, the written premium of life insurance reaches USD156 billion which was more than double of non-life insurance at the same period of USD58 billion. It is well believed that though life insurance and non-life insurance share some characteristics, such as financial intermediation, risk transfer and indemnification, in common, the benefits of risk transfer and indemnification are likely to be major characteristics of non-life insurance, while financial intermediation is a primary aspect of life insurance (Ward and Zurbruegg, 2000). As such, compared to non-life insurance, life insurance may have its own special way to promote economy; the determinant factors for life insurance development may also be significantly different from those for non-life insurance. Few studies have used unit root tests to investigate the stationarity characteristics of insurance markets development. Cummins and Outreville (1987) implement unit root tests with panel data to investigate the stationary processes of property-liability insurance premiums. Niehaus and Terry (1993) test written premiums, losses paid and surpluses and find that the hypothesis of a unit root is not rejected, which is inconsistent with stationarity. Ward and Zurbruegg (2000) employ the Phillips and Perron (1988) unit root test and demonstrate that the insurance premiums written are non-stationary for nine selected OECD countries. Harrington and Yu (2003) try to apply a battery of unit root tests to investigate whether underwriting margins are stationary under different assumptions concerning deterministic components in the data generating process (DGP). Lee et al. (2010) implement panel seemingly unrelated regressions augmented Dickey–Fuller unit root test to examine the stationarity of non-life insurance consumptions during the period 1979–2005 for 31 countries in the world, and find that whether non-life insurance consumptions are stationary or not will be affected by different regions and their levels of development. The stationary characteristics of insurance market development should be seriously considered when conducting economic or financial policies. In the case of life insurance market, a rejection of the null supports the alternative hypothesis of a stationary series in which shocks to life insurance market development have temporary effects. When the development of life insurance markets are trend stationary (mean-reverting), then a series should return to its trend path over time, and it should be possible to forecast future movements in life insurance activities based on past behavior. By contrast, series that are non-stationary in levels have a unit root, and shocks change the long-run level of the series permanently. In that case, life insurance market development are characterized by hysteresis or path dependency, the volatility of life insurance market can grow without bound in the long run, so that it is not possible to forecast the future movement based on the history. In that sense, Diebold and Kilian (2000) propose that pretesting for unit roots before applying forecasts yields superior forecasting performance, as opposed to the alternatives of working always with differenced series or working always with level series. Moreover, stationarity test also has great implication for policy making. A rejection of the null supports the alternative hypothesis of a stationary series in which shocks to life insurance market have temporary effects, life insurance market will adjust itself and restore to its original developing path over time. In that case, government or regulators need not to react overly to adopt some radical policies to intervene in the process; chances are that kind of policies may drive the results to other end. If development of life insurance market is non-stationary, then shocks have permanent effects on life insurance market. Government should assess the shock carefully and come up with proper policies which may have long-lasting effects and can lead the development of life insurance market to somewhere it desires. Our purpose in this study is to compare the results of stationarity tests for series of life insurance premiums written in different income levels of China and explore the regional differences in life insurance markets development. In the wake of Nelson and Plosser (1982), a substantial amount of literature to find the latent presence of unit roots in macroeconomic time series data demonstrating that variables are non-stationary (Wasserfallen, 1986 and Cheung and Chinn, 1996). They demonstrate that presence of an unit root in time series model has consequence for the way we predict economic activity. Moreover, Perron (1989) argued that if there is a structural break in time trend or levels, the power of conventional unit root test, such as Augmented Dickey and Fuller (1981) and Phillips and Perron (1988), to reject a unit root decreases when the stationary alternative is true and the structural break is ignored in the model. Meanwhile, structural changes present in the data generating process (DGP), but have been neglected, sway the analysis toward accepting the null hypothesis of a unit root. The general method to account for breaks is to approximate those using dummy variables. However, this approach has several undesirable consequences. First, recent development in the econometrics literature highlights major drawbacks of commonly used unit root tests based on search procedures. When the break dates are unknown, it is useful to have information regarding the presence or absence of a change in order to investigate the potential presence of a unit root. These are not usually known and therefore need to be estimated. This in turn introduces an undesirable pre-selection bias (Maddala and Kim, 1998). Second, current available tests account only for one to two breaks. Nunes et al. (1997), Lee and Strazicich, 2001 and Lee and Strazicich, 2003 and Kim and Perron (2009), among others, demonstrate that such tests suffer from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. Third, the use of dummies suggests sharp and sudden changes in the trend or level. As a result, the test may reject the unit root null when the noise component is integrated but the trend is changing, leading to spurious evidence in favor of broken trend stationarity. However, for low frequency data it is more likely that structural changes take the form of large swings which cannot be captured well using only dummies. Breaks should therefore be approximated as smooth and gradual processes (see Leybourne et al., 1998). These arguments motivate the use of a recently developed set of unit root and stationary tests that avoid this problem. Enders and Lee (2012) develops tests which model any structural break of an unknown form as a smooth process via means of Flexible Fourier transforms. Several authors, including Gallant (1981), Becker et al. (2004) and Enders and Lee (2012), and Pascalau (2010), show that a Fourier approximation can often capture the behavior of an unknown function even if the function itself is not periodic. The authors argue that their testing framework requires only the specification of the proper frequency in the estimating equations. By reducing the number of estimated parameters, they ensure the tests have good size and power irrespective of the time or shape of the break. Additionally, the existence of structure changes in series might imply broken deterministic time trends and the result is a nonlinear pattern (Bierens, 1997). It should, therefore, not be unexpected that these shortcomings have seriously called into questioning many of the earlier findings based on a unit root in convergence hypothesis tests. As we cover a much shorter time period, we interpret the broken deterministic terms differently. In particular, we think of them as representing changes in the political and economic environment in China due to structural reforms in the political and legal system, changes in the competition policy, and specific economic policy programs. In this sense the broken deterministic terms refer to exogenous events. Cummins (1973), Beenstock et al. (1986), Truett and Truett (1990), Browne and Kim (1993), Outreville (1996) and Beck and Webb (2003) discover that the development of life insurance can be affected by a variety of factors, thus a natural derivation from those evidences are that development of life insurance markets can vary dramatically in different income levels with special characteristics. Taking the life insurance market of China for instance, the market structure, specific lines of life insurance and the capability of operation for insurance companies play an important role in affecting the regional development of life insurance markets. First, life insurance markets in relatively high income regions are typified as fierce competition. Beenstock et al. (1986), Browne and Kim (1993), Beck and Webb (2003) find that the market development of life insurance is highly related with income level. Eastern regions used to lead in the process of reform and opening and life insurance demand increased as the economy boomed. All the life insurance companies running in China took these regions as their target markets for priority and put most of their marketing resources in them. At the same time, monopolistic structure of life insurance market appeared in other economically backward regions. Second, number of insurance institutions keeps growing and new institutions are extending from high-income regions to low-income regions. The life insurance market used to be dominated by several state-owned life insurance companies. After China was permitted to become a member of World Trade Organization (WTO) in 2011, deregulation has been seen in insurance industry. More and more insurance companies, either domestic or alien, were allowed to enter the insurance market of China. From 2003 to 2012, the number of life insurance companies increased from 32 to 62. Attracted by the relatively high demand for insurance in eastern provinces, most insurance companies took setting up affiliates in these high-income regions as their first choice. Recently, more and more companies began to extend their affiliates to central and western area where income level is comparatively lower to create new business. Third, development of business lines was extremely unbalanced for life insurance. In order to gain more competitiveness, most newly founded life insurance companies adopted expansion strategy by selling deposit-featured short-term policies which competed with savings of banks or/and some investment-featured policies, like unit-linked policies, which stressed the investment side of life policies and could benefit policyholders more if the investment of premium make good profits. These lines of business are highly correlated with capital market and currency market. When all these factors belonging to demand side or supply side mix up and interact with one another in different regions, the development of life insurance markets in various regions of China can be expected to significantly differ from each other. In this study, we explore the characteristics of convergence for life insurance market by examining more homogeneous groups of regions. Our aim is to investigate whether or not tendency towards convergence exists in life insurance sectors among the provinces of China during the period January 2006 to February 2012 using the unit root test with a Fourier function proposed by Enders and Lee (2012). Testing whether a time series can be characterized by a broken trend is complicated by the fact that the nature of persistence in the errors is usually unknown. The lack of econometric studies on this issue may be explained by the difficulties involved in modeling acceding China data: only relatively few time series observations are available and structural changes occurred frequently. We use Lagrange Multiplier (LM) unit root tests that allow for breaks in the trend and the level of a series at unknown time. With this, the current research hopes to fill the existing gap in the literature. To the best of our knowledge, this study is the first, to date, that utilizes the unit root test with a Fourier function in time series convergence tests allowing for structural breaks to the development of life insurance markets for China. This empirical study contributes to the field of empirical research by determining whether or not the unit root process is characteristic of the life insurance convergences in China. On the other side, as Becker et al. (2006) stressed, Flexible Fourier transforms has robustness to structural breaks of an unknown form, irrespective of the date and location of the breaks. If the result of Fourier unit root test concludes that certain provinces converge that it would offer an alternative explanation for the difficulty researchers have encountered in capturing the feature of breaks. The remainder of this empirical study is organized as follows. Section 2 outlines the methodology of the Fourier unit root test. Section 3 presents the data used and discusses the empirical findings and policy implications. Our conclusion is presented in the last section.

The aim of this study is to examine the regional differences in development of life insurance markets in China with monthly data from 31 provinces from January 2006 to February 2012 by using Fourier unit root test by Enders and Lee (2012). Fourier unit root test is not only considered a better way to approximate breaks than conventional Dummy variable approach but also has higher power than standard univariate unit root test. Empirical results show that whether life insurance developments are stationary or not is significantly affected by income levels in China. Specifically, life insurance markets in high-income provinces tend to be non-stationary, while stationarity prevails in provinces with middle and low income. As property of stationarity/non-stationarity reflects certain patterns of development for life insurance markets, further analyses show that the unbalanced development of financial market, market structure of life insurance and business strategy of life insurance companies are the main factors underlying the different patterns of development for life insurance markets in different regions. Implication from this study is that for insurance companies in high-income regions emphasis should be put on products stressing functions of risk transfer and indemnification, but not investment-featured type. At the same time, more businesses should be spread to inland where the capability of consumption for life insurance might be lower at present, but the potential is immense. For the government, issue of unbalanced development of financial market as well as economic growth should be paid more attention, systemic risk in life insurance industry and the inter-connectedness of systemic risks between capital markets and life insurance markets should get a close watch. Furthermore, deregulation of life insurance markets in lower income regions should be promoted. Notably, this study contributes to the existing literature in two aspects. First, stationarity for series of life insurance premium is tested for 31 provinces in China, which is useful for further researches trying to probe the relationships between life insurance development and other macroeconomic variables. Second, regional differences in patterns of life insurance markets development in China are investigated and the underlying factors are analyzed, which has practical policy implications for China under study.